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Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C000 Final Proof page i
25.4.2007 7:31pm Compositor Name: BMani
Computational Fluid Dynamics in Food Processing
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C000 Final Proof page ii 25.4.2007 7:31pm Compositor Name: BMani
Contemporary Food Engineering Series Editor
Professor Da-Wen Sun, Director Food Refrigeration & Computerized Food Technology National University of Ireland, Dublin (University College Dublin) Dublin, Ireland http://www.ucd.ie/sun/
1. Computational Fluid Dynamics in Food Processing, edited by Da-Wen Sun
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Computational Fluid Dynamics in Food Processing
edited by
Da-Wen Sun
Boca Raton London New York
CRC Press is an imprint of the Taylor & Francis Group, an informa business
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CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2007 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-10: 0-8493-9286-1 (Hardcover) International Standard Book Number-13: 978-0-8493-9286-3 (Hardcover) This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Computational fluid dynamics in food processing / editor Da-Wen Sun. p. cm. -- (Contemporary food engineering series) Includes bibliographical references and index. ISBN-13: 978-0-8493-9286-3 (alk. paper) ISBN-10: 0-8493-9286-1 (alk. paper) 1. Food industry and trade--Fluid dynamics. 2. Food industry and trade--Technological innovations. I. Sun, Da-Wen. TP370.C66 2007 664’.02--dc22 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com
2006101711
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Table of Contents Preface to Contemporary Food Engineering Series ................................................................ix Preface...................................................................................................................................xi Editor...................................................................................................................................xiii Contributors .........................................................................................................................xv Chapter 1
An Overview of CFD Applications in the Food Industry ..................................1
Toma´s Norton and Da-Wen Sun Chapter 2
CFD Optimization of Airflow in Refrigerated Truck Configuration Loaded with Pallets ...........................................................................................43
Jean Moureh Chapter 3
CFD Aided Retail Cabinets Design ..................................................................83
Giovanni Cortella Chapter 4
Improving Performance of a Chilled Multideck Retail Display Cabinet by CFD ................................................................................ 103
Alan M. Foster Chapter 5
CFD Design of Air Curtain for Open Refrigerated Display Cases ................ 129
Homayun K. Navaz, Ramin Faramarzi, and Mazyar Amin Chapter 6
Investigation of Methods to Improve Retail Food Store Environment Using CFD ...................................................................... 143
Savvas Tassou and Weizhong Xiang Chapter 7
CFD Optimization of Air Movement through Doorways in Refrigerated Rooms ........................................................................................ 167
Alan M. Foster Chapter 8
CFD Modeling of Simultaneous Heat and Mass Transfer in Beef Chilling ................................................................................. 195
Francisco Javier Trujillo and Q. Tuan Pham Chapter 9
CFD Prediction of the Air Velocity Field in Modern Meat Dryers ............... 223
Pierre-Sylvain Mirade v
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Chapter 10
CFD Simulation of Spray Drying of Food Products.................................... 249
Han Straatsma, M. Verschueren, M. Gunsing, P. de Jong, and R.E.M. Verdurmen Chapter 11
Three-Dimensional CFD Modeling of a Continuous Industrial Baking Process .............................................................................. 287
Weibiao Zhou and Nantawan Therdthai Chapter 12
Computation of Airflow Effects in Microwave and Combination Heating .......................................................................................................... 313
Pieter Verboven, Bart M. Nicolaı¨, and Ashim K. Datta Chapter 13
Thermal Sterilization of Food Using CFD ................................................... 331
A.G. Abdul Ghani and Mohammed M. Farid Chapter 14
CFD Analysis of Thermal Processing of Eggs .............................................. 347
Sieg fried Denys, Jan Pieters, and Koen Dewettinck Chapter 15
CFD Simulation of Stirred Yoghurt Processing in Plate Heat Exchangers............................................................................................ 381
Joa˜o M. Maia, Joa˜o M. No´brega, Carla S. Fernandes, and Ricardo P. Dias Chapter 16
CFD Modeling of the Hydrodynamics of Plate Heat Exchangers for Milk Processing ....................................................................................... 403
Koen Grijspeerdt, Dean Vucinic, and Chris Lacor Chapter 17
Plate Heat Exchanger: Thermal and Fouling Analysis ................................. 417
Soojin Jun and Virendra M. Puri Chapter 18
CFD Applications in Membrane Separations Systems ................................. 433
Sean X. Liu Chapter 19
Applications of CFD in Jet Impingement Oven............................................ 469
Dilek Kocer, Nitin Nitin, and Mukund V. Karwe Chapter 20
CFD Modeling of Jet Impingement during Heating and Cooling of Foods .......................................................................................... 487
˚ rdh ¨ ga Eva E.M. Olsson and Christian Tra Chapter 21
Use of CFD for Optimization, Design, and Scale-Up of Food Extrusion ......................................................................................... 505
Bharani K. Ashokan, Jozef L. Kokini, and Muthukumar Dhanasekharan
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Chapter 22
Modeling of High-Pressure Food Processing Using CFD ............................ 537
A.G. Abdul Ghani and Mohammed M. Farid Chapter 23
Analysis of Mixing Processes Using CFD..................................................... 555
Robin K. Connelly and Jozef L. Kokini Chapter 24
CFD Simulation of Multiphysical–Multi(bio)chemical Interactions of Tea Fermentation and Infusion ................................................................ 589
Guoping Lian Chapter 25
CFD Prediction of Hygiene in Food Processing Equipment ........................ 603
Bo Boye Busk Jensen and Alan Friis Chapter 26
CFD Design and Optimization of Biosensors for the Food Industry........... 631
Pieter Verboven, Yegermal T. Atalay, Steven Vermeir, Bart M. Nicolaı¨, and Jeroen Lammertyn Chapter 27
Modeling Airflow through Vented Packages Containing Horticultural Products .................................................................................. 649
Maria J. Ferrua and R. Paul Singh Chapter 28
CFD Modeling of Indoor Atmosphere and Water Exchanges during the Cheese Ripening Process ......................................................................... 697
Pierre-Sylvain Mirade Index................................................................................................................................... 727
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Preface to Contemporary Food Engineering Series Food engineering is the multidisciplinary field of applied physical sciences combined with the knowledge of product properties. Food engineers provide technological knowledge essential to the cost-effective production and commercialization of food products and services. In particular, food engineers develop and design processes and equipment in order to convert raw agricultural materials and ingredients into safe, convenient, and nutritious consumer food products. However, food engineering topics are continuously undergoing changes to meet diverse consumer demands, and the subject is being rapidly developed to reflect the market needs. In the development of food engineering, one of the many challenges is to employ modern tools and knowledge, such as computational materials science and nanotechnology, to develop new products and processes. Simultaneously, improving food quality, safety, and security remain critical issues in food engineering study. New packaging materials and techniques are being developed to provide a higher level of protection to foods and novel preservation technologies are emerging to enhance food security and defense. Additionally, process control and automation regularly appear among the top priorities identified in food engineering. Advanced monitoring and control systems are developed to facilitate automation and flexible food manufacturing. Furthermore, energy saving and minimization of environmental problems continue to be important food engineering issues and significant progress is being made in waste management, efficient utilization of energy, and the reduction of effluents and emissions in food production. Consisting of edited books, the Contemporary Food Engineering book series attempts to address some of the recent developments in food engineering. Advances in classical unit operations in engineering applied to food manufacturing are covered as well as such topics as progress in the transport and storage of liquid and solid foods; heating, chilling, and freezing of foods; mass transfer in foods; chemical and biochemical aspects of food engineering and the use of kinetic analysis; dehydration, thermal processing, nonthermal processing, extrusion, liquid food concentration, membrane processes and applications of membranes in food processing; shelf-life, electronic indicators in inventory management, and sustainable technologies in food processing; and packaging, cleaning, and sanitation. These books are intended for use by professional food scientists, academics researching food engineering problems, and graduate level students. The editors of the books are leading engineers and scientists from many parts of the world. All the editors were asked to present their books in a manner that will address the market’s needs and pinpoint the cutting edge technologies in food engineering. Furthermore, all contributions are written by internationally renowned experts who have both academic and professional credentials. All authors have attempted to provide critical, comprehensive, and readily accessible information on the art and science of a relevant topic in each chapter,
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with reference lists to be used by readers for further information. Therefore, each book can serve as an essential reference source to students and researchers at universities and research institutions. Da-Wen Sun Series Editor
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Preface Computational fluid dynamics (CFD) is a state-of-the-art numerical technique for solving fluid flow problems. CFD calculations use a computational grid to solve the governing equations describing fluid flow, i.e., the continuity equation and the set of Navier–Stokes equations, and any additional conservation equations, such as energy balance, across each grid cell by means of an iterative procedure in order to predict and visualize the profiles of velocity, temperature, pressure, etc. Early users of CFD are found in the automotive, aerospace, and nuclear industries. With the enhancement of computing power and efficiency, and the availability of affordable CFD packages, applications of CFD have extended into the food industry for modeling industrial processes, thereby generating comprehensive analyses leading to designing more efficient systems. The implementation of early-stage simulation tools is an international trend so that engineers can test concepts all the way through the development of a process or a system. CFD serves as such a powerful design and analysis tool to the food engineer. In the food industry, many processes such as mixing, drying, cooking, sterilization, chilling, and cold storage involve fluid flow and heat and mass transfer. CFD provides an ideal tool for gaining a qualitative and quantitative assessment of the performance of these processes. With CFD, numerous different combinations of design parameters and working conditions can be experimented on the computer, thus overcoming the need to test the actual design with each modification, leading to the optimization of existing and new processes or systems. Therefore, as the first book in the area of CFD application in food processing, Computational Fluid Dynamics in Food Processing will greatly benefit the food industry in its continual quest for process and product improvement. The book begins with a chapter on overview of technology. The rest of the chapters can be broadly divided into the following three parts: CFD applications in analyzing and optimizing cold-chain facilities (Chapter 2 through Chapter 8); modeling of drying (Chapter 9 and Chapter 10) and heating (Chapter 11 through Chapter 14), processes and analysis of heat exchangers (Chapter 15 through Chapter 17); and other applications in separation (Chapter 18), jet impingement (Chapter 19 and Chapter 20), extrusion (Chapter 21), high-pressure processing (Chapter 22), mixing (Chapter 23), tea fermentation (Chapter 24), equipment hygiene (Chapter 25), biosensor (Chapter 26), packaging (Chapter 27), and cheese ripening (Chapter 28). The chapters in Computational Fluid Dynamics in Food Processing are authored by international peers who have both academic and professional credentials, and this book is intended to provide the engineer and technologist working in research, development, and operations in the food industry with critical, comprehensive, and readily accessible information on the art and science of CFD technology. It should also serve as an essential reference source to undergraduate and postgraduate students and researchers at universities and research institutions. Da-Wen Sun National University of Ireland, Dublin
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Editor Born in southern China, Professor Da-Wen Sun is an internationally recognized figure for his leadership in food engineering research and education. His main research activities include cooling, drying, and refrigeration processes and systems, quality and safety of food products, bioprocess simulation and optimization, and computer vision technology. Especially, his innovative studies on vacuum cooling of cooked meats, pizza quality inspection by computer vision, and edible films for shelf-life extension of fruits and vegetables have been widely reported in national and international media. Results of his work have been published in over 150 peer-reviewed journal papers and in more than 200 conference papers. He received BSc honors and a MSc in mechanical engineering, and a PhD in chemical engineering in China before working at various universities in Europe. He became the first Chinese national to be permanently employed at an Irish university when he was appointed college lecturer at the National University of Ireland, Dublin (University College Dublin) in 1995, and was then continuously promoted in the shortest possible time to senior lecturer, associate professor, and full professor. Dr. Sun is now professor and director of the Food Refrigeration and Computerized Food Technology Research Group at University College Dublin. As a leading educator in food engineering, Professor Sun has significantly contributed to the field of food engineering. He has trained many PhD students, who have made their own contributions to the industry and academia. He has also given lectures on advances in food engineering on a regular basis at academic institutions internationally and delivered keynote speeches at international conferences. As a recognized authority in food engineering, he has been conferred adjunct=visiting=consulting professorships from ten top universities in China including Shanghai Jiaotong University, Zhejiang University, Harbin Institute of Technology, China Agricultural University, South China University of Technology, Southern Yangtze University. In recognition of his significant contributions to food engineering worldwide and his outstanding leadership, the International Commission of Agricultural Engineering (CIGR) awarded him the CIGR Merit Award in 2000 and in 2006; the Institution of Mechanical Engineers (IMechE) based in the UK named him ‘‘Food Engineer of the Year 2004.’’ He is a fellow of the Institution of Agricultural Engineers. He has also received numerous awards for teaching and research excellence, including the President’s Research Fellowship, and twice received the President’s Research Award of University College Dublin. He is a member of the CIGR executive board and honorary vice-president of CIGR, editor-in-chief
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of the newly established Food and Bioprocess Technology—An International Journal (Springer), editor of Journal of Food Engineering (Elsevier), series editor of the ‘‘Contemporary Food Engineering’’ book series (CRC Press=Taylor & Francis), and an editorial board member for the Journal of Food Process Engineering (Blackwell), Sensing and Instrumentation for Food Quality and Safety (Springer), and the Czech Journal of Food Sciences. He is also a chartered engineer registered in the UK Engineering Council.
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Contributors Mazyar Amin Department of Aeronautics and Astronautics University of Washington at Seattle Seattle, Washington
Koen Dewettinck Department of Food Safety and Food Quality Ghent University Ghent, Belgium
Bharani K. Ashokan Department of Food Science and Center for Advanced Food Technology Cook College at Rutgers The State University of New Jersey New Brunswick, New Jersey
Muthukumar Dhanasekharan Fluent Inc. Lebanon, New Hampshire
Yegermal T. Atalay Department of Biosystems Katholieke Universiteit Leuven Leuven, Belgium Robin K. Connelly Departments of Food Science and Biological Systems Engineering University of Wisconsin-Madison Madison, Wisconsin Giovanni Cortella Department of Energy Technologies University of Udine Udine, Italy Ashim K. Datta Department of Biology and Environment Engineering Cornell University Ithaca, New York Siegfried Denys Department of Biosystems Engineering Ghent University Ghent, Belgium
Ricardo P. Dias School of Technology and Management Polytechnic Institute of Braganc¸a Braganc¸a, Portugal Ramin Faramarzi Refrigeration and Thermal Test Center Southern California Edison Irwindale, California Mohammed M. Farid Department of Chemical and Materials Engineering The University of Auckland Auckland, New Zealand Carla S. Fernandes School of Technology and Management Polytechnic Institute of Braganc¸a Braganc¸a, Portugal Maria J. Ferrua Department of Biological and Agricultural Engineering University of California Davis, California
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Alan M. Foster Food Refrigeration and Process Engineering Research Center University of Bristol Bristol, UK Alan Friis BioCentrum-DTU, Soltofts Plads Technical University of Denmark Lyngby, Denmark A.G. Abdul Ghani Department of Chemical and Materials Engineering The University of Auckland Auckland, New Zealand Koen Grijspeerdt Institute for Agricultural and Fisheries Research Unit Technology & Food Melle, Belgium M. Gunsing Maritime Research Institute Netherlands Wageningen, The Netherlands Bo Boye Busk Jensen BioCentrum-DTU, Soltofts Plads Technical University of Denmark Lyngby, Denmark P. de Jong NIZO Food Research Ede, The Netherlands
Dilek Kocer Department of Food Science Cook College at Rutgers The State University of New Jersey New Brunswick, New Jersey Jozef L. Kokini Department of Food Science and Center for Advanced Food Technology Cook College at Rutgers The State University of New Jersey New Brunswick, New Jersey Chris Lacor Department of Fluid Mechanics Free University of Brussels Brussels, Belgium Jeroen Lammertyn Department of Biosystems Katholieke Universiteit Leuven Leuven, Belgium Guoping Lian Colworth Laboratory Unilever Corporate Research Bedford, UK Sean X. Liu Department of Food Science Cook College at Rutgers The State University of New Jersey New Brunswick, New Jersey
Soojin Jun Department of Human Nutrition, Food and Animal Sciences University of Hawaii Honolulu, Hawaii
Joa˜o M. Maia Department of Polymer Engineering University of Minho Guimara˜es, Portugal
Mukund V. Karwe Department of Food Science Cook College at Rutgers The State University of New Jersey New Brunswick, New Jersey
Pierre-Sylvain Mirade Department for Science and Process Engineering of Agricultural Products National Institute for Agronomic Research Saint Gene`s Champanelle, France
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Jean Moureh Refrigerating Process Engineering Research Unit Cemagref Antony, France
Virendra M. Puri Department of Agricultural and Biological Engineering The Pennsylvania State University University Park, Pennsylvania
Homayun K. Navaz Department of Mechanical Engineering Kettering University Flint, Michigan
R. Paul Singh Department of Biological and Agricultural Engineering University of California Davis, California
Bart M. Nicolaı¨ Department of Biosystems Katholieke Universiteit Leuven Leuven, Belgium
Han Straatsma NIZO Food Research Ede, The Netherlands
Nitin Nitin Department of Food Science Cook College at Rutgers The State University of New Jersey New Brunswick, New Jersey
Da-Wen Sun Department of Biosystems Engineering University College Dublin National University of Ireland Dublin, Ireland
Joa˜o M. No´brega Department of Polymer Engineering University of Minho Guimara˜es, Portugal
Savvas Tassou School of Engineering and Design Brunel University Uxbridge, UK
Toma´s Norton Department of Biosystems Engineering University College Dublin National University of Ireland Dublin, Ireland
Nantawan Therdthai Department of Product Development Kasetsart University Bangkok, Thailand
Eva E.M. Olsson Fluid Dynamics FS Dynamics AB Go¨teborg, Sweden
Christian Tra¨ga˚rdh Department of Food Technology, Engineering, and Nutrition Lund University Lund, Sweden
Q. Tuan Pham School of Chemical Sciences and Engineering University of New South Wales Sydney, Australia
Francisco Javier Trujillo Food Science Australia North Ryde, New South Wales, Australia
Jan Pieters Department of Biosystems Engineering Ghent University Ghent, Belgium
Pieter Verboven Department of Biosystems Katholieke Universiteit Leuven Leuven, Belgium
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R.E.M. Verdurmen Numico Research B.V. Wageningen, The Netherlands Steven Vermeir Department of Biosystems Katholieke Universiteit Leuven Leuven, Belgium M. Verschueren NIZO Food Research Ede, The Netherlands
Dean Vucinic Department of Fluid Mechanics Vrije Universiteit Brussel Brussels, Belgium Weizhong Xiang Hoare Lea Consulting Engineers Bristol, UK Weibiao Zhou Department of Chemistry National University of Singapore Singapore
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An Overview of CFD Applications in the Food Industry Toma´s Norton and Da-Wen Sun
CONTENTS 1.1 1.2
1.3
1.4
1.5
1.6
1.7
Introduction .................................................................................................................. 2 Fundamentals of CFD Modeling.................................................................................. 5 1.2.1 Governing Equations......................................................................................... 5 1.2.1.1 Turbulence Modeling .......................................................................... 8 1.2.1.2 Porous Media and Multiphase Modeling .......................................... 11 1.2.1.3 Non-Newtonian Fluid Modeling ....................................................... 12 1.2.2 Numerical Analysis.......................................................................................... 14 Methods for Improving Modeling Accuracy .............................................................. 14 1.3.1 Convection Schemes ........................................................................................ 14 1.3.2 Unstructured Mesh.......................................................................................... 16 1.3.3 Sliding Mesh .................................................................................................... 16 1.3.4 Multiple Frames of Reference ......................................................................... 17 1.3.5 Spatial Convergence Technique....................................................................... 18 Commercial CFD Codes............................................................................................. 18 1.4.1 CFX (ANSYS, Inc.) ........................................................................................ 19 1.4.2 PHOENICS (CHAM Ltd.) ............................................................................. 20 1.4.3 FLUENT (FLUENT, Inc.) ............................................................................. 20 Performing a CFD Analysis with Commercial Software ............................................ 21 1.5.1 Preprocessing ................................................................................................... 21 1.5.2 Solving ............................................................................................................. 21 1.5.3 Postprocessing ................................................................................................. 22 Applications in the Food Industry.............................................................................. 23 1.6.1 Food Production Facilities .............................................................................. 23 1.6.2 Air Blast and Jet Impingement........................................................................ 25 1.6.3 Cold Storage Facilities..................................................................................... 25 1.6.4 Refrigerated Display Cases.............................................................................. 26 1.6.5 Household and Industrial Refrigeration.......................................................... 26 1.6.6 Sterilization...................................................................................................... 26 1.6.7 Stirred Tanks ................................................................................................... 28 1.6.8 Drying.............................................................................................................. 30 Challenging Issues Confronting CFD Modelers ......................................................... 30 1.7.1 Nonhomogenous Fluid Domain...................................................................... 30 1.7.2 Turbulence Modeling....................................................................................... 31 1
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Computational Fluid Dynamics in Food Processing
1.7.3 y+ Criterion..................................................................................................... 1.7.4 Model Simplification ....................................................................................... 1.7.5 Uneven Meshing .............................................................................................. 1.7.6 Time-Step Selection ......................................................................................... 1.8 Opportunities for Food Industry and Benefits for Consumer .................................... 1.8.1 Software Pricing .............................................................................................. 1.8.2 Processing System Design................................................................................ 1.8.3 Product Quality ............................................................................................... 1.9 Conclusions................................................................................................................. Nomenclature ...................................................................................................................... References ...........................................................................................................................
31 32 32 33 33 33 34 34 34 35 36
1.1 INTRODUCTION Engineers are presently turning to the power of computational fluid dynamics (CFD) to model industrial processes, accomplish comprehensive analyses, and design more efficient systems. The adoption of CFD over the recent years has been inevitable and progressive, as the high costs and time consumption associated with experimentation have often precluded the desire to produce efficient in-depth results. Moreover, associated assumptions, generalizations, and approximations have inhibited analytical models from developing comprehensive flow solutions. By coupling these limitations with the recent advances in the development of numerical solutions for the Navier–Stokes equations, and the enhancement of computing power and efficiency, it is easy to understand why the application of CFD has developed into a viable alternative in the food industry. CFD is maturing into a powerful and pervasive tool with each solution representing a rich tapestry of mathematical physics, numerical methods, user interfaces, and stateof-the-art visualization techniques. In its present-day form, it can be used to efficiently quantify the complex dynamic processes that occur during fluid motion and as a result has developed into a multifaceted industry, generating billions of euros worldwide in a wealth of different disciplines [1,2]. Such disciplines include process engineering, aerospace, hydrology, bioengineering, and meteorology. Among the processes quantifiable by CFD are heat and mass transfer, phase change, solid and fluid interactions, prediction of solid stress, and chemical reactions. These processes and associated industries are summarized in Table 1.1. The links between CFD and the processes associated with the food and beverage industry such as mixing, drying, cooking, sterilization, chilling, and cold storage are profound. Such processes are used regularly to enhance quality, safety, and shelf life of foodstuffs and have been evolving over the years to become more efficient [9]. The adoption of CFD technology by food engineers began in the 1990s, predominately due to the advent of inexpensive powerful computers and CFD software [10]. Today, because of the direct benefits for both the consumer and environment, applications of CFD have become an essential part of system design in the food industry (Figure 1.1). Recent advances in unstructured and adaptive meshing, moving boundaries, and multiple frames of reference now cooperate with physical models to confront the complex phenomena that the food industry has faced over the decades [11]. In addition, CFD can aid food companies to respond to an expanding marketplace by enhancing and developing processing strategies, while endeavoring to maintain high levels of product quality. Table 1.2 highlights the number of CFD modeling applications related to the food industry published by food engineering related journals.
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An Overview of CFD Applications in the Food Industry
TABLE 1.1 Industrial Processes Quantifiable by CFD Dynamic Processes
Industry
Heat and Mass Transfer
Solid and Fluid Interactions
Chemical Reactions
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
Biomedical engineering Food and beverage Agriculture Building simulation Aerospace Chemical
Transport
Phase Change
Examples of CFD Application
Radiation p
p
Visualization of blood flow through heart valves [3] Design and optimization of chillers, ovens, and dryers [1] Design of climate within agricultural buildings [4] Human microclimate studies to aid room design [5] Modeling of space shuttle in ascending flight [6] Complex flow in mixing and reactions at microeddy scale [7] Enhancement of vehicle designs [8]
70
60
Number of papers
50
40
y = 4.7833x1.5351 R 2 = 0.9703
30
20
10
0 1993−1995
1996−1998
1999−2001
2002−2004
2005−2006
Period
FIGURE 1.1 The number of published papers with CFD applications in the food industry.
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Computational Fluid Dynamics in Food Processing
TABLE 1.2 Number of Applied CFD Articles Related to Food Engineering Published in English Journals Period
Journals
1993– 1995
1996– 1998
1999– 2001
2002– 2004
2005– 2006a
% of Total
0 0
1 0
0 0
0 1
0 1
0.71 1.42
D HT, HE
1
1
1
1
2
4.25
ST, DR, HE
1 2
0 0
0 4
0 6
0 7
0.71 12.8
0
1
1
1
0
2.12
0
6
11
18
16
0 0
0 0
0 0
1 0
4 3
3.54 2.12
HT, DR, HE, STER, CH, CR, OV, F, V HE, V, MIX, CH HE, CH, AC
0 0 0
0 1 0
0 0 0
0 0 9
1 0 0
0.71 0.71 6.38
HE HE CH, STER, HT
0
0
2
1
0
2.12
DR, STER
0 0 1 0 0
0 0 1 0 0
1 0 0 0 5
0 1 0 0 7
1 0 4 1 3
1.42 0.71 4.25 0.71 10.64
0
0
0
0
1
0.71
STER
0
0
0
5
2
4.9
0
0
0
0
2
1.42
ST, DR, MIX, FP, CIP, BC STER, CIP
0
1
0
0
0
0.71
CR
0 0
0 0
0 1
2 0
0 0
1.42 0.71
DR CH
0
0
0
1
2
2.12
DR
Computers and Fluids International Journal of Heat and Fluid Flow Computers and Chemical Engineering Food Control Chemical Engineering Science Trends in Food Science and Technology Journal of Food Engineering Applied Thermal Engineering Energy Conversion and Management Journal of Dairy Technology Revue Ge´ne´rale de Thermique Computers and Electronics in Agriculture Chemical Engineering and Processing Chemical Engineering Journal Food Research International Journal of Membrane Science International Dairy Journal International Journal of Refrigeration International Journal of Heat and Mass Transfer Food and Bioproducts Processing Journal of Food Process Engineering Chemical Engineering Research and Design Drying Technology International Journal of Food Science and Technology Le Lait
36.2
Modeling Applications
HT ST, STER, DR, HOM, PF, MIX RS
ST, DR CH MF CH CH, CR, AC
Abbreviations: D, disinfection (UV reaction); HT, heat transfer; HE, heat exchangers; DR, dryers; ST, stirred tanks; STER, sterilization; HOM, homogenization; PF, pneumatic flows; MIX, mixers; CH, chillers; OV, ovens; AC, air curtains; MF, membrane flows; CIP, cleaning in place; CR, clean rooms; BC, Belt cooling; RS, review studies; V, valve; F, fouling. a
Data collected on April 12, 2006.
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1.2 FUNDAMENTALS OF CFD MODELING The CFD codes are developed around numerical algorithms that solve the nonlinear partial differential equations governing all fluid flow, heat transfer, and associated phenomena. If used correctly, CFD provides understanding on the physics of a flow system in detail, and does so through nonintrusive flow and thermal and concentration field predictions. Obtaining accurate CFD solutions requires a large amount of insight into the problem that has to be solved, and the appropriate implementation of both physical models and numerical schemes, either at the user interface or through user-defined codes within the software. Table 1.3 summarizes the modeling techniques used by some recent CFD studies and highlights the attention paid to numerical accuracy. In this section, the governing equations and fundamental principles upon which CFD codes are based will be described followed by a state-of-the-art review on the different CFD codes that exist in the marketplace.
1.2.1 GOVERNING EQUATIONS The governing equations of fluid flow and heat transfer can be considered as mathematical formulations of the conservation laws of fluid mechanics. When applied to a fluid continuum, these conservation laws relate the rate of change of a desired fluid property to external forces and can be considered as 1. The law of conservation of mass (continuity), which states that the mass flows entering a fluid element must balance exactly with the flows leaving it 2. The conservation of momentum (Newton’s second law of motion), which states that the sum of the external forces acting on the fluid particle is equal to its rate of change of linear momentum 3. The conservation of energy (the first law of thermodynamics), which states that the rate of change of energy of a fluid particle is equal to the heat addition and the work done on the particle By enforcing these conservation laws over discrete spatial regions in the flow domain, it is possible to achieve a systematic account of the changes in mass, momentum, and energy as the fluid crosses the region boundaries [21]. The resulting equations of fluid motion are referred to as the Navier–Stokes equations, and can be written as Conservation of mass equation: @r @ þ ruj ¼ 0 @t @xi
(1:1)
@ @ @ @ui @uj ð rui Þ þ rui uj ¼ pdij þ m þ þ rgi @t @xj @xj @xj @xi
(1:2)
Conservation of momentum:
Conservation of energy: @ @ @ @T ð rCa T Þ þ ruj Ca T l ¼ sT @t @xj @xj @xj
(1:3)
Drying Fluent 5.4
Fluent
Kaya et al. [16] 2D
2D
3D
Fluent 6.0
Kocer and Karwe [14]
Mirade [15]
3D
3D
CFX 4.3
Fluent 6.0
Mirade et al. [12]
Dimension
Verboven et al. [13]
CFD Code
Authors
Determining variation of HTC and MTC
Predicting AP in meat dryer
Modeling oven fluid flow and heat transfer
Determining AP, RT, HTC
Predicting AP and temperature in baking tunnel
Objective
Unstructured mesh
NS
None
Conjugate heat transfer
Std. k–«
Reynolds stress model
Rotating BCs
Unstructured mesh
CFD Feature
Laminar, RT
Std. k–«
Turb and Supp Models
Placement of inlet and outlet will improve uniform heating and reduce moisture Heat transfer depends velocity of impinging jets only Predictions accurately show the effect of ventilation cycle on AP homogenity With food products of small-aspect ratios drying time is reduced
CFD was a useful tool
Study Conclusion
No validation with EM although account of model limitations CS ¼ HYBRID, GIS, validation with literature data
GIS, CS ¼ NS, good agreement with EM
CS ¼ NS, GIS ¼ NS, Comprehensive on flow characteristics in oven QUICK CS, good agreement with EM, good GIS
Comments
6
Baking
Process
TABLE 1.3 Recent Publications in CFD Applications
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STAR-CD
CFX 5.7
Foster et al. [20]
CFX
Xu and Burfoot [18]
Jensen and Friis [19]
Fluent 6
Mirade and Picgirard [17]
2D
3D
3D
3D
Determining air curtain velocity
Determining CIP effectiveness
Predicting of HT, MT, and AP in storage rooms
Developing solutions to enhance ventilation
Body-fitted mesh
NS
Std. k–«
NS
None
k–« RNG with OEM in near-wall region
Unstructured mesh
Std. k–«
Effectiveness of air curtain can be enhanced with CFD visualization of flow field
Enhanced indoor environment by modifying ventilation configuration Good agreement with EM. Spatial and temporal quality of the indoor environment was determined Critical shear stress not overcome in the CIP procedure GIS. Good account of limitations of the model and improvement strategies No GIS, CS ¼ NS
Porous media models used, no GIS, good account of model limitations GIS ¼ NS, CS ¼ NS, weight loss and temperature distribution predicted
Abbreviations: turb, turbulence; supp, supplementary; AP, airflow patterns; Std. k–«, standard k–« turbulence model; CS, convection scheme; NS, not specified; GIS, grid independence study; RT, radiative heat transfer; BC, boundary condition; EM, experimental measurements; HTC, heat transfer coefficient; MTC, mass transfer coefficient; OEM, one equation model.
Air curtains
Ventilated room
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There are two ways to model the density variations in the flow field that occur due to buoyancy. The first is to assume that the density differentials in the flow are only required in the momentum equations and are represented by r ¼ rref ½1 bðT Tref Þ
(1:4)
This method is known as Buossinesq approximation and has been used successfully in many food engineering applications [22]. At high-temperature differentials the approximation is no longer valid and another method must be applied [23]. One way is to treat the fluid as an ideal gas and express the density difference by means of the following equation: r¼
rref Wa RT
(1:5)
This method can be considered as a weakly compressible formulation, i.e., the density of the fluid is dependent on temperature and composition, but not pressure. This assumption has also been used successfully in food engineering applications [13,24]. However, modeling buoyancy this way is numerically complex and attaining a converged solution has proved, in some cases, to be more difficult than with the Buossinesq relationship [24]. On their own, the Navier–Stokes equations have a limited amount of applications in many areas of food engineering. This means that the additional processes, which play a major role in influencing the dynamics of a system, must be taken into account in a simulation. In these cases, the governing equations may need to be fortified with additional approximations or physical models to fully represent the modeled flow regime. Important physical models commonly used in food engineering applications include turbulence models, porous media and multiphase modeling, and non-Newtonian modeling. 1.2.1.1
Turbulence Modeling
Turbulence momentum and scalar transport play an essential role in many engineering applications and its simulation has undergone intensive research throughout the years. In the food industry it is often necessary to predict surface heat and mass transfer coefficients, heat-dependent properties of food, and flow characteristics of systems under various scenarios to develop safe and efficient plant processes [9]. These processes are usually associated with turbulent flows, primarily due to the complex geometry and=or high flow rates involved. While the Navier–Stokes equations can be solved directly for laminar flows, the current state of computational capability is unable to resolve the fluid motion in the Kolmogorov microscales associated with turbulent flow regimes [25]. However, in most cases engineers are not interested in the detailed structures of turbulence but need a few specific quantitative features of the flow in order to undertake suitable design strategies. Such details are afforded by the Reynolds-averaged Navier–Stokes (RANS) equations, which are determined by averaging the ergodic processes that typify turbulent flows. Reynolds averaging essentially disregards the stochastic properties of the flow and results in six additional unknowns (i.e., Reynolds stresses) that need to be modeled by a physically well-posed equation system in order to obtain a closure that is consistent with the flow regime. The eddy viscosity hypothesis states that an increase in turbulence can be represented by an increase in effective fluid viscosity, and that the Reynolds stresses are proportional to the mean velocity gradients via this viscosity [23]. The RANS equations can then be written as @r @ þ (ruj ) ¼ 0 @t @xi
(1:6)
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@ @ @ @ui @uj @p0 ( r ui ) þ ( r ui mtot þ þ rgi þ fi uj ) ¼ @t @xj @xj @xj @xi @xi @ @ @ @T ( rCa T) þ ( ruj Ca T) ltot ¼ sT @t @xj @xj @xj
(1:7)
(1:8)
where the effect of turbulence in the total viscosity and heat transfer is given by mtot ¼ mlam þ mturb ltot ¼ llam þ mturb ¼
mturb Ca sturb
@u0i u0j @xj
(1:9) (1:10)
(1:11)
Unfortunately, eddy viscosity models assume isotropic turbulence resulting in diffusion acting in all directions, which is a limitation that has encroached upon its range of applications. Nevertheless, this hypothesis forms the foundation on which many of today’s most widely used turbulence models are based. These range from simple one-equation models based on empirical relationships to variants of the sophisticated but inveterate two-equation k–« model, which describes the eddy viscosity through the production and destruction of turbulence. The commonly used high Reynolds-number standard k–« model can be represented by the following equations: @k @ @ mturb @k þ ( r uj k) mlam þ ¼ Pk r« @t @xj @xj sk @xj @k @ @ m @k « «2 þ ( r uj «) mlam þ turb ¼ C1« Pk C2« r @t @xj @xj k s« @xj k 2 p0 ¼ p rk 3 mtot ¼ rCm
k2 «
(1:12)
(1:13) (1:14) (1:15)
There are many k–« type turbulence models embedded in commercial codes and it is left to the user to assert the model that is appropriate for the application in hand. As illustrated by Bartosiewicz et al. [26] (Figure 1.2), large discrepancies can occur in predictions made by different models, which emphasize the need for validation with experimental measurements. Of all turbulence models available, the standard k–« model still remains an industrial standard and its successful applications are found in recent literature [27,28]. In some cases it has even been found to perform as well as more advanced turbulence models [29,30]. Although, due to the assumptions and empiricism upon which the model is based, there are just as many situations where the k–« model has failed to sufficiently represent the modeled turbulent regime and the predictions have proved inadequate [9,31]. Consequently, engineers have turned to other advanced turbulence models like the renormalization group (RNG) and Reynolds stress-transport models (RSM), which are not so reliant on empiricism and can
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0.995
0.99
P t (MPa)
0.985
k-epsilon k-omega-sst RNG
0.98 20
(a)
30 Secondary nozzle
40 Mixing chamber
X (mm) 1.001 1 0.999 0.998
P t (MPa)
0.997 0.996 0.995 0.994 20
(b)
k-epsilon k-omega-sst RNG
30 Secondary nozzle
40 Mixing chamber
FIGURE 1.2 Predictions by three turbulence models of pressure in an ejector. (From Bartosiewicz, Y., Aidoun, Z., and Mercadier, Y., Appl. Therm. Eng., 26, 604, 2006.)
account for anisotropy of highly strained flows (as shown in Figure 1.3). Yet there have also been cases where the limitations of computational power or convergence difficulties have precluded the use of these models [33,34]. Engineers have also addressed other simulation methodologies such as direct numerical simulation (DNS), detached eddy simulation (DES), and large eddy simulation (LES) to correctly predict turbulent flow and transport phenomena. DNS is a solution to the threedimensional, time-dependent Navier–Stokes set of equations. No turbulence models are involved in the governing equations; consequently, a DNS is conducted on a fine mesh to reproduce all length scales within turbulent flow regime. This obviously necessitates the invocation of intensive computer power, much of which is presently unavailable to the engineer, thereby rendering DNS a research tool for studying turbulence momentum and heat-transfer dynamics. The advantages offered to the food industry by DNS include detailed information regarding turbulent channel flows of dilute polymer solutions [35], the effect of
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(a)
Experiment (1080 measurement points)
(b)
RSM
(c)
High Reynolds k −e model
(d)
LRN k−e Lam−Bremhorst model
11
FIGURE 1.3 Comparison between experimental and predicted results. (From Moureh, J. and Flick, D., Int. J. Refrig., 26, 12, 2005.)
buoyancy on turbulent transfer [36], and information regarding the effective control of turbulence and heat transfer [37]. Large eddy simulation forms a solution given the fact that large turbulent eddies are highly anisotropic and dependent on both the mean velocity gradients and geometry of the flow domain. With the advent of more powerful computers, LES now offers a way of alleviating the errors caused by the use of RANS turbulence models. However, the lengthy time involved in arriving at a solution means that it is an expensive technique of solving the flow [38]. LES provides a solution to large-scale eddy motion in methods akin to those employed for DNS. It also acts as spatial filtering, thus only the turbulent fluctuation below the filter size is modeled. Over recent years, LES has been applied in areas related to food processing [39]. More recently, a methodology has been proposed by which the user specifies a region where the LES should be performed, with RANS modeling completing the rest of the solution; this technique known as DES and is found to increase the solution rate by up to four times [38]. 1.2.1.2 Porous Media and Multiphase Modeling Many large-scale processes in the food industry may have the potential to be grid point demanding in CFD models, owing to the complex geometry of the modeled structures. For example, to predict the detailed transfer processes within a cold store containing stacked foods one must mesh all associated geometry with a complex unstructured or body-fitted system, which is a highly arduous and in many cases inaccessible task. In any case, both
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computational power and CFD algorithms have not yet reached such levels of maturity that these types of computations can be achieved. Therefore, other methods must be used to exploit the physical relationships that exist on a macroscopic level and sufficiently represent the dynamic flow effects that are representative of the modeled material. The porous media assumption, which relates the effects of particle size and shape, alignment with airflow, and void fraction to the pressure drop over the modeled products, has been used in recent studies [40–42]. This method basically applies Darcy’s law to a porous media by relating the velocity drop through the pores to the pressure drop over the material. An extension of this law to account for most commonly encountered nonlinear relationship between pressure drop and velocity is represented by the Darcy–Forchheimer equation [42]: @p m ¼ v þ rC2 v2 @x K
(1:16)
Equation 1.16 is the most common relationship that is used to represent pressure drop through packed beds. In the CFD model, this equation is added as an additional sink term to the momentum equations. The general relationships to determine both the permeability and the inertial loss coefficient can be obtained by inference from the Ergun equation. However, considerable information regarding the detailed flow and transfer processes taking place within the stacked material is lost in this type of modeling strategy. Therefore before modeling a porous media, one must ensure that the parameters in the momentum source terms represent the physical media as closely as possible. Verboven et al. [42] illustrated this point by modifying the Darcy–Forchheimer pressure drop relation using experimental results to accurately represent the resistance to airflow imposed by beds of apples and chicory roots. To organize the model to comprise the main geometry is another means of circumventing detailed meshing while improving upon accuracy of pressure drop relationships, within which lies a subdomain filled with a porous medium to represent the stacked foods. Fluid flow and heat transfer are described by the laws of conservation of mass, momentum, and energy. These particular forms of transport equations in porous media are derived in terms of macroscopic variables. The macroscopic velocity is provided by the volume-averaged Navier–Stokes equations, which are a generalized version of Darcy’s law. This type of computational model can be regarded as a two-phase flow. Because the volume-averaging process causes loss of details regarding the microscopic flow regime, empirical parameters such as the thermal Forchheimer constant, thermal and mass dispersion, and interfacial heat and mass transfer coefficients are required to complete the equation system [44]. Recent studies have used a two-phase modeling technique to predict the environmental conditions of product stores [34]. As shown in Figure 1.4, Zou et al. [43,44] used this method successfully to predict temperature distribution and airflow patterns in ventilated stacked goods. 1.2.1.3
Non-Newtonian Fluid Modeling
Any fluid that does not obey the Newtonian relationship between the shear stress and shear rate is called a non-Newtonian fluid. Many food processing media have non-Newtonian characteristics and the shear thinning or shear thickening behavior of these fluids greatly affects their thermal-hydraulic performance [45]. Over recent years, CFD has provided better understanding of the mixing, heating, cooling, and transport processes of non-Newtonian substances. Indeed, a source of continuous research within this modeling discipline is the effect imposed by the rheological behavior of materials like yoghurt, soup, and milk on equipment design and performance [46,47]. Processing equipment such as heat exchangers, stirred tanks, heaters, and flow conveyors are all connected with the rheological properties of
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Airflow
Airflow
273.8 K 275.8 K 277.8 K 279.9 K 281.9 K 283.9 K 285.9 K 288.0 K 290.0 K 292.0 K
Porous media
Airflow
Bottom layer (XY plane, Z = 1)
Lower middle layer (XY plane, Z = 2)
Upper middle layer (XY plane, Z = 3)
Top layer (XY plane, Z = 4)
Airflow
Solid region (tray)
FIGURE 1.4 (See color insert following page 142.) The modeling of flow through ventilated packaging using a multiphase flow technique. (From Zou, Q., Opara, L.U., and McKibbin, R., J. Food Eng., 77, 1037, 2006; Zou, Q., Opara, L.U., and McKibbin, R., J. Food Eng., 77, 1048, 2006.)
foods, and CFD studies have elucidated numerous methods of equipment optimization [48]. Figure 1.5 illustrates the modeling of a heat exchanger with CFD. Of the several constitutive formulas that describe the rheological behavior of substances, which include the Newtonian model, power-law model, Bingham model, and the Herschel–Bulkley model, the power law is
Corrugations
Velocity (Streamline 1) 0.183 0.137 0.091 0.046 Side channel
Side channel 0.000 [m s−1] z y x
FIGURE 1.5 Modeling of the flow through a heat exchanger. (From Kanaris, A.G., Mouza, A.A., and Paras, S.V., Chem. Eng. Res. Des., 83, 460, 2006.)
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the most commonly used model in food engineering applications [50]. This governs the relationship between shear thinning fluids and the shear rate, and can be shown as . n1 t¼m g
(1:17)
Variants of this model have been incorporated to many non-Newtonian CFD simulations with success. Nevertheless, as shown by Abdul Ghani et al. [51], the complex functions relating fluid viscosity to the performed operation need not always be described, and in some cases the fluid may be treated as Newtonian.
1.2.2 NUMERICAL ANALYSIS A fundamental consideration for CFD code developers is the choice of suitable techniques to discretize the modeled fluid continuum. Of the many existing techniques, the most important include finite difference, finite elements, and finite volumes. Although all of these produce same solution at high-grid resolutions, the range of suitable problems is different for each. Finite difference techniques are of limited use in many engineering flows due to difficulties in their handling of complex geometries. Finite elements can be shown to have optimality properties for some type of equations [23]. However, only a limited number of commercial finite-element packages exist, which is undoubtedly a reflection of the difficulties involved in the programing and implementation of these techniques. Such difficulties are obviated through implementation of finite volume methods. When the governing equations are expressed through finite volumes they form a physically intuitive method of achieving a systematic account of the changes in mass, momentum, and energy as fluid crosses the boundaries of discrete spatial volumes within the computational domain [21]. The ease in the understanding, programing, and versatility of finite volumes has meant that they are now the most commonly used techniques by CFD code developers.
1.3 METHODS FOR IMPROVING MODELING ACCURACY Often times, the details of Navier–Stokes equations are smeared with general assumptions and poor modeling techniques that can impair the quality of CFD simulations. Past examples of this range from inadequate application of turbulence models to the inaccuracies caused by poor quality geometry, meshes, and first-order convection schemes [52]. Fortunately as the acceptance of CFD has grown, emphasis on developing quantitatively accurate solutions for all types of flow applications has increased. Now CFD codes offer a large range of convection schemes, turbulence models, and meshing features such as unstructured mesh, sliding mesh, and multiple frames of reference, which have developed progressively to meet the demands of the food industry [53,54].
1.3.1 CONVECTION SCHEMES As noted previously, the partial differential equations governing fluid flow are solved over discrete volumes within the computational domain. It is therefore necessary to represent these equations as accurately as possible at each location. By increasing the number of volumes on subsequent CFD computations, one would intuitively expect the difference between the solutions to be reduced. However, this leads to an unfavorable increase in
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computational time, especially when using segregated solvers. Over recent years, there has been a continual improvement in the representations of the convection terms in the finite volume equations to reduce the number of grid points involved in a solution. The ultimate accuracy, stability, and boundedness of the solution depend on the numerical scheme used for these terms. A numerical or convection scheme can be perceived as a tool with which the boundary conditions are transmitted into the computational domain and the descretized equations are solved. The performance of a convection scheme is delimited by the ability of the scheme to reduce the error once the mesh is refined. The first-order HYBRID or UPWIND convection schemes are bounded and stable but are predisposed to numerical diffusion and exhibit a sluggish response to grid refinement. Also, owing to their favorable convergence attributes, these schemes are still prevalent in the food engineering literature, which obviously casts serious doubts on the validity of some solutions especially when grid-refinement studies proved unattainable. This point was also confirmed by Harral and Boon [55] when they showed that coarse grid predictions agreed more favorably with experimental measurements than the grid-independent solution. The higher-order scheme QUICK is more accurate and responsive to grid refinement but due to its unbounded nature, it often develops solutions with unphysical under-shoots and over-shoots when strong convection is present. Convergence may also be difficult, especially when nonlinear sources are present in the simulation. Nevertheless, favorable results have been attained when high-order schemes have been used [13,29,56]. Figure 1.6 illustrates the disparity between the velocity predictions of an air jet entering a ventilation room made by a first- and second-order convection schemes at the same grid resolution [57].
Distance from floor (m)
(a)
2.8
2.4 First-order upwind Second-order upwind
2 0
(b)
0.5
1 1.5 Air velocity (m s⫺1)
2
FIGURE 1.6 Prediction of isothermal wall-jet close to the opening. (From Sorensen, D.N. and Nielsen, P.V., Indoor Air, 13, 2, 2003.)
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Cavity wall Outlet Inlet
Rectangular objects
Food surface
FIGURE 1.7 Comparison of unstructured and structured meshes. (From Verboven, P., Datta, A.K., Anh, N.T., Scheerlinck, N., and Nicolai, B., J. Food Eng., 59, 181, 2003; Mirade, P.S., J. Food Eng., 60, 41, 2003.)
1.3.2 UNSTRUCTURED MESH Most commercial CFD codes have emerged from typical Cartesian-type academic programs and for many years the actual geometry criteria of the modeled process could not be fully met and had to be altered to suit the code configuration [52]. One of the major advances to occur in meshing technology over recent years was the ability for hexahedral hybrid meshes to be incorporated into general codes. This allowed a mesh to be fit to any arbitrary geometry, thereby enhancing the attainment of CFD solutions for many industrial applications. A major advantage of unstructured and hybrid meshes is their relaxation of the block structure, a past formal requirement of many general CFD codes. Local mesh refinement can now be achieved more effectively and a solution can be developed to capture all the desired flow features without creating badly distorted cells. The versatility of these meshes has led to an increased take-up by the CFD community and their uses are finding accurate solutions in many applications within the food industry [24]. This form of meshing requires different programing and solution techniques that are not quite as intuitive in implementation as their Cartesian-based counterparts. Therefore, unstructured meshing has not yet fully infiltrated the CFD market, with codes such as PHOENICS remaining faithful to traditional structured methods [51]. Figure 1.7 shows the ability of unstructured mesh to conform to arbitrary geometry without compromising resolution elsewhere within the computational domain.
1.3.3 SLIDING MESH This type of meshing technique is commonly used to model the stirring or moving effect of adjacent geometry and can therefore simulate factory processes such as baking and mixing. This methodology has been used in some areas of food engineering. It allows certain portions of a mesh to slide relative to each other at a common interface, which in the case of a mixing tank is the interface between the tips of the blades and the baffles, and in baking is the continuous movement of the product in the oven [56,58]. Figure 1.8 illustrates the use of the sliding grid technique in a stirred tank.
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f = 0⬚
f = 15⬚
f = 30⬚
f = 45⬚
(a)
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(b)
FIGURE 1.8 Use of sliding mesh in stirred tank application. (From Ng, K., Fentiman, N.J., Lee, K.C., and Yianneskis, M., Chem. Eng. Res. Des., 76, 737, 2006.)
1.3.4 MULTIPLE FRAMES OF REFERENCE This type of meshing introduces an additional assumption that can account for any stationary parts of a flow existing in sliding mesh simulations. Instead of invoking the rotation of the grid directly, the rotation is simulated by inserting suitable body force terms in the momentum equations. By making suitable transformations in the CFD calculations at the interface between rotating and stationary flow regimes, a steady-state simulation can then be conducted on a static mesh [52]. For example, in applying this approach to stirred tanks, which is the most common application in the food industry (illustrated in Figure 1.9), the equations in the flow domain attached to the impeller are solved in a simulated rotating frame of reference whereas the equations in the remaining domain are solved in a frame of reference at rest [60].
T BW
BL H
D/2
b a C
FIGURE 1.9 Simulation of stirred tank using multiple frame of reference technique. (From Li, M., White, G., Wilkinson, D., and Roberts, K.J., Chem. Eng. J., 108, 81, 2005.)
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1.3.5 SPATIAL CONVERGENCE TECHNIQUE When designing a CFD model, one must preconceive potential gradients that may occur so that the computational domain can be suitably meshed. This mesh must then be refined to obtain, as nearest as possible, a grid-independent solution. Unfortunately with today’s computational power, it is not yet possible to obtain a grid-independent solution in some cases [33,57]. Thus the requirements must be relaxed, while still maintaining confidence in the discrete solutions for the governing equations. A spatial convergence technique proposed by Roache [61] based on Richardson extrapolation [62] has been used in many CFD engineering applications [57]. The basic priority of this method is to furnish the CFD user with a conservative estimate of the error (GCI) between the fine grid solution and the unknown exact solution. The requirement is a solution set of the same governing equations from two different grid resolutions. Both CFD solutions must be on a grid, that is, within the asymptotic range of convergence. This means that the fine grid CFD solution must be obtained at, or close to, the upper limit of the available computer power. The coarse grid solution can then be achieved by removing grid lines in each coordinate direction. To ensure that the coarse grid does not fall outside asymptotic range of convergence, the grid refinement ratio (r) between the two grids should be a minimum of 1.1. This also allows the discretization error to be differentiated from other error sources [63]. The GCI can be described as GCI ¼
Fs j«j (rp 1)
(1:18)
where the relative error « between fine and coarse grid solutions is defined as «¼
f2 f1 f1
(1:19)
where Fs is the factor of safety that is usually 3 for two grid comparisons [63], fn is the solution function (i.e., velocity at a location), and p is the formal order of accuracy of the convection scheme (i.e., UPWIND is first order therefore p ¼ 1). This method has recently been used in the food industry to show the convergence of surface-averaged heat-transfer coefficients of food in a microwave oven using QUICK convection scheme [13]. No other recent applications of this technique have been found in the literature pertaining to the food industry. It would, however, seem conceivable that this type of method should take preference in CFD studies, especially where grid independency is unattainable due to computational power, or when first-order convection schemes are used.
1.4 COMMERCIAL CFD CODES Over the last two decades there has been enormous development of commercial CFD codes to enhance their union with the sophisticated modeling requirements of many research fields, thereby accentuating their versatility. These challenges have led to unprecedented competition between developers and have expedited nonuniform development, causing the range of afforded functionalities to vary from code to code. Thus, among the many codes that exist today not all provide the features required by the food engineer. Such requirements include the ability to import grid geometry, boundary conditions, and initial conditions from an external text file as well as the modeling of non-Newtonian fluids, two-phase flows, flow-dependent properties, phase change onset, and flow through porous media [64]. Therefore, functional considerations of a code should be taken into account before selection.
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TABLE 1.4 Commercial CFD Codes with Associated Companies, Cost, and Features Company
Costa
CFD Code b
c
CHAM Ltd. www.cham.co.uk
PHOENICS 3.6.1
ANSYS, Inc. www.ansys.com
CFX 5.1
e1.2 ; e4.8k (þ e0.9k)d; e3.75ke; e14.5kf (þ e2.2k)d e2.4kb; e11.2ke
Fluent, Inc. www.fluent.com
FLUENT 6.1 FIDAP 8.6 STAR-CD 3.2
e3.88kb; e21.5ke,f e3.88kb; e21.5ke,f e2.19kb; e18.33ke,f
FLOW-3D 8.2
$2kb,e; $4kb,e,f; $11kb,c
ANDINA-F CFDþþ
e1.5kb; e17.4kc ~ e7.5kc; APDAg
CD Adapco Group www.cd-adapco.com Flow Science, Inc. www.flow3d.com ADINA, Inc. www.adina.com Meta comp Technologies, Inc. www.metacomptech.com
Features LEVL, SG, FV
USG, LAG þ PT, MPH þ IPH USG, FV, FE CREM Large amount of meshing capabilities Advanced moving obstacle capabilities FE þ FV, SG, ALE UFG
Source: From Kopyt, P. and Gwarek, W., A comparison of commercial CFD software capable of coupling to external electromagnetic software for modeling of microwave heating process. Proceedings of 6th Seminar on Computer Modeling and Microwave Power Engineering, 2004. Abbreviations: FV, finite volume; SG, structured grid; LVEL, wall distance turbulence model; USG, unstructured grid; LAG þ PT, coupled Lagrangian and particle tracker; MPH þ IPH, coupled multiphase and interphase models; CREM, complex rheology and electrohydrodynamic modeling; FE, finite element; ALE, arbitrary Lagrangian and Eulerian formulation; UFG, unified grid for ease of treatment of complex geometries. a b c d e f g
Quotations collected in April 2006. Annual educational. Permanent educational. Technical support. Annual commercial. Permanent commercial. APDA ¼ academic price depends on application.
Most commercial software featured in this chapter incorporate at least a minimum of all these functionalities, employ graphical user interfaces, and support Windows, UNIX, and Linux platforms. The most common general-purpose codes available are elucidated with their associated cost in Table 1.4. Details on three of the most routinely used commercial codes are elaborated below.
1.4.1 CFX (ANSYS, INC.) CFX had long been one of the leading suppliers of CFD software and services to the chemical, food, manufacturing, and power generating industries under its parent company AEA Technology before its $21 million take over by ANSYS, Inc. in 2003. The takeover was seen as an opportunity to broaden the scope of physics and engineering solutions that could be offered to ANSYS, Inc. consumers [65]. Within the framework of ANSYS, Inc., numerous different types of software packages exist that can be used to solve various types of flow problems. ANSYS ICEM CFD offers both unstructured and structured grid generation compliant with the CFX package, postprocessing, and grid optimization tools. ANSYS
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Multiphysics is a coupled physics tool that amalgamates structural, thermal, CFD, acoustic, and electromagnetic tools into one software product. Within the ANSYS CFX workbench contains a large amount of up-to-date fully functional physical models, which include multiphase flow, porous media, heat transfer, combustion, radiation, and moving mesh. Advanced turbulence models are also a feature of ANSYS CFX and it boasts the first commercially available predictive laminar to turbulent flow transition model (Menter–Langtry g–u model). ANSYS CFX also offers a fully parametrical CAD tool with a bidirectional link compatible with most CAD software. The ANSYS CFX software has been used by numerous authors in food engineering including Nahor et al. [34] and Verboven et al. [13].
1.4.2 PHOENICS (CHAM LTD.) PHOENICS is a powerful multipurpose CFD package developed by Brian Spalding, one of the leading pioneers in CFD modeling. PHOENICS simulates a range of processes involving fluid flow, multiphase flows, heat or mass transfer, chemical reaction, and combustion, and has been used successfully by many individuals in the food industry to quantify complex flow processes [66]. It has numerous modeling capabilities that embrace many scenarios faced by the food engineer, of which include Newtonian and non-Newtonian fluid modeling, flow through porous media with direction-dependent resistances, conjugate heat transfer, specification of temperature-dependent sources, and import of CAD geometry. Among the many turbulence models offered, the unique wall distance turbulence (LVEL) model and multifluid model (MFM) are included. The LVEL model circumvents the inaccuracies associated with wall-function computations of most turbulence models by using the knowledge of wall distances (L) and local velocities (VEL) to compute the near-wall flow. The MFM calculates the population distribution of fluids contained within a turbulent mixture and determines its influences on the mean flow. Because the PHOENICS CFD code is based on a structured grid, it necessitates the use of body-fitted coordinates to model complex geometry. This can substantially increase the preprocessing time. In recent months, CHAM in tandem with Symban Power Systems Ltd. have introduced an unstructured grid option in an effort to conform to the needs of the CFD community. Other options that are unique to the PHOENICS software include multiple shared space modeling (MUSES), modeling of objects moving through a Cartesian grid (MOFOR), and modeling curved objects in a Cartesian grid (PARSOL).
1.4.3 FLUENT (FLUENT, INC.) FLUENT, Inc. offers three software packages within the CFD framework that are suitable for the food engineer’s modeling needs. The three packages are FLUENT (general purpose with multiphysics capabilities), FIDAP (for modeling complex physics), and POLYFLOW (polymer modeling). FLUENT, Inc. is presently one of the leading suppliers of CFD software in the world. FLUENT uses unstructured grid technology so that complex geometry can be easily modeled. Among a large range of turbulence models, FLUENT contains large eddysimulation and direct eddy-simulation capabilities, and has a dynamic meshing capability that allows the modeling of different moving parts with the same simulation. The most interesting features of the FLUENT software include models for heat exchangers, discrete phase models for multiphase flows, numerous high-quality reaction models, and the phase change model, which tracks the melting and freezing in the bulk fluid. It also contains a preprocessing tool GAMBIT that employs facilities for the direct import of CAD geometries. FLUENT has recently been used successfully in the food industry by Mirade et al. [41]. FIDAP is finite
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element-based software that offers unique abilities for modeling non-Newtonian flows and free surface flows. It also contains sophisticated radiation, dispersion, and heat transfer models. FIDAP has been used extensively in the food industry [67]. POLYFLOW is a general-purposed finite-element CFD tool for the analysis of polymer processing such as glass forming, thermoforming, and fibre spinning. It has a range of applications that can be extended into the food industry [45].
1.5 PERFORMING A CFD ANALYSIS WITH COMMERCIAL SOFTWARE Undertaking a CFD study demands the use of three predefined environments within the software, with each environment representing an equally important section of the modeling process. The first environment, i.e., the preprocessor, embodies the most important phase of model definition. The ultimate success of the simulation relies upon the modeling constraints and conditions input by the user via mathematical statements to the preprocessor. The second environment, i.e., the solver, takes these mathematical statements, structures them into a solvable arrangement, and solves for the specified boundary conditions by iterative methods. The third environment, i.e., the postprocessor, is used to visualize the solution field. Usually, the stand-alone postprocessing techniques provided by the software are adequate, but in many codes the solution files can be changed into an adequate format and imported by popular spreadsheet or other visualization programs. The following provides an introduction to the different modules comprising a CFD software package.
1.5.1 PREPROCESSING The preprocessor of CFD software holds all the raw data and mathematical statements attributable to the potential success of a modeling exercise. The main tasks facing a user in the preprocessing environment include problem consideration, geometry creation or import, mesh development, physical property set-up, and numerical implementation. As highlighted by Xia and Sun [1], the first important step in a CFD study is to consider the physics of the tackled problem. In doing this, the user determines the physical processes that can be accurately represented in a CFD model and expound suitable mathematical strategies to determine the desired variables. The second stage in model development is geometry design and mesh specification. The geometry is defined by either choosing a predesigned structure from the software database or more commonly by importing the geometry from any standard CAD program. Most packages employ object-orientated automatic grid generation that allows mesh to be defined around the modeled geometry. In a lot of cases specifying a good-quality mesh, a large amount of effort by the user is required. The next step is to define the fluid properties, physical models, and boundary conditions. This phase of preprocessing requires both knowledge regarding the initial status of the model and a preconception of the potential solution. The appropriate selection of convection schemes and relaxation places a large bearing on both the efficiency and accuracy of computations, therefore circumspective choices must be made. Preprocessing is completed once the user finishes all the specified tasks as illustrated in Figure 1.10.
1.5.2 SOLVING The solver environment within CFD software organizes the mathematical input from the preprocessor into numerical arrays and solves them by an iterative method. Iterative methods are commonly used to solve a whole set of discretized equations so that they may be applied
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Structured, BFC's, unstructured
CAD import, predesigned
2. Create mesh
Turbulence, porous media, radiation, reaction
1. Create geometry
3. Specify physical models
Preprocessor
5. Choose numerical options
4. Specify boundary conditions Fluid properties, initial values
Convection scheme, solver type, relaxation
Solve
Postprocessor
Contour plots
Vector plots
Line plots
Animation
FIGURE 1.10 The simulation and analysis within a CFD environment.
to a single-dependent variable. An example of an iterative method used in CFD is the segregated solver, semi-implicit method for pressure-linked equations (SIMPLE), devised by Patankar and Spalding [68], and its descendents, i.e., SIMPLEST, SIMPLER, SIMPLEC, and PISO, which have now become traditional techniques employed by many commercial packages to solve the discretized general equations. These methods determine the pressure field indirectly by closing the discretized momentum equations with the continuity equations in a sequential manner. Consequently, as the number of cells increases, the elliptic nature of the pressure field becomes more profound and the convergence rate decreases substantially [69]. This has led to the development of multigrid techniques that compute velocity and pressure corrections in a simultaneous fashion, thus enhancing convergence rates. The improvement in solver efficiency afforded by multigrid is foiled by memory requirements that increase simultaneously with the number of cells, thus making it difficult in some cases to achieve grid independency with current-computing capabilities. Nevertheless, many CFD packages, even those based on unstructured grids, now successfully employ multigrid as the default solver option. Detailed techniques used by multigrid are available in the literature [69].
1.5.3 POSTPROCESSING The postprocessing environment allows the user to visualize and scrutinize the resulting field solution. Contour, vector, and line plots enhance interpretation of results and are progressively fortified in commercial software packages. Some packages also allow the export of field data to external modeling programs so that it can be processed further. Figure 1.11 illustrates the visualization techniques that can provide sufficient information to move forward in the design process. Animated flow fields have also become increasingly popular and can now accompany peer-reviewed studies on some scientific journal Web sites [29]. Figure 1.12 shows that by examining the progressive development of the flow field a user can gain insight into
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Rear duct
Evaporator
Z Y
Turning vane
X
(a1)
(a2) Y Z
Dead space
Velocity Side of duct 0.8
Rest of duct not modeled
X
Velocity 1.1 0.8
0.5 0.5
110 mm
0.3
0.3
0.0 −1
0.0
[m s ] Y
(b1)
Z
Evaporator moved forward
50 mm
[m s−1] Y X
(b2)
Temperature
15 mm
−0.0
Z
Angle X
60 mm
Temperature −0.0
−0.8
−0.8
−1.5
Product −2.3
Product
−3.0
−3.0
Y
(c1)
Z
Y X
(c2)
Z
X
FIGURE 1.11 (See color insert following page 142.) Visualizations of air curtain used to modify cabinet design. (From Foster, A.M., Madge, M., and Evans, J.A., Int. J. Refrig., 28, 698, 2005.)
the time-dependent features, which can aid in the efficient and accurate development of design solutions.
1.6 APPLICATIONS IN THE FOOD INDUSTRY 1.6.1 FOOD PRODUCTION FACILITIES Food production facilities continuously face challenges in reducing contamination risk by airborne microorganisms. These facilities place heavy demands on ventilation systems to maintain indoor air quality and thermal conditions at near optimal levels for processes to operate successfully. Moreover, food production processes require low air temperatures around food while retaining comfort levels within the workspace, thus rendering the provision of air at a predetermined condition a difficult task. Such difficulties illuminate computational and experimental flow field studies as essential tools in the development of these facilities. CFD coupled with experimental techniques can be used to study airflow behavior and provide ventilation system design as a function of various aspects including room geometry, outdoor climate, and indoor heat and contaminant sources, and have become increasingly popular over recent years [70,71]. A fundamental objective of ventilation is to achieve acceptable levels of indoor air quality. The ventilation system must be satisfactorily effective at removing contaminants, with their distribution directly related to the position of inlets and outlets, strength of pollutant sources, and the ventilation system itself. Both passive and the dynamic transport of contaminants can
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(a)
(b)
(c)
(d)
(e)
(f)
−2 1 4 7 10 13 16 19 22 25⬚C
FIGURE 1.12 Temperature fields at display cabinet taken at 1 s intervals. (From Cortella, G., Comput. Electron. Agr., 34, 43, 2002.)
be studied using CFD [71]. Passive contaminant transport is modeled using a passive scalar (species concentration) transport equation coupled with the equations governing air motion. This is also known as the Eulerian approach and has been recently used to quantify the effectiveness of ventilation systems in clean rooms [72]. Burfoot et al. [70] noted that the complex processes governing the dispersion of contaminant particles may not be fully quantified by the Eulerian approach, and elucidated the advantages of Lagrangian (dynamic) models. These models account for the stochastic treatment of turbulent–particle interactions, inertia, and trajectory crossing and are consequently more difficult to program and implement. Harral and Burfoot [116] studied the ability of two dynamic models to predict the movement of dispersed particles from a contaminant source within a food factory and found a recent random flight model developed by Reynolds [73] to outperform the standard particle tracker of Gosman and Ioannides [74] offered by the ANSYS CFX software package. Ventilation studies generally quantify the efficiency of fresh air delivery and effectiveness of removing contaminants through the use of ventilation scales. These can be computed
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within the framework of CFD and are related to the flow quantities that play an individual part on the quality of the indoor environment. The most regularly used scales in the food industry are a function of the mean age of air. A traditional method of calculating the mean age was to determine the mean turnover time or residence time in a system irrespective of the amount of air recirculation. This led to the development of scales that gave a crude description of the ventilation effectiveness [71]. Another more descriptive method of calculating the local mean age of air is by passively tracking the airflow in the system. This is done by adding another equation to the CFD model, which is derived from a passive scalar that statistically expresses the mean time taken for air to reach any arbitrary point after entering the system: @u @ mlam mturb @u þ rui u þ ¼1 @t @xi slam sturb @xi
(1:20)
This has been used alongside a passive contaminant transport equation in a recent clean room study and has found good agreement with experimental measurements, and has provided insight into system design [75].
1.6.2 AIR BLAST AND JET IMPINGEMENT Heat and mass transfer exchanges between air and food products are proportional to the heat and mass transfer coefficients and therefore affect the surface and core temperatures of food products. Numerous CFD models have been used to calculate the local surface convective heat transfer from the cooling media to food products. These studies have found that k–« turbulence models are generally poor at predicting solutions that closely correspond to experimental data [76–78]. Kondjoyan and Boisson [76] attributed this reason to the misrepresentation of the near-wall flow by the standard wall functions and suggested that this wall treatment be abandoned for heat-transfer calculations. Olsson et al. [78,79] assessed the heat-transfer characteristics of a jet impinging on a cylindrical food product under various conditions with the shear stress transport (SST) turbulence model. Heat-transfer predictions agreed with measurements in the upper part of the cylinder but not in the wake. This was similarly experienced by Kondjoyan and Boisson [76]. Also, heat transfer did not exhibit a relation between jet and cylinder distance, which was in contrast to experimental data. Hu and Sun [77,80,81] have also examined various parameters associated with jet impingement during the air-blast chilling process. Verboven et al. [82] noted that due to the complexities involved in resolving the governing equations in the boundary layer, obtaining appropriate numerical solutions was still an active area of research in thermal analysis.
1.6.3 COLD STORAGE FACILITIES Horticultural produce is commonly cooled by forced air-ventilation through ventilated packaging to achieve efficient and uniform cooling. The cooling rate depends on the rate of heat transfer between the cooling medium and the produce, which is directly related to the air velocity within the packaging. Cost-effective design strategies proffered by CFD have led numerous studies to employ this technique in predicting the environmental variables within ventilated packaging and refrigerated store rooms [34,43,44,83]. The storage process can be simulated in a CFD model by representing the contained goods as a porous medium and employing a predetermined void fraction and average diameter of the produce. This method has yielded reasonable agreement with measurements, although it has been recognized that
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results could further be improved by adding more model details [83]. Other CFD studies have successfully used a two-phase modeling technique to simulate cooling conditions within bulk containers [34,84]. CFD studies of cold storage along with other studies that compute the mass transfer process are summarized in Table 1.5.
1.6.4 REFRIGERATED DISPLAY CASES The use of refrigerated display cases allows good visibility and ensures free access to stored food for shop customers. A virtual insulation barrier called the air curtain is developed by the recirculation of air from the top to the bottom of the case [89]. The effectiveness of the air curtain can be impaired by irregularities in the ambient shop environment, thus it is easily understood why display cases may be perceived as one of the weakest links in the chilled food chain [90]. Numerous CFD studies on the ability of the air curtain to maintain food at a predefined temperature have been conducted over recent years [27,29,90]. Because these environmental irregularities cannot be directly incorporated into CFD models, steady-state and two-dimensional assumptions are often made that may in some cases limit solution accuracy [29]. Nevertheless, numerous successful design solutions have been developed on the basis of CFD studies. Foster et al. [27] modeled different regions of a display case to evaluate problems and develop subsequent design solutions. The study highlighted the exacerbating effect of cabinet sidewalls on maintaining design temperature and energy consumption. D’Agaro et al. [29] also found that sidewall effects are the main mechanism for ambient entrainment and thermal losses in refrigerated display cases. Navaz et al. [91] have shown that it is through digital particle image velocimetry (DPIV) and CFD simulations that the entrainment of ambient environment exhibits a linear relationship with the turbulence intensity in the air curtain. The need to maintain turbulence within the air curtain was also studied by Chen and Yuan [92], who proposed a minimum Reynolds number for sealing ability. Their analysis provided a quantitative understanding of the insulation properties of the air curtain as a function of different Grashof, Reynolds, and Richardson numbers.
1.6.5 HOUSEHOLD
AND INDUSTRIAL
REFRIGERATION
The desire for thermal uniformity within household refrigerators has also advanced the application of CFD modeling [93,94]. Fukuyo et al. [94] used CFD to develop a new airsupply system for improving the thermal uniformity as well as the cooling rate experienced within a household refrigerator. A more recent application of CFD was in the study of the flow structure in ejector cycles within commercial refrigerators [95].
1.6.6 STERILIZATION Sterilization is one of the many heat-transfer applications in which CFD is enjoying more widespread use (Table 1.6). In the thermal processing of foods, rapid and uniform heating is desirable to achieve a predetermined level of sterility with minimum destruction of the color, texture, and nutrients of food products [67,99]. Traditionally, mean-temperature approximations have been used in analytical studies to calculate both the sterility and quality of food products. However, CFD studies have proved that both of these parameters are overestimated using this approximation [67]. The ubiquity of canned food has resulted in many numerical studies investigating food quality and sterility. The two main techniques of assessing these parameters with CFD are through the calculation of spore survival rate and temperature history at the slowest heating
Two-phase model
p
New
New
New
New
New
Non-New
Fluid Type
Reasonable agreement with measurements
Successful prediction and optimization Validate LM, optimize ventilation system Prediction of interparticle collisions is important
Successful prediction and optimization
Shapes of corrugations can inhibit fouling
Conclusion
Nahor et al. [34]
Li et al. [88]
Harral and Burfoot [87]
Athanasia et al. [86],
Hu and Sun [80,81]
Jun and Puri [85]
References
Abbreviations: temp, temperature; vel, velocity; FR, fouling rate; FM, fouling model; non-New, non-Newtonian model; HTC, heat-transfer coefficients; CONDIS, contaminant dispersion; LM, Lagrangian model; BFC, body-fitted coordinates; k–«–V, k–« turbulence model variants; New, Newtonian model; PVM, porous vapor model; DEM, discrete element method; HF, heating function.
To validate heat and mass transfer in a cold store
—
p
CFD þ DEM,
vel, CONDIS
Ventilation modeling Solid and fluid conveying in pipes Cold stores
vel, solid deposition, temp vel, temp, weight loss
vel, FR, temp
Spray drying
p
—
3D, unsteady, steady, k–«–V, BFC, PVM 3D, unsteady, LM
To predict chilling process under various conditions To predict operating conditions on FR Dispersion modeling for effective ventilation To predict solid deposition in pipes
vel, HTC, temp
p
Temp Model
3D, unsteady, LM
3D, unsteady, FM
Model Constraints
To predict fouling process in PHE
Objective
temp, FR
Derived Variables
Plate heat exchangers (PHE) Air-blast chilling
System Studied
TABLE 1.5 Comparison of CFD Application of Flows with Combined Mass Transfer
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TABLE 1.6 Comparison of CFD Applications in Combined Flow and Heat Transfer System Studied Mixing jets
Chiller display cabinet Sterilization in food pouches
Derived Variables
Objective
Model Constraints
Mixing index Mixing 2D, steady, characteristics laminar of opposing jets 3D, steady, Std. Temp To enhance k–« design of cabinet Temp To understand 3D, unsteady, sterilization laminar process
Heat-transfer To predict heattransfer coefficients characteristic (HTC), temp Climate in Temp, vel To enhance supermarkets design for costumer comfort Temp, vel To enhance Climate in ventilation refrigerated configuration trucks Heat exchanger
BFC
Steady, Std. k–«
RSM
Fluid Type
Conclusions
Authors
New
Mixing depends on Dt of jets
Wang et al. [96]
New
Successful modifications
Foster et al. [27]
New* Transient nature of SHZ observed New Correlation established with Nusselt number New Optimization parameters proposed New
Abdul Ghani et al. [51]
Rennie and Raghavan [97]
Foster and Quarini [98]
Ventilation duct Moureh and produced more Flick [32] uniform airflow
Abbreviations: vel, velocity; temp, temperature; New, Newtonian model; New*, Newtonian model used to model non-Newtonian fluid; Std. k–«, standard k–« turbulence model; SHZ, slowest heating zone; BFC, body-fitted coordinates; RSM, RSM turbulence model.
zone (SHZ) [100]. CFD has shown the transient nature of the SHZ in the sterilization of a canned food in a stationary position (natural convection) [101]. These studies illustrated the considerable time needed for heat to be transferred throughout the food in a static process. More recent CFD studies have found that uniform heating can be obtained throughout the food by rotating the can (forced convection) intermittently in the sterilization process [102]. Abdul Ghani et al. [22] studied the combined effect of natural and forced convection heattransfer during sterilization of viscous soup and showed that the forced convection was about four times more efficient than natural convection. CFD has recently been used to study the effect of container shape on the efficiency of the sterilization process [103,104]. Conical-shaped vessels pointing upward were found to reach appropriate sterilization temperature the quickest [103]. Full cylindrical geometries performed best when sterilized in a horizontal position [104]. The sterilization of food pouches has also been studied using CFD [51].
1.6.7 STIRRED TANKS Many numerical studies on the mixing of liquids within stirred tanks have been carried out over the last two decades [56]. The main problem facing modelers is in the development of a
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TABLE 1.7 Comparison of CFD Application in Isothermal Flows System Studied
Derived Variables
Stirred tank
Mixing time
Static mixer
Dp
Ventilation of clean room
To analyze impeller design Observe effect of shear thinning
Model Constraints Std. k–«, SM PL
a
To solve problems arising from complex flow field trajectories
NS
Vel, passive contaminant transport
Determine flow patterns in clean room Determine flow patterns in clean room Determine airflow
k–« RNG, contaminant model
Vel, LMA
Airflow in largescale chillers
Objective
Vel
Fluid Type
Conclusions
New
Suitable designs proposed Non-New Pressure drop reduce by shear thinning Non-New Determined striation thinning behavior according to micromixing theory New Proposed design optimization
References Kumaresan and Joshi [53] Liu et al. [48]
Fourcade et al. [108]
Rouaud and Havet [72]
k–« RNG, contaminant model
New
Quantified ventilation effectiveness
Rouaud and Havet [75]
k–«, 2D
New
Optimized chiller layout
Mirade [15]
Abbreviations: vel, velocity; PL, power-law model; New, Newtonian fluid; non-New, non-Newtonian; SM, sliding mesh; Std. k–«, standard k–« turbulence model; a, striation thinning parameter; Dp, pressure drop; k–« RNG, k–« RNG turbulence model; LMA, local mean age of air.
system that proffers the most efficient blending of fluids. This depends on a number of fundamental requirements including correct choice of tank and impeller geometry, rotation speed, and location of fluid inlet and outlets. Table 1.7 summarizes some recent studies on stirred tank development. Essential requirements for tank development are knowledge of power consumption, flow velocity, and mixing characteristics of different stirred tank configurations. This knowledge can be afforded by accurate CFD simulations. Early attempts to solve the flow system and select suitable impeller geometry using CFD were made by Ranade et al. [106]. Unfortunately, the conclusions drawn from their results were questionable and conflicted with other studies [107]. As computer power became increasingly cheaper and CFD techniques rapidly advanced, numerical predictions have found better agreement with experimental data. The blending behavior of stirring tanks for highly viscous flow has been studied by many authors. Kumaresan and Joshi [53] compared the energy consumption of different mixing systems as a function of different impeller parameters. A Newtonian-type pressure drop
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correlation for a shear thinning fluid in a stationary mixing element (SMX) static mixer was devised by Liu et al. [48], who found shear thinning fluids to exhibit better mixing quality than Newtonian fluids. Other studies examine the effects of the modeling approaches such as sliding mesh, moving reference frames, etc. Aubin et al. [56] found that turbulence model had little effect on mean flow compared to effects created by the choice of convection scheme or modeling approach. Song and Han [105] utilized numerical solutions to derive a correlation that expresses the pressure drop characteristic of the Kenic static mixer in terms of the Reynolds number and aspect ratio of the mixing element. More recently CFD has been used to examine the effects of tank and impeller parameters on enzyme deactivation [109].
1.6.8 DRYING Drying of different types of food products has been a challenge faced by the food industry over the centuries. Over recent years, not only have substantial improvements been made to traditional techniques such as tray and spray drying, but also new innovative drying methods like pulse combustion have been developed and optimized using CFD [31]. The nonuniformity of the air-drying process is a common problem associated with batch type drying and CFD modeling techniques are employed to provide design solutions [28,110]. Mathioulakis et al. [110] were one of the first people to use CFD to model airflow in a tray-drying chamber and highlighted the high level of nonuniformity that existed in such processes. Recently, Margaris and Ghiaus [28] used CFD to successfully optimize the tray arrangement and inlet configuration within a tray-drying chamber. Spray drying is another traditional drying technique and is used to derive powders from products associated with the dairy, food, and pharmaceutical industries. The main objective of this technique is to create a product that is easy to store, handle, and transport [111]. Many numerical studies have been conducted to optimize spray driers so that the resultant product has the appropriate rheological properties, particle size distribution, and solubility to achieve its desired function [112,113]. Straatsma et al. [112] developed a drying model based on CFD to calculate flow pattern, temperature, particle trajectories, and particle-drying behavior, and two case studies were presented to illustrate the ability of the model to optimize dryer design. Langrish and Fletcher [31] presented a comprehensive review of the state of the art in spray-drier modeling. Recent numerical studies have focused on investigating the dispersion and fouling rates of particles as well as their evaporation and coalescence within a spray drier [114].
1.7 CHALLENGING ISSUES CONFRONTING CFD MODELERS 1.7.1 NONHOMOGENOUS FLUID DOMAIN As noted above, both Eulerian and Lagrangian techniques can be used to model flows with two or more phases, e.g., water vapor, airborne microbes, and powder. The Eulerian representation treats the particulate phase as a continuum and describes the temporal and spatial concentration of the flow. However, the disadvantages associated with this technique, which include loss of time history of particles, outweigh the potential benefits [115]. Moreover, the Eulerian concept is invalid when particles of size 1 mm are present in the flow regime [73]. Lagrangian stochastic models, i.e., random flight models (using a Lagrangian autocorrelation function) allow particles that are thrown into the near boundary region of the flow stream to experience velocities lower than those sufficient to maintain streamline trajectory. Lagrangian and Eulerian techniques have been used by the spray-drier community, with the former
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allowing far more opportunities for design as it can take into account turbulent structures and inertia crossing [115]. It has been noted in the literature that rigorous random flight models are necessary to ensure accurate predictions [70]. Moreover, a lot of work still has to be done to ensure comprehensive validation of such models [116]. Because CFD models consider the movement of fluid as a continuum, flows involving equal amounts of both fluids and powders cannot be modeled solely by CFD. Other techniques must be employed to account for the complex interactions of the individual particles. A modeling technique called the discrete element method (DEM) has recently been used with good qualitative accuracy to model a large range of granular mixing applications [117]. This method, i.e., DEM, has the ability to take into account powder cohesion and can also be coupled with CFD to simulate the transport of powder materials through pneumatic pipes [60]. DEM is very computationally expensive and often simulations require many days before arriving at a solution. This has meant that the extension of this model to other modes of dense gas–solids flow exhibited by fine powders (particle size less than 100 mm) is impractical. Therefore, it may be some time before such techniques can be incorporated into process design [118].
1.7.2 TURBULENCE MODELING One of the main issues faced by the food industry over the last two decades is the lack of understanding surrounding the efficient discrete quantification of turbulence in fluids and its effect on system performance. Over the years, simplifying assumptions have been made by turbulence modelers to make this problem more approachable. These assumptions have often proved to be unreasonable in many applications. A typical example of this is the Reynolds-number assumption, whereby either a high or low Reynolds-number flow regime is assumed a priori to a simulation. The most outstanding misapplication of this is in studies where turbulent and laminar flow regimes coexist, e.g., clean rooms or food factories. Recent modeling advancements have addressed this issue by developing a predictive laminar to turbulent flow transition model, which has been incorporated in the ANSYS CFX 10.0 software [119]. Unfortunately, as of yet no research employing this model is available. Certainly, modern variants of the k–« model have proved to be more successful than the standard k–« model in similar studies, and in applications involving swirling flow regimes or jet impingement [76]. Nevertheless, from published studies it can be concluded that confidence in k–« model can be upheld in other flow applications provided good agreement is found with measurements under grid-independent conditions [29].
1.7.3
+ Y
CRITERION
Another feature of RANS turbulence models is the near-wall treatment of turbulent flow. Treatment of the near-wall flow in all CFD software packages is specialized according to employed turbulence model. For example, low Reynolds-number turbulence models solve the governing equations all the way to the wall. This requires a high degree of mesh refinement in the boundary layer in order to satisfactorily represent the flow regime, i.e., yþ 1. Conversely, high Reynolds-number turbulence models use empirical relationships arising from the log–law condition that describe the flow regime in the boundary layer of a wall. This means that the mesh does not have to extend into this region; consequently, the number of cells involved in a solution is reduced. The use of this method requires 30 < yþ < 500 [21], although yþ 10 is also acceptable [57]. Generally these wall treatment assumptions do not adversely affect solutions and many studies have employed them with relative impunity provided yþ constraints specific to the turbulence model were adhered.
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Unfortunately, standard wall-treatment functions have failed to satisfactorily predict the phenomenon in applications involving the heat transfer associated with impinging airflow [76]. Recent studies have successfully circumvented this problem by using a blended walltreatment assumption that uses either the low Reynolds number or high Reynolds-number relationship depending on local flow condition in the wall region [78]. Before embarking on CFD modeling, it should be noted that the limitations of the turbulence models available and their associated wall functions must be taken into consideration. Models appropriate for the study should be chosen based on the experiences of similar applications in the literature. Meshing should be then carried out using an iterative procedure that involves repeated CFD solution and mesh adjustment until the yþ criteria is satisfied [21].
1.7.4 MODEL SIMPLIFICATION Large-scale simulations have the potential to be very grid point demanding and can therefore take a large amount of computing time and effort to obtain a detailed field solution. CFD modelers in the food industry have simplified computational models to cut down on both preprocessing and solving time. For example, three-dimensional systems have been modeled in two-dimensions [90], and large-scale models have been reduced in size by modeling only the region of interest [27]. In the physical world, all objects occupy a three dimensional space. Thus to accurately predict the phenomena occurring in any system, each dimension must be represented in a model. This is where CFD has an advantage over many other analytical techniques. However, some applications in the food industry are on such a large scale that modern workstations are not yet capable of efficiently yielding feasible CFD predictions [15]. Moreover, in other applications, such as refrigerated display cases, the interesting features of flow phenomena are not occurring in three dimensions [90]. The two-dimensional modeling technique assumes that the length of a system is much greater than its other two dimensions, and that the flow is normal to the systems length. This assumption essentially disregards the effects of the confining geometry and will therefore hamper the development of an accurate solution, unless it can be explicitly shown through experiments that three-dimensional flows do not impose any effects on the modeled system. Other assumptions used in the literature include those involved when modeling the region of interest of large systems, i.e., refrigeration display cabinets [27], and those used when integrating CFD computations with analytical models and experimental data in optimization of system design, i.e., food chillers [120]. Although these novel techniques may yield predictions in reasonably short time periods, the errors associated with the assumptions may preclude the development of accurate solutions [120]. Precise predictions of the phenomena in large-scale systems may not be achievable until the capacity and calculation power of workstations are developed further. Nevertheless, reasonable solutions can be presently attained provided good modeling practices are enforced including circumspective selections of turbulence model and near-wall treatment, convection scheme, and time-step. The heat and mass transfer must also be taken into account, especially when it is conceived that these processes may influence the flow regime. Additionally, concurrent validation of predictions with experimental measurements is paramount for the future success of simplified CFD modeling.
1.7.5 UNEVEN MESHING To achieve a good level of accuracy one must ensure that the mesh is appropriately refined in areas of interest and in regions where gradients occur in the flow field. Unstructured meshing
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features generally overcome difficulties associated with mesh refinement. Yet, problems can still arise, and even in recent studies the mesh has precluded the use of high-order convection schemes and high-quality turbulence models [33]. In some cases these difficulties are unavoidable, but in many others the problematic regions of the mesh can be diagnosed and repaired. Accurate representations of convective and diffusive fluxes require cells with high aspect ratios or highly skewed cells to be removed from the simulation. Some CFD packages offer means of locating these cells. However, in many cases the CFD modelers often resort to using their experience with a CFD software package to assert the quality of the mesh.
1.7.6 TIME-STEP SELECTION Many of the flow regimes encountered in the food industry are unsteady. Transient processes arise as a result of either moving boundaries, e.g., impeller blades in stirred tanks; unsteady boundary conditions, e.g., variable flow fans; or inherent physical instabilities, e.g., vortex shedding behind obstacle in free-stream flow. In these cases, a steady-state flow regime does not exist and numerical difficulties are often encountered when trying to solve the steady governing equations [29]. Time stepping is an important mechanism that allows a CFD solution to march forward in time. An optimum time-step can be considered as a trade-off between computational efficiency, temporal accuracy, and stability of the employed numerical scheme. Explicit numerical schemes generally require time-steps that are less than or equal to the CFL (Courant–Friedrichs–Lewy) condition in order to retain stability [121]. To uphold this criterion time-steps usually must be very small. Consequently, the computational overhead associated with explicit schemes has impeded their use in industry. The maximum time-step selection of implicit schemes is bounded by the accuracy requirements of the simulation. Therefore, the time-step must be small enough to resolve the frequencies of importance=interinterest in the unsteady phenomenon being modeled. Generally, an appropriate characteristic length and velocity of the problem is necessary to determine the dominant frequency of the flow regime. Sometimes this can be obtained from nondimensional numbers such as the Stroudal number, from experimental data, or from previous computations. An assumption of this frequency does not have to be precise in the first instance, as it can be refined in subsequent computations depending on the desired level of accuracy and what is demanded of the simulation. Using this technique should result in a small number of outer-iterations required to converge each time-step, which has been shown to be the most accurate way of simulating transient flows [122].
1.8 OPPORTUNITIES FOR FOOD INDUSTRY AND BENEFITS FOR CONSUMER 1.8.1 SOFTWARE PRICING The efficacy of modern workstations has been progressing incessantly over the last two decades. This has meant that complex mesh-demanding solutions can now be obtained at the workplace both cost effectively and without recourse to specialized consultancy firms. For example, in a CFD review conducted by Scott and Richardson [123] about a decade ago, price levels for both CFD and a workstation were around e60,000 to e70,000, whereas today e25,000 to e30,000 should be sufficient to purchase a high-end workstation and CFD software for a commercial company with academic prices ranging from 20% to 50% of this cost. Also, the typical processing speeds in workstations today range from 2 to 3.8 GHz with RAM capacities of 1–4 GB. Thus, with this amount of computing power available at
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reasonable prices, CFD studies will become more prevalent in developing cost-effective design solutions for the food industry.
1.8.2 PROCESSING SYSTEM DESIGN Enhancing the design of systems for the production of food products has benefits for both the food industry and consumer alike, and requires research and development of new tools and processing methodologies. Besides the expansion of the food industry, energy and workforce costs are growing rapidly. Consequently, the impetus in recent research has been directed toward the development of processing systems that can integrate multiple operations, which, depending on the requirements of the system, allow the coupling and uncoupling of elementary processes [124]. For example, the development of food powders requires both the drying and transport of ingredients. The governing dynamics in such systems include coupled heat and mass transfer and require in-depth knowledge for optimization and development. CFD modeling can be seen as the next progressive step from expensive laboratory studies and can account for the complex geometries experienced in industry to predict the governing phenomena of the processing system in an unobtrusive manner. As a result of CFD modeling, processing systems have been reduced in size and optimized to become more energy efficient. CFD can then create a climate in which both the industry and consumer can benefit, and food products can be developed with better equipment performance, less pollution impact, faster time to market, and lower design and production costs.
1.8.3 PRODUCT QUALITY Food quality is a critical issue in the food industry. The importance of food quality has heightened over recent years in tandem with the lifestyle changes experienced by many people. Sterilization and hygiene protocols have thus become paramount, and thrust has been toward maintaining high-quality food products from factory to fork. In sterilization applications, CFD modeling has helped to alleviate the difficulties in relating heat transfer in food products to sterility levels and loss of both sensory and nutritional quality. CFD has also changed the way of thinking in the operation of conventional sterilization practices. For example, CFD has proven the high-temperature short-time (HTST) approximation to be invalid under some operating conditions [67]. In addition, CFD has shown the efficacy of the sterilization process to be a function of both food properties and container geometry. Therefore, CFD can assist the understanding of the physical mechanisms that govern the thermal, physical, and rheological properties of foods and benefit the food industry by enhancing confidence and efficiency in sterilization processes [50]. The transport of airborne microbes is significant in high-care food factories and CFD simulations have been used effectively to devise strategies that minimize the movement of contaminated air toward food products [70]. Further advances in physical modeling techniques will allow the dynamic mapping of the airborne particle trajectories to be predicted before implementing cleaning strategies [116].
1.9 CONCLUSIONS The objective of this chapter is to shed light on not only the recent intricacies of fluid flow expounded by leading academics but also the remunerative advantages that CFD can offer in a commercial setting. The literature abounds with captivating and compelling CFD applications in this incessantly expanding industry. CFD has played an active part in system design including refrigeration, sterilization, ventilation, mixing, and drying. This has been aided by
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the ability of commercial companies to conform to the needs of the industry. The recent developments in CFD include greater refinement in areas of adaptive meshing, moving reference frames, and solver efficiency. Physical modeling has also reached higher levels of sophistication with the development of new models and validated by numerous experts and subsequently employed in the chemical and food engineering industry. Notwithstanding this, the CFD modeler must maintain high level of accuracy during the modeling process to uphold confidence of CFD predictions. This means that concurrent experimentation must be carried out to validate predictions, particularly where simplifying assumptions are incorporated into the model. Undoubtedly, with current computing power progressing unrelentingly, it is conceivable that CFD will continue to provide explanations for more fluid flow, heat and mass transfer phenomena, leading to better equipment design and process control for the food industry.
NOMENCLATURE u t g Ca x sT P T R Wa fi k CF K n
velocity component (m s1) time (s) acceleration due to gravity (m s2) specific heat capacity (W kg1 K1) Cartesian coordinates (m) thermal sink or source (W m3) pressure (Pa) temperature (K) gas constant (J kmol1 K1) molecular weight of air (kg kmol1) momentum source (N m3) turbulent kinetic energy (m2 s2) Forchheimer drag coefficient (m1) Darcy permeability (m2) power-law index
GREEK LETTERS r m d b l s « g_ u
density (kg m3) dynamic viscosity (kg m1 s1) Kroneckor delta thermal expansion coefficient (K1) thermal conductivity (W m1 K1) Prandtl number for enthalpy turbulent dissipation rate (m2 s3) shear rate (s1) local mean age of air (s)
SUBSCRIPTS i, j ref turb lam
Cartesian coordinate index reference turbulent laminar
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93. S. Lee, S.J. Baek, M.K. Chung, D.I. Rhee, A. Kaga, and Y. Katsuhito. Study of airflow characteristics in the refrigerator using PIV and computational simulation. Journal of Flow Visualization and Image Processing 6: 333–342, 1999. 94. K. Fukuyo, T. Tanaami, and H. Ashida. Thermal uniformity and rapid cooling inside refrigerators. International Journal of Refrigeration 26: 249–255, 2003. 95. Y. Bartosiewicz, Z. Aidoun, P. Desevaux, and Y. Mercadier. Numerical and experimental investigations on supersonic ejectors. International Journal of Heat and Fluid Flow 26: 56–70, 2005. 96. S.J. Wang, S. Devahastin, and A.S. Mujumdar. Effect of temperature difference on flow and mixing characteristics of laminar confined opposing jets. Applied Thermal Engineering 26: 519– 529, 2006. 97. T.J. Rennie and V.G.S. Raghavan. Numerical studies of a double-pipe helical heat exchanger. Applied Thermal Engineering 26(11–12): 1266–1273, 2006. 98. A.M. Foster and G.L. Quarini. Using advanced modeling techniques to reduce cold spillage from retail display cabinets into supermarket stores to maintain costumer comfort. Proceedings of the I MECH E Part E, Journal of Process Mechanical Engineering 215: 29–38, 2001. 99. J. Tattiyakul, M.A. Rao, and A.K. Datta. Simulation of heat transfer to a canned corn starch dispersion subjected to axial rotation. Chemical Engineering and Processing 40: 391–399, 2001. 100. S. Siriwattanayotin, T. Yoovidhya, T. Meepadung, and W. Ruenglertpanyakul. Simulation of sterilization of canned liquid food using sucrose degradation as an indicator. Journal of Food Engineering 73: 307–312, 2006. 101. A.G. Abdul Ghani, M.M. Farid, X.D. Chen, and P. Richards. An investigation of deactivation of bacteria in a canned liquid food during sterilization using computational fluid dynamics (CFD). Journal of Food Engineering 42: 207–214, 1999. 102. J. Tattiyakul, M.A. Rao, and A.K. Datta. Heat transfer to a canned corn starch dispersion under intermittent agitation. Journal of Food Engineering 54: 321–329, 2002. 103. M.N. Varma and A. Kannan. Enhanced food sterilization through inclination of the container walls and geometry modifications. International Journal of Heat and Mass Transfer 48: 3753–3762, 2005. 104. M.N. Varma and A. Kannan. CFD studies on natural convective heating of canned food in conical and cylindrical containers. Journal of Food Engineering 77(4): 1027–1036, 2006. 105. H.S. Song and S.P. Han. A general correlation for pressure drop in a kenics static mixer. Chemical Engineering Science 60: 5696–5704, 2005. 106. V.V. Ranade, J.B. Joshi, and A.G. Marathe. Flow generated by pitched blade turbines II: simulation using k–« model. Chemical Engineering Communications 81: 225–248, 1989. 107. A.W. Nienow. On impeller circulation and mixing effectiveness in the turbulent flow regime. Chemical Engineering Science 52: 2557–2565, 1997. 108. E. Fourcade, R. Wadley, H.C.J. Hoefsloot, A. Green, and P.D. Iedema. CFD calculation of laminar striation thinning in static mixer reactors. Chemical Engineering Science 56(23): 6729– 6741, 2001. 109. R.S. Ghadge, A.W. Patwardhan, S.B. Sawant, and J.B. Joshi. Effect of flow pattern on cellulase deactivation in stirred tank bioreactors. Chemical Engineering Science 60: 1067–1083, 2005. 110. E. Mathioulakis, V.T. Karathanos, and V.G. Belessiotis. Simulation of air movement in a dryer by computational fluid dynamics: application for the drying of fruits. Journal of Food Engineering 36: 183–200, 1998. 111. J.J. Nijdam and T.A.G. Langrish. The effect of surface composition on the functional properties of milk powders. Journal of Food Engineering 77(4): 919–925, 2004. 112. J. Straatsma, G. Van Houwelingen, A.E. Steenbergen, and P. De Jong. Spray drying of food products: 1. Simulation model. Journal of Food Engineering 42: 67–72, 1999. 113. L.X. Huang, K. Kumar, and A.S. Mujumdar. A parametric study of the gas flow patterns and drying performance of cocurrent spray dryer: results of a computational fluid dynamics study. Drying Technology 21: 957–978, 2003. 114. J.J. Nijdam, B. Guo, D.F. Fletcher, and T.A.G. Langrish, Challenges of simulating droplet coalescence within a spray. Drying Technology 22: 1463–1488, 2004.
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115. D.F. Fletcher, B. Guo, D.J.E. Harvie, T.A.G. Langrish, J.J. Nijdam, and J. Williams. What is important in the simulation of spray dryer performance and how do current CFD models perform? Applied Mathematical Modeling 30(11): 1281–1292, 2006. 116. B. Harral and D. Burfoot. A comparison of two models for predicting the movements of airborne particles from cleaning operations. Journal of Food Engineering 69: 443–451, 2005. 117. F. Bertrand, L.A. Leclaire, and G. Levecque. DEM-based models for mixing of granular materials. Chemical Engineering Science 60: 2517–2531, 2005. 118. J.J. Fitzpatrick and L. Ahrne. Food powder handling properties: industry problems, knowledge barriers, and research opportunities. Chemical Engineering and Processing 44: 209–214, 2005. 119. Anonymous. ANSYS CFX release 10.0 technical specifications. Public notice, ANSYS Inc., Southpointe, Canonburg, PA, 2006. 120. P.S. Mirade, A. Kondjoyan, and J.D. Daudin. Three-dimensional CFD calculations for designing large food-chillers. Computers and Electronics in Agriculture 34: 67–88, 2002. 121. R. Courant, K. Friedrichs, and H. Lewy. Die partiellen differenzengleichungen der mathematischen physik. Mathematische Annalen (Historical Archive) 100: 32–74, 1928. 122. Y. Liu, A. Moser, D. Gubler, and A. Schaelin. Influence of time step length and subiteration number on the convergence behavior and numerical accuracy for transient CFD. In: Proceedings of the 11th Annual Conference of the CFD Society of Canada, Vancouver, 2003, pp. 480–485. 123. G. Scott and P. Richardson. The application of computational fluid dynamics in the food industry. Trends in Food Science and Technology 8: 119–124, 1997. 124. J.C. Charpentier. The triplet ‘‘molecular processes–product–process’’ engineering: the future of chemical engineering? Chemical Engineering Science 67: 4667–4690, 2002.
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CFD Optimization of Airflow in Refrigerated Truck Configuration Loaded with Pallets Jean Moureh
CONTENTS 2.1 2.2 2.3 2.4 2.5
2.6
2.7
Introduction ................................................................................................................ Refrigerated Truck...................................................................................................... Numerical Modeling ................................................................................................... Turbulence Models ..................................................................................................... Experimental Device ................................................................................................... 2.5.1 Empty Configuration....................................................................................... 2.5.2 Impermeable Pallets Configuration ................................................................. 2.5.3 Slotted Pallets Configuration........................................................................... Modeling Approach .................................................................................................... 2.6.1 Governing Equations....................................................................................... 2.6.2 Boundary Conditions ...................................................................................... 2.6.3 Numerical Resolution...................................................................................... 2.6.3.1 Modeling the Pallets’ Interstices ........................................................ 2.6.3.2 Modeling the Slotted Wall................................................................. 2.6.3.3 Analysis of Ventilation Efficiency ..................................................... Results and Discussion ............................................................................................... 2.7.1 General Description of the Flow-Field Related to Empty and Loaded Configurations ................................................................................................. 2.7.1.1 Turbulence Behavior ......................................................................... 2.7.1.2 Airflow Rate Evolution through the Truck....................................... 2.7.2 Empty Truck Case ........................................................................................... 2.7.3 Loaded Configuration with Impermeable Pallets ............................................ 2.7.3.1 Airflow Behavior and Velocity Characteristics above the Pallets...... 2.7.3.2 Influence of Airspace Thickness between Wall and Pallets ............... 2.7.3.3 Influence of the Air Duct on Airflow and Temperature Distribution ....................................................................................... 2.7.4 Loaded Configuration with Slotted Pallets ..................................................... 2.7.4.1 Jet Characteristics.............................................................................. 2.7.4.2 Comparing with the Case of Empty Truck ....................................... 2.7.4.3 Comparing with the Case of Impermeable Pallets ............................
44 44 45 46 47 48 48 49 50 50 50 51 51 52 53 55 55 57 58 58 60 60 61 63 65 65 66 67
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2.7.4.4 2.7.4.5
Airflow Characteristics Inside the Pallets .......................................... Interactions between Flows Around and Inside Pallets at the Load Interface ......................................................................... 2.7.4.6 Ventilation Efficiency ........................................................................ 2.7.5 Turbulence Modeling Performance ................................................................. 2.7.5.1 Empty Truck ..................................................................................... 2.7.5.2 Slotted Pallets .................................................................................... 2.8 Conclusions................................................................................................................. Nomenclature ...................................................................................................................... References ...........................................................................................................................
70 71 73 74 74 75 78 79 80
2.1 INTRODUCTION This work is part of a research activity aiming to improve and to optimize air-distribution systems in refrigerated vehicles in order to decrease the temperature differences throughout the palletized cargos. This condition is essential to preserve the quality, safety, and shelf life of perishable products. The present study reports on the numerical and experimental characterization of airflow patterns within a semitrailer. In addition to the empty configuration, two loaded configurations consisting of two rows of impermeable and slotted, but empty pallets, were studied. The experiments were carried out on a reduced-scale (1:3.3) model of a refrigerated-vehicle trailer equipped with a laser Doppler anemometer under isothermal conditions. The numerical modeling of airflow was performed using the computational fluid dynamics (CFD) code Fluent. Two levels of turbulence modeling are performed: the standard k–« and a second-moment closure with the Reynolds stress model (RSM). Comparisons with experimental data obtained allow a critical evaluation of the performance of these models in internal flows. Only the results obtained using the RSM model showed good agreement with the experimental data. Numerical and experimental results make it possible to highlight the confinement effect due to enclosure and the influence of load characteristics on the jet penetration, its development, and hence the overall heterogeneity of ventilation within the truck. In the case of slotted pallets (SPs), results also allow the characterization of airflow patterns around and inside the load, and the analysis of their dynamic interactions.
2.2 REFRIGERATED TRUCK During transportation using refrigerated vehicles, this being an important link in the cold chain, maintaining regular temperature throughout the cargo is essential to preserve quality, safety, and shelf life of perishable foods. In the refrigerated enclosure, heat is transferred primarily by convection; therefore, temperature and its homogeneity are directly governed by the patterns of airflow. Air renewal provided by these airflows should compensate the heat fluxes exchanged through the insulated walls or generated by the products. This process is essential in order to decrease temperature differences throughout the cargo. Within the refrigerated-vehicle enclosure, the air is supplied at relatively high velocities through a small inlet section located adjacent to or near the ceiling. Due to the adherence of the jet on this boundary by the Coanda effect, this design should allow the confined jet to expand while following the room wall surfaces and hence provide a high degree of ventilation throughout the entire enclosure. From an aerodynamic perspective, the key characteristic of transport equipment is the placement of both the air delivery and the return on the same face. This configuration is
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almost universally used as it is practical to place all the refrigerating equipment at one end of the transport unit. The drawback of this asymmetrical design is the presence of a strong pathway between the two sections, implying high velocities in the front of the refrigerated enclosure. In addition, the compactness of the cargo and high resistance to airflow due to narrow airspaces between pallets result in an uneven air distribution in the cargo where stagnant zones with poor ventilation can be observed in the rear part of the vehicle. In these zones, higher temperatures can occur locally within the load [1–5] even though the refrigerating capacity is higher than heat fluxes exchanged by the walls and the products [6]. With an increasing emphasis on the power consumption of refrigeration systems, and an increasing awareness of temperature heterogeneity and its implications for food safety, characterizing and developing effective air-distribution systems will continue to be an important area of research in food refrigeration. Because of the complexity of direct measurement of local air velocities within a refrigerated truck, CFD has become the methodology of choice for the development of airflow models.
2.3 NUMERICAL MODELING Numerical predictions of air velocities and temperature distributions can be obtained by solving sets of differential equations of mass, momentum, and energy written in their conservative form using the finite-volume method. To ensure the accuracy and reliability of CFD simulations, predictions need to be validated against reliable measurements obtained in parametric studies where the influence of all pertinent parameters is investigated separately. In the case of complex 3D systems, comparisons of local velocities and comparisons of global airflow patterns are required. Nonintrusive techniques for velocity measurements such as the laser Doppler velocimetry (LDV) and particle image velocimetry (PIV) provide more reliable data for validation. These measurement technologies also provide a means to improve the reliability of simulations through the imposition of more accurate boundary conditions. Using CFD codes, computers, and processing facilities, complex configurations such as refrigerated transport or storage have been studied by many authors [11–20]. Moureh and Flick [15,16] tested numerous grids and turbulence models to numerically investigate the airflow behavior within an empty enclosure as a function of inlet flow arrangement. The computations were carried out in 3D using Fluent. The governing equations were solved using the finite-volume method in a staggered grid system. The author used the quick scheme, based on the three-point upstream-weighted quadratic interpolation rather than linear interpolation between consecutive grid points. The principal advantage of using the quick scheme is to reduce the number of cells required to yield a grid-independent solution, in comparison to a lower-order scheme. Moureh et al. [17] used Fluent with the Reynolds stress turbulence model (RSM) to predict the airflow pattern within a 3D configuration of a typical refrigerated vehicle loaded with two rows of pallets. The numerical results were validated by experimental measurements of velocity and turbulence obtained using LDV on a 1:3.3 scale model of a trailer under isothermal conditions. The results of this study demonstrated the ability of the RSM to predict the global behavior of the airflow in the highly turbulent wall jet zone and in the narrow air spacings around the pallets. It also provided improved understanding of the mechanisms governing the stability of the confined wall jet on the ceiling and its point of separation. Moureh and Flick [18] used the numerical approach developed previously [17] to characterize the influence of an air-duct system and the narrow airspace separation (1–2 cm) between the pallets and the walls in terms of the ventilation homogeneity throughout the enclosure. The findings underlined the importance of these airspaces, in achieving sufficient
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ventilation around the pallets, to remove infiltration heat and thereby reduce temperature variability. This result agrees with Nordtvedt [19] who also recommended maintaining these airspaces to achieve these outcomes. Tapsoba et al. [20] also used Fluent with the RSM turbulence model to predict the 3D airflow pattern within a refrigerated vehicle, with and without an air-duct system, loaded with two rows of SPs. The Ergun relation was used to express the pressure loss within the pallets. The experimental device was the same as that used previously [18]. The results showed substantial ventilation heterogeneity inside pallets without the air duct, with the rearmost pallet 40 times less ventilated than the fifth pallet. This ratio was reduced to 25 and 8 where the length of the duct was 33% and 66% of the length of the vehicle, respectively. Lindqvist [7,8] used the commercial CFD code Kameleon (SINTEF, Trondheim, Norway) to predict the pressure and velocity distribution in a typical reefer hold filled with pallets in 3D. The aim was to analyze the influence of numerous arrangement factors on the air distribution within the hold. Validation was performed using pressure measurements taken inside a full-scale laboratory model of a section of a reefer hold loaded with pallets. Comparison of predicted and measured pressures showed substantial disagreement. Overall, the air distribution was uneven and thus insufficient for a large number of pallets.
2.4 TURBULENCE MODELS According to the complexity of the airflow in a room, rigorous validation for numerical models is needed before they can be applied to wide ranging air-distribution problems. This validation concerns primarily the choice of turbulence model, for which it is necessary to investigate performance by comparing numerical predictions with experimental data. The selection of the appropriate turbulence model strongly depends on the complexity of the flow. To illustrate the complexity of this selection, this section provides a critical discussion of turbulence models generally used for confined flows encountered in a refrigerated truck. The turbulent wall jet (even with an isothermal co-flowing or stationary external stream) is known to be a difficult flow to predict [21]. An undeniable difficulty arises through the confinement effect induced by wall boundaries, and increased by the compactness of the load, which in turn implies the formation of an adverse pressure gradient along the jet axis. The resulting flow is complicated since it is often the combination of free turbulent shear flows, near-wall effect, and recirculation areas (including high streamline curvature and probably local separation). In addition, the complexity of the system is increased by the presence of the load, which increases the confinement effect and the adverse pressure gradient. Pallets and boxes affect the airflow through surface stresses, porous infiltration, deviations and reattachment, and also turbulence generation. They may create secondary recirculating flows, including stagnant zones, and induce high velocities elsewhere. To predict the turbulent airflow patterns and temperature distribution in such configurations, many authors [7–9,12,13,22–29] have used the Reynolds averaged equations, employing the standard k–« model described by Launder and Spalding [30], since it is easy to program and has broad applicability. However, in the major cases the validation of the turbulence model lacks comparisons with accurate experimental data concerning airflow patterns, especially in 3D cases. According to the complexity of the indoor flows underlined above, different authors [31–35] agree on the inadequacy of the k–« model to predict airflow patterns and underline its limitation by comparison with experimental data. According to Wilcox [31] and Menter [32], the k–« model predicts significantly too high shear–stress levels and thereby delays or completely prevents separation. According to Launder [34], this trend can be more pronounced in the presence of adverse pressure gradient and leads to overprediction of the
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wall shear stress. Aude et al. [35] pointed out the difficulty in accurately predicting the airflow characteristics concerning the velocity levels, the turbulent kinetic energy, its dissipation rate, and the turbulent viscosity in the stagnant regions with the k–« model. In this case, improving predictions can be achieved by taking into account the effect of the turbulence anisotropy by using more advanced turbulence models, such as those based on the second-moment closure, or large eddy simulation. Many authors have reported that the Coanda effect (governing the attachment of the jet on the ceiling) was not well predicted by the k–« model. Moureh and Flick [15,16] observed that the standard k–« model overestimated the Coanda effect of the wall jet and failed to predict its separation under adverse pressure gradient. Verboven et al. [27] pointed out the limitation of this model with respect to the air jet above pallets and near walls in a coolstore. Nady et al. [29] also underlined the inability of the k–« model to predict the detachment of the jet from the ceiling as observed experimentally under nonisothermal conditions. To improve numerical predictions in a ventilated enclosure with a strong Coanda-effect influence, Choi et al. [22] suggested modifying the multiplier coefficient (Cm ¼ 0.09) of the turbulent viscosity given by the standard k–« model. The author recommended Cm ¼ 0.12 or 0.15 if the inlet is near or far from the ceiling, respectively. However, the fact that this modified model cannot be universally applied will discourage further use without comparative experimental data. Although CFD continues to be the modeling methodology most frequently employed for airflow prediction in refrigerated food applications, network models provide an alternative approach for transport systems. Several modeling approaches using electrical analogies to predict the airflow rate in spacing or channels between pallets or boxes were developed [10,36–38]. These approaches could give qualitative information on the air circulation rate and do not require much time or memory capacity. However, these simplified modeling approaches were not able to provide quantitative predictions of airflow patterns, local air velocities, and turbulence levels, which are important in heat transfer phenomena. In addition, predictions cannot take into account the behavior, the stability, and the diffusion of the supplied forced air jet.
2.5 EXPERIMENTAL DEVICE According to the complexity of direct measurement of local air velocities in the truck, the experiments were carried out on a scale model of a trailer built with a length scale ratio of 1=3.325 with respect to the adimensional Reynolds number (Re ¼ rW0DH=m). Airflow inlet and outlet were located in the front face of the parallelepiped as shown in Figure 2.1 where the full-scale geometry is represented. All dimensions and results in this paper are given in connection with the full-scale geometry using the Reynolds analogy. The walls of the scale model were composed of wood except one side constructed of glass to allow internal air velocity measurement using 1D LDV system (Laservec) manufactured by TSI. The LDV consists of an LDP-100 probe and the raw data are processed by an IFA 600 signal processor. This system does not interfere with the flow and is able to correctly resolve the sign as well as the magnitude of velocity and to determine mean velocity and its fluctuation. It comprised a 50 mW laser diode emitting a visible red beam at 690 nm wavelength, a beam splitter, a Bragg (acousto-optic) cell, a focusing and receiving lens to collect scattered light from the measurement point, and a photomultiplier. Since the basic input to the processor is a frequency, this permits a very wide potential range of velocities from millimetre per second to over 1000 m s1. The accuracy is considered to be less than 1%. The air supplied to the model was seeded with atomized oil particles of 4 mm mean diameter that scatters light as the flow carries them through the measurement volume. The probe was carried on an automatic displacement system that provides a resolution of +0.5 mm in three directions.
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y
AA
z x L = 13.3
D = 0.0 or 0.18
0.14
Inlet 1 Walls H = 2.5 BB
0.18 0.15 1.22
Outflow Wd = 2.46
FIGURE 2.1 Dimensions of the truck enclosure (m).
The scale model was supplied with air from a fan, which can go up to 5800 m3=h. The airflow was introduced in the enclosure perpendicular to the front face with a mean velocity of U0 ¼ 11.5 m s1, i.e., a Reynolds number of 1.9 105. The two inlet arrangements studied were the ceiling-slotted case (D ¼ 0, D is the distance of the jet inlet slot below the ceiling) and the downward displace slot case (D ¼ 0.18 m). Excepting the Coanda effect at the ceiling level, these two cases lead to similar results. Unless otherwise stated, D ¼ 0 was considered. Three configurations were investigated, which are discussed below.
2.5.1 EMPTY CONFIGURATION According to the complexity of factors affecting the homogeneity of ventilation, it is of great interest, as a first step, to study the case of an empty semitrailer container not loaded with pallets. The comparison between the loaded and unloaded configurations allows to better understand and to quantify separately the influence of the geometrical factors related to the enclosure (L=H > 5) and to the presence of inlet and outlet sections on the same side, from those related to the load: stowing patterns, pallet dimensions and porosity, and spaces between pallets.
2.5.2 IMPERMEABLE PALLETS CONFIGURATION Impermeable pallets (IPs) represent the case of frozen foods and they are considered as obstacles. Inside the scale model, closed glass boxes are used to represent pallets. The loaded configuration consists of two rows of 16 pallets. The dimensions of this device, expressed using the actual scale are represented in Figure 2.2. This configuration was investigated in two cases: Without air ducts. The whole airflow rate is blown at the front of the truck. In this case, two airspaces distances between pallets and walls are considered: the reference case with e ¼ 2 cm and e ¼ 1 cm. With air ducts. The airflow rate was blown on three positions: z ¼ 0 (front), z ¼ L=3, and z ¼ 3L=4 with 35%, 50%, and 15% as flow rate repartition, respectively (Figure 2.3).
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Shift-slotted case: D = 0.18
Ceiling-slotted case: D = 0 Jet axis
y 1.7 z 0.02
0.1
0.8
Wood blocks
(a) 0.02 x
1.2
0.02 z 0.02
(b)
0.1
0.1
FIGURE 2.2 Configuration of the load in the enclosure. (a) Side view of the load (section AA of Figure 2.1) and (b) top view of the load (section BB of Figure 2.1).
2.5.3 SLOTTED PALLETS CONFIGURATION Porous pallets represent the case of fresh products where bulk ventilation is needed to evacuate heat fluxes and gas concentration generated by the products. Given the difficulties concerning direct air velocity measurements inside filled pallets, this study will consider the case of slotted but empty pallets. This allows obtaining reliable velocity measurements with the LDV system within SPs and therefore to validate the numerical model within these enclosed pallets. This configuration also allows studying airflow around and inside pallets and to analyze their dynamic interactions. The enclosure was loaded with two rows of 32 polystyrene SPs of size 1.7 0.8 1.2 m as shown in Figure 2.2. The slots were spread out over the six faces of each box and allowed air to go through 15% of the surface (Figure 2.4). The pallets were set resting on wooden blocks of dimension 0.1 0.1 0.1 m, allowing air circulation under them. Small gaps of 0.02 m were maintained between the pallets.
35%
50%
15%
FIGURE 2.3 Schematization of air ducts and airflow distribution in the truck.
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FIGURE 2.4 Photograph of a SP.
To allow velocimetry measurements within the load, one box had been equipped with a slotted Plexiglas wall. This box was displaced in the enclosure to investigate each position.
2.6 MODELING APPROACH 2.6.1 GOVERNING EQUATIONS The time-averaged Navier–Stokes differential equations for steady, high-Reynolds numbers, and incompressible flows expressed in their conservative form for mass and momentum conservation were solved by a finite-volume method using the Fluent solver. Turbulence was predicted with the standard k–« turbulence model and RSM, which is an advanced model for which an individual transport equation is derived for each shear-stress component. The RSM was used as the default turbulence model.
2.6.2 BOUNDARY CONDITIONS The computational domain may be surrounded by inflow and outflow boundaries in addition to symmetry and solid walls. At the inlet, uniform distribution is assumed for velocity components, kinetic energy of turbulence k0, and the energy dissipation rate «0. The numerical values are specified as .
(U ¼ V ¼ 0; W ¼ W0 ¼ 11.5 m s1 representing the mean longitudinal velocity, giving an inlet flow rate Q0 ¼ 5500 m3 h1,
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CFD Optimization of Airflow in Refrigerated Truck Configuration Loaded with Pallets .
.
.
51
pffiffiffiffiffiffi k0 ¼ 3=2 (U0I0z)2; where I0z ¼ 10% (I0z ¼ w2 =W0 ) represents the turbulence intensity of the z-component of velocity at the inlet as obtained from experiments, «0 ¼ (Cm0.75 k01.5=0.07DH) where DH represents the hydraulic diameter of the inlet section, and For the RSM model, turbulence is assumed to be isotropic: ui uj ¼ 2=3 k0 dij .
According to these conditions, the Reynolds number is considered as being equal to 2 105 in experiments and numerical simulations. At the outflow, pressure is supposed to be uniform and zero gradient is applied for all transport variables. The turbulence models are only valid in fully turbulent regions. Close to the wall, where viscous effects become dominant, the model is used in conjunction with wall functions. For this study, the conventional equilibrium logarithmic law governing the wall is used [30]. At the symmetry plane, zero normal velocity and zero normal gradients of all variables are assigned. For thermal simulations, the following boundary coefficient conditions were assumed: . . . .
External temperature (Te): 308C. Blowing temperature (T0): 288C. Overall heat transfer through the insulating wall: 0.3 W m2 K1. The pallets are considered to be adiabatic. Only convective exchange between the truck wall and the air is taken into consideration.
2.6.3 NUMERICAL RESOLUTION The computations were carried out using Fluent, a commercial CFD code on a 3D configuration. The governing equations are solved using the finite-volume method in a staggered grid system. A nonuniform grid was implemented, with a high-density mesh in regions near the inlet, outlet, and walls where high gradients were expected. In these simulations, the quick scheme, based upon three-point upstream-weighted quadratic upstream interpolation was used instead of a linear interpolation between consecutive grid points [39]. The principal objective in using the quick scheme is to reduce the number of cells required to yield a grid-independent solution, in comparison to a lower-order scheme. In order to test the influence of the number of cells used in the solution, many grid sizes comprised between 240,000 and more 106 cells were used. However, simulations show for greater than 450,000 cells that the predicted values are grid-independent. Unless otherwise stated, the presented numerical data are grid-independent. 2.6.3.1 Modeling the Pallets’ Interstices As there was a big difference between pallet dimensions and the small gaps between them (Figure 2.2b), direct meshing of all these gaps would lead to very large grid size (exceeding the memory capacity) and a high computing time, especially if a gradual grid refinement is applied where the size ratio between two consecutive cells should not exceed 20%. To avoid this difficulty, we replaced thin airspaces between pallets along the vehicle by a fictitious, aerodynamically equivalent, porous medium for which the permeability coefficient was chosen so as to ensure the same airflow resistance as the actual medium. This approach was made possible because air velocity measurements showed that laminar flow was dominant between pallets (Re < 500) [11]. Consequently, there is a linear
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relationship between airflow rate and pressure gradient as in a porous medium governed by Darcy’s law. In the proposed method, the permeability coefficient for this fictitious porous medium was chosen in order to ensure that for a given pressure gradient, the same flow rate as for the actual medium is obtained. Consequently, the analogy between the laminar flow between two parallel plates separated by a distance e and a flow in a porous medium between two parallel plates separated by a distance e0 are related as follows:
0
(Umean e)actual medium ¼ (Umean e )porous medium )
Kp dp 0 dp e2 e e¼ dx 12m m dx
(2:1)
Thus the equivalent permeability is equal to Kp ¼
e3 12e0
(2:2)
The use of this analogy allows the reduction in grid size because airspaces separating pallets were represented by relatively large porous cells (e0 ¼ 0.06 m) with a permeability coefficient that was calculated from Equation 2.2. Figure 2.5 illustrates the effect of this analogy on grid refinement and consequently on grid size. 2.6.3.2
Modeling the Slotted Wall
Fluid flow was sensitive to the slotted wall effect by the means of the normal pressure jump through the wall, which is characterized by C1 the pressure loss coefficient: 1 DP ¼ C1 rU? 2 2
(2:3)
where DP is the total pressure drop and U? is the mean velocity normal to the wall. The pressure drop for a single slotted wall was measured and the coefficient C1 equals 80. Direct meshing
Palette n
Porous media analogy
Palette n + 1
e
Palette n
Pallet domain
Palette n + 1
e⬘
Porous media Grid Free zone
FIGURE 2.5 Analogy between laminar flow and porous medium flow on the grid refinement.
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2.6.3.3 Analysis of Ventilation Efficiency The overall ventilation efficiency is often characterized by the number of times the enclosure’s air volume is replaced during one time unit: t0 ¼
Inlet flow rate (m3 h1 ) Enclosure volume (m3 )
(2:4)
An extension of this concept is proposed here in order to characterize the local ventilation _ , flowing in and out of the volume efficiency of the pallets. Thus we analyze the flow rate m _ can be (Vp) of one pallet of surface S (Figure 2.6a) . According to numerical simulations, m computed by the following integration: _ out ¼ _ ¼m _ in ¼ m m
1 2
ð
~~ r U ndS
(2:5)
S
where ~ n is the unit normal vector of the elementary surface dS. For each pallet, a local ventilation efficiency can be written as t¼
_ 1 m r Vp
(2:6)
However, air flowing in the volume of a pallet is not only composed of fresh injected air at temperature T0 but also of heated air from the surrounding pallets (Figure 2.6b). If ventilation is used to extract heat that is generated in the enclosure, only the fresh
. m , Tin (mixed air entering the pallet) . m , Tout (a) . m eq, T0 (fresh air from the inlet)
. m , Tout . . Useless air, (m eq −m ) Tout (b)
FIGURE 2.6 Introducing the concept of equivalent fresh air renewal for one pallet. (a) Heat balance on the considered pallet and (b) heat balance with the concept of equivalent fresh air.
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injected air is efficient. In order to characterize the quantity of the fresh air part entering a pallet, a fictitious and uniform volumetric heat load per unit volume, q, is applied throughout the pallet domain. This simulates for example heat generation due to respiration of a load of fruit or vegetable. In steady state, the heat balance of a pallet can be expressed using bulk average air temperatures of the air flowing in and out, named Tin and Tout, respectively. _ Cp (Tout Tin ) U ¼ qVp ¼ m
(2:7)
Moreover, the incoming airflow can be considered as the mixing of a quantity of fresh air _ m _ eq) at temperature Tout _ eq at temperature T0 and a recirculating air flow rate (m named m (Figure 2.6b). Thus the heat balance can be rewritten: _ eq Cp (Tout T0 ) U ¼m
(2:8)
This means that, in terms of heat extraction capacity, the process gives rise to an equivalent _ eq entering the volume. The additional airflow part: m _ m _ eq flow rate of fresh injected air m flows in a circular manner and does not affect the heatÐ balance. From the simulations, the following quantity A ¼ S rj~ v ~ njTdS can be computed: A¼
ð
ð rj~ v ~ njT dSin þ rj~ v ~ njT dSout Sin Sout ð ð ¼ Tin rj~ v ~ nj dSin þ Tout rj~ v ~ nj dSout
rj~ v ~ njT dS ¼
S
ð
Sin
Sout
_ ¼ (Tin þ Tout )m
(2:9)
From Equation 2.7 and Equation 2.9, the temperatures Tin and Tout can be calculated and _ eq can be obtained from Equation 2.10: finally m U A Cp 1 U Aþ ¼ _ 2m Cp
1 Tin ¼ _ 2m Tout
_ eq ¼ m
U Cp (Tout T0 )
_ ¼m
(2:10) Tout Tin Tout T0
We can then define a local ventilation efficiency based on the equivalent fresh air renewal: t eq ¼
_ eq 1m r Vp
(2:11)
A heat load of 50 W m3 was applied in the simulations. Adiabatic boundary conditions were applied on the enclosure walls and free convection was not taken into account in order to point out only the effect of forced convection inside the enclosure. For these conditions, a dimensional analysis showed that t and teq are independent of the heat load.
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2.7 RESULTS AND DISCUSSION 2.7.1 GENERAL DESCRIPTION CONFIGURATIONS
OF THE
FLOW-FIELD RELATED
TO
EMPTY AND LOADED
Figure 2.7 presents a comparison between loaded and empty enclosures showing the behavior of the streamlines related to the mean flow-field in the symmetry plane. These streamlines are obtained from 1080 (24 45) measurement points made using the LDV system for empty and SPs and numerically for IPs. On the same plane, Figure 2.7 presents the velocity decay along the jet axis for the different studied cases.
Height (m) 2.5 2 1.5 1 0.5 0 0
2
4
6
8
10
12
14
Length (m) (a) y/H 1 0.90
0.44
0.22
0.07
0.02
8
10
0.01
Loaded with SPs, experimental 0 (b) Height (m) 2.5 2 1.5 1 0.5 0 0
2
4
6
12
14
Length (m) 11.5 m s−1
0 m s−1 Air velocity (m s−1) (c)
FIGURE 2.7 Influence of the load on the streamline behavior in the symmetry plane. (a) Empty configuration: experimental data (1080 LDV measurement points); (b) slotted configuration: experimental data (LDV measurement points); (c) loaded with IPs: numerical data with RSM model.
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For the empty configuration, Figure 2.7a clearly shows that the wall jet separates from the ceiling at approximately 8.5 m (z=L ¼ 65%). This separation splits the jet into two regions dominated by two vortices of opposite circulation. The primary recirculation located in the front part of the enclosure delimits the reach and the action of the inlet jet. Conversely, the secondary flow located in the rear part is poorly supplied by the primary jet. In addition, the velocities are very low. This type of airflow is highly undesirable because the stagnant zone aspect is related to the secondary recirculating area, where high levels of temperature and contaminant could be expected due to the poor mixing with the primary recirculating air. Concerning the IPs case (Figure 2.7c), the impermeability of the load increases the confinement effect, which in turn causes a more pronounced adverse pressure gradient. This limits the jet development and strongly affects its stability. As a consequence, the separation point is located more upstream at z=L ¼ 40% in the case of the loaded configuration instead of z=L ¼ 65% for the empty configuration. This trend was also confirmed on Figure 2.8 showing that the jet penetration decreased as the load permeability decreased.
1 Empty enclosure SPs IPs
0.8
W/ W0
0.6 0.4 0.2 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
z /L
−0.2 (a)
11 Exp.-empty truck Exp.-loaded truck Model-empty truck Model-loaded truck
W (m s−1)
9 7 5 3 1 −1 0
2
4
6 8 Length of the truck (m)
10
12
14
(b)
FIGURE 2.8 Decay of the jet velocity along the truck in empty and loaded configurations. (a) Experimental data, (b) empty and loaded with IPs. (continued)
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1 Experiment
W/ W0
0.8
RSM
0.6
0.4
0.2
0 0
0.2
0.4
0.6
0.8
1
z /L (c)
FIGURE 2.8 (continued) (c) Loaded with SPs.
In the case of SP (Figure 2.7b), the velocity tended asymptotically to zero but remained positive on the jet axis. The separation point is transformed to a stagnation point at z=L ¼ 0.5. This means that no recirculating pattern occurred in the symmetry plane. Another common characteristic of confined configuration concerns the apparition of an adverse pressure gradient preceding the stagnant zone [11,15]. 2.7.1.1 Turbulence Behavior Figure 2.9 shows comparisons between numerical and experimental data concerning the evolution of the mean-square of the turbulent velocity in the z direction (w2 ) through the inlet section along the enclosure in an empty configuration. Similar trend of w2 was obtained for loaded configurations (data not shown). As it can be seen on Figure 2.9, w2
4
RSM Experiment
3.5 3 2.5 2 1.5 1 0.5 0 0
2
4
6
8
10
12
14
Length of the enclosure (m)
FIGURE 2.9 Evolution of the mean-square of the longitudinal fluctuating velocity (w2 ) along the jet axis: comparison between experiment and numerical results.
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numerical and experimental data experience two peaks. The first peak is a common characteristic of turbulent jet expansion due to diffusion of the turbulence from the edge to the core of the jet. The second peak located near the separation area of the jet from the wall reflects the extra amount of turbulence generated in this region where high gradients of velocities were locally present. Even if the trend of numerical and experimental values is similar, the RSM seemed to overestimate the diffusive character of the turbulence. This could be explained by the complexity of the flow at the separation point where the wall shear stress vanishes and the logarithmic law of the wall is not valid. 2.7.1.2
Airflow Rate Evolution through the Truck
Figure 2.10 shows a comparison between empty and loaded configurations concerning the longitudinal evolution along the truck of the dimensionless airflow rate (Q(z)=Q0), obtained using numerical data. For a given cross-section along the enclosure, the circulating flow rate Q(z) was calculated as follows: ð Q(z) ¼ 0:5 (2:12) jW j ds Sz
where Sz represents the cross-section considered at z coordinate and W represents the local velocity. This comparison also shows that the presence of pallets significantly increases the confinement effect and reduces the development of the jet and the entrainment phenomena with the surrounding ambience. Consequently, the evolution of dimensionless airflow rate (Q(z)=Q0) in the loaded configuration is lower than in the empty configuration. According to Figure 2.10, the maximum values of (Q(z)=Q0) are 1.5 for loaded configuration and 3 for empty configuration and they are reached at 1 and 3.5 m, respectively. The following section discusses separately the main aspects related to the different configurations.
2.7.2 EMPTY TRUCK CASE Figure 2.11 and Figure 2.12 present velocity profiles in the symmetry and the inlet centered plane and turbulence profiles in the symmetry plane. 3 Model-loaded truck Model-empty truck
Q (z )/Q 0
2
1
0 0
2
4
6
8
10
12
14
Length of the truck (m)
FIGURE 2.10 Longitudinal evolution along the truck of the dimensionless airflow rate (Q(z)=Q0) in empty and loaded configurations (IP).
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2.5
Height: y (m)
2.25 2 1.75
1m 2m 6m 9m
1.5 1.25 1 −2
0
2
4 W (m
6
8
10
s−1)
(a) 1.25
Width: x (m)
1.00
0.05 m
0.5 m
1m
2m
5.5 m
6.5 m
7.5 m
8m
12 m
0.75
0.50
0.25
0.00 −1
0
1
3
5
7
9
11
13
−1)
W (m s (b)
FIGURE 2.11 Experimental longitudinal velocity component (W ). (a) Vertical profiles along the symmetry plane at 1, 2, 6, and 9 m and (b) horizontal profiles in the inlet centered at 0.05, 0.5, 1, 2, 5.5, 6.5, 7.5, 8, and 12 m.
Just after the inlet, the jet attached to the ceiling by Coanda effect and flowed along it until its separation while entraining the surrounding fluid. Between the inlet (z ¼ 0) and up to z ¼ 4 m, the airflow rate increased (Figure 2.10) and the jet decay is similar to an unbounded 2D wall jet [16]. The confinement effect due respectively to the interaction with the lateral enclosure wall and with the reverse flow (Figure 2.11) tends to reduce the entrainment of the jet with its surroundings and causes the stabilization of dimensionless airflow rate: Q(z)=Q0 (Figure 2.9). Owing to the airflow rate stabilization, the mixing process causes the velocity profile to flatten with distance (Figure 2.11) and in turn implies the decreasing of the total flux of
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2.5
Height: y (m)
2
1.5 2m 3m 4m 9m
1
0.5 0
0.5
1
1.5
2
2.5
3
3.5
Mean square of horizontal turbulent velocity: w 2 (m2 s−2)
FIGURE 2.12 Vertical profiles of the mean-square of the longitudinal fluctuating velocity (w2 ) along the symmetry plane.
momentum. This decay can only be compensated for by an adverse pressure gradient that causes the separation of the wall jet at 8.5 m. Consequently, a stagnant zone with low velocities and a quasiuniform pressure is present at the rear between the end wall and the zone of separation.
2.7.3 LOADED CONFIGURATION 2.7.3.1
WITH IMPERMEABLE
PALLETS
Airflow Behavior and Velocity Characteristics above the Pallets
In order to illustrate the overall behavior of the airflow above the pallets, experimental and numerical contours of velocity fields are presented and compared in Figure 2.13 in three cross-sections at L=4, L=2, and 3L=4 of the vehicle. Each figure is obtained with 90 experimental points. At L=4 (Figure 2.13a) velocity fields show that the wall jet moves along the ceiling, where it is maintained by the Coanda effect, and returns along the side walls and above the pallets. Near side walls velocities are very low. At L=2, in the middle of the vehicle (Figure 2.13b), located downstream of the separation of the wall jet, the behavior of the airflow is completely different. After its separation from the wall, the jet reattaches on the top of the pallets where velocities become positive. Simultaneously, the jet returns along the ceiling where the velocities are negative. At 3L=4 (Figure 2.13c), velocities are still positive above the pallets and negative on the ceiling where the returning airflow occupies the whole width. Figure 2.14 shows a comparison between numerical and experimental data concerning the w2 field values in a cross-section at L=4 above the pallets. High turbulence near the jet boundaries of the mixing area and low values for the returning flow under the jet and near the wall boundaries can be seen. Figure 2.15 shows numerical data concerning contours of air velocities and temperatures for the external planes of the truck. However, the predicted temperatures should be interpreted with caution because it cannot be verified experimentally on the isothermal reduced-scale model.
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Ceiling
Y
W (m s−1)
Top of pallets
X
−2.5 −1.1 Numerical results
2.8
1
Y
W (m s−1) −0.5 −0.3 Numerical results
4.9
3.8
X
0
−0.2 - 0
0.2
−0.4 - −0.2
2 – 4 m s−1 0 – 2 m s−1
0.1
0.3
m s−1
m s−1
−2 – 0 m s−1 0 - 0.2 m s-1
−4 – −2 ms−1
0.2 - 0.4 m s-1 Experimental results
Experimental results
(a)
(b)
Y
W (m s−1) −0.02
−0.01
X 0
0.01
0.02
Numerical results
−0.2 - 0.1 m s-1 -0.1 - 0 m s-1
0 - 0.1 m s-1 0.1 - 0.2 m s-1 Experimental results
(c)
FIGURE 2.13 (See color insert following page 142.) Velocity field above the loading at (a) L=4, (b) L=2, and (c) 3L=4: comparisons between numerical and experimental data.
2.7.3.2 Influence of Airspace Thickness between Wall and Pallets The thin airspace (ew ¼ 1 – 2 cm) located between the lateral wall and pallets (Figure 2.2) represents the most sensitive area in the load. As regards the low velocities between the wall and the pallets, heat fluxes exchanged through the insulated wall with the
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w2 (m 2 s −2)
0
0.1
1
2
3
4
(a) 3 − 4 m2 s−2 1 − 2 m2 s−2
2 − 3 m2 s−2
0 − 1 m2 s−2
(b)
FIGURE 2.14 (See color insert following page 142.) Contours of the mean-square of the turbulent velocity in the z direction (w2 ) above the loading at L=4. (a) Numerical values and (b) experimental values.
0
0.2
0.4
0.6
0.8
1
(a)
−10 −12 −13 −15 −16 −18 −19 −20 −22 −24 −25 −26 −28
(b)
FIGURE 2.15 (See color insert following page 142.) Numerical contours of velocity and temperature in the most sensitive planes of the truck: (a) velocity contours: W=W0, (b) contours of temperature (8C); T0 ¼ 288C; Te ¼ þ308C.
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Velocity magnitude (m s−1)
4 Exp.− e w = 1 cm Exp.− e w = 2 cm Model− e w = 1 cm Model− e w = 2 cm
3
2
1
0 0
5
10
15
Length of the truck (m)
FIGURE 2.16 Evolution of air velocity magnitude between the lateral wall and pallets at the medium level of pallets along the truck for e ¼ 1 and 2 cm.
surrounding atmosphere are difficult to remove in this space and high temperatures are expected locally. Figure 2.16 presents a comparison between numerical and experimental data concerning velocity magnitude at the medium level along the enclosure for two airspaces: 1 and 2 cm. This figure clearly shows that in these spaces the air velocity magnitudes are governed by the behavior of the air wall jets. Downstream from the separation of the jet, beyond 6 m from the inlet, the velocities are very low and close to zero. Conversely, high velocities correspond to the zone of primary recirculation. It is interesting to note that for ew ¼ 2 cm, velocities are overall higher than obtained with ew ¼ 1 cm. This underlines the importance of this separation to improve the ventilation efficiency in this area and thus reduce temperature levels. We also noted the qualitative good agreement between numerical and experimental data. 2.7.3.3 Influence of the Air Duct on Airflow and Temperature Distribution Figure 2.17 shows a comparison with and without the use of air ducts concerning (from numerical data given by the RSM model) the longitudinal evolution along the truck of the dimensionless airflow rate (Q(z)=Q0), obtained by numerical data. This result clearly shows that ventilation of the rear of the truck is improved by the use of air ducts. In this area, the flow rate is increased from 100 to 1000 m3=h approximately. Conversely, it is reduced at the front of the truck. This reflects a better uniformity of the ventilation in the truck. Figure 2.18 presents a comparison between experimental and predicted values of air velocities at medium level between the wall and pallets with and without an air duct. These figures clearly show that in these spaces the air velocity magnitudes are governed by the behavior of the overall airflow rate. As observed in numerical and experimental results, the use of air ducts improves air circulation and its homogeneity along this sensitive plane. Most importantly, the occurrence of low velocities and a stagnant zone in the rear part of the truck is avoided. Air velocities here are maintained at around 1 m s1 instead of 0.1 m s1, as would have occurred without this device.
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2 1.75 With air ducts Without air ducts
1.5
Q (z)/Q 0
1.25 1 0.75 0.5 0.25 0 0
2
4
6 8 Length of the truck (m)
10
12
14
FIGURE 2.17 Longitudinal evolution along the truck of the dimensionless airflow rate (Q(z)=Q0) with and without air ducts.
To evaluate the benefit of an air duct on temperature levels and their uniformity, Figure 2.19 presents a numerical comparison concerning the contours of air temperatures in this most sensitive plane with and without this device. As can be seen, when air ducts are used, the zones of higher temperature move from the rear of the truck to the middle position located between two air-duct nozzles where lower velocity is expected. The use of an air duct makes it possible to decrease the higher temperature (Tmax) from 168C to 208C. In addition, the dispersion of the air temperature, defined as (Tmax Tmin), decreases from 128C for a vehicle without air ducts to 88C for a vehicle with air ducts.
4 Model-with air ducts
Velocity magnitude (m s−1)
3.5
Model-without air ducts Exp.-without air ducts
3
Exp.-with air ducts 2.5 2 1.5 1 0.5 0 0
2
4
6 8 Length of the truck (m)
10
12
14
FIGURE 2.18 Evolution of air velocity magnitude between lateral wall and pallets on the medium level with and without air ducts.
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CFD Optimization of Airflow in Refrigerated Truck Configuration Loaded with Pallets
T (⬚C)
−28
−26
−24
−22
−20
−18
65
−16
(a)
(b)
FIGURE 2.19 (See color insert following page 142.) Numerical results concerning contours of isotemperatures in the most sensitive plane of the truck located between lateral wall and pallets with and without air ducts. (a) Without air duct and (b) with air duct.
2.7.4 LOADED CONFIGURATION
WITH
SLOTTED PALLETS
2.7.4.1 Jet Characteristics Figure 2.20 plots the downshifted case (D ¼ 0.18 m), the contour levels of longitudinal normalized velocity W=W0 in the symmetry plane, and in the inlet-centered horizontal plane, respectively. They lead to several conclusions on the general pattern of the jet. Due to the confinement effect, two lateral vortices structures were induced by the jet intrusion into the enclosure as can be seen in Figure 2.20b (negative values of W). These structures controlled the initial growth of the jet and limited its diffusion in the transverse direction. In the inlet region z=L 2 [0, 0.15], the jet attaches rapidly to the ceiling by the Coanda effect and the decay of the maximal velocity followed the characteristic decay of the theoretical 2D unbounded wall jet until z=L ¼ 0.2 [40]. In the intermediate region z=L 2 [0.15, 0.5], due to the confinement effect, the jet vanishes at z=L ¼ 0.5 approximately (Figure 2.8c) and attaches the top of pallets at row 8 and flows over it to the rear (Figure 2.23). In the rear region (z=L 2 [0.5, 1]), flow is weak; W velocity levels were less than 0.2 W0 (Figure 2.8 and Figure 2.20), from z=L > 0.7 these levels did not even exceed 5% of W0.
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0.2
0 0.
0.4
0.5
1 0.
0.9
0.80.6 9 . 0 0.7
0.3
1.0
Computational Fluid Dynamics in Food Processing
0.0
0.1
0.1
0.0
0.8
y /H
0.2 0
0.7
0.2
0.4
0.6
0.8
1 z /L
0.6
0.5
0.4 Vector reference: 1 (a)
Vector reference 0.6
−0.2 −0.1 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
1
0.4 -0.1 0 0 0. .7 8
0. 9
0
0.5 0.6
x /W d
0.2
0.1
Jet boundary
0.2
0.4
0.3
−0.2 −0.4 0
0.2
0.4
0.6
0.8
1
z/L (b)
FIGURE 2.20 Velocity contours above the SPs. (a) The symmetry plane and (b) inlet centered plane.
2.7.4.2
Comparing with the Case of Empty Truck
Figure 2.21 plots the contour of W=W0 on the inlet centered horizontal plane and shows a major difference in jet diffusion between the empty and the loaded case. In the empty enclosure there was a head-on flow moving forward and occupying the full width of the enclosure from z=L ¼ 0.1 to z=L ¼ 0.5. But in the SPs case, the geometrical confinement effect due to the presence of the load was reinforced dynamically by the two lateral vortices, which tended to reduce the jet diffusion and lead to a centered flow. As a consequence, the inlet decay of the jet (z=L 2 [0, 0.15]) in the empty case is higher than in the loaded case. For z=L 2 [0.15, 0.5] the tendency was inversed; the decay in the loaded case was higher than in the empty case. The load limited the entrainment flow and hence tended to decrease the velocity level on the jet axis.
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0.5
0.1
0
0.3
0.4
0.4
0.2
1 0.
0.3
0.8
0.2
0.9
0
0.5 0.6
(a)
0.1
0.1 0.2 0.3
0 0.7
0
0.2
0.2
0.4
0.6
0
0.8
1
0.5 −0.1 0
0.1
0
5
(b)
0.2
0.
0.8 7 0. 9
0.6
0.
0.2
0.4
0.3
0.4
0.6
0.8
1
FIGURE 2.21 Velocity contours W=W0 in the inlet centered plane. (a) Empty truck and (b) loaded truck (SP).
Another comparison concerning velocity profiles between the empty enclosure and the enclosure loaded with SP is shown in Figure 2.22. 2.7.4.3 Comparing with the Case of Impermeable Pallets To highlight the load porosity effect on the airflow pattern and the jet behavior, experimental longitudinal velocity concerning SPs and IPs is compared in Figure 2.23. These comparisons concern three cross-sections of the enclosure above the pallets: z=L ¼ 1=4, z=L ¼ 1=2, and z=L ¼ 3=4. Contours of W=Wmax are presented and Wmax is the maximum of jW j in each section. In the three sections, higher positive velocities were observed in the SPs case. In the first quarter, for example, the values of Wmax=W0 are 50% and 30% for SPs and IPs, respectively. This clearly indicates that the pallets’ porosity contributes to a better wall jet development along the enclosure by enabling the airflow entrainment through the load. In addition, the impermeability of the load (IPs case) tends to confine the return flow principally above the pallets where higher negative velocity values are observed in the IPs case. For this configuration there are higher velocity gradients between the two opposed streams and consequently more aerodynamic interaction and friction between them. This aspect also limits the wall jet development in the IPs case. As a consequence, the jet axis moves from the ceiling and attaches to the top of the pallets in the IPs case at z=L ¼ 1=2. On the contrary, in the SPs case, the jet progressively occupies the full width above the pallets and can be seen at z=L ¼ 3=4. Obviously, the return flow took place partially within the load in the SPs case. Other local aspects concerning airflow patterns observed in Figure 2.23 could be noticed: . .
At z=L ¼ 1=4, the two cases presented a reverse flow on the wall sides. At z=L ¼ 1=2 in the IPs case, due to the wall jet separation, the velocity varied principally from the top of the pallets, where the wall jet attached by Coanda effect flowed to the rear, and then to the ceiling (W > 0), where reverse flow took place
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RSM: slotted boxes Experiment: slotted boxes
0.5
0.1
−0.1 -0.1
0.3
0.3
0.3
−0.5 -0.5
0.5
x /Wd
0.5
x /Wd
x /W /Wd
Experiment: empty enclosure
0.1
W/W0 0
0.5
1
−0.4
−0.2 0 −0.1
-0.3 −0.3
0.1
W/W0 0.2
0.4
0.6
0.8
−0.4
−0.2
−0.1
0.4
0.6
-0.5 −0.5
-0.5 −0.5
z/L = 1/13.3
0.2
−0.3
−0.3 -0.3
−0.5 -0.5
W/W0 0
z/L = 2/13.3
z /L = 4/13.3
0.8
y/H
1
y/H
y/H y/H
(a) 1
1
0.8
0.8 Top of the pallets
Top of the pallets
Top of the pallets
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2 W/W0
W/W0 −0.2 -0.2
W/W0 0
0
0 0
0.2 0.2
z/L = 1/13.3
0.4
0.6
0.8 0.8
1
−0.2
0
z/L = 2/13.3
0.2
0.4
0.6
0.8
−0.2
0
0.2
0.4
0.6
z /L = 4/13.3
(b)
FIGURE 2.22 Experimental longitudinal velocity component (W=W0) at z=L ¼ 1=13.3, 2=13.3, and 4=13.3. (a) Horizontal profiles in the inlet centered plane and (b) vertical profiles along the symmetry plane.
.
(W < 0). This reveals a vertical recirculation bubble, which occupies the full width of the enclosure. With the SPs, the velocity varied principally from the centre, where W > 0, to the lateral side, where W < 0. This reveals a horizontal recirculation bubble, which occupies the full height above the pallets. At z=L ¼ 3=4, with the IP, air was almost stagnant; the maximum W velocity was very low (Wmax=W0 ¼ 0.5%). With the SP the velocity levels remained significant (Wmax=W0 ¼ 4.5%) without reverse flow (W > 0). This confirmed a better wall jet development and penetration into the enclosure for SP case.
These conclusions clearly embody the importance of load porosity on the jet behavior. Figure 2.24 shows the approximate outlines of air patterns for the different configurations.
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CFD Optimization of Airflow in Refrigerated Truck Configuration Loaded with Pallets
1
y /H
.6
1
0
2
0.4 .2 0 0 0.
0.75 Section z/L = 0.25; W max /W 0 = 51%; W max = 6.4 m s−1
0.75
−0 .6
0.8
−0.2
−0.4
0.2 0.0
−0 .
0.4
0.8
0. 8
y /H
Section z /L = 0.25; W max /W 0 = 31%; W max = 3.6 m s−1
−0.4 −0.6
.4 −0 2 − 0. 0.0 0.2
0.4
0.6
0.8
0.6
0.0
.6
0.0
0.6
0.2
0.0
(a)
−0
4
0.2
Section z/L = 0.75; W max /W 0 = 4.5%; W max = 0.6 m s−1
−0. 4
Section z /L = 0.5; W max /W 0 = 3.1%; W max = 0.36 m s−1
0.
0.2
0.8
Section z /L = 0.5; W max /W 0 = 7.5%; W max = 0.86 m s−1
0.0 0.4
0.2
−0 .2
−0.2
−0.6 Section z /L = 0.75; W max /W 0 = 0.5%; W max = 0.06 m s−1 (b)
FIGURE 2.23 Velocity contours above the load at z=L ¼ 0.25, z=L ¼ 0.5, z=L ¼ 0.75. (a) SPs and (b) IPs.
Symmetry plane. Side view
Inlet-centered horizontal plane. Top view
(a) Empty enclosure
(b) Loaded with slotted boxes
(c) Loaded with impermeable boxes
FIGURE 2.24 Approximate outlines of air patterns, comparison between the empty enclosure and the loaded cases.
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Vector reference 0.5 m s−1
V W
Inlet
1
2
3
4
5
6
7
8
15
16
Outlet
Vector reference 0.2 m s−1
V W
9
10
11
12
13
14
FIGURE 2.25 Velocity vectors of V and W inside the middle plane of SPs (6 10 LDV measurement points per pallet).
2.7.4.4
Airflow Characteristics Inside the Pallets
Velocity profiles were measured in the middle longitudinal plane of the pallets (6 10 measurement positions per pallet). The components V and W have been captured separately. The mean velocity of components V and W is plotted in Figure 2.25. The z-component of velocity is plotted in plain vectors and y-component of velocity is plotted in dashed lines. Figure 2.26 shows air velocities in the middle plane of pallets 3, 6, 8, and 10 measured with a fine grid (11 21 measurement positions per pallet). With the exception of the top, W was negative everywhere in the load (Figure 2.25) and the mean values of W were much higher than those of V from pallets 2 to 16. This demonstrates that the general trend of flow in the load was horizontal from the rear to the front exit. The mean value of W was the lowest at the rear; it increased from pallets 16 to 6 and decreased from pallets 4 to 2. This was a consequence of mass balance, i.e., of the exchanges between the headspace (above the pallets) and the load; the downward flow (coming into the load) in the rear half of the enclosure explains the increasing flow rate in the load (from box 16 to 6) whereas the upward entrainment flow induced by the inlet jet explains the decreasing flow rate (from pallets 4 to 2). The maximum W vector is always located at the fourth position from the top in pallets 8 to 14. This location corresponds to the bottom of the vortices, which have all almost the same position in these pallets. Pallet 1, which is the closest to the exit, is particularly unique compared to the others. Flow direction in this box was mainly vertical; there was very strong aspiration at the outlet leading to a short circuit from inlet to outlet throughout the first box.
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Reference vector 0.5 m s−1 y = 1.7
Reference vector 0.5 m s−1
V2 + W2 (m s−1) 0.45 0.43 0.40 0.38 0.35 0.33 0.30 0.28 0.25 0.23 0.21 0.18 0.16 0.13 0.11 0.08 0.06
Slots
Plain walls
V2 + W2 (m s−1) 0.52 0.49 0.46 0.43 0.39 0.36 0.33 0.30 0.27 0.24 0.20 0.17 0.14 0.11 0.08 0.05 0.01
Zoom in figure 10
y = 0.2 0.56 m
Pallet 3
Pallet 6
Reference vector 0.5 m s−1
Reference vector 0.5 m s−1
V2 + W2 (m s−1)
V2 − W2 (m s−1)
0.51 0.48 0.45 0.42 0.39 0.36 0.34 0.31 0.28 0.25 0.22 0.19 0.16 0.13 0.11 0.08 0.05
Pallet 8
0.41 0.39 0.38 0.34 0.31 0.29 0.26 0.24 0.21 0.19 0.16 0.14 0.11 0.09 0.07 0.04 0.02
Pallet 10
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi FIGURE 2.26 Velocity vectors and magnitude ( V 2 þ W 2 ) in the middle plane of the pallets: 3, 6, 8, and 10 (11 21 LDV measurement points).
2.7.4.5 Interactions between Flows Around and Inside Pallets at the Load Interface In the load next to the top faces, the flow pattern was strongly affected by the main flow developed by the turbulent wall jet in the headspace. From W velocity vectors in Figure 2.25, one can notice that next to the top face, W < 0 from box 1 to 7 and W > 0 from box 8 to 16. This could be easily explained by the flow behavior above the pallets; it notably has been
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shown that the jet in the symmetry plane started to deflect from the ceiling at z=L ¼ 0.3 (fourth box position) and reattached by Coanda effect at the top faces of the pallets at z=L ¼ 0.5 approximately (eighth box position) where it flows to the rear. Due to this reattachment, a vertical shear appeared at the top of pallets from 8 to 16, which were located downstream of the jet reattachment and the internal flow was entrained by the external flow developed in the headspace. A horizontal shear zone was also observed at the top of each box from position 6 to 16 on the vertical velocity profiles (Figure 2.25); W was positive (upward) at the left side and negative at the right side (the effect was less distinct from pallets 13 to 16). Concerning airflow patterns, these shearing flows developed vertically and horizontally revealed the presence of vortices created at the top of pallets from 8 to 16 and framed between the vertical slotted walls. This phenomenon is highlighted by the recirculating pattern at the top of pallets 8 and 10 in Figure 2.25. We assumed that such vortices also exist for pallets 6 and 7 but the vortex centres were on the top of these pallets (which could explain that W was everywhere negative in these pallets). So it seems that there were vortices near the top of pallets 6–16 and that the position of the vortex centres followed the same trend that the jet, which attached the load top approximately at box 8. This is schematized in Figure 2.27. These vortices highlight the aerodynamic interaction that occurred through the top slotted wall between the external main flow developed by the inlet jet and the secondary return flow developed inside the pallets. By increasing velocities and turbulence, these aerodynamic structures improve the transfer mechanisms between the pallets and the external flow. The presence of a recirculation bubble between a jet and the reattachment wall, represented by the top of the pallets, is a well-known phenomenon in fluid dynamics. However, two aspects highlight the principal characteristics of the studied configuration. The first denoted the aerodynamic influence exerted by the separations between the pallets and rows of pallets, which obviously lead to split this theoretical global recirculation in many individual structures related to different pallet zones (Figure 2.26 and Figure 2.27). The second concern is the ‘‘aerodynamic permeability’’ of the top slotted wall of the pallets, which enables to y z Ceiling coanda effect
Vortices in the shear zone
Top faces coanda effect
Jet entrainment
1
4
8
Short-circuit to the exit
FIGURE 2.27 Outline of air path lines inside the load.
12
16
Main horizontal flow in the boxes
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0.2
Mean velocity (m s−1)
0.1
1
2
3
4
5
6
7
8
9
10
11
12
−0.1
13
14
15
16
Pallet number
−0.2
Mean W Mean V
−0.3
−0.4
FIGURE 2.28 Mean values of V and W components in SPs.
develop vortices inside the pallets that are located downstream the reattachment point of the jet, i.e., after the eighth position (Figure 2.25). From pallets 2 to 5, the vertical velocity was always positive near the top (Figure 2.25 and Figure 2.28). This revealed the air entrainment coming from the load and supplying the inlet jet. 2.7.4.6 Ventilation Efficiency Figure 2.29 and Figure 2.30 respectively present the evolution of the local ventilation efficiency and the fresh air renewal obtained numerically in each of the 16 pallets. The results show a high degree of ventilation heterogeneity along the vehicle, especially between the rear and the front sides. As it can be seen from Figure 2.8, the local ventilation efficiency tendency 1400 1200
t (h−1)
1000 800 600 400 200 0 1
2
3
4
5
6
7
8 9 10 11 12 13 14 15 16 Pallet number
FIGURE 2.29 Local ventilation efficiency within pallets: t numerical data.
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180 160 140
teq (h−1)
120 100 tn
80 60 40 20 0 1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16
Pallet number
FIGURE 2.30 Equivalent fresh air renewal efficiency: teq numerical data.
shows a plateau for the five first pallets at 1200 h1 approximately. From pallet 6 to pallet 16, ventilation efficiency decreases progressively. The flow rate throughout the last pallet is about 35 times smaller than for the five first pallets. Concerning the fresh air renewal distribution (Figure 2.30), the ratio between the pallets placed in the front part and in the rear of the vehicle is smaller than that observed for the ventilation in Figure 2.8. The value of teq obtained for the last pallet is only six times smaller that the highest value obtained for pallet 4. This figure also indicates that the fresh air renewal for the last pallets is three times smaller than the overall value. This means that maintaining the appropriate temperature for the last pallets necessitates an air flow rate three times higher than the global heat balance of the truck. This is important to take into account for refrigerated-vehicle design and for temperature regulation, because often refrigeration control is only based on an outlet temperature sensor. For the first pallets, the equivalent fresh air flow rate is about eight times smaller than the total air flow rate. This means that the air flowing into one of these pallets contains only about one-eighth of fresh air (coming directly from the enclosure inlet at T0). The rest was warmed up by flowing first throughout other pallets or by mixing in the different flow structures (jet mixing layer, lateral vortices above the load, etc.). Because of the low flow rate encountered in the rear of the vehicle, large temperature differences between air currents flowing in and out of the last pallets are observed. In fact, free convection is also expected in the last pallets (which are not taken into account in these simulations) and this increases air flow rate and limits temperature rise.
2.7.5 TURBULENCE MODELING PERFORMANCE 2.7.5.1
Empty Truck
The comparisons concerning streamline behavior (Figure 2.31) show that only RSM is able to correctly predict the separation of the wall jet and the general behavior of the motion of air related to the primary and to the secondary recirculations. The same figure also shows the poor predictions given by the k–« turbulence model and underlines its inability to predict flow separation.
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Experiment
RSM
k−e Model
RSM with a coarse grid (3e)
FIGURE 2.31 Influence of the turbulence model and the grid size on the flow pattern at the symmetry plane.
The good predictions given by the RSM with 624,000 cells were altered by using a more coarse grid (238,560 cells). In this case, the detachment point was located further downstream and in turn the second recirculation area was reduced and the primary recirculation enlarged. The altered RSM predictions were similar to those of the k–« based models. This behavior can be explained by increased numerical diffusion resulting from the coarser grid. 2.7.5.2 Slotted Pallets 2.7.5.2.1
Above the Pallets
Figure 2.32 shows that the standard k–« turbulence model and the RSM give similar results. However, the major difference observed between the two models concerns the jet behavior rather than local velocity values. As observed in Figure 2.33, the jet trajectory predicted by the k–« model was still close to the ceiling whereas experimental data showed a detachment from this wall followed by a deflection toward the top faces of the pallets by Coanda effect. This clearly indicates that the k–« model lacks sensitivity with respect to the adverse pressure gradient, overpredicts the ceiling Coanda effect, and hence increases the jet penetration distance into the enclosure. This could explain the higher velocities obtained by this model, notably in the rear. On the contrary, the RSM better performed the partial jet detachment from the ceiling and its progressive deflection toward the top of the pallets. However, the aerodynamic interaction between the jet and the slotted wall need to be improved by taking into account the horizontal
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Computational Fluid Dynamics in Food Processing W/W0 1
0.90
0.44
0.07
0.02
0.01
0.22
1.00 0.90 0.56 0.44 0.22 0.07 0.02 0.01 0.00 −0.05 −0.08 −0.12 −0.23 −0.34
Experiment 0 1 0.90
0.44
0.22
0.02
0.01
0.00
y/H
0.07
Simulation, RSM
0 1 0.90
0.44
0.22
0.07
0.02
0.01
Simulation, k−e
0 0
0.5 z /L
1
FIGURE 2.32 Velocity contours (W=W0) in the symmetry plane above the pallets: Comparison between experiments and turbulence models.
frictional resistance exerted by the top of the pallets against the jet. Although this horizontal friction could be neglected in terms of pressure losses compared with the perpendicular effect, it becomes essential for the numerical model to be able to predict the jet attachment on the top of the pallets by Coanda effect as it can be seen experimentally in Figure 2.32 and Figure 2.33. Experimental and RSM predictions showed that the area of the lateral vortex structures, delimited by the zero velocity contour, is confined near the inlet section in the front part of the enclosure (Figure 2.34). The k–« model predicts more stretched structures covering the whole side wall from the front to the rear. This could be explained by the high rate of entrainment
Experiment Simulation, RSM Simulation, k −e 1
y /H = 1 Ceiling
y /H
0.9 0.8 y/H = 0.72 Top of pallets
0.7 0
0.2
0.4 z /L
0.6
0.8
1
FIGURE 2.33 Jet trajectory in the symmetry plane (downshifted case: D ¼ 0.18 m).
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0.5 −0.10
0.01 0.10
0.71 0.89
0
0.03
W/W0
0.05
0.15 0.46
1.00 0.89 0.71 0.46 0.34 0.15 0.10 0.00 −0.01 −0.10 −0.16 −0.22
0.34
Experimental 0.5 −0.01
x /Wd
−0.16 −0.10
0.00 0.01
0.15
0
0.89 0.71
0.10
0.003 0.002
0.46 0.34
Simulation, RSM 0.5
−0.16
−0.10
0.00
−0.01
0.15
0.10
0.46 0.34 0.89 0.71
0
0.03 0.05
0.003
0.002
Simulation, k−e 0
0.5 z /L
1
FIGURE 2.34 Contour levels of longitudinal normalized velocity W=W0 in the inlet centered horizontal plane (downshifted case: D ¼ 0.18 m).
flow predicted by this model (data not shown) due to its greater, but not physical, jet stability and penetration along the enclosure. However, it should be stated that neither model agrees closely with the shape of the contours. Although experiments show that lateral vortices affect and slightly predominate jet diffusion, both models display an inversed tendency. Another aspect displayed by experimental data concerns the evolution of the horizontal velocity contours along the enclosure. These contours show that the maximum of the jet velocity is still in the symmetry plane up to z=L ¼ 0.5. Further downstream, the jet tends to deviate toward the lateral walls and brings out a curved velocity profile on the axis as shown in Figure 2.34. RSM reflects qualitatively this tendency, whereas the k« fails to predict this deviation. 2.7.5.2.2
Flow Inside the Load
Figure 2.35 presents the longitudinal velocity profile on the vertical center line of four pallets (namely 3, 5, 12, and 16). In pallet 3 and pallet 5, air flows toward the front face, where the outlet is located, along the whole height with a rather uniform velocity. The measured values are about 0.3 m s1, the predicted ones are slightly lower. In pallet 12 and pallet 16, velocity is very low. At the top of these pallets, measurements as well as simulations display positive values. This means that air flows toward the rear in the upper part of the load. This can be explained by the drag exerted by the air flow just above the load, which is also directed toward the rear. There are clearly some differences, particularly with the results for the pallets 12 and 16 where numerical results, in contrast to the measured results, reveal air velocity profiles very close to zero. The slotted wall effect was only taken into account through a normal pressure drop (with a uniform pressure drop coefficient), whereas there were other effects: alternation of slotted and plain zones, tangential drag, turbulence production, turbulent stresses redistribution, etc.
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y (m)
2
Experiment RSM
Experiment RSM
W (m s−1) −1.5 −1
2
y (m)
W (m s−1) −0.4
0 −0.5
0
0.5
Pallet 3
0 −0.2
0
Pallet 5 2
2
W (m s−1) −0.4 −0.2 Pallet 12
y (m)
y (m)
Experiment RSM
Experiment RSM
0 0
0.2
W (m s−1)
0.4 Pallet 16
−0.05
0 0
0.05
FIGURE 2.35 Longitudinal velocity inside the load on the vertical center line of the pallets.
To improve predictions, there is a need to take into account tangential frictions, especially at the top slotted walls where strong interactions between the main flow above the load and the return flow in the pallets were observed.
2.8 CONCLUSIONS In this study, experiments and numerical simulations performed using the CFD code Fluent were carried out in order to characterize velocities and airflow patterns within a typical refrigerated truck in empty and loaded configurations. The experiments were carried out on an isothermal reduced-scale model with laser-Doppler velocimetry.
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Experiments and simulations highlight the importance of the load and confinement effect in reducing the reach of the jet within the truck, which in turn maintains a high degree of ventilation heterogeneity between the front and the rear where stagnant zones and low velocities are present. The main conclusions were as follows: .
.
.
The load modified strongly the flow patterns but the velocity levels remained similar in all cases: jet velocity decreased rapidly in the first half and in the rear half the velocity was low. The jet penetration and the main recirculating flow were reduced as the load porosity decreased. The sideways diffusion was reduced as the porosity of the load decreased. The loaded cases presented a back flow on the sides of a centered jet.
In the case of IP, the simulations show the ability of the RSM model to accurately predict the overall behavior of the airflow patterns and velocity characteristics. The good predictions also concern the thin airspace separation (1–2 cm) between pallets and walls, which constitute the most sensitive plane in the load. The results also underline the importance of these separations in maintaining the ventilation around the pallets in order to better remove the heat exchanged through insulated walls and thus to decrease the higher temperatures reached locally in this most sensitive area. Numerical and experimental results show that the use of air-duct systems improves the overall homogeneity of the ventilation in the truck and avoids the occurrence of stagnant zones and low velocities in the rear part of the load. In this zone, velocities are maintained at around 1 m s1 instead of 0.1 m s1 without this air duct. These aspects contribute to a decrease in the temperature differences throughout the palletized cargo and thus to the preservation of the quality, safety, and shelf life of perishable products. In the case of the SPs, the results clearly show the predominance of the return flow directed from the rear toward the outlet inside the SPs. The result also shows a high rate of shear on the top of the pallets, revealing strong interactions with the main flow developed outside the pallets. This denotes the presence of individual vortices delimited by pallet separations and caused by the deflecting of the wall jet and its reattachment on the top of the pallets. The results also show a high degree of ventilation heterogeneity inside the load. The velocity level was lowest at the rear, and maximum near the fourth pallet. There was a short circuit from inlet to exit throughout the first box. The numerical results show a qualitatively good agreement with experimental data. The RSM better performed predictions than the k–« model especially on the top faces of the pallets where strong aerodynamic interactions are observed with the main flow. Velocity levels were overall underestimated within pallets and there was a lack of sensitivity in shearing zones. However, the Coanda effect at the top of the pallets could be better predicted if the model includes the wall friction on the slotted walls.
NOMENCLATURE C1 Cp D DH e ew H
pressure drop coefficient specific heat of air (J kg1 K1) ceiling-inlet distance (m) hydraulic diameter of the inlet section (m) airspaces separation pallets (m) airspaces separation between wall and pallets (m) height of the enclosure (m)
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I K k Q L _ m p Re T U, V, W u, v, w Wd x, y, z
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turbulence intensity (%) porous media permeability (m2) kinetic energy of turbulence (m2 s2) flow rate (m3 s1) length of the enclosure (m) flow rate flowing in and out of one pallet (m3 s1) static pressure (Pa) Reynolds number, Re ¼ rW0DH=m temperature (K) lateral, vertical, and longitudinal mean velocity components (m s1) lateral, vertical, and longitudinal fluctuating velocity components (m s1) width of the enclosure (m) lateral, vertical, and longitudinal coordinates (m)
GREEK SYMBOLS « m n r t ?
turbulence energy dissipation rate (m2 s3) dynamic viscosity (kg m1 s1) kinematic viscosity (m2 s1) density (kg m3) ventilation efficiency (h1) normal
SUBSCRIPTS 0 eq in out p t i, j, k
inlet equivalent in term of fresh air flowing in the considered pallet flowing out the considered pallet porous medium turbulent vector directions in x, y, and z
REFERENCES 1. Lenker, D.H., Wooddruff, D.W., Kindya, W.G., Carson, E.A., Kasmire, R.F., and Hinsch, R.T. Design criteria for the air distribution systems of refrigerated vans. American Society of Agricultural Engineers, 28(6): 2089–2097, 1985. 2. Go¨gus, A.Y. and Yavuzkurt, S. Temperature pull-down and distribution in refrigerated trailers. In: Proceedings I.I.F–I.I.R commissions D2, Wageningen, pp. 189–193, 1974. 3. LeBlanc, D., Beaulieu, C., Lawrence, R., and Stark, R. Evaluation of temperature variation of frozen foods during transportation. The Refrigeration Research Foundation Information Bulletin (Bethesda, MD), December 1994. 4. Bennahmias, R. and Labonne, G. Etude de la distribution de l’air et de la dispersion des tempe´ratures dans une semi-remorque frigorifique, Re´union des commissions C2, D1 et D2=3 de l’IIF, Fez (Morocco), pp. 241–256, 1993. 5. Meffert, H.F.Th. and Van Nieuwenhuizen, G. Temperature distribution in refrigerated vehicles. In: Proceedings I.I.F.–I.I.R. Commissions D1, D2, and D3, Barcelona, Spain, pp. 131–135, 1973. 6. Billiard, F., Bennahmias, R., and Nol, P. Nouveaux de´veloppements dans les transports a` tempe´rature dirige´e routiers. In: Proceedings I.I.F–I.I.R. Commissions B2, C2, D1, D2=3, Dresden, Germany, pp. 793–802, 1990.
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7. Lindqvist, R. Reffer hold distribution, Preprint Conferences. I.I.F.–I.I.R., Cambridge, UK, 1998. 8. Lindqvist, R. Air distribution design for controlled atmosphere in reefer cargo holds, 20th International Congress of Refrigeration, I.I.R.–I.I.F., Sydney, 1999. 9. Wang, H. and Touber, S. Simple non-steady state modelling of a refrigerated room accounting for air flow and temperature distributions. In: Proceedings of I.I.F.–I.I.R. Commissions B1, B2, C2, D1, D2=3, Wageningen, pp. 211–219, 1988. 10. Meffert, H.F.Th. and Van Beek, G. Basic elements of a physical refrigerated vehicles, air circulation and distribution. In: 16th International Congress of Refrigeration, I.I.F–I.I.R., Paris, pp. 466–475, 1983. 11. Me´nia, N.Z. Etude nume´rique et expe´rimentale de l’ae´raulique dans un ve´hicule frigorifique, The`se INA-PG, 2001. 12. Wang, H. and Touber, S. Distributed dynamic modelling of a refrigerated room. International Journal of Refrigeration, 13: 214–222, 1990. 13. Van Gerwen, R.J.M. and Van Oort, H. Optimization of cold store using fluid dynamics models. In: Proceedings I.I.F.–I.I.R. Commissions B2, C2, D1, D2=3, Dresden, Germany, 4: pp. 473–480, 1990. 14. Hoang, M.L., Verboven, P., De Baermaeker, J., and Nicolaı¨, B.M. Analysis of air flow in a cold store by means of computational fluid dynamics. International Journal of Refrigeration, 23: 127–140, 2000. 15. Moureh, J. and Flick, D. Wall air-jet characteristics and airflow patterns within a slot ventilated enclosure. International Journal of Thermal Sciences, 42: 703–711, 2003. 16. Moureh, J. and Flick, D. Airflow characteristics within a slot-ventilated enclosure. International Journal of Heat and Fluid Flow, 26: 12–24, 2005. 17. Moureh, J., Menia, N., and Flick, D. Numerical and experimental study of airflow in a typical refrigerated truck configuration loaded with pallets. Computer and Electronics in Agriculture, 34: 25–42, 2002. 18. Moureh, J. and Flick, D. Airflow pattern and temperature distribution in a typical refrigerated truck configuration loaded with pallets. International Journal of Refrigeration, 27: 464–474, 2004. 19. Nordtvedt, T. Cold air distribution in refrigerated trailers used for frozen fish transport, I.I.F.– I.I.R. Commissions B1, B2, D1, D2=3, Palmerston North (Nouvelle Ze´lande), 2: pp. 539–544, 1993. 20. Tapsoba, M., Moureh, J., and Flick, D. Airflow pattern in an enclosure loaded with pallets: the use of air ducts. Eurotherm seminar 77, Heat and Mass Transfer in Food Processing, June 20–22, Parma, Italy, 2005. 21. Craft, T.J. and Launder, B.E. On the spreading mechanism of the three-dimensional turbulent wall jet. Journal of Fluid Mechanics, 435: 305–326, 2001. 22. Choi, H.L., Albright, L.D., and Timmons, M.B. An application of the k–« turbulence model to predict how a rectangular obstacle in a slot-ventilated enclosure affects air flow. Transactions of the American Society of Agricultural Engineers, 33: 274–281, 1990. 23. Chen, Q., Comparison of different k–« models for indoor air flow computations. Numerical Heat Transfer Part B, 28: 353–369, 1995. 24. Awbi, H.B. Application of computational fluid dynamics in room ventilation. Building and Environment, 24: 73–84, 1989. 25. Davidson, L., Ventilation by displacement in a three-dimensional room: a numerical study. Building and Environment, 24: 263–272, 1989. 26. Hoang, M.L., Verboven, P., De Baermaeker, J., and Nicolaı¨, B.M. Analysis of air flow in a cold store by means of computational fluid dynamics. International Journal of Refrigeration, 23: 127–140, 2000. 27. Verboven, P., Hoang, M.L., and Nicolaı¨, B. Numerical computation of air moisture and heat transfer in chicory root cool stores, Ae´raulique et Industries Alimentaires, ENSIA France, 2001. 28. Mariotti, M., Rech, G., and Romagnoni, P. Numerical study of air distribution in a refrigerated room. Proceedings of the 19th International Congress of Refrigeration, pp. 98–105, 1995. 29. Nady, A., Saı¨d, M., Shaw, C.Y., and Zhang, J.S. Computation of room air distribution. ASHRAE Transactions: Symposia, 101: 1065–1077, 1995. 30. Launder, B.E. and Spalding, D.B. The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering, 3: 269–289, 1974.
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31. Wilcox, D.C. Turbulence modeling for C.F.D. DCW Industries, Inc., La Can˜ada, California, 1994. 32. Menter, F.R. Eddy viscosity transport equations and their relation to the k–« model. ASME Journal of Fluids Engineering, 119: 876–884, 1997. 33. Nallasamy, M. Turbulence models and their applications to the prediction of internal flows: a review. Computers and Fluids, 151–194, 1987. 34. Launder, B.E. On the modeling of turbulent industrial flows, Proceedings of Computational Methods in Applied Sciences, Hirsch, C., et al. (ed.), Elsevier, Amsterdam, pp. 91–102, 1992. 35. Aude, P., Be´ghein, C., Depecker, P., and Inard, C. Perturbation of the input data of models used for the prediction of turbulent air flow in an enclosure. Numerical Heat Transfer Part B, 34: 139–164, 1998. 36. Smale, N.J. Mathematical modelling of airflow in shipping systems: model development and testing. PhD Thesis, Massey University, New Zealand, 2005. 37. De Kramer, J., Kelder, J., Canters, R. Airflow and climate distribution in reefer containers—a network model. Poster presented at Model-IT, Katholieke Universiteit, Leuven, Belgium, 2005. 38. Me´nia, N.Z., Moureh, J., and Flick, D. Mode´lisation simplifie´e des e´coulements d’air dans un ve´hicule frigorifique. International Journal of Refrigeration, 25: 660–672, 2002. 39. Leonard, B.P. A stable and accurate convective modeling procedure based on quadratic upstream interpolation. Computer Methods in Applied Mechanics and Engineering, 19: 59–98, 1979. 40. Mitoubkieta, T. Etude expe´rimentale et nume´rique de l’ae´raulique dans un ve´hicule frigorifique, The`se INA-PG, 2006.
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CONTENTS 3.1 3.2
Introduction ................................................................................................................ Retail Cabinet ............................................................................................................. 3.2.1 Classification ................................................................................................... 3.2.1.1 Storage Temperature ......................................................................... 3.2.1.2 Geometry........................................................................................... 3.2.1.3 Refrigeration Equipment ................................................................... 3.2.1.4 Air Circulation .................................................................................. 3.2.1.5 Energy Consumption......................................................................... 3.2.2 Standardized Temperature Tests ..................................................................... 3.2.3 Air Curtains..................................................................................................... 3.3 Applications of CFD to Display Cabinets.................................................................. 3.3.1 Modeling Product Temperature Distribution.................................................. 3.3.2 Modeling Airflow ............................................................................................ 3.3.2.1 Air Curtains....................................................................................... 3.3.2.2 Shelves ............................................................................................... 3.3.2.3 Evaporator and Rear Ducts .............................................................. 3.3.3 Modeling the Influence of Air Humidity......................................................... 3.3.4 Modeling Interactions with the Ambient Conditions ...................................... 3.3.4.1 Radiation........................................................................................... 3.3.4.2 Ambient Air Movement .................................................................... 3.3.5 Glass Doors Fogging and Defogging .............................................................. 3.3.6 Mist Cooling—Humidification ........................................................................ 3.4 CFD Codes ................................................................................................................. 3.4.1 Methodology ................................................................................................... 3.4.1.1 Preprocessing ..................................................................................... 3.4.1.2 Solving ............................................................................................... 3.4.1.3 Postprocessing ................................................................................... 3.4.2 Turbulence Models .......................................................................................... 3.4.3 Mass Transfer .................................................................................................. 3.4.4 Validation ........................................................................................................ 3.5 Conclusions................................................................................................................. References ...........................................................................................................................
84 84 84 84 85 86 87 87 87 89 90 91 92 92 93 93 94 94 94 94 95 95 95 96 96 97 97 97 97 98 99 99
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3.1 INTRODUCTION In retail stores, refrigerated cabinets are used to display perishable food. For merchandizing purposes, the main function of such equipment is the effective display of products to make them visible and easily accessible to customers. At the same time, food should be maintained at the prescribed temperature, and preserved from radiant heat. The safety and quality of perishable foodstuffs are strongly affected by inappropriate storage temperature and by uneven temperature fluctuations, which are regrettably encountered to a large extent in display cabinets [1]. For this reason, from the point of view of storage conditions, retail cabinets are considered to be one of the weakest links in the cold chain, and only the typical short-residence time of food in such appliances reduces the risk of quality loss. It is therefore essential that the efficacy of retail cabinets in terms of food preservation is improved. The people who can play an important role in this improvement are the manufacturer, the person in charge of installation and maintenance, and the shop manager. The cabinet is certified by the manufacturer to comply with the testing standards currently in place for a specified climate class defined by ambient temperature and relative humidity. Actually, the performance of display cabinets in terms of food temperature is strongly affected by ambient conditions, particularly air velocity and direction, and radiative heat load [2–5]. For this reason, particular care is necessary for the installation; and furthermore, accurate maintenance and operation are essential to accomplish correct food storage conditions. The manufacturer is the only person who can take advantage from the use of computational fluid dynamics (CFD). Thus, the contents of this chapter will mainly focus on problems related to the design of retail cabinets, giving only some suggestions about installation and proper use.
3.2 RETAIL CABINET The main features of a retail cabinet can be summarized with the following statements: . .
Food should be displayed in the most efficient way to promote selling. Correct food storage temperature should be ensured, with temperature fluctuations reduced as much as possible.
The preservation and the display functions are contrasting requirements, because the best way to protect the product from temperature fluctuations is to keep it as far as possible from the shop environment; thus keeping it out of sight of customers. Furthermore, the manufacturer must operate an optimization process aiming to fulfill another important requirement, which is low energy consumption. In fact, while retaining the preserving function, a better display function usually requires higher energy consumption. Low energy consumption is becoming increasingly important, and the manufacturer should make huge efforts trying to cope with all these requirements.
3.2.1 CLASSIFICATION Retail cabinets are classified according to various criteria [2–4,6]. Among them, the most important are the storage temperature and the cabinet geometry, which are the key factors for the choice of the most suitable unit. Another important classification can be made according to the kind of air circulation, which is crucial for certain food. Finally, a further classification can be made according to energy consumption. 3.2.1.1
Storage Temperature
Retail cabinets are intended to host almost every kind of perishable food, from frozen food at 188C to some kind of fruits and pastry at þ108C. For this reason, they are usually classified
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as ‘‘low temperature’’ cabinets in the case of storage and display of frozen food, and ‘‘medium temperature’’ cabinets in the case of storage and display of chilled food. A more detailed classification is defined in the testing standards currently in place and will be discussed in Section 3.2.2. 3.2.1.2 Geometry As regards geometry, retail cabinets can be [2] . .
.
Closed (in the presence of doors or sliding covers=glasses) or open Vertical multideck (Figure 3.1), horizontal single deck (Figure 3.2), or horizontal serve-over counters A combination of these, e.g., a horizontal open-top cabinet combined with a vertical multideck closed cabinet
Of course, the various geometries of cabinets are not suitable for all foods and temperatures. As an example, closed cabinets are the most suitable for frozen food, in order to reduce heat
FIGURE 3.1 Vertical multideck display cabinet.
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FIGURE 3.2 Horizontal display cabinet.
infiltration from the ambient; in this case, horizontal open-top cabinets are to be preferred, while vertical open cabinets are to be avoided. 3.2.1.3
Refrigeration Equipment
Display cabinets are designed only to maintain the correct storage temperature of food. Therefore, they are not capable of reducing the temperature of products if they are too warm when loaded [2,6]. However, the cabinets’ refrigeration equipment is forced to perform heavy duty because of the huge amount of heat due to air infiltration, radiative heat transfer, and product manipulation by the customers. Depending on the refrigerating equipment, display cabinets can be classified as incorporated condensing units and remote condensing units. In the cabinets with incorporated condensing units, also named ‘‘stand alone,’’ the whole vapor compression refrigerating equipment is contained within the cabinet, which only needs a power supply connection and a drainage piping. In the remote condensing units, the cabinet is connected to a refrigerating unit that usually supplies several cabinets, both at low and medium temperatures. The remote condensing units can be further distinguished depending on the refrigerating system as a compression-type refrigerating system or an indirect-type refrigerating system. In the cabinets of the first category only the expansion valve and the evaporator are contained in the cabinet, which is fed with liquid refrigerant from a centralized refrigerator. Because the compression-type refrigeration system is complex and affords limited flexibility under changes to supermarket layout, it is typically used only in medium to large size stores. However, this configuration is preferable because of its enhanced energy efficiency. The recent issue about halocarbon refrigerants is pushing interest toward employing systems of the second category, in which a secondary refrigerant circulating system is installed between a central refrigerating system (usually placed in an outbuilding) and the cabinets. This configuration reduces dramatically the amount of refrigerant circulated, and allows to use toxic or flammable refrigerants with lower environmental impact (e.g., ammonia) at the expense of a more complicated circuitry.
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3.2.1.4 Air Circulation A further classification can be made with reference to air circulation inside the cabinet. Cold-air distribution can be ensured by forced or natural circulation, the choice depending mostly on the kind of foodstuff. As a general rule, forced air circulation is preferable, because it is much more effective in transferring the refrigerating power, thus enabling the correct operation of almost every kind of display cabinet. Natural air convection should be preferred for the display of unwrapped sensitive food like meat, pastry, and ice cream, where water loss coupled with heat transfer on the food surface can give rise to significant quality damage due to dehydration. It is mostly used on horizontal serve-over units, where air stratification helps in reducing warm-air infiltration inside the load volume. 3.2.1.5 Energy Consumption Supermarkets are intensive users of energy in all countries. Electricity consumption in large supermarkets represents a substantial share of about 4% of the national electric energy use, either in the US or in France. A large part of this consumption, varying from 50% to 70%, is due to air conditioning and refrigeration [7,8]. In the US, typical supermarkets with approximately 3700 to 5600 m2 of sales area consume about 2 to 3 million kWh annually for total store energy use [9]. The national average electricity intensity (the annual electricity use divided by the size of the facility) of a grocery store in the US is about 565 kWh m2 per year [8,10], and 400 kWh m2 per year for Europe [7]. These figures are a real challenge for energy savings, and the supermarket chains are spending a substantial proportion of money on the yearly energy consumption compared to the investment costs. For this reason, the evaluation and certification of the energy consumption of display cabinets is becoming an essential step in the future development of such equipment. In Europe, 15 national associations of manufacturers of air handling, air conditioning, and refrigeration equipment joined Eurovent–Cecomaf, which represents more than 800 companies. Eurovent–Cecomaf set up a voluntary certification program also for retail display cabinets, whose performance and daily energy consumption have been certified and classified. A list of the certified cabinets is freely available on the web site [11]. The decision maker of the supermarket chain is thus given the chance to be aware of the energy costs and compare different solutions.
3.2.2 STANDARDIZED TEMPERATURE TESTS Various testing standards for retail display cabinets are currently in place, e.g., the EN standard 23953 [12,13] in Europe, and the ASHRAE standards 72–2005 [14] in the US. The objective of such standards is to specify requirements for the construction, characteristics and performance of refrigerated display cabinets used in the sale and display of foodstuffs, . . . . to specify test conditions and methods for checking that the requirements have been satisfied, as well as classification of the cabinets, their marking and the list of their characteristics to be declared by the manufacturer [13].
Apart from the requirements about construction, the main scope of these standards includes classifying retail cabinets as a function of their storage temperature, and giving instructions for measuring their energy consumption. Specific conditions for the ‘‘temperature test’’ are thus defined in the standards. The cabinet is loaded with packages made of a specified composition of water, cellulose, and
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FIGURE 3.3 A display cabinet during a standardized temperature test.
additives; it is placed in a test room (Figure 3.3) where air temperature and humidity, and air velocity and radiant heat are controlled; and the temperature of a certain number of ‘‘measure packages’’ is recorded over a period of 24 hours after having reached steady state. Various temperature classes are identified, depending on the load temperature measured during such tests. The European standard identifies the temperature classes through the definition of the highest and lowest temperatures of the warmest and coldest packages, as reported in Table 3.1 [13]. The test room conditions are identified through the definition of the ambient psychrometric conditions (climate classes), as reported in Table 3.2 [13]. For all of them, air velocity and radiant heat are the same. In particular, air velocity should be equal to 0.2 m s1 parallel to the plane of the cabinet display opening and to the longitudinal axis. Radiant heat is controlled by the prescription of the wall temperature and emissivity, and the level of illumination. It should be noted that compliance of a retail cabinet with the standards does not mean that the correct storage temperature will be kept during normal operation in the retail store, even if the cabinet has been set up and situated in accordance with the recommendations of the manufacturer (normal conditions of use). This is almost due to the dissimilar thermal properties of foodstuffs and test packages, and to some differences in ambient conditions (i.e., air velocity, air temperature, radiative heat load). The EN standard 23953-2 [13] highlights this argument in the Annex C ‘‘Comparison between laboratory and in-store conditions.’’ It states thus:
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TABLE 3.1 Temperature Classes according to the EN Standard 23953 Highest Temperature of the Warmest Package (8C)
Class
Lowest Temperature of the Coldest Package (8C)
15 12 12 þ5 þ7 þ10 þ10 Special classification
L1 L2 L3 M1 M2 H1 H2 S
Lowest Temperature of the Warmest Package (8C) 18 18 15 — — — —
— — — 1 1 þ1 1
The complete range of various climate conditions and various ways of loading in stores cannot be simulated in the laboratory. For these reasons, specific climate classes and loading are defined for tests in the laboratory to classify cabinets and to make comparisons. For open refrigerated display cabinets, test results in laboratory cannot be directly transposed in stores.
For this reason, it is crucial that the cabinet is installed and operated with awareness. For the same reason, designers can make use of the great advantage offered by the use of CFD, because the designers can check different configurations, thereby saving the huge amount of time required for the standardized tests (at least a couple of days each), and can predict the performance of the apparatus at operating conditions different from the standardized ones.
3.2.3 AIR CURTAINS In an open cabinet, refrigerated air curtains are established at the cabinet opening when cooling of the load is achieved via forced air distribution. The reason for the choice of this
TABLE 3.2 Climate Classes according to the EN Standard 23953 Test Room Climate Class 0 1 2 3 4 5 6 7 8
Dry Bulb Temperature (8C)
Relative Humidity (%)
20 16 22 25 30 40 27 35 23.9
50 80 65 60 55 40 70 75 55
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position is the need of reducing heat transfer from the external environment by creating a barrier between the load volume and the external ambience. Heat transfer through the solid walls surrounding the load volume can be effectively cut by means of adequate insulating material. On the contrary, load is subject at the opening to both radiative and convective heat transfer from the ambient. Both of them cause heating of the food surface. Radiative heat transfer takes place between the load surface and the room walls, lights, and all other objects surrounding the opening. It plays an important role, since emissivity of the food packaging and of the surrounding objects is usually high (in the range 0.8–0.9). It has been measured that the temperature of the exposed surface of frozen food can increase up to 5–10 K due to the absorption of radiant heat. Radiant heat can be reduced by using low emissivity materials for food packaging, high efficiency (low temperature) lights in the environment, and shielding coatings on the glass door surfaces, if any [15]. Convective heat transfer is due to the temperature difference between the load volume and the environment. Air movement caused by natural convection unavoidably causes infiltration of warm air through the opening, which is enhanced in the presence of even slight air movements in the room. The air curtain is capable of effectively restraining the convective heat transfer and the warm-air infiltration, in the meantime reducing the surface heating due to radiation. In the case of open cabinets, more than one air curtains are used, the temperature of the external air curtain being higher than that of the internal one for the sake of a better flow stability. Air from the curtains is then extracted through a grille and forced by fans through a finned cooling coil where heat is removed. The surface temperature of the cooling coil is usually below the dew-point temperature of air; thus water condensation takes place. In the frequent case of surface temperature of the coil below 08C, frost formation takes place, which requires cyclical coil defrosting operations. Finally, refrigerated air is supplied to a plenum and then, through a honeycomb, to the supply grille, thus creating the air curtains. In the case of closed cabinets, usually only one air curtain is established, which flows close to the internal surface of the door. When the door is open, the air curtain helps prevent warm-air infiltration. When the door is closed, the air curtain extracts heat from the load volume and particularly from the food surface, which is still subject to radiant heat. Air curtains will be discussed more in detail in Section 3.3.2.1 and in Chapter 4 and Chapter 5.
3.3 APPLICATIONS OF CFD TO DISPLAY CABINETS CFD is a successful tool for the designer of display cabinets, who can take advantage from this tool to improve load temperature distribution, predict the airflow pattern and its efficacy, reduce warm-air entrainment, and improve product refrigeration. As previously mentioned, the main concern arises from the necessity to ensure an effective display, while preserving the optimal storage conditions and achieving the lowest energy consumption. The manufacturer must face this challenge and find the solution that better fits such requirements. Air movement inside the cabinet plays the key role in this challenge, essentially because it is in charge of product refrigeration. The thorough comprehension of the phenomena associated with airflow in display cabinets is in turn a difficult task, almost due to the various interdependent factors that act simultaneously. Often a trial and error process has to be established, requiring numerous experimental tests that entail spending a huge amount of time and money. Numerical modeling performed by a skilled person can be a viable alternative, once its reliability has been validated against experimental data. Sensitivity analyses can be easily executed, efforts can be directed to optimize the most critical components, and improvements in the performance of the whole cabinet can be achieved in a much shorter time than through
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experimental testing. Furthermore, the performance of the cabinet at different ambient conditions (e.g., temperature, humidity, air velocity) or operating conditions (e.g., load arrangement) can be predicted with sufficient accuracy, thus leading to a better awareness of the possible performance of the unit in the actual conditions at the retail store. In the following, the most important applications of CFD to retail cabinets are briefly described and the possible advantages of numerical modeling are discussed.
3.3.1 MODELING PRODUCT TEMPERATURE DISTRIBUTION Product temperature inside a display cabinet suffers from an uneven distribution, both from left to right and from back to front of the shelves. Temperature differences up to about 5 K for chilled food and about 10 K for frozen food can be encountered, which can be unacceptable. The difference from the left to the right side is often due to uneven air distribution, and will be discussed later on. The main reasons for the difference from back to front are the proximity of the cooling coil to the back or bottom of the load volume and the effect of radiant heat on the front surface. Radiant heat can account for up to 12% [16] of the total load, and therefore cannot be neglected. Furthermore, as radiation is concentrated on the surface, it leads to a significant local temperature increase. Experimental tests [17] showed a reduction of up to 10 K of the surface temperature of the upper layer of products in a horizontal frozen-food cabinet, thanks to the application of a low emissivity shield. This is because food packaging has an average emissivity of about 0.9, which is also the value required by the EN standard for the test packages. The main problem when simulating the product temperature distribution resides on the necessity to adopt a transient state model. In fact, heat exchanges through radiation and with the cooling coil are both time-dependent phenomena, linked to the shop opening time, to the presence of covers or night curtains, to the on–off cycling of the refrigerating equipment, and to the defrosting operations. Figure 3.4 reports as an example the temperature of the warmest and the coldest test packages measured at different locations in a frozen-food cabinet. Further to the influence of the location, the temperature fluctuation due to the defrosting operations is also clearly visible. The defrosting operations can be performed by heating the coil or simply by switching-off the refrigerating equipment. The missed refrigerating power leads to a step increase in food temperature, which requires a few hours to completely recover.
Temperature (°C)
−12 −14 −16 −18 −20 −22
0
4
8
12
16
20
24
Time (h)
FIGURE 3.4 Temperature of the warmest and coldest packages during a temperature test.
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For this reason, modeling the product temperature distribution inside a cabinet should be performed via a transient state simulation adopting a reliable model of radiation. In this case, it is not convenient to model concurrently the airflow pattern in the air curtains because of the great disparity between the time constants of the two phenomena. A satisfactory transient model of the airflow should require a time step of a few hundredths of a second, whereas for the food temperature a few minutes could be enough. When modeling the load temperature distribution, the air curtain could be simulated as a convective boundary condition with an average convective coefficient evaluated by means of previous simulations or through classical correlations. In this case, the CFD model becomes a much simpler coupled conduction–convection model that can also be easily solved with in-house codes [17,18].
3.3.2 MODELING AIRFLOW From the point of view of the designer, the effective simulation of the airflow pattern inside the whole display cabinet is the most interesting result. However, there are too many factors regarding the geometry of the cabinet, the operating conditions of the cabinet, and the ambient conditions, which interact and influence the performance of the unit. This would require a very complex model with an almost unpredictable accuracy that probably could not fit the actual operating conditions well [19]. A solitary paper is present in the literature with a simulation of a whole vertical open chilled cabinet in 3D, with the purpose of obtaining steady-state temperature distribution in the product [20]. The whole cabinet including the load, the air curtains, the air ducts, and a portion of the ambient is included in the domain, and the authors claim reasonable agreement with the load temperature distribution obtained from spot thermocouple measurements and infrared camera images. It is much more effective to split the whole flow course into a few sections, and set up simplified models where some variables can be disregarded, after verification by means of a sensitivity analysis. With such models, it will become almost impossible to closely reproduce the operation of the whole cabinet, however they will be much more effective for a quick comparison of various configurations [19,21–23]. The most widely used simplified models relate to the air curtain, the air distribution between two shelves, the airflow at the evaporator, and the airflow in the rear ducts. In all of them, load surface can be considered as an adiabatic surface at the storage temperature. The effect of radiation on the load surface can be considered through a suitable increase in the food surface temperature. Usually, simulations are performed for a cabinet fully loaded, because this operating condition is required for the standard test and it is the most common in supermarkets. 3.3.2.1
Air Curtains
The function of the air curtain has already been introduced, and will be further detailed in Chapter 4 and Chapter 5. It is indeed the most investigated part of the display cabinet, because of its crucial influence in the performance of the unit, in terms of both product temperature and energy consumption. This is almost due to the warm-air infiltration, which accounts for 60%–75% of the total refrigeration load [2,24]. In fact, as soon as the air curtain leaves the air discharge, entrainment of warm air takes place due to the increase in the width of the curtain. Because of the necessity to maintain the mass balance, a portion of the flow rate will be lost at the air return and will overspill at the bottom of the cabinet, thus causing the so-called ‘‘cold feet effect.’’
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The induction factor a is defined for a single air curtain as the ratio of the mass flow rate of ambient air entrained to the total mass flow rate at the return grille [2,23]: a¼
_ ambient treturn tdischarge m ffi _ return tambient treturn m
(3:1)
It can be computed also in the case of multiple air curtains, through the calculation of the average values of air temperature weighed with the respective mass flow rates. The induction factor is commonly considered for the evaluation of the effectiveness of the air curtain, especially because the variables required for its calculation are easily measurable. It has been found to depend upon several factors, among which the most important are the initial turbulence intensity, the Reynolds number, and the velocity profile at the air discharge [25]. Early simulations of the air curtains were performed using in-house codes in 2D domains. As an example, Cortella [26] utilized a finite element code based on the stream functionvorticity formulation, with a turbulence model similar to an LES procedure. Transient simulations were performed in a 20,000 grid-points domain of a vertical open cabinet for chilled food. The induction factor and the refrigerating power were found to be in good agreement with experimental values, and some suggestions could be given to enhance curtain stability. Also, Ge and Tassou [27] used an in-house code based on finite differences, which also took into account the moisture content in the air curtain. From this model, the authors derived some correlations for the estimation of the heat flow rate and of the return air temperature at various conditions. The employment of commercial codes made simulations much easier, because the main problems of computational efficiency and user friendliness of in-house codes were overcome. In the last decade, many authors published 2D simulations of air curtains in horizontal and vertical cabinets, with the aim of the prediction of the airflow pattern and of the evaluation of the curtain efficacy at various conditions [22,28–34]. A 3D simulation of air curtains has been developed by D’Agaro et al. [23] and will be discussed in more detail in Section 3.3.4.2. In all the studies mentioned here, CFD has always proved to be a successful tool for the optimization of the air curtain. 3.3.2.2 Shelves In open vertical cabinets, air curtains are deeply influenced by the shape, length, and loading of shelves. As regards loading, the best air-curtain efficacy is encountered when the cabinet is fully loaded, which is the standard test and design condition and also the most common condition in retail stores. As regards geometry, at the design stage a lot of experimental tests or CFD simulations are required to minimize air-curtain disruption at the front of the shelves [35]. 3.3.2.3 Evaporator and Rear Ducts Uneven distribution of air at the evaporator ducts is crucial because it could lead to an uneven air-curtain velocity at the air discharge, thus causing differences in product temperature from left to right in the load volume. Foster et al. [35] investigated the flow of air as it exited the evaporator and entered the rear duct. The effects of a dead space were identified and modifications were suggested in order to reduce the formation of vortices and to improve air distribution in the back plenum. Similar simulations can be performed on different geometries of cabinets, and not only the shape of the rear ducts, but also the position of the evaporator and of the fans can be investigated. More details are given in Chapter 4.
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3.3.3 MODELING
THE INFLUENCE OF
AIR HUMIDITY
Commercial codes give the user the opportunity to include moisture content in the airflow models, in order to investigate both heat and mass entrainment in the cabinet. Some authors did use this feature when performing their simulations [20,27,28]. Actually, presence of humidity is crucial for the cabinet performance, because humidity entrainment leads to performance detriment due to evaporator frosting. However, the increase in computer power requirements due to the inclusion of moisture content in the CFD model can be avoided by estimating the latent heat from a mass balance on the water vapor content of the air curtain, once the induction factor and the humidity ratio of the ambient air are known, and assuming that air is saturated at the evaporator outlet. More details about the numerical methodology are given in Section 3.4.3.
3.3.4 MODELING INTERACTIONS
WITH THE
AMBIENT CONDITIONS
Display cabinets operation, especially for open cabinets, is crucially influenced by ambient conditions. Radiant heat, ambient air velocity, and direction are only the most important variables that must be considered when designing such units. 3.3.4.1
Radiation
In the previous section, the effect of radiant heat has been described, and some suggestions have been given on how to reduce radiant heat gain on the load surface. As regards simulations, it has been clarified that radiation has to be accounted for only when simulations of the load temperature distributions are being performed, whereas it is unnecessary for the evaluation of airflow patterns when load surface can be considered as a constant temperature surface. 3.3.4.2
Ambient Air Movement
Air velocity in the ambient environment and its direction are also crucial for the performance of the cabinet, and for this reason standard tests prescribe both of them. Furthermore, airflow visualizations performed on the air curtains during cabinet testing showed that 3D effects take place and can be significant, even with still air in the ambient. For these reasons, we realize that it is necessary to investigate more thoroughly the 3D effects in the air curtains. Typically, almost all papers in the literature describe 2D simulations, for the sake of CPU time and memory requirement reduction, assuming that simulations are performed on the median section and that end effects can be negligible. In fact, especially for short length cabinets, end effects can be significant, and lead to uneven air-curtain velocity and food temperature distribution. D’Agaro et al. [23] performed 3D simulations on a 2.44 m long vertical cabinet for frozen food, and investigated the effect of longitudinal air movement. The authors report that 3D flow structures that may originate from slow air movements in the ambient are responsible for 20% decay in the performance of the unit between a 2 m and a 1 m long cabinet, thus underlining the importance of 3D simulations in the design of short to medium cabinets. Another important interaction between the cabinet and the ambient is the accumulation of cold air, which overspills the return air grille and accumulates on the floor in front of the unit. This situation is named cold feet effect because of the unpleasant sensation on the customer who walks close to vertical open cabinets. Some authors [36] tried to simulate the whole sales area of a store, but the model was too complex and time consuming. For this reason, they moved to a simplified model of a chilled aisle, simulated on the three symmetry
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planes, and investigated different ventilation and heating strategies. More details on the topic are reported in Chapter 4.
3.3.5 GLASS DOORS FOGGING
AND
DEFOGGING
On closed display cabinets with doors, mist deposition occurs on the internal side of the door each time it is open, especially for frozen-food cabinets. In the case of transparent doors, a quick defogging must be achieved to recover product visibility through the glass. For this purpose, an air curtain is established flowing along the internal glass surface, and an electric heater is sometimes embedded in the multiglazed door. Demisting time can be estimated through the application of CFD. Croce et al. [37] and D’Agaro et al. [38] coupled a CFD commercial code with an in-house code for the evaluation of the airflow pattern and of the water layer evolution, respectively. More details on the numerical procedure are given in Section 3.4.3. The computation enables the prediction of the water layer height during condensation when the door is open, and also during evaporation in the presence of electrical heaters. Various parameters of the refrigerated cabinet (e.g., geometry, air-curtain velocity, and temperature) and the glass door (e.g., geometry, global heat transfer coefficient, and presence of electrical heaters) can be considered. The model also takes into account condensation as a thin film or a collection of water droplets. Results showed the model to be reliable for the evaluation of the entity of defogging time reduction that might be expected with different solutions.
3.3.6 MIST COOLING—HUMIDIFICATION Unwrapped food products like fruits and vegetables are subject to dehydration when displayed in open cabinets. This is due to air dehumidification that takes place on the cooling coil surface, especially when forced convection cabinets are employed. The importance of relative humidity on the shelf life of products is well known, and all efforts are made to limit quality decay and weight loss when it is possible. In display cabinets, air dehumidification can be limited by choosing appropriate air velocity and temperature at the design stage, however the solution is not fully satisfactory. Another approach is derived from the air-conditioning plants, and from some vegetable refrigerated storage rooms, where air humidification is sometimes exploited through water spray. This technique has the only disadvantage of being a possible way to bacteria growth, and therefore requires strict control from the microbiological point of view. Tests have been performed on humidification equipment that use water-mist sprayed over the products’ surface above each shelf and the well [39]. Results were encouraging, since weight loss was reduced, at the expense of a slightly higher refrigeration load requirement. This device is already commercially available, and supplied upon request by display cabinet manufacturers, however it has not yet been thoroughly investigated. Commercial codes are available to treat heat and mass transfer, and some research has been performed in the similar field of weight loss during blast chilling [40]. Thus, in the near future some research work will be probably devoted to this interesting topic.
3.4 CFD CODES CFD is based on the solution of the governing flow (i.e., the continuity and the Navier– Stokes) equations, the energy conservation equations, and sometimes on the conservation of other factors (e.g., water moisture). It has become popular only recently, when the availability
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of more powerful and affordable computers made it possible to investigate practical problems that were previously too computationally expensive. When applied to display cabinets, CFD can model fluid flow; conductive, convective, and radiative heat transfer; and moisture transfer. In addition to numerous in-house codes, there are a number of commercial codes that can now cope with a high level of complexity. However, most of them are general purpose software designed for use in many different research fields. Therefore, robustness sometimes is enhanced to the detriment of accuracy, which still needs to be improved [41].
3.4.1 METHODOLOGY Every CFD simulation can be split into three consecutive phases: preprocessing, solving, and postprocessing [41]. 3.4.1.1
Preprocessing
Preprocessing starts with the choice of the computational domain to be simulated, includes the mesh generation, the definition of material properties, and ends with the application of boundary conditions. It is a crucial phase for obtaining reliable results. The users must be fully aware of the physics of the problem, because in this phase they set up the model of their practical problem. The choice of the domain to be investigated needs to be carefully considered in order to include all possible effects on the object of investigation. As an example, CFD simulation of an open display cabinet requires a portion of the external ambient to be included in the computational domain, in order to evaluate correctly the warm-air entrainment and the coldair overspill. Two dimensional or three dimensional domains can be considered for display cabinets. Until now, almost all the simulations about air curtains have been performed in 2D because of the necessity to reduce the computational load. However, D’Agaro et al. [23] have shown that in short length cabinets the end effects cannot be disregarded, thus demonstrating that in certain cases 3D simulations could be necessary. For the simulation of air ducts (e.g., rear ducts, evaporator, and fans), 3D simulations are usually indispensable because of their complicated geometry. The dimension of the elements in the grid influences the level of accuracy of the solution. Usually, the dimension must be reduced in the portions of domain where an accurate solution is required (e.g., in the presence of turbulence or of high velocity gradients) or close to solid boundaries, where the requirements of the turbulence model must be satisfied. Of course the computational time increases with the number of elements in the domain, thus suggesting the limiting of grid refinements to those areas where it is strictly necessary. For an accurate simulation, it should be necessary to check that the solution is not ‘‘grid dependent,’’ i.e., it does not depend on the dimension of the elements. Otherwise, mesh refinements are still required. Once all the properties of the various solid and fluid substances have been identified, the boundary conditions must be defined. This is another important step in the simulation, whose effect in the solution can be significant. Usually it is necessary to introduce assumptions at this step, because the available boundary conditions do rarely match the actual conditions. In many cases, different boundary conditions must be checked, the results compared, and a sensitivity analysis performed for the identification of the best conditions. More specific information about different boundary conditions used to simulate display cabinets is reported in Chapter 4.
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3.4.1.2 Solving The solution of the governing equations requires their discretization and an iterative process to obtain an approximation of the value of each variable at specific points in the domain. Calculation is stopped when the residuals in the calculation of the balance of one or more properties are below a specified value, and the solution is said to converge. Reaching convergence is not trivial, and also the choice of the threshold value of residuals is not easy. Some suggestions are given in Chapter 4. Another main concern about solving in CFD simulation is the choice between steady state or transient calculations. The choice depends on the phenomena to be investigated, and some suggestions have been given in the previous sections depending on the object of the simulation. In general, transient simulations should be performed only in the case where the time evolution of a phenomenon is under investigation, because convergence must be reached at each time step, and therefore they are much more time consuming. 3.4.1.3 Postprocessing When the solution reaches convergence, a distribution of the values of all the variables throughout the whole domain is produced. Such values must be processed to obtain visualizations and some required numerical results (e.g., the induction factor, the refrigerating power). The postprocessing phase is thus essential for the evaluation of the simulation results, and it is also an important tool for their most thorough understanding. In fact, the postprocessor also performs calculations and balances, thus giving further precious information.
3.4.2 TURBULENCE MODELS Turbulence models must be adopted to take into account the turbulence effects, which cannot be evaluated through a direct simulation. In fact, direct simulation of turbulence in large domains as those used for display cabinets would require a really huge amount of memory and CPU time. There are many turbulence models available, and unfortunately the choice of the model significantly affects the results. Literature works can be helpful with this respect, however experience is fundamental. The basic turbulence models are the so-called ‘‘two equations models,’’ which are the default choice for many commercial codes. Among these, the k–« and the RNG k–« models are the most widely used. Although easy to implement, they require the previous evaluation of the turbulence kinetic energy and dissipation rate, which is a matter of difficult measurements or experience. Furthermore, they are not considered as the best choice because of the poor accuracy sometimes encountered. Other models are those based on the Reynolds stresses and the large Eddy simulation. The former was found to be accurate [42] even if it required a quite fine mesh. The latter was successfully used by Cortella et al. [26] in the framework of a stream function-vorticity in-house code. Some more suggestions, particularly on the initial turbulence intensity, will be given in Chapter 4, while a deeper discussion of turbulence models is left to specific literature.
3.4.3 MASS TRANSFER It has already been pointed out in Section 3.3.3 that the moisture content of the air is a critical factor influencing the performance of display cabinets, because humidity entrainment
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involves an additional latent heat that shall be removed at the cooling coil. Furthermore, also in the case of chilled cabinet, the surface temperature of the cooling coil is often below 08C, thus leading to frost formation and to the need for cyclical defrosting operations. The evaluation of the latent heat does not strictly require a coupled heat and mass transfer simulation. The induction factor can be once again considered from the evaluation of the water mass balance in the air curtain: a¼
_ ambient xreturn xdischarge m ffi _ return xambient xreturn m
(3:2)
where x is the humidity ratio (kgvap=kgdry air). The ambient humidity ratio is known, while the discharge humidity ratio can be easily estimated by assuming saturation for the discharge air [2,23]. On the contrary, there are some particular cases where coupled heat and mass transfer must be simulated, like for example the simulation of door fogging and defogging in closed display cabinets. This topic has already been introduced in Section 3.3.5. In the following, more details are given on the numerical procedure, which involves coupling of two different codes, for the dry heat or flow and for the mass transfer [38]. The problem is split into two phases, the first regarding the dew deposition on the internal face of the glass when the door is open and the second regarding the defogging operation once the door is closed. As regards the heat transfer, the evaluation of the local heat transfer coefficient for the airflow on the internal face of the glass is performed with a single phase solver. In fact, the phase change during evaporation is limited to a thin layer on the solid surface, and therefore it is accounted for through proper boundary conditions. Conductive heat transfer through the multiglazed glass can be solved by means of a steady-state network of thermal resistances, which can also take into account radiation in the air cavities, thus leading to a very simple conduction problem easily solvable with simple in-house codes. Finally, the external heat transfer coefficient can be effectively estimated by means of the classical empirical correlations for steady-state natural convection on a vertical plate. The different domains and solvers are coupled through an exchange of boundary conditions, thus leading to a more flexible algorithm. As regards the mass transfer, an in-house code was used, where the latent heat contribution due to condensation or evaporation appeared as a heat source or sink, respectively, and the code was placed at the interface between the solid and the fluid domain. Thermal and mass balances can be established at the interface and solved taking advantage of the heat and mass transfer analogy. A detailed description of this procedure is given in Ref. [38]. It is interesting to note that in this model the water layer can be considered as a continuous film or as a number of droplets, whose geometry changes during the condensation and evaporation processes. Furthermore, the effect of electric heaters can be accounted for, in order to speed up the demisting process. The simulation showed to be reliable when compared to experimental tests, especially using the droplet model.
3.4.4 VALIDATION It is common opinion that CFD simulations must be validated, and this is especially true in the case of display cabinets, where the simulation of such a complex problem requires a number of assumptions to set up the model. Usually, validation is performed against experimental tests at controlled conditions, like those in accordance with the standards in force. The variables that can be compared are essentially load temperature, air temperature, and air velocity.
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Measurements of load temperature can be easily performed, and the effect of radiative heat transfer can be highlighted by means of infrared thermal imaging systems. Measurements of air temperature can be easily performed at the discharge and return grille, although it is quite complicated to measure air temperature along the air curtain. Infrared systems cannot visualize air temperature, because it is transparent under infrared radiation. Some images taken with infrared cameras and willing to show air temperature are actually infrared visualization of the cabinet end-wall temperature. Accurate measurements of air velocity are difficult, especially along the air curtain. At the discharge and return grille, the use of hot wire anemometers allows for a sufficiently accurate evaluation of the velocity distribution, even if important information about direction and turbulence is lost. Anemometers placed along the air curtain are susceptible to disturb the airflow pattern, thus giving place to an incorrect evaluation. Axell [43] reported a strong influence of the distance and shape of the sensors, and claimed to have measured values in ‘‘good qualitative agreement’’ with the numerical results. Much more reliable results can be obtained using the particle image velocimetry (PIV), which is a very accurate method for flow pattern measurements. Air has to be seeded; the field of investigation is lighted with a laser sheet; and a number of subsequent images are taken by a digital video camera placed perpendicular to the laser plane. Processing of the images allows for the identification of the movement of each seeding particle, thus leading to the complete flow pattern recognition. Rather than for CFD validation, this is a valuable tool for the adoption of the best CFD boundary conditions, especially at the discharge air (air velocity and direction, turbulence intensity), which are crucial to obtain reliable results [44].
3.5 CONCLUSIONS Retail display cabinets design can take great advantage of CFD, in terms of both time and money savings. It is rather difficult to replicate experimental results, due to flow complexity and difficulties in reproducing the actual ambient conditions. However, CFD is very effective for sensitivity analyses, and can be very helpful to compare the performance at different operating conditions and find the optimal design of the unit. In the near future, CFD will surely grow in popularity, and probably it will be much easier to perform even complicated simulations due to the increasing computational power. Three dimensional simulations will be more affordable, and larger computational domains will permit a more thorough evaluation of the influence of ambient air, as an example. Nevertheless, a lot of critical assumptions or choices must be made to perform a CFD simulation, and the outcomes will always depend on the judgment of the operator. Furthermore, commercial codes tend to improve robustness at the expense of accuracy every time convergence is difficult, thus leading to incorrect results. For these reasons, CFD must be always operated by skilled people, the results accurately assessed and, whenever possible, boundary conditions and results of some reference cases should be validated by comparison with experimental tests.
REFERENCES 1. Spiess W.E.L., Boehme T., and Wolf W. Quality changes during distribution of deep-frozen and chilled foods: distribution chain situation and modeling considerations. In: Food Storage Stability, Taub I.A. and Singh R.P. (eds.), CRC Press, Boca Raton, FL, pp. 399–417, 1997. 2. Rigot G. Meubles et vitrines frigorifiques, Pyc Edition, Paris, 1990. 3. Gac A. and Gautherin W. Le froid dans les magasins de vente de denree´s pe´rissables, Pyc Edition, Paris, 1987.
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28. Van Oort H. and Van Gerwen R.J.M. Air flow optimisation in refrigerated display cabinets. In: Proceedings of the 19th International Congress of Refrigeration, IIR=IIF, The Hague, the Netherlands, pp. 446–453, 1995. 29. Bale´o J.N., Guyonnaud L., and Solliec C. Numerical simulation of air flow distribution in a refrigerated display case air curtain. In: Proceedings of the 19th International Congress of Refrigeration, IIR=IIF, The Hague, the Netherlands, pp. 681–688, 1995. 30. Laguerre O., Moureh J., Srour S., Derens E., and Commere B. Predictive modelling for refrigerated display cabinets. In: Proceedings of IIR International Conference Advances in the Refrigeration Systems, Food Technologies and Cold Chain, Sofia, Bulgaria, pp. 480–487, 1998. 31. Cortella G., Manzan M., and Comini G. Computation of air velocity and temperature distributions in open display cabinets. In: Proceedings of IIR International Conference Advances in the Refrigeration Systems, Food Technologies and Cold Chain, Sofia, Bulgaria, pp. 617–625, 1998. 32. Wu Y., Xie G., Chen Z., Niu L., and Sun D.W. An investigation on flowing patterns of the airflow and its characteristics of heat and mass transfer in an island open display cabinet with goods, Applied Thermal Engineering, 24: 1945–1957, 2004. 33. Cortella G. and D’Agaro P. Air curtains design in a vertical open display cabinet. In: Proceedings of IIR International Conference New Technologies in Commercial Refrigeration, Hrnjak P.S. (ed.), Urbana, USA, pp. 55–63, 2002. 34. Cui J. and Wang S. Application of CFD in evaluation and energy-efficient design of air curtains for horizontal refrigerated display cases, International Journal of Thermal Sciences, 43: 993–1002, 2004. 35. Foster A.M., Madge M., and Evans J.A. The use of CFD to improve the performance of a chilled multi-deck retail display cabinet, International Journal of Refrigeration, 28: 698–705, 2005. 36. Foster A.M. and Quarini G.L. Using advanced modelling techniques to reduce the cold spillage from retail display cabinets into supermarket stores to maintain customer comfort. In: Proceedings of the Institution of Mechanical Engineers, Part E—Journal of Process Mechanical Engineering, 215: 29–38, 2001. 37. Croce G., Nonino C., and Della Mora F. Numerical simulation of defogging conditions. In: Proceedings of the 3rd ICCHMT, Banff, Canada, 2003. 38. D’Agaro P., Croce G., and Cortella G. Numerical simulation of glass doors fogging and defogging in refrigerated display cabinets, Applied Thermal Engineering, 26: 1927–1934, 2006. 39. Brown T., Corry J.E.L., and James S.J. Humidification of chilled fruit and vegetables on retail display using an ultrasonic fogging system with water=air ozonation, International Journal of Refrigeration, 27: 862–868, 2004. 40. Hu Z. and Sun D.W. CFD simulation of heat and moisture transfer for predicting cooling rate and weight loss of cooked ham during air-blast chilling process, Journal of Food Engineering, 46: 189– 197, 2000. 41. Xia B. and Sun D.W. Application of computational fluid dynamics in the food industry: a review, Computer and Electronics in Agriculture, 34: 5–24, 2002. 42. Moureh J. and Flick D. Airflow characteristics within a slot-ventilated enclosure, International Journal of Heat and Fluid Flow, 26: 12–24, 2005. 43. Axell M., Fahlen P.O., and Tuovinen H. Influence of air distribution and load arrangements in display cabinets. In: Proceedings of the 20th International Congress of Refrigeration, IIR=IIF, Sydney, Australia, paper 152, 1999. 44. Casarsa L. and Arts T. Experimental investigation of the aerothermal performance of a high blockage rib roughened cooling channel, Journal of Turbomachinery, 127: 580–588, 2005.
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Improving Performance of a Chilled Multideck Retail Display Cabinet by CFD Alan M. Foster
CONTENTS 4.1 4.2
Introduction ............................................................................................................... 104 Description of Cabinet............................................................................................... 104 4.2.1 Air Curtain ..................................................................................................... 105 4.2.2 Defrost............................................................................................................ 107 4.3 Standard Testing ........................................................................................................ 108 4.4 CFD Analysis ............................................................................................................ 108 4.4.1 Experimental Investigation ............................................................................. 109 4.4.2 Setting Up the CFD Model ............................................................................ 109 4.4.2.1 Two or Three Dimensional............................................................... 109 4.4.2.2 Mesh Size.......................................................................................... 111 4.4.2.3 Turbulence Model ............................................................................ 111 4.4.2.4 Buoyancy .......................................................................................... 112 4.4.2.5 Steady State or Transient? ................................................................ 113 4.4.2.6 Humidity .......................................................................................... 113 4.4.2.7 Boundary Conditions ....................................................................... 113 4.4.3 Convergence and Mesh Independence............................................................ 116 4.4.4 Postprocessing ................................................................................................ 117 4.5 Results from Typical Simulations .............................................................................. 118 4.5.1 Air Curtain ..................................................................................................... 118 4.5.2 Modeling of the Duct ..................................................................................... 119 4.5.3 Shelving .......................................................................................................... 120 4.5.4 Cold Feet Effect.............................................................................................. 121 4.5.4.1 Whole Store ...................................................................................... 121 4.5.4.2 Aisle.................................................................................................. 123 4.6 Verification ................................................................................................................ 124 4.7 Conclusions................................................................................................................ 125 Nomenclature ..................................................................................................................... 126 References .......................................................................................................................... 126
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4.1 INTRODUCTION In the UK, retail sales of frozen and prepared chilled food were worth £118 billion per annum between 2005 and 2006. The majority of which was sold from refrigerated display cabinets. Being able to maintain the temperature of this food is of vital importance to retailers to ensure optimal food quality, safety, and shelf life [1]. It has been shown that mean food temperatures between chilled multideck cabinets can range from 18C to þ168C [2]. This range causes food manufacturers problems when defining the shelf life of products and results in shelf lives that are either unduly cautious or potentially risky. Open display cabinets are one of the weakest links in the chilled food chain [3] and large (>5 K) temperature differences are found in most cabinets. This is due to the technical difficulties in reducing the difference between the lowest temperature packs, which are usually sited at the rear of the cabinet, and the highest temperature packs sited at the front of the cabinet. Technical problems in the even supply of air from the evaporator and the design of the air curtain can result in uneven temperatures across the cabinet (left to right) and too much entrainment of ambient air at the front of the cabinet. Multideck cabinets are extremely sensitive to ambient conditions. Small changes in ambient temperature, humidity, or airflow can have a large impact on food temperature. This is not a problem during the setting up and testing of a cabinet where it is kept in a temperature-controlled test room. However, in reality the ambient conditions are unlikely to be controlled. Many authors [4–9] have shown computational fluid dynamics (CFD) modeling to be a valuable tool to rapidly provide design options to improve airflow within display cabinets. Due to the speed that a variety of scenarios can be predicted, CFD provides the ideal means to improve the performance of display cabinets. The aims of this chapter are to provide a CFD user with an understanding of retail display cabinets and a retail display cabinet designer with an understanding of CFD. This chapter is specific to multideck chilled cabinets and the use of commercial CFD codes. It is hoped that this chapter will further stimulate the use of CFD to improve the design and more cost-effective testing of the multideck chilled retail display cabinets.
4.2 DESCRIPTION OF CABINET In the majority of multideck retail display cabinets, the evaporator is in the base of the cabinet (although it is becoming more common for them to be in the rear duct) and the fans draw air through the evaporator and up the duct at the rear of the cabinet. Air exits the duct through holes or slots in the cabinet rear grille and also through a slot or honeycomb grille placed at the front of the cabinet canopy, termed the discharge grille (Figure 4.1). The purpose of the discharge grille is to create a vertical air curtain from the front of the cabinet canopy to a grille placed at the front of the cabinet well (termed the return grille). The air curtain creates a nonphysical barrier between the cold air in the cabinet and the ambient air outside. Due to the air from the curtain being colder than the surrounding air it will also fall due to buoyancy. As the air curtain falls from the cabinet discharge grille, the curtain entrains cold air from inside the cabinet (entered through the rear grille) and warm air from the environment. The entrainment of warm air from the environment causes the air curtain to become warmer as it passes down the cabinet. Entrainment causes the mass flow rate of the air curtain to increase as it moves down the front of the cabinet. Due to conservation of mass flow, not all of the air in the air curtain will be taken away by the return grille: a significant portion will overspill onto the floor. As this air will be colder and denser than the ambient air, it stays on the floor, causing a customer comfort issue which is commonly termed the ‘‘cold feet effect.’’
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Rear duct Rear grille
Discharge grille
Fan Shelf
Return grille Evaporator
FIGURE 4.1 Vertical section of multideck display retail cabinet with the evaporator fan in the rear duct.
The purpose of the rear grille is to provide cold air over the products and to provide a pressure in the display area that counteracts the deflection of the air curtain into the display area caused by the stack effect (discussed in detail in Chapter 7).
4.2.1 AIR CURTAIN The air curtain is by far the most researched element of multideck display cabinets. It is essentially a turbulent recirculated plane air curtain. Setting up of the air curtain is critical in the correct operation of the cabinet and also because infiltration through the air curtain is by far the largest heat load. It has been reported to be between 60% and 70% of the heat load on the cabinet by Axell and Fahlen [10], 73% by Faramarzi [11], and 76% by Van Baxter [12]. Turbulent recirculated plane air curtains were studied by Howell and Shibata [13]. They showed that .
.
.
.
There will be a break in the air curtain if the deflection modulus is not reached. (The deflection modulus is used to describe the sealing ability of the air curtain. It is the ratio of initial momentum in the air curtain jet to the transverse forces (buoyancy forces) that the air curtain is attempting to seal against. This is fully described by Hayes and Stoecker [14] and also in Chapter 7 of this book.) Initial turbulence intensity has a significant effect on the rate of heat transfer through the air curtain, as long as the initial velocity is large enough to maintain a continuous air curtain. The total heat transfer through the air curtain is directly proportional to the initial jet velocity and the temperature difference across it. There is a value of the deflection modulus, which exists for each air curtain configuration that minimizes the rate of heat transfer across it.
Finding the value of the deflection modulus that minimizes the rate of heat transfer across it is the holy grail of display cabinet designers. It is mainly found by trial and error, if at all. CFD offers the opportunity to predict the values of jet temperature, velocity, and turbulence that will minimize heat transfer across the curtain.
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There are two important dimensionless numbers which are used to categorize the air curtains. The Reynolds number (Re) is the ratio of momentum to viscous forces: Re ¼
ruD m
(4:1)
As display cabinet air curtains are refrigerated, they are negatively buoyant. The Richardson number (Ri) is the ratio of gravitational to momentum forces: Ri ¼
bgDTH u2
(4:2)
As the air leaves the discharge grille it starts to entrain air from both inside the cabinet and the ambient. This entrainment causes mixing in the jet. The air jet can be separated into distinct regions from the jet outlet at the discharge grille to the jet return at the return grille [15] (Figure 4.2). In the flow development region, the centerline velocity and temperature remain constant. Ambient air is unable to cross the curtain and enter the cabinet in this region. As the jet travels beyond this region, the jet centerline velocity will decrease and the temperature increases as air entrained from the ambient mixes through the curtain. Even though the momentum of the curtain remains constant (if we ignore buoyancy), the width and volume flow rate of the air curtain increase. This increase in flow rate is called entrainment. The level of entrainment can be defined by the entrainment ratio or coefficient: e¼
QRG QDG QDG
(4:3)
Potential core Discharge grille
Flow development region
Fully developed flow
Center line
FIGURE 4.2 Plane turbulent jet.
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In a retail display cabinet, air curtains are more complicated than the idealized jet described. Buoyant forces in a refrigerated air curtain mean that the air curtain will deflect from its path. The curtain will also probably impact on food and shelves on its way to the discharge grille. These factors will likely increase the level of entrainment. The sum of the mass flow rate through the discharge grille and rear grille will return through the return grille. The extra mass flow rate caused by entrainment cannot enter the return grille. Therefore, the entrained air from inside the cabinet will spill back into the cabinet warming the cabinet and entrained air from outside the cabinet will spill out of the cabinet causing the environment to cool (cold feet effect). A dimensionless number is commonly used to characterize the thermal influence of this entrainment: a¼
TRG TDG Tamb TDG
(4:4)
This number will always be between 0 and 1. A value of 0 means no entrainment (return temperature equals discharge temperature) and 1 is complete entrainment (return temperature equals ambient temperature). Navaz et al. [16] have established three phenomena which affects the level of entrainment. These are: (a) turbulence intensity, (b) Reynolds number (based on discharge grille width), and (c) velocity profile at the discharge grille. Chen and Yuan [17] measured the effect of the environment on air curtain heat loads. They showed that both increases in ambient temperature and relative humidity cause heat gain through the curtain to rise.
4.2.2 DEFROST The vast majority of multideck display cabinets will require defrosting of the refrigerant heat exchanger (evaporator coil). This is because ambient air of high moisture content will mix with the air curtain as explained above and some of this moisture will condense on the heat exchanger. In almost all cases the heat exchanger will be running below 08C and therefore the water will turn to ice. This ice needs to be removed from the heat exchanger before it becomes blocked. As ice builds up the velocity of the air passing through the heat exchanger drops, this can have a significant impact on product temperatures. There are three common methods of removing the ice: 1. With off cycle defrost, the ice is melted during the off cycle. When there is no demand for cooling, refrigerant is not passed through the heat exchanger. However, the heat exchanger fan is allowed to run until the heat exchanger rises to a set temperature above 08C. 2. Electric heaters in front of the heat exchanger or in the heat exchanger block are used to (generally at set time intervals) melt the ice. 3. Hot or warm gas defrost involves using either hot refrigerant gas from the compressor discharge or warm gas from the top of the receiver. The important thing to remember when modeling a display cabinet is that moisture buildup and defrosts cause a transient effect, where temperatures in the cabinet and the velocity through the discharge grille cycle up and down. Therefore, it is important to know when defrosts are taking place, so that boundary condition and verification measurements can be made at appropriate times.
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4.3 STANDARD TESTING Most retail display cabinets within Europe are tested to the European testing standard, EN441 [18–21]. This has recently been superseded by BS EN ISO 23953-1:2005, Part 1 and 2 [22,23] that has similar tests but slightly more stringent test room requirements. Within EN441-6 [20] chilled cabinets are described as M1 if all the temperatures of test packs are maintained between 18C and 58C, M2 if between 18C and 78C, or H if between 18C and 108C. A further, more stringent, temperature classification M0 is often used in the UK to describe cabinets that maintain the temperature of all the test packs between 18C and 48C. At present few cabinets conform to the M0 classification. A database of cabinets sold in the UK, which comply with the enhanced capital allowance scheme (ECAS) (a UK government scheme to allow incentives for purchasing energy efficient products [24]) contained 56 integral multideck cabinets that were classified as M1 or M2; however, only three cabinets were classified as M0. The airflow in the test room may be an important factor in the performance of the cabinet. Chen and Yuan [17] showed that increases in air speed parallel to the cabinet had a small effect on infiltration. D’Agaro et al. [25] showed that ambient air entrains preferably at the upstream side, which is estimated to increase the required refrigerating power by 30%. For the European standards the airflow must be parallel to the plane of the cabinet display opening and to the longitudinal axis. The velocity of this parallel flow should be in the range 0.1–0.2 m s1. This environmental flow is in the other plane to the cabinet flow and therefore to accurately model the display cabinet and the environment in an EN441 test requires a three-dimensional (3D) model. Testing in the US is carried out to a slightly different standard (ASHRAE 72-193). In this standard, ambient air currents must be parallel to the cabinet display opening but must not be more than 0.25 m s1. This means that the airflow could be the same as the European standard (0.1–0.2 m s1). There are other differences between the two standards in relation to the dummy product, loading of product, lighting level, etc. Testing of a display cabinet is very time-consuming. The cabinet needs to be loaded with test packs (either 1 or 0.5 kg). A typical cabinet will require over 300 of the 1 kg and 150 of the 0.5 kg packs. At least 50 of the 0.5 kg packs will require a thermometer inserted into their geometric center (m-packs). It is important to load the cabinet to a set specification as cabinet loading will greatly affect the performance of the cabinet. A logging system is required to record the temperature of all of the m-packs during a 24 h test. The cabinet will have to be left (generally for 24 h) to stabilize after any changes have been made. A major benefit of CFD modeling is the ability to reduce the amount of time required for cabinet testing.
4.4 CFD ANALYSIS Many authors [4–9] have shown CFD modeling to be a valuable tool to rapidly provide design options to improve airflow within display cabinets. Due to the speed that a variety of scenarios can be predicted, CFD provides an ideal means to both understand the airflow within the cabinet as well as determine which design options would provide improvements to the cabinet. These improvements may be required to meet the intended classification or to meet a tighter classification which may allow a premium price to be charged for CFD studies. There are a number of commercially available CFD codes that can be used; four popular codes are ANSYS CFX, FLUENT, STAR-CD, and PHOENICS. Modern codes are easier to use than codes in the past. Features such as automatic mesh generation can reduce the time
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to create a mesh from days to seconds. Moreover, today’s standard desktop PCs are easily capable of running these models. Other more specific codes have been used to good effect. For example, Axell et al. [26] have used a code designed for the simulation of fires in enclosures (SOFIE) successfully in the modeling of retail display cabinets.
4.4.1 EXPERIMENTAL INVESTIGATION Currently it is not feasible to create a CFD model of a whole cabinet that includes the necessary detail with which to troubleshoot all the cabinet performance failings. Instead, it is more appropriate to generate predictive models of different regions of the cabinet where problems have already been identified during the standard testing. Examples of problem areas found by the author in past testing are as follows: .
.
.
.
Large temperature gradients between the back and front of the cabinet, i.e., product at the back of the shelf will be too cold and product at the front too warm. This is either due to too little air entering from the holes in the rear grille and=or that the air curtain is ineffective. Temperatures too warm at the top of the cabinet—this is most likely to be caused by an air curtain that is being bent in towards the top shelves. Temperatures too warm at the bottom of the cabinet—this is often caused by too little air entering from the holes in the rear grille, specifically near the bottom. One side of the cabinet warmer than the other—this may be caused by an uneven geometry inside the cabinet, e.g., evaporator extends further on one side than the other. It may also be the consequence of the test standard, i.e., EN standards require air to flow across the face of the cabinet and this can cause uneven temperatures.
Once a problem area has been found, further testing with thermocouples and smoke visualization will lead to a better understanding of the problem. It is possible that this level of investigation is all that is required to fix the problem. However, if it is not, CFD has the potential to increase the understanding further and allows you to try ‘‘what-if ’’ scenarios.
4.4.2 SETTING UP
THE
CFD MODEL
Howell [27] assigned generic operating variables for the range of display cabinets in operation (Table 4.1). These data are a useful means of specifying boundary condition data if measured data is not available. Although modern CFD software has removed some of the required fluid dynamics knowledge of the user, some understanding of fluid dynamics is still required. An expert CFD user also needs an understanding of the physics of the problem they are trying to model. It is not currently possible to create a CFD model of a retail display cabinet that simulates everything perfectly. Assumptions will have to be made that will simplify the model, reducing its complexity and the computer resources required to solve the relevant equations. Below are some of the assumptions which will need to be considered. 4.4.2.1 Two or Three Dimensional Historically it has been commonplace to model the air curtain of a display cabinet in two dimensions (2D), this is very efficient in computer resources as a 3D model would require many times more memory and processor time. As the air curtain is long, a 2D model of the
22
24
Source: From Howell, R.H., Trans. ASHRAE, 99, 667, 1993. Note: Converted from imperial to metric units.
2 2 5 3 4 4 22 28 18
4 4 2 0 2 2 25 31 21 70 75 75 110 100 40 70 65 65 65
19
Discharge Thickness (mm)
1 1 8 6 7 7 19 26 15
Return Temperature (8C)
2.0
1.0 1.1 0.9 0.9 0.6 0.6 1.0 1.0 2.0
Discharge Velocity (m s21)
1.5
0.8 1.0 1.4 1.3 1.0 1.2 0.8 0.8 1.5
Distance from Discharge to Return (m)
Vertical
Horizontal Vertical Vertical Vertical Horizontal Vertical Horizontal Horizontal Vertical
Orientation of Air Curtain
110
Single shelf meat Multishelf meat Multishelf dairy Multishelf deli Single shelf produce Multishelf produce Single shelf frozen Single shelf ice cream Glass door reach-in frozen food (with=air curtain) Glass door reach-in ice cream (with=air curtain)
Case Description
Case Temperature (8C)
Discharge Temperature (8C)
TABLE 4.1 Generic Operating Variables for the Range of Display Cabinets in Operation
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central plane is commonly taken. As CFD codes are generally 3D, creating a model in 2D requires modeling of the third dimension with only one grid cell in that direction and using symmetry boundaries either side of the cell. Recently, increases in computer power have allowed 3D models of the air curtain to be produced. D’Agaro et al. [25] showed that the extremity effects caused by the side walls in reduced length cabinets lead to inaccurate results unless a 3D simulation tool is used. Axell et al. [26] produced a 3D model just for one shelf of a display cabinet to allow the flow from the pattern of holes in the rear grille to be predicted. 4.4.2.2 Mesh Size In the past, creating a computational mesh was a very time-consuming task. Since the advent of unstructured meshing, most CFD codes are able to create a mesh that fits the geometry efficiently. It is sometimes necessary to refine this mesh in specific areas to provide the best accuracy for given computer resources. If computer resources are large and the problem to be meshed small, the simple solution is to create lots of small grid cells. This is often not the case and it is more appropriate to have a finer mesh in certain areas than others. The areas which require a fine mesh will be the areas which are of most interest and have the largest velocity and temperature gradients. If vortices are likely, a mesh in the area of the vortex needs to be fine enough to resolve it. In the case of air curtain predictions, it is usual to have the finest mesh covering the likely position of the air curtain as it drops down the cabinet and the coarsest mesh in the ambient space outside the cabinet. The number of cells required will vary depending on whether the simulation is 2D or 3D, the overall size of the geometry, the size of the smallest element in the geometry, and the type of turbulence model used. The amount of mesh points available will depend on the computer hardware and the central processing unit (CPU) time available. The amount of random access memory (RAM) required for the meshing will depend on the CFD code, 100,000 mesh cells will require between 40 and 300 Mb of RAM. It is obvious from the literature that computer resources limit the accuracy and resolution of CFD results. For example, Cortella et al. [28] restricted their mesh to 20,000 grid points to reduce CPU time on a Hewlett-Packard (HP) C100 workstation using a large-eddy simulation (LES) turbulence model. 4.4.2.3 Turbulence Model Turbulence consists of fluctuations in the flow field in time and space. It is a complex process, mainly because it is 3D, unsteady, and consists of many scales. It can have a significant effect on the characteristics of the flow and the magnitude of heat transfer. Turbulence occurs when the inertia forces in the fluid become significant compared to viscous forces, and is characterized by a high Reynolds number (Equation 4.1). It is possible to directly predict turbulence using the Navier–Stokes equations that form the basis of CFD, however, the range of length scales and timescales required to do this requires enormous computer resources. Instead, turbulence models can be used, which account for the effects of turbulence without requiring a prohibitively fine mesh. The simplest of these are the statistical turbulence models. When looking at timescales much larger than the timescales of turbulent fluctuations, turbulent flow could be said to exhibit average characteristics, with an additional time-varying component. The Navier– Stokes equations are modified to produce the Reynolds averaged Navier–Stokes (RANS) equations. These equations model the mean flow quantities only. The averaging procedure introduces additional unknown terms containing products of the fluctuating quantities, which
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act like additional stresses in the fluid. These terms, called ‘‘turbulent’’ or ‘‘Reynolds’’ stresses, are determined using the turbulence model. Two-equation turbulence models are the most commonly used. This is because they offer a good compromise between numerical effort and computational accuracy. The k–« model [29] is the industry standard model and the most commonly used turbulence model found in the literature [6,8,9,30,31]. It uses two variables, the turbulent kinetic energy, k, and turbulence dissipation rate, «. It is, however, reputed to overestimate the air entrainment at the edge of the jet [4]. Navaz et al. [7] used the k–« model for the core flow, in combination with Cebeci–Smith algebraic model near the wall region, to avoid a high-resolution grid near the wall. There is another form of the k–« model called the renormalization group (RNG) k–« model. It is basically the same as traditional k–« model, the transport equations for turbulence generation and dissipation are the same, but the model constants differ. This model offers little improvement over the standard model and other authors [3] have obtained almost identical results with the two models. The biggest problem that the k–« model provides to the CFD user is that both k and « need to be defined at the inlets. To define k requires a knowledge of the turbulence intensity. Turbulence intensity can be measured using a very fine hot-wire anemometer. This equipment is expensive (>£2500), delicate, and generally not in the hands of retail display cabinet manufacturers, because of this, k is often estimated. Modern CFD codes offer reasonable default values and advice on how it can be estimated. « can be estimated using k and an appropriate length scale. If the level of turbulence is unknown and cannot be measured, a sensitivity analysis could be performed. This analysis could be used to see the effect of high and low levels of turbulence on the system, if the level of turbulence does not significantly affect the results then it is not important to know it accurately. Because the length to width ratio of a display cabinet air curtain is high, Ge and Tassou [31] suggested that the effect of initial turbulence intensity will be quite small. Stribling [9] compared the k–« and Reynolds stress model. The Reynolds stress model does not use the eddy viscosity hypothesis, but solves an equation for the transport of Reynolds stresses in the fluid and is therefore more computationally intensive. The difference between the two models was found to be less than that found between predicted and measured velocities. Statistical models are satisfactory in steady-state conditions; however, they can lead to errors in transient simulations. LES estimates the turbulent fluxes on the basis of vorticity theory. Cortella and D’Agaro [3] have found very different results when comparing LES and k–« models. 4.4.2.4
Buoyancy
The purpose of the air curtain is to provide a momentum force to oppose the buoyant force caused by the difference in density=temperature between the air inside and outside of the cabinet. The buoyant force therefore requires modeling to predict the system. One way of doing this is to model air as an ideal gas where its density is linked to the temperature by the ideal gas law: p ¼ rRT
(4:5)
However, this is numerically more complex and generally unnecessary given the limited temperature differences experienced with display cabinets. A numerically simpler approach is to use the Boussinesq approximation: r rref ¼ rref b(T Tref )
(4:6)
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This model uses a constant density fluid, but applies a local gravitational body force throughout the fluid, which is a linear function of fluid thermal expansivity and the local temperature difference with reference to a datum. The Boussinesq approximation is appropriate only if density variations are small, e.g., a few percent or less. Buoyant flow is more difficult to solve than nonbuoyant flow. The flow is likely to be unstable and can cause the CFD solver to crash or fail to reach an acceptable answer. It may be better to use a transient model and accept that there is no steady-state solution. If the model is of the ducting rather than the air curtain, the temperature differences are low and the forced convection component high and therefore a buoyant model will have little benefit over a nonbuoyant model. 4.4.2.5 Steady State or Transient? The airflow in the cabinet can generally be modeled as steady state. There will be a reduction of flow rate between defrost cycles as the evaporator coil ices up but this can be examined by carrying out steady-state models at both the higher and lower flow rate condition. Although turbulence is a transient phenomenon, statistical turbulence models allow a steady-state mean flow to be predicted. Food temperature will vary between defrost cycles and this effect could be modeled using a transient model. However, mean food temperatures could be predicted using a steady-state model. If using LES turbulence models the numerical solutions do not achieve a steady state, Cortella et al. [32] stopped their calculations when the time-averaged value of return air temperature stopped varying with time. 4.4.2.6 Humidity Humidity of the air has a significant effect on the display cabinet. A higher humidity in the ambient air will increase the heat load on the cabinet due to latent heat exchange through infiltration and will cause the evaporator to frost. Van Oort [8] and Ge and Tassou [31] have incorporated moisture content of the air into their CFD models. However, it is possible to solve the flow field for dry air and calculate the increase in load caused by the humidity using _ Lw Q1 ¼ awa m
(4:7)
4.4.2.7 Boundary Conditions The first stage of creating a CFD model is defining the domain to model. This can be deduced after careful consideration of the results gathered from the experimental investigation. The most common area of investigation is the air curtain. The boundaries of this domain are the discharge and return grille, rear grille, and the outside environment (ambient). A description of these boundary conditions follows. If another domain was chosen, e.g., the air inside the ducting of the cabinet, a different set of boundary conditions would be chosen. 4.4.2.7.1
Discharge Grille
The boundary condition used for the discharge grille is generally termed an ‘‘inlet.’’ A simple assumption used for the flow from the discharge grille is a constant velocity across the grille. This can be obtained by using a vane anemometer with a measurement head of similar size to the grille. In real cases, the air velocity from the grille is probably not uniform. Figure 4.3 shows measured velocities from a discharge grille, both before and after defrost. A more accurate profile can be entered into the model only if there are enough mesh cells covering this boundary to resolve it.
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1 0.9
Vertical velocity (m s−1)
0.8 0.7 0.6 0.5 0.4 0.3 Just after defrost Just before defrost
0.2 0.1 0 0
20
40
60
80
100
Distance from front of discharge grille (mm)
FIGURE 4.3 Velocity profile exiting discharge grille.
Turbulence will vary along the length of the jet, with the highest at the interface [16]. An accurate model of entrainment requires both setting the velocity and turbulence profiles at the outlet or predicting them by modeling the flow further upstream in the duct. 4.4.2.7.2
Rear Grille
The boundary condition for the rear grille is also set as an inlet. The rear grille usually comprises an array of holes punched out of a plate. To model the air flowing through each of the holes in the rear panel while also modeling the air curtain would require far too many grid cells and therefore would be too computer intensive. It would also require a 3D model unless the holes were modeled as slots. It is common to assume that all of the flow enters the rear grille through one large hole that covers the entire area of the rear grille. This assumption is probably correct a few hole diameters downstream of the rear panel, as all of the small highvelocity jets would entrain together to form one large low-velocity jet. Axell et al. [26] carried out simulations using three different assumptions for the round holes: (a) square holes (with the same hydraulic diameter as the circular holes), (b) thin slots (with the same opening area as a whole row of circular holes), and (c) wide slots (the width of a slot was the same as the diameter of the holes). The square-shaped holes gave the most accurate flow profile. However, by the time the flow had reached the front of the shelf, the profiles for all three assumptions were similar. 4.4.2.7.3
Return Grille
The return grille can be set as an ‘‘outlet’’ where the mass flow rate through the outlet is equal to the mass flow rate through all of the inlets (discharge grille and rear grille). 4.4.2.7.4
Ambient
If the entrainment of air from the surroundings is to be investigated, a boundary condition that simulates the ambient is required. Placing an ‘‘opening’’ type boundary, a few meters in front of the cabinet can be used. This opening boundary allows air to travel out or in depending on the pressure at that position.
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Product
As the primary function of a display cabinet is to keep food cold and not to cool it down, modeling the product temperature is often not necessary. The product may be modeled as an adiabatic or constant temperature obstruction to the flow and a steady-state solution carried out. The ability of the cabinet to keep the product cold can be derived from the air temperatures around the product. In reality the product will be warmer than the air around it because it gains heat via radiation. Faramarzi [11] showed the radiation load on the cabinet to be 12% and Madireddi and Agarwal [33] showed this to be 10% of the total load and therefore significant. The product temperature can be predicted by a combination of convection from the air to the product surface, conduction from the food surface into the body of the product, and radiation between the food surface and other surfaces in view. There are a number of radiation models available in CFD code. In the situation of modeling the radiation between surfaces of a display cabinet, the air is transparent to radiation. In this case, the radiation only affects the air by heating or cooling the surfaces of the domain, with no radiant energy transfer directly to the air. For this particular case the Monte Carlo model is the most appropriate. The Monte Carlo method simulates the physical interactions between photons and their environment. There is a computational overhead associated with tracking the photons across the domain and therefore a coarser mesh is used for the radiation field. In addition to the surface temperatures, the emissivity will also be required. Hawkins et al. [34] have carried out a study of the effects of low emissivity materials on display cabinets; this paper is a useful source to establish product emissivities. However, if none of the surfaces are shiny it is safe to assume all surfaces have an emissivity of 0.9. Heat transfer through the product (conjugate heat transfer (CHT)) requires that only the energy equation is solved in these regions, so compared with the same number of nodes in a fluid region CPU usage is reduced. Cortella [5] separated the prediction of load temperature and airflow due to the very different time constants of the transient phenomena involved. He used a finite element model to predict the product temperature and coupled this with a CFD code to predict fluid properties. 4.4.2.7.6
Walls
Walls of the cabinet can be modeled as nonslip walls, either adiabatic or constant temperature, if the temperature is known. It is of course possible to model the heat load through the walls of the cabinet given a known thickness and thermal conductivity. However, the heat load from conduction is only 4% of the total heat load [11] and therefore generally ignored. 4.4.2.7.7
Rear Duct
It is possible to extend the model of the air curtain to an entire circuit, i.e., for the flow to be modeled from the return grille through the evaporator and out through the discharge grille. In this case, the discharge return grille and rear grille would not be specified as inlet and outlet boundary conditions; instead the velocities and temperatures through these grilles would be predicted. Lan et al. [6] have carried out such a simulation. They used a porous region to simulate the rear grille. The advantage of this method is that the effect of holes within the plate (porous plate) can be modeled without the need for a complex mesh. The porous region effectively acts as a resistance to flow. Two parameters are required, the volume porosity and the Darcy coefficient. Lan et al. measured a volume porosity (the ratio of area of holes to total area) of 0.036.
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They used a Darcy coefficient of 0.2 to calculate the flow resistance in the direction through the holes. They used a large value for the Darcy coefficient for the direction perpendicular to this, as flow through the rear grille is unidirectional. They treated the perforated return grille and the evaporator in the same way. The evaporator is also a thermal sink. Heat can be removed from the volume to simulate the cooling of the evaporator. Lan et al. [6] adjusted the magnitude of the heat loss until it matched experimental measurements of temperature at the exit.
4.4.3 CONVERGENCE AND MESH INDEPENDENCE The level of accuracy of the predictions is defined by the residual error. This residual error should decrease with each iteration; if this happens, the solution is said to be converging. When the residual error has converged to a satisfactory level, the predicted values can be taken as the output and viewed by a graphical viewer. It is at this point where the CFD user who has knowledge of the fluid dynamics of the system he or she is trying to model will hopefully spot any errors or misjudged assumptions in the predictions. It is likely the first predictions may contain errors, may not have converged to the necessary accuracy, or the mesh was not fine enough. After corrections have been made to the model, the numerical error should be assessed. Judgment of convergence is a bit of a black art, however, the following rules [35] are a guide. The size of the maximum residual if .
. . .
.
.
>5 104 is very poor, global balances will be poor and quantitative data is largely unreliable (this is good enough for getting a rough idea of flow phenomena or making pretty pictures) 5 104 is loose convergence, but good enough for most engineering applications 1 104 is good convergence, often sufficient for most engineering applications 5 105 is tight convergence (if geometry and boundary conditions are not well defined, then this may be more than necessary (since errors in the geometry=boundary undary conditions will be greater than this) and it is often not possible to achieve this level of convergence) 1 105 or lower is very tight convergence, sometimes required for geometrically sensitive problems 1 106 to 1 107 is machine round-off (this level of convergence is not possible without double precision, in most cases and convergence this tight is only of academic interest)
Typically root mean square (RMS) residuals are about a factor of 10 smaller than the maximum residual, and so the above guidelines for maximum residuals can also be applied to RMS residuals, with the targets reduced appropriately. If the solution is still converging beyond your specified residual level, it is valuable to converge to a lower solution to establish whether further convergence will change your results appreciably. If a buoyant model is being used, which will be the case if the air curtain is being studied, convergence will be more difficult. A solution to this problem is to reduce the size of the time step; this will make the model take longer to run, but will increase its accuracy. Cortella and D’Agaro [3] used a time step of 0.01 s and RMS residual of 104 for transient simulation of the air curtain. Opening boundaries, which have both inflow and outflow, may be required in modeling the ambient entrainment for the air curtain. These boundaries can lead to instabilities that
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impede convergence to the desired residual level. By keeping these boundaries a distance from the area of interest, e.g., the air curtain, it is less likely that they will effect it. By monitoring the result of interest, e.g., a product or return grille temperature, etc., during the convergence it will be possible to assess whether the desired result has reached a constant value. Once the solution has converged satisfactorily, a check will need to be made that the solution is mesh independent. This means that if the mesh is refined, the solution will not change. This can happen if the mesh that has been applied to the problem is not small enough to resolve the physics, e.g., to pick up recirculation zones. If heat transfer is being predicted from a wall to the air it is important to ensure that wall boundary layers have adequate mesh resolution. The mesh resolution in a boundary layer affects the prediction of convective heat transfer and the temperature gradient near the wall. For walls without a specified temperature, e.g., the surface of the product, the temperature gradient near the wall affects the calculated surface temperature and, consequently, the amount of radiation emitted (if radiation is being modeled).
4.4.4 POSTPROCESSING Visualization of the results is arguably the most exciting part of the CFD analysis. It is at this point where it may become obvious that the CFD model is an error and the reasons why may or may not be obvious. If the model is correct, the results may reinforce what is already known. This may not be a bad thing since one of the advantages of CFD is its ability to convey knowledge of how a retail display cabinet works. The author has shown CFD visualization to people who have worked with display cabinets for many years but had never seen the airflow represented in such a clear manner as with CFD. It is also possible that the visualization will show something unexpected; this can be very exciting, especially if it can be experimentally verified. A personal example of this was when a CFD model predicted an unexpected vortex in the corner of display cabinet, which was later verified using laser doppler anemometry (LDA) [36]. Modern CFD software has a multitude of colorful ways of representing the predictions. For 2D models of display cabinets, color contours representing the temperature and vectors representing the air velocity are most commonly used (Figure 4.4). For 3D models the contours and vectors can be plotted in representative planes. It is sometimes necessary to visualize the flow through the whole 3D region without being confined to 2D planes. This can be achieved by plotting streamlines (Figure 4.6). The airflow from a region, e.g., from the air discharge grille, can be followed through the 3D domain and out through another boundary, e.g., through an ambient opening. Postprocessing is an important step in the CFD analysis process. CFD generates large quantities of data and this must be clearly presented. The postprocessing tool allows the user to qualitatively visualize flow and also to extract quantitative numbers for direct comparison with experimental data and assessment of performance. These postprocessors are normally built into the CFD suite of software and often not available when the results are to be presented to an external audience. Exporting graphical images of areas of interest and displaying in Microsoft PowerPointß are a common ways of disseminating the results. Postprocessors often allow animations to be exported so that transients can be more easily represented and these can be imported into Microsoft PowerPoint. The problem with this type of dissemination is that 3D models cannot be rotated, which can be very useful for visualizing the flow. If data is exported in virtual reality modeling language (VRML) output, this holds the 3D geometry and using a VRML viewer this geometry can be rotated.
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Temperature
15 mm
−0.0
−0.8
−1.5
−2.3
Product
−3.0 [°C] Y
z
X
CFX
FIGURE 4.4 (See color insert following page 142.) Velocity vectors predicted by CFD in a vertical plane at the top of the cabinet. The length of the vector is proportional to the air velocity, the color represents the temperature (air curtain 1.5 m s1 and 15 mm).
Presenting CFD visualization in scientific publications is difficult as they are generally grayscale. Although CFD visualization can be output in grayscale, it is not easy conveying all the information in a grayscale figure. Many publications now have a Web-based version and this will usually allow color figures.
4.5 RESULTS FROM TYPICAL SIMULATIONS The following section shows results from typical simulations, which have been published by this author.
4.5.1 AIR CURTAIN A multideck cabinet originally designed to meet the EN441 M2 (18C to 78C) classification was required to perform to the M0 (18C to 48C) temperature classification. CFD was used as a tool to recommend design improvements to achieve this. The cabinet was lightly loaded (in accordance with the requirements for loading a cabinet intended for storage of sensitive products) with gaps present between shelves that enabled vortices to be generated. Prior to modifications the temperature of all ‘‘m’’ packs was above 18C and below 78C. However, only 42 m-packs (out of 54) spent the entire test period between 18C and 48C. A maximum temperature of 6.98C was measured in the m-pack positioned at the top right front of the well. A minimum temperature of 18C was recorded in the m-pack situated at the top rear left of the well. The area of most concern in terms of high temperatures was located at the center and right front of shelf 1 and the front edges of the well. The flow of air as it exited the discharge grille and traveled down the cabinet was simulated. To reduce complexity of the model and concentrate on the area of interest, the air curtain for only the top shelf was modeled. The existing air curtain exiting the discharge
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60 mm
Temperature −0.0
−0.8
−1.5 Product −2.3
−3.0 [°C]
Y Z
X
CFX
FIGURE 4.5 Velocity vectors predicted by CFD in a vertical plane at the top of the cabinet. The length of the vector is proportional to the air velocity; the color represents the temperature (air curtain 0.375 m s1 and 60 mm).
grille had a velocity of 1.5 m s1 and a temperature of 18C, with the jet pointing vertically downwards. The width of the air curtain was 15 mm. The problem was considered to be 2D as the cabinet and air curtain were very long; therefore, end effects could be ignored. Turbulence was likely to be an important factor and was therefore modeled using the k–« model. Buoyancy was also another important factor as it is the difference in density caused by temperature difference between inside and outside the cabinet, which causes deflection of the air curtain. The CFD model predicted that the air curtain would be bent towards the product and hit the outer corner of the product (Figure 4.4). A vortex was then created, which draws warmer air over the front of the product. The air curtain would also be disrupted bringing warmer air onto the shelves below. CFD modeling was used to investigate the effect of a number of modifications including changing the width and angle of the curtain. Increasing the width of the air curtain to 60 mm, while keeping the volume flow rate through the air curtain constant, was predicted to remove the vortex. This was likely to keep the product cooler and also maintain a better air curtain for the next shelf down (Figure 4.5). The CFD predictions also showed that there were benefits in angling the air curtain away from the shelves, and that the optimum angle depends on the width and velocity of the curtain.
4.5.2 MODELING OF
THE
DUCT
The cabinet used in the previous section also had an uneven temperature left to right, which could not be attributed to the airflow in the room. Asymmetries within the duct were examined. It is not possible for the evaporator to run the full width of the cabinet due to the turns at the ends of the evaporator; these are often greater on one side of the evaporator than the other. These problems can lead to both a 3D and unsymmetrical flow within the duct.
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Rear duct
Evaporator Z Y
X
Dead space CFX
FIGURE 4.6 Streamlines predicted by CFD from the exit of the evaporator for the unmodified cabinet.
The cabinet presented in the previous section had a 110 mm gap between each end of the duct and the evaporator. Air, which exited the evaporator, had therefore to change in direction by 908 to enter the edge of the duct. CFD was used to model the flow of air as it exited the evaporator and entered the rear duct. Only the bottom edge of the cabinet was considered, where air from the evaporator was required to fill the dead space previously identified at the edges of the cabinet. Figure 4.6 shows streamlines predicted by CFD from the exit of the evaporator for the unmodified cabinet. The predictions show that as air leaves the evaporator it moves out to the side to fill the dead space and then travels up the rear duct. In doing so the air spirals up the rear duct at the edge. This type of airflow was likely to result in vortices as the air entered the cabinet rather than the uniform flow required. To address this problem the following design solutions were proposed: 1. Make the evaporator as wide as possible (reducing the length of the dead space). 2. Move the evaporator towards the front of the cabinet and create an angle such that the air would more easily move to the edge of the duct. 3. Insert an angled plate at the bottom of the duct to increase the pressure and even-out the flow. Figure 4.7 shows streamlines predicted by CFD from the exit of the evaporator for the modified cabinet (length of evaporator extended such that there was only a 50 mm dead space at each end of the cabinet, evaporator moved forward by 80 mm, angle to expand air to the edge of the duct and a turning vane). With these modifications the CFD predicted that no vortex would develop.
4.5.3 SHELVING To minimize disruption of the air curtain it is ideal to have the front of the shelves present as flat a face as possible [37]. Shelves fully loaded with product to the edge of the shelf help
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Turning vane
Z Y
X
CFX
FIGURE 4.7 (See color insert following page 142.) Streamlines predicted by CFD from the exit of the evaporator for the modified cabinet.
achieve this. As the product is removed from the shelves during the buying process a larger gap appears for the air curtain to negotiate. This causes the air curtain to bend inwards, causing more entrainment (Figure 4.8). Infiltration rates with varying shelving=product were predicted using the CFD model. These infiltration rates were put into a refrigeration model to predict energy consumption of the compressor. They showed that when the cabinet was fully loaded the energy consumption was least (570 W per meter length of cabinet). The energy consumption increased to a maximum when all shelves=product were removed (653 W per meter length of cabinet).
4.5.4 COLD FEET EFFECT The cold feet effect is caused by mixing between the air curtain and environment as discussed in Section 4.2. Foster and Quarini [38] studied the cold feet effect. The aim of the work was to quantify the effect in three supermarket chains and use CFD to investigate ways of alleviating it. Two different scales of CFD model were used. 4.5.4.1 Whole Store The first was of the whole store sales area; this was run on a Silicon Graphics R10000 workstation with 256 Mb RAM. The store was ventilated by inlet diffusers, which forced air out in four directions (towards the front, back, and both sides of the store). Because of this, each of the 13 diffusers had to be modeled as 4 separate inlets, giving a total of 52 inlets in the model. The inlets were modeled as constant velocities of 4.2 m s1 at an angle of 458 to the ceiling. The temperature of the air at the inlet was 268C. These data were taken from measurements carried out at the store. The eight return diffusers were modeled as mass flow boundaries. By design, only half the air that entered the store, left through these diffusers.
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FIGURE 4.8 (See color insert following page 142.) 2D model of a multideck display cabinet showing velocity vectors and temperature contours. The air curtain is bent in toward the cabinet where shelves have been removed.
This was to keep the store at a slightly higher pressure than outside to avoid ‘‘dirty’’ air entering the store. It was considered that most of this air would exit through doorways. Putting each of the doorways into the model would have made it too complex (in terms of the number of mesh points). Therefore, a mass flow boundary was set along the bottom of the four side walls. The cabinets and shelving were modeled as solid blocks to restrict flow around the store. For the refrigerated cabinets (chilled and frozen) a heat sink was set in front of the blocks. This simulated the quantity of heat removed from the store. The values were chosen from ASHRAE [39] and varied for the different types of refrigerated cabinet. The store had a heated floor in the chilled and frozen aisles during the winter. The heated floor was simulated by setting a constant temperature boundary condition of 198C and a heat transfer coefficient of 9.3 W m2 K1. The internal dimensions of the store were 64 m 37 m 24 m. The geometry was divided into a grid of 130,000 cells, with a resolution of between 30 and 600 mm. This number of grid cells was quite large when the work was carried out in 1997 and needed to be run on a UNIX workstation. This is now considered to be a small number of grid cells and could easily be run on a desktop personal computer (PC). Figure 4.9 shows predicted and measured temperatures of the supermarket store at two heights. Although the temperatures predicted were not the same as measured, the trends were very similar. The model clearly showed that the level of stratification reduced significantly between the chilled and ambient aisles. It showed that the temperature at floor level was dictated by the location of the chilled cabinets. At a height of 2 m the model showed that the cabinets had little effect and that the temperature range was small. The model also showed that warm air from the inlets did not spread very far.
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19.1
21.7
19.6
22.1
21.9
21.5
21.8
22.1
22.0
18.0
22.0
18.1 16.7
> 2.9000E + 02 2.8773E + 02 2.8462E + 02 2.8150E + 02 2.7838E + 02 2.7527E + 02 < 2.7300E + 02
22.4
18.2
> 2.9800E + 02 2.9720E + 02 2.9610E + 02 2.9500E + 02 2.9390E + 02 2.9280E + 02 < 2.9200E + 02
13.3
13.3 14.3 12.6
0.25 m above floor
21.8
21.6
21.1
21.7 22.2 22.4 22.4
16.5
23.3
2 m above floor
FIGURE 4.9 (See color insert following page 142.) Plan view of store at a height of 0.25 m and 2.0 m. Colors show predicted temperatures (K) and values of measured temperature (8C) are superimposed.
4.5.4.2 Aisle The computer model of the whole store was too large to model detail in the store and the time taken for convergence was too long to carry out many what-if scenarios in a limited time. To reduce the complexity of the model, just a chilled aisle was modeled. Three symmetry planes were used to reduce the number of grid cells further. The cabinet was modeled as a solid object with an inlet boundary at the top face blowing cold air vertically downward. An outlet boundary was positioned at the bottom of the cabinet. The temperature and velocity at the inlet were 28C and 1.0 m s1, respectively. Warm ambient air was required to enter and leave the domain. Previous modeling and experiment showed that cold air escaped at floor level out of the aisle and warm air entered at high level. Because of the positions of the symmetry planes, the floor and ceiling of the model, there was only one boundary face that could exchange this air and it was at the end of the aisle. A constant pressure boundary was chosen to simulate the air entering and leaving the aisle. The temperature of air entering the aisle was 228C and the temperature of the floor wall–boundary was 148C (these were taken from measurements). Predicted and measured temperatures in chilled aisles in three different supermarkets are shown in Figure 4.10. The simulation was found to be a good approximation of the three different stores. The temperature near the floor, the gradient of the temperature stratification, and the constant temperature region above the cabinet were all predicted accurately. This model was then used to predict the effect of different heating and ventilation strategies. These were heated floors, air mixing, which drew cold air from under the cabinet and projected it upwards between the cabinets and high velocity vertically blowing fans in the center of the aisle. The CFD model was able to predict the effect of these strategies and relay them back to the supermarket heating and ventilation engineers. Tassou and Xiang [40] carried out a very similar study. They also found the complexity of modeling the entire store too great and chose to model an aisle using the same symmetry planes. However, with more modern hardware, they were able to model the food within the
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25 23
Temperature (°C)
21 19
Safeway center Sainsbury center ASDA center CFD center Safeway end Sainsbury end ASDA end CFD end
17 15 13 11 9 7 0.0
1.0
2.0
3.0
4.0
5.0
Distance from floor (m)
FIGURE 4.10 Temperatures measured at two positions in three different stores in the coldest aisles and temperatures predicted from the numerical model.
cabinet. They showed that under-floor heating had little effect on air temperatures in the aisle (18C or 28C in the center of the aisle); this is in agreement with the work by Foster and Quarini. It is important to note that although the cabinet has an effect on the store environment, the store environment also has an effect on the cabinet. As Tassou and Xiang’s model included the product they were able to simulate this. They showed that the heated floor causes a temperature rise on the surface of the products facing the aisle of around 2.28C and a rise at the core of the product of approximately 0.88C. This was due to heat transfer by radiation between the floor and the chilled products in the cabinet. Increasing the heat flux on the floor would reduce cold discomfort but would have a detrimental effect on the chilled products in the cabinet.
4.6 VERIFICATION Verification is an important part of any type of simulation. Navaz et al. [7] state that CFD needs to be calibrated. It is all too easy to accept the simulation as correct because it looks right. Only through verification of your simulation will you gain the confidence to trust further simulations. Due to the complexities of the flow within retail display cabinets, many assumptions are used to create a CFD simulation. Verification will provide the only real proof of the accuracy of these assumptions. If verification shows the model to be inaccurate these assumptions will need to be reviewed and a more accurate simulation attempted. Verification can range in complexity and there are a number of methods that can be used to validate a CFD model. These extend from the simplest methods that may provide just one important value by which to validate the model, to highly complex experimental methods that provide transient values at many positions. Measurement of temperature is the easiest method of validation, as this can be measured simply and cheaply using thermocouples at multiple positions. Madireddi and Agarwal [33]
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used an infrared (FLIR Systems) thermal imaging camera to compare temperature contours of the air curtain with those predicted by CFD, although the method in which this was done has not been reported. Measurement of velocity is more expensive and complicated. As velocity is a vector quantity, a direction as well as a magnitude needs to be measured. Vane anemometers can be used; however, they need to be lined up with the direction of the flow, which needs to be ascertained if not known. They are also large and therefore give an average velocity over a relatively large area. Hot-wire anemometry is another method by which to measure velocity. They are less susceptible to the direction of flow and measure over a much smaller area. A large number of hot-wire anemometer measurements are required to build up a picture of the airflow of a refrigerated display cabinet and their use can disrupt the already turbulent airflow. Axel et al. [26] showed that hot-wire anemometers should not be installed too close to each other. They showed that disturbances between sensors can be created by natural convection and by the size and shape of the sensor. If it is connected to a traverse, as used by Howell and Shibata [13] to study heat transfer through turbulent recirculated plane air curtains, the velocity at known positions in the air curtain can be measured without too much disruption. If the hot wire is fine enough and connected to a high-frequency data logger, the turbulence of the jet can also be measured. Direction of the velocity is a more difficult value to measure; it can be done using smoke or tufts of tissue paper. Recording the flow direction at multiple points requires some image analysis. If infiltration through the curtain is the important value you are trying to validate, then validating the air curtain velocity is an indirect way of doing this. A better and more direct way to do this would be to measure the infiltration by tracer gas techniques. Axell and Fahlen [10] have used a tracer gas to study infiltration through the air curtain. There are many types of gases which can be used. Sulfur hexafluoride (SF6) is advantageous as it can be detected at extremely low concentrations; however, it requires expensive mass spectrometry to do this. Carbon dioxide (CO2) has disadvantages in that there is a fine line between high enough concentrations to measure and low enough to be safe. However, it can be detected using much cheaper infrared meters. Particle image velocimetry (PIV) offers an ideal method of verifying CFD simulations, as it can provide a similar level of resolution of the flow field as the simulation. PIV has been used by Navaz et al. [41] together with LDA and CFD to study the flow field of an air curtain in a fully loaded open vertical display cabinet with horizontal shelves. Particle image velocimetry provides noninvasive velocity measurements and visualization in a cross section of airflow. The velocity vectors are derived from the movement of seeding particles between two light pulses. The target area for the measurements is illuminated with a light sheet and a digital camera is used to image the target area onto a charge-coupled device (CCD) array. The CCD is able to capture each light pulse in separate image frames. Once a sequence of two light pulses is recorded, the images are divided into small subsections called interrogation areas. The interrogation areas from each image frame are cross-correlated with each other thus identifying a common particle displacement and hence velocity. This is repeated for each interrogation area, creating a vector map of the complete target area.
4.7 CONCLUSIONS Chilled multideck retail display cabinets are a common mechanism for displaying chilled food. Getting these cabinets to meet the tight temperature standards required by supermarkets and also to be energy efficient is expensive by conventional means.
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CFD modeling has been proved by many authors to be an invaluable tool in understanding the heat transfer mechanisms of retail display cabinets. Although CFD modeling in this industry is still in the hands of academics, whose project timescales are an order of magnitude longer than industrial project timescales, this is beginning to change. CFD software has become more user-friendly, operates on standard desktop PCs, and reasonable predictions can be obtained in days rather than months (total timescale of generating the model to final conclusions ready to test). However, it should be remembered that anybody can obtain a colorful picture that looks correct, it is still necessary to have a user with an understanding of the physics and to experimentally validate test results. CFD is not yet at the stage and may never be, where testing and validation can be eliminated. For this reason CFD should be considered as a tool to allow the reduction of testing not its elimination.
NOMENCLATURE D e g H QDG QRG Re Ri DT TRG TDG Tamb Tref u
Hydraulic diameter (m) Entrainment ratio, dimensionless Acceleration due to gravity (9.81 m s2) Height (m) Mass flow rate at the discharge grille (kg s1) Mass flow rate of the jet at the return grille (kg s1) Reynolds number, dimensionless Richardson number, dimensionless Temperature difference (K or 8C) Temperature at return grille (K or 8C) Temperature at discharge grille (K or 8C) Temperature at ambient (K or 8C) Reference temperature (K or 8C) Velocity (m s1)
GREEK SYMBOLS a b r rref m
Thermal entrainment coefficient, dimensionless Coefficient of expansion, dimensionless Density (kg m3) Reference density (kg m3) Viscosity (kg m1 s1)
REFERENCES 1. P Olsson. Chilled cabinet surveys. In: Processing and Quality of Foods. Vol. 3. London: Elsevier Applied Science, 1990, pp. 279–288. 2. SJ James, JA Evans. Temperatures in the retail and domestic chilled chain. In: Processing and Quality of Foods. Vol. 3. London: Elsevier Applied Science, 1990, pp. 273–278. 3. G Cortella, P D’Agaro. Air curtains design in a vertical open display cabinet. In: Proceedings of International Institute of Refrigeration, Urbana, 2002, pp. 57–65. 4. JN Baleo, L Guyonnaud, C Solliec. Numerical simulations of air flow distribution in a refrigerated display case air curtain. In: Proceedings of International Institute of Refrigeration, The Hague, 1995, pp. 681–687. 5. G Cortella. CFD aided retail cabinets design. Computers and Electronics in Agriculture 34: 43–66, 2002.
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6. TH Lan, DHT Gotham, MW Collins. A numerical simulation of the air flow and heat transfer in a refrigerated food display cabinet. In: Proceedings of the European Thermal Sciences, Rome, 1996, pp. 1139–1146. 7. HK Navaz, R Faramarzi, M Gharib, D Dabiri, D Modaress. The application of advanced methods in analyzing the performance of the air curtain in a refrigerated display case. Transactions of the American Society of Mechanical Engineers, Journal of Fluids Engineering 124(3): 756– 764, 2002. 8. H Van Ort, RJM Van Gerwen. Air flow optimisation in refrigerated cabinets. In: Proceedings of International Institute of Refrigeration, The Hague, 1995, pp. 446–453. 9. D Stribling, SA Tassou, D Marriot. A two dimensional CFD model of a refrigerated display case. Transactions of the American Society of Heating Refrigerating and Air Conditioning Engineers 103(1): 88–95, 1997. 10. M Axell, P Fahlen. Climatic influence on display cabinet performance. In: Proceedings of International Institute of Refrigeration, Urbana, 2002, pp. 175–184. 11. R Faramarzi. Efficient display case refrigeration. Ashrae Journal 41(11): 46–54, 1999. 12. Van Baxter. Energy-efficient supermarket display cases. IEA Heat Pump Newsletter 22(3): 14–16, 2004. 13. RH Howell, M Shibata. Optimum heat transfer through turbulent recirculated plane air curtains. Transactions of the American Society of Heating Refrigerating and Air Conditioning Engineers 86(1): 188–200, 1980. 14. FC Hayes, WF Stoecker. Heat transfer characteristics of an air curtain. Transactions of the American Society of Heating Refrigerating and Air Conditioning Engineers 2120: 168–180, 1969. 15. N Rajaratnam. Turbulent Jets. Amsterdam: Elsevier Scientific, 1976. 16. HK Navaz, BS Henderson, R Faramarzi, A Pourmovahed, F Taugwalder. Jet entrainment rate in air curtain of open refrigerated display cases. International Journal of Refrigeration 28(2): 267–275, 2005. 17. YG Chen, XL Yuan. Experimental study of the performance of single-band air curtains for a multi-deck refrigerated display cabinet. Journal of Food Engineering 69(3): 261–267, 2005. 18. EN441-4:1995. Refrigerated Display Cabinets. General Test Conditions. CEN, European Standard. 19. EN441-5:1996. Refrigerated Display Cabinets. Temperature Test. CEN, European Standard. 20. EN441-6:1995. Refrigerated Display Cabinets. Classification According to Temperature. European Standard. 21. EN441-9:1995. Refrigerated Display Cabinets. Electrical Energy Consumption Test. European Standard. 22. BS EN ISO 23953-1:2005. Refrigerated Display Cabinets–Part 1: Vocabulary. 23. BS EN ISO 23953-2:2005. Refrigerated Display Cabinets–Part 2: Classification, Requirements and Test Conditions. 24. Enhanced Capital Allowance Scheme, The Carbon Trust, http:==www.eca.gov.uk, London, UK. 25. P D’Agaro, G Croce, G Cortella, P Schiesara. Investigation on air curtains behavior in display cabinets by means of 3-d computational fluid dynamics. In: Proceedings of International Institute of Refrigeration, Vicenza, 2005, pp. 71–78. 26. M Axell, PO Fahlen, H Tuovinen. Influence of air distribution and load arrangements in display cabinets. In: Proceedings of International Institute of Refrigeration, Sydney, 1999, paper 152. 27. RH Howell. Effects of store relative humidity on refrigerated display case performance (rp-596). Transactions of the American Society of Heating Refrigerating and Air Conditioning Engineers 99(1): 667–678, 1993. 28. G Cortella, M Manzan, G Comini. CFD simulation of refrigerated display cabinets. International Journal of Refrigeration 24(3): 250–260, 2001. 29. BE Launder, DB Spalding. The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering 3: 269–289, 1974. 30. W Xiang, SA Tassou. A dynamic model for vertical multideck refrigerated display cabinets. In: Proceedings of International Institute of Refrigeration, Sofia, 1998, pp. 637–644. 31. YT Ge, SA Tassou. Simulation of the performance of single jet air curtains for vertical refrigerated display cabinets. Applied Thermal Engineering 21(2): 201–220, 2001.
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32. G Cortella, M Manzan, G Comini. CFD simulation of refrigerated display cabinets. International Journal of Refrigeration 24(3): 250–260, 2001. 33. S Madireddi, R Agarwal. Computation of three-dimensional flow field and heat transfer inside an open refrigerated display case with an air curtain. In: Proceedings of International Institute of Refrigeration, Vicenza, 2005, pp. 79–86. 34. AC Hawkins, CA Pearson, D Raynor. Advantages of low emissivity materials to products in commercial refrigerated open display cabinets. In: Proceedings of Institute of Refrigeration, London, 1973, pp. 54–64. 35. ANSYS CFX User Manual, online. 36. Application of CFD and 3 component LDA to refrigerated cabinet flows. FPERC Newsletter, University of Bristol, 16: 4–5, 1997. 37. AM Foster, SJ James. Using CFD in the design of food cooking, cooling and display plant equipment. In: Second European Symposium on Sous vide, Leuven, 1996, pp. 43–57. 38. AM Foster, GL Quarini. Using advanced modelling techniques to reduce the cold spillage from retail display cabinets into supermarket stores to maintain customer comfort. Proceedings of the Institution of Mechanical Engineers Part E. Journal of Process Mechanical Engineering 215(1): 29–38, 2001. 39. ASHRAE (American Society of Heating, Refrigeration and Air Conditioning Engineers), Handbook, Applications, 1991, pp. 2,3. 40. SA Tassou, W Xiang. Interactions between the environment and open refrigerated display cabinets in retail food stores-design approaches to reduce shopper discomfort. Transactions of the American Society of Heating Refrigerating and Air Conditioning Engineers 109(1): 299–306, 2003. 41. HK Navaz, R Faramarzi, M Gharib, D Dabiri, D Modarress. The application of advanced methods in analyzing the performance of the air curtain in a refrigerated display case. Transactions of the American Society of Mechanical Engineers Journal of Fluids Engineering 124(3): 756–764, 2002.
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CFD Design of Air Curtain for Open Refrigerated Display Cases Homayun K. Navaz, Ramin Faramarzi, and Mazyar Amin
CONTENTS 5.1 5.2 5.3
Background................................................................................................................ 129 Introduction ............................................................................................................... 130 Model Description ..................................................................................................... 131 5.3.1 Outside Domain ............................................................................................. 134 5.3.2 Inside Domain ................................................................................................ 136 5.4 Conclusion ................................................................................................................. 139 Acknowledgment................................................................................................................ 140 Nomenclature ..................................................................................................................... 140 References .......................................................................................................................... 140
5.1 BACKGROUND Open vertical refrigerated display cases are widely used in supermarkets and grocery stores to maintain the food products at a prescribed temperature while allowing the customers to easily reach for the food products. The operation and main features of all contributors to the dynamics of an air curtain are shown in Figure 5.1. The cold air is supplied to the case through a discharge air grille (DAG) at the top and in some cases through a perforated back panel (BP). A fan located at the lower portion of the case pulls the air flow toward a return air grille (RAG) that is recirculated after coming into contact with cold coils. The air curtain is referred to the region of air flowing from the DAG to the RAG. The existence of a momentum gradient between the air curtain and its surrounding air causes an entrainment of the outside warm air that will partially mix with the cold air forming the air curtain. Therefore, the temperature of the air curtain as it travels down toward the RAG increases. Since the total air flow rate inside the display case is constant, a portion of the entrained air will overspill from the case after mixing with the cold air curtain. The overspill air temperature is higher than the cold air temperature originating from the DAG and lower than the room temperature. Similarly, the temperature of the air at the RAG is between the cold air and warm air temperatures. The magnitude of the air temperature at the RAG and also for the overspill air is a function of the amount of entrained air and turbulence-enhanced mixing
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Discharge air grille (DAG) or honeycomb
Entrained air
Overspilled air (mixture of warm and cold air)
Air curtain
Return air grille (RAG)
Coil
Back panel (BP)
Fan
Coils
FIGURE 5.1 Main features of an open refrigerated display case.
of cold and warm air along the air curtain flow. The portion of the warm air that is mixed with the cold air and is going through the RAG is referred to as the infiltration rate. It appears that the infiltration rate is directly proportional to the entrainment rate; however, this may not be a sufficient condition, i.e., higher entrainment rate does not necessarily result into an increase in infiltration rate. The ‘‘effectiveness’’ of mixing and structural integrity of the air curtain thereafter has also a significant effect on the infiltration of the warm air into the display case.
5.2 INTRODUCTION The motion of fluids is controlled by the mass and momentum conservation differential equations referred to as the Navier–Stokes (NS) equation. In many engineering applications a flow of heat (energy) also is accompanied by the transport of mass and momentum. The NS equations are usually augmented by adding the energy conservation equation, resulting from the first law of thermodynamics. Therefore, referring to NS equations usually includes the energy conservation equation. Before the advent of computers, the solution to these nonlinear set of equations could have only been obtained for a limited number of simple problems involving fluid flow and heat transfer. In the past, most of the equations developed for engineering applications mostly relied on dimensional analysis (similitude) and calibration of such correlations based on experimental data and curve fitting. Although this provided a very practical tool for engineers in terms of a global approach, it lacked the detailed information needed for close examination of a system leading to an optimized design. Obtaining solutions to NS equations became more of a reality with the development of faster computers during the 1980s and gave birth to the computational fluid dynamics (CFD) area in engineering and mathematical sciences. One of the first NS solvers was developed at Los Alamos National Laboratory called VNAP [1] and was based on MacCormack explicit predictor–corrector scheme. A semi-implicit algorithm for incompressible flow was developed by Qin and Spalding [2] and a family of semi-implicit commercial codes [3–5] was spun off the
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original algorithm thereafter, and all of them are commercially available through different vendors. A more detailed discussion of the CFD genesis is given by Navaz and Berg [6]. However, it was not until mid-1990s that the commercial industry felt comfortable with CFD applications mainly due to the difficulties that were usually encountered in tedious process of setting up a model for a CFD run including the mesh generation. Introducing interactive front end (IFE) for data entry and advances in grid generation somewhat simplified this process. In recent years, using CFD application has become an integrated part of most design processes involving fluid flow or heat transfer. In spite of all the progress in the field of CFD, care should be taken in using and interpreting the results of a CFD code. The numerical solution to NS equations is still an approximation; they still rely on embedded models such as turbulence, evaporation, etc., and last but not least the existence of multiple solutions for a problem is a possibility. So, it is fair to state that the CFD technique is still evolving and at this point they are not independent of validation and verification tests. For several years CFD tools were mainly used in aerospace industry for finding solutions to rocket engine and shock layer flows. It was not until 1990s that CFD found its way into the automotive industry due to the ongoing progress in the field of numerical techniques. During late 1990s CFD applications found their way into analyzing mainly the air flow, heating and=or cooling in food industry [7,8]. A comprehensive review of the previous literature demonstrates that CFD is a powerful tool that can be implemented for parametric study of air flow as applied to air curtains or refrigeration systems [8,9]. Such studies, if performed in a systematic and meaningful way, can lead to design optimization of such systems. The intention of this work is not only to demonstrate that CFD can be used as a viable design tool, but also to lay out a methodology of implementing it in a systematic and cohesive manner to ensure reliable results. Before attempting such extended and comprehensive studies a protocol should be designed and followed. The purpose of this research was to develop such a protocol or methodology to show the effectiveness of CFD tools in performing parametric studies to lower infiltration of the warm air into the air curtain leading to the design of more energy-efficient open refrigerated display cases.
5.3 MODEL DESCRIPTION CFD provides detailed local information about the fluid flow, therefore, giving insight into ways to alter a design for better performance. Furthermore, when validated, it can be used as a tool to perform parametric studies with a high level of confidence leading to optimization of a design. Generally, in open refrigerated display cases, it is desired not only to reduce the entrainment of warm and moist air onto the air curtain air flow stream, but also to minimize its mixing rate with the cold air. Achieving these two goals will reduce the infiltration of the warm moist air into the display case through the RAG. It is important to quantify the amount of entrained warm and moist air and its partial infiltration into the cold air curtain as a function of design parameters. To accomplish this, it is preferred to decouple the flows inside and outside of the display case. This approach will eliminate the need for the modeling of the fan by only considering the end result of its operation, i.e., the total air flow rate inside the display case. However, this approach requires a priori knowledge of velocity profile, volumetric flow rate, and turbulence intensity at certain boundaries of the domain. This information can only be achieved by direct measurements at these boundaries referred to as boundary conditions that are needed for the CFD applications. To clarify the proposed two-domain approach, the schematics of ‘‘inside’’ and ‘‘outside’’ domains are shown in Figure 5.2. The cold air exits from the DAG and the BP and after mixing with the outside warm air, it enters the display case through the RAG. Since the problem is divided into two
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BPF
DAG
Shelf
BPF Outside domain Shelf
BPF
Inside domain
Constant temperature open boundary
Wall
Wall
Shelf
BPF
RAG Plexiglas Coils Wall
FIGURE 5.2 Schematic of the inside and outside domains with boundary conditions.
domains, care must be taken in implementing the boundary conditions for the CFD analysis. This is important because the boundary conditions set the process of information propagation throughout the domain and the final solution thereafter. Experimental methods are used to properly specify the boundary conditions that are required for each domain as discussed later. Experimental methods can also be used to validate and verify the computational procedure. Accurate definition of boundary conditions for the DAG is even more important than other boundaries because it is the origin of the air curtain and its characteristics will affect the behavior of an air curtain. The boundaries that need to be specified are shown in Figure 5.2 and they will be discussed further. Earlier studies [10] have indicated that for the range of Reynolds number considered in this work (>2000), the temperature gradient across the air curtain does not contribute to the entrainment and infiltration as much as the momentum gradient. Therefore, temperature will not be considered as a major contributor to the infiltration rate in this work. An open vertical refrigerated display case manufactured by Hill Phoenix was used to vary the Reynolds number and the velocity profile at the DAG. Dummy food products filled with test packages (or product simulator) were put on shelves to simulate the presence of food product in the display case according to ASHRAE Standard 72-1983. The food products are composed of 80% to 90% water, fibrous materials, and salt. A plastic container completely filled with a sponge material that is soaked in a brine solution of water and salt (6% by mass) was used to simulate the product. Air flows in three-dimensional space requiring excessive computational resources for parametric studies. On the other hand, since the length of DAG and RAG is much greater than their width, a two-dimensional analysis can be justified if the velocity profile maintains the same basic shape along the DAG grille. The velocity and temperature profiles across the RAG should also be known by measurements. The first quantity is used to find the total mass
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LDV at 1.22 m from one end (middle) PIV at 1.22 m from one end (middle) LDV at 1.83 m from one end (1/4 distance from one end)
Vertical velocity (m s−1)
−0.2 −0.4 −0.6 −0.8 −1 −1.2 −1.4 −1.6 0.01 0.02 0.03 0.04 0.05 0.06 Distance across the DAG from inside to outside (m)
FIGURE 5.3 Vertical velocity profiles along the display case by LDV and PIV measurements. (Courtesy of Navaz, H.K., Henderson, B.S., Faramarzi, R., Pourmovahed, A., and Taugwalder, F., Int. J. Refrig., 28, 267, 2005. With permission.)
(or volumetric) flow rate inside the display case and the latter measurement will determine the average temperature at the RAG. This average temperature is needed to calculate the infiltration rate based on the enthalpy method described in Ref. [11]. Two experimental methods that can effectively yield information about the velocity and turbulence intensity profiles are the laser Doppler velocimetry (LDV) and particle image velocimetry (PIV) techniques. Both methods can be used in parallel (for more reliability) or independently to define the velocity and turbulence intensity profiles at the DAG and RAG. The velocity profile exiting the DAG is maintained somewhat unchanged to about 5 cm of the two ends. Figure 5.3 shows some of the measurements made about 0.6 m (2 ft) apart, with one being the center of the display case. It is seen that the basic characteristics of the vertical velocity profile are unchanged as predicted by both LDV and PIV measurements. This finding justifies a two-dimensional CFD modeling that is more feasible and practical approach. Generally, three-dimensional flow fields are more complex and computationally more demanding. Therefore, a two-dimensional CFD modeling can be used to proceed to the next step. It should also be noted that these measurements are performed at about 2.5 cm below the DAG plane. To model the BP geometry in two dimensions, the number of perforations and their area were measured and they were incorporated as eight longitudinal slots along the display case representing an identical area in two dimensions. The flow distribution through these perforations was not equal. The mass outflow rate through these slots was changed until the temperature distribution inside the case became similar to that of an infrared (IR) measurements as will be pointed out later. To have an accurate measurement of the display case total air mass flow rate, the front of the RAG was replaced by a Plexiglas to allow the laser beam to go through the RAG for velocity measurements as indicated in Figure 5.2. The velocity profile across the RAG was measured and was similar to a typical turbulent profile and remained the same along the display case. The average velocity at the RAG provided an accurate measurement of the total volumetric air flow rate that is needed for the two-domain analysis [11]. This preliminary
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study was necessary to understand the individual flow situation and to provide justification for the two-dimensional CFD model.
5.3.1 OUTSIDE DOMAIN It is necessary to develop a model for this portion of the flow because it defines the characteristic of flow and the mixing level that is present along the air curtain. It also specifies the amount of entrained air and infiltration rates because both are a part of this domain. Due to elliptic nature of the flow in any display case the incorrect specification of boundary conditions will propagate into the domain resulting in erroneous prediction of entrainment and infiltration rates. Furthermore, parametric studies will be reliable after the validation of the CFD code. It should be noted that the validation and specification of proper boundary conditions to a certain extent are analogous. For instance, measuring the velocity profile at the DAG not only serves as a boundary condition for the outside domain, but also can be compared to the velocity profile resulting from the CFD solution of the inside domain for validation. Basically, the presence of significant turbulence intensity at the DAG will trigger more mixing from the origination point of the air curtain (or jet). The development of turbulence will speed up the existence of a high shear segment in the profile. When Figure 5.3 is examined, the velocity profile at the DAG has two distinct maxima. Figure 5.4 shows the turbulence intensity at the DAG as predicted by LDV and PIV. The turbulence intensity increases significantly at the interface of the two velocity peaks due to an increase in shear stress. At this point we can define the following boundary conditions for this domain: 1. Velocity profile, turbulence intensity at the DAG as specified by LDV and PIV and shown in Figure 5.3 and Figure 5.4. The temperature is assumed to be constant for the air at DAG. 2. Left wall at room pressure and temperature. 3. No-slip wall at the bottom, top, and back wall. 4. Display case walls and shelves are defined as no-slip adiabatic wall.
Turbulence intensity (% of the mean flow)
DPIV LDV
30
25
20
15
10 0
0.06 0.02 0.04 Distance across and 2.5 cm below the DAG (m)
FIGURE 5.4 Experimental turbulence intensity at the DAG. (Courtesy of Navaz, H.K., Henderson, B.S., Faramarzi, R., Pourmovahed, A., and Taugwalder, F., Int. J. Refrig., 28, 267, 2005. With permission.)
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5. Specified exiting mass flow rate (also display case total mass flow rate) at RAG as specified by LDV and PIV measurements through the Plexiglas. 6. By knowing the display case total (measured at RAG) and DAG mass flow rates, the total mass flow rate through the BP can be found. The temperature of the exiting air from the BP is constant and equal to that of DAG, and by knowing the total area of the perforated spots, the velocity can be calculated. Now the question is how to distribute the _ RAG ¼ Total ¼ m _ DAG þ m _ BP) among slots? To accomplish this, remaining mass flow rate (m an IR camera mapped the temperature distribution throughout the outside domain then the mass was distributed arbitrarily until the CFD generated the same temperature field. It was found that the flow of mass through the perforated BP reduces from bottom to top. The computational analysis for the inside domain further verified this proposed approach and is discussed in the next section. The temperature fields obtained by CFD and mapped by IR camera are forced to match in boundary condition (6) as seen from Figure 5.5 by varying the mass distribution among shelves. The data for velocity field and streamlines taken by PIV match with those of the simulation analysis as seen in Figure 5.6. The agreement between the calculated and observed IR image defines the air distribution among shelves. These values will serve to specify the exit boundary conditions excluding DAG for the inside domain (boundary condition (2) in the inside domain). The verification of the simulation with experiment for the final result, i.e., the infiltration rate is necessary. To accomplish this, the amount of entrained air is calculated from Figure 5.6 for the CFD and PIV results by extracting the data in front of the display case and integrating
Temperature (⬚C) 25 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 −1 −2.2
88.75 80.70 72.64 64.59 56.53 48.48 40.42 32.36 24.30
FIGURE 5.5 Comparison between the CFD and IR image for temperature field. (Courtesy of Navaz, H.K., Henderson, B.S., Faramarzi, R., Pourmovahed, A., and Taugwalder, F., Int. J. Refrig., 28, 267, 2005. With permission.)
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Vertical velocity (m s−1) 0.65 0.55 0.45 0.35 0.25 0.15 0.05 −0.05 −0.15 −0.25 −0.35 −0.45 −0.55 −0.65 −0.75 −0.85 −0.95 −1.05 −1.15 −1.25
1.5
1
0.5
Vertical velocity (m s−1)
Y
2
Distance in y-direction (m)
Distance in y-direction (m)
2
X
1
0.65 0.55 0.45 0.35 0.25 0.15 0.05 −0.05 −0.15 −0.25 −0.35 −0.45 −0.55 −0.65 −0.75 −0.85 −0.95 −1.05 −1.15 −1.25
0 0
1.5 0.5 1 Distance in x-direction (m)
(DPIV)
2
0
1 2 Distance in x-direction (m)
(CFD)
FIGURE 5.6 Vertical velocity contours and streamlines by PIV and CFD. (Courtesy of Navaz, H.K., Henderson, B.S., Faramarzi, R., Pourmovahed, A., and Taugwalder, F., Int. J. Refrig., 28, 267, 2005. With permission.)
it over the area. It was found that the entrainment rates predicted by CFD and PIV were, respectively, 9.20 m3 min1 (325 CFM, cubic feet per minute) and 9.06 m3 min1 (320 CFM). Again, it is important to realize that the entrainment and infiltration rates are two different parameters and it should be understood that an increase in entrainment does not necessarily translate directly to an increase in infiltration rate. This correlation only exists under enhanced mixing conditions throughout the air curtain necessitating calculation or direct measurement of the infiltrated outside air through the RAG. For this particular case, the infiltrated amount of warm air was calculated by using the enthalpies as shown in the previous work [11]. The enthalpy method derived in Ref. [11] requires the average temperature at the Ð RAG to evaluate the infiltration rate. The average temperature can be obtained _ , where y and m _ are the local vertical velocity and the total mass flow fromT ¼ RAG ryTdA=m rate, respectively. Based on the enthalpy method, the amount of infiltrated warm air was calculated to be about 35% of the entrained air that is about 3.20 m3 min1 (114 CFM). The amount of infiltrated warm air by collecting the condensate from the coil and relating it to the room humidity was measured to be 3.00 m3 min1 (100 CFM). Although these quantities are close, a direct measurement of the infiltrated warm air through other methods will be advantageous and is a part of the scope of the ongoing research. The meticulous validation and verification that is laid out increases the confidence in any parametric study. Any parameter such as the turbulence intensity, velocity at the DAG, and=or dimensions of the display case can be altered for the outside domain and the entrained and=or infiltrated air can be calculated to examine the effects of each parameter on the infiltration.
5.3.2 INSIDE DOMAIN The prior research [12] has indicated that the velocity profile (shape) affects the mixing and entrainment rate. In principle, the two-peak shape that was shown in Figure 5.3 should be
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0
Height (cm)
Vertical velocity (m min−1)
−50
−100
200 150 100 50 0 −50 −100 −150 −200 −250 −300
0 50 Horizontal distance (cm)
FIGURE 5.7 Vertical velocity contours and vectors at the DAG (inside domain).
avoided. This shape or the velocity profile is a function of the geometry inside the display case particularly the DAG region. Now the question is how to perform reliable parametric studies to obtain the desired velocity profile at the DAG by altering the DAG geometry before its exit plane. For this purpose, a CFD model is built for the interior region of the display case. The evaporator coil is modeled as an obstruction and the honeycomb at the DAG is modeled as series of small slots. The actual geometry of the DAG is taken from the computer-aided design (CAD) files. The following boundary conditions are imposed: 1. Inlet velocity (or mass flow rate) at the RAG is specified as measured by LDV. 2. The velocity through the BP was specified as outlets with the values obtained from boundary conditions of the outside domain. 3. DAG was specified as a jet with no specified velocity and room pressure. The total volumetric flow rate in the display case was about 32.8 m3 min1 (930 CFM) that generated the RAG average velocity of about 100 m min1 (300 ft min1). The velocity contours and vectors at the DAG are shown in Figure 5.7. The velocity profile at the DAG is the outcome of the modeling solution and it should resemble the experimental data. This velocity can be extracted from Figure 5.7 and is shown and compared with experimental PIV and LDV measurements in Figure 5.8a. Considering that the PIV and LDV data are taken about 2.5 cm below the exit plane of the DAG whereas the velocity profile for the inside domain model is extracted exactly at the DAG exit, some ‘‘spreading’’ can be expected. Figure 5.8a clearly demonstrates this fact therefore, it can be concluded that this is an excellent agreement. For further validation, the geometry of the DAG is altered to a 208 slanted surface shifting the more pronounced peak toward the outside of the display case. Figure 5.8b shows this new geometry with its corresponding turbulence kinetic energy as the flow approaches the exit plane of the DAG. It can be seen that the turbulence intensity has somewhat decreased inside the DAG. The 208 slanted nozzle caused the flow to have a more
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8 6 4 2 0 0
5 10 Horizontal distance (cm)
0.84000 0.50622 0.30507 0.18385 0.11079 0.06677 0.04024 0.02425 0.01461 0.00881 0.00531 0.00320 0.00193 0.00116 0.00070
0 −50
−20
−100 −40 −150 −60
−80
−200 CFD prediction PIV LDV
−250
−20 Vertical velocity (m min−1)
Vertical velocity at the DAG (m min−1)
0
Vertical velocity at the DAG (ft min−1)
Vertical distance (cm)
Turbulent kinetic energy (J kg−1)
−60 −80
−100
CFD LDV 2.5 cm below the DAG
−120
6 8 2 4 Distance from outside to inside at the DAG (cm)
(a)
−40
2 3 4 5 6 7 8 9 Distance from outside to inside (cm)
(b)
FIGURE 5.8 Two DAG geometries with corresponding experimental and analytical exit velocities. (Courtesy of Navaz, H.K., Amin, M., Dabiri, D., and Faramarzi, R., ASHRAE Trans., 111(Part 1), 1084, 2005. With permission.)
pronounced peak toward the outside of the display case as seen in Figure 5.8b. From these results it can be concluded that the model for the inside domain is fairly robust and it can be used for further studies. In an attempt to eliminate the two-peak configuration to postpone turbulence development along the air curtain, and also trying to avoid a ‘‘sharp’’ velocity peak responsible for large velocity gradients that can contribute to the turbulence intensity development, another configuration was considered in the modeling. This configuration had a 578 slanted surface with widen throat before the air curtain exit. Figure 5.9 shows this geometry and its corresponding velocity at the exit as compared to the previous validated cases. This appeared to be an improvement over the other two cases. In fact the 208 slanted nozzle produced a sharp peak toward the outside of the display case that will create an increased shear stress and it is expected to increase the entrainment rate. Furthermore, the peak of the velocity should be more toward the inner section of the display case to enhance mixing in the colder region and not the outside of the case. Therefore, the latter case should yield the least entrainment rate. Parametric studies reveal that this is the case at all turbulence levels as seen from Figure 5.10. It is also seen that the entrainment rate for the 208 slanted surface has a more pronounced entrainment rate than the original case, as expected.
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Vertical velocity across the DAG (m min−1)
Turbulence kinetic energy (J kg-1) 578 Slanted surface
0.84000 0.41339 0.20344 0.10012 0.04927 0.02425 0.01193 0.00587 0.00289 0.00142 0.00070
0
0
−50
−20
Vertical velocity across the DAG (ft min−1)
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−100
−40
−150
−60
−200 −250
−80
−300
−100
Original DAG design 20⬚ Slanted surface 57⬚ Slanted surface
−120
−350 −400 −450
−140 0
1 2 3 4 5 6 7 8 Distance across the DAG from outside to inside (cm)
−500
FIGURE 5.9 The improved DAG geometry and its vertical velocity profile compared to previous cases. (Courtesy of Navaz, H.K., Amin, M., Dabiri, D., and Faramarzi, R., ASHRAE Trans., 111(Part 1), 1084, 2005.)
5.4 CONCLUSION
surface 578 Slanted
7 6 5 4 3 2 1 0
0
0.1 0.2 0.3 0.4 0.5 Entrainment rate/ total case flow rate
8
0
n
Original desig
9
Entrainment rate (ft3 min-1)
Entrainment rate (m3 min-1)
10
50
11
0
ce 208 Slanted surfa
12
100 150 200 250 300 350 400
A methodology that is based on a hybrid experimental=computational approach was developed to study the air curtain of a refrigerated display case. The experimental data were used to not only specify the correct boundary conditions for the CFD analysis, but also they were compared to the analytical results for the purpose of validation. It was also shown that how the two-domain approach, if posed correctly, can eliminate the need for inclusion of a fan model that introduces a significant uncertainty to the overall problem. A protocol was also developed for using CFD to generate accurate and meaningful results for entrainment, infiltration, and temperature field that are dictated by the velocity and turbulence distribution
10 5 15 20 Turbulence intensity at the discharge air grille
FIGURE 5.10 Entrainment for three geometries as a function of turbulence intensity at the DAG. (Courtesy of Navaz, H.K., Amin, M., Dabiri, D., and Faramarzi, R., ASHRAE Trans., 111(Part 1), 1084, 2005. With permission.)
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within the flow applicable to any open refrigerated display case configuration. It was also demonstrated that a calibrated CFD tool can be used to conduct parametric studies that can lead to an optimized display case, i.e., minimizing the infiltration of warm air.
ACKNOWLEDGMENT This work was partially sponsored by the US Department of Energy, Office of Building Technology, State and Community Programs under contract DE-AC05-00OR22725 with UT-Battelle, LLC. The authors wish to thank Southern California Edison (SCE) Company for allowing us to use their RTTC facilities for our testing and also Mr. Van D. Baxter from the Oak Ridge National Laboratory for monitoring the project and providing us with his support and advice.
NOMENCLATURE back panel flow (m3 min1) computational fluid dynamics cubic feet per minute (ft3 min1) discharge air grille digital particle image velocimetry pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 turbulence intensity, for isotropic fluctuations: I ¼ 2k=3Vmean , dimensionless turbulence kinetic energy (m2 s2 or J kg1) mass flow rate (kg s1) particle image velocimetry return air grille Reynolds number, based on DAG width, Re ¼ rVw=m, where r is the density, w is the DAG width, m is the viscosity, and V is the average discharge velocity, dimensionless IR infrared RTTC refrigeration and thermal test center SCE Southern California Edison T temperature (K or 8C) u0 horizontal velocity fluctuation (m s1) v0 vertical velocity fluctuation (m s1) w DAG width (m)
BPF CFD CFM DAG DPIV I k _ m PIV RAG Re
GREEK SYMBOLS r m
density (kg m3) molecular viscosity (N s m2)
REFERENCES 1. Cline, M.C., VNAP2: A Computer Program for Computation of Two-Dimensional, TimeDependent Compressible Turbulent Flow, LANL Report LA-8872, August 1981. 2. Qin, H.Q., and Spalding, D.B., The Lagrangian hydrodynamical calculations in PHOENICS code, Computational Fluid Dynamics Unit, Imperial College, London, UK, 1989. 3. CFD-ACE, Theory Manual, CFD Research Corporation, Version 1.0, Huntsville, AL, 1993. 4. The Fluent Code, Users Manual, Fluent, Inc.
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5. STAR-CD Code, Users Manual, Adapco Corp. 6. Navaz, H.K. and Berg, R.M., Numerical treatment of multi-phase flow equations with chemistry and stiff source terms, Journal of Aerospace Science and Technology, 2(3): 219–229, 1998. 7. Stribling, D., Tassou, S.A., and Mariott, D., A two-dimensional CFD model of a refrigerated display case, ASHRAE Transactions, 103(Part 1): 88–94, 1997. 8. Modarress, D., Gharib, M., Dabiri, D., and Navaz, H.K., Experimental and computational analysis of an air curtain display case, Technical Report Prepared for the Southern California Edison Company, Contract No. K1069006, December 1999. 9. Navaz, H.K., Amin, M., Dabiri, D., and Faramarzi, R., Past, present, and future research towards air curtain performance optimization, ASHRAE Transactions, 111(Part 1): 1084–1088, 2005. 10. Navaz, H.K., Faramarzi, R., Dabiri, D., Gharib, M., and Modarress, D., The application of advanced methods in analyzing the performance of the air curtain in a refrigerated display case, Journal of Fluid Engineering, ASME Transactions, 124: 756–764, 2002. 11. Navaz, H.K., Henderson, B.S., Faramarzi, R., Pourmovahed, A., and Taugwalder, F., Jet entrainment rate in air curtain of open refrigerated display cases, International Journal of Refrigeration, 28(2): 267–275, 2005. 12. Navaz, H.K., Amin, M., Srinivasan, C.R., and Faramarzi, R., Jet entrainment minimization in air curtain of open refrigerated display cases, International Journal of Numerical Methods for Heat and Fluid Flow, 16(4): 417–430, 2006.
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Investigation of Methods to Improve Retail Food Store Environment Using CFD Savvas Tassou and Weizhong Xiang
CONTENTS 6.1 6.2 6.3 6.4
Introduction ............................................................................................................... 143 Model of Vertical Multideck Display Cabinet........................................................... 144 Modeling a Display Cabinet Zone in Retail Food Stores.......................................... 146 Display Cabinet Zone without Accessory Heating System........................................ 146 6.4.1 Effect of Distance between Free Boundary and Display Cabinets ................. 146 6.4.2 Modeling the Display Cabinet Zone without Heating System ....................... 147 6.5 Factors that Could Influence the Simulation Results ................................................ 151 6.5.1 Ambient Air Temperature .............................................................................. 151 6.5.2 Cabinet Air Circulation Rate ......................................................................... 151 6.5.3 Air Supply (Evaporator Coil Air off ) Temperature ....................................... 152 6.6 Display Cabinet Zone with Hot Air Heating System ................................................ 152 6.7 Display Cabinet Zone with Underfloor Heating System ........................................... 154 6.8 Extract and Supply System ........................................................................................ 155 6.8.1 Top Suction and Bottom Supply System........................................................ 157 6.8.2 Bottom Extract System................................................................................... 159 6.8.3 Bottom Extract and Top Supply .................................................................... 160 6.9 Conclusions................................................................................................................ 165 References .......................................................................................................................... 166
6.1 INTRODUCTION Food display cabinets are the main refrigerated fixtures in modern food retail stores. The refrigeration systems that serve the refrigerated cabinets and other refrigerated fixtures, such as walk-in coolers, consume close to 50% of the total energy consumption of the store and so their efficiency and food storage integrity are critical to the economic viability of the store and to the impact of retail food stores on the environment. The most common type of cabinet, certainly for medium temperature applications, is the open vertical multideck display cabinet. This design has become popular due to its large display area and ease of access for customers. An air curtain is normally used to reduce the heat and moisture exchange between the cabinet and the store environment. However, irrespective of the design and efficiency of the air curtain, there is always an interaction between the air curtain and the environment, causing entrainment and mixing of warm air 143
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from the environment with cold air in the display cabinet. As a result of the additional air drawn in from the ambient, there is a corresponding quantity of cold air spilling out of the cabinet into the aisles formed between rows of display cabinets. This cold air spillage causes discomfort to customers shopping in the retail food store. In order to improve thermal comfort, measures should be taken to raise the air temperature at low level in the aisles without affecting the product temperature and refrigeration load. To investigate ways to improve thermal comfort in retail food stores, the computational fluid dynamics (CFD) technique was employed to study the effect of different approaches in heating the air at low level within the aisles located in the refrigerated food area of the store. The study involved the development and validation of a vertical multideck chilled food display cabinet model. This cabinet model was then used to develop a model of a display cabinet zone in a food retail store, which incorporated a row of cabinets and the aisle between the cabinets. The model considered the interactions between the display cabinet air and the air in the aisle as well as the effect of different heating approaches on the air in the cabinet zone, product temperature, and display cabinet thermal load. The heating systems that were investigated included a hot air system, an underfloor heating system, and thermal destratification systems (bottom extract and top supply and top extract and bottom supply).
6.2 MODEL OF VERTICAL MULTIDECK DISPLAY CABINET The open vertical multideck display cabinet was first modeled and validated against test results obtained in an environmental test chamber. A cross section of the cabinet and measuring points during tests in the chamber are shown in Figure 6.1. Construction details and the geometric characteristics of the cabinet as well as modeling and test procedures are described in Ref. [1]. The flow in the environmental chamber and the display cabinet was
Temperature sensor Relative humidity sensor Air velocity sensor 20 20 Product temperature sensor arrangement 20
20
1500
Sensor arrangement at return grille 500
500 100
FIGURE 6.1 Display cabinet and measuring points in the environmental test chamber.
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modeled using the Renormalization Group (RNG) k« model. The products in the cabinet were assumed to be of rectangular shape and stacked uniformly, which made it possible to model them as a conducting solid. With this approach, the solid region was not taken as a boundary but calculated as a part of the fluid that has infinite viscosity. The heat transfer between the fluid and solid can then be solved using the equation proposed in Ref. [2]. To model the radiative heat transfer between the display cabinet and the environment the discrete transfer radiation model (DTRM) was used [3,4]. The perforated back panel and the honeycomb of the air curtain outlet were modeled using the porous media approach [5]. The solution of the conservation equations for mass, momentum, energy, species, and turbulent quantities is based on the control volume technique. This consists of . .
.
Division of the domain into discrete control volumes using a general curvilinear grid Integration of the governing equations on the individual control volumes to construct the algebraic equations for discrete unknowns (velocities, pressure, scalars) Solution of the discretized equations
To achieve accurate representation of the flow, when meshing the computational geometry, grids are concentrated in the positions where the temperature and velocity gradients are high, such as the air supply tunnel, the air curtain outlet, and the air return grille. Following this principle, the cabinet and test chamber geometry was meshed as 51 72 30 (i, j, k) grids. Grid independence tests were carried out to ensure that the grid chosen provided the best compromise between speed and solution accuracy. Figure 6.2 shows the baseline mesh scheme of the computational domain. A detailed comparison of simulation and test results was carried out to validate the CFD model [1]. It was found that the model could predict product and air temperatures in the cabinet with a maximum error of 1.08C.
FIGURE 6.2 Meshing scheme of the display cabinet in the environmental chamber.
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6.3 MODELING A DISPLAY CABINET ZONE IN RETAIL FOOD STORES Display cabinets in retail food stores are linked to the store environment system by the mass and heat transfer between the display cabinets and the surrounding air. To model display cabinets in the store, ideally the whole store together with the display cabinets and the products in the cabinets should be taken into consideration. For this purpose, for a medium size store, the grid size will be very large. However, if it is assumed that the display cabinet only exchanges heat and moisture with the local environment (air surrounding the display cabinets), and the store air movement is not very strong, then the display cabinet zone can be treated in isolation from the rest of the store. The effect of air movement caused by the operation of the display cabinets and heating terminal devices within the display cabinet zone and the interactions between adjacent zones can be accounted for by treating the boundaries between zones as pressure boundaries. Previous studies have shown that the display cabinet in the environmental chamber under the effect of low side airflow could be modeled as a display cabinet in open space with free boundaries [1]. That is, the walls of the environmental chamber could be replaced by pressure boundary conditions. The display cabinet zone modeled consisted of two rows of cabinets facing each other as shown in Figure 6.3. The velocity distribution on the pressure boundary is unknown but the total pressure on the boundary can be assumed to be 0 Pa (gauge) if the airflow through the boundary is low. The distance between the free boundary and display cabinet should be large enough to eliminate the effect of the position of the boundary on the simulation results. To investigate this, simulations were carried out to determine the minimum distances X and Y between the free boundary and display cabinets. Because the display cabinet zone is symmetrical in two directions, only a quarter of the zone was modeled.
6.4 DISPLAY CABINET ZONE WITHOUT ACCESSORY HEATING SYSTEM 6.4.1 EFFECT
OF
DISTANCE
BETWEEN
FREE BOUNDARY AND DISPLAY CABINETS
Simulations were carried out to assess the effect of distance between the free boundary and the display cabinets. The inputs to the model can be seen in Table 6.1. Two cases were Symmetrical surface Free boundary Free boundary
H
X Y
L
1000 W 1000
Y
X
FIGURE 6.3 Two rows of display cabinets in the retail food store (dimensions in mm).
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TABLE 6.1 Model Inputs for Display Cabinet Zone without Accessory Heating System Length of the display cabinet zone (m) Store floor to the ceiling height (m) Distance between display cabinet rows (m) Ambient air temperature (8C) Ceiling and wall surface temperature (8C) Ambient air moisture content (g=kg) Display cabinet air supply temperature (8C) Display cabinet air supply moisture content (g kg1 ) 1 Display cabinet airflow rate per meter length (m3 s1 m )
12 3.5 2.5 21 21 8 2 2.6 0.1
investigated, for Case 1, X ¼ 1:0 m and Y ¼ 1:2 m, and for Case 2, X ¼ 2:0 m and Y ¼ 2:0 m. The resulting average velocity and air temperature at low level (0.3 m above floor level), product temperature on top, third, and bottom shelves, and cooling load are compared in Table 6.2. It can be seen that increasing X and Y from 1.0 and 1.2 m to 2.0 m had only a very small effect on the air temperature, product temperature, and cooling load, so it was concluded that it would be safe to use 2.0 m for X and Y for the simulations.
6.4.2 MODELING THE DISPLAY CABINET ZONE WITHOUT HEATING SYSTEM In this section, the results from modeling the store at summer conditions are presented. The inputs to the model are given in Table 6.1. To validate the model, results from measurements of temperature, velocity, and humidity carried out at five stores from three supermarket chains by Foster and Quarini [6] were used. The results from one of the stores (Supermarket A, store 2) are shown in Table 6.3. Figure 6.4 shows the air temperature distribution on a horizontal plane 0.3 m above floor level. It can be seen that the air temperature in the aisle between the display cabinets is around 7.58C. Towards the edges of the zone, section A in Figure 6.4, the temperature increases slightly as the air leaving the zone is replaced by warmer air entering from outside the zone.
TABLE 6.2 Effect of Distance between Free Boundary and Display Cabinets Comparison Items Average velocity at low level (m s1 ) Air temperature at low level (8C) Average product temperature (8C) at positions indicated in Figure 6.1
Cooling load (kW m1 )
Top shelf Third shelf Bottom shelf
Case 1
Case 2
X ¼ 1:0, Y ¼ 1:2 (m)
X ¼ 2:0, Y ¼ 2:0 (m)
0.31 7.20
0.30 7.30
3.10 2.10 3.80 1.14
3.10 2.00 3.80 1.12
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TABLE 6.3 Measurements at One Supermarket Store floor to ceiling height (m) Length of the display cabinet zone (m) Distance between display cabinet rows (m) Mean highest temperature in all aisles (8C) Minimum temperature (8C)
Winter Summer Winter (heated by floor heating) Summer (floor heating off)
3.5 12 2.5 21.5 21 10.7 8.5
Source: From Foster, A.M. and Quarini, G.L., IIF-IIR-Commission D2=3, Cambridge, UK, 217–225, 1998.
Figure 6.5 shows the temperature contours on sections A, B, C, and D (only the display cabinet on the left hand side plotted). It can be seen that the zone is divided into two areas: the low-temperature area close to the floor and the high-temperature area at high level. The height of the boundary from the floor is a function of the position along the aisle. In the middle of the aisle, section D, the height of the low temperature region is highest and at the end of the aisle, section A the height is lowest. The minimum temperature predicted in the aisle is 7.58C compared to a minimum of 8.58C in an actual store measured by Foster and Quarini [6]. Figure 6.6 shows the velocity vectors at section D in the aisle. It can be seen that the cold air overspill from the cabinet descends to the floor and leaves towards the center of the aisle where it meets with the overspill from the opposite row of cabinets. The air then rises and turns back towards the display cabinet, forming local recirculation. Figure 6.7 shows temperature-coded velocity vectors on horizontal planes: (a) 0.3 m above the floor and (b) 2.0 m above the floor. It can be seen that the air leaves the display cabinet zone at low level at both ends of the aisle and warm air enters the zone at high level. The velocity at low level is high (0:30:5 m s1 ) and at high level is much lower (0:050:1 m s1 ). 2.94E + 02 2.93E + 02 2.93E + 02 2.92E + 02 2.92E + 02 2.91E + 02 2.91E + 02 2.90E + 02 2.90E + 02 2.90E + 02 2.89E + 02 2.89E + 02 2.88E + 02 2.88E + 02 2.87E + 02 2.87E + 02 2.86E + 02 2.86E + 02 2.85E + 02 2.85E + 02 2.84E + 02 2.84E + 02 2.83E + 02 2.83E + 02 2.82E + 02 2.82E + 02 2.81E + 02 2.81E + 02 2.80E + 02 2.80E + 02 2.79E + 02
2m 2m 2m
Section A Section B Section C Section D
FIGURE 6.4 Temperature contours (K) on a horizontal plane 0.3 m above floor level (without HVAC system).
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1350 mm
2.90E + 02 2.89E + 02
1100 mm
2.88E + 02 2.87E + 02 2.87E + 02 2.86E + 02 2.85E + 02 2.84E + 02 2.83E + 02
Section B
Section A
2.82E + 02 2.81E + 02 2.80E + 02 2.80E + 02 2.79E + 02 2.78E + 02 2.77E + 02 2.76E + 02
1600 mm
1650 mm
2.75E + 02 2.74E + 02 2.74E + 02 2.73E + 02 2.72E + 02 2.71E + 02
Section C
Section D
FIGURE 6.5 Temperature contours (K) at sections A, B, C, and D (without HVAC).
The air temperature at high level is maintained constant and equal to the store temperature due to air entering the zone from the rest of the store. Figure 6.8 shows air temperature, moisture content, and relative humidity along the aisle centerline. It can be seen that the moisture content distribution mirrors well the air temperature distribution. At low level in the aisle, the moisture content is quite low and the relative humidity is of the order of 70%. The relative humidity reduces as the temperature increases to a value of 50% just outside the cold temperature zone. Figure 6.9 shows the variation of product temperature in the display cabinets. The average temperatures are 3.18C on the top shelf, 2.18C on the third shelf, and 3.88C on the bottom shelf (the measurement positions are shown in Figure 6.1). The cooling load was found to be 1:05 kW m1 .
2.94E+02 2.93E+02 2.92E+02 2.91E+02 2.91E+02 2.90E+02 2.89E+02 2.88E+02 2.87E+02 2.87E+02 2.86E+02 2.85E+02 2.84E+02 2.84E+02 2.83E+02 2.82E+02 2.81E+02 2.80E+02 2.80E+02 2.79E+02 2.78E+02 2.77E+02 2.76E+02 2.76E+02 2.75E+02 2.74E+02 2.73E+02 2.73E+02 2.72E+02 2.71E+02
FIGURE 6.6 Temperature-coded velocity vectors (K) at section D (without HVAC).
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0.3 m above floor
2.0 m above floor
FIGURE 6.7 Temperature-coded velocity vectors (K) on two horizontal planes (without HVAC system). 8.00E−03 7.88E−03 7.77E−03 7.65E−03 7.53E−03 7.42E−03 7.30E−03 7.18E−03 7.07E−03 6.95E−03 6.83E−03 6.72E−03 6.60E−03 6.48E−03 6.37E−03 6.25E−03 6.13E−03 6.02E−03 5.90E−03 5.78E−03 5.67E−03 5.55E−03 5.44E−03 5.32E−03 5.20E−03 5.09E−03 4.97E−03 4.85E−03 4.74E−03 4.62E−03 4.50E−03 2.94E+02 2.94E+02 2.93E+02 2.93E +02 2.92E +02 2.92E +02 2.91E +02 2.91E +02 2.90E +02 2.90E +02 2.89E +02 2.89E +02 2.88E +02 2.88E +02 2.87E +02 2.87E +02 2.87E +02 2.86E +02 2.86E +02 2.85E +02 2.85E +02 2.84E +02 2.84E +02 2.83E +02 2.83E +02 2.82E +02 2.82E +02 2.81E +02 2.81E +02 2.81E +02 2.80E +02
50% (RH)
75% (RH)
72% (RH)
70% (RH)
72% (RH) 75% (RH)
Moisture content (kg kg−1)
Air temperature (K)
FIGURE 6.8 Variation of temperature and moisture content along the aisle centerline (without HVAC system).
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2.78E+02 2.78E+02 2.78E+02 2.77E+02 2.77E+02 2.77E+02 2.77E+02 2.76E+02 2.76E+02 2.76E+02 2.76E+02 2.75E+02 2.75E+02 2.75E+02 2.75E+02 2.75E+02 2.74E+02 2.74E+02 2.74E+02 2.74E+02 2.73E+02 2.73E+02 2.73E+02 2.73E+02 2.72E+02 2.72E+02 2.72E+02 2.72E+02 2.71E+02 2.71E+02 2.71E+02
FIGURE 6.9 Product temperature distributions (K) in the display cabinets (without HVAC system).
6.5 FACTORS THAT COULD INFLUENCE THE SIMULATION RESULTS 6.5.1 AMBIENT AIR TEMPERATURE To investigate the effect of ambient temperature on the thermal environment in the aisles, two simulations were carried out for ambient temperatures of 218C and 238C. Inputs to the CFD model are listed in Table 6.4. The results given in Table 6.5 show that increasing the ambient air temperature from 218C to 238C caused a small increase in the minimum air temperature in the zone from 7.58C to 8.38C, and a small increase in the cooling load of the cabinets from 1:05 to 1:14 kW m1 .
6.5.2 CABINET AIR CIRCULATION RATE The air circulation rate in the cabinet will vary due to frost formation on the evaporator coil. This will in turn influence the product temperature and the thermal environment in the display cabinet zone. To investigate these effects, simulations were carried out for two air circulation rates of 0:07 and 0:1 m3 s1 using the data in Table 6.6 as inputs to the CFD model.
TABLE 6.4 Inputs to the Display Cabinet Zone Model Length of the display cabinet zone (m) Store floor to ceiling height (m) The distance between display cabinet rows (m) Ambient air temperature (8C) Ambient air moisture content (g kg1 ) Display cabinet air supply temperature (8C) Display cabinet air supply moisture content (g kg1 ) 1 Display cabinet air supply flow rate per meter length (m3 s1 m )
12 3.5 2.5 21 or 23 8.0 2 2.6 0.1
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TABLE 6.5 Cooling Load and Product Temperature Ambient Temperature 218C 238C
Product Temperature (8C)
Cooling Load (kW m1 )
Top Shelf
Third Shelf
Bottom Shelf
Minimum Temperature in Zone (8C)
0.91 0.98
3.1 4.2
2.1 2.6
3.8 4.7
7.5 8.3
The results are given in Table 6.7. It can be seen that as the air circulation rate is reduced, the cooling load of the cabinet reduces slightly and the product temperature increases by approximately 1.08C. The minimum air temperature in the display cabinet zone also increases from 7.58C to 8.88C due to reduced cold air overspill in the zone.
6.5.3 AIR SUPPLY (EVAPORATOR COIL AIR
OFF)
TEMPERATURE
The air temperature at the outlet of the evaporator coil will have an impact on the product temperature in the cabinet, the temperature of the air overspill from the cabinet, and the air temperature in the aisle. To investigate these effects, simulations were carried out with evaporator coil air off temperatures of 2 C and 4 C. The inputs to the model are given in Table 6.8 and the results in Table 6.9. It can be seen that reducing the evaporator coil supply temperature by 28C causes, on average, a 1.08C reduction in the product temperature. The temperature of the air overspill from the cabinet also reduces and this causes a reduction in the minimum temperature in the aisle from 7.58C to 6.88C. The lower product and air temperatures in the cabinet cause an increase in the heat transfer between the cabinet and the surrounding environment, which leads to a slight increase in the cooling load of the cabinet.
6.6 DISPLAY CABINET ZONE WITH HOT AIR HEATING SYSTEM The last two sections demonstrated that the aisle temperature would be too low if no heating system is employed in the zone. Hot air heating systems can be found in some supermarkets but their effects on product temperature and aisle temperature need to be
TABLE 6.6 Inputs to the Display Cabinet Zone Model—Air Circulation Length of the display cabinet zone (m) Store floor to ceiling height (m) The distance between the display cabinet rows (m) Ambient air temperature (8C) Ambient moisture content (g kg1 ) Display cabinet air supply temperature (8C) Display cabinet air supply moisture content (g kg1 ) 1 Display cabinet air supply flow rate for per meter length (m3 s1 m )
12 3.5 2.5 21 8 2 2.6 0.1 or 0.07
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TABLE 6.7 Cooling Load and Product Temperature at Different Air Circulation Rates Air Circulation Rate (m3 s1 m1 ) 0.07 0.10
Product Temperature (8C)
Cooling Load (kW m1 )
Top Shelf
Third Shelf
Bottom Shelf
Minimum Temperature in Zone (8C)
0.81 0.91
4.1 3.1
2.8 2.1
5.0 3.8
8.8 7.5
assessed. In this section, the results of simulations to investigate the effect of an air heating system to increase the temperature at low level in the aisle are presented. The hot air was assumed to be supplied through diffusers at ceiling level, 3.5 m above floor level. The diffuser positions are shown in Figure 6.10. For the hot air heating system, one of the main concerns is whether the hot air can reach the low level of the display cabinet zone. For this reason, simulations were carried out for 1 vertical air velocities of 2 and 3 m s1 corresponding to flow rates of 1.6 and 2:4 m3 s , respectively, and supply temperature of 308C. Figure 6.11 shows temperature-coded velocity vectors at section C when the air supply velocity was 2 m s1 . It can be seen that the hot air jet reaches the floor level just under the diffusers. However, in other areas in the zone the temperature remains quite low as can be seen from Figure 6.12, which presents the temperatures in the zone 0.3 m above the floor surface. Figure 6.13 shows temperature-coded velocity vectors at section C for a hot air supply 1 velocity of 3 m s1 (air supply flow rate 2:4 m3 s ), and Figure 6.14, temperature contours on a horizontal plane 0.3 m above floor level. It can be seen that at section C, below the diffuser, the cold aisle effect disappears but the temperature remains low in most other areas of the zone. These results indicate that hot air supply systems are quite inefficient in eliminating the cold aisle effect in the display cabinet zone. With the heat input required for 1 1 an air supply system flow rate of 1:6 m3 s of 16.2 kW and for 2:4 m3 s of 24.3 kW, hot air systems are also inefficient in terms of energy usage. The effect of the hot air system on product temperature and cooling load is shown in Table 6.10. It can be seen that the cooling load and product temperature increase with increasing supply airflow rate. For the higher flow rate the product temperature increases by 0.88C compared to the case where no heating system is used. The minimum
TABLE 6.8 Inputs to the Display Cabinet Zone Model—Air Supply Temperature Length of the display cabinet zone (m) Store floor to ceiling height (m) The distance between the display cabinet rows (m) Ambient air temperature (8C) Ambient air moisture content (g kg1 ) Display cabinet air supply temperature (8C) Display cabinet air supply moisture content (g kg1 ) 1 Display cabinet air supply flow rate per meter length (m3 s1 m )
12 3.5 2.5 21 8 2 or 4 2.6 0.1
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TABLE 6.9 Cooling Load and Product Temperature at Different Air Supply Temperatures Coil Air Off Temperature (8C) 2 4
Product Temperature (8C)
Cooling Load (kW m1 )
Top Shelf
Third Shelf
Bottom Shelf
Minimum Temperature in Zone (8C)
0.91 1.03
3.1 1.9
2.1 1.0
3.8 3.1
7.5 6.8
air temperature in the aisle also increases by 2.58C but it is not enough to eliminate the cold aisle effect.
6.7 DISPLAY CABINET ZONE WITH UNDERFLOOR HEATING SYSTEM Floor heating systems can be found in some supermarkets [6]. In this section, the effect of underfloor heating systems on the aisle temperature, cooling load, and product temperature is investigated. In the simulations, a heat flux of 150 W m2 was employed [7]. Figure 6.15 shows the resulting air temperature distribution at low level in the display cabinet zone. It can be seen that the air temperature is low and only slightly higher than the zone without any heating system. Figure 6.16 shows temperature contours at different sections in the zone. They are very similar to those for no heating in the zone. From the simulation results the average heat transfer coefficient (not including the radiation element) from the floor surface was determined to be 5:94 W m2 K and the average floor surface temperature 308C, giving a heat input to the zone air of 3.87 kW. Increasing the heat flux to 200 W m2 increased the floor surface temperature to 388C but had only a very small effect on the aisle temperature. A comparison of cooling load, air, and product temperature of a zone with the underfloor heating system and zone without heating is given in Table 6.11. It can be seen that the underfloor heating system causes a 0.88C rise in product temperature and increases very slightly the cooling load of the cabinet. Its effect on increasing the air temperature is quite small. A floor surface temperature of 308C and a heat flux of 150 W=m2 only lead to a 1.58C rise in the minimum aisle temperature from 7.58C to 9.08C. It can thus be concluded that underfloor heating systems are not effective in reducing the cold aisle effect in the display cabinet zone. Section C Section D 3510
2120
3510
Air supply grille, 640 ⫻ 570, 2 off
6000
6000
FIGURE 6.10 Diffuser positions in the display cabinet zone (dimensions in mm).
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FIGURE 6.11 Temperature-coded velocity vectors (K) at section C (hot air, V ¼ 2 m s1 ).
6.8 EXTRACT AND SUPPLY SYSTEM The results in the previous sections indicate that when no heating is used in the aisles, temperature stratification occurs from floor to around 1.65 m above floor level. A hot air system with air supplied from ceiling diffusers can increase the air temperature at low level in
3.02E+02 3.01E+02 3.00E+02 2.99E+02 2.98E+02 2.98E+02 2.97E+02 2.96E+02 2.95E+02 2.95E+02 2.94E+02 2.93E+02 2.92E+02 2.92E+02 2.91E+02 2.90E+02 2.89E+02 2.89E+02 2.88E+02 2.87E+02 2.86E+02 2.85E+02 2.85E+02 2.84E+02 2.83E+02 2.82E+02 2.82E+02 2.81E+02 2.80E+02 2.79E+02 2.79E+02
Section A 2m Section B 2m Section C 2m Section D
12 m
2.5 m
FIGURE 6.12 Temperature contours (K) on a horizontal plane 0.3 m above floor level (hot air system, V ¼ 2 m s1 ).
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3.03E+02 3.02E+02 3.01E+02 3.00E+02 2.98E+02 2.97E+02 2.96E+02 2.95E+02 2.94E+02 2.93E+02 2.92E+02 2.91E+02 2.90E+02 2.89E+02 2.87E+02 2.86E+02 2.85E+02 2.84E+02 2.83E+02 2.82E+02 2.81E+02 2.80E+02 2.79E+02 2.78E+02 2.76E+02 2.75E+02 2.74E+02 2.73E+02 2.72E+02 2.71E+02
FIGURE 6.13 Temperature-coded velocity vectors (K) at section C (hot air, V ¼ 3 m s1 ).
the aisles but the effect is localized and at the expense of high-energy consumption. A way of reducing or eliminating the temperature stratification in the aisles is to recirculate the air in the aisles. Two ways of achieving this are: (1) top suction and bottom supply and (2) bottom suction and top supply system.
3.02E+02 3.01E+02 3.01E+02 3.00E+02 2.99E+02 2.98E+02 2.98E+02 2.97E+02 2.96E+02 2.95E+02 2.94E+02 2.94E+02 2.93E+02 2.92E+02 2.91E+02 2.91E+02 2.90E+02 2.89E+02 2.88E+02 2.87E+02 2.87E+02 2.86E+02 2.85E+02 2.84E+02 2.84E+02 2.83E+02 2.82E+02 2.81E+02 2.81E+02 2.80E+02 2.79E+02
FIGURE 6.14 Temperature contours (K) on a horizontal plane 0.3 m above floor level (hot air system, V ¼ 3 m s1 ).
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TABLE 6.10 Cooling Load, Product and Aisle Temperature for Hot Air Heating System Hot Air Supply Flow Rate (m3 s1 )
Product Temperature (8C)
Cooling Load (kW m1 )
Top Shelf
Third Shelf
Bottom Shelf
Minimum Temperature in Zone (8C)
0.91 0.94 1.09
3.1 3.5 3.6
2.1 2.3 2.4
3.8 4.3 4.6
7.5 9.0 10.0
0 (No heating) 1.6 2.4
6.8.1 TOP SUCTION
AND
BOTTOM SUPPLY SYSTEM
In top suction and bottom supply, air can be extracted from close to the ceiling of the supermarket, heated if necessary, and returned at low level in the display cabinet zone. This arrangement is shown in Figure 6.17. The geometry modeled is shown in Figure 6.18. The extract grille is at the center of the zone and the supply grille is at the bottom of the display cabinet, 100 mm above floor level. In order to achieve good performance, the supply grille is the same length as the display cabinet row. The inputs to the model are listed in Table 6.12. Figure 6.19 shows the resulting temperature contours at low level in the display cabinet zone. It can be seen that air temperature at low level is divided into two different areas: the low-temperature area near the display cabinets and the higher temperature area near the center of the aisle. In the low-temperature area, the air temperature is around 138C–148C and in the high-temperature area, the air temperature is around 168C–178C. Figure 6.20 shows temperature contours at different sections in the display cabinet zone. It can be seen that the temperature distribution in the aisle is different from the previous cases
2.95E+02 2.94E+02 2.93E+02 2.93E+02 2.92E+02 2.91E+02 2.90E+02 2.89E+02 2.89E+02 2.88E+02 2.87E+02 2.86E+02 2.85E+02 2.85E+02 2.84E+02 2.83E+02 2.82E+02 2.81E+02 2.81E+02 2.80E+02 2.79E+02 2.78E+02 2.77E+02 2.77E+02 2.76E+02 2.75E+02 2.74E+02 2.73E+02 2.73E+02 2.72E+02 2.71E+02
2m
Section A Section B
2m Section C 2m Section D 12 m
2.5 m
FIGURE 6.15 Temperature contours (K) on a horizontal plane 0.3 m above floor level for underfloor heating system.
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Section A
Section B
Section C
Section D
FIGURE 6.16 Temperature contours (K) at different sections (underfloor heating system).
studied. The temperature in the aisle is not stratified into two zones. This is due to the fact that the warm air supplied at low level mixes with the cold air overspill from the cabinet and the mixture is extracted from the zone at high level by the extract grille. At sections A and B, the air temperature is around 168C and at sections C and D the air temperature is around 158C. From Figure 6.20 it can be also seen that the air temperature close to the air curtain is lower than the store temperature by between 38C and 58C. This reduction in temperature causes a reduction in the sensible cooling load of the display cabinet. For the display cabinet zone without heating system, the sensible cooling load was 0:63 kW m1 whereas that for the top extract and bottom supply system is 0:59 kW m1 , representing a 7% reduction. For an average air temperature at the top extract grille of 19.48C and a supply temperature to the zone of 218C, the heating power required by the system is around 7.5 kW. Figure 6.21 shows the moisture content at different sections of the display cabinet zone. It can be seen that the moisture content contours mirror the temperature contours in Figure 6.20. The moisture content around the air curtain (warm side) reduces due to the operation of the top extract and bottom supply system. The moisture content at sections A and B is about 7 g kg1 and at sections C and D is around 6:5 g kg1 . This gives a latent load
TABLE 6.11 Cooling Load, Product and Aisle Temperature for Underfloor Heating System Heat Flux (W m--2 ) 0 (No heating) 150 200
Product Temperature (8C)
Cooling Load (kW m--1 )
Top Shelf
Third Shelf
Bottom Shelf
Minimum Temperature in Zone (8C)
0.91 0.93 0.96
3.1 3.7 3.9
2.1 2.5 2.6
3.8 4.7 4.9
7.5 9.0 9.5
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Heat from main refrigeration rack
0.1 m3 s−1 m−1
Dehumidifying cooling coil
Evaporator
0.1 m3 s−1 m−1
FIGURE 6.17 Display cabinet zone with top extract and bottom supply system.
of 0:24 kW m1 compared to 0:28 kW m1 latent load for the case of no heating in the aisle, which represents a 14% reduction.
6.8.2 BOTTOM EXTRACT SYSTEM With this system air is removed from the low level in the cabinet zone and no air is supplied at high level in the store. The position and dimensions of the return grille are the same as those of the supply grille in Figure 6.18. The extract flow rate used in the simulations was 0:1 m3 s1 m1 , which is the same as the air circulation rate in the cabinets. Figure 6.22 shows air temperature contours on a horizontal plane 0.3 m above floor level. It can be seen that the air temperature is quite uniform at around 158C, approximately 78C above the minimum zone temperature without a heating system.
6000
Bottom supply
Suction grille 720 ⫻ 630
Y
1250 Suction grille
Supply grille 12000⫻ 100 X
FIGURE 6.18 Scheme of top suction and bottom supply system (dimensions: mm).
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TABLE 6.12 Inputs to the Display Cabinet Zone with Destratification Unit (Top Extract and Bottom Supply System) Length of the display cabinet zone (m) Store floor to ceiling height (m) Distance between display cabinet rows (m) Ambient air moisture content (g kg1 ) Ambient air temperature (8C) Display cabinet air supply temperature (8C) Display cabinet air supply moisture content (g kg1 ) 1 Display cabinet air supply flow rate per meter length (m3 s1 m ) 1 3 1 Air supply rate for suction and supply system (m s m ) Air supply temperature for suction and supply system (8C)
12 3.5 2.5 8 21 2 2.6 0.1 0.1 21
Figure 6.23 shows air temperature distribution at sections A, B, C, and D. It can be seen that the zone air is stratified into two distinct zones with the height of the low temperature zone being approximately 0.6 m from the floor. The bottom extract system has significantly reduced the height of the low temperature zone and increased the minimum air temperature. Although the minimum temperature in the display cabinet zone is still low, it is possible to increase the minimum air temperature by increasing the suction flow rate or supplying warm air from the top of the display cabinet zone.
6.8.3 BOTTOM EXTRACT
AND
TOP SUPPLY
With this system the air removed at low level is heated to 218C and supplied back into the zone from an air supply slot (200 12,000 mm) at high level along the center of the display cabinet 2.94E+02 2.94E+02 2.93E+02 2.93E+02 2.93E+02 2.92E+02 2.92E+02 2.92E+02 2.91E+02 2.91E+02 2.91E+02 2.90E+02 2.90E+02 2.90E+02 2.89E+02 12 m 2.89E+02 2.89E+02 2.88E+02 2.88E+02 2.88E+02 2.87E+02 2.87E+02 2.87E+02 2.87E+02 2.86E+02 2.86E+02 2.86E+02 2.85E+02 2.85E+02 2.85E+02 2.84E+02
Section A 2m Section B 2m Section C 2m Section D
2.5 m
FIGURE 6.19 Temperature contours (K) on a plane 0.3 m above floor level (top suction and bottom supply system).
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2.94E + 02 2.93E + 02 2.92E + 02 2.92E + 02 2.91E + 02 2.90E + 02 2.89E + 02 2.89E + 02 2.88E + 02 2.87E + 02 2.86E + 02 2.86E + 02 2.85E + 02 2.84E + 02 2.83E + 02 2.83E + 02 2.82E + 02 2.81E + 02 2.80E + 02 2.79E + 02 2.79E + 02 2.78E + 02 2.77E + 02 2.76E + 02 2.76E + 02 2.75E + 02 2.74E + 02 2.73E + 02 2.73E + 02 2.72E + 02 2.71E + 02
Section A
Section C
Section B
Section D
FIGURE 6.20 Temperature contours (K) at different sections of the zone (top extract and bottom supply).
zone. The supply velocity is 1:0 m s1 . It can be seen from Figure 6.24 that the temperature at low level is quite uniform with the minimum temperature at around 178C. Figure 6.25 shows temperature contours at sections A, B, C, and D. It can be seen that the air temperature distribution on different sections is similar and the low temperature zone is pushed very close to the floor. The interaction between the air curtain and the warm air
8.00E − 03 7.79E − 03 7.58E − 03 7.37E − 03 7.16E − 03 6.94E − 03 6.73E − 03 6.52E − 03 6.31E − 03 6.10E − 03 5.89E − 03 5.68E − 03 5.47E − 03 5.25E − 03 5.04E − 03 4.83E − 03 4.62E − 03 4.41E − 03 4.20E − 03 3.99E − 03 3.78E − 03 3.57E − 03 3.35E − 03 3.14E − 03 2.93E − 03 2.72E − 03 2.51E − 03 2.30E − 03 2.09E − 03 1.88E − 03 1.67E − 03
Section A
Section C
Section B
Section D
FIGURE 6.21 Moisture content (kg kg1 ) at different sections (top extract and bottom supply).
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Section A 2m Section B 2m Section C 2m Section D 12 m
2.5 m
FIGURE 6.22 Temperature contours (K) on a horizontal plane 0.3 m above floor level (bottom extract system).
stream can be seen in Figure 6.26. A recirculation area between the air curtain and the warm air stream can be observed. The impact of this, however, on the product temperature is quite small (see Table 6.14). The display cabinet zone model predicted the air temperature at the 1 bottom suction grille to be around 11.48C. Because the total air suction flow rate is 2:4 m3 s for the zone, the heating load for heating the air up from 11.48C to 218C is 28.5 kW. This load
2.94E + 02 2.93E + 02 2.92E + 02 2.92E + 02 2.91E + 02 2.90E + 02 2.89E + 02 2.89E + 02 2.88E + 02 2.87E + 02 2.86E + 02 2.86E + 02 2.85E + 02 2.84E + 02 2.83E + 02 2.83E + 02 2.82E + 02 2.81E + 02 2.80E + 02 2.79E + 02 2.79E + 02 2.78E + 02 2.77E + 02 2.76E + 02 2.76E + 02 2.75E + 02 2.74E + 02 2.73E + 02 2.73E + 02 2.72E + 02 2.71E + 02
Section A
Section C
Section B
Section D
FIGURE 6.23 Temperature contours (K) at different sections (bottom extract system).
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Section A 2m Section B 2m Section C 2m Section D
12 m
2.5 m
FIGURE 6.24 Temperature contours (K) on a horizontal plane 0.3 m above floor level (bottom extract and top supply system).
is quite high but can be satisfied by using the heat rejected from the central refrigeration equipment. Figure 6.27 shows the moisture content distribution in the display cabinet zone. The moisture content at the bottom suction grille was predicted to be 0:004 kg kg1 and this was used as the top supply moisture content. It can be seen that the moisture content close to the
2.94E + 02 2.93E + 02 2.92E + 02 2.92E + 02 2.91E + 02 2.90E + 02 2.89E + 02 2.89E + 02 2.88E + 02 2.87E + 02 2.86E + 02 2.86E + 02 2.85E + 02 2.84E + 02 2.83E + 02 2.83E + 02 2.82E + 02 2.81E + 02 2.80E + 02 2.79E + 02 2.79E + 02 2.78E + 02 2.77E + 02 2.76E + 02 2.76E + 02 2.75E + 02 2.74E + 02 2.73E + 02 2.73E + 02 2.72E + 02 2.71E + 02
Section A
Section B
Section C
Section D
FIGURE 6.25 Temperature contours (K) at different sections (bottom extract and top supply system).
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2.94E+02 2.93E+02 2.92E+02 2.92E+02 2.91E+02 2.90E+02 2.89E+02 2.89E+02 2.88E+02 2.87E+02 2.86E+02 2.86E+02 2.85E+02 2.84E+02 2.83E+02 2.83E+02 2.82E+02 2.81E+02 2.80E+02 2.79E+02 2.79E+02 2.78E+02 2.77E+02 2.76E+02 2.76E+02 2.75E+02 2.74E+02 2.73E+02 2.73E+02 2.72E+02 2.71E+02
FIGURE 6.26 Temperature-coded velocity vectors (K) at section D (bottom extract and top supply system).
air curtain is only 0:005 kg kg1 , much lower than the ambient moisture content of 0:008 kg kg1 . This can significantly reduce the latent load and therefore reduce the defrost energy of the display cabinets. A comparison between the cooling load of the display cabinet zone with bottom suction and top supply and a zone without any heating is shown in Table 6.13.
8.00E− 03 7.82E− 03 7.64E− 03 7.46E− 03 7.28E− 03 7.10E− 03 6.92E− 03 6.74E− 03 6.56E− 03 6.38E− 03 6.20E− 03 6.02E− 03 5.84E− 03 5.66E− 03 5.48E− 03 5.30E− 03 5.12E− 03 4.94E− 03 4.76E− 03 4.58E− 03 4.40E− 03 4.22E− 03 4.04E− 03 3.86E− 03 3.68E− 03 3.50E− 03 3.32E− 03 3.14E− 03 2.96E− 03 2.78E− 03 2.60E− 03
Section A
Section B
Section C
Section D
FIGURE 6.27 Moisture content (kg kg1 ) at sections A, B, C, and D (bottom extract and top supply system).
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TABLE 6.13 Latent and Total Cooling Load for Different Systems Zone Type
Latent Cooling Load (kW m1 )
Total Cooling Load (kW m1 )
0.28 0.24 0.16
0.91 0.82 0.84
No heating Top suction and bottom supply Bottom suction and top supply
It can be seen that the bottom suction and top supply system can reduce the latent cooling load by about 40% and this will greatly reduce the defrost energy of the display cabinets and improve energy efficiency of the display cabinet refrigeration systems. A comparison between the bottom extract system, bottom extract and top supply system and no heating on product temperature, and minimum air temperature is given in Table 6.14. It can be observed that the bottom suction and top supply system is much more effective in reducing the cold aisle effect with only a very small impact on product temperature.
6.9 CONCLUSIONS The cold aisle effect, low temperatures at low level between rows of open vertical multideck refrigerated display cabinets in food retail stores, is a problem that has not, as yet, been satisfactorily resolved. The low temperatures in the refrigerated aisles cause discomfort to customers and may influence sales of refrigerated foods. A number of approaches have been employed over the years to address the problem with variable levels of success. This chapter, through the technique of CFD has investigated the effectiveness of some early approaches to reduce the cold aisle effect, such as the use of HVAC systems to supply hot air from ceiling diffusers to the display cabinet zone, and underfloor heating systems. Results from actual store measurements and simulations indicate that both methods are unable to eliminate the cold aisle effect. A hot air system can provide localized heating at low level in the aisle but not uniform heating over the whole cabinet zone. High temperatures and air velocities can also have an impact on the cabinet performance and product temperature and require high thermal energy inputs. Underfloor heating, although has the ability to provide uniform heating of the air at low level in the aisle, is unable to destratify the air and thus its impact in reducing the cold aisle effect is limited.
TABLE 6.14 Comparison between Bottom Suction System, Bottom Suction and Top Supply System, and No Heating System Zone Type Bottom extract Bottom extract and top supply No heating
Temperature Top Shelf (8C)
Temperature Third Shelf (8C)
Temperature Bottom Shelf (8C)
Zone Minimum Air Temperature (8C)
3.6
2.4
4.7
13
3.7 3.1
2.4 2.1
4.7 3.8
17 7.5
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More effective approaches in reducing the cold aisle effect are through the elimination of thermal stratification in the aisle. Ways of achieving this are through the removal of cold air in the aisle and replacing it with warmer air from the rest of the store with or without supplemental heating. Three possible systems were investigated: (a) simple removal of air from low level in the aisle and discharging it at high level outside the cabinet zone; (b) removal of air at low level, heating it using heat generated, for example, by the condensers of the refrigeration plant, and supplying at high level in the display cabinet zone, and (c) removing warm air at high level in the aisle, heating it and supplying at low level in the aisles. These three destratification approaches are more effective in reducing the cold aisle effect than hot air or underfloor heating systems. The most effective of the three approaches was found to be the bottom extract and top supply system. This system can lead to acceptable air temperatures in the aisles and lower latent loads on the cabinets. The lower latent load should lead to a reduction in evaporator coil frosting and defrosting losses.
REFERENCES 1. Xiang, W. Performance improvement of multideck display cabinets and reduction of their impact on the store environment. PhD thesis, Brunel University, England, 2003. 2. Hinze, J.O. Turbulence. McGraw-Hill, New York, NY, 1975. 3. Shah, N.G. A new method of computation of radiant heat transfer in combustion chambers. PhD thesis, Imperial College of Science and Technology, London, England, 1979. 4. Carvalho, M.G., Farias, T., and Fontes, P. Predicting radiative heat transfer in absorbing, emitting and scattering media using the discrete transfer method, Fundamental of Radiation Heat Transfer, ASME HTD, American Society of Mechanical Engineers, New York, Vol. 106, pp. 17–26, 1991. 5. Stribling, D., Tassou, S.A., and Marriott, D. Optimization of the design of refrigerated display cases using computational fluid dynamics. Proceedings of the Institute of Refrigeration, 92, 7.1–7.7, 1996. 6. Foster, A.M. and Quarini, G.L. Using advanced modeling techniques to reduce the cold spillage from retail cabinets into supermarket stores, IIF-IIR-Commission D2=3, Cambridge, UK, pp. 217–225, 1998. 7. Faber, O. Advanced supermarket refrigeration and HVAC systems, Notes of Discussion, January 2000. 8. European Standard EN 441-4. Refrigerated display cabinets. General test conditions, CEN, European Standard, 1995.
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CFD Optimization of Air Movement through Doorways in Refrigerated Rooms Alan M. Foster
CONTENTS 7.1 7.2 7.3
Introduction ............................................................................................................... 168 Natural Convention through an Opening.................................................................. 168 Cold Stores................................................................................................................. 170 7.3.1 Chilled Stores.................................................................................................. 170 7.3.2 Frozen Stores.................................................................................................. 170 7.3.3 Door Protection.............................................................................................. 171 7.3.3.1 Strip Curtain..................................................................................... 171 7.3.3.2 Loading Docks and Vestibules ......................................................... 172 7.3.3.3 Flexible Fast-Opening Doors ........................................................... 172 7.3.3.4 Air Curtains...................................................................................... 172 7.4 Prediction ................................................................................................................... 172 7.4.1 Analytical and Empirical Models ................................................................... 172 7.4.2 Computational Fluid Dynamics ..................................................................... 174 7.4.2.1 Theory .............................................................................................. 174 7.4.3 Applications.................................................................................................... 175 7.4.3.1 Cold Stores ....................................................................................... 176 7.4.3.2 Air Curtains...................................................................................... 178 7.5 Validation .................................................................................................................. 185 7.5.1 Temperature Measurement............................................................................. 185 7.5.2 Velocity Measurement .................................................................................... 186 7.5.2.1 Vane Anemometry............................................................................ 186 7.5.2.2 Hot-Wire Anemometry..................................................................... 186 7.5.2.3 Laser Doppler Anemometry............................................................. 186 7.5.2.4 Digital Particle Image Velocimetry................................................... 187 7.5.3 Infiltration ...................................................................................................... 188 7.5.3.1 Flow Rates ....................................................................................... 188 7.5.3.2 Gas Decay ........................................................................................ 188 7.6 Conclusions................................................................................................................ 189 Nomenclature ..................................................................................................................... 190 References .......................................................................................................................... 191
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7.1 INTRODUCTION Most unwrapped meat, poultry, fruits, and vegetables and all types of wrapped foods are stored in large air-circulated rooms. Specific rooms are used for the storage of chilled or frozen foods. A reduction in the average storage temperature can significantly increase the length of retention and quality of many chilled foods. Bacterial counts will decrease, leading to an increase in safety and shelf life of the product. Olafsdottir et al. [1] found that reducing the storage temperature of cold fillets from 0.58C to 1.58C increased the minimum sensory life from 12.5 to 15 days. The weight loss from unwrapped foods will reduce, thus increasing quality and productivity. Reduced temperature cycling in frozen storage rooms reduces the moisture drawn from the foods, which reduces in-pack frosting and freezer burn. Improvements such as the introduction of state-of-the-art refrigeration systems with advanced controls that include subcooling, floating head pressures, high-efficiency evaporators, condensers, and motors, and also variable speed drives, can help reduce energy usage and temperature control [2]. However, in any refrigerated store, entrances are required for loading and unloading raw materials or finished products and they are a major source of heat infiltration. Air infiltration can account for more than half the total heat load for refrigerated stores [3]. Refrigerated stores are one of the highest consumers of electric energy in the commercial building sector [4]. The electric usage of these refrigerated stores often ranges from 400 to 600 kW h m2 per year, with refrigeration accounting for more than 70% of overall electric usage [2]. Infiltration of warm moist air through doorways into refrigerated rooms during loading and unloading causes many problems to the operators. These include . .
.
.
Increased costs for running [3] and defrosting the refrigeration system Safety problems associated with the mist formed in the doorway, as the cold air mixes with the ambient air [5] Safety problems associated with ice forming around the door opening (of freezer rooms), on the floor, and on the ceiling [5] Food quality, safety, and weight loss caused by temperature fluctuations
The design of an entrance in a temperature-controlled space is always a conflict between operators, who would prefer a completely unrestricted access, and the needs of temperature control, which would prefer no doors or openings. The positioning and design of entrances are often decided on ease of use criteria with temperature control and interaction with the refrigeration system as a secondary consideration. Azzouz et al. [6] measured a heat infiltration of 3.4% between the cold store and ambient during a door opening. The cold air leaves at the bottom and warm moist air enters at the top. However, this is only true if one door is opened. If more than one door is opened in the same room at the same time, then air will flow in through one door and leave out of the other depending on the atmospheric pressure differences around each door. There are a limited number of computational fluid dynamics (CFD) modeling studies carried out on natural convection through cold store entrances. By far, the majority of CFD studies of air curtains have been on refrigerated display cabinets, which are of a much smaller scale (less height and lower velocity) and recirculating. This chapter details the work carried out in this area and other relevant areas.
7.2 NATURAL CONVENTION THROUGH AN OPENING The theory of natural convection through an opening has been developed by a number of authors; the actual models are described in Table 7.1. Natural convection through an opening
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169
TABLE 7.1 Analytical Models of Infiltration Rate through an Open Door due to Natural Convection "
Brown and Solvason (1963)
I
Tamm (1966)
I
Fritzsche and Lilienblum (1968)
I
Gosney and Olama (1975)
I
Pham and Oliver (1983)
I
#0:5 ( ri ro ) b ¼ 0:343 A(gH) 1 0:498 ravg H 1:5 ( ri ro ) 0:5 2 ¼ 0:333 A(gH)0:5 ri 1 þ (ro =ri )0:333 0:5 1:5 ( ri ro ) 2 ¼ 0:333 Kf,L A(gH)0:5 0:333 ri 1 þ (ro =ri ) 0:5 1:5 ( ri ro ) 2 ¼ 0:221 A(gH)0:5 ri 1 þ (ri =ro )0:333 0:5 1:5 ( ri ro ) 2 ¼ 0:226 A(gH)0:5 ri 1 þ (ro =ri )0:333 0:5
is caused by the temperature difference and thus density difference between the air inside and outside the room. This effect is commonly known as the stack effect. Eighty years ago Emswiler [7] expressed the basic theory for natural convection through openings in a partition separating fluids at different densities. His investigation concentrated on multiple openings and his theory was based on the Bernoulli equation for ideal flow and introduced the concept of the neutral level. This is the height at which the pressure is the same either side of the partition. Brown and Solvason [8] developed a theory of natural convection through single vertical rectangular openings in partitions. They showed that a pressure profile is developed in the opening that is caused by the difference in density due to temperature difference between the environments on either side of the partition. This velocity profile generated from this pressure distribution is shown in Figure 7.1. They assumed that the neutral height was half the height of the entrance. Tamm [9] improved on this model, calculating the height of the neutral level and using inside and outside densities for inflow and outflow, respectively, where appropriate, instead of an average value. Fritzsche and Lilienblum [10], who conducted experiments using vane
Cold store To
Ti
u
Entrance
Pressure = Po
hn
FIGURE 7.1 Schematic showing natural convection through a refrigerated room entrance.
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anemometers, added a correction factor to Tamm’s equation. The correction factor takes into account the contraction of the flow, friction, and thermal effects. Fritzsche and Lilienblum’s equation assumed that the volume flow rate into and out of the room were the same. This is only the case if the air entering the room does not cool. This may be a good approximation for a small room, where infiltration through the door causes the air in the refrigerated room to rise in temperature. If the room is large and the air entering the room cools to the refrigerated room air temperature, the mass flow rate into and out of the room will be the same but not the volume flow rate. Gosney and Olama [11] provided an equation for constant mass flow rate and by fitting measurements with their model provided a different correction factor. Pham and Oliver [12] conducted experiments on airflow through refrigerated room doors and produced a factor of 0.68 that should be applied to Tamm’s equation to fit their experimental data. Whereas Jones et al. [13] investigated moisture transfer through openings and showed that the mass transfer of water vapor could be adequately described by the air convection currents at the opening, which is much greater than the diffusion.
7.3 COLD STORES Refrigerated rooms are primarily used for the storage of food. To give an idea of size and layout of cold storage rooms, Pham and Oliver [12] studied rooms covering volumes of 177–37,000 m3 , heights of 3.8–21.2 m, and temperature differences between room and ambient from 19.58C to 348C. Door sizes ranged from w h ¼ 1.08 1.98 m to 3.0 3.6 m. Cold stores are generally constructed from prefabricated insulated panels and contain floor-to-ceiling racking or pallets. Usually, the doors of large cold stores are pneumatically actuated, horizontally sliding, insulated doors. Smaller storage rooms may have manually activated hinged or sliding doors. There are two main types of cold storage room—chilled and frozen—each having different problems associated with infiltration.
7.3.1 CHILLED STORES The chilled cold store will usually run between 08C and 58C and the food within it will usually be stored for short periods of time (days). However, meat may be aged (matured) in chill rooms for up to 7 weeks and vacuum-packaged products can be stored for up to 16 weeks in chill rooms operating at 1 + 0.58C. Because the chilled store is often used for shorter storage times it is often quite small and product is moved in and out regularly. As the food in chilled stores is close to temperatures where bacteria can grow, hygiene and temperature control is the major consideration. Heat infiltration will raise air and inevitably product temperatures. It is an accepted crude approximation that bacterial growth rates can be expected to double with every 108C rise in temperature [14]. However, below 108C, the effect is far more pronounced and chilled storage life is halved for each 28C to 38C rise in temperature. In the normal temperature range of 1.58C and 58C for chilled meat, there can be as much as an eightfold difference in growth rate between the upper and lower temperatures [15]. Door openings can therefore have a critical impact on product temperature and storage life.
7.3.2 FROZEN STORES The frozen cold store will usually run below 188C and the food within it will be stored for long periods of time. Storage times are dependent on enzymic and oxidative reactions,
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which are a function of temperature. They range from 3 to 4 months for shrimps at 188C [16] to 2.5 years for lamb stored at 258C [15]. As long as the food remains below 128C, there will be no growth of pathogenic or spoilage microorganisms and so the food will remain safe [17], therefore, hygiene and temperature control is not the major consideration. The energy required to keep the food at this very low temperature for a longtime is now one of the prime considerations. Another important consideration is the moisture entering the store. This moisture quickly turns into ice. The ice can be found around the door, above the door, and on the evaporators. The ice causes a slip hazard to personnel and forklift trucks and also a falling hazard as large lumps of ice can fall from above the door onto personnel. This ice may need regular removal, which is also expensive. Condensing moisture in the doorway causes a mist (fogging) that is another safety hazard as visibility of the forklift drivers is impaired. Boast [18] states that snow, ice, and frost are responsible for over 90% of accidents in cold storage areas, from slippage and damage caused by and to the mechanical-handling equipment.
7.3.3 DOOR PROTECTION To reduce infiltration while the door is open, cold stores often contain one or more infiltration-reducing devices. The ability of these devices to reduce infiltration is defined as the effectiveness and is derived by the following equation: E¼
Qb Qa Qb
(7:1)
An effectiveness of 1.0 means that infiltration is totally eliminated, 0 means that there is no effect on the infiltration, and a negative value indicates that the infiltration is worse. Measured values of the static effectiveness of infiltration devices by a wide range of authors are shown in Table 7.2. 7.3.3.1 Strip Curtain The traditional, and most common, equipment for reducing infiltration is the strip curtain. This consists of a number of overlapping transparent PVC strips. Chen et al. [3] found that TABLE 7.2 Reported Effectiveness Values for Infiltration Protection Devices Device
Type
Strip curtain
Air curtain
Combined air and strip curtains Fast doors
Dual Vertical nonrecirculating
Vertical double nonrecirculating Vertical recirculating Horizontal recirculating Horizontal double recirculating Horizontal air curtain
Effectiveness 0.86 to 0.96 static 0.83 to 0.93 traffic 0.92 to 0.98 0.44 to 0.83 1.58 to 0.54 negative pressure 0.6 to 0.93 0.36 to 0.8 0.59 to 0.82 0.74 0.9 to 0.92 0.63 to 0.93
Source [12,21,44] [44] [6,37,38,44,45,46]
[47] [45] [12,45,46] [21] [12] [44]
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strip curtains in good condition reduce infiltration by 0.92; however, for a damaged strip curtain the infiltration was about three times higher. Ligtenburg and Wijjfels [5] claim that the strip curtains are generally considered unsafe, are not particularly efficient, are unhygienic, and require much maintenance. It is possible that this equipment may be banned in the future. 7.3.3.2
Loading Docks and Vestibules
Loading docks are commonly seen on large frozen storage depots. They allow the movement of food between the cold store and refrigerated motortruck without interaction with the ambient air. The motortruck backs up to the loading dock (of which there will probably be more than one) and seals restrict-air infiltration between the ambient and the loading dock. The store door directly feeds into the dock. These loading docks are normally refrigerated to a temperature between that of the outside ambient and the store and may also be dehumidified. Air lock vestibules can also be used for personnel or forklift access; however, they have their own problems in that they restrict access, are difficult to fit to existing sites, can be bulky, and have a high capital cost. 7.3.3.3
Flexible Fast-Opening Doors
Flexible, fast-opening doors can be a replacement to normal insulated doors. They operate much faster than normal insulated doors ( 2 m s1 ) and therefore limit the time that the door is partially open to a minimum. The reasons for low take-up of these devices are that they have heavy maintenance requirements, can jam, and are known to reduce vision of forklift truck operators, which result in accidents. 7.3.3.4
Air Curtains
An air curtain is effectively a plane turbulent jet of air forming a barrier between the cold air in the store and the warm ambient air. The theory of air curtains are described in more detail in Chapter 4. Air curtains reduce infiltration without taking up as much space as vestibules and without impeding traffic. Their origin dates back to a patent applied for by Van Kennel in 1904 and they have been popular for around 50 years. Air curtains consist of a fan unit that produces a jet of air forming a barrier to heat, moisture, dust, odors, insects, etc. In the case of cold store air curtains, the fan unit is usually above the door, blowing a jet of air vertically downward. Some air curtains recirculate their air via a return duct but it is simpler and more common not to do so. The effectiveness of air curtains has been shown to vary considerably (Table 7.2). Micheal [19] and Foster et al. [20] have shown that incorrect specification, installation, set-up, and adjustment can have an adverse effect on effectiveness of the air curtains.
7.4 PREDICTION 7.4.1 ANALYTICAL
AND
EMPIRICAL MODELS
The equations for the analytical models, which have been outlined in Section 7.2, are given in Table 7.1. All of these analytical models are based on ideal flow theory, and the later models contain an empirical coefficient to account for viscous and thermal effects. Hendrix et al. [21] have compared these models against real measurements and found that they generally overpredict the volume flow rate through the door. The Gosney and Olama [11] model exhibited the ability to predict experimentally observed values for volume flow rate, mass flow rate, and heat infiltration. The deviations were less than 25% for volume and mass flow
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rates. Chen et al. [3] found that Tamm’s model overpredicted the air infiltration rate through an open door by 30%. Chen suggested that further measurements were needed to be carried out on a wider range of cold stores, door sizes, and operating conditions to confirm results and establish the generality of the empirical factors. When Foster et al. [22] compared analytical models to measurements they concluded that the Brown–Tamm models substantially overpredict the infiltration for all of the measurements (between 52% and 123% overprediction). Tamm’s modified model predicts the measurements much more closely than the original (it was within the experimental error for a cold store at 08C). Taking all of the experiments into account, the Gosney model performed best (maximum of 39% overprediction), followed by the Fritzsche model (maximum of 43% overprediction). Most air curtains are essentially plane turbulent jets and the physics of these jets are also well documented [23–25]. Solving the equations for natural convection through openings and also for turbulent jets allows the interaction between the air curtain and infiltration through the entrance to be evaluated. Hayes and Stoecker [26,27] developed an analytical model to predict heating and cooling loads across nonrecirculatory air curtains (Equation 7.2). Their model allows the calculation of the ‘‘deflection modulus,’’ which is the ratio of air curtain momentum to transverse forces, caused by temperature difference on either side of the curtain (stack effect). The stack effect is created by the difference in air densities on the two sides of the doorway and results in a linear variation in pressure from the top to the bottom of the opening:
Dm ¼ gH 2
bu2 ro bu2 ¼ 2 To To gH ðrc rw Þ Tc Tw
(7:2)
They also presented a chart showing the minimum outlet momentum required to maintain an unbroken curtain (Figure 7.2). 0.24
0.20
gH 2(rc − rw)
(ro bu 2) min
15⬚ toward cold side 0.16 0⬚ 15⬚ toward warm side 30⬚ toward warm side
0.12
0.08 0
0
20
40
60
80
100
H /bo
FIGURE 7.2 Minimum outlet momentum required to maintain an unbroken curtain. (Design Data for Air curtains, 1969 ß ASHRAE Inc. (www.ashrae.org). With permission.)
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From the chart and equation it is possible to calculate the minimum air curtain velocity to provide an unbroken curtain. However, because this velocity is at the borderline of stability, a higher outlet velocity must be selected to provide a factor of safety. They showed that the heat transfer through the curtain is proportional to the jet velocity for velocities above the borderline of stability and it is not therefore beneficial to have too high a safety factor. The literature suggests a range of safety factors between 1.3 and 2.0 to use in this model [27]. Foster et al. [22] compared this analytical model to measured data. Using this range of safety factors, a number of velocities could be chosen from 11 to 17 m s1 . Using these velocities resulted in an experimental effectiveness of the air curtain varying from 0.37 to 0.70. A higher safety factor of 2.2 yielded the best effectiveness in these tests.
7.4.2 COMPUTATIONAL FLUID DYNAMICS Many authors have used CFD to predict heat and mass transfer inside refrigerated rooms [28–31], but it has been used far less to predict natural convection through cold store entrances. 7.4.2.1
Theory
The time-averaged continuity, momentum, and energy equations for a constant property incompressible fluid in absence of volumetric heating and neglecting the effects of viscous dissipation can be written as follows in their conservative form: rw¼0 r
@w þ rr (w w) ¼ rp þ mr2 w þ rb T Tref g r rw0 w0 @t
(7:3) (7:4)
@T þ rcp r wT ¼ lr2 T r rw0 T 0 (7:5) @t The unknown Reynolds stresses rw0 w0 and Reynolds fluxes rw0 T 0 appear on the right-hand sides of Equation 7.4 and Equation 7.5, respectively. If the temperature variations are small, then the Boussinesq approximation can be used to simulate buoyancy. Following such an approximation, the density is assumed constant in the transient and convective terms, while it is linearly dependent on temperature in the buoyancy term rb T Tref g. By far the most common turbulence model used is the k« turbulence model; this is adopted to model the Reynolds stresses and fluxes. As it uses an eddy-viscosity hypothesis, the Reynolds stresses can be linearly related to the mean velocity gradients as follows: rcp
2 2 rw0 w0 ¼ rkd mt r wd þ mt r w þ ðrwÞT 3 3
(7:6)
where mt is the turbulent viscosity, k ¼ 1=2(w0 )2 is the turbulent kinetic energy, and d is the identity matrix. Analogously, the Reynolds fluxes are linearly related to the mean temperature gradient as (7:7) rw0 T 0 ¼ rcp at rT with at ¼
mt rst
(7:8)
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where at and st are known as the turbulent diffusivity and the turbulent Prandtl number, respectively. As we are now dealing only with mean quantities, we shall drop the over bar for the sake of simplicity. In the k« model, it is assumed that the turbulence viscosity is linked to the turbulence kinetic energy and dissipation via the following equation: mt ¼ Cm r
k2 «
(7:9)
where Cm is a constant. The values of k and « come directly from the differential transport equations for the turbulence kinetic energy and turbulence dissipation rate: @rk mt þ r (rwk) r m þ rk ¼ P r« @t sk @r« mt « þ r (rw«) r m þ r« ¼ ðCe1 P Ce2 r«Þ @t k se
(7:10) (7:11)
where P is the shear production defined by 2 P ¼ mt rw rw þ rwT r wðmt r w þ rkÞ 3
(7:12)
where Ce1 , Ce2 , sk , and se are constants.
7.4.3 APPLICATIONS Many of the investigations of natural convection through openings are not for cold storage rooms but for other types of building, e.g., warehouses, offices, retail outlets, etc. It is more common for the building to be at a warmer temperature than the environment and therefore the airflow through the opening is the reverse of that found in a cold store. Wind effects are a common problem with natural convection in buildings. This is also true for refrigerated rooms where the door opens into the environment; however, many refrigerated rooms are within factories where wind effects are negligible. Probably, Schaelin et al. [32] carried out the first CFD study of the airflow pattern through large openings that allow bidirectional flow. They simulated airflow through large openings in buildings with and without an external wind. The airflow pattern was calculated where warm air leaves a room through the upper part of the large opening and rises as a thermal plume. Although this work was done for a heated room, the same effect can be seen in a cold store where warm air enters the top of the door and rises to the ceiling of the cold store. They found that both twodimensional (2D) and three-dimensional (3D) CFD models agreed well with analytical models [33] and the predictions were supported by experiments [27,34]. In addition to investigating the thermal plume outside of the room, they also investigated the velocity and temperature field inside the room and through the opening, with and without wind effects. They showed that the CFD prediction of the doorway velocity profile was more realistic than that obtained by an analytical Bernoulli model. The 3D model yielded about 20% more flow through the doorway with wind than the 2D model, and the suggested reason for this was that the heater (used to heat the room) was wider than the full width of the door. A common problem with CFD modeling of flow through an
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entrance is the extent of the ambient environment that should be included in the computational domain. This issue is important with 3D models where the computational resources required can be prohibitive. Schaelin et al. [32] showed that in free convection cases, the length of the ambient domain can be set to about half of the opening height. It is becoming more common to design natural convection ventilation systems in buildings due to their environmental impact (zero fan power). These systems use a chimney (with or without an extraction fan) for their ventilation. While the stack effect is the enemy in the cold storage industry, it is the friend in modern building design. Wong and Heryanto [35] studied the stack effect to enhance natural ventilation using wind tunnel experiments and CFD. Their study revealed that external wind effect is still the most important factor that determines natural ventilation performance. It is therefore important not to ignore the wind effect when studying cold storage rooms, which open into the environment. 7.4.3.1
Cold Stores
There are very few studies where CFD has been used to predict infiltration through an unprotected cold store entrance. In the studies of Foster et al. [36], CFD studies were carried out on a purpose-built refrigerated test room of internal dimensions 5 6 4 m high. The room had a large single opening, 2.3 m wide 3.2 m high. The room was constructed within a large hall to avoid wind effects and to keep the ambient air temperature steady. The entire cold store, as well as a region outside, was modeled. The initial conditions (time ¼ 0) of the air were zero velocity, 208C inside the room, and 208C outside the room. A full buoyancy model was not used, instead the Boussinesq model was used. Turbulence of the air was modeled using the k–« turbulence model. A thermal energy model was used to model the change in temperature of the air once the door was opened. Air flowing out through the door was a transient effect and there was no steady state. The model was run for a period of 30 s from the moment the door was opened and a solution obtained every second. To simplify the model, a number of assumptions were made. These were as follows: 1. There was no heat flow through the walls of the test room. 2. The test room had no thermal mass. 3. Humidity had no effect on the flow rate through the door (it does, however, have an effect on heat transfer through the door). 4. The evaporator had no effect on the airflow. 5. How the door was opened did not affect the airflow through it. 6. The simplification of outside-room conditions had no effect. 7. The room was leak proof, i.e., air can only move through the entrance. 8. The initial conditions of constant temperature and velocity inside and outside the room before the door is opened were true. The geometry was discretized with a tetrahedral mesh. The mesh size was 113,188 tetrahedral elements and 21,626 nodes. Vane anemometer measurements, carried out at different heights in the door opening, and CFD predictions showed that the airflow decreased with time. Velocities measured by the top and bottom vanes and predicted velocities in the same positions for a period between 10 and 30 s post door opening are shown in Figure 7.3. The predicted velocity into the room at the top and its decay with time is well within the repeatability of the measurements. The predicted velocity out of the room at the bottom was 0:30:5 m s1 lower than the measured velocity.
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Velocity (m s−1)
1.5 1 0.5 0 −0.5 −1 −1.5 10
15
20
25
30
Time (s)
FIGURE 7.3 Velocities measured by both the top (triangular marker) and bottom (square marker) vane anemometer (mean of six replicates, error bars represent +1 standard deviation) and predicted velocities (dashed lines) in the same positions (room temperature 208C) during a period 10 to 30 s after opening. A positive velocity is out of the room.
Vane anemometry measurement and CFD prediction both showed that air flows out (positive) of the bottom of the entrance and in (negative) through the top. The highest velocity out of the room was near the floor and the highest velocity in the room is close to the top. The velocity profile with height, one-third of the width of the entrance from the left-hand end after 20 s, is shown in Figure 7.4. The shape of the profile was well predicted by the CFD. However, the CFD underpredicted the velocity of the air leaving the chamber at the bottom of the opening. Foster et al. [22] also used CFD to predict infiltration rates. A tracer gas technique was used to measure the rate of infiltration against the length of time the door was open and the resulting data were compared to the CFD predictions (Figure 7.5). Two CFD models were used, one that had the domain boundary 3 m from outside the walls of the cold room and one
1.5 Velocity (m s−1)
1 0.5 0 −0.5 −1 −1.5 0
0.5
1
1.5
2
2.5
3
Height (m)
FIGURE 7.4 Velocities measured inside the large entrance 20 s post door opening at each anemometer position (six replicates) plotted against height. The CFD predicted velocity profiles are represented by the dashed lines.
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Infiltration (m3)
150
100
50 Measured CFD CFD extended boundaries
0 0
10
20
30
40
50
Door-opening times (s)
FIGURE 7.5 Measured and predicted infiltration through the 2.3 m wide door for different dooropening times. The CFD predictions are for both the standard and extended boundary models.
with the boundary 6 m away. Both CFD models predict a similar infiltration rate to that measured. However, both models, especially the model without the extended boundary predicted a reduction of infiltration rate with time, which was not apparent in measurements. The reason for this was probably due to the region outside the cold store reducing in temperature faster (and therefore reducing the driving force) in the model than in reality. This was because the region outside was finite in the model and effectively infinite in reality. The predictions also showed that infiltration varied with time and that the predictions could be split into three separate stages. The first stage was the lag stage covering the time required before the flow became fully developed. This was followed by a steady-state stage where there was a constant flow rate through the entrance. The final stage was the tail-off stage, where the temperature difference (driving force) between the cold store and the surroundings was reducing. The lag stage was predicted to be between 0.3 and 1.6 s for the different models. This lag stage has been measured by Azzouz et al. [6] to be of the order of 1.5 s. For long dooropening times of 30 s, a 1.5 s lag time will reduce the infiltration by only 5% compared to no lag, while for shorter door-opening periods of, for example 10 s, the infiltration will be reduced by 15%. 7.4.3.2
Air Curtains
There have been many academic studies using CFD to simulate the air curtains used for refrigerated display curtains (Chapter 3 through Chapter 6). Fewer studies have been carried out on air curtains used on buildings. Perhaps the first reported study in this area was by SenterNovem (an agency of the Dutch Ministry of Economic Affairs), TNO (a Dutch Research Institute), and the University of Groningen, together with Biddle Air curtains in the early 1990s [37]. They used the PHOENICS code to develop the CFD model using the k« model to predict turbulence and fullscale testing to validate. Their 3D model contained about 25,000 grid cells, which took about 300 h to converge; however, this is a very small mesh by today’s standard.
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The predictions showed that there was a 3D effect not seen with the 2D model, whereby air leaks through the side of the curtain. They also showed that the air curtain is not effective when there is a ventilation rate through the entrance. This ventilation rate is often a necessary design requirement to allow air changes within the building. The predictions concluded that air curtains used in shop doorways should condition the incoming air (heat it to a comfortable temperature) rather than try to reduce it. This is not, however, the case for cold room curtains on sealed cold stores, where the flow through the entrance is buoyant and there is no net ventilation rate (equal flow in and out). A major conclusion of the CFD studies was that the incoming air is conditioned most effectively at the lowest applicable air velocity, which was contradictory to past popular belief. The Building Services Research and Information Association (BSRIA) used specialpurpose CFD software, FLOVENT (developed by BSRIA and Flomerics Limited), for the analysis of air movement, temperature distribution, and airborne contaminant dispersion in the context of the built environment [38]. They studied the effect of building leakage on air curtain performance. They showed that for leaky buildings, when air curtains are subjected to large wind forces, there will be a significant pressure difference retained across the doorway and the net volume flow rate through the doorway will hardly be affected by the operation of the air curtains. Ligtenburg and Wijjfels [5] from Biddle bv (Netherlands) in collaboration with TNO Environment and Energy used CFD to study an air curtain used on frozen-food stores. They used the PHOENICS code and verified with experimental data obtained from a mock-up. The air curtain modeled had three jets blown downward at the same velocity (5 m s1 ). The inside jet (cold store side) was drawn from the cold store (308C to 208C, 80%–100% RH). The outside jet (ambient side) was drawn from the ambient (08C to 208C, 60%–100% RH). The middle jet was drawn from the cold store and heated, giving a very low relative humidity and thus reducing any condensation mist between the other two jets (perhaps 58C, 23% RH). The CFD predictions indicated that an effectiveness of 0.84 can be achieved with this air curtain. Foster et al. [20] simulated a 1.0 m long air curtain with a 30 mm slot, which was fitted centrally above the door on the outside of a cold store. For this study, a 2D model was created to allow accurate prediction of the narrow (30 mm) air curtain jet while still allowing all of the cold store and some of its surroundings to be modeled. The 2D model was created using CFX (ANSYS Inc.) 3D finite-volume code and by fixing only one numerical mesh cell over the width of the domain and applying symmetrical boundary conditions to the faces at either side. The domain of the model contained the volume inside the cold store for the width of the air curtain (initially at 208C) and a much larger volume outside the cold store (initially at þ208C), to provide a source of warm air for exchange. The volume outside the cold store was between four and eight times larger than the volume inside the cold store. This gave a good compromise between accuracy and numerical speed. The jet from the air curtain was modeled as an inlet into the domain with a constant velocity, temperature, and turbulence intensity. The magnitude of the inlet velocity was varied from 0 to 18 m s1 and the direction was taken to be normal to the boundary. The temperature of the jet was set at 208C, which was the initial temperature of the ambient, and the turbulence intensity was 10%. An opening boundary condition was set at the top side of the air curtain, removing an identical mass of air that entered from the inlet. All boundaries except the inlet and outlet of the air curtain were modeled as nonslip walls where the velocity of the fluid at the wall boundary was set to zero. The wall-function approach was an extension of the method of Launder and Spalding [39]. In the log–law region, the near-wall tangential velocity is related to the wall-shear-stress
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by means of a logarithmic relation (Equation 7.13 through Equation 7.15). In the wallfunction approach, the viscosity affected sublayer region is bridged by employing empirical formulas to provide near-wall boundary conditions for the mean flow and turbulence transport equations. These formulas connect the wall conditions (e.g., the wall-shear-stress) to the dependent variables at the near-wall mesh node, which is presumed to lie in the fully turbulent region of the boundary layer: uþ ¼
U 1 ¼ ln ( yþ ) þ C uf k
(7:13)
rDyuf m
(7:14)
12 tw uf ¼ r
(7:15)
where yþ ¼ and
The numerical mesh was at its finest (8 mm) at the entrance of the door and around the air curtain nozzle. This was in order to accurately resolve the large shear created by the air jet at the nozzle exit. The total number of grid nodes for the problem was 42,000. The k« turbulence model was used to predict turbulence effects. The hardware used to run the model was a Viglen Genie PC with an Intel Pentium 4 processor running at 1.6 GHz with 1 GB RAM. The CFD model was used to predict the effectiveness of the air curtain at differing jet velocities; this is shown against measured values in Figure 7.6. The maximum predicted effectiveness (0.84) was higher than that measured (0.72). The air curtains–measured effectiveness
Measured
1.0
Predicted 2D
Predicted 3D
Effectiveness
0.8
0.6
0.4
0.2
0.0 5
10
15
20
25
Jet velocity (m s−1)
FIGURE 7.6 Measured and predicted effectiveness of the air curtain for different air jet velocities for both 2D and 3D models.
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CFX 80 Velocity (vector 1) 6
Temperature (contour 1) (10) 20 (9) 16 (8) 12
5
3
2
(7)
8
(6)
4
(5) −0 (4) −4
7 6 5 4
(3) −8 (2) −12
3
(1) −16
0
Y
[m s−1] 2
1
X
FIGURE 7.7 (See color insert following page 142.) CFD predicted velocity vectors and temperature contours for a vertical section through the entrance with a jet velocity of 6 m s1 .
was still increasing when it reached the maximum obtainable velocity (18 m s1 ) of the air curtain. The optimum jet velocity (velocity at which maximum effectiveness is obtained) was predicted (10 m s1 ) to be lower than the measured velocity (>18 m s1 ). As discussed earlier, 2D models tend to predict a higher effectiveness than measured, as end effects allow air to leak around the edge of the air curtain, causing increased infiltration. Also, a higher measured optimum velocity is required than predicted to counteract this effect. Figure 7.7 through Figure 7.9 show the predicted velocity vectors and temperature contours for air jet velocities of 6, 10.4, and 18 m s1 , and these correspond to a lower than optimum, optimum, and above optimum velocity, respectively. For a jet velocity of 6 m s1 (Figure 7.7), the air curtain is bent into the cold store such that it does not reach the floor and therefore does not seal the entrance. For a jet velocity of 10:4 m s1 (Figure 7.8), the air curtain is vertical providing optimum sealing. For the jet velocity of 18 m s1 (Figure 7.9), the increased entrainment caused by the high velocity air curtain causes a pressure buildup inside the cold store, which forces the air curtain outward reducing its effectiveness. Foster et al. [40] extended their CFD model to a 3D model. The geometry of the modeled air curtain was an approximation of the real air curtain (Figure 7.10); the exact geometry would have required a finer mesh than was possible with the given computing resources, when used in conjunction with such a large domain. Important geometrical dimensions, such as the nozzle thickness and its relative position to the fan body, were modeled as accurately as possible. The air return grille on the air curtain was modeled as being at the top of the air curtain. This was because the real return grille characteristics were complex and attempts at modeling it with the size of mesh used in the model caused unrealistic flows. The door rail obstructed entrainment to the room side
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CFX 80 Temperature (contour 1) (10) 20
Velocity (vector 1) 10
(9) 16 (8) 11
8
5
(7)
7
(6)
3
(5) −1 (4) −6
3
(3) −10 (2) −14 (1) −18
0 [m s
Y
−1]
1
2345
X
FIGURE 7.8 (See color insert following page 142.) CFD predicted velocity vectors and temperature contours for a vertical section through the entrance with a jet velocity of 10:4 m s1 .
CFX 80 Velocity (vector 1) 18
2
1 Temperature (contour 1) (10) 20 (9) 17
14
(8) 14 (7) 11 (6) 8
9 (5) 5 (4) 2 5
(3) −1 (2) −4
0 [m s
−1]
(1) −7 Y
z
X
FIGURE 7.9 (See color insert following page 142.) CFD predicted velocity vectors and temperature contours for a vertical section through the entrance with a jet velocity of 18 m s1 .
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Return air 60
1000 620
100
Simplified door rail
120
100 30
Fan body
Air curtain jet
Air curtain jet Cold store entrance
Cold store entrance
1360
FIGURE 7.10 Front and side elevations of the modeled air curtain device and air curtain inlet and outlet boundaries. Dimensions are in millimeters.
of the outlet nozzle and so a simplified geometry was created to give the same effect (shown as the block labeled ‘‘simplified door rail’’ to the left of the outlet and return ducts in Figure 7.10). The numerical mesh ranged from 30 mm at its finest point to 500 mm at its largest point, with an expansion factor of 1.2 between these mesh sizes. The width of the air jet boundary is the same as the minimum cell size, thus there is only one cell across the width of the air jet. In the plane of the door entrance, and for a radius of 0.5 m from this plane, the mesh was 100 mm with an expansion factor of 1.2 outside the radius of influence. The total number of grid nodes for the model was 383,945. To test the convergence of the mesh, finer meshes were used on a ‘‘cut down’’ geometry. This ‘‘cut down’’ geometry was essentially the same, except a symmetry plane was used to reduce the number of mesh points. Mesh sizes of 100, 70, and 40 mm in the plane of the door entrance were produced. In this model, computer resources did not allow meshes smaller than 40 mm within the entrance. Computer simulation times were approximately 22 h for a transient run of 30 s with a mesh size of 100 mm to a normalized residual of 1 104 . For each solution variable, w, the normalized residual, rw0 , is given in general by the following equation: [rw0 ] ¼
[rw ] ap Df
(7:16)
where rw is the raw residual control volume imbalance, ap is representative of the control volume coefficient, and Df is a representative range of the variable in the domain. Figure 7.6 shows that the predicted effectiveness was always lower than measured (0.10 lower at the minimum and 0.15 lower at the maximum measured velocity). This
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model was more accurate than the 2D model, which overpredicted the effectiveness of the curtain. The trends of the predicted and measured data are similar up to the maximum measured velocity, in that they had a similar, positive gradient that reduced with jet velocity. The predicted effectiveness reached a maximum of 0.66 at a jet velocity of 22 m s1 . It was not possible to increase the measured jet velocity above 18 m s1 in these experiments due to limitations in the installed system. However, the only data found in the literature [41] show the shape of the predicted curve to be accurate, essentially a polynomial curve with one maximum effectiveness at a specific velocity. It is not possible to predict from the data at what jet velocity the maximum effectiveness would be. However, the (average) positive gradient between the highest two measured velocities indicates that the maximum effectiveness would be greater than 0.72, at a jet velocity above 18 m s1 . Figure 7.11 shows predicted velocity vectors for a vertical elevation in the central plane of the entrance. Although the air curtain leaves the nozzle pointing straight down, the air is very soon deflected away from the room by the Coanda effect due to the proximity of the fan body. It is not possible to see the 3D effects of this flow from a single 2D plane and therefore 3D isovelocity plots for three different views are shown in Figure 7.12. The isovelocity plots show the direction of airflow for all positions at 3 m s1 . The front elevation shows that the jet narrows in the plane of the entrance. The side elevation highlights that the center of the jet is bent out away from the room but the sides are folded back into the room. The plan view shows that the central part of the jet is deflected out of the room
CFX
Temperature (contour 1) 22
Velocity (vector 2) 18
17 12
14
7 2 −2
9
−7 −12
5
−17 −22 [C]
0 [m s−1]
FIGURE 7.11 Predicted velocity vectors and temperature contours in the plane of the entrance for a jet velocity of 18 m s1 .
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FIGURE 7.12 Velocity vectors at a isovelocity of 3 m s1 in the region of the entrance for a jet velocity of 18 m s1 . Front elevation (left), side elevation (right), and plan view (bottom).
(upwards in the figure) and narrows, but that the sides of the jet are drawn into the room and cross one another.
7.5 VALIDATION Validation of CFD models is a difficult task, but is extremely important [42]. A numerical discrepancy between predicted and measured data is often put down to the measured conditions not being the same as the predicted conditions [12]. This is often due to an inability to accurately measure all of the boundary conditions for the model. Validation of the CFD models has been carried out using a number of different experimental methods.
7.5.1 TEMPERATURE MEASUREMENT Azzouz et al. [6] used an array of 16 temperature probes to measure the air temperature in the entrance of a cold room while the door was open. Hendrix et al. [21] used 28 type T
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thermocouples mounted on four separate strings, three of these were hung from cold store and loading bay ceilings (4.5 m high with four equally spaced thermocouples and 9 m high with seven equally spaced thermocouples) and the fourth was mounted on a 3 m stand in the entrance with 10 thermocouples. This data were rapidly passed to a personal computer via an RS232 link.
7.5.2 VELOCITY MEASUREMENT 7.5.2.1
Vane Anemometry
Fritzsche and Lilienblum [10] used vane anemometers to measure velocity across an entrance. Similarly, Foster et al. [36] used an array of 16 minivane-anemometer heads (diameter of 25 mm) (2 columns 8 vanes) on movable frames to determine airflow through door openings. The advantage of this system was that it was a cheap way of measuring transient air velocity in multiple positions at the same time. However, the vanes were not accurate at low velocity (below 0:3 m s1 the vanes would intermittently stop spinning giving a reading of 0 m s1 ). Vane anemometers measure velocity in only one direction. This is fine where the direction of velocity is known (in this case perpendicular to the face of the entrance, in at the top and out at the bottom). However, if there are external forces on the flow, e.g., wind or an air curtain, direction of the flow will need to be first determined and the vanes aligned. If the wind is erratic this will not be possible.
7.5.2.2
Hot-Wire Anemometry
Hendrix et al. [21] used eight hot-wire anemometers in a ‘‘tree’’ support structure with a data acquisition system to measure one-dimensional velocities through the entrance. These devices were constant temperature devices and therefore required steady-state air temperatures to allow accurate velocity measurement. Placement of these devices before door opening was critical such that a step change in temperature of the device did not happen when the door was opened (this would happen if the lower anemometers were initially placed outside of the cold room). 7.5.2.3
Laser Doppler Anemometry
Laser Doppler anemometry (LDA) has the advantage that it can measure velocity in all three dimensions, is nonintrusive to the airflow, and allows rapid measurement and will therefore measure turbulence. LDA was used by Foster et al. [36] to measure velocity closer to the walls than was practical using vane anemometry. The LDA used was a threecomponent, fiber-optically coupled system using a 5 W argon ion laser, with precision three-axis traversing gear. Unlike the array of vane anemometers, the LDA was unable to measure the velocity at multiple points simultaneously. Due to the length of time for an LDA measurement to be taken and then to traverse to the next position (approximately 30 s), the data could not be taken sequentially in a single run. Measurements were taken at a single point before the door was closed and the room equalized in temperature before moving to the next position. The size of the entrance also had to be reduced such that a steady-state flow was measured, i.e., the temperature change (driving force) between the room and ambient must not change significantly over the measurement period.
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Velocity (m s−1)
1 0.5 0 −0.5 −1
0
0.2
0.4
0.6
0.8
Height (m) CFD
LDA mean
Velocity (m s−1)
0.8 0.6 0.4 0.2 0 0
0.1 0.2 Distance from left-hand side (m) LDA mean
0.3
CFD
FIGURE 7.13 Velocities measured using LDA and predicted using CFD through the small entrance against height. Vertical line 0.143 m from the left-hand edge of the entrance (top chart); horizontal line at a height of 0.134 m (bottom chart).
Measurements were made along a vertical line and a horizontal line; these measurements were compared to CFD predictions and are shown in Figure 7.13. CFD predictions of the velocity profile along the vertical line were accurate; however, predictions of the horizontal line were not so. The reason for this was that there were not enough grid cells around the entrance for the CFD to capture the vena contracta caused by the door sides. The vena contracta is caused at a sudden contraction where the flow contracts to a diameter smaller than the contraction. This vena contracta can be seen from the LDA measurements as a region of zero flow near the sidewall (Figure 7.13, bottom chart). However, due to the coarseness of the mesh in the entrance, the CFD model predicted higher velocities near the side of the door. 7.5.2.4 Digital Particle Image Velocimetry Digital particle image velocimetry (DPIV) offers an ideal method of verifying CFD simulations, as it can provide a similar level of resolution of the flow field to that of the simulation. This author has no knowledge of this technique being used for cold room entrance infiltration. However, it has been used comprehensively for refrigerated display cabinet air curtains (more details in Chapter 4). The reason for this may be that the size of plane required to
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capture the flow through the entrance is much larger than for a refrigerated display cabinet, and therefore will require a more powerful laser to illuminate it.
7.5.3 INFILTRATION It is more valid to verify infiltration caused by the door opening, as this is the parameter by which the effect of door opening on cold rooms is assessed. To verify the infiltration caused by door opening requires either measuring the flow rates in and out of the entrance, or measuring the decay of a gas that is at a higher concentration in the room than outside. 7.5.3.1
Flow Rates
Hendrix et al. [21] showed that air velocities at as few as eight heights in the doorway were required for calculating volume flow rates. This small number of points was found to be adequate, since the air velocities at the floor and neutral level are known to be zero and the air velocity profile at the top of the door is approximately flat. The volume flow rate into the room and out of the room can be calculated by integrating the velocity profile above and below the neutral level, respectively. To establish the mass flow rate involves integrating the velocity density profile. The density is calculated from the temperature using the ideal gas law (Chapter 4, Equation 4.5). It is an important point to note that the mass of air entering and leaving the room may not be the same. This will be the case if the cold room warms during the door opening; the density of the air in the cold room will decrease, and as the cold room is of fixed volume, a net mass of air must leak from the room. 7.5.3.2
Gas Decay
Tracer gas techniques can been used to measure the infiltration through a cold store. There is a standard tracer gas technique [43] applicable with many types of tracer gas. As shown in Equation 7.17, concentrations measured immediately before and after the door opening can be used to calculate the infiltration: c ln ¼ rt co
(7:17)
This method assumes that the tracer gas is fully mixed with the air in the room. Sulfur hexafluoride (SF6 ) has been used successfully [3,12] to measure infiltration. Chen et al. [3] had a system, which included a gas chromatograph and electron-capture detector with an automatic tracer gas SF6 delivery, and sampling system to monitor tracer gas concentration simultaneously at three locations. The differences between the three sampling locations were small, suggesting that it was reasonable to assume the air in the cold store was well mixed. For trials with large rates of infiltration there was a slight delay between the start of the door-opening regime and detection in changes in the tracer gas concentration. This was attributed to the partitioning effect described by Pham and Oliver [12]. They showed that the presence of product racking tends to divide the room into several zones, so that some of the air entering the building goes out without thoroughly mixing with the air in the rest of the room. Carbon dioxide (CO2 ) is another gas that can be used; its disadvantage over SF6 is that it can only be detected at much larger concentrations; however, its advantage is that it can be detected with infrared absorption equipment rather than the much more expensive electroncapture gas chromatograph.
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Foster et al. [22] used CO2 to determine the volume of air exchange in the test room during a period with the door open. The concentration of CO2 was recorded before and after a set door-opening time. Carbon dioxide was released into the room and mixed using the evaporator fans to give a concentration of approximately 0.5% (5000 ppm). This was measured using a CO2 infrared analyzer (accuracy 5% of full scale). The room was small and contained no product racking and therefore partitioning effects were not considered important. Immediately before each door-opening test, the evaporator fans were switched off to allow the air movement to settle for 30 s. The door was fully opened for the set door-opening time and then closed. All trials were carried out with an initial cold room temperature of 208C. The concentration of CO2 immediately before opening the door and immediately after closing the door was used to calculate the infiltration rate.
7.6 CONCLUSIONS CFD models of the velocity profile through cold store entrances presented in this chapter have been shown to be generally accurate; however, there are areas where the accuracy is less than satisfactory. Reasons for this can usually be put down to limitations in the number of mesh cells allowed due to the computer hardware (memory). The mesh cells need to be small around the entrance to capture the vena contracta, but larger away from the entrance to reduce the overall number of cells. Control of the ambient conditions is also an important consideration, wind effects have been shown to be very important and therefore either need to be included in the model or known to be insignificant in reality. The extent of the ambient domain that needs to be modeled is another important consideration. If the ambient is small and the door is opened for a longtime, the ambient temperature may rise, causing a drop-off in the driving force, which may not be apparent in reality, where the ambient may be effectively infinite. CFD predictions have been shown to give a significant improvement in accuracy over the fundamental analytical equations (Brown and Tamm); however, the empirical coefficients added by Gosney and Fritzsche gave more accurate predictions than the CFD models. More detailed CFD models with more grid cells in the entrance may give a better prediction. CFD models show a lag time that analytical predictions ignore, however, unless the door-opening time is very short this reduction in flow is quite insignificant. A 2D CFD model was unable to accurately predict the optimum jet velocity of an air curtain. However, it predicted a value equivalent to that predicted by an analytical model with a low safety factor. The CFD model showed how the shape of the air curtain varied with different jet velocities as the air curtain traveled down the entrance and how these different jet velocities affected the effectiveness of the curtain. The analytical model of Hayes and Stoecker predicts optimum jet velocity of an air curtain on a cold store; however, it does not predict effectiveness of the air curtains. The model only gives a guide to the optimum jet velocity; depending upon the safety factor chosen, a large range of air curtain effectiveness can therefore be achieved. A 2D CFD model can predict the effectiveness of an air curtain; however, the predictions were higher than measured. This is because end effects will allow air to leak around the edge of the air curtain, causing increased infiltration, which are not predicted in 2D. Higher jet velocities will to some extent negate this problem and this is a probable explanation for the increased optimum jet velocity of the real air curtain compared to the 2D CFD model. A 3D CFD model was able to provide a better prediction of effectiveness and optimum jet velocity than the 2D model. The predicted effectiveness was lower and optimum jet velocity higher than measured, the opposite to the 2D model. The model showed that the flow from
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an air curtain cannot be considered as 2D. For the air curtain studied a complex 3D flow pattern was apparent. Many different experimental approaches have been used to provide data to verify these CFD models. These include thermometry, arrays of minivane anemometers, hot-wire anemometry, LDA, and tracer gas techniques, which include both SF6 and CO2 . Each approach has its own advantages and disadvantages and therefore a complete validation may be better carried out using a range of these methods. A more complete validation of the 3D interaction between the air curtain and the natural convection in the entrance requires a tool such as DPIV. This has been used in refrigerated display air curtains but not yet with cold store air curtains. Current computer power is still a limitation for accurate 3D predictions. Future increases in computer power, especially with the advent of 64-bit hardware and parallel processing should allow more accurate predictions.
NOMENCLATURE at A b c cp C Cm Ce1 Ce2 E g k Kf,L H p P Q r t T u uþ U yþ
turbulent diffusivity (m2 s1 ) area of entrance (m2 ) wall thickness (m) concentration 1 specific heat at constant pressure (J kg1 K ) log layer constant k« turbulence model constant (0.09) k« turbulence model constant (1.44) k« turbulence model constant (1.92) effectiveness, dimensionless acceleration due to gravity (9:81 m s2 ) turbulent kinetic energy per unit mass (J kg1 ) correction factor height of entrance (m) static pressure (Pa) 3 shear production of turbulence (kg m1 s ) 3 infiltration (m ) air change rate, dimensionless time (s) temperature (K) velocity (m s1 ) near-wall velocity (m s1 ) velocity tangent to the wall at a distance Dy from the wall (m s1 ) dimensionless distance from the wall
GREEK SYMBOLS b d « k l r se
coefficient of thermal expansion (K1 ) identity matrix, dimensionless 3 turbulence dissipation rate (m2 s ) von Karman constant 1 thermal conductivity (W m1 K ) 3 density (kg m ) k« turbulence model constant (1.3)
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sk st t m
191
k« turbulence model constant (1.0) turbulent Prandtl number shear stress (N m2 ) 1 dynamic viscosity (kg m1 s )
SUBSCRIPTS a with air curtain avg average b without air curtain f friction i inside n neutral o outside ref reference t turbulent 0 initial
SUPERSCRIPTS — 0
T w
turbulent mean quantities turbulent fluctuating quantities inverse matrix wall
REFERENCES 1. G. Olafsdottir, H.L. Lauzon, E. Martinsdottir, J. Oehlensschlager, and K. Kristbergsson. Evaluation of shelf life of superchilled cod (Gadus morhua) fillets and the influence of temperature fluctuations during storage on microbial and chemical quality indicators. Journal of Food Science 71: 2 S97–S109, 2006. 2. R. Faramarzi, B.A. Coburn, and R. Sarhadian. Showcasing energy efficiency solutions in a cold storage facility. Energy Efficiency in Buildings; Teaming for Efficiency 3: 107–118, 2002. 3. P. Chen, D.J. Cleland, S.J. Lovatt, and M.R. Bassett. Air infiltration into refrigerated stores through rapid-roll doors. In: Proceedings of International Institute of Refrigeration, Sydney, 1999. 4. D. Leue and P. Eilert. Industry transformation in refrigerated warehouses. In: Proceedings of the American Council for an Energy Efficient Economy, Washington, DC, 2000. 5. P.J.J.H. Ligtenburg and D.J. Wijjfels. Innovative air curtains for frozen food stores. In: Proceedings of International Institute of Refrigeration, The Hague, 1995, pp. 420–437. 6. A. Azzouz, J. Gosse, and M. Duminil. Experimental determination of cold loss caused by opening industrial cold room doors. International Institute of Refrigeration 16(1): 57–66, 1993. 7. J. Emswiler. The neutral zone in ventilation. Journal of the American Society of Heating and Ventilating Engineers 32(1): 1–16, 1926. 8. W.G. Brown and K.R. Solvason. Natural convection in openings through partitions-1, vertical partitions. International Journal of Heat and Mass Transfer 5: 859–868, 1963. 9. W. Tamm. Kalterveluste durch kuhlraumoffnungen. Kaltetechnik-Klimatisierung 18: 142–144, 1966. 10. C. Fritzsche and W. Lilienblum. Neue messengun zur bestimmung der kalterluste an kuhlraumturen. Kaltetechnik-Klimatiserung 20: 279–286, 1968. 11. W.B. Gosney and H.A.L. Olama. Heat and enthalpy gains through cold room doorways. Proceedings of the Institute of Refrigeration 72: 31–41, 1975. 12. Q.T. Pham and D.W. Oliver. Infiltration of air into cold stores. In: Proceedings of the International Institute of Refrigeration, Paris, 1983, 4: pp. 67–72.
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13. B.W. Jones, B.T. Beck, and J.P. Steele. Latent loads in low humidity rooms due to moisture. ASHRAE Transactions 89: 35–55, 1983. 14. C.O. Gill. The microbiology of chilled meat storage. In: Proceedings of the 24th Meat Industry Research Conference, Hamilton: MIRINZ Publication, 1986, pp. 210–213. 15. S.J. James and J.E. Evans. Frozen storage of meat and meat products. FAIR Concerted Action PL95–1180, 1997. 16. G. Londahl and C.E. Danielson. Time temperature tolerances for some meat and fish products. In: Proceedings of International Institute of Refrigeration, Warsaw, 1972. 17. S.J. James and C. James. Microbiology of refrigerated meat. In: Meat Refrigeration. Cambridge: Woodhead Publishing Limited, 2002. 18. M. Boast. Frost free operation of large and high rise cold storage. Proceedings of the Institute of Refrigeration 6: 1–11, 2003. 19. W.R. Micheal. Air curtains for use on cold stores. In: Proceedings of International Institute of Refrigeration, Marseille, 1960, pp. 489–495. 20. A.M. Foster, M.J. Swain, R. Barrett, P. D’Agaro, and S.J. James. Effectiveness and optimum jet velocity for a plane jet air curtain used to restrict cold room infiltration. International Journal of Refrigeration 29(5): 692–699, 2006. 21. W.A. Hendrix, D.R. Henderson, and H.Z. Jackson. Infiltration heat gains through cold storage room doorways. ASHRAE Transactions 95(2): 1158–1168, 1989. 22. A.M. Foster, M.J. Swain, R. Barrett, and S.J. James. Experimental verification of analytical and CFD predictions of infiltration through cold store entrances. International Journal of Refrigeration 26(8): 918–925, 2003. 23. G.N. Abramovitch. The Theory of Turbulent Jets. Cambridge, MA: The MIT Press, 1963. 24. N. Rajaratnam. Turbulent Jets. Amsterdam: Elsevier Scientific, 1976. 25. C.J. Chen and W. Rodi. Vertical Turbulent Buoyant Jets—A Review of Experimental Data. Oxford: Permagon Press, 1980. 26. F.C. Hayes and W.F. Stoecker. Heat transfer characteristics of the air curtain. ASHRAE Transactions 2120: 153–167, 1969. 27. F.C. Hayes and W.F. Stoecker. Design data for air curtains. ASHRAE Transactions 2121: 168–180, 1969. 28. H.W. Wang and S. Touber. Simple non-steady-state modeling of a refrigerated room taking account air flow and temperature distributions. In: Proceedings of the International Institute of Refrigeration, Wageningen, 1989, pp. 211–219. 29. M. Mariotti, G. Rech, and P. Romagnoni. Numerical study of air distribution in a refrigerated room. In: Proceedings of the International Institute of Refrigeration, The Hague, 1995, pp. 98–105. 30. M.L. Hoang, P. Verboven, J. de Baerdemaeker, and B.M. Nicolai. Analysis of the air flow in a cold store by means of computational fluid dynamics. International Journal of Refrigeration 23: 127–140, 2000. 31. H.H. Nahor. CFD model of the airflow, heat, and mass transfer in cool stores. Revue internationale du froid 28(3): 368–380, 2005. 32. A. Schaelin, J. van der Maas, and A. Moser. Simulation of airflow through openings in buildings. ASHRAE Transactions 2: 319–328, 1992. 33. W. Schmidt. Turbulente Ausbreitung eines Stromes erhizter Luft. Zeitschrift fu¨r Angewandte Mathematik und Mechanik 21(5): 264–278; 21(6): 351–363, 1941. 34. W. Rodi. Turbulent Buoyant Jets and Plumes. Oxford: Permagon Press, 1982. 35. N.H. Wong and S. Heryanto. The study of active stack effect to enhance natural ventilation using wind tunnel and computational fluid dynamics (CFD) simulations. Energy and Buildings 36(7): 668–678, 2004. 36. A.M. Foster, R. Barrett, S.J. James, and M.J. Swain. Measurement and prediction of air movement through doorways in refrigerated rooms. International Journal of Refrigeration 25(8): 1102–1109, 2002. 37. P. Ligtenburg and P. Waldron. Open door trading: Cutting out the energy waste. Heating and Ventilating Engineer 65(713): 14–20, 1992. 38. F. Alamdari. Air curtains: Commercial applications. BSRIA Application Guide 2=97, Berkshire, 1997.
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39. B.E. Launder and D.B. Spalding. The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering 3: 269–289, 1974. 40. A.M. Foster, M.J. Swain, R. Barrett, P. D’Agaro, L.P. Ketteringham, and S.J. James. Threedimensional effects of an air curtain used to restrict cold room infiltration. Applied Mathematical Modelling 31(6): 1109–1123, 2007. 41. G.R. Longdill, L.F. Frazerhurst, and L.G. Wyborn. Air Curtains—MIRINZ Report Number 385. Hamilton: Meat Research Institute of New Zealand, 1974. 42. M.N.A. Said, C.Y. Shaw, J.S. Zhang, and L. Christianson. Computation of room air distribution. ASHRAE Transactions 101(1): 1065–1077, 1995. 43. A.S.T.M. Standard practice for measuring air leakage rate by the tracer dilution method. ASTM standard E741–83, Annual Book of ASTM Standards. Philadelphia: American Society for Testing and Materials, 1983. 44. C.C. Downing and W.A. Meffert. Effectiveness of cold-storage door infiltration protective devices (rp-645). Transactions of the ASHRAE: 99–356, 1993. 45. K. Takahashi and M. Inoh. Some measurements on air curtain efficiency for cold rooms. In: Proceedings of the International Institute of Refrigeration, Munich, 1963, 2: pp. 1035–1039. 46. G.R. Longdill and L.G. Wyborn. Performance of air curtains in single-storey cold stores. In: Proceedings of the International Institute of Refrigeration, Venice, 1978, 4: pp. 77–88. 47. J. Van Male. A new vertical air curtain design for cold-storage doors. In: Proceedings of the International Institute of Refrigeration, Paris, 1983, 4: pp. 74–82.
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8
CFD Modeling of Simultaneous Heat and Mass Transfer in Beef Chilling Francisco Javier Trujillo and Q. Tuan Pham
CONTENTS 8.1 8.2
Introduction ............................................................................................................... 195 CFD Modeling of Heat and Mass Transfer on a 2D Model of a Beef Leg—A Rigorous Approach .............................................................................. 197 8.2.1 Problem Statement ......................................................................................... 197 8.2.2 Mathematical Model ...................................................................................... 198 8.2.2.1 Transport Equations in the Air ........................................................ 198 8.2.2.2 Transport Equations in the Meat ..................................................... 200 8.2.2.3 Boundary Conditions and CFD Modeling....................................... 200 8.2.2.4 Initial Conditions.............................................................................. 202 8.2.2.5 Boundary Layer Treatment .............................................................. 202 8.2.3 Details of Numerical Solution ........................................................................ 202 8.2.4 Results and Analysis....................................................................................... 204 8.3 CFD Modeling of Heat and Mass Transfer on a Three Dimensional Model of a Beef Carcass—The Three-Step Method .................................................. 205 8.3.1 Mathematical Model ...................................................................................... 207 8.3.2 Validation ....................................................................................................... 209 8.4 A Simplified Combined CFD-Conduction Model for Beef Chilling ......................... 214 8.5 Conclusions................................................................................................................ 217 Nomenclature ..................................................................................................................... 218 References .......................................................................................................................... 219
8.1 INTRODUCTION Refrigeration is the most widely used method for preserving the quality of fresh meat. In industrial beef processing, after the animal is killed, it is de-hided, eviscerated, sawn into halves (called sides), then chilled in an air chiller for 16 h or more. During this process, cooling and water movement proceed together and interact to influence surface water activity, microbial growth, weight loss, meat temperature, and meat tenderness, all of which have important economic consequences. As the meat cools, heat is conducted through the product and carried away by the air. The meat surface is warmer and more humid than the air, resulting in surface evaporation. Water from inside diffuses towards the surface to make up for the evaporation. The balance between evaporation and diffusion governs the water activity near the surface, which together with temperature determines the potential for
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microbial growth. It is therefore important to be able to calculate the evolution of temperature and moisture during this chilling process in order to optimize it, or at least to ensure that the quality standards to the consumer are maintained. Both heat and mass transfer are affected by the flow characteristics and the development of the momentum, heat, and mass boundary layers. They are the function of air properties, the geometry of the product, that of the chiller room, and the flow characteristics (temperature, humidity, velocity, and turbulence). Therefore, local variations in the heat and mass transfer coefficients are expected along the surface [1], producing local differences in temperature and water activity. These variations are important because they may cause hot or moist spots where unacceptable microbial growth takes place. Early numerical models of meat chilling [2–7] have focused on solving the equations for conduction and=or diffusion in the meat. A common shortcoming of these methods is that they use empirical equations to determine the average heat and mass transfer coefficients. These equations have been developed for airflow around simple geometries but do not necessarily apply to the complex flow pattern around real carcasses. It is known that the value of the surface heat transfer coefficients (HTC) varies along the surface of the product, depending on the development of the boundary layer. Kondjoyan and Daudin [8] showed that the convective transfer coefficient value varies from 40% to þ40% of the mean value around a circular cylinder. Variations in the case of real food geometries, such as a pork hindquarter [9], are even more complex. Recently, computational fluid dynamics (CFD) has been used to model the chilling process of beef carcasses in order to determine local variations of heat and mass transfer coefficients around real food geometries. Nguyen and Pham [10] used CFD to simulate the heat transfer process in beef carcass chilling. The complex geometry of the beef carcasses was represented in three dimensions by a grid of about 100,000 nodes. Nguyen and Pham took into account heat conduction inside the meat and heat convection in the air phase, but they did not take into account evaporation and mass transfer. Hu and Sun [11] modeled the heat and mass transfer on the air side during the cooling of cylindrical-shaped cooked meat. They used the CFD software CFX to calculate the average heat transfer coefficient ht but did not predict local (ht ) variations. Hu and Sun [12] improved the previous model by calculating the local heat transfer coefficient cell by cell around a 3D model of the surface, but the mass transfer was not treated rigorously via CFD modeling. For example, the Lewis relationship was used to calculate mass transfer from heat transfer, and the surface water activity of the meat was assumed to be equal to the relative humidity of the air (on a scale of 0 to 1), which is not necessarily true. Most models calculate the average mass transfer coefficient hm using the Lewis relationship and assume a constant value for water activity [5,6,11,12]. A source of difficulty is that heat and mass transfer happen on vastly different scales due to the big difference in heat and mass diffusivity in the meat. By the time the whole product is cooled, only the surface layer (a few mm) loses water. This makes it difficult to model the two processes efficiently and accurately using a homogeneous grid. To solve this problem, Pham and Karuri [13] used a secondary grid for moisture calculations, but they solved the transport equations only for the solid phase and not for the air phase, relying instead on an empirical ht and the Lewis relationship to calculate the hm . A complete and rigorous approach for the simultaneous heat and mass transfer on a 2D model of a beef leg was presented by the authors [14] using Fluent 6.0. Special techniques were used to solve the heat and mass transport equations for both the air and meat phases, due to some limitations in the software. In the air, turbulent flow was modeled with the renormalization group (RNG) k–« model and the boundary layer was fully solved using the Fluent’s enhanced wall treatment. This model predicted local variations in the heat and mass transfer
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coefficients and temperature and water activity around the elliptical surface. The model was then extended [15] to a complete 3D beef carcass model and it was able to predict weight loss, heat load, surface and center temperatures. For the complex carcass geometry, a three-step method was used to simulate the simultaneous heat and mass transfer process in order to reduce the computational time. In the first step, a steady-state simulation of the flow field was conducted. In the second step, the local heat and mass transfer coefficients were calculated. Finally, the third step consisted of the simultaneous heat and mass transfer process simulation in the meat carcass only using the previously obtained transfer coefficients as boundary conditions. A separate 1D grid was used to calculate the moisture diffusion in the meat. The model allowed calculating and predicting the heat load, temperatures, weight loss, and water activity. Local variations in the heat and mass transfer coefficients, temperature, and water activity were found around the beef carcass. The CFD model gave temperature predictions that agree with experimental data better than any previous model. This chapter is divided into three main sections. Section 8.2 describes the rigorous approach for the simultaneous heat and mass transfer [14] and its implementation in Fluent. This model is implemented in a 2D geometrical representation of a beef leg cross section. Section 8.3 explicates a three-step method applied to the complex 3D carcass geometry. Finally, Section 8.4 illustrates the use of CFD to calculate local heat and mass transfer coefficients and their subsequent incorporation into faster simplified models.
8.2 CFD MODELING OF HEAT AND MASS TRANSFER ON A 2D MODEL OF A BEEF LEG—A RIGOROUS APPROACH A numerical simulation of the simultaneous unsteady heat and mass transfer in an elliptical model of a beef leg is carried out using Fluent 6.1. Special programming techniques are used to solve the heat and mass transport equation for both the air and meat phases, due to some limitations in the software. The meat was treated as a fluid subregion where the heat and mass transport equations are modeled by different scalar variables, which are however linked at the interface with the heat and mass transfer modeling of the air phase. In the air, turbulent flow was modeled with the RNG k–« model and the boundary layer was fully solved using Fluent’s ‘‘enhanced wall treatment.’’ The model predicts local variations in the heat and mass transfer coefficients and temperature and water activity around the ellipse’s surface.
8.2.1 PROBLEM STATEMENT A beef leg undergoing chilling is modeled as an ellipse [6] with minor and major diameters of 0.22 and 0.29 m, respectively, placed inside a wind tunnel 1.5 m wide by 2.3 m long (Figure 8.1). Air enters the tunnel at 277.95 K, 98% relative humidity, atmospheric pressure, 0:54 m s1 normal to the inlet plane, and with a turbulence intensity of 10%. The product is initially at 315.15 K with a moisture content of 75% wet basis. The properties of air were assumed constant except the density that was expressed as function of temperature and pressure. For the meat, we assume a density of 1111 kg m3 , specific heat of 3407 J kg1 K1 , and thermal conductivity of 0:397 W m1 K1 . The moisture diffusivity can be calculated with the equation obtained by curve-fitting drying data for lean beef meat samples [16]: Dm ¼ 4:67 105 exp(3757:26=T) m2 s1
(8:1)
In the drying tests for determining moisture diffusivity (Dm ), it was found that the effective diffusivity varied with time. The above equation corresponds to the initial drying period,
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Moisture Heat
FIGURE 8.1 Representation of the beef leg as an ellipse.
where the meat shrinkage of the samples is less than 10%. It was expected that the initial drying period simulates best the conditions in carcasses chilling, where shrinkage of the meat is negligible and water diffusion from inside the meat constantly rewets the meat surface. The effect of the external fat cover on the water diffusivity was neglected in the model.
8.2.2 MATHEMATICAL MODEL 8.2.2.1
Transport Equations in the Air
In the air, a set of six transport equations are solved: a. The Continuity Equation @r v ¼ 0 þ r r~ @t
(8:2)
v is the mean velocity vector. where r is the density, t is the time, and ~ b. The Momentum Equation @( r~ v) þ r r~ v~ v ¼ rp þ r ( teff ) @t
(8:3)
where p is the pressure and teff the effective stress tensor given by teff ¼ meff
h i T vI v þ r~ v 2 r ~ r~ 3
with meff being the effective viscosity.
(8:4)
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c. The Energy Transport Equation @(rE ) v (rE þ p) ¼ r þr ~ @t
leff rT
X
Jj þ teff Hj ~
! v ~
(8:5)
j
where leff is the effective thermal conductivity, Hj the enthalpy of the species j, ~ Jj the diffusion flux of species j, E the specific energy of the fluid defined as p v2 E ¼ H þ r 2
(8:6)
where H is the enthalpy and v2 =2 represents the kinetic energy. d. The Water Transport Equation @(rY ) vY ¼ r ~ þ r r~ Jw @t
(8:7)
~ Jw ¼ rDeff rY
(8:8)
where Deff is the effective water diffusivity and Y the water mass fraction. e. The Turbulent Kinetic Energy Equation X @ X @ @ @k ð rk Þ þ rkvj ¼ ak meff þ Gk þ Gb r« YM @t @xj @xj @xj j j
(8:9)
f. The Turbulent Dissipation Rate Equation X @ X @ @ @« « «2 (r«) þ r«vj ¼ a« meff þ C1« ðGk þ C3« Gb Þ C2« r R« @t @xj @xj @xj k k j j
(8:10)
The RNG k–« model [17,18] was used to calculate the turbulent kinetic energy, k, and its rate of dissipation, « (Equation 8.9 and Equation 8.10). In these equations, Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients. Gb is the generation of turbulence kinetic energy due to buoyancy. YM represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate. C1« , C2« , and C3« are constants. The quantities ak and a« are the inverse effective Prandtl numbers for k and «, respectively. The scale elimination procedure in RNG theory results in a differential equation for turbulent viscosity: 2 r k y^ d pffiffiffiffiffiffi ¼ 1:72 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d^ y «m y^3 1 þ Cy where y^ ¼ meff =m Cy 100
(8:11)
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Equation 8.11 is integrated to obtain the effective viscosity turbulent viscosity meff . It gives an accurate description of how the effective turbulent viscosity varies with the effective Reynolds number, allowing the model to better handle low Reynolds number and near-wall flows [18]. The effective thermal conductivity is calculated from leff ¼ aCp meff
(8:12)
a 1:3923 0:6321 a 2:3923 0:3679 m
¼
a 1:3929
a 2:3929
m 0 0 eff
(8:13)
where a is calculated from [17]
and a0 ¼ 1=Pr ¼ k=mCp . The effective diffusivity Deff is calculated in a manner that is analogous to the method used for heat transport. For this case, the value of a0 in Equation 8.13 is a0 ¼ 1=Sc, where Sc is the ‘‘molecular Schmidt number.’’ 8.2.2.2
Transport Equations in the Meat
In the meat, only the transport equations for thermal energy and moisture need to be solved. The energy transport equation is @ rm cp,m T ¼ r(lm rT) (8:14) @t where rm , cp,m , lm , and T are the density, heat capacity, thermal conductivity, and temperature of the meat, respectively. The moisture transport equation is @(rm W ) ¼ r(rm DmrW ) @t
(8:15)
where W is the water mass fraction in the meat (wet basis) and Dm the water diffusivity. 8.2.2.3
Boundary Conditions and CFD Modeling
Conditions at the inlet of the wind tunnel containing the beef leg are as given under ‘‘Problem specifications.’’ At the tunnel outlet, zero normal gradients are assumed for all variables: v, T, Y, «, k. At the walls of the tunnel, zero velocity, zero heat flux, and zero water flux are assumed. At the meat surface, thermal and species equilibrium, and conservation of heat and mass apply. With regard to conservation of heat and mass, special computational techniques have to be applied to balance the heat and mass fluxes coming out of the solid (beef carcass) with those entering the air phase; the heat and moisture leave the beef region to enter the air region. If the mesh is fine enough to get into the thermal and mass boundary sublayers, the water flux that enters the air can be calculated cell by cell using the concentration profile in the air control volume next to the solid surface, using the equation Jw ¼ rD
Ys Yc ds
(8:16)
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where Jw is the local water flux on a particular surface element, Ys and Yc are the water mass fraction in the air at the meat surface and center of the volume element, respectively, ds is the distance between the meat surface and the center of the volume element. The heat flux (q) entering the air was calculated as the sum of convection (qconv ), evaporative (qevap ), and radiative (qrad ) components: q ¼ qconv þ qevap þ qrad
(8:17)
qevap ¼ Jw DHvap qrad ¼ s«r Ts4 Ta4
(8:18) (8:19)
where DHvap is the latent heat of vaporization of water, Ts the temperature on the meat surface, and Ta is the bulk temperature of the air. qconv was calculated using the temperature gradient of the air control volume next to the surface: qconv ¼ l
Ts Tc ds
(8:20)
where Ts and Tc are the air temperate on the meat surface and center of the volume element, respectively. The following equilibrium conditions between the air in contact with meat and the meat surface must also hold: a. Thermal Equilibrium Ts ¼ Ta,s ¼ Tm,s
(8:21)
where Ta,s is the temperature of the air phase on the meat surface and Tm,s is the temperature of the meat at the surface. b. Chemical Potential or Water Activity Equilibrium aw ¼ aw,m,s ¼ aw,a,s
(8:22)
where aw,m,s and aw,a,s are the superficial water activity of the meat and air, respectively. As a consequence of Equation 8.22, the absolute humidity (water mass fraction dry basis) of the air on the meat surface (Ys ) can be calculated from the following equation: Ys ¼
aw PV =PT 18 1 aw PV =PT 29
(8:23)
The surface water activity aw is calculated as a function of the water content of the meat at the surface using the Lewicki equation [19]: Xm ¼
0:0488 0:0488 34:7794 (1 aw )0:8761 1 þ aw
(8:24)
where Xm is the dry basis water content of the meat at the surface (g water g dry solid1 ). The Lewicki equation was chosen for its applicability to the high water activity range. This equation fits well the moisture sorption isotherm data at high humidities and predicts that the water content Xm tends to infinity when aw ! 1, as expected. Other models, such as
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the Guggenheim–Anderson–de-Boer (GAB) or Peleg equations, are inaccurate in the high water activity range. For instance, the GAB equation is applicable to a wide range of aw (0.1–0.9) but it has been reported that the error increases sharply for values of aw above 0.9. The surface water activity during meat cooling has been found to be in the high range [20] caused by continuous moisture diffusion from inside the meat to the surface. Thus, the Lewicki model is considered more appropriate. The model neglects the effect of the external fat cover on the water activity. 8.2.2.4
Initial Conditions
At zero time, the meat temperature and moisture content are uniform as per ‘‘Problem Statement.’’ It was also assumed that the airflow was fully developed. Thus, a steady-state solution for the air phase was done as a preliminary step before starting the transient simulation, with the air temperature near the meat surface kept at 315.15 K and the humidity corresponding to equilibrium with the meat. 8.2.2.5
Boundary Layer Treatment
The temperature and concentration gradients next to the surface must be accurately known because they are used to calculate the mass and heat fluxes between the meat surface and the air. Therefore, we used the Fluent’s enhanced wall treatment [18] in order to model the fluid all the way to the wall. This near-wall modeling method combines the two-layer model, where the viscosity affected near-wall region is completely resolved all the way to the viscous sublayer, using enhanced wall functions. In this approach, the whole domain is subdivided into a viscosity-affected region and a fully turbulent region. The demarcation of the two regions is determined by a wall-distance-based turbulent Reynolds number [18]. In the fully turbulent region the k–« model is used. The turbulent viscosity in the viscosity-affected nearwall region is determined with the one-equation model of Wolfstein [21]. The turbulent viscosities in the two regions are smoothly blended using a blending function. To extend its applicability throughout the near-wall region, Fluent formulates the law of the wall (enhanced wall function) as a single expression for the entire wall region by blending the linear (laminar) and logarithmic (turbulent) laws of the wall using a function suggested by Kader [22]. The latter is a near-wall modeling method that combines a two-layer model (the viscosity affected near-wall region is completely resolved all the way to the viscous sublayer) with enhanced wall functions. The near-wall mesh must be fine enough to resolve the transport equations down to the laminar sublayer. This is also important given that the wall functions (Fluent adapted them from Ref. [23]) are valid for fully developed turbulent flows (high Reynolds numbers) and this is not the case for carcass chilling. Therefore, it is not recommended to use the common simplification of using a gross mesh altogether with wall functions to accurately model beef chilling processes.
8.2.3 DETAILS
OF
NUMERICAL SOLUTION
The equations were solved using Fluent’s segregated method, where the governing equations are solved sequentially. In that method, each discretized transport equation is linearized implicitly with respect to the equation’s dependent variable. Because the equations are nonlinear and coupled, iterations must be performed before a converged solution is obtained. A point implicit (Gauss–Seidel) linear equation solver is used by Fluent in conjunction with an algebraic multigrid (AMG) method. The pressure–velocity coupling method used was pressure-implicit with splitting of operators (PISO), which is recommended for unsteady
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problems. Time steps of 1 s were used at the beginning, gradually increasing up to 10 min at the end of the simulation. Up to 40 iterations were done for each time step. If the meat is defined in Fluent as a solid region, the mass transfer processes cannot be solved because Fluent cannot solve the mass transfer equation in a solid. Thus, the meat had to be defined as a fluid phase. However, the heat and mass transfer modeling obtained by Fluent in that ‘‘meat fluid region’’ is not valid because Fluent adds convective and other extra terms that are not part of the transport equations in the meat. To overcome this problem, Fluent allows the user to define new field variables called user-defined scalars (UDS). The moisture and temperature inside the meat are considered as new field variables or UDS with their own associated transport properties (diffusivity and density). Defining a UDS simply involves specifying whether there are convective, diffusive, and transient terms in the transport equations, and specifying expressions for the transport properties mentioned above. The Fluent default menu allows only fixed boundary conditions. Because the boundary conditions at the air–meat interface change with time and are dependent on the values of the field variables, they have to be modeled using user-defined functions (UDFs), which are functions programmed by the user in Cþþ that can be automatically linked with the Fluent Solver. With a UDF, we can take the present values of the local field variables (temperature, moisture content, etc.) and use them to calculate the boundary conditions at that particular instant. The UDFs are incorporated in the set of equations solved by the segregated solver, such that the values they predict are updated in each new time step iteration. There are four UDFs representing the moisture balance, the heat balance, moisture equilibrium, and thermal equilibrium at the interface: 1. DEFINE_PROFILE (mass_flux_meat, tm, j): Calculates the moisture flux leaving the meat at the interface by convection, using Equation 8.16. It is used as a boundary condition of the UDS2 that represents the mass transport equation in the meat. 2. DEFINE_PROFILE (heat_flux_meat, tm, j): Calculates the heat flux leaving the meat at the interface by convection, radiation, and evaporation according to Equation 8.17. It is used as a boundary condition of the UDS1 that represents the energy transport equation in the meat. 3. DEFINE_PROFILE (temperature_air_interf, t, n): Makes the air temperature at the meat interface equal to the meat surface temperature (Equation 8.21). It is used as a boundary condition of the air phase energy equation. 4. DEFINE_PROFILE (water_air_interf, t, n): Calculates the moisture concentration in the air at the interface by the following procedure: . Read the meat surface temperature (Equation 8.21). . Read the moisture concentration at the meat interface and calculate the water content. . Calculate the water activity with Equation 8.24 using the Newton–Raphson method. . With the water activity and the meat surface temperature, calculate the moisture content of the air using Equation 8.23. This UDF is used as a boundary condition of the mass equation of the air phase. In each iteration the segregated method solver does the following: . . .
Solve the linearized discretized momentum equation in the air phase. Solve total mass conservation in the air phase and update velocities. Solve energy equation in the air phase—this involves calls to UDF3 for a boundary condition.
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. . .
.
. .
Solve moisture equation in the air phase—this involves calls to UDF4 for a boundary condition. Solve for turbulent kinetic energy in the air phase. Solve for eddy dissipation in the air phase. Solve energy (UDS1) equation in the meat phase. This involves calls to UDF2 for the boundary condition. Solve moisture (UDS2) equation in the meat phase. This involves calls to UDF1 for the boundary condition. Update all properties. Check for convergence.
For each time step, this procedure is carried out until convergence is obtained or 40 iterations have been done. In order to enhance the stability of the procedure, the UDFs 1 to 4 were calculated after getting convergence in the previous time step.
8.2.4 RESULTS
AND
ANALYSIS
Figure 8.2 shows the changes of the surface temperature with the position over the elliptical cylinder (given by the angle) after 1 and 5 h. As can be seen in the figure, the temperature varies by up to 58C around the ellipse at a particular time. Local variations of the water activity with position can be seen in Figure 8.3. Figure 8.4 shows the water concentration profile deep inside the meat at 08 (the impact or stagnation point), indicating that the mass transfer inside the meat is noticeable only in a 25 mm surface layer (about one-fifth of the mean radius). The heat transfer on the other hand affects the entire domain inside the meat, as seen in Figure 8.5, which shows the temperature profiles at time 0 min, 30 min, and 5 h. This modeling proved that it is feasible to conduct a rigorous unsteady-state simulation of the simultaneous heat and mass transfer process during beef chilling. However, the computational cost is very high. To model 20 h of chilling on this simple 2D object took about 6 days on a Pentium 1.5 GHz computer, making it unpractical for normal industrial calculations.
296 Temperature 1 h Temperature 5 h
294 Temperature (K)
292 290 288 286 284 282 280 0
20
40
60
80 100 Angle (⬚)
120
140
160
FIGURE 8.2 Surface temperature profile as a function of the angle at 1 and 5 h.
180
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0.978
aw 1 h aw 5 h
0.976
Water activity
0.974 0.972 0.97 0.968 0.966 0.964 0.962 0.96 0.958 0
20
40
60
80 100 Angle (⬚)
120
140
160
180
FIGURE 8.3 Surface water activity as a function of the angle at 1 and 5 h.
8.3 CFD MODELING OF HEAT AND MASS TRANSFER ON A THREE DIMENSIONAL MODEL OF A BEEF CARCASS—THE THREE-STEP METHOD In this section the unsteady heat and mass transfer process is modeled on a 3D beef carcass geometric model. The 3D geometry of the carcass was constructed from the set of 2D crosssectional data of Davey [5,24]. The geometric generation procedure is similar to the one used by Nguyen and Pham [10] (details of the geometric construction are explained in Ref. [15]). The beef side was placed inside a wind tunnel of dimensions 650 1100 2775 mm height. This apparatus, used by Davey, was placed inside a small industrial beef chiller to conduct experimental trials. Both phases, air and beef, were meshed with Gambit using tetrahedral unstructured meshes. The mesh on the air side next to the beef surface was constructed in a fine manner in order to solve the transport equations in the fluid all the way to the wall as explained before. The mesh on the meat side needs to be very fine close to the surface in order to model the water diffusion on the meat, which takes place only near the surface. Unfortunately, it cannot
80
Water fraction (%)
75 70 65 60 55 Water concentration 20 h Water concentration 10 h Water concentration 1 h
50 45 0
5 10 15 20 25 Distance deep inside the ellipse (mm)
30
FIGURE 8.4 Water concentration profile deep inside the meat at 08 (stagnant point) at 1, 10, and 20 h.
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3.15e+02 3.11e+02 3.08e+02 3.04e+02 3.00e+02 2.97e+02 2.93e+02 2.89e+02 2.85e+02 2.82e+02 2.78e+02 Aug 04, 2003 Contours of Static Temperature (k) (Time = 0.0000e+00) FLUENT 6.0 (2d, dp, segregated, spe2, rngke, unsteady)
Temperature profile at time 0 min 3.15e+02 3.11e+02 3.08e+02 3.04e+02 3.00e+02 2.97e+02 2.93e+02 2.89e+02 2.85e+02 2.82e+02 2.78e+02 Aug 04, 2003 Contours of Static Temperature (k) (Time = 1.8000e+03) FLUENT 6.0 (2d, dp, segregated, spe2, rngke, unsteady)
Temperature profile at time 30 min 3.15e+02 3.11e+02 3.08e+02 3.04e+02 3.00e+02 2.97e+02 2.93e+02 2.89e+02 2.85e+02 2.82e+02 2.78e+02 Aug 04, 2003 Contours of Static Temperature (k) (Time = 1.8000e+04) FLUENT 6.0 (2d, dp, segregated, spe2, rngke, unsteady)
Temperature profile at time 5 h
FIGURE 8.5 Temperature profile inside the meat time 0 min, 30 min, and 5 h.
be made sufficiently fine due to the constraints of the software and the hardware. Thus, in order to solve the water transport equation inside the meat, a separate set of supplementary 1D grids was constructed using the idea of Karuri and Pham [13]. The main 3D volume elements are used by Fluent to solve the heat transfer inside the meat. The secondary grid in 1D is implemented in an additional piece of code programmed via a Fluent UDF to solve the water diffusion equation. Each instance of this grid is ‘‘attached’’ to one of the face centroids
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Wind tunnel Unstructured mesh
Gy
Beef phase mesh Gy
Beef
Gx
Air phase mesh
Gz
Gx
Boundary layer mesh
Beef
Boundary layer mesh
Fine 1D mesh normal vector
Triangular base
Fine boundary layer mesh
Face centroid
Air
Prismatic volume element Beef surface
Meat 3D cell element
FIGURE 8.6 Details of the generated mesh.
around the beef surface, penetrating the meat in the direction perpendicular to the surface. The mesh goes 24 mm into the meat. Twenty elements of different lengths were placed in that distance. Close to the surface, where the concentration gradients are greater, the elements are shorter. Deeper in the meat, where the mass flux is very small, the elements are longer. The mesh was made 1D because the mass transfer only occurs a few centimeters next to the surface of the meat and hence the mass flux direction is almost perpendicular to the meat surface. Figure 8.6 displays details of the generated mesh.
8.3.1 MATHEMATICAL MODEL The same set of equations as in Section 8.2.2 applies and in theory it is also possible to simultaneously model the unsteady heat and mass transfer process for the 3D carcass model. However, given the high computational time required (especially in three dimensions), a threestep method [12,25] was followed to simplify and accelerate the simulation. The steps consist of firstly conducting a CFD steady-state simulation only in the air phase, secondly, determining the local heat and mass transfer coefficients, and thirdly, doing the unsteady-state simulation on the meat only using the heat and mass transfer coefficients from the previous step. Three runs were completed and the heat load, weight loss, surface and center leg, loin and shoulder temperatures were compared with the experimental data obtained by Davey [5,24]. The three-step process is valid if the heat and mass transfer coefficients are constant during the chilling period. The forced convection heat and mass transfer coefficients depend on the Reynolds number and the turbulent intensity. If buoyancy effects are taken into
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TABLE 8.1 Initial and Boundary Conditions for Runs 14, 18, and 32
Weight (kg) Fat thickness (mm) at Aus-Meat P8 (rump) position Aus-Meat fatness grade Air relative humidity (%RH) Air temperature (8C) Air tunnel velocity (m s1 ) Slaughter floor time (min) Initial beef temperature (8C)
Run 14
Run 18
Run 32
113.5 14 4 98.5 6.02 0.99 90 42.4
108 6 2 98 4.88 0.538 120 42.4
140 12 3 99.9 6.57 0.69 85 42.4
account, the transfer coefficients will also depend on the wall temperature, air temperature, and water content. However, the effects of buoyancy on the heat and mass transfer coefficients for air velocities higher than about 0:5 m s1 may be considered unimportant [26]. Thus, the heat and mass transfer coefficients can be considered constant during each computational run if the air velocity ( 0:5 m s1 ) and the turbulence intensity are constant. The experimental runs number 14, 18, and 32 by Davey [24] were modeled via CFD with the three-step technique. The initial and boundary conditions for those runs are listed in Table 8.1. The local heat and mass transfer coefficients in the chilling period were determined via CFD knowing the air velocity, temperature, and the turbulence intensity. The following boundary conditions were applied in order to calculate the heat and mass transfer coefficients in the first step: at the tunnel’s inlet the air velocity, humidity, and temperature must be known. The boundary conditions for the k–« model were specified with the turbulence intensity and the hydraulic diameter. At the tunnel outlet, zero normal gradients are assumed for all variables: v, T, Y, «, k. At the walls of the tunnel, zero velocity, zero heat flux, and zero water flux are assumed. Finally, at the beef surface, zero velocity was assumed and initial values were applied for surface temperature and air moisture content. With the boundary conditions defined, a steady-state CFD simulation was conducted for the air phase only. After the transport equations have been solved, the heat and mass transfer coefficients can be calculated cell by cell using the concentration profile in the air control volume next to the solid surface. The near-wall mesh must be fine enough to resolve the transport equations down to the laminar sublayer. Thus, the water flux at the beef surface can be calculated cell by cell using the concentration profile in the air control volume next to the solid surface by using Equation 8.16. Subsequently, the local mass transfer coefficient can be calculated from the local water flux: hm ¼
Jw (Ys Ya )
(8:25)
where Ya is the bulk water content of the air. Similarly, the convective heat flux qconv is calculated using Equation 8.20 and the local heat transfer coefficient can be obtained from ht ¼
qconv (Ts Ta )
(8:26)
The transfer coefficients calculated with the chilling room specifications cannot be used to model the slaughter floor period given that the flow patterns are different. Thus, another
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steady-state CFD modeling of the slaughter floor was conducted to determine the local heat and mass transfer coefficients in this stage [15]. The local heat and mass transfer coefficients during the slaughter and chilling periods can be used to conduct the unsteady-state simulation on the meat side. The slaughter floor period is modeled first. At zero time, the product is initially at 42.48C with a moisture content of 75% wet basis. After modeling this initial period, the obtained temperature and moisture profiles are used as the initial conditions for the chilling stage. The boundary conditions at the carcass surface are defined as follows: for the water transport equation, a convective boundary condition is defined as Jw ¼ hm (Ys Ya )
(8:27)
where the moisture content of the air on the meat surface (Ys ) is assumed to be in equilibrium with the meat surface and is calculated from Equation 8.23. For the energy transport equation the boundary conditions 8.17–8.19 apply and the convective heat flux is calculated from qconv ¼ ht (Ts Ta )
(8:28)
The three-step method enables the first 20 h of chilling plus the slaughter period to be simulated for 5 days using a 2.5 GHz Pentium 4 computer. The method is accurate if the heat and mass transfer coefficients are constant during each of the stages (slaughter floor and chilling). This assumption is largely valid if the air velocity and turbulent intensity are constant and if buoyancy effects can be ignored.
8.3.2 VALIDATION Figure 8.7 shows the experimental and CFD-calculated heat loads for Davey’s Run 32 and compares it with the 1D finite difference (FD) [5] and the 2D finite element (FE) [6] models of Davey and Pham. It can be seen that the values predicted by all the three models are in good agreement with the experimental data. Figure 8.8 shows the calculated and experimental leg
1000 900
CFD FD FE Exp
800 Heat load (W)
700 600 500 400 300 200 100 0 0
2
4
6
8
10 12 Time (h)
14
16
18
20
FIGURE 8.7 Comparison of the heat load profiles calculated with the CFD, FE, and FD models with experimental data for run 32.
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50 CFD FE FD Exp
45 Temperature (⬚C)
40 35 30 25 20 15 10 5 0 0
2
4
6
8
10 12 Time (h)
14
16
18
20
FIGURE 8.8 Comparison of leg center (top) and leg surface (bottom) temperatures calculated with the CFD, FE, and FD models with experiment for run 32.
center, and surface temperature histories. The CFD center temperature prediction is quite accurate during the 20 h of chilling. A slight under-prediction during the peak may be due to the use of an average initial temperature at slaughter, which is a value that can change between particular runs. The leg surface temperature is also very well predicted, matching almost perfectly the experimental values. Figure 8.9 shows the shoulder center and surface temperature profiles for run 14. CFD predicts very well both the shoulder center and surface temperatures. Figure 8.10 shows the center and surface loin temperatures for run 18. The CFD and FE models underpredict both center and surface temperatures during the first 10 h of chilling. A similar trend was observed in all the runs. Since the same discrepancy appears at both the surface and the center, it seems that the error in the CFD prediction is due to overestimation of the effective surface
45 CFD FE FD Exp
40
Temperature (⬚C)
35 30 25 20 15 10 5 0 0
2
4
6
8
10 12 Time (h)
14
16
18
20
FIGURE 8.9 Comparison of the shoulder center (top) and shoulder surface (bottom) temperatures calculated with the CFD, FE, and FD models with experiment for run 14.
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35
CFD FE FD Exp
Temperature (⬚C)
30 25 20 15 10 5 0 0
2
4
6
8
10 12 Time (h)
14
16
18
20
FIGURE 8.10 Comparison of the loin center (top) and loin surface (bottom) temperatures calculated with the CFD, FE, and FD models with experiment for run 18.
heat transfer coefficient rather than an error in loin thickness or composition. A possible factor is that the insulating effect of surface fat, for both heat and mass transfer, has not been taken into account. The average root mean square percentage difference (%RMS) between the experimental and calculated data for the center and surface leg, loin and shoulder temperatures showed that in general, the 3D CFD model gives the best temperature predictions, closely followed by the 2D FE model [15]. The highest %RMS in all cases is obtained with the 1D FD model, showing its inaccuracy for predicting temperatures. This better performance was also confirmed by analyzing the relative value residuals (RVR) and the cumulative residual distribution of the three models (CFD, FE, and FD); both the FE and CFD models exhibit normal shape residual distributions [15]. The temperature predictions improved from the FD to the FE model because of the better geometrical representation: the FD model is a composite of 1D objects while the FE model is a composite of 2D objects. The slight improvement from the FE to the CFD can be attributed to improvements in geometrical representation (from 2D to 3D), in the local heat and mass transfer coefficient calculations by CFD, and in the more accurate modeling of mass transfer. CFD modeling can also predict local variations on the surface temperature, water activity, and heat and mass transfer coefficients. Figure 8.11 displays the temperature distribution over the carcass surface after 5 h of chilling, showing local temperature differences of up to 98C. Figure 8.12 displays the heat transfer coefficient distribution over the carcass leg, showing a peak in the regions where the air directly impacts the carcass surface. For instance, the heat transfer coefficient changes from 4.1 to 8:8 W m2 K1 around the leg in the reference plane in the graphic. Figure 8.13 shows the weight loss in run 18. All the models underpredict the weight loss of run 18 but overpredict it in runs 14 and 32 [15]. The overprediction may be caused by external fat that acts as a resistance to mass transfer. For run 18, the fat cover is just 6 mm while for runs 14 and 32 it is 14 and 12 mm, respectively. Figure 8.14 shows the calculated water activity profile (around the positions in Figure 8.11) for run 18. Local variations of up to 0.09 in aw can be seen, caused by local differences in heat and mass transfer coefficients. It is also seen that the water activity drops to a minimum value during the initial period with its high
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2.95e+03 2.94e+03 2.93e+03 2.92e+03 2.91e+03 2.90e+03
Leg a
2.89e+03 2.88e+03 2.87e+03 2.86e+03 2.85e+03 2.84e+03
Loin c
2.83e+03 2.82e+03 2.81e+03 2.80e+03 2.79e+03 2.78e+03
Sho b
2.77e+03 2.76e+03 2.75e+03
Temperature (K) External view
Internal view
FIGURE 8.11 Temperature profile around the carcass for run 32 after 5 h of chilling.
1.20e+01 1.15e+01 1.10e+01
Airflow
1.04e+01 9.90e+00 9.38e+00 8.85e+00 8.33e+00 7.81e+00
Reference plane
7.28e+00 6.76e+00
Higher h t
6.23e+00 5.71e+00 5.18e+00 4.66e+00 4.14e+00 3.61e+00 3.09e+00 2.56e+00 2.04e+00 1.51e+00
h t (W m–2 K–1)
FIGURE 8.12 Heat transfer coefficient around the carcass leg for run 18.
Lower h t
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1.8 1.6
Weight loss (kg)
1.4 1.2 1.0 0.8 0.6 Weight loss CFD Weight loss FD Weight loss FE Weight loss exp
0.4 0.2 0.0 0
2
4
6
8
10 12 Time (h)
14
16
18
20
FIGURE 8.13 Weight loss calculated with the CFD, FE, and FD models for run 18.
cooling and evaporation loads, then increase again as the rate of evaporation drops off and the surface is rewetted by water diffusion from inside the meat carcass [13,27]. The water activity changes with position depending on the local heat and mass transfer coefficients. The water activity is higher in the loin than in the leg and shoulder, because the loin cools faster given its small thickness and hence the surface water vapor pressure reduces faster, slowing down the evaporation process. The leg on the other hand is the thickest part of the carcass. The meat at that location cools more slowly; therefore, the surface vapor pressure remains higher, enhancing the evaporation. Overall, the water activity remains in the range 0.89–0.98 during the chilling period. Lovatt and Hill [20] reported experimental water activity values mostly between 0.88 and 0.94, which agrees with the CFD predictions.
1.000
Water activity
0.980 0.960 0.940 0.920 Sho b Loin c Leg a
0.900 0.880 0
2
4
6
8
10 12 Time (h)
14
16
18
20
FIGURE 8.14 Surface water activity profiles around leg (Leg a), loin (Loin c), and shoulder (Sho b) for run 18. Positions are marked on Figure 8.11.
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8.4 A SIMPLIFIED COMBINED CFD-CONDUCTION MODEL FOR BEEF CHILLING A rigorous CFD model (Section 8.2) and even the three-step simplification (Section 8.3) are still too time consuming for routine use. We have therefore developed a simplified combined model in which CFD was used to estimate the local heat and mass transfer coefficients, assuming uniform surface temperatures, and applying these values to Davey and Pham’s composite 2D finite element model [6] to solve the heat transfer equation in the product, which has an elongated shape. The 2D model was enhanced by adding another set of 1D grids [13] to solve the water transport equation near the surface of the meat. The local surface transfer coefficients were calculated by CFD for various combinations of air orientations and speeds, and summarized in a set of regression equations. Fluent was used to calculate heat transfer coefficients as explained in Section 8.2.1. A series of calculations was carried out at all combinations of three different approach velocities (0.07, 0.7, and 1:7 m s1 ), eight different airflow directions (shown beside the carcass in Figure 8.15), and three different turbulence intensities (10%, 20%, and 60%), making a total of 72 runs. The air velocity and turbulence values were chosen to coincide with the 5%, 50%, and 95% percentiles of experimental data gathered across a number of industrial chillers. The heat and mass transfer coefficients vary from one cross section to another and within each cross section. Therefore, the perimeter of each cross section was divided into subsections, as shown in Figure 8.16, and the transfer coefficients were averaged over each subsection. A regression equation was found to calculate the htc and mtc in each section and subsection as a function of velocity and turbulence intensity. To allow the equations to be
Section 1 Section 2 Section 3 8 7
Section 4 Section 5 Section 6
1 2
6 5
3 4
Section 7 Section 8 Section 9 Section 10 Section 11
Section 12
FIGURE 8.15 Cross sections of a beef side and numbering of airflow directions. The air velocity is always in the front-to-back plane of the beef side.
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Section 3-2 Section 9-3 Section 3-1
b/4
b/4
b/4
Section 9-4
Section 9-2
b/4
Section 3-3 Section 9-1
Section 9-6 Section 9-5
Section 3-4
FIGURE 8.16 Details of two cross sections showing subdivisions of boundary. Sections i–j refer to the j-th division of the i-th cross section of Figure 8.15. Arrow or segments show boundaries between subdivisions.
used over a wide range of temperature and carcass sizes, they were expressed in terms of dimensionless numbers: Nu ¼ C Rem Pr1=3 TuA
(8:29)
Sh ¼ F Rer Sc1=3 TuN
(8:30)
The exponents of Pr and Sc are chosen according to Chilton and Colburn [28]. The length scale used for Re and Nu is the total length of the carcass, as it is a less ambiguous and more readily measurable quantity than, say, the mean diameter of the cross section, which may be physically more significant. Since only one carcass shape is being modeled, this will not affect the scientific validity of the approach. Using any other dimensions as basis will lead to the same results. C, m, A, F, r, and N are empirical constants that depend on airflow direction, section, and subsection. There were a total of 472 combinations of air directions, sections, and subsections, i.e., 472 pairs of equations such as the above. The simplified combined model takes only a few minutes, rather than hours or days, to simulate a chilling run. It was verified with data from Davey’s [24] chilling tests. Calculated and measured total heat loads are compared in Figure 8.17, total weight losses in Figure 8.18,
Calculated heat load (kJ)
15,000
10,000
5,000
0 0
5,000
10,000
15,000
Measured heat load (kJ)
FIGURE 8.17 Comparison of calculated and measured total heat loads for wind tunnel tests.
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Calculated weight loss (kg)
2
1.5
1
0.5
0 0
0.5
1
1.5
2
Measured weight loss (kg)
FIGURE 8.18 Comparison of calculated and measured total weight losses for wind tunnel tests.
deep meat temperatures after 10 h chilling in Figure 8.19, and surface temperature after 5 h in Figure 8.20. Reasonable agreement was obtained in most cases. The surface temperature at 5 h and deep meat temperature at 10 h were chosen because at those respective times these temperatures are changing quickly, and so any discrepancy would show up most clearly. The scatter is rather large for surface temperatures (discrepancy of 48C in one case), but these are always difficult to measure accurately and surface temperatures will vary from one location to another on the surface anyway. In most cases the errors are within 28C. The agreement is also good for heat loads and weight losses, except for one case; there is an outlier in the weight loss plot (Figure 8.18), the calculated loss being 30% lower than the measured loss. This point represents a run with a carcass that is unusually lean, with P8 fat thickness of
Calculated center temperature (⬚C)
40 35 30 25 20 15 10
Leg Loin y=x
5 0 0
5 10 15 20 25 30 35 Measured center temperature (⬚C)
40
FIGURE 8.19 Comparison of calculated and measured deep meat temperatures after 10 h for wind tunnel tests.
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Surface temperature after 5 h Calculated surface temperature (⬚C)
15
10
5 Leg Loin y=x 0 0
5 10 Measured surface temperature (⬚C)
15
FIGURE 8.20 Comparison of calculated and measured surface temperatures after 5 h for wind tunnel tests.
only 1 mm (all others have P8 thicknesses 7 mm or more). This fact was not taken into account as we assumed an average fat cover for all carcasses.
8.5 CONCLUSIONS The rigorous unsteady-state simulation of the simultaneous heat and mass transfer process during beef chilling is not straightforward. Many difficult practical problems are caused by the coupling of several transport equations, the existence of a solid phase and a fluid phase, the species and thermal balances and equilibria at the interface of these phases, the simultaneous heat and mass transfer that occur on vastly differing scales inside the meat, and the complexity of the geometry. Special techniques, using Fluent’s UDS and UDF, have to be applied to model the simultaneous heat and mass transfer across two phases. Fluent’s enhanced wall treatment combined with a very fine grid near the wall must be used in order to accurately model the fluid all the way to the wall and calculate the convection fluxes. Given the present state of computer hardware, a fully rigorous unsteady-state simulation could only be carried out for a 2D geometry. For the complex 3D carcass geometry, a threestep method has been used to reduce the computational time. In the first step, a steady-state flow field was simulated. In the second step, the local heat and mass transfer coefficients are calculated cell by cell around the beef surface with the information obtained on step 1. Finally, the third step consists of the simultaneous heat and mass transfer process simulation only on the meat carcass. The mass transfer was simulated using a secondary 1D mesh to reduce the computational cost, caused by mass and heat transfer occurring on different scales. Local variations on the heat and mass transfer coefficients were found around the beef carcass surface caused by the development of the momentum, heat and mass boundary layers. CFD predicted local temperature variations of up to 98C, and water activity variations of up to 0.09, around the beef surface. The model also shows that the water activity decreases to a minimum value during the first chilling hours followed by an increase (rewetting). The water activity changes with position depending on the local heat and mass transfer coefficients, which depend on the geometry, air velocity, and turbulent intensity.
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For industrial applications, where faster simulations are needed, we have developed a simplified combined model in which CFD is used to estimate the local heat and mass transfer coefficients, assuming uniform surface temperatures, and a finite element model using a set of 2D grids is used to solve the heat transfer equation in the product. Such simplifications will continue to be needed in industrial simulation at least for the next few years.
NOMENCLATURE aw aw,a,s aw,m,s cp,m ds D Deff Dm E Gb Gk H hm hm ht ht I ~ Jj Jw k Nu p Pr PT PV q qconv qevap qrad Re Sh Sc t T Ta Ta,s Tc Tm,s Ts Tu v
water activity superficial water activity of the air superficial water activity of the meat meat specific heat (J kg1 K1 ) distance from the superficial face node to the cell center node (m) water diffusivity in air (m2 s1 ) effective diffusivity of water in air (m2 s1 ) water diffusivity in meat (m2 s1 ) specific energy of fluid (J kg1 ) generation of turbulence kinetic energy due to buoyancy generation of turbulent kinetic energy due to mean velocity gradients enthalpy (J kg1 ) local mass transfer coefficient (kg dry air m2 s1 ) average mass transfer coefficient (kg dry air m2 s1 ) local heat transfer coefficient (W m2 K1 ) average heat transfer coefficient (W m2 K1 ) unit tensor diffusion flux of species j (kg m2 s1 ) water mass flux (kg m2 s1 ) turbulent kinetic energy (m2 s1 ) Nusselt number pressure (Pa) Prandtl number total pressure (Pa) vapor pressure of pure water (Pa) heat flux (W m2 ) convective heat flux (W m2 ) evaporative heat flux (W m2 ) radiative heat flux (W m2 ) Reynolds number Sherwood number Schmidt number time (s) temperature (K) bulk air temperature (K) temperature of the air phase on the meat surface (K) temperature at the center of the air volume element besides the meat surface (K) temperature of the meat at the surface (K) temperature at the meat surface (K) turbulence intensity velocity (m s1 )
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~ v T ~ v W Xm Y Ya Yc Ys YM
219
mean velocity vector (m s1 ) transposed mean velocity vector (m s1 ) water mass fraction in the meat (kg water kg total1 ) water content at the meat surface (kg water kg dry solid1 ) water mass fraction in the air (kg water kg dry air1 ) bulk water mass fraction in the air (kg water kg dry air1 ) water mass fraction of the air at the center of the volume element besides the meat surface (kg water kg dry air1 ) water mass fraction of air at the meat surface (kg water kg dry air1 ) contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate
GREEK SYMBOLS a« ak DHvap « «r l leff lm m meff r rm s teff y^
inverse effective Prandtl numbers for « inverse effective Prandtl numbers for k latent heat of vaporization of water (J kg1 ) turbulent energy dissipation rate radiation emissivity air thermal conductivity (W m1 K1 ) effective thermal conductivity (W m1 K1 ) meat thermal conductivity (W m1 K1 ) air viscosity (kg m1 s1 ) effective viscosity of air (kg m1 s1 ) air density (kgm3 ) meat density (kg m3 ) Stefan–Boltzmann constant effective stress tensor (N m2 ) ¼ meff =m
SUBSCRIPTS a c conv evap s m rad
air phase cell node convective evaporation at the meat surface meat radiation
REFERENCES 1. P. Verboven, B.M. Nicolai, N. Scheerlinck, and J. De Baerdemaeker. The local surface heat transfer coefficient in thermal food process calculations: A CFD approach. Journal of Food Engineering 33: 15–35, 1997. 2. S.J. Lovatt, Q.T. Pham, A.C. Cleland, and M.P.F. Loeffen. A new method of predicting the timevariability of product heat load during food cooling—Part 1. Theoretical considerations. Journal of Food Engineering 18: 13–36, 1993. 3. A. Kuitche, J.D. Daudin, and G. Letang. Modeling of temperature and weight loss kinetics during meat chilling for time-variable conditions using an analytical-based method—I. The model and its sensitivity to certain parameters. Journal of Food Engineering 28: 55–84, 1996.
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4. S. Chuntranuluck, C.M. Wells, and A.C. Cleland. Prediction of chilling times of foods in situations where evaporative cooling is significant—Part 1. Method development. Journal of Food Engineering 37: 111–125, 1998. 5. L.M. Davey and Q.T. Pham. Predicting the dynamic product heat load and weight loss during beef chilling using a multi-region finite difference approach. International Journal of Refrigeration 20: 470–482, 1997. 6. L.M. Davey and Q.T. Pham. A multi-layered two-dimensional finite element model to calculate dynamic product heat load and weight loss during beef chilling. International Journal of Refrigeration 23: 444–456, 2000. 7. P. Mallikarjunan and G.S. Mittal. Heat and mass transfer during beef carcass chilling—Modeling and simulation. Journal of Food Engineering 23: 277–292, 1994. 8. A. Kondjoyan and J.D. Daudin. Determination of transfer coefficients by psychrometry. International Journal of Heat and Mass Transfer 36: 1807–1818, 1993. 9. A. Kondjoyan and J.D. Daudin. Heat and mass transfer coefficients at the surface of a pork hindquarter. Journal of Food Engineering 32: 225–240, 1997. 10. A.V. Nguyen and Q.T. Pham. A computational fluid dynamic model of beef chilling, in 20th International Congress of Refrigeration, IIR=IIF. Sydney, 1999. 11. Z. Hu and D.-W. Sun. CFD simulation of heat and moisture transfer for predicting cooling rate and weight loss of cooked ham during air-blast chilling process. Journal of Food Engineering 46: 189–197, 2000. 12. Z. Hu and D.-W. Sun. Predicting local surface heat transfer coefficients by different turbulent k–« models to simulate heat and moisture transfer during air-blast chilling. International Journal of Refrigeration 24: 702–717, 2001. 13. Q.T. Pham and N.W. Karuri. A computationally efficient technique for calculating simultaneous heat and mass transfer during food chilling, in 20th International Congress of Refrigeration, IIR=IIF, Sydney, 1999. 14. F.J. Trujillo and Q.T. Pham, CFD modeling of heat and moisture transfer on a two-dimensional model of a beef leg, in 21st International Congress of Refrigeration, Washington, DC, 2003. 15. F.J. Trujillo and Q.T. Pham. A computational fluid dynamic model of the heat and mass transfer during beef chilling. International Journal of Refrigeration 29: 998–1009, 2006. 16. F.J. Trujillo, C. Wiangkaew, and Q.T. Pham. Drying modeling and water diffusivity in beef meat. Journal of Food Engineering 78: 74–85, 2007. 17. V. Yakhot and S.A. Orszag. Renormalization group analysis of turbulence. I. Basic Theory. Journal of Science Computing 1: 3–51, 1986. 18. Fluent Inc., Modeling turbulence, in FLUENT 6.2 user’s guide, Vol. 2. F. Inc., Editor. 2005, Fluent Inc., Lebanon, NH. 19. F.J. Trujillo, P.C. Yeow, and Q.T. Pham. Moisture sorption isotherm of fresh lean beef and external beef fat. Journal of Food Engineering 60: 357–366, 2003. 20. S.J. Lovatt and H.K. Hill. Surface water activity during meat cooling, in IIR Proceedings Series Refrigeration Science and Technology, Sofia, Bulgaria, 1998. 21. M. Wolfshtein. The velocity and temperature distribution in one-dimensional flow with turbulence augmentation and pressure gradient. International Journal of Heat and Mass Transfer 12: 301–318, 1969. 22. B.A. Kader. Temperature and concentration profiles in fully turbulent boundary layers. International Journal of Heat and Mass Transfer 24: 1541–1544, 1981. 23. B.E. Launder and D.B. Spalding. The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering 3: 269–289, 1974. 24. L.M. Davey, Measurement and prediction of product heat load and weight loss during beef chilling, PhD thesis, 1998, School of Chemical Engineering and Industrial Chemistry, University of New South Wales, Sydney, p. 299. 25. A.V. Nguyen and Q.T. Pham. Mean convective heat transfer coefficient of beef carcases computed by a computational fluid dynamic model, in FOODSIM 2000: International Conference on Simulation in Food and BioIndustries, Nantes, France, 2000.
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26. F.J. Trujillo, A computational fluid dynamic model of heat and moisture transfer during beef chilling. PhD thesis, 2004, School of Chemical Engineering and Industrial Chemistry, University of New South Wales, Sydney, p. 352. 27. L.S. Herbert, D.A. Lovett, and R.D. Radford. Evaporative weight loss during meat chilling. Food Technology in Australia 30: 145–148, 1978. 28. T.H. Chilton and A.P. Colburn. Mass transfer (absorption) coefficients. Industrial and Engineering Chemistry 26: 1183–1186, 1934.
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CFD Prediction of the Air Velocity Field in Modern Meat Dryers Pierre-Sylvain Mirade
CONTENTS 9.1 9.2 9.3
Introduction ............................................................................................................... 223 Operation of Modern Meat Dryers ........................................................................... 224 Air Velocity Fields in Modern Meat Dryers.............................................................. 227 9.3.1 Experimental Investigation ............................................................................. 227 9.3.2 Steady-State Numerical Investigation............................................................. 227 9.3.3 Unsteady Numerical Investigation ................................................................. 232 9.3.3.1 Features of Unsteady Modeling ....................................................... 233 9.3.3.2 Influence of the Amplitude of the Ventilation Cycle........................ 234 9.3.3.3 Influence of the Form of the Ventilation Cycle................................ 237 9.3.3.4 Consequences of Dissymmetry in the Ventilation Cycle .................. 238 9.4 Modern Meat Dryers of Large Height ...................................................................... 240 9.4.1 Problematic..................................................................................................... 240 9.4.2 Mean Age of Air ............................................................................................ 241 9.5 Conclusion ................................................................................................................. 245 References .......................................................................................................................... 246
9.1 INTRODUCTION No other technology creates such an aromatic and desired flavor of meat products as fermentation and drying [1]. Dry sausages are one of the most important fermented meat products. In Europe, total production of nonsmoked molded dried sausages is about 350,000 tonnes a year, a significant proportion of which comes from southern European countries including Italy, Spain, and France (90,000 tonnes a year). In northern European countries such as Germany, Denmark, Sweden, and Norway, almost all dry sausages produced are smoked during processing. In Hungary, the traditional salami is even smoked in a first drying step, before being molded in a second ripening step [1]. In the successive operations involved in the manufacture of dry sausage, namely grinding of lean meat and fat, mixing with additives, stuffing in casings, and drying, the drying process is crucial. Indeed, to obtain a well-balanced drying of all sausages, airflow patterns and indoor climate (temperature and relative humidity) should be homogeneous throughout the drying room. In practice, water loss differences between sausages are observed in the dryer, which result from local heterogeneities in the air velocity distribution. This problem is
223
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partially addressed through the rearrangement of the trolleys of sausages in the room during the drying process. Nevertheless, many authors have reported that poor control of drying conditions is the main raison for low quality [2,3]. During drying, the water content of the sausages should decrease homogeneously. When the rate of water evaporation from the surface of the sausage is higher than the rate of water migration from inside the sausage, a dry crust (also called ‘‘dry rim’’) is formed, which adversely affects sausage texture and flavor. Conversely, when the evaporation rate is lower, the surface remains too moist, which favors the growth of undesirable molds that can impair product texture, flavor, and safety. Hence, the drying process consists in continuously fitting the drying rate to a product undergoing perpetual biochemical and biological evolution, and maintaining water activity at the product surface at an ideal value in order to develop the desirable flora. In other words, ripening has an influence over the main physical, chemical, and microbiological transformations that take place inside the products and which define the final organoleptic properties of dried products. As water exchanges at the product surface are directly related to the characteristics of the surrounding air (temperature, velocity, and relative humidity), it is of paramount importance to identify global airflow patterns inside the dryer. In Europe, dry sausage and especially ham were originally manufactured in mountainous highlands, since the outside air could be used inside the meat dryers almost all year round without conditioning, due to the fresh temperature and high relative humidity. More recently, static dryers equipped with cooling batteries level with the ceiling and heating batteries level with the floor have appeared in geographic areas with a less favorable natural climate. They operate by mixing descending fresh air volumes with ascending hot air volumes, thus generating natural ventilation with very low air velocity. Hygrometric control was achieved by condensation of water on the cooling batteries. This type of meat dryer was used to manufacture hams and low-diameter dry sausages [3]. To reduce ripening time, fans were introduced into the meat dryers to force air to circulate around the products at a velocity of 0:1 m s1 . At the very beginning, blowing ducts were placed level with the floor while suction ducts were placed level with the ceiling. Although the direction of air movement could be inverted in this type of dryer, heterogeneity in air distribution remained in the full volume filled with the products, causing strong heterogeneity in drying between the upper and lower part, thus compelling professionals to regularly move their products. To even out the drying conditions, and thereby product processing, throughout the entire volume of the plant, modern meat dryers were created where air distribution was time-dependent. This chapter reports on scientific studies aimed at analyzing the significance and effects of the specific operation of modern meat dryers through numerical modeling, with particular emphasis on dryers of large height, which are currently increasingly used in industry.
9.2 OPERATION OF MODERN MEAT DRYERS Figure 9.1 shows the layout of a typical modern meat dryer with a schematic description of the airflow pattern. The geometry of this type of meat dryer is simple; the airflow is generally supplied through two stainless steel ducts of rectangular cross section fitted with plastic conical jets placed on each side of the plant, and is extracted level with the ceiling by means of two or three stainless steel ducts fitted with adjustable plastic extraction apertures. These modern meat dryers are characterized by a main upward airflow generated by two downstream airflows generated by conical jets, which merge over the plant floor. As indicated earlier, when attempting to create homogenous drying conditions throughout the entire volume of a plant, it is important to take into account the fact that the operation of a modern meat dryer is time-dependent, and this is due to two reasons.
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Extraction ducts fitted with extraction apertures
Height: from 2 to 6m
Blower ducts fitted with conical jets
Area of filling with meat products About 0.5 m
Width: from 2 to 7 m (Length: from 2 to 20 m)
FIGURE 9.1 Layout of a typical modern meat dryer according to a vertical section with a schematic description of the airflow patterns (black arrows).
Firstly, as regards air distribution, the airflow supplied by two lateral blower ducts ranges from a high to a low rate in the first duct in a few tens of seconds while it reciprocally ranges from a low to a high rate in the second duct, thus giving rise to a periodic ventilation cycle (Figure 9.2). However, the overall blower airflow rate remains steady at any given time, at 100%. Figure 9.2 highlights that the ventilation cycle has a sinusoidal form, since the distribution of airflow rate in the two blower ducts is generally set by adjusting a regulation valve placed on the duct supplying air to the two blower ducts. The two inlet airflows are then directed downstream, descending along the lateral room walls before merging over the floor in a location that depends on the value of the ventilation cycle. The more unbalanced the ventilation cycle, the more distant the location of the merging area from the middle of the dryer. Once merged, the airflow then moves upward toward the extraction ducts, at the same time bathing the meat products filling the plant and exchanging heat and moisture with them. This ventilation cycle means that the merging location of the upward airflow moves cyclically over the drying floor. All meat products are consequently bathed by the same airflow during full periods of the ventilation cycle, and a priori are thus dried in a homogeneous way.
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Percentage of overall blower airflow rate (%)
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Left-hand blower duct
Right-hand blower duct
High
50
Low One period of the ventilation cycle 0
15
30
45
60
75
Time (s)
FIGURE 9.2 Description of the airflow rate evolution between each of the two blower ducts during one period of the ventilation cycle in a modern meat dryer (the sinusoidal form is truly representative of what occurs in industrial plants).
Furthermore, during ventilation, air velocity ranges from 5 to 20 m s1 at the output of the conical jets of the blower ducts, and is on average 0:4 m s1 around the products. Secondly, the specific ventilation pattern previously described and which is intended to supply air to the dryer alternates rapidly with a rest sequence in which there is no ventilation, depending on the level of relative humidity in the volume filled with the products; this relative humidity increases due to water evaporating from the surface of the sausages. Ventilation is reactivated once a high level of relative humidity is reached in order to reduce relative humidity until a low level is reached. Periods of ventilation generally correspond to around one-third of the total ripening time (Figure 9.3). 90 Air relative humidity of the dryer (%)
Periods with ventilation 85 80 75 70 65 60 Rest periods (no ventilation) 55 3500
4500
5500
6500
Time (s)
FIGURE 9.3 Evolution in air relative humidity during the operation of a modern meat dryer according to the ventilation and rest periods.
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A modern meat dryer therefore works by a series of ventilation cycles and rest sequences (Figure 9.3) managed by an operator who generally uses empirical rules to adjust the drying conditions. In practice, these rules are known to be affected by the design (dimensions, location of the blower and extraction ducts, etc.), and filling level of the dryer, as well as by the amplitude of the ventilation cycle. In other words, both the design of modern meat dryers and the optimal process conditions are based more on the practical experience accumulated by plant designers and dried meat manufacturers over the years than on the results of academic research.
9.3 AIR VELOCITY FIELDS IN MODERN MEAT DRYERS The majority of research on the processing of dried sausages or hams reported in the literature deals with fermentation, transfers from inside the product, or drying kinetics as a function of air properties [1,4–11]. For example, Daudin et al. [8] highlighted steep gradients in water content in the first 10 mm close to the surface of drying sausages; they also indicated that accurate control of the air characteristics around the sausages was essential in order to control water activity at the sausage surface [8].
9.3.1 EXPERIMENTAL INVESTIGATION There are few experimental and numerical studies available on the overall operation of modern meat dryers [12–16]. Experimental analyses carried out in modern meat dryers are understandably rare since the measurements are particularly laborious and time-intensive due to the natural unsteadiness of the airflows and especially the ventilation cycle, which continuously modifies the air velocities at the output of the conical jets. The only method that can be used to measure air velocities in this kind of plant is the standard average procedure that consists in averaging velocity measurements over a sufficiently long length of time (over one or several ventilation cycles at each measurement point) to obtain a constant value for mean velocity [12,14]. In a 134 m3 small-scale sausage dryer filled with 108 objects made of polystyrene (1:70 0:25 0:15 m) arranged in six rows in order to reproduce industrial filling levels, Mirade and Daudin [14] measured air velocity distribution in five configurations corresponding to two different steady distributions of the ventilation cycle, namely 50%=50% and 20%=80% per blower duct. The first airflow distribution gave a large area with air velocities reaching 2 m s1 in the middle of the dryer, but a wider airflow than expected as a result of slow and slight time variations in the blower airflow rate from each duct. Moreover, the authors noted that changing the distribution of the airflow rate from 50%=50% to 20%=80% completely disrupted airflow patterns, with the appearance of a poorly ventilated area at the center of the dryer and air velocities of about 1:5 m s1 close to the blower ducts. In the 20%=80% configuration, the authors concluded that the large airflow blown in from the right-hand side duct to the floor moved along the floor and up the opposite wall, drawing in the airflow from the left-hand side duct.
9.3.2 STEADY-STATE NUMERICAL INVESTIGATION Numerical studies of airflows in modern meat dryers have often been performed using CFD techniques. With the development of cheaper, more powerful computers and commercial packages, over the years CFD has been increasingly applied to assess airflow patterns in modern meat dryers [13–16], ever since the pioneering studies performed by EDF, the French producer of electricity, and cited by Dabin and Jussiaux [3] that aimed to optimize air circulation inside the drying room in order to obtain more regular product drying.
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From two calculations using steady-state boundary conditions and corresponding to two different distributions of airflow rate between the two blower ducts of the room (50%=50% and 30%=70%), these original studies indicated a complex air circulation pattern including two swirls that shifted laterally as a function of the air distribution between the two blower ducts. Consequently, the velocities of air in contact with dried sausages ranged from 0.4 to 0:6 m s1 , and were threefold to fivefold higher than the theoretical velocity determined from the total airflow rate blown in the room divided by its surface [3]. A similar approach, namely three steady-state and two-dimensional CFD simulations corresponding to airflow rate distributions between the two blower ducts of 50%=50%, 59%=41%, and 67%=33%, respectively, identified a strong heterogeneity in airflow pattern in a salami dryer, with air velocities ranging from 0.2 to 0:8 m s1 in the volume filled with the products [13]. The heterogeneity in air velocity magnitudes in the volume filled with the products was confirmed by 3D numerical results obtained by Mirade and Daudin [14] using the commercially available CFD code Star-CD [17], in the case of a 134 m3 small-scale sausage dryer for two steady-state ventilation cycle configurations between the two blower ducts (50%=50% and 20%=80%). Calculations were made on a Sun Sparc 10=41 workstation with 128 Mb of RAM. Airflow was considered as steady, incompressible, and isothermal. Main flow turbulence was taken into account using the tried and tested k« model [18] when far from the walls—which were assumed to be smooth—and where the standard wall function was applied [19]. Even though the k« model is known to perform poorly in a variety of important cases, such as some unconfined flows or flows with large extra strains, it is currently widely used for turbulence modeling since it is robust, time-efficient, and fairly accurate. The SIMPLE algorithm [20] was chosen for coupling pressure and velocity and to introduce pressure into the continuity equation. A first-order upwind differencing scheme was incorporated into the computational model as discretization scheme for the convection terms of each governing equation. First-order schemes are known to increase numerical diffusion due to discretization errors, especially when the flow is not aligned with the grid [19]. Although they therefore yield less accurate results, first-order schemes give better convergence of calculation than secondorder schemes. Complete convergence of the discretized differential equations ranged from 5 to 8 days, reaching 8 days when using 300,000 vertices for meshing the 134 m3 small-scale sausage dryer [14]. Figure 9.4a and Figure 9.4b show the distribution of the simulated air velocity patterns according to a vertical section located approximately in the middle of the dryer for inflow distributions of 50%=50% and 20%=80%, respectively [14]. When the distribution of the airflow rate was balanced between the two blower ducts (50%=50%), calculations revealed that the higher air velocities were located level with the floor and in the middle of the dryer. On either side of this central area, poorly ventilated areas with air velocities lower than 0:6 m s1 were highlighted (Figure 9.4a). Conversely, unbalancing the distribution of the airflow rate from 50%=50% to 20%=80% completely disrupted the airflow patterns, as illustrated in Figure 9.4b, where the lower air velocities were concentrated in the middle of the dryer whereas the higher air velocities were found close to the two blower ducts. Using 2D CFD modeling, Mirade and Daudin [14] also highlighted a very unsteady airflow pattern when the airflow rate was closer to 50%=50%. An imbalance of only 4% between the left- (54%) and the right-hand side (46%) blower ducts greatly modified the location of the wellventilated central area, which shifted over 60 cm toward the right, as indicated in Figure 9.4c, thus confirming the findings of the original study carried out by EDF [3]. Furthermore, and again using the Star-CD code, Mirade and Daudin [21] studied the effect of changes in airflow structure in relation to amplitude from 50%=50% to 10%=90% and dissymmetry of +5% in the ventilation cycle; it was assumed that the ventilation cycle was
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linear and that this non-steady-state problem (due to the ventilation cycle) could be numerically approached as a series of steady-state problems. By integrating the air velocities simulated between a low level and a high level during one period of the ventilation cycle, they identified 60%=40% as the amplitude giving the most homogeneous airflow inside the
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FIGURE 9.4 Distribution of the air velocities calculated from 3D CFD modeling on a vertical section located at half-length of a 134 m3 small-scale sausage dryer corresponding to three steady-state configurations of the ventilation cycle: (a) 50%=50%, (b) 20%=80%, and (continued)
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FIGURE 9.4 (continued) (c) 54%=46%.
area filled with the sausages despite the fact that there was a gradient in air velocity distribution in relation to the height within the plant (Figure 9.5a). They also highlighted the need for controlled regulation of the ventilation cycle in modern meat dryers since a slight variation of +5% in the airflow rate at a distribution of around 60%=40% markedly disrupted the airflow pattern, which became strongly dissymmetric (Figure 9.5b). On account of the simplicity of the system regulating and distributing airflow between the two blower ducts and due to the marked unsteadiness of the airflow around the 50%=50% blower conditions, dysfunction in the ventilation cycle frequently occurs in industrial settings, leading to slight variations around the low and high levels with no change in the overall blower airflow rate. Hence, in practice, there is greater heterogeneity in sausage product treatment between different locations in the plant. Figure 9.5b indicates the appearance of a poorly ventilated area with velocities lower than 0:4 m s1 on the left-hand side of the sausage dryer, i.e., where the air velocities at the output of the conical jets were the highest. The slight variation in airflow rate distribution between the two blower ducts globally increased the air velocity gradients. All these simulations were performed using the same modeling procedure as previously [14], i.e., the k–« model [18] for modeling turbulence, the SIMPLE algorithm [20] for coupling pressure and velocity, and a first-order upwind differencing scheme [19] as discretization scheme for the convection terms in the governing equations. Without using CFD, Rizzi [22] developed a parametric model to rapidly predict airflow velocity patterns in ascending flow ripening chambers, with the idea of improving the operation and design of these industrial plants by means of dynamic ripening simulation software coupling a fluid dynamics model to a numerical model of the sausage drying process. The fluid dynamics model was built to give the air velocity module as output and to give direction as a function of the geometrical characteristics of the drying chamber (dimensions, location of the blower and extracting ducts, number and location of the products loaded) and of the inlet airflow conditions (overall mass flow rate and inflow sharing ratio between the two blower ducts).
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FIGURE 9.5 Distribution of the air velocity means calculated from 2D CFD modeling on a vertical section of a 134 m3 small-scale sausage dryer for a ventilation cycle of linear form at amplitude 60%=40%: (a) without dissymmetry and (b) with a dissymmetry of +5% between the left- and righthand side blower ducts (the ventilation cycle was discretized in a series of steady-state configurations so as to be taken into account in the CFD modeling).
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Several assumptions (incompressible fluid, steady and uniform motion) have been made in order to construct an accurate, flexible, and computationally ‘‘light’’ fluid dynamics model. Moreover, the main idea upon which this model is based consisted in defining an imaginary 2D pipe network inside the drying room, thus assuming all parameters to be constant along the room depth. Once both geometrical and fluid dynamics parameters have been set, the pipe network was then solved using an iterative technique specially developed to solve hydraulic problems, i.e., the Hardy–Cross method [23,24]. This specific method makes it possible to determine the airflow rates in each network duct as defined by the room walls and product surfaces from the mass flow rate at the boundary conditions. However, as the Hardy–Cross method neglected fluid momentum and considered that pressure gradients were the basic driving forces within the network, a customization of pressure drop coefficients was set up in order to avoid the solving of additional partial differential momentum equations, which would have compromised both the computational simplicity and the rapidity of the model. Indeed, as it was well known that in some areas of a modern ripening chamber—above all the inlet and downward areas and level with the room floor and the extraction region—fluid momentum took precedence over pressure gradients, this phenomenon had to be taken into account when modeling the evolution of the airflows. The customization of pressure drop coefficients amounted to introducing factors to artificially increase or decrease certain head drop coefficients to force the airflows to follow preferential paths inside the pipe network. The first step in using the fluid dynamics model consists in defining the degree of precision required and assessing both the main geometrical and fluid dynamic characteristics of each duct in the pipe network as a function of the room’s geometrical characteristics and of the type, number, and relative location of the products. Pressure drop coefficients are then calculated from the classical rules of hydraulics and calibrated by means of corrective factors determined from relations established on the basis of general information obtained from experimental data processing. For each mesh of the pipe network, the model checks whether the energy balance equation is satisfied with a degree of precision lower than that actually required, and if necessary adds a corrective mass flow rate. The process is iterated throughout the entire pipe network until the energy balance equation is satisfied for every mesh with the required degree of precision. When considering a network configuration corresponding to a single rack filled with 18 salamis (three rows per six columns) with degree of precision set to 50 Pa, Rizzi [22] indicated that the resulting network made of 90 nodes and 72 cells was solved in about 600 iterations, with an average computation time of about 5 s when using a Pentium II 400 MHz processor. The fluid dynamics model satisfactorily predicted air velocity distribution as a function of overall mass flow rate entering the drying room and, above all, as a function of steady-state sharing of the airflow rate between the plant’s two blower ducts [22]. Together, these numerical studies [13,14,21,22] have provided useful information on air circulation during the ventilation cycle, but have not accurately analyzed the dynamic operation of the meat dryers since only steady-state numerical models were built.
9.3.3 UNSTEADY NUMERICAL INVESTIGATION The ability of CFD to dynamically predict airflow patterns inside a modern sausage dryer by means of 2D numerical models using time-dependent boundary conditions (i.e., an unsteady model) to accurately reproduce real operating conditions was recently assessed [15,16]. Mirade [15,16] studied the effect on ventilation homogeneity of modifying amplitude (four levels tested: 80%=20%, 70%=30%, 65%=35%, and 60%=40%) and form (linear [15] or sinusoidal [16]) during one period of the ventilation cycle. In the case of a sinusoidal form,
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Mirade [16] also numerically evaluated the change in airflow structure due to dissymmetry of 2%, 5%, or 10% of the ventilation cycle due to a dysfunction of the plant, which could occur in industry due to the simplicity of the system regulating airflow rate distribution between the two blower ducts and the marked unsteadiness of the airflow around a 50%=50% distribution. The layout of the small industrial sausage dryer used in the studies of Mirade [15,16] for building the dynamic CFD model was absolutely identical to that of Figure 9.1, with a height of 2.96 m and a width of 2.45 m. In this plant, the air was blown in through two stainless steel ducts placed on each side that were fitted with eight plastic conical jets 0.195 m long and 0.063 m in diameter. The air was extracted at the top through two other stainless steel ducts set 0.50 m apart and fitted with ten plastic extraction apertures of 0.08 m in diameter. The height of the free space from the ends of the conical jets to the floor was 2.32 m and the air velocity at the output of the jets was 5 m s1 when the ventilation corresponded to a 50%=50% configuration. The filling of the dryer in the numerical models was represented using 24 sausages of rectangular cross section (0:50 0:05 m), with eight sausages set 0.15 m apart at each of the three heights. The distance between two consecutive heights was 0.3 m, and the distance between the first rack of sausages and the floor was 0.35 m. 9.3.3.1 Features of Unsteady Modeling Starting with the geometrical configuration presented in Figure 9.1, the CFD code Fluent v.5.1.1 and 5.4.8 [25] was used to build a numerical model based on an unstructured 2D mesh of 25,500 tetrahedral cells. From the previous mesh, several variants of the 2D numerical model were constructed that corresponded to different forms and amplitudes of the ventilation cycle [15,16]. Given that 2D modeling was used, the results had to be viewed with caution, not due to the 2D representation of a presumably 3D airflow blown by the conical jets, but rather due to the representation of the objects filling the device. Indeed, in 2D calculations, objects can act as a barrier, since the airflow cannot skirt around them as it does in reality, which almost certainly contributes to an increase in the heterogeneity of the airflow patterns. On the other hand, despite being performed in 2D, an unsteady CFD model has to be particularly useful for assessing the dynamic operation of modern meat dryers. To account for time-dependent boundary conditions due to the ventilation cycle, specific user-defined functions (UDF) were written in Cþþ programming language and applied to the inlet areas of the CFD models. In all calculations [15,16], airflow was considered as incompressible, isothermal and—unlike the previous studies [13,14,21,22]—unsteady. From preliminary tests, the time step increment was evaluated at 0.02 s so that the convergence of the calculations obtained for residuals lower than 103 needed no more than 25–30 iterations at each time step [15]. A total 3000 time steps was therefore required to fully simulate just one period of the ventilation cycle that lasted 60 s. More complex and costly—in terms of computation time—modeling procedures were used than in the previous studies [13,14,21,22]. Indeed, main flow turbulence was taken into account by means of the Reynolds-stress model [26], which needed the resolution of six equations instead of two for the k« model [18]—far from walls and objects, where a ‘‘nonequilibrium’’ wall function was applied. Moreover, a second upwind-differencing scheme [19] and the PISO algorithm [27], instead of the SIMPLE algorithm, were also necessary in order to obtain accurate results. Calculations were performed either on a 266 MHz Pentium II PC with 384 Mb of RAM or on a 2.2 GHz Pentium IV PC with 1.5 Gb of RAM. Calculation time ranged from 55.2 to 59.6 h on the Pentium II PC and from 8.3 to 9 h on the Pentium IV PC, depending on the variant of the numerical model being solved.
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Given that unsteady modeling was used, an initialization of the calculations, i.e., the air velocity patterns at time zero, was required; this was obtained from a preliminary calculation where the inlet boundary conditions were steady and equal to 50% of the overall airflow rate in each of the two blower ducts. However, as this preliminary calculation needed unsteady modeling to reach convergence owing to the strong unsteadiness of the airflow in a 50%=50% configuration, it generated many air velocity patterns, thus forcing the author to check that the mean airflow structure determined over the full period of the ventilation cycle was not sensitive to initial conditions [16]. To do this, Mirade [16] performed three different simulations corresponding to different initial conditions and noted that the three mean airflow patterns obtained on the full period were the same. 9.3.3.2
Influence of the Amplitude of the Ventilation Cycle
Regardless of the form of the ventilation cycle, i.e., whether linear or sinusoidal, the influence of the ventilation cycle on airflow patterns can be summed up as follows [15,16]: (i) air velocity distribution truly varies with the amplitude of the ventilation cycle; consequently, modern meat dryer has an optimum amplitude depending on its geometry (dimensions and location of the blower and extraction ducts) and filling level; (ii) above this optimal amplitude, there appears a marked heterogeneity in the ventilation, mainly according to the height between the lower part that is poorly ventilated and the upper part of the plant; and (iii) below the optimal amplitude, the heterogeneity also exists, but more according to the width of the plant, with high velocities concentrated toward the center. Figure 9.6a through Figure 9.6d give the distribution of the air velocity means calculated on a vertical section of the dryer for a ventilation cycle of linear form, thus illustrating the 2750 2450 2150
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FIGURE 9.6 Distribution of the air velocity means calculated from 2D unsteady CFD modeling on a vertical section of a small sausage dryer over one period of ventilation cycle of linear form, at amplitudes of: (a) 80%=20%,
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FIGURE 9.6 (continued) (b) 70%=30%, (c) 65%=35%, and (continued)
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FIGURE 9.6 (continued) (d) 60%=40% (given the unsteady modeling, the ventilation cycle was directly incorporated into the CFD model by means of a user-defined function. The black rectangle in the figures outlines the area usually filled with sausages.).
influence of the amplitude of the ventilation cycle on airflow patterns [16]. Before analyzing Figure 9.6a through Figure 9.6d, it should be noted that the symmetrical air velocity distribution in relation to the median plane of the plant proves that the unsteady CFD models correctly took into account the dynamic operation of the dryer induced by the ventilation cycle. Comparison of Figure 9.6a through Figure 9.6d shows large differences in the distribution of air velocity means according to the linear ventilation cycle studied, with the best homogeneity corresponding to an amplitude of 65%=35% (Figure 9.6c), even though air velocity means ranged from 0.6 to slightly higher than 1:2 m s1 in the area filled with objects and despite the fact that a significant stratification of air velocities with height appeared in the plant, with air velocities higher than 1:2 m s1 for widths ranging from 975 to 1475 mm and for heights ranging from 1050 to 2250 mm [16]. These findings are consistent with numerous industrial observations indicating that, in this type of dryer, the driest meat products are very often located in the upper part. Over and above this amplitude considered as an effective value to even out the air velocity distribution in the dryer, numerical results accounted for a marked heterogeneous distribution of air velocities with means ranging from 0.3 to more than 1:2 m s1 , as well as poorly ventilated areas in the lower part of the plant and at half-height at the left and right of the area filled with the objects, together with a highly ventilated upper part of the dryer, with air velocity means peaking at 1:5 m s1 locally. Below the amplitude of 65%=35%, air velocity means higher than 0:9 m s1 appeared in the lower part of the dryer (Figure 9.6d) compared with the three other cases (Figure 9.6a through Figure 9.6c), thus giving rise to heterogeneity in ventilation according to the width of the dryer, with an area in the middle that was more ventilated than on either side.
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9.3.3.3 Influence of the Form of the Ventilation Cycle Unlike the cycle of linear form, with a sinusoidal form of the ventilation cycle that is certainly closer to industrial reality, a large poorly ventilated area with means lower than 0:6 m s1 appears in the lower part of the plant (Figure 9.7a) at an amplitude of 65%=35%, i.e., the value identified as the best amplitude for evening out the drying conditions in the case of a linear ventilation cycle. The airflow structure given by Figure 9.7a resembles that of a linear ventilation cycle of 70%=30% (Figure 9.6b). In view of the marked heterogeneity in the distribution of the airflow, an amplitude of 65%=35% was not optimal for a sinusoidal ventilation cycle [16], meaning that, in addition to amplitude, the form of the ventilation cycle also has an influence on airflow patterns inside modern meat dryers. Scaling down the amplitude of the ventilation cycle from 65%=35% to 60%=40% (Figure 9.7b) made the airflow patterns more homogeneous, as the poorly ventilated area in the lower part of the plant disappeared, leading to an airflow structure identical to the best one obtained for a linear ventilation cycle (Figure 9.6c). The best results in terms of ventilation homogeneity were obtained for an amplitude of 65%=35% with a ventilation cycle of linear form, and for an amplitude of 60%=40% with ventilation cycle of sinusoidal form. This difference due to the form of the ventilation cycle can be explained from the findings of a previous 2D CFD study [14]. Indeed, in an empty sausage dryer of similar geometry, Mirade and Daudin [14] demonstrated that for steadystate conditions of ventilation, (i) slight variations of +4% around 50%=50% in the low and high levels of the ventilation cycle provided adequate ventilation of the whole width of the dryer where the products are usually placed, and (ii) a strong imbalance between the airflow 2750 2450 2150
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FIGURE 9.7 Distribution of the air velocity means calculated from 2D unsteady CFD modeling on a vertical section of a small sausage dryer over one period of ventilation cycle of sinusoidal form, at amplitudes of: (a) 65%=35% and (continued)
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FIGURE 9.7 (continued) (b) 60%=40% (given the unsteady modeling, the ventilation cycle was directly incorporated into the CFD model by means of a user-defined function. The black rectangle in the figures outlines the area usually filled with sausages.).
rates of the two blower ducts caused poor ventilation around the sausages. As the sinusoidal form leads rapidly to stronger imbalances than the linear form, the same ventilation homogeneity thus logically occurred with a ventilation cycle of lower amplitude [16]. 9.3.3.4
Consequences of Dissymmetry in the Ventilation Cycle
As mentioned earlier, dysfunction in the ventilation cycle frequently occurs in industry as a result of the simplicity of the system distributing the airflow between the two blower ducts and due to the marked unsteadiness of the airflow around the 50%=50% blower conditions. Figure 9.8a through Figure 9.8c show the unsteady numerical model results achieved for a sinusoidal ventilation cycle of amplitude 60%=40% when a dissymmetry of 2% (Figure 9.8a), 5% (Figure 9.8b), or 10% (Figure 9.8c) is taken into account. The air velocity means were calculated over five full ventilation cycles, i.e., for a length of time (5 min) that is truly representative of what occurs in a real industrial setting when the ventilation is activated [16]. Figure 9.8a through Figure 9.8c can be compared with Figure 9.7b to evaluate the change in airflow patterns due to dissymmetry. According to Figure 9.8a, a dissymmetry of 2% did not really affect the airflow distribution since the results were quite similar to those of the numerical model with no dissymmetry. The higher air velocities were still concentrated at half-width and half-height in the modern sausage dryer. The only significant difference was an increase in air velocity means in the lower part of the dryer, for widths ranging from 1175 to 1275 mm and heights ranging from 450 to 850 mm. Increasing the dissymmetry of the ventilation cycle from 2% to 5% clearly affected airflow patterns, leading to the appearance of dissymmetry between the two sides of the plant together
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FIGURE 9.8 Distribution of the air velocity means calculated from 2D unsteady CFD modeling on a vertical section of a small sausage dryer over five periods of ventilation cycle of sinusoidal form and amplitude 60%=40%, with a dissymmetry equal to: (a) 2%, (b) 5%, and (continued )
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FIGURE 9.8 (continued) (c) 10% (given the unsteady modeling, the ventilation cycle was directly incorporated into the CFD model by means of a user-defined function. The black rectangle in the figures outlines the area usually filled with sausages.).
with poorly ventilated areas with means lower than 0:6 m s1 in the lower part on each side (Figure 9.8b). The stratification of air velocity means according to height in the dryer also increased, almost certainly contributing to heterogeneity in product drying not only between top and bottom but also between the left and the right of the dryer. Predictably, a further increase in the dissymmetry of the ventilation cycle strongly disrupted means distribution for air velocity (Figure 9.8c). In the area filled with objects, air velocity means ranged from 0:3 m s1 in the lower part, where they formed a large area, to over 1:2 m s1 in the upper part. According to Figure 9.8a through Figure 9.8c, beyond 2% dissymmetry in the high and low levels of the ventilation cycle, it is essential to carefully regulate the ventilation cycle in order to prevent unwanted changes in airflow patterns that will almost certainly impair meat product drying.
9.4 MODERN MEAT DRYERS OF LARGE HEIGHT 9.4.1 PROBLEMATIC In the race to increase the competitiveness of dried meat products, production has been mechanized excessively in recent years with the introduction of robots to automatically move the trolleys filled with products from the manufacturing area to the drying area, and then, when dried, from the drying area to the packaging area. Consequently, modern meat dryers
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have become higher, reaching and sometimes exceeding 6 m, thus allowing the manufacture of the same quantity of dried meat products with a lower floor surface. Many manufacturers have reported poor meat drying in this type of dryer, particularly in the upper half just above the lateral blower ducts, where sausages appear too moist and too molded during the drying process, thus revealing insufficiently ventilated areas. To cope with this problem, some plant designers have installed a specific system in order to invert airflows during the ventilation periods. Some systems blow air with a steady airflow rate without ventilation cycle via the ducts placed level with the ceiling and extract it via ducts fixed to the lateral walls of the plant. All the difficulty lies in adjusting the duration of the periods where the airflow is inverted in relation to the periods where the air is introduced through the lateral blower ducts according to the ventilation cycle. Chanteloup [28] recently studied the airflow patterns in two modern 6 m-high industrial sausage dryers based on unsteady 2D CFD modeling performed with the CFD code Fluent [25], highlighting heterogeneity in airflow patterns in the case of standard dryer configurations. With the aim of evening out the airflow distribution, the author then tested the effects of modifying the amplitude and duration of the ventilation cycle, changing the height of the blower ducts, adding deflectors to force the air to penetrate inside the area filled with the sausages, adding a third extraction duct level with the ceiling, and inverting the airflow inlet.
9.4.2 MEAN AGE
OF
AIR
To investigate the effect of the previous modifications on the airflow patterns, the notion of mean age of air (MAA) was introduced into the CFD models. MAA, which is widely used in building or clean-room ventilation sciences, can be defined as the average lifetime of air at a particular location, giving an indication on the ‘‘freshness’’ of the air. In the framework of a ventilated room with a single inlet and a single outlet, local MAA corresponds to the average time it takes for air to travel from the inlet to any point inside the room [29–33]. Moreover, MAA can be solved by CFD codes as an additional user-defined transported scalar following the equation corresponding to steady-state configurations: @ @t rui t Gt ¼ St @xi xi
(9:1)
where t is the MAA scalar, rui is the mass flow rate (r is the air density and ui is the air velocity), G is the diffusion coefficient of t for the air mixture, and St is the source term of t, which depends on the density of the air mixture. Several authors have reported that the diffusion coefficient and the source term of t could be written following the two equations [29–34]: G t ¼ 2:88r 105 þ St ¼ 1
mEFF 0:7
(9:2) (9:3)
where mEFF is the effective viscosity, which is related to both molecular viscosity and turbulent viscosity. The boundary conditions for the solution of Equation 9.1 are zero value at the air inlet and zero gradient at the air outlet and wall surfaces. Furthermore, age of air is a passive quantity that does not affect airflow patterns; hence, the local MAA is obtained from the solution of the airflow equation [34].
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By solving this scalar transport equation by means of a user-defined function incorporated into the Fluent code, Chanteloup [28] calculated MAA distribution in different configurations of two modern sausage dryers of large heights with the aim of identifying a technical solution that evens out at best ventilation. In the standard dryer configuration, i.e., for one period of the ventilation cycle (amplitude of 90%=10%) and without air inlet inversion, the calculations indicated a lack of ventilation in the upper half of the plants compared with the lower half, with air velocities locally lower than 0:1 m s1 and an MAA peaking at 80 s at the level of the two rows immediately located just above the lateral blower ducts. Air velocities in the lower half of the dryer were higher, ranging from 0.3 to 0:6 m s1 , and the MAA values were lower, ranging from 58 to 70 s. These findings undoubtedly corroborate the observations made in industry, i.e., the appearance of overmoist and excessively molded sausages just above the lateral blower ducts during the drying process in modern sausage dryers of large height. Figure 9.9 displays the local MAA calculated in a 4.3 m-wide sausage dryer, taking into account an air inlet inversion of 2 min (Figure 9.9a), 3 min (Figure 9.9b), 4 min (Figure 9.9c), or 5 min (Figure 9.9d) during 10 min of ventilation [28]. Even though numerical results revealed few differences in the air velocity distribution between the four configurations (air velocity means ranged from 0.17 to 0:24 m s1 in the area filled with the sausages), analysis of Figure 9.9 shows marked differences in local MAA distribution. Increasing the inversion of the air inlet led to marked gradients in MAA distribution in relation to height; 531 477 423
315 261
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369
207 153 99
57 (a)
121
185
249
313
45 377
Area of filling with sausages
Mean age of air (s) >105 95–105 85–95 75–85 65–75 55–65 <55
Width (cm)
FIGURE 9.9 Distribution of the local mean age of air (MAA) calculated from 2D unsteady CFD modeling on a vertical section of a 6 m-high and 4.3 m-wide industrial sausage dryer over 10 min of ventilation corresponding to: (a) 8 periods (then 8 min) of ventilation cycle of sinusoidal form and amplitude 90%=10%, without dissymmetry, and 2 min where the air inlet was inverted and then blown by the extraction ducts.
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57 (b)
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45 57 (c)
121
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>105 95–105 85–95 75–85 65–75 55–65 <55
Width (cm)
FIGURE 9.9 (continued) (b) 7 periods of ventilation cycle and 3 min of air inlet inversion; (c) 6 periods of ventilation cycle and 4 min of air inlet inversion; and (continued)
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207 153 99 45 57 (d)
121
185
249
313
377
Mean age of air (s) >105 95–105 85–95 75–85 65–75 55–65 <55
Width (cm)
FIGURE 9.9 (continued) (d) 5 periods of ventilation cycle and 5 min of air inlet inversion (in this unsteady modeling, two user-defined functions were used: the first to take into account the form and amplitude of the ventilation cycle, and the second to calculate the local MAA).
when the inversion reached 5 min (Figure 9.9d), local MAA values ranged from less than 55 s level with the ceiling near the extraction ducts to over 105 s (exactly 130 s) in the lower part of the dryer (giving a mean of 79 s with a standard deviation of 27 s), whereas the heterogeneity of MAA distribution was much lower when using an inversion time of 2 min (Figure 9.9a), i.e., a mean of 67 s and a standard deviation of below 5 s between the top and bottom of the dryer. In light of these results, local MAA seems to be a better and a more sensitive parameter than air velocity for highlighting pockets of inadequate ventilation and thus for assessing ventilation efficiency in industrial food plants. From the analysis of the local air velocity in combination with the local MAA distribution, Chanteloup [28] numerically demonstrated that changing the height of the lateral blower ducts between 2 and 4.1 m had a very poor effect in evening out the ventilation in the area filled with the sausages, whatever the width of the dryer, 4.3 or 5.3 m. The air velocity means ranged from 0.38 to 0:44 m s1 (with a standard deviation of 0:19=0:20 m s1 ), and MAA means ranged from 33 to 35 s with a standard deviation below 5 s in all cases. Halving the duration of the ventilation cycle from 60 to 30 s combined with the addition of a third extraction duct level with the ceiling slightly affected airflow patterns inside the large-height dryers studied. As indicated in Figure 9.9, inverting the air inlet in the dryer significantly modified air distribution in the plant, even improving ventilation homogeneity around the sausages compared with a standard operation without air inlet inversion, provided that the inversion time did not exceed one-fifth of the total ventilation time. On the other hand, scaling down the amplitude of the ventilation cycle from 90%=10% to 60%=40% without inverting the
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349 Area of filling with sausages
Height (cm)
448
250
151
52 66
132
198
264
330
396
462
Mean age of air (s) >20 18–20 16–18 14–16 12–14 10–12 <10
Width (cm)
FIGURE 9.10 Distribution of the local mean age of air (MAA) calculated from 2D unsteady CFD modeling on a vertical section of a 6 m-high and 5.3 m-wide industrial sausage dryer over 10 min of ventilation (8 periods of ventilation cycle of sinusoidal form and amplitude 90%=10%, without dissymmetry, and 2 min of air inlet inversion) and where two 0.35 m-long horizontal deflectors were fitted just above each blower duct (in this unsteady modeling, two user-defined functions were used: the first to take into account the form and amplitude of the ventilation cycle, and the second to calculate the local MAA).
air inlet during ventilation logically led to an increase in air velocities around the sausages located in the lower half of the plant to the detriment of the upper half, thus increasing the height stratification phenomenon, particularly in terms of local MAA distribution. Finally, the numerical investigation carried out revealed that the best distribution of local MAA (mean value of 18 s and standard deviation below 1 s) was obtained when a 0.35 m-long horizontal deflector was fitted just above each lateral blower duct in the 5.3 m-wide modern sausage dryer, for an air inlet inverted for 2 min for every 10 min of ventilation (Figure 9.10). On the other hand, the air velocities were not homogeneously distributed around the sausages since standard deviation reached 0:17 m s1 for a mean of 0:37 m s1 . In addition, the strong impact on the homogeneity of MAA distribution was much lower when the same deflectors were added in the numerical model corresponding to the second sausage dryer, which was less wide. Taken together, these numerical conclusions confirm that airflow patterns are very difficult to assess a priori; they also underline that numerical results absolutely must be validated by experimental results.
9.5 CONCLUSION This chapter clearly shows that CFD techniques can be very useful tools for assessing and improving airflow patterns in modern industrial meat dryers of medium or large height,
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particularly those operating due to the ventilation cycle. The effect of the amplitude and form of the ventilation cycle on the homogeneity of the distribution of the air velocity means has been illustrated, together with the effect of a dissymmetry in the ventilation cycle. The results obtained confirmed the industrial observations on poor process efficiency in some parts of the plants, such as, for example, that the driest products are often located in the upper part of medium-height meat dryers. The need for controlled regulation of the ventilation cycle was also highlighted. Calculations performed in modern sausage dryers of large height proved that local MAA distribution was a highly promising and very useful parameter for assessing ventilation efficiency compared with the usual air velocity, even if numerical results needed to be validated by experimental data. With CFD techniques, the significance and effects of operating conditions and design parameters can therefore be analyzed to gain a better understanding of the dynamics of the meat drying. Furthermore, more recent studies assessing airflow patterns via unsteady modeling will shortly provide professionals with a rational approach to help them in the operation and design of modern dryers, once they will have been validated by experimental data. However, a full numerical model of how a modern meat dryer operates would be ideal, i.e., a model describing the homogeneity of the drying conditions and the interaction between the meat products being dried and the indoor atmosphere (velocity, turbulence, temperature, and relative humidity). This remains difficult because very refined meshes will need to be constructed, yielding 3D numerical models requiring immense memory size. However, further progress can be expected in the years to come as the CFD codes become more and more flexible in use while the calculating power of computers currently used in practice continues to increase.
REFERENCES 1. V. Kottke, H. Damm, A. Fischer, and U. Leutz. Engineering aspects in fermentation of meat products. Meat Science 43(Supplement S): 243–255, 1996. 2. C. Noel. Etude du processus de se´chage des saucissons en vue d’e´viter le crouˆtage, accident de fabrication pre´judiciable a` la qualite´. DESS report, University of Bourgogne, Dijon, France, 1991. 3. E. Dabin and R. Jussiaux. Le Saucisson Sec. Paris: Erti e´diteur, 1994, pp. 120–127. 4. J. Lenges, A. Sterckendries, and A. Drouet. Etude des processus de se´chage des saucissons. In: Proceedings of CERIA Conference. Brussels, 1973, 6 p. 5. P. Baldini. De´termination de l’activite´ de l’eau aw des produits ensache´s crus en fonction de la teneur en eau. Viandes et Produits Carne´s 2: 8–14, 1981. 6. A. Stiebing and W. Rodel. Influence of the pH on the drying pattern in dry sausage. Fleischwirtschaft 70: 1039–1043, 1990. 7. F. Lucke and H. Hechelmann. Starter cultures for dry sausages and raw ham. Fleischwirtschaft 71: 307–313, 1991. 8. J.D. Daudin, A. Kondjoyan, and J. Sirami. Water and salt transfers analysis in drying of sausages. In: Proceedings of the 38th International Congress of Meat Science and Technology. ClermontFerrand, 1992, pp. 1199–1202. 9. P. Baldini, E. Cantoni, F. Colla, C. Diaferia, L. Gabba, E. Spotti, R. Marchelli, A. Dossena, E. Virgili, S. Sforza, P. Tenca, A. Mangia, R. Jordano, M.C. Lopez, L. Medina, S. Coudurier, S. Oddou, and G. Solignat. Dry sausages ripening: influence of thermohygrometric conditions on microbiological, chemical and physicochemical characteristics. Food Research International 33: 161–170, 2000. 10. T. Bolumar, P. Nieto, and J. Flores. Acidity, proteolysis, and lipolysis changes in rapid-cured fermented sausage dried at different temperatures. Food Science and Technology International 7: 269–276, 2001. 11. A.I. Andre´s, R. Cava, J. Ventanas, V. Thovar, and J. Ruiz. Sensory characteristics of Iberian ham: Influence of salt content and processing conditions. Meat Science 68: 45–51, 2004.
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12. P.S. Mirade and J.D. Daudin. Analyse expe´rimentale de l’ae´raulique d’un se´choir a` saucisson. In: Proceedings of 5th French Congress on Chemical Engineering. Lyon, 1995, pp. 83–88. 13. R. Braconnier, J.R. Fontaine, and J. Gillet. Etude des e´coulements d’air dans une e´tuve de se´chage de charcuterie. National Symposium on Qualite´ de l’air dans les IAA, Cemagref, Rennes, France, 1997. 14. P.S. Mirade and J.D. Daudin. A numerical study of the airflow patterns in a sausage dryer. Drying Technology 18: 81–97, 2000. 15. P.S. Mirade. Assessment of ventilation homogeneity in a modern sausage dryer by a dynamic CFD approach. In: Proceedings of the 1st International Conference on Simulation in Food and Bio-Industries. Nantes, 2000, pp. 43–47. 16. P.S. Mirade. Prediction of the air velocity field in modern meat dryers using unsteady computational fluid dynamics (CFD) models. Journal of Food Engineering 60: 41–48, 2003. 17. Anonymous. Star-CD Manuals. London: Computational Dynamics Limited, 1994. 18. B.E. Launder and D.B. Spalding. Mathematical Models of Turbulence. New York: Academic Press, 1972, pp. 90–109. 19. C. Hirsch. Numerical Computation of Internal and External Flows: Computational Methods for Inviscid and Viscous Flows. Chichester: John Wiley, 1988, pp. 408–517. 20. S.V. Patankar and D.B. Spalding. A calculation procedure for heat, mass, and momentum transfer in three-dimensional parabolic flows. International Journal of Heat and Mass Transfer 15: 1787– 1806, 1972. 21. P.S. Mirade and J.D. Daudin. Etude nume´rique en 2 dimensions du cycle de ventilation d’un se´choir a` saucisson moderne. Entropie 226: 54–62, 2000. 22. A. Rizzi. Development of a numerical model for the fluid dynamic simulation of an ascending flow ripening chamber. Journal of Food Engineering 58: 151–171, 2003. 23. J.M. Martinez-Benet and L. Puigjaner. A powerful improvement on the methodology for solving large-scale pipeline networks. Computers and Chemical Engineering 12: 261–265, 1988. 24. M. Djuric and M. Novakovic. Numerically oriented improved Hardy–Cross method. Software for Engineering Workstations 5: 54–64, 1989. 25. Anonymous. Fluent 6: User’s Guide. Lebanon, NH: Fluent Inc., 2001. 26. Z.U.A. Warsi. Fluid Dynamics: Theoretical and Computational Approaches. Boca Raton, FL: CRC Press, 1993, pp. 540–552. 27. R.I. Issa. Solution of the implicitly discretized fluid flow equations by operator-splitting. Journal of Computational Physics 62: 40–65, 1985. 28. V. Chanteloup. Imple´mentation de la notion d’aˆge moyen de l’air a` l’aide d’une ‘‘User-Defined Function’’ dans le code Fluent. Master report, Blaise Pascal University, Clermont-Ferrand, France, 2005. 29. W.J. Fisk, D. Faulkner, D. Sullivan, and F. Bauman. Air change effectiveness and pollutant removal efficiency during adverse mixing conditions. Indoor Air 7: 55–63, 1997. 30. C.C. Federspiel. Air-change effectiveness: theory and calculation methods. Indoor Air 9: 47–56, 1999. 31. J. Abanto, D. Barrero, M. Reggio, and B. Ozell. Airflow modeling in a computer room. Building and Environment 39: 1393–1402, 2004. 32. Z. Lin, T.T. Chow, K.F. Fong, C.F. Tsang, and Q. Wang. Comparison of performances of displacement and mixing ventilations. Part II: Indoor air quality. International Journal of Refrigeration 28: 288–305, 2005. 33. O. Rouaud and M. Havet. Numerical investigation on the efficiency of transient contaminant removal from a food processing clean room using ventilation effectiveness concepts. Journal of Food Engineering 68: 163–174, 2005. 34. G. Gan. Effective depth of fresh air distribution in rooms with single-sided natural ventilation. Energy and Buildings 31: 65–73, 2000.
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CFD Simulation of Spray Drying of Food Products Han Straatsma, M. Verschueren, M. Gunsing, P. de Jong, and R.E.M. Verdurmen
CONTENTS 10.1 10.2
10.3 10.4
10.5
10.6
10.7
Introduction ............................................................................................................. 250 Flow Field Calculation ............................................................................................ 252 10.2.1 Transient versus Steady State ..................................................................... 252 10.2.2 Turbulence .................................................................................................. 252 10.2.3 Gas Flow Solving........................................................................................ 252 Particle Tracking ...................................................................................................... 252 Particle Drying Models ............................................................................................ 254 10.4.1 Introduction ................................................................................................ 254 10.4.2 Transport Phenomena................................................................................. 254 10.4.3 Drying Model Approaches ......................................................................... 256 10.4.4 Drying Model based on Diffusion Concept................................................ 256 10.4.4.1 Introduction ................................................................................ 256 10.4.4.2 Internal Moisture Transport ....................................................... 257 10.4.4.3 External Moisture Transport ...................................................... 258 10.4.4.4 External Heat Transport ............................................................. 259 10.4.4.5 Shrink of Particles ....................................................................... 260 10.4.5 Sorption Isotherms ..................................................................................... 261 10.4.5.1 Introduction ................................................................................ 261 10.4.5.2 GAB Relation ............................................................................. 261 10.4.5.3 Determination of Sorption Isotherms ......................................... 262 10.4.6 Diffusion Coefficient Relations................................................................... 263 10.4.6.1 Introduction ................................................................................ 263 10.4.6.2 Expression 1 ................................................................................ 263 10.4.6.3 Expression 2 ................................................................................ 264 10.4.6.4 Determination of Diffusion Coefficient ...................................... 264 Submodels for Thermal Reactions ........................................................................... 265 10.5.1 Introduction ................................................................................................ 265 10.5.2 Forming of Insoluble Material ................................................................... 266 Submodel for Stickiness ........................................................................................... 267 10.6.1 Introduction ................................................................................................ 267 10.6.2 Glass Transition Temperature .................................................................... 268 10.6.3 Relation between Glass Transition and Sticky-Point Temperature ............ 271 Fouling of Equipment .............................................................................................. 271
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10.8
Interparticle Collision Models................................................................................ 272 10.8.1 Introduction ............................................................................................ 272 10.8.2 Sampling Statistical Data ........................................................................ 272 10.8.3 Collision Probability ............................................................................... 273 10.8.4 Rebound after Collision .......................................................................... 274 10.8.5 Other Postcollision Events ...................................................................... 274 10.9 Coalescence and Agglomeration Model ................................................................. 275 10.9.1 Introduction ............................................................................................ 275 10.9.2 Classification of Collision Partners ......................................................... 275 10.9.3 Types of Collision Events........................................................................ 276 10.9.4 VD–VD=DRY Collision Type ................................................................ 276 10.9.5 DRY–DRY Collision Type..................................................................... 277 10.9.6 Properties of Agglomerates ..................................................................... 277 10.9.7 Conservation of Mass after Agglomeration ............................................ 278 10.10 Implementation of a CFD Model for Spray Dryers .............................................. 278 10.10.1 Introduction ............................................................................................ 278 10.10.2 Spray-Dryer Simulation .......................................................................... 279 10.11 Conclusions ............................................................................................................ 283 Nomenclature ..................................................................................................................... 283 References .......................................................................................................................... 284
10.1 INTRODUCTION Spray drying is an essential unit operation for the manufacture of many consumer food products, such as milk and whey powders, infant formula powders, coffee creamers, and other powders with proteins, fats, and sugars from animal (e.g., milk) or vegetable origin, egg powders, and coffee powders. In a spray dryer, the feed of a solution or suspension is atomized and the droplets are dried with a hot gas. The dryer can have one or more gas inlets and atomizers. Some dryers have one outlet for the gas as well as for the product. In that case the product has to be separated from the gas by a cyclone or bag filter. However, most dryers are provided with a product outlet, for example at the bottom of the dryer and one or more separate gas outlets. These gas outlets are placed in such a position (e.g., at the top of the dryer) so that minimal quantities of product leave through them. Simultaneous to the drying process, coalescence or agglomeration of droplets can also take place. The highest probability of agglomeration is in the neighbourhood of the atomizers. In practice, agglomeration is stimulated by using multiple atomizers spraying toward each other or by injecting fine particles (e.g., separated from the outlet gas) near the atomizers. Figure 10.1 shows an example of an industrial two-stage dryer consisting of a spray drying chamber and a vibrating fluid bed. The spray dryer is provided with one hot air inlet, which is constructed in such a way that a strong swirl component is added to the gas velocity. The dryer has one atomizer placed in the center of the air inlet and has one air outlet, which is placed in the center of the dryer. Because of the swirl of the gas, this is a suitable place for an air outlet. Fines, separated from the outlet gas of the drying chamber and the fluid bed, are returned near the atomizer. The layout of the equipment and the operating conditions play a major role in processrelated aspects as well as product-related aspects. Process-related aspects are, for example,
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Atomizer wheel/nozzles
Hot air inlet
Fines return
Spray chamber
Cyclone
Bag filter
Concentrated product Vibrating fluid bed
Warm air
(Agglomerated) powder
Cold air
FIGURE 10.1 An industrial two-stage spray dryer with fines return. (Courtesy of Anhydro A=S.)
fouling of the equipment and product losses with the outlet gas. Fouling of equipment is a serious practical problem when droplets reach the wall while they are still very sticky. Other aspects such as the thermal load, the retention of volatile components, and the agglomeration are product related. As food products are heat sensitive, the thermal load during drying is of great importance for the final quality. A too-high thermal load can lead to degradation of valuable components such as proteins and vitamins, brown coloring, forming of insoluble material, or other undesired components. High-quality instant powders require optimal free-flowing properties, absence of dust, and quick dissolution or dispersion in water or other solvent without the formations of lumps. The degree of agglomeration is an important factor for these properties. By agglomeration, small particles are combined to form larger particles in which the original particles are still identifiable (see Figure 10.2). In this way the characteristics of a single particle are maintained while the bulk powder properties are improved. Agglomeration of particles can be carried out as a separate process after drying, but it is more convenient to combine it with the drying process. It is clear that a good simulation technique is very valuable for the design of spray dryers, solving process-related problems, and finding conditions to get the best product properties.
200 µm
FIGURE 10.2 SEM-photograph of spray-dried and agglomerated powder. (From Verdurmen, R.E.M., Menn, P., Ritzert, J., Blei, S., Nhumaio, G.C.S., Sonne Sørensen, T., Gunsing, M., Straatsma, J., Verschueren, M., Sibeijn, M., Schulte, G., Fritsching, U., Bauckhage, K., Tropea, C., Sommerfeld, M., Watkins, A.P., Yule, A.J., and Schønfeldt, H., Dry. Technol., 22, 1403, 2004.)
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A full 3D simulation of a spray drier is possible with CFD. With almost all basic CFD software packages it is possible to simulate the flow pattern of the gas in the dryer and the trajectories of the particles. For food processing these basic techniques alone are not enough. The value of these simulations increases when these basic techniques are extended with additional submodels such as a drying model, kinetic models of thermal reactions, submodels describing the stickiness of the product, an agglomeration model, and so on. In this chapter several submodels will be discussed in more detail.
10.2 FLOW FIELD CALCULATION 10.2.1 TRANSIENT
VERSUS
STEADY STATE
Often transient as well as steady-state flow field calculations are possible with CFD software packages. In transient calculations, the changes during the run time of an instationary process are simulated. For spray drying this would, for example, be useful to study the dynamic behavior of the dryer during the start-up or shutdown of the installation. Normally, spray drying is a continuous process and the steady-state situation will be of most interest. However, it is useful to make some marginal notes here. When looking through the peep window of an industrial dryer, it can be seen that the flow pattern is rather chaotic and permanently fluctuating like the wind in our earthly atmosphere. It seems that a pure steady state can never be reached. For some engineers, this is a reason to do transient simulations instead of steady-state simulations for spray dryers. However, steady-state simulation is a good approximation for most spray dryers and in the remainder of this chapter the steady-state approach will be assumed.
10.2.2 TURBULENCE The gas flow in a spray dryer is turbulent. To simulate the flow field, several turbulence models are available to approximate the influence of turbulent fluctuations on large-scale flow behavior [1]. A popular turbulence model is the k« model [1]. This model uses a specific relation to determine the local value of the eddy viscosity from the turbulent kinetic energy (k) and its dissipation («). It assumes that the turbulence is isotropic (the same in all directions). This assumption strongly reduces the required CPU-time of the calculation. That is why the k« model is currently one of the most popular turbulence models for technical calculations. The assumption of an isotropic turbulence is not permitted for strongly swirling flows (e.g., in cyclones). The k« model is suitable for most spray-dryer simulations, because the swirling motion is not so strong that the accuracy is reduced. In some designs of spray dryers a strong swirling motion is introduced. In such cases another turbulence model such as the Reynolds stress turbulence model is a better choice.
10.2.3 GAS FLOW SOLVING To predict the profiles of the gas flow velocity, temperature, and pressure, a calculation grid is set up for the spray-dryer volume. For each volume cell in the grid, the equations describing the fluid flow are solved in an iterative process. After each iteration a better solution of the equations will be reached. The iterative procedure will be continued until sufficient convergence has been reached.
10.3 PARTICLE TRACKING In spray drying, the flow consists of a continuous gas phase and dispersed phase in the form of liquid or solid particles. The motion of the particles will be influenced by that of the gas
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phase and vice versa via displacement and interphase momentum, mass, and heat transfer effects. Moreover, gravitational forces also act on the particles. The strength of the interactions will depend on the particle’s size, density, and number density. The particle trajectories can be calculated by solving the momentum conservation equations for droplets. A widely used approach is the Lagrangian=Eulerian method. With this method the residence time of a particle is divided into small time steps. After each time-step a new position and velocity of the particle is calculated. In this way the whole trajectory from injection point to outlet is calculated. This time-step method should not be confused with transient calculation mentioned in Section 10.2.1. In fact, the Lagrangian method describes the place-dependent particle behavior in a steady-state situation. Indispensable is the inclusion of the phenomena that occur when a droplet strikes a wall. In the simplest case, the result is an elastic or inelastic bounce. Optional submodels can be added that describe the effects of phenomena such as sticking or shattering at the wall, interparticle collisions followed by rebounding, break up, coalescence, or agglomeration. In industrial spray dryers, billions of particles are atomized each second. It is extremely time consuming to calculate all these trajectories for large-scale dryers, so a more statistical approach is more suitable. In this approach, the total population of droplets is represented by a finite number of computational parcels, each of which represents a group of particles having the same properties. Each parcel has its own initial properties, such as injection point, velocity, diameter, density, temperature, and so on. Of course, the number of parcels must be large enough so that the properties of the full population are well represented. This can be assessed, in the absence of any other measures, by performing calculations with different numbers of parcels and comparing the results. In turbulent flows, the random walk technique is employed to introduce the fluctuating nature of the turbulent velocity gas field. This means that the gas velocity that the particle feels is not the local mean velocity, but the mean value added with a random turbulent contribution. In general, the flow field and particle trajectories are calculated separately. The gas flow solver and particle tracker are then alternately run in a calculation loop, as shown in Figure 10.3. The gas flow solver calculates the gas conditions, such as temperature, moisture, velocity, and degree of turbulence, in each volume cell of the grid. The particle tracker reads in these data in order to calculate the trajectories. When the parcel passes a cell of the grid the amounts of energy, mass, and momentum transferred to the gas are calculated and added to the source terms of that cell. In this way all trajectories are calculated one by one. In the next iteration, the gas flow solver uses these source terms for a new calculation. The calculation loop is repeated until sufficient convergence is achieved. Gas flow solver
Gas conditions
Source terms for energy, mass, and momentum Particle tracker
Particle trajectories
FIGURE 10.3 Calculation flowchart.
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It can occur that a lot of volume cells are not visited within one particle tracking loop with a limited number of parcels, especially when the grid is fine. Caused by the random nature of the turbulence, in the next particle tracking loop the parcels will follow other trajectories and other volume cells will be or will not be visited. This results in inhomogeneous source terms over the entire domain. A good strategy to smooth these inhomogeneities is averaging the source terms over multiple iterations.
10.4 PARTICLE DRYING MODELS 10.4.1 INTRODUCTION Many CFD software packages support particle tracking combined with heat and mass transfer. However in most packages, the transport limitations within a particle are not taken into account. These packages are suitable for evaporation of pure solvent droplets, but are not suitable for spray drying of food products, because the internal mass transport determines the drying rate of these products. For that purpose, a package is needed that can be called a drying model during particle tracking.
10.4.2 TRANSPORT PHENOMENA For mass and heat transport during spray drying, external and internal phenomena can be distinguished. External transport phenomena take place from the particle surface to the surrounding air and internal transport phenomena from the inner to the outer side of the particle. The heat of evaporation is withdrawn from the particle by evaporation of water, so there is a coupled heat and mass transfer. The external transport rate can be described by a transfer coefficient and a driving force. The transfer coefficient is strongly determined by the Reynolds number based on the velocity difference between particle and surrounding air. The driving force for mass transfer is the difference in water concentrations (or vapor pressure) in the gas phase at the droplet’s surface and the bulk of the air. So, a relation is needed to describe the equilibrium vapor pressure of the product as a function of its moisture content and temperature. The internal transport rate is strongly determined by the effective diffusion coefficient (for mass) or thermal conductivity (for heat). In most cases, water concentration gradients are the driving force for internal moisture transport. However, when the particle temperature exceeds the boiling temperature, a vapor pressure gradient becomes the driving force. Internal heat transport (conduction) takes place faster in comparison with internal mass transport (diffusion). For droplets with small diameters, such as for spray drying, the assumption of a uniform temperature within the particle is a valid approximation. An example of a calculated time evolution of moisture and temperature during drying of a single skim-milk droplet with a diameter of 100 mm in an ideal mixed volume of air is shown in Figure 10.4. When the initial moisture content of the particle is high, in the first stage of drying, the external mass transport is the rate-limiting factor. The water evaporation rate is high and the particle temperature will approach the wet-bulb temperature. The wet-bulb temperature depends upon the temperature and moisture content of the surrounding air but is typical in the range of 408C–508C. Figure 10.4 shows that this drying stage is very short (0.01 s). When the outer shells of the particle get dry, the internal mass transport becomes dominant and the water evaporation rate strongly decreases. The particle temperature approaches the temperature of the surrounding air and the moisture content of the outer shell will approach equilibrium with the surrounding air. In this stage there is a sharp moisture gradient within the particle, which equalizes gradually. After a drying time of 30 s, the mean moisture content
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Air Particle Boiling T
Temperature (⬚C)
160
120
80
40 0.00
0.02
0.04 0.05
0.45
0.85
1
11
21
Time (s) 1.0
Mean Inner shell Outer shell Equilibrium
Moisture (kg kg −1)
0.8
0.6
0.4
0.2
0.0 0.00
0.02
0.04 0.05
0.45 0.85 Time (s)
1
11
21
FIGURE 10.4 Calculated drying of a single skim-milk particle (100 mm) in an ideal mixed volume of air. Mass ratio dry solids=dry air: 0.05; relative particle velocity: 0:1 m s1 ; initial conditions: particle moisture: 1 kg kg1 dry solids; particle temperature: 708C; air moisture: 8:5 g kg1 dry air; air temperature: 1808C. Top: Air temperature (Tair ), particle temperature (Tp ), and boiling temperature (Tboil ) as a function of time. Bottom: Moisture content (average, inner shell, outer shell) and equilibrium moisture content as a function of time.
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of the particle has approached but not yet reached the equilibrium value. In the figure, the boiling point of the inner of the particle (wettest part) is also plotted. Although the air-inlet temperature is far above the water-boiling temperature, the highest particle temperature remains just below its boiling point. The particle behavior strongly depends on the type of the product and the process conditions. During drying, a particle can shrink, but full shrink is not very likely. In general, the particle becomes porous by the forming of vacuoles or open channels. Under certain conditions, for example, when the feed contains a high amount of dissolved gas or when the droplet exceeds the boiling point, the particle can be inflated like a balloon and dry further as a hollow particle or burst into small pieces.
10.4.3 DRYING MODEL APPROACHES Many particle drying models have been developed with various approaches of the drying kinetics. An example is the approach to describe the rate of evaporation as the rate of the unhindered evaporation (without internal transport limitations), multiplied by a factor which decreases with the particle’s moisture content [2]. The factor is based on a characteristic drying rate curve of the specific product. Another approach is based on a reaction-engineering concept, assuming drying as a competitive process between an evaporation and a condensation reaction [3]. Both approaches consider only the course of the overall moisture content of the drying particle. In more extended models, the differential equation that describes the instationary diffusion process in a spherical particle [4] is solved numerically [5,6]. In this approach the time evolution of the moisture gradients within the particle is included. Other variants add special particle behavior to the model, for example, for particles that are inflated to hollow spheres [7,8]. Each model has its advantages and disadvantages and is more or less suitable for a specific product. In this chapter, a model that describes the drying kinetics by the diffusion concept will be worked out. The advantage of this concept is the inclusion of the moisture gradients within the particles. For particle collisions with the wall or with other particles, the moisture content of the outer shell of the particles is relevant, while for thermal reactions during drying the local moisture content in combination with the temperature is needed. A disadvantage is that the effective diffusion coefficient as a function of moisture content and temperature must be known. Advanced experiments are needed to obtain that information.
10.4.4 DRYING MODEL 10.4.4.1
BASED ON
DIFFUSION CONCEPT
Introduction
In this section, a particle drying model is worked out. The internal moisture transport is described by the diffusion concept, the external heat and mass transport by the theory of a turbulent boundary layer. A number of assumptions are made: . . .
Particles are spherical. Temperature within the particle is homogeneous. No effect of exceeding the boiling temperature.
The drying model can be applied to Lagrangian particle tracking in CFD calculations or to batch drying of one or more particles in a fixed quantity of air. The latter is equivalent to continuous drying in a cocurrent process.
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10.4.4.2
Internal Moisture Transport
Within a powder particle the moisture is transported by diffusion. For a thin spherical shell (thickness dr) the mass balance of water can be set up as Fin ¼ Fout þ Fac
(10:1)
where F is the mass flow of water going into, going out of, and accumulated in the shell. Working out this balance gives dcp Fin ¼ 4p r2 D (10:2) dr r 2 dcp Fout ¼ 4p r D (10:3) dr rþdr Fac ¼ V
dcp dcp ¼ 4pr2 dr dt dt
(10:4)
Finally, this leads to the common differential diffusion equation: @cp 1 @ 2 @cp r D ¼ 2 r @r @t @t
(10:5)
where cp is the moisture content (kg m3 ) and D the (local) water diffusion coefficient. This differential equation cannot be solved analytically. For simplicity, a numerical solution according to a first-order method is chosen. In general, a disadvantage of a firstorder method is that it needs smaller calculation steps than a higher-order method. An advantage of this method is that it is much easier to implement and that it can more easily be combined with effects like shrink and agglomeration: for example, the time-step sizes can be varied depending on the transport rate so that instabilities can be avoided; shell radii need not to be equidistant and can be varied during the drying process. The particle is divided in a number of shells. Equation 10.2 through Equation 10.4 are written in the differential form for each shell i, where 1 is the innermost and n the outermost shell: Fin, 1 ¼ 0 Fin, i ¼
(Di þ Di1 ) (cp,i cp,i1 ) 4pr20,i (i > 1) (rm,i rm,i1 ) 2
(10:6) (10:7)
Fout,i ¼ Fin,iþ1 (i < n)
(10:8)
Fout , n ¼ Fev
(10:9)
Fac,i ¼ Mdp,i
Dcdp,i Dt
(10:10)
where Fev is the rate of evaporation at the outside of the particle (kg s1 ), Mdp,i the dry solids mass of shell i, cdp,i the moisture content (kg kg1 ) of shell i based on the dry solids mass, r0,i the outer radius of shell i. rm,i is defined as rm,i ¼
r0,i þ r0,1þi 2
(10:11)
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cp and cdp are related as cp ¼ r p
cdp 1 þ cdp
(10:12)
where rp is the density of the particle (kg m3 ). The rate of evaporation (Fev ) is determined by the external mass transport from the particle to the surrounding air (see Section 10.4.4.3). With these equations the new moisture content of each shell after a time-step Dt can be calculated. In case of a CFD calculation, the total amount of mass transferred to the surrounding air is obtained by summation of Fev Dt for each Lagrangian time-step that the particles reside in the volume cell. The value obtained by summation is saved in a source term for that cell and is used in the next iteration of the flow solver to calculate the new moisture content of the air in that volume cell. In case of batch drying of one or more particles in a fixed quantity of dry air, the new air moisture content can be calculated with dxa Fev,total ¼ dt Mda
(10:13)
where xa is the moisture content of air based on dry air, Fev,total is the total water flow transferred from the particles to the surrounding air, and Mda the mass of dry air. 10.4.4.3
External Moisture Transport
The external moisture transport from the particle j to the surrounding air can be written as [11] Fev, j ¼ kj Aj ca, j ca
(10:14)
where kj is the mass transfer coefficient (m s1 ), Aj the surface area of the particle (m2 ), ca, j the water concentration in air (kg m3 ) at equilibrium with the particle surface, and ca the water concentration in the bulk of the surrounding air. The water concentration in air (ca ) is related to the partial water pressure ( pa ) according to the ideal gas law pa ¼
ca RT Mw
(10:15)
where Mw is the molecular weight (kg mol1 ) of water, R the ideal gas constant (J mol1 K1 ), and T the absolute temperature (K). Equation 10.14 can be rewritten as Fev, j
Mw pa, j pa ¼ kj Aj R Tp Ta
(10:16)
where Tp is the particle temperature and Ta the bulk air temperature. pa, j can be calculated with the sorption isotherms of the product (see Section 10.4.5).
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In drying practice, the moisture content of air is usually expressed as kg water=kg dry air (xa ). This content is related to pa by pa ¼
xa pt xa pt ¼ Mw 0:622 þ xa þ xa Ma
(10:17)
where pt is the total pressure and Ma the molecular weight of dry air. The mass transfer coefficient (k) can be calculated from the Sherwood number (Sh) obtained from empirical relations for spherical particles, for example, the Ranz–Marshall equation [10,11]: Sh ¼ 2 þ 0:58Re0:5 Sc0:33
(10:18)
where Re is the Reynolds number and Sc the Schmidt number. The Sherwood number is defined as Sh ¼
kd D
(10:19)
where d is the particle diameter and D the diffusion coefficient of water vapor in air. 10.4.4.4
External Heat Transport
Heat transport from particle to the surrounding air takes place due to temperature differences. Besides that, heat is withdrawn from the particles by water evaporation. The heat balance of the particle can be written as Qout þ Qev þ Qac ¼ 0
(10:20)
where Qout is the heat flow transferred to the surrounding (J s1 ), Qev the heat flow withdrawn by evaporation, and Qac the accumulated heat flow. Working out the balance gives Qout ¼ aA Tp Ta
(10:21)
Qev ¼ Fev Hev þ Tp Cp,wv
(10:22)
Qac ¼ Mdp
dHdp dt
(10:23)
where a is the heat transfer coefficient (W m2 K1 ), T the temperature (8C) of the particle (p ) or air (a ), Cp the specific heat capacity of water vapor (wv ), Hev the heat of evaporation (J kg1 ) of water at 08C, Mdp the total dry mass of the particle, and Hdp the total enthalpy of the particle based on the mass of dry solids. Hdp can be written as Hdp ¼ Tp Cp,p ¼ Tp Cp,dp þ Cp,w cdp
(10:24)
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where Cp is the specific heat capacity of the dry solids (dp) or water (w) and cdp is the overall moisture content of the particle based on the dry solids mass. In analogy with the mass transfer, the heat transfer coefficient (a) can be calculated from the Nusselt number (Nu) obtained from empirical relations for spherical particles, for example, the Ranz–Marshall equation: Nu ¼ 2 þ 0:58Re0:5 Pr0:33 where Re is the Reynolds number and Pr the Prandtl number. The Nusselt number is defined as ad Nu ¼ l
(10:25)
(10:26)
where d is the droplet diameter and l the thermal conductivity of the surrounding air. With these equations the new enthalpy of the particle (Hdp,tþDt ) after a time-step Dt can be calculated. When the new enthalpy and the new overall moisture content of the particle are calculated, the new particle temperature can be calculated with Tp,tþDt ¼
Hdp,tþDt Cp,dp þ Cp,w cdp,tþDt
(10:27)
In case of a CFD calculation, the total amount of heat transferred to the surrounding air is obtained by summation of Qout Dt for each Lagrangian time-step that the particles reside in the volume cell. The value obtained by summation is saved in a source term for that cell and is used in the next iteration of the flow solver to calculate the new air temperature in that volume cell. In case of batch drying of one or more particles in a fixed quantity of air, the following equations can be used to calculate the new air temperature. The change of the enthalpy of air based on the mass of dry air (Hda ) is dHda Qout,total ¼ dt Mda
(10:28)
where Qout,total is the summed heat flow (J s1 ) transferred from the particles to the surrounding air and Mda the mass of dry air. The enthalpy of air is defined as Hda ¼ Ta Cp,a þ xa Cp,wv þ xa Hev (10:29) First, the new enthalpy after a time-step Dt is calculated with Equation 10.28 and Equation 10.29. When the new enthalpy (Hda, tþDt ) and moisture content of air (xa, tþDt ) are known, the corresponding temperature of the air can be calculated with Ta,tþDt ¼ 10.4.4.5
Hda,tþDt xa,tþDt Hev Cp,a þ xa,tþDt Cp,wv
(10:30)
Shrink of Particles
During drying the particles will shrink. On the other hand, vacuoles or open pores can be formed during drying, so there is no full shrink. It is not easy to predict the shrink behavior. One approach is to define a shrink factor (Sf ) as Vp ¼ Sf Vmassive þ (1 Sf)Vini
(10:31)
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where V is the actual (p ), massive (massive ) (no vacuoles), and initial (ini ) volume of the particle. According to this equation, the volume of the particle is a linear combination of the massive and the initial volume. The shrink factor is a value between 0 (no shrink, constant volume) and 1 (full shrink). The volume of the massive-product changes with the moisture content and can be calculated from the actual density of the massive product and the actual particle weight. The density of the massive product can be approximated as 1 rmassive
¼
mp 1 mp þ rw rds
(10:32)
where mp is the moisture content based on total mass (kg kg1 ), rw the density of water (kg m3 ), and rds the density of dry solids. When the (local) particle volume is known, the radii of the particle’s shells can be recalculated.
10.4.5 SORPTION ISOTHERMS 10.4.5.1
Introduction
For modeling of the external moisture transport from a drying particle to the surrounding air (see Section 10.4.4.3), an equilibrium relation is needed to obtain the water vapor pressure of the wet product as a function of its temperature and moisture content. For this purpose, mainly sorption isotherms are used. With a sorption isotherm, the moisture content of the product is related to the water activity. The water activity (aw ) is defined as the ratio between the partial water vapor pressure of the air that is in equilibrium with the product (pa ) and the water vapor pressure of pure water (p0w ) at one and the same temperature: aw ¼
pa p0w
(10:33)
The advantage of the use of sorption isotherms is that a great part of the temperature dependence of the water vapor pressure is described by the well-known relation for pure water. In spite of that, the water activity is not fully temperature independent. The sorption isotherms determined at room temperature are not sufficient for drying purposes. A sorption isotherm at elevated temperature is needed and sometimes it is necessary to determine sorption isotherms at different temperatures. In literature several physical or mathematical models are presented to describe the sorption isotherms as reviewed in Ref. [12]. For food products the GAB (Guggenheim, Anderson, de Boer) equation is widely used, which is worked out in the next section. 10.4.5.2
GAB Relation
The GAB relation has the following form: " W ¼ Wm
# cg 1 Kaw Kaw þ 1 þ cg 1 Kaw 1 Kaw
(10:34)
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where aw is the water activity, W the powder moisture content, and Wm , cg , and K productspecific constants. To calculate the water activity at given moisture content, the GAB equation can be rewritten as
aw ¼ where
and
H1
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi H12 4H2 2H2
(10:35)
Wm H1 ¼ K cg 1 2 W
(10:36)
H 2 ¼ K 2 1 cg
(10:37)
These GAB constants can be temperature dependent. There are some mathematical expressions available to describe the temperature dependence of these constants (e.g., Arrhenius alike relations). Alternatively, the water activity as a function of temperature can be obtained by interpolation between experimental sorption isotherms at a limited number of temperatures. 10.4.5.3
Determination of Sorption Isotherms
There are several ways to determine sorption isotherms. A common complication for food products with a high content of carbohydrates is the crystallization during determination [15]. As spray drying is a fast process, there is no time for crystallization and the carbohydrates generally remain in the amorphous state. However, when the powders are rewetted during experiments to determine the sorption isotherms, crystallization can occur after some time. The sorption behavior of crystallized product is rather different from that of amorphous product [16], so data are not representative for the spray drying process. In practice this can mean that the sorption properties cannot be determined above a critical moisture content. The value of the critical moisture content depends on the type of product and the method of determination. In many cases, the sorption data beyond the critical point is not relevant for spray drying. In cases that it is relevant, it is possible to extrapolate valid data beyond the critical moisture content. Several methods to determine sorption isotherms are described in literature [13]. A widely used method is bringing the sample with known weight and moisture content in a vacuum desiccator over a saturated salt solution with known relative humidity. After equilibrating for about 24 h, the sample is weighed again and the equilibrium moisture content is calculated [14,15]. Kockel et al. [12] have presented a method where fresh powder is brought to equilibrium with conditioned air in a stirred fluidized bed. With this method, the time to reach equilibrium is reduced to about 3 h. A more direct method is described by Hols et al. [16]. Here, a laboratory scale dryer is applied to produce powder samples with a range of moisture contents. The samples are placed in a closed holder with a small headspace, supplied with a humidity sensor. After 10–90 min the equilibrium air humidity can be measured. Several researchers have reported experimental sorption data [8,12,15,16]. In Figure 10.5 the sorption isotherms of milk powder are shown as an example. The experimental data are fitted with the GAB relation (see Section 10.4.5.2). The moisture content is based on the fat-free dry matter. Because fat has no interaction with water, the same sorption
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1.0
Water activity (−)
0.8
Sorption isotherms milk powder 23⬚C 45⬚C 75⬚C
0.6
0.4
0.2
0.0 0.00
0.05 0.10 0.15 0.20 Moisture content in fat-free dry matter (kg kg−1)
0.25
FIGURE 10.5 Sorption isotherms of milk powder [16]. GAB constants: 238C: Wm ¼ 0.059, cg ¼ 11.4, k ¼ 1.04; 458C: Wm ¼ 0.043, cg ¼ 9.8, k ¼ 1.10; 758C: Wm ¼ 0.019, cg ¼ 8.2, k ¼ 1.19.
data can be applied for milk powders with various fat contents (and the same nonfat dry-matter composition).
10.4.6 DIFFUSION COEFFICIENT RELATIONS 10.4.6.1
Introduction
As explained in Section 10.4.2, diffusive transport of water from the inner to the outer side of the drying particle plays a major role in internal transport phenomena. The water diffusion coefficient strongly depends on the moisture content. The diffusion coefficients should be determined experimentally. Numerous forms of a mathematical expression to describe the diffusion coefficient are reported in literature [8]. Two mathematical expressions are worked out in the next sections. 10.4.6.2
Expression 1
The diffusion coefficient (D) as a function of the moisture content (W ) and the temperature (T ) is described with the equations ln DW ¼ a1,T
b1,T c1,T þ W
(10:38)
b2,W T
(10:39)
and ln DT ¼ a2,W þ
where a1 , b1 , c1 , a2 , and b2 are product-specific model constants. When the model constants a1 , b1 , and c1 are known at two temperatures (T1 and T2 ), both moisture and temperature
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dependence can be expressed in the following equation, which is in fact a linear interpolation between two points with coordinates (1=T1 , ln DT1,W ) and (1=T2 , ln DT2,W ): ln DT,W ¼
½ln DT2 ,W ln DT1 ,W 1 1 þ ln DT1 ,W 1 1 T T1 T2 T1
(10:40)
So, for a given moisture content ln DT1,W and ln DT2,W can be calculated with Equation 10.38. After that ln DT,W can be calculated at given temperature T with Equation 10.40. For this model six parameters (a1 , b1 , and c1 at two temperatures) have to be obtained by fitting to experimental data. Users have to be aware that extrapolation to temperatures out of the experimental range can lead to unrealistic diffusion coefficients. 10.4.6.3
Expression 2
A good alternative description of the diffusion coefficient has been developed and described in Ref. [9]. In this description, the whole temperature and moisture dependence is fit with only two parameters a and b. The diffusion coefficient is described by the following expression, which is a modification of the expression suggested in Ref. [8] and used for skim milk: b þ cW DH 1 1 DT,W ¼ exp exp 1 þ aW R T 303
(10:41)
where W is the moisture content based on total mass; and a, b, c, and DH are product-specific parameters. To restrict the degrees of freedom of Equation 10.41, but keep getting good fits with various products, the parameters are reduced as b ¼ 38:912 (constant) c ¼ 323:29a bþc a ¼ 16:84 1 b þ 323:39 DH ¼ 1:799 104 bW 0:445 The constants are obtained by fitting data reported by Wijlhuizen et al. [8] for skim milk. For that data set a and b are set to 1. The moisture dependence and the temperature dependence are adapted especially with a and b, respectively. This expression is applied to various food products (not published) and values of a and b are found in the range of 0.6–1.6 and 1.0–1.2, respectively. 10.4.6.4
Determination of Diffusion Coefficient
Diffusion coefficients can be determined in single droplet drying experiments, for example, in an acoustic levitator [17,18]. In that experimental setup, a vertical standing acoustic wave is generated. A drying droplet is levitated within the pressure node of the standing wave. The vertical position is recorded from which the droplet mass can be derived. The droplet contour is recorded with a camera that yields the droplet volume. By comparing the experimental
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T = 70⬚C T = 30⬚C
Diffusion coefficient (m2 s−1)
10−10 10−11 10−12 10−13 10−14 10−15 0
20
40 60 Moisture content (% m/m)
80
100
FIGURE 10.6 Diffusion coefficient of skim-milk powder as a function of temperature and moisture content according to Wijlhuizen et al. [8]. (From Wijlhuizen, A.E., Kerkhof, P.J.A.M., and Bruin, S., Chem. Eng. Sci., 34, 651, 1979.)
results at different temperatures with theoretical model calculations for a drying droplet, the diffusion coefficients can be derived [9]. In Figure 10.6 the diffusion coefficient of skim-milk powder is shown as an example.
10.5 SUBMODELS FOR THERMAL REACTIONS 10.5.1 INTRODUCTION Because food products are heat sensitive, the thermal load during drying is of great importance for the final quality. When submodels for the thermal reactions are available, they can be used in combination with the particle drying model (see Section 10.4). In general, the history of the particles’ temperature and moisture gradients are stored during the simulation of CFD. In that case the submodels can be applied subsequently in the postprocessing step. During the heat treatment of food products (thermization, pasteurization, sterilization) heat-induced reactions such as destruction of food nutrients, inactivation of enzymes, denaturation of proteins, destruction of microorganisms, and formation of new components take place. Most of these reactions can be described by simple nth-order (often first-order) reaction kinetics, where the reaction rate constant is dependent on the temperature according to the Arrhenius relation. In general, such a simple approach cannot be applied for spray drying. The reaction rate constant will strongly change with the dry solids content as a consequence of the change in the mobility of the molecules. Therefore, additional experiments and research are needed to describe the heat-induced reactions. One example of a thermal reaction during spray drying is the formation of insoluble material, which is undesirable especially for instant powders. In the next section we demonstrate how to carry out experiments in order to derive a kinetic model for this reaction during the drying of concentrated milk [19]. This method is also suitable for other food products or other thermal reactions.
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10.5.2 FORMING
OF INSOLUBLE
MATERIAL
The forming of insoluble material during the spray drying of concentrated milk is studied in the previous work [19]. The method and results are briefly described in this section. The mechanism by which insoluble material is formed is not yet fully understood. The current view is that the mechanism involves the unfolding of b-lactoglobulin, followed by aggregation with casein. It appears that other mechanisms also play a role. It is known that high-pressure atomization causes considerable amounts of insoluble material with a relatively high fat content. However, a kinetic model based on quantitative data can be set up, without knowing the exact mechanism. The easiest way to get quantitative data is by doing heating tests. Samples are prepared in a range of moisture contents, placed in a holder with a high area to volume ratio, and heated in a water bath for a certain time and temperature and cooled. Finally, the insolubility index is determined. Such heating tests with milk indicated that concentrates with a moisture content higher than 50% and powders with a moisture content lower than 10% needed several minutes more heating time at a temperature of 958C to form insoluble material. These heating times are much higher than the residence time in a spray dryer (20–40 s). Samples with moisture contents in the range of 10%–50% were difficult to homogenize and difficult to handle in heating tests. Samples with moisture content in the range of 12%–35% already had a high insolubility index directly after preparation without any heat treatment, probably caused by gelation of proteins. Another restriction of the heating tests is that short heating times (<7 s) are difficult to realize. Therefore, additional experiments were carried out on a pilot-scale spray dryer. The feed flow was kept very low with respect to the airflow, so that the air temperature and humidity hardly changed during the drying process. The concentrated milk feed was atomized with a pneumatic nozzle to obtain a large variety of droplet sizes. Experiments were done at air outlet temperatures in the range of 778C–1148C. The powder produced was sieved into three size fractions. The insolubility index of each size fraction was determined. The drying history of the particles was simulated with the drying model, as described in Section 10.4.4, and a CFD simulation is not needed for this purpose. Because the air conditions remain constant during the experiments, a simple simulation of batch drying of a particle in a quantity of air will do. The time that a particle needs to traverse the critical moisture range during drying depends on the particle diameter. So, in fact the variation of particle diameters generates a variation in heating times. A simple kinetic model is assumed: .
. .
Insoluble material is formed during spray drying only when the moisture content is between 10% and 30%. In this range, the rate of formation is independent of the moisture content. The rate of formation exhibits zero-order kinetic behavior with temperature dependency according to Arrhenius.
The rate of formation (rISi ) is described by the equation rISi
Ea 1 1 ¼ k0 exp R T T0
(10:42)
where k0 is the reaction rate constant, Ea the energy of activation (J mol1 ), R the universal gas constant (J mol1 K1 ), T the temperature, and T0 the reference temperature (K).
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10 7
3
Insolubility index (mL)
4
1 2
0.7 0.4
1
0.10 0.07 0.04 20
40
60
80
100
120
140
160
180
Diameter (µm)
FIGURE 10.7 Insolubility index (ISi) versus particle diameter. Experimental results (symbols) and model calculation (lines). Temperatures: 868C (1, *), 968C (2, &), and 1148C (3, ~). Model constants: k0 ¼ 0:054 mL s1 ; Ea ¼ 2:7 105 J mol1 ; T0 ¼ 348 K.
The kinetic constants k0 and Ea were determined by regression analysis. Figure 10.7 shows the experimental results and the model fits.
10.6 SUBMODEL FOR STICKINESS 10.6.1 INTRODUCTION The stickiness of particles plays a major role in the fouling of the equipment and in the agglomeration of colliding particles during spray drying. In general, the stickiness depends on the products’ dry solids composition, the moisture content, and temperature. Agglomeration or fouling takes place when a sticky particle collides with another object (wall or another particle) and forms a liquid bridge that is strong enough to resist mechanical deformations. Various researchers have calculated the critical viscosity for sticking during contact times of a few seconds by applying various models. The critical viscosity is in the range of 106 –108 Pa s. This value has been confirmed experimentally by various investigators [20–25]. At a viscosity higher than the critical value the particles will not stick. The critical viscosity occurs at a temperature that is called the sticky-point temperature. Especially, food products with a high content of carbohydrates are known as sticky products. During the fast spray drying process, carbohydrates do not crystallize, but get in an amorphous state with a liquid-like rubbery structure, which gradually changes to a glassy state. For this type of product, the sticky-point temperature can be related to the glass transition temperature.
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10.6.2 GLASS TRANSITION TEMPERATURE At the glass transition temperature (Tg ) the amorphous material changes from a liquid-like rubbery structure to a glassy state or vice versa. The Tg values of amorphous compounds and food materials are usually experimentally determined by differential scanning calorimetry (DSC), although other methods, such as nuclear magnetic resonance (NMR) can be applied as well [27]. DSC detects a characteristic change in specific heat (DCp ) at Tg . The glass transition temperature (Tg ) values may differ slightly depending on the applied analytical method, and also because of their thermal history. Roos [27,28] determined Tg and DCp for various sugars experimentally. These are given in Table 10.1, together with experimental data TABLE 10.1 Glass Transition Temperatures and Specific Heat Changes for Pure Compounds Compound Water
Mw 18
Pentoses Arabinose Ribose Xylose Hexoses Fructose Fucose Galactose Glucose Mannose Rhamnose Sorbose Disaccharides Lactose Maltose Melibiose Sucrose Trehalose
180 180 180
342 342 342
Alditols Maltitol Sorbitol Xylitol Maltodextrinsa DEb 36 DE 25 DE 20 DE 10 DE 5 Starch a b c
500 (370) 720 900 (504) 1800 (640) 3600 (991)
Tg (8C) Onset
Midpoint
135
DCp ( J=g)
Reference
3+0.5
[27,29]
2 20 6
3 13 14
0.66 0.67 0.66
[27,28] [27,28] [27,28]
5 26 30 31 25 7 19
10 31 38 36 31 0 27
0.75 — 0.50 0.63 0.72 0.69 0.69
[24,27,28] [27,28] [27,28] [24,27,28] [27,28] [27,28] [27,28]
101 87 85 62 100
92 91 67 107
0.45 0.61 0.58 0.60 0.55
[27,28] [27,28] [27,28] [24,27,28] [27,28]
39 9 29
44 4 23
0.56 0.96 1.02
[27,28] [27,28] [27,28]
0.58
[25,29] [25] [25,29] [25,29] [25,29] [25]
100 121 141 160 188 243c
0.45 0.40 0.30
Molecular weight according to manufacturer, effective molecular weight in parenthesis. Dextrose equivalent. Predicted.
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for maltodextrins [25]. Often Tg is reported as midpoint value, but Roos argues that the onset value is more important as most mechanical properties change above the onset value of Tg [28]. A decrease in viscosity is already observed above the onset value of Tg , which is particularly important for carbohydrate materials with respect to stickiness or crystallization. In spray drying, often mixtures of components are dried instead of the pure compounds. The Tg of these mixtures, containing two or more components and water can be estimated with the equation of Couchman and Karasz [25,26]: P wi DCp,i Tg,i Tg ¼ i P (10:43) wi DCp,i i
where wi is the mass fraction of component i, DCp,i the specific heat change of component i at Tg,i , and Tg,i the glass transition temperature of the pure component i. This equation is applied to multicomponent mixture systems. It proved to fit very well for data at higher concentration of solids (>70 m=m%), which means that it can be applied under spray drying conditions [25]. From this equation it can be derived that the presence of moisture decreases the glass transition temperature, as Tg for water is 1358C. Already, at very low moisture contents Tg decreases significantly. As an example, in Figure 10.8, the glass transition temperature of lactose is plotted against the moisture content. For a binary mixture the Couchman–Karasz equation can be rewritten as the simpler Gordon–Taylor equation: Tg ¼
w1 Tg1 þ kgt w2 Tg2 w1 þ kgt w2
(10:44)
DCp2 DCp1
(10:45)
where kgt ¼
The glass transition temperature (Tg ) values of many anhydrous high molecular weight food polymers cannot be experimentally determined as the Tg values of these are usually high, and materials tend to decompose at temperatures below Tg . In that case an estimate has to be made, 110
Temperature Tg (⬚C)
90
70
50
30
10 0
2
4 Moisture content (% m/m)
6
8
FIGURE 10.8 Glass transition temperature of lactose as a function of the moisture content according to the Couchman and Karasz equation. Tg,lactose ¼ 1018C; DCp,lactose ¼ 0.45 J g1; Tg,water ¼ 1358C; DCp,water ¼ 3.0 J g1:
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based on the Tg for homopolymers. It was observed that for glucose polymers, such as maltodextrins, Tg increases with the molecular weight in a similar way as for synthetic polymers. Therefore, Tg can be predicted for high molecular weight compounds according to the Fox and Flory relationship: Kg (10:46) Tg ¼ Tg1 M where Tg1 is the limiting Tg at high molecular weight, Kg a constant, and M the molecular weight. For maltodextrins Tg1 ¼ 243 C and Kg ¼ 52:8 K kg mol1 [25–27]. Also, Tg values for complex food mixtures have been determined experimentally. The Tg values of a number of dry products are listed in Table 10.2. TABLE 10.2 Glass Transition Temperature for Food Products Product Good start
Prosobee
Fish protein hydrolysate
Fish protein hydrolysate FPH 1 Fish protein hydrolysate FHP 2 Fish protein hydrolysate FHP 3 Whey protein hydrolysate LE 80-BT
Whey protein hydrolysate WE 80-M
Whey protein hydrolysate WE 80-BG
Casein hydrolysate CAS 90-STL
Casein hydrolysate CAS 90-GBT
a
Specifications
Tg (8C)
Reference
Lactose=maltodextrin: Carbohydrate 59% Protein 13% Fat 28% Corn syrup solids Carbohydrate 55% Protein 16% Fat 29% Molecular weight average: 10.5 kDa DCp ¼ 0:44 J g1 High molecular weight fraction 89.2% High molecular weight fraction 65.4% High molecular weight fraction 70.4% Molecular weight average: 1.95 kDa Free amino acids 35% Degree of hydrolysis: 41 Molecular weight average: 3 kDa Free amino acids 2% Degree of hydrolysis: 16 Molecular weight average: 0.47 kDa Free amino acids 4% Degree of hydrolysis: 30 Molecular weight average: 0.81 kDa Free amino acids 17% Degree of hydrolysis: 44 Molecular weight average: 0.35 kDa Free amino acids 13% Degree of hydrolysis: 23
74
[32]
82
[32]
71.9
[33]
49.2a 30.1a 42.2a 58.3a
[31] [31] [31] [31]
84.0a
[31]
69.9a
[31]
60.9a
[31]
87.3a
[31]
Tg extrapolated from measurements at various aw in Ref. [31].
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1012 1011
Viscosity (Pa s)
1010 109 108 107 106 105 0
5
10
15
20
25
30
Temperature difference T – Tg (⬚C)
FIGURE 10.9 Viscosity above glass transition temperature according to WLF relation. c1 ¼ 17.44; c2 ¼ 51.6; viscosity at Tg : 1012 Pa s.
The moisture content of a food polymer also determines the water activity. So, the glass transition temperature can also be related to the water activity instead of the water content. It appears that in many cases Tg decreases linearly with increasing water activity [29,30].
10.6.3 RELATION
BETWEEN
GLASS TRANSITION
AND
STICKY-POINT TEMPERATURE
For amorphous products, at temperatures below Tg the viscosity is higher than 1012 Pa s and no viscous flow will occur. At temperatures above Tg the molecular mobility is greatly increased while the viscosity rapidly decreases. The decrease in viscosity above the glass transition temperature and below the melting temperature can be described very well with the WLF relationship [27]: h log hg
!
c1 T T g ¼ c2 þ T T g
(10:47)
where h is the dynamic viscosity at temperature T, hg the viscosity at Tg , and c1 and c2 are constants. The most commonly used values of c1 and c2 are 17.44 and 51.6, respectively. This relation is plotted in Figure 10.9. As stated above (see Section 10.6.1), the critical viscosity for stickiness is 106108 Pa s. As the figure shows, this viscosity occurs at 158C–278C above the glass transition temperature.
10.7 FOULING OF EQUIPMENT The submodel for stickiness (see Section 10.6) can be used to get the fouling pattern of the dryer equipment. During particle tracking of a CFD simulation, when a parcel collides with a wall the sticky state of that particle can be determined. When it is in the sticky state and some other criteria with respect to velocity and angle of impact are satisfied, the particle sticks to the wall. Monitoring the locations where particles stick to the wall gives a good impression of the fouling pattern.
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10.8 INTERPARTICLE COLLISION MODELS 10.8.1 INTRODUCTION In a spray dryer, locations can exist where the particle concentration is so high that collisions between particles are probable. These interparticle collisions can have several consequences such as a rebound (dry particles), disintegration (especially at high velocities), coalescence (liquid particles), or agglomeration (sticky particles). Detailed reviews of theoretical studies on the collision rates of particles in turbulent flows are given in the literature [34,35]. Sommerfeld [36] has developed an interparticle collision model that is applicable if a sequential tracking of the parcels is adopted, as usually employed in the Euler–Lagrange approach for stationary flows. This matches with the particle-tracking approach described in Section 10.3. In the next sections, the setup of this model is described in more detail.
10.8.2 SAMPLING STATISTICAL DATA As described in Section 10.3, the parcels are tracked one by one, so there is no way to interact with other parcels passing the same volume cell of the grid. Therefore, the model relies on the generation of fictitious collision partners and the calculation of the collision probability according to kinetic theory. The generation of a fictitious particle requires local statistical information, which has to be sampled and stored. For each volume cell in the entire computational domain the following particle statistics are stored: number of particles, momentum vector, dry solids mass, water mass, and enthalpy. Because a number of these values depend on the particle diameter, particle size classes are defined and separate values of each size class are kept. At the beginning of a flow solver=particle tracking iteration loop the values of these data set are reset to zero. At each Lagrangian time-step (Dt), during tracking, volume cell in which the particle resides is known and size class of the particle is determined. The statistics of the volume cell are updated and restored using the equations
Np,i, j
new
¼ Np,i, j old þ Rp Dt
(10:48)
and xi, j new ¼ xi, j old þ Rp Dtxp
(10:49)
where Np is the total number of particles, Rp the particle number flow of the specific parcel, and xp a particle property (momentum, mass, or enthalpy). The cell index and the size class index are indicated by i and j, respectively. It can occur that a lot of volume cells are not visited within one particle tracking loop with a limited number of parcels, especially when the grid is fine. Caused by the random nature of the turbulence, in the next particle tracking loop the parcels will follow other trajectories and other volume cells will be or will not be visited. This results in an inhomogeneous particle distribution over the entire domain. A good strategy to smooth these inhomogeneities is averaging over multiple iterations. For this purpose a second data set of the same structure as described above is kept to store the ‘‘moving averages.’’ After all parcels are tracked, the first data set is used for averaging with the second data set. Different techniques can be used to get a weighted average, for example, a first-order filter approach according to the equation V2,new ¼ ð1 f ÞV2,old þ f V1
(10:50)
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where V2 is the value in data set 2, V1 the value of data set 1, and f a weight factor between 0 and 1. With this approach a moving average is reached in which the last iteration has the highest weight and previous iterations a lower weight. The lower the weight factor f, the higher the number of previous iterations taken into account. The most suitable value of the weight factor f will depend on the number of parcels and the fineness of the grid. Trials have to indicate the most suitable value. There are good experiences with a value of 0.01. The second data set is used to calculate the probability of a collision and to generate a fictitious collision partner.
10.8.3 COLLISION PROBABILITY During tracking of a parcel, with each Lagrangian time-step (Dt) the collision probability (Pcoll ) of a single particle from the parcel (real particle) with a fictitious particle in the same volume cell is calculated [36]: Pcoll ¼
p ðdreal þ dfict Þ2 j~ ufict jnp Dt ureal ~ 4
(10:51)
where d is the diameter of the real and fictitious particle, j~ ureal ~ ufict j the instantaneous relative velocity between the real and fictitious particle, and np the number of particles per unit volume in the volume cell. This probability is calculated for each sampled size class. The needed values for dfict and ufict and np are derived from the sampled statistical data set as described in the previous section. The probabilities of the size classes are stacked in a bar as illustrated in Figure 10.10. The time-step size Dt should be small enough so that the sum of the collision probabilities of all size classes is less than 1. In order to decide whether a collision takes place, and if so, in which size class, the collision partner is, a random number from a uniform distribution in the interval from 0 to 1 is generated (see Figure 10.10). A computational parcel represents a group of particles having the same properties and behavior. When a collision occurs, it is assumed that it is the case for all particles in the parcel.
Probability
1
Class
n
Random
Class
i
Class
2
Class
1
number
0
FIGURE 10.10 Stacked bar of probabilities in order to decide whether a collision occurs.
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When a collision occurs, it has to be decided at which location on the surface of the real particle it takes place. This location can be identified by two angles with the moving path. It has to be taken into account that the probability density for the point of impact is not the same for every point on the surface, so the angles cannot simply be generated with a random number from a uniform distribution. As described in Ref. [36], these angles can be found after the problem is transformed into a coordinate system, in which the fictitious particle is fixed and three uniform random numbers are generated. Now all information is known to continue with postcollision calculations.
10.8.4 REBOUND
AFTER
COLLISION
When both collision partners are hard spheres a rebound will take place. As described in Ref. [36], the new velocities can be calculated by solving the momentum equation in connection with Coulomb’s law of friction and neglecting particle rotation. For this, the problem can be transformed to a 2D coordinate system, in which the fictitious particle is fixed. The 2D plane is identified by the point of impact and the moving path of the real particle. The relative velocity can be decomposed in a normal component (u); this is in the direction of the center of the fixed particle and a component perpendicular to the normal component (n). Now, sliding and nonsliding collisions have to be distinguished. The condition for a nonsliding collision is up1 7 < m(1 þ e) np1 2
(10:52)
The velocities of the real particle after rebound can be calculated with the following equations: up1,new ¼ up1,old
1þe 1 1 þ Mp1=Mp2
(10:53)
and vp1,new ¼ vp1,old
2=7 1 1 þ Mp1=Mp2
(10:54)
for a nonsliding condition and up1 1 vp1,new ¼ vp1,old 1 m(1 þ e) vp1 1 þ Mp1=Mp2
(10:55)
for a sliding condition. Here e is the coefficient of restitution, m the coefficient of friction, Mp the mass of the particle. Indexes 1 and 2 refer to the real and fictitious particle, respectively. Finally, the new velocities are retransformed to the original coordinate system.
10.8.5 OTHER POSTCOLLISION EVENTS If rebound was the only postcollision event, the effects for spray drying would not be very spectacular. The moving direction and velocity of a particle would regularly be changed by such collisions, just as already happens by the gas turbulence. The particle properties and drying behavior would remain unchanged and the mean residence time would hardly be affected. So, the implementation of a collision model without other postcollision events is not very useful for spray drying.
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Other postcollision events are as follows: . . .
Disintegration (especially at high velocities) Coalescence (liquid particles) Agglomeration (sticky particles)
These events are much more complex to handle than rebound, because new particles have to be built from the collision partners. In the next section a coalescence and agglomeration model is worked out.
10.9 COALESCENCE AND AGGLOMERATION MODEL 10.9.1 INTRODUCTION Recently, in the framework of a European project entitled EdeCad, the agglomeration of particles during spray drying is studied in detail and published [9,37,38]. Before that study, only little information concerning the modeling of agglomeration processes was available. The setup of the coalescence and agglomeration model as described in this chapter is a result of the just-mentioned EdeCad project.
10.9.2 CLASSIFICATION
OF
COLLISION PARTNERS
The material properties of each of the collision partners have a significant impact on the postcollision behavior. The most important properties are the surface tension, the effective density, and the dynamic viscosity. During spray drying these properties, especially the dynamic viscosity, are changing. Therefore, a classification of the collision partners is required with regard to the material properties affecting the collision process. Three main classes of particles are defined: . . .
STD: the particle behavior is dominated by surface tension forces VD: the particle behavior is dominated by viscous forces DRY: the particles are dry and surface tension and viscous forces do not play a role anymore
The STD and VD classes are distinguished from each other by the Ohnesorg number (Oh), representing the ratio between viscous and surface tension forces of a fluid: h Oh ¼ pffiffiffiffiffiffiffiffiffiffiffi drsA
(10:56)
where h is the dynamic viscosity of the particle material, d the particle diameter, r the density, and sA the static surface tension of the particle material. For the collision behavior, the dynamic viscosity and static surface tension of the outside of the particle are relevant. If Oh < 1, the particle is considered to be in the STD class. Figure 10.11 shows an example of the critical dynamic viscosity representing the distinction between STD and VD particles as a function of the particle diameter. In this example, a product density of 1100 kg m3 and a surface tension of 44 mN m1 is assumed. For spray drying of food products the diameter of the atomized particles is expected to be in the range of 60–150 mm. For several preconcentrated food liquids the viscosity at atomization is already higher than the critical value of about 80 mPa s. As shown in Figure 10.11, particles of these products will never be in the STD class. However, particles of less viscous liquid feeds can be in this class, but only for a short duration. As shown in Figure 10.4, the outer shell of a particle will dry very fast and causes a fast increase of the viscosity.
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Critical viscosity (mPa s)
160
120
Oh > 1: VD class
80 Oh < 1: STD class
40
0 0
100
200
300
400
500
Particle diameter (m)
FIGURE 10.11 Critical viscosity representing the distinction between the STD and VD class as a function of the particle diameter. Density: 1100 kg m3 , surface tension: 44 mN m1 .
The VD and DRY classes are distinguished from each other by the sticky point. The sticky point can be determined by the submodels described in Section 10.6. If the particle is not in the STD class and the outer side of a particle is in the sticky region, the particle is considered to be in the VD class, else it is in the DRY class. During drying of sticky food products, such as products with a high content of carbohydrates, the particles may reside for a longtime or even for the whole drying trajectory in the VD class.
10.9.3 TYPES
OF
COLLISION EVENTS
On the basis of the classification of the collision partners, there are six types of collisions: STD–STD, STD–VD, STD–DRY, VD–VD, VD–DRY, and DRY–DRY. However, some types need not be distinguished and four types remain: . . . .
STD–STD: both collision partners in the STD class STD–VD=DRY: one partner in the STD class and the other in the VD or DRY class VD–VD=DRY: one partner in the VD class and the other in the VD or DRY class DRY–DRY: both partners in the DRY class
The postcollision behavior of these four types is modeled separately. The models of the latter two types of collision are described briefly in the next sections.
10.9.4 VD–VD=DRY COLLISION TYPE The VD–VD=DRY collision is treated as a penetration of the particle with the higher viscosity into the fluid of the particle with the lower viscosity. If the high-viscosity particle comes to a standstill during the penetration then an agglomeration occurs, else there is a pass through. For the modeling of the penetration some assumptions are made: . . .
Only viscous forces with Newtonian behavior are considered. The particles behave as fully plastic spheres without elastic restitution. The particles keep their size during the penetration.
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Force balances are formulated to describe the motion of the higher-viscosity droplet, which is resisted by the viscous forces of the lower-viscosity droplet liquid. The frictional force (Ff ) is based on Stoke’s law for a spherical particle moving in a viscous medium at low Reynolds numbers: Ff ¼ 6prs hv
(10:57)
where h is the dynamic viscosity of the medium, rs the Stoke’s radius, and v the particle velocity. The penetrating particle has a circular contact area with the other particle. The radius of that circle is adopted as the Stoke’s radius. The penetration depth (sp ) is defined as sp ¼
d1 þ d2 r 2
(10:58)
where d1 and d2 are the particle diameters and r is the distance between the centers of the partners. The final penetration depth is stored and used for further calculation of the agglomerate properties.
10.9.5 DRY–DRY COLLISION TYPE In theory, colliding dry particles can form an agglomerate that is held together by van der Waals forces. This agglomeration can only be expected when one of the dry particles is small (< 20 mm) and the relative velocity between the collision partners is small. Because van der Waals forces are weak, such agglomerates will not be very strong and will easily break up during powder handling in the dryer or transport pipes. Therefore, this type of agglomeration is not taken into account and it is assumed that a DRY–DRY collision results in a rebound as described in Section 10.8.4.
10.9.6 PROPERTIES
OF
AGGLOMERATES
During particle tracking the number of particles within the agglomerate is monitored and an agglomerate porosity is calculated. The new porosity after an agglomeration is found by calculating the volume between particles and tangents, as shown in Figure 10.12, and adding this volume to the current porous volume. After an agglomeration a nonspherical particle with a nonsymmetric moisture distribution can be formed. For further modeling of the behavior of such particles, approximations have to be made. For further particle tracking and collision probability, the agglomerate is
Porous volume
Tangent
FIGURE 10.12 Determination of porous volume after agglomeration.
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approximated as a spherical particle with a mass equal to that of the individual particles and a volume equal to that of the individual particles plus the porous volume. For further drying behavior, the agglomerate is approximated as a hollow sphere with a surface area equal to that of the agglomerate and a shell thickness derived from the total mass of the agglomerate. The radial moisture gradient is derived from the gradient of the real particle.
10.9.7 CONSERVATION OF MASS AFTER AGGLOMERATION Because the agglomeration partner of a real particle is always a fictitious particle, action has to be taken to avoid an increase of the total mass of the real particles. So, there also have to be real particles that are donated due to the agglomeration. There are several ways to conserve the mass of the real particles. One way is to donate the parcel of real particles when the diameter of the real particle is smaller than that of the fictitious particle. However, in this way it can never be guaranteed that the statistical probability of increase and decrease of mass is fully in balance, especially when the number of parcels is limited. So, when applying this technique it is strongly advised to check for deviations in the mass balance. An alternative way is to adapt the number of particles in the parcel after an agglomeration in such a way that the mass of the parcel remains the same. In this way exact conservation of mass is guaranteed.
10.10 IMPLEMENTATION OF A CFD MODEL FOR SPRAY DRYERS 10.10.1 INTRODUCTION In a former study a simulation model for spray dryers was implemented in a 2D CFD package [6]. This package was successfully applied to explain the behavior of an industrial spray dryer. The operators suspected a shortcut airflow from the inlet to the outlet, which was out of question according to the manufacturer. Simulations showed that the gradual increase of the capacity of the dryer and rotary speed of the atomizer in the course of years has pushed too far and caused a reversal of the main airflow circulation involving a short cut airflow from inlet to outlet. This case and another industrial case are worked on in more detail in Ref. [6]. Now, the simulation model for spray dryers is implemented in the commercially available CFD software package Star-CD of the CD-Adapco group, which makes a full 3D simulation possible. The package is able to generate both structured and unstructured meshes and can also be used for the pre- and postprocessing. Flow field calculations and particle tracking are carried out as described in Section 10.2 and Section 10.3. Simulations are run in a steady-state mode. During particle tracking at each Lagrangian time-step an interparticle collision model (see Section 10.8) and a drying model based on the diffusion concept (see Section 10.4.4) are called. In the collision model it is decided if collision has occurred and if so, the agglomeration model as described in Section 10.9 is called. Two types of collision events are supported: VD–VD=DRY and DRY–DRY (see Section 10.9.3). When an agglomeration takes place, the number of particles in a parcel is adapted to assure exact conservation of mass (see Section 10.9.7). During the simulation several user-defined subroutines are called .
.
.
Subroutines for product-specific physical properties as a function of temperature and moisture content: among others viscosity, stickiness Subroutine called when a parcel collides with a wall (with the current position and properties (among others temperature, velocity vector, moisture gradient) of the parcel as arguments, it can be decided if the parcel sticks on the wall (fouling)) Subroutines for monitoring the progress of the simulation and generating output of additional user data
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10.10.2 SPRAY-DRYER SIMULATION As an example a CFD simulation of an industrial spray dryer (diameter 9.5 m; height 14 m) producing skim-milk powder is worked out. The spray dryer is the first stage of a two-stage dryer, the powder is dried to the final moisture content in a vibrated fluid bed. The spray dryer is equipped with one air inlet at the center of the roof and four air outlets at the upper side of cylindrical part of the dryer. The powder can leave the dryer at the bottom. Just below the air inlet channel a rotary wheel atomizer is placed. In the simulation 200 parcels are tracked. For the atomized droplets a log normal volume distribution is assumed, characterized by a geometric mean diameter and a standard deviation. The process conditions are listed in Table 10.3. In Figure 10.13 the airflow pattern is shown. The arrows indicate the flow direction and the length is proportional to the magnitude of the velocity. At the axis of the dryer a downward flow is to be seen that reverses in the conical part of the dryer. In Figure 10.14 and Figure 10.15 the contours of the temperature and the moisture content of the air of a cross section are shown. Below the air inlet, a region of hot and dry air can be observed. In the other parts of the dryer the air conditions already are nearly equal to the outlet conditions. In Figure 10.16 ten particle trajectories are shown. In Table 10.4 additional simulation results are given. Due to agglomeration the powder particles are bigger than the atomized droplets. Figure 10.17 shows the cumulative size distribution of the atomized feed and the final powder. The median diameter (at mass fraction 0.5) of the feed and the powder are 80 and 112 mm, respectively. In Figure 10.18 the positions in cylinder coordinates of the first collisions of the parcels with the wall of the dryer are shown. The bottom of the dryer has a z-coordinate of 0. Most of the collisions are in the conical part of the dryer (z < 8.1 m). The glass transition temperature of the outer shell of the colliding particles is calculated (see Section 10.6) and applied to determine if the particles are sticky or not. In Figure 10.18 the parcels that have a temperature exceeding the glass transition temperature by more than 258C are marked as sticky. However, sticking at the wall is not taken into account in the simulation and all particles rebound from the wall. This dryer in practice has no fouling problems. According to the simulation, 46% of the powder leaves the dryer at the bottom. The other part is dragged along with the outlet air. In practice, a much bigger part of the powder (75%–85%) leaves the dryer at the bottom. Observations in a practical situation gave more insight into the flow of the particles. The spray dryer is provided with pneumatic hammers that frequently beat at the walls. Particles
TABLE 10.3 Process Conditions of Simulated Spray Dryer (5d23_011=09k) Main Air
Feed
Atomization
Flow (kg h1 ) T (8C) Moisture content (g kg1 ) Flow (kg h1 ) T (8C) Dry solids (% m=m) Mean droplet diameter (mm) Sg
63,000 185 10 4,990 25 55 80 0.6
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STAR
pro-STAR 3.2 21-July-06 Velocity magnitude m s−1 ITER = 1700 Local MX = 18.18 Local MN = 0.1470 18.18 16.89 15.60 14.31 13.03 11.74 10.45 9.163 7.875 6.587 5.299 4.011 2.723 1.435 0.1470
Z Y
X
FIGURE 10.13 (See color insert following page 462.) Airflow pattern.
STAR
pro−STAR 3.2 12−July−06 Temperature (°C) ITER = 1700 Local MX = 185.0 Local MN = 75.36 185.0 177.2 169.3 161.5 153.7 145.8 138.0 130.2 122.3 114.5 106.7 98.86 91.02 83.19 75.36
Z Y
X
FIGURE 10.14 (See color insert following page 462.) Contour of air temperature.
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STAR
pro-STAR 3.2 21−July−06 ITER = 1700 Local MX = 45.91 Local MN = 10.00 Moisture in dry air (g/kg) 45.91 43.35 40.78 38.22 35.65 33.09 30.52 27.96 25.39 22.83 20.26 17.70 15.13 12.57 10.00
Z Y
X
FIGURE 10.15 (See color insert following page 462.) Contour of moisture content of air.
STAR
pro-STAR 3.2 21-July-06
Z Y
FIGURE 10.16 (See color insert following page 462.) Particle trajectories.
X
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TABLE 10.4 Simulation Results (5d23_011=09k) Outlet Air
T (8C) Moisture content (g kg1 ) T (8C) Moisture content (% m=m) Mean residence time (s) Particles=agglomerate Median diameter (D50,3 ) (mm) Leaving bottom outlet (% m=m)
Powder
1.0
82.2 42.4 82.5 7.7 31.6 6.7 112 46
Feed Powder
Mass fraction (−)
0.8
0.6
0.4
0.2 0.0 0
80
160 240 Diameter (µm)
320
FIGURE 10.17 Cumulative size distribution of droplet feed and powder particles. 16
Coordinate z (m)
12
8
4
0 -180 -140
-100
-60
-20 20 Alpha (⬚)
60
100
140
180
FIGURE 10.18 Positions of parcels colliding with spray dryer wall. Symbols: ~ ¼ not sticky, ~ ¼ sticky.
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colliding with the walls slightly stick, are released with a beat of the pneumatic hammers, and slide along the walls to the bottom outlet. Minor improvements are necessary to make the simulation more realistic at this point.
10.11 CONCLUSIONS In the course of years spray drying models based on CFD simulations have improved stepby-step. The first step has been the simulation of patterns of the airflow and the particle trajectories. Nowadays, this can be done by most of the basic CFD packages that are commercially available. In the next step, a submodel for the drying behavior is added. In recent years, interparticle collision models and an agglomeration model and several submodels (thermal reactions, stickiness) were developed. The simulations have been successfully applied for a number of industrial dryers. It is expected that in the near future the majority of the process simulation and optimization software will be based on CFD, not only for design purposes but also more and more for improvement of powder properties and trouble shooting in existing dryers. Faster processors and better techniques to reduce the CPU-time of CFD calculations make it possible that CFD can even be used for in-line control purposes. In some industries, the CFD application for in-line control already exists [39,40]. These techniques are also applicable to spray dryers.
NOMENCLATURE A a, b, c aw ca cdp cg cp Cp D d e Ea F f Hdp Hev Isi k K k0 Kg kgt M Ma Mda Mdp
area (m2 ) coefficient of regression water activity water concentration in air (kg m3 ) moisture content based on dry solids mass (Kg kg1 ) GAB constant moisture content (kg m3 ) specific heat capacity (J kg1 K1 ) diffusion coefficient (m2 s1 ) diameter (m) coefficient of restitution energy of activation (J mol1 ) mass flow (kg s1 ) weight factor enthalpy of particle based on mass of dry solids (J kg1 ) heat of evaporation (J kg1 ) insolubility index (mL) mass transfer coefficient (m s1 ) GAB constant pre-exponential factor (mL s1 ) parameter in Fox–Flory equation (kg mol1 ) factor in Gordon–Taylor equation molecular weight (kg mol1 ) molecular weight of air (kg mol1 ) mass of dry air (kg) mass of dry solids (kg)
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mp Mp Mw Np np Nu Oh pa Pcoll Pr pt Q r R Re rIsi Rp Sc Sf Sh sp t T u V v W w Wm xa xp
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moisture content based on total mass (kg kg1 ) particle mass (kg) molecular weight of water (kg mol1 ) number of particles particle concentration (m3 ) Nusselt number Ohnesorg number partial water pressure (Pa) collision probability Prandtl number total pressure (Pa) heat flow (J s1 ) radius (m) gas constant (J mol1 K1 ) Reynolds number formation rate of insoluble material (mL s1 ) particle number flow (s1 ) Schmidt number shrink factor Sherwood number penetration depth (m) time (s) absolute temperature (K) velocity (m s1 ) volume (m3 ) velocity (m s1 ) moisture content (kg kg1 ) mass fraction GAB constant (kg kg1 ) moisture content base on dry air (kg kg1 ) particle property (momentum, mass, or enthalpy)
GREEK SYMBOLS a a, b l r h sA m
heat transfer coefficient (W m2 K1 ) parameters describing diffusion coefficient thermal conductivity (W m1 K1 ) density (kg m3 ) dynamic viscosity (Pa s) static surface tension (N m1 ) coefficient of friction
REFERENCES 1. B.E. Launder and D.B. Spalding. The numerical computation of turbulence flows. Computer Methods in Applied Mechanics and Engineering 3: 269–289, 1974. 2. T.A.G. Langrish and T.K. Kockel. The assessment of a characteristic drying curve for milk powder for use in computational fluid dynamics modelling. Chemical Engineering Journal 84: 69–74, 2001. 3. X.D. Chen and S.X.Q. Lin. Air drying of milk droplet under constant and time-dependent conditions. AIChE Journal 51(6): 1790–1799, 2005.
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4. J. Crank. Mathematics of Diffusion. Oxford: Oxford University Press, 1967. 5. G. Ferrari, G. Meerdink, and P. Walstra. Drying kinetics for a single droplet of skim-milk. Journal of Food Engineering 10: 215–230, 1989. 6. J. Straatsma, G. van Houwelingen, A.E. Steenbergen, and P. de Jong. Spray drying of food products: 1. Simulation model. Journal of Food Engineering 42: 67–72, 1999. 7. Y. Sano and R.B. Keey. The drying of a spherical particle containing colloidal material into a hollow sphere. Chemical Engineering Science 37(6): 881–889, 1982. 8. A.E. Wijlhuizen, P.J.A.M. Kerkhof, and S. Bruin. Theoretical study of the inactivation of phosphatase during spray drying of skim-milk. Chemical Engineering Science 34: 651–660, 1979. 9. R.E.M. Verdurmen, P. Menn, J. Ritzert, S. Blei, G.C.S. Nhumaio, T. Sonne Sørensen, M. Gunsing, J. Straatsma, M. Verschueren, M. Sibeijn, G. Schulte, U. Fritsching, K. Bauckhage, C. Tropea, M. Sommerfeld, A.P. Watkins, A.J. Yule, and H. Schønfeldt. Simulation of agglomeration in spray drying installations: The Edecad project. Drying Technology 22(6): 1403–1461, 2004. 10. W.E. Ranz and W.R. Marshall. Evaporation from drops. Part I and II. Chemical Engineering Progress 48(3=4): 141–146, 173–178, 1952. 11. R.B. Bird, W.E. Stewart, and E.N. Lightfoot. Transport Phenomena. New York: Wiley, 1960. 12. T.K. Kockel, S. Allen, C. Hennigs, and T.A.G. Langrish. An experimental study of the equilibrium for skim-milk powder at elevated temperatures. Journal of Food Engineering 51(6): 291–297, 2002. 13. T.P. Labuza. Moisture Sorption: Practical Aspects of Isotherm Measurement and Use. St. Paul, MN: American Association of Cereal Chemists, 1984. 14. W.E.L. Spiess and W.R. Wolf. In: R. Jowitt, F. Escher, B. Hallsto¨m, H.F.T. Meffert, W.E.L. Spiess, G. Vos (eds.). Physical Properties of Foods. London: Applied Science Publishers, 1983. 15. K. Jouppila and Y.H. Roos. Water sorption and time-dependent phenomena of milk powders. Journal of Dairy Science 77(7): 1798–1808, 1994. 16. G. Hols, H.J. Klok, and P.J.J.M. van Mil. Desorption isotherms of dairy liquids. Voedingsmiddelen Technologie 23(7): 13–16, 1990. 17. A.L. Yarin, M. Pfaffenlehner, and C. Tropea. On the acoustic levitation of droplets. Journal of Fluid Mechanics 356: 65–91, 1998. 18. A.L. Yarin, G. Brenn, O. Kastner, D. Rensink, and C. Tropea. Evaporation of acoustically levitated droplets. Journal of Fluid Mechanics 399: 151–204, 1999. 19. J. Straatsma, G. van Houwelingen, A.E. Steenbergen, and P. de Jong. Spray drying of food products: 2. Prediction of insolubility index. Journal of Food Engineering 42: 73–77, 1999. 20. D.A. Wallack and C.J. King. Sticking and agglomeration of hygroscopic, amorphous carbohydrate and food powders. Biotechnology Progress 4(1): 31–35, 1988. 21. G.E. Downton, J.L. Flores-Luna, and C.J. King. Mechanism of stickiness in hygroscopic, amorphous powders. Industrial and Engineering Chemistry Fundamentals 21: 447–451, 1982. 22. C.J. King. Transport processes affecting food quality in spray drying. Engineering and Food. Processing Applications G 2: 559–574, 1984. 23. J.M. Aguilera, J.M. Del Vall, and M. Karel. Caking phenomena in amorphous food powders. Trends in Food Science and Technology 6: 149–155, 1995. 24. D.H. Bergquist, G.D. Lorimor, and T.E. Wildy. Mechanism and method for agglomerating food powders. US Patent 5130156, Henningsen Foods, Inc., US, 1991. 25. B.R. Bhandari and T. Howes. Implication of glass transition for the drying and stability of dried foods. Journal of Food Engineering 40: 71–79, 1999. 26. B.R. Bhandari, N. Datta, and T. Howes. Problems associated with spray drying of sugar-rich foods. Drying Technology 15(2): 671–684, 1997. 27. Y. Roos. Characterization of food polymers using state diagrams. Journal of Food Engineering 24(3): 339–360, 1995. 28. Y. Roos. Melting and glass transition of low molecular weight carbohydrates. Carbohydrate Research 238: 39–48, 1993. 29. Y. Roos. Water and molecular weight effects on glass transitions in amorphous carbohydrates and carbohydrate solutions. Journal of Food Science 56(6): 1676–1681, 1991. 30. R.J. Lloyd, X.D. Chen, and J.B. Hargreaves. Glass transition and caking of spray-dried lactose. International Journal of Food Science and Technology 31(4): 305–311, 1996.
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31. F.M.D. Netto and T.P. Labuza. Effect of water content on the glass transition, caking and stickiness of protein hydrolysates. International Journal of Food Properties 1(2): 141–161, 1998. 32. L.E.L. Chuy. Caking and stickiness of dairy-based food powders as related to glass transition. Journal of Food Science 59(1): 43–46, 1994. 33. J.M.L. Aguilera and M. Karel. Effect of water content on the glass transition and caking of fish protein hydrolyzates. Biotechnology Progress 9: 651–654, 1993. 34. J.J.E. Williams and R.I. Crane. Particle collision rate in turbulent flow. International Journal of Multiphase Flow 9: 421–435, 1983. 35. H.J. Pearson, I.A. Valioulis, and E.J. List. Monte Carlo simulation of coagulation in discrete particle size distributions. Part 1. Brownian motion and fluid shearing. Journal of Fluid Mechanics 1: 16–30, 1984. 36. M. Sommerfeld. Validation of a stochastic Lagrangian modeling approach for inter-particle collisions in homogeneous isotropic turbulence. International Journal of Multiphase Flow 27: 1829–1858, 2001. 37. S. Blei and M. Sommerfeld. Lagrangian modeling of agglomeration during spray drying processes. 9th International Conference on Liquid Atomization and Spray Systems. Sorrento, 2003. 38. S. Blei and M. Sommerfeld. Computation of agglomeration for nonuniform dispersed phase properties—an extended stochastic collision model. Paper 1064. 5th International Conference on Multiphase Flow. Yokohama, 2004. 39. L. Huisman. Control of glass melting processes based on reduced CFD models. PhD thesis, Technical University, Eindhoven, The Netherlands, 2005. 40. P. Astrid. Reduction of process simulation models. PhD thesis, Technical University, Eindhoven, The Netherlands, 2004.
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Three-Dimensional CFD Modeling of a Continuous Industrial Baking Process Weibiao Zhou and Nantawan Therdthai
CONTENTS 11.1 11.2
Introduction ............................................................................................................. 288 Baking Process ......................................................................................................... 288 11.2.1 Heat and Mass Transfer Mechanisms ......................................................... 290 11.2.1.1 Heat Transfer Mechanism ........................................................... 290 11.2.1.2 Mass Transfer Mechanism .......................................................... 291 11.2.2 Changes during Baking Process .................................................................. 292 11.2.2.1 Volume Expansion ...................................................................... 292 11.2.2.2 Solidification................................................................................ 292 11.2.2.3 Color Development ..................................................................... 293 11.2.2.4 Flavor Development.................................................................... 293 11.3 CFD Modeling......................................................................................................... 294 11.3.1 Industrial Continuous Traveling-Tray Baking Oven................................... 294 11.3.2 Oven Monitoring System in the Industrial Continuous Traveling-Tray Baking Oven....................................................................... 295 11.3.3 Quality Measurement of Baked Bread ........................................................ 295 11.3.4 CFD Modeling ............................................................................................ 296 11.3.4.1 Simplification of the Baking Oven Geometry ............................. 296 11.3.4.2 Model Assumption ...................................................................... 297 11.3.4.3 Volume Condition Settings.......................................................... 298 11.3.4.4 Boundary and Initial Condition Settings..................................... 299 11.3.4.5 Solving the Model ....................................................................... 300 11.3.5 Model Validation ........................................................................................ 300 11.4 Applications of CFD Model .................................................................................... 304 11.4.1 Simulation of Oven Operation under Increasing Oven Load...................... 304 11.4.2 Simulation of Baking Index ........................................................................ 306 11.4.3 Design of Operating Condition to Achieve the Optimum Tin Temperature Profiles ............................................................................ 308 11.5 Conclusions .............................................................................................................. 309 Nomenclature ..................................................................................................................... 310 References .......................................................................................................................... 310
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11.1 INTRODUCTION Baking process is a key step in which the raw dough piece is transformed into a light, porous, readily digestible, and flavorful product under the influence of heat. With the requisite quality attributes, the bread production presumes a carefully controlled baking process. Factors playing vital influence on the final product quality include the rate and amount of heat application, the humidity level in baking chamber, and baking time. During baking, the most apparent interactions are volume expansion, crust formation, inactivation of yeast and enzymatic activities, protein coagulation, gelatinization of starch in dough [1], and moisture loss. Heat distribution in an oven depends on a number of parameters including heat source, airflow pattern, flow rate, oven load, baking time, etc. To manipulate the oven condition at the optimum temperature profiles, the relationship among these important parameters needs to be established. Computational fluid dynamics (CFD) modeling may be the only method to effectively solve such a complicated problem. This chapter presents the results on the threedimensional CFD modeling of an industrial continuous bread baking process. The effect of heat source, flow rate through convection fans, baking time, and oven load on baking temperature profiles will be investigated. The results of the simulation can be used for manipulating an oven control to maintain its baking temperature profile at the optimum condition.
11.2 BAKING PROCESS During baking, heat is applied and the final leavening occurs until yeast is destroyed at 608C. As a result, rapid expansion of water vapor and carbon dioxide produces oven spring in the early stage of baking. The top crust is pushed up. Optimal baking temperature depends on the size and richness of the product. For example, small products should be baked at 2048C–2388C, whereas richer products should be baked at lower temperatures. Baking process is the key step in breadmaking. An exemplary baking process may be divided into three stages [2]. The first stage starts at around 2048C and takes onefourth of a total baking time of 26 min. The temperature of the outer crumb increases at an average rate of 4.78C per minute to 608C. An increase in temperature enhances enzymatic activity and yeast growth resulting in an oven rise (a perceptible increase in loaf volume). When temperature reaches 508C–608C, most enzymes are inactivated and yeast is killed. The volume increases by one-third of the original. Furthermore, surface skin loses elasticity, thickens, and begins to appear brown color. In the second stage, oven temperature is maintained at 2388C for 13 min. Crumb temperature increases at a rate of 5.48C per minute to 98.48C–98.98C before keeping constant. At this temperature, all reactions are maximized, including evaporation, starch gelatinization, and protein denaturation. Dough’s structure becomes that of crumb from outer to inner portions by the penetrated heat. A typical brown crust can be observed when the crust temperature reaches 1508C– 2058C. Finally, in the third stage the volatilization of some organic substances is designated as the bake-out-loss. This period also takes one-fourth of the total baking time. There are many types of baking ovens. Among them, the traveling-tray oven is efficient in space utilization because it can be made for long horizontal runs and does not require high ceilings. The trays can be conveyed from the front to the back of the oven and then returned to the front by a lower track. In addition, a double lap oven can be designed, resulting in twice the capacity in the same space. Ducts below and above a tray conveyer are arranged to regulate temperatures in each part of the oven by forming control zones. Each control zone contains its individual air and gas supply, temperature controller, and groups of burners. The operation of a baking oven is crucial for producing high-quality products. Even though
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a well-adjusted oven cannot fully compensate for the errors committed earlier in the processing sequence, it can bring about the potential of a well-processed dough piece. As stated earlier, temperature dominates product quality during baking. This is because it affects enzymatic reaction, volume expansion, gelatinization, protein denaturation, nonenzymatic browning reaction, and water migration [3]. Temperature gradient provides a pressure gradient accordingly in the product. The pressure gradient causes the lattice to dilate in one dimension, from the center of bread towards the surface. If such an expanded foam lattice is transformed to be a pore system, the pore structure will show the same dilatation. As a result, such bread is easily fractured along the inside of the crust. Therefore, to avoid the dilatation effect, the heat gradient in an oven has to be adapted to the strength of the gluten film forming the interface of the gas cells [4]. Not only does the value of the temperature matter, but also when it should be applied is also important. The optimum temperature is needed to be maintained at the right time. Otherwise, product quality can be compromised. For example, supplying too high temperature at the early stage of baking might cause an early crust formation, shrunk bread loaf, and too dark crust. Use of too high temperature at the bottom may cause holes towards the bottom of a loaf, and then triangular shape. Moreover, cavity may be found at the bottom [5]. Baking air temperature profile is important for bread baking. However, the correlation between air temperature and product quality is poor because there are some other parameters affecting the product quality at the same time. Instead of air temperature, product surface temperatures were used to study the consequent quality of a hi-top bread. It was noticed that the bottom surface was heated up slightly faster than the side surface. This was due to the heat conduction through the plate. At temperatures below 808C, the top temperature was about 08C–108C lower than the bottom temperature [6]. Then it became higher than both the bottom and side temperatures, which contacted the tin. An alternative way to measure the combined influence of the baking temperature and other baking parameters is the heat flux measurement. Heat flux is defined as the heat transfer rate per unit area that is required for baking from the oven chamber to the product [7]. Heat flux measurement was claimed to be a more useful method than air temperature measurement for controlling the quality of bakery products [7–9]. In addition to temperature, airflow velocity affects baking quality. Lack of product uniformity is possibly due to the nonuniformity of airflow around the product during baking. It was confirmed that heat flux to a product could be increased by increasing airflow velocity [9,10]. According to Sato et al. [11], increasing airflow velocity results in a higher weight loss, lower softness, and darker surface. Therefore, either baking time or baking temperature should be reduced with respect to an increase in heat transfer rate. However, baking process requires a minimum temperature to produce an adequate color. When bread is baked under very low temperature, very high airflow velocity is required to increase the drying rate at surface. Nonetheless drying rate alone is not enough to produce an acceptable crust color [12]. Similarly, in the case of a microwave baking oven, product is baked at low environment temperature and short time. Not only the lack of typical color and flavor of baked goods, but condensation at the product surface is also among the major problems for microwave-baked products [13]. To overcome the problem, in one study, airflow velocity was increased. As a result, heat and mass transfer coefficients in the air were increased. However, the mass transfer coefficient at the surface was still not high enough to rapidly remove the significant amount of moisture accumulated. Therefore, higher forced airflow velocity should be applied at the selected areas to increase the surface mass transfer coefficients [14]. When mass transfer coefficients in the air and at the surface are high enough to significantly reduce the water content on the surface, color and flavor development can be enhanced at the same time as texture improves.
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Kinetic reactions including starch gelatinization and browning reaction depend not only on temperature, but also baking time. Therefore, to reduce the baking time by increasing either airflow velocity or baking temperature, it has to be ensured that gelatinization or browning reactions are completed. Otherwise product quality can be degraded. Even though the starch gelatinization and browning reactions are completed, quality of the product baked by short and long baking times can still be quite different. Longer baking time can produce caving on the loaf side as well as less softness [5]. With the same oven temperature and airflow velocity, increasing air humidity by either injecting water vapor into the oven chamber or water vapor migration from the product increases heat flux. According to a CFD model, the average temperature of an oven composed of 100% water vapor can be 58C higher than that of an oven containing only dry air [10]. However, water vapor could limit the crust formation [15]. Therefore, water vapor is normally applied to an oven only at the beginning of a baking process for bread products. On the other hand, an improper water vapor control and damper control could render the humidity being too low in an oven chamber. As a result, baking loss might increase [2].
11.2.1 HEAT AND MASS TRANSFER MECHANISMS 11.2.1.1
Heat Transfer Mechanism
During baking, heat is transferred through the combination of all the three well-known mechanisms: conduction, convection, and radiation. However, the actual form of combination and proportions are very different for heat transfer within dough pieces and heat transfer within an oven chamber. Heat transfer inside dough is the combination of conduction from band or tins to the dough, conduction in the continuous liquid=solid phase of the dough, and evaporation– condensation in the gas phase of the dough. In one study [16], an evaporation-front temperature was assumed to be 1008C at which massive unbound water evaporates with water boiling phenomenon. There were four steps involved in the heat transport inside dough. Firstly, water evaporates at the warmer side of a gas cell that absorbs latent heat of vaporization. Then water vapor immigrates though the gas phase. When it meets the cooler side of the gas cell, it condenses and becomes water. Finally, heat and water are transported by conduction and diffusion through the gluten gel to the warmer side of the next cell. The water diffusion mechanism becomes very important to heat transfer as dough tends to be a poor conductor that limits the heat transfer via conduction [17]. In an oven chamber, molecules of air, water vapor, or combustion gases circulate throughout the oven and transfer heat by convection until they contact solid surfaces such as tin, band, conveyor and so on. Then heat transfer mode is changed to conduction. Radiant energy coming from the burner flames and all hot metal parts in ovens travels in a straight line. Much of it never reaches the product because it is intercepted by some substances not transparent to the radiation. Radiation has two characteristics different from the other means of heat transfer. Firstly, it is subject to shadowing or blocking by intervening layers that are opaque to the radiation. Secondly, it is responsive to changes in the absorptive capacity of the dough. For example, color changes influence the progression of baking by increasing the absorption of infrared rays. An increase in the absorptive capacity for infrared rays, although not apparent visually, is a concomitant of the visible change. As a result, there is a tendency for color changes to accelerate after the first browning appears. Such a tendency might be either good or bad depending on the desired characteristics in the final products. Therefore, radiation tends to cause localized temperature differentials of an
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exposed surface, particularly the darkened area, whereas convection tends to even out temperature gradients [18]. Radiation was confirmed to be the most important heat transfer mode to bake a sandwich bread [9,16], whereas conduction was found to be the most important heat transfer mode from the oven chamber to an Indian flat bread [19]. According to several studies [10,20–22], increasing airflow velocity in an oven chamber would increase heat flux to the product. In addition, a change in the chamber gas composition during baking also affects the heat flux. When the oven chamber was filled with radiation absorbing gases (water vapor and carbon dioxide), the average temperature was estimated to be increased by 58C [10]. The effect of the migration of water and water vapor has not been integrated into the account of the heat transfer in an oven chamber yet. 11.2.1.2
Mass Transfer Mechanism
Diffusion together with evaporation and condensation has been assumed to be the mass transfer mechanisms inside dough [16,23–25]. The transport of water is driven by the gradients in water content. At the center of a loaf, the measured water content decreased until the center temperature was at 708C + 58C because of the volume expansion. However, the total water content of the loaf should be constant because dough does not have a continuous pore system. When the temperature reached 708C, some structural changes commenced; as a result, the discrete pores became continuous and then allowed water to move freely [6]. To reduce the partial water vapor pressure due to the temperature gradient, water moves towards the loaf center and the surface by condensation and evaporation. As a result, crumb temperature increasing is accelerated. At the surface exposed to oven air whose partial water vapor pressure is far from saturation, the water vapor diffuses into the air; as a result, the surface starts to dry out [4]. At this stage, a differentiation in bread structure is observed. Crumb is a wet core that contains as much moisture as the dough. Crust is a dried portion, the longer the baking is, the higher the thickness [24]. In one study [25], the moisture content in the center of crumb was measured at 45.7%, whereas the edge was at 37.2%. The moisture movement in crumb and crust can be described by Fick’s law [25,26]. Almost all moisture loss in bakery products happens during the baking process because of evaporation. Variations in the moisture loss are caused by the nature of different dough and the baking condition [2]. As stated earlier, due to the effect of heat during baking, dough structure is changed to a continuous pore structure to allow water to move. Some water vapor loses through the crust layer by evaporation, while some other water vapor condenses at the dough center. Consequently, the moisture content and water activity change and moisture gradients are formed [27]. The moisture differential may have an impact on staling mechanisms. For example, it can affect the activity of heat-stable antistaling amylolytic enzymes, because the amylolytic activity increases when the hydration in dough increases [28]. According to the models based on water evaporation and diffusion, the water content of crumb after baking remains the same as the initial dough water content, whereas the crust water content is close to zero [29]. Therefore, the total moisture loss is basically from the loss at the surface. It was found that a total moisture loss of 53 g per loaf could be from the top crust (29 g), the layer below the top crust (12 g), and the side crust (12 g) [6]. In the case of a frozen bun, during re-heating, the moisture loss from bread buns without crust was three times greater than the moisture loss from bread buns with crust. This is because crust acts as a barrier to the mass transfer. Heat supplied to the surface is used for heating the surface and then conducted through the crust. Without a crust, heat supplied to the surface is used for evaporating water from the buns. As a result, the center temperature of the buns without crust levels off at a lower level than that of the buns with crust [30].
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11.2.2 CHANGES DURING BAKING PROCESS 11.2.2.1
Volume Expansion
In typical bread dough, carbon dioxide gas is mainly produced by the yeast fermentation process. The stoichiometry of the reaction is as follows: C6 H12 O6 ! 2C2 H5 OH þ 2CO2 þ 2ATP The production of carbon dioxide gas by yeast continues at an increased rate during the first stage of baking until yeast is destroyed at a temperature of about 558C. According to GayLussac law, occluded gas expands when temperature increases from 258C to 708C [31]. At temperatures below 558C, volume expansion is slightly influenced by temperature. However, temperature shows significant effect on volume expansion, after dough temperature reaches 608C [32]. When temperature increases during baking, the solubility of carbon dioxide in a liquid dough phase decreases. Then dissolved carbon dioxide vaporizes. At the same time, saturated vapor pressure of water increases rapidly; as a result, gas cells expand. In the presence of a constant pressure, the volume of the occluded gas increases by a factor of 1.15 [31]. However, the pressure remains constant until dough temperature reaches 508C because dough viscosity does not affect oven rise up to this temperature. After that, the increased viscous resistance causes an increase in pressure [32]. If the pressure increases, the expansion will be accordingly decreased. The expansion is ceased by the exhaustion of baking powder if used, by the inactivation of yeast at higher temperature, and by the resistance of the dough to extension. The resistance can be due to either the viscous resistance of the bulk to deformation or a crust formation at the surface [31]. 11.2.2.2
Solidification
A metamorphosis from dough to bread involves crucial steps induced by starch gelatinization and transition from gel to coagel. The most striking changes are the opening of foam type of gas cells to produce pores and the solidification of aqueous bulk medium. The solidification is caused partly by gelatinization and partly by the loss of cohesiveness during transition from gluten gel to coagel. Bread is ready when the entire crumb reaches 1008C [4]. 11.2.2.2.1
Starch Gelatinization
Starch granule is composed of amylose and amylopectin, which forms crystals together. The space between crystals is called amorphous layer. In the presence of water, when molecules are heated up to the point that water has enough energy to break the bond in the amorphous area, gelatinization starts [33]. According to a nuclear magnetic resonance (NMR) baking study [34], gelatinization starts at 558C and finishes at 858C when evaporation at the surface dominates. A series of processes at molecular scale include swelling, melting, disruption of starch granules, and exudation of amylose [31]. As a result of starch gelatinization, the partially swollen granules can be stretched into elongated forms to allow gas cells to expand. Therefore, texture and structure of the product is dependent on starch gelatinization [33]. The extent of starch gelatinization; can be used as a baking index. Besides the baking condition, addition of some ingredients would also influence the starch gelatinization. Emulsifiers, for example, delay the gelatinization, as a result, the period of time for volume expansion is prolonged or the increase in viscosity is delayed. Therefore, adding emulsifiers are expected to improve the baking performance [4]. 11.2.2.2.2
Protein Denaturation
In wheat flour-based products (bread, cracker, cookies, etc.), dough is prepared through the formation of a wheat gluten network. When dough is subject to high temperature during
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baking, changes in its viscoelastic properties are found depending on the physicochemical characteristics of the wheat gluten [35]. Heating at temperatures above 608C leads to an increase in the storage modulus that characterizes elastic properties. This effect can be explained by the polymerization of glutenins as a result of thiol–disulfide interchange reaction. Thermal effect induces the change from gluten gel to coagel [31]. A previous study [36] hypothesized that changes in the solubility of wheat gluten during baking were dependent on its gliadin fraction. Otherwise, the changes might depend on the level of high temperature, which allowed the activation of thermosetting reactions producing intra- and intermolecular covalent bonds of protein network. The change in gluten phase also enhances the effect of starch gelatinization, such as the transformation from viscous dough into an elastic material [31]. After the protein is denatured during baking, water adsorbed in the gluten is released. Then starch uses this water for gelatinization [33,37]. Consequently, dough becomes a semirigid bread. Before baking, water in the dough is estimated to be combined with starch (46%), proteins (31%), and pentosan (23%) [38]. Freshly after baking, gelatinized starch granule is in amorphous phase. When bread is cooled down, water is redistributed as more starch turns to be in crystalline phase. More water from gluten is released to incorporate into the crystalline structure of starch; as a result, staling is developed [39]. At this time, it is estimated that no water is associated with proteins. However, some water is still combined with pentosan due to the high hydration capacity of pentosan [38]. 11.2.2.3
Color Development
Color is one of the important characteristics of baked products, contributing to consumer preference. In bread crust, the higher temperature and lower water content activate nonenzymatic browning reactions including Maillard reactions (sugar-amine) and caramelization [40]. At the beginning of a Maillard reaction, furosine amino acid is formed. However, the furosine decreases after a high intensity is reached. In contrast, hydroxymethylfurfural, an intermediate product in the Maillard reactions and sugar degradation, keeps increasing with higher temperature and baking time [41]. The resulting brown polymeric compound is called melanoidine. The browning reaction rate depends on water activity and temperature. The water activity that produces the maximum browning reaction rate is in the range of 0.4–0.6 depending on the type of food substance [40]. At temperatures below 608C, the browning reaction performs as a zero-order reaction. When temperature is higher, reaction curve follows the first-order reaction. Due to the short period of sub-608C surface temperature in baking processes, the overall color reaction is assumed to follow the first-order kinetics [42–45]. Its kinetic constant increases with increased temperature [46] and decreased moisture content [43] following Arrhenius equation. In bread baking, crust browning reaction occurs at temperature greater than 1108C [30]. Crust color intensity can be measured by infrared engineering (Colorex) sensor or Hunterlab [47], a monochrome or color image [48], and a food analyzer [30]. However, one study [41] claimed that color intensity measurement was less sensible than measuring the intermediate compound, hydroxymethylfurfural. Therefore, hydroxymethylfurfural was suggested to be used as a browning indicator for sliced bread toasting. 11.2.2.4
Flavor Development
Flavor is another quality attribute developed during baking process in the form of n-heterocycles via Maillard reactions. 2-Acetyl-1-pyroline and 2-acetyltetrahydropyridine are the major flavor compounds formed in wheat bread crust. Based on the relationship between flavor development and progress of baking, a flavor sensor was developed to be used as a process indicator for baking and toasting processes [49]. During baking, the flavor compounds
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formed are adsorbed by pore curvatures. Crust structure also provides a barrier against the loss of flavors [4].
11.3 CFD MODELING 11.3.1 INDUSTRIAL CONTINUOUS TRAVELING-TRAY BAKING OVEN In a continuous baking process, dough pieces placed inside trays are delivered continuously from a prover to entering an oven. As dough moves into the oven, it is gradually baked until exiting the oven. After the baking period, bread is depanned and cooled down. Baking ovens that can be used for continuous baking could be either tunnel oven or traveling-tray oven. The tunnel oven has its entrance and exit at the different ends. In contrast, a traveling-tray oven brings the trays in and discharges them both at the front end. It requires less space than the tunnel oven [18]. In this chapter, an indirect-heating traveling-tray oven is studied. In the indirect-heating system for the oven, hot air is generated from two burners located in the bottom part of the oven. The area of the burners is separated from the baking chamber by metal plates. The hot air is then supplied to ducts in the oven chamber through tubes. As shown in Figure 11.1, the oven chamber can be systematically divided into four Front zone
Return air duct
Supply air duct
Return air duct
Supply air duct
Convection fan Burner
Recirculation fan
Zone 1
Zone 2
Duct
Duct
Duct
Duct
Duct
Duct
Duct
Duct
Dough
Bread
Zone 4
Burner
Zone 3
Burner
FIGURE 11.1 Schematic diagram of the industrial bread-baking oven. (Reprinted from Therdthai, N., Zhou, W., and Adamczak, T., J. Food Eng., 60, 211, 2003. With permission from Elsevier.)
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24 23 22 21
20 19 18 17
16 15 14 13 Moving direction 12 11 10 9
8 7 6 5
4 3 2 1
FIGURE 11.2 Illustration of the traveling trays and tins in the oven.
zones. Each zone contains their own ducts to transfer heat to the traveling trays. Because there are no solid walls between the zones, heat supplies to the baking zones interfere with each other. Therefore, it is a difficult task to be able to operate the oven such that a set level of temperature in each zone can be achieved. In addition, zones 3 and 4, which are below zones 1 and 2, have two convective fans in the middle area of the heating ducts, respectively. The convective fans force the hot air to move horizontally towards the front and back of the oven. In the oven chamber, there are 26 traveling rows, each row consists of 12 trays, and each tray is composed of four tins (Figure 11.2).
11.3.2 OVEN MONITORING SYSTEM IN THE INDUSTRIAL CONTINUOUS TRAVELING-TRAY BAKING OVEN The oven monitoring system included 15-type K thermocouples, an in-line anemometer [50], and a Bakelog (BRI Australia Ltd). Stationary-type K thermocouples were installed in the oven chamber to monitor temperatures at different locations as shown in Figure 11.3. To monitor the temperature and velocity near the traveling trays, traveling sensors including thermocouples and the in-line anemometer were also attached to a traveling tin, as shown in Figure 11.4.
11.3.3 QUALITY MEASUREMENT
OF
BAKED BREAD
Baked bread was sampled from an industrial production process to determine the variation of bread quality including crust color by a colorimeter (Minolta CR-310) and weight loss
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12 10
11
8 9
7 1
2
4
3
5
Burner
6
Burner
Air in duct Air in convective fan Air in oven Air at duct wall
FIGURE 11.3 Diagram of the placement of the stationary thermocouples in the oven.
by a scale with accuracy up to 0.1 g. The color was expressed as the lightness (L), redness (a), and yellowness (b). To measure weight loss, 24 dough pieces of white sandwich bread were sampled from a conveyor before entering a prover in the industrial production line and marked on the surface. The initial weight (W0 ) of a sample was recorded before returning it to the prover. After the baking was completed, the bread samples came out of the oven and were depanned automatically. Then the weight of the samples were individually checked and recorded as W1 . The weight loss was the difference between W0 and W1 .
11.3.4 CFD MODELING 11.3.4.1
Simplification of the Baking Oven Geometry
Due to the complexity of the oven geometry, it was necessary to simplify the oven to reduce processing time during CFD simulation. In the actual industrial baking process, lids are 1 2
B
4
3
1. Lid temperature D
2. Side temperature
C B A
5
3. Bottom temperature 4. Dough temperature 5. Velocity and air temperature
Tray moving direction
FIGURE 11.4 Diagram of the placement of the traveling sensors on the tin.
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Travelling tray is composed of four tins
Blocks representing convection fans Exhaust (Flow outlet) Flow outlet
Air gap between tins
Air gap between trays
Flow outlet
Flow inlet
FIGURE 11.5 Illustration of the simplified baking oven.
preheated before covering the tins. Thus the initial tin temperature on the top is always higher than those on the bottom and side, which are approximately the same as the dough temperature after proving. To simulate this situation, a preheat block was created to heat up the top surface of dough to the actual initial top tin temperature before the dough moved into the oven (Figure 11.5). By this set up, when dough entered the oven, its initial bottom and side temperatures were the same as the dough temperature, whereas its initial top temperature was higher and equivalent to the actual heated lid temperature in the industrial operation. One traveling tray (0:55 0:12 0:28 m) actually consists of four tins (0:12 0:12 0:28 m) with air gaps between them. To predict the side temperature, the tins were individually simulated with air gaps between them. In addition, two convection fans in zones 3 and 4 were simplified as blocks in the middle of the duct panels to simulate the flow generated by the convection fan to the left and right sides of the oven. To reduce the numbers of cells, nonuniform mesh was used. A coarser mesh was applied inside the oven chamber, whereas a finer mesh was applied to the traveling tins. Consequently, the number of cells and faces became 93,654 and 323,786, respectively. 11.3.4.2 11.3.4.2.1
Model Assumption Three-Dimensional Flow
To simulate the moving of trays into the oven as in the continuous baking process, a threedimensional cross section of the oven was taken as the calculation domain (Figure 11.5).
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At the cross section (280 mm thickness which is equivalent to the width of a baking tray), there were 52 trays of dough continuously moving via both the top and bottom tracks in the oven. 11.3.4.2.2
Turbulent Flow
Due to the convection fans generating flow above the bottom ducts, air in the oven can be influenced by both forced convection and natural convection. Flow can be observed to have three characteristics: laminar, transitional, and turbulent. Reynolds number (NRe ) is used to describe the flow characteristics. It provides an insight into energy dissipation caused by viscous effects. When viscous forces dominate the effect on energy dissipation, the Reynolds number is small. In the oven that contained 3:65 0:90 m2 of opening area and typical 0:3 m s1 of airflow velocity, the Reynolds number (NRe ) was approximately 2:7255 104 . Thus, the flow characteristics were assumed to be turbulent. 11.3.4.2.3
Transient State Computation
The objective of this chapter is to simulate the continuous baking process with a constant mass flow rate through the oven. Both temperature and airflow velocity depend on time and location. Therefore, transient state was set up for the simulation. 11.3.4.3 11.3.4.3.1
Volume Condition Settings Dough Properties
The physical properties of dough and bread including density, specific heat, and thermal conductivity were set up as variables depending on temperature. The physical properties were also dependant on moisture content. However, in the case of bread, the difference between the moisture content of crumb and that of dough was not significant. Furthermore bread is composed of dominantly crumb rather than crust. Therefore, in the model, dough properties were set as piece-wise linear functions of temperature only, as shown in Table 11.1. 11.3.4.3.2
Flow Source
Due to the convection fans located at the bottom ducts, small blocks of convection fans were added at the middle of the bottom duct panels, as shown in Figure 11.5. Therefore, flow sources were set up in the small blocks. In addition, the sides of the blocks were set up as flow inlets with fixed velocity on x-axis to generate flow to the oven chamber. At the top of the blocks, boundary condition was set as a wall to prevent air from flowing up. In the real oven, there were plates on top of the fans to force air to move towards the front and the back of the oven rather than the top area. In addition to the sides and top of the blocks, boundary condition at the bottom of the blocks was set up as flow outlet to suck air out of the oven chamber.
TABLE 11.1 Thermal Properties of Dough and Bread Temperature (8C) 28 120 227
Density (kg m23)
Specific Heat (J kg21 8C21)
Thermal Conductivity (W m21 8C21)
420 380 340
2883 1470 1470
0.20 0.07 0.07
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11.3.4.3.3
Heat Source
The U-turn movement in the actual oven (Figure 11.1) could not be modeled due to the limitation of grid deformation in the software code (CFD-ACEþ). Therefore, the system was simplified by having only the top shelf moving towards the back of the oven, then moving out. After that, hot dough, equivalent to dough, which has been baked for 50% baking time, moved in via the bottom shelf towards the front end of the oven. To heat up the dough entering the bottom shelf to be equivalent to the last dough of the top shelf, heat blocks with a total length covering 50% baking time were set up as isothermal heat sources. 11.3.4.4 11.3.4.4.1
Boundary and Initial Condition Settings Convection Heat Transfer from Duct Surfaces
The burners were to supply hot air to the ducts. Then the hot air heated up and maintained the duct surfaces at certain temperatures. Therefore, in the model, the duct surfaces were set up as isothermal walls. Finally, the temperature gradient due to convective heat transfer from the isothermal duct surfaces to air in the oven chamber was computed by the CFD-ACEþ codes (Equation 11.1). Heat transfer coefficient (ha ) was calculated according to flow status inside the oven chamber: qa ¼ ha ðTduct Tair The initial condition was Tair inside tions are shown in Table 11.2. 11.3.4.4.2
oven
inside oven Þ
(11:1)
¼ Ta0 at t ¼ 0. Duct temperatures at different loca-
Radiation Heat Transfer from All Metal Surfaces Inside Oven Chamber
In addition to the convective heat transfer, radiant heat came from all hot metal parts in the oven. It traveled straight through the space, and caused localized temperature differentials. In the model, it was calculated as follows: h i qb ¼ s« ðTA þ 273Þ4 ðTB þ 273Þ4 (11:2) where s is Stefan–Boltzmann constant (5:669 108 W m2 K4 ), « is emissivity (it was assumed to be at 0.95 [42]), TA is temperature of heat source (8C), and TB is temperature of heat absorbed (8C). The initial condition was TB ¼ TB0 ¼ 408C at t ¼ 0. 11.3.4.4.3
Heat Loss through Oven Walls
Due to the insulation, heat loss through the oven walls was very small. The overall heat transfer coefficient from the combined conduction and convection was approximately 0:3 W m2 8C1 . Heat loss can be calculated by qc ¼ hc ðToven The initial condition was Toven
inner wall
inner wall
Tair
outside oven Þ
(11:3)
¼ Tc0 at t ¼ 0.
TABLE 11.2 Duct Temperatures Duct Temperature (8C) At supply air duct At return air duct
Zone 1
Zone 2
Zone 3
Zone 4
336 311
336 300
397 300
370 311
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Traveling Trays
The boundaries of the traveling trays and the oven chamber above and below the traveling trays were set as arbitrary interfaces. This allowed fluid to flow between the traveling trays and the static oven chamber, when the trays were traveling inside the oven. There was no fluid flow between the oven chamber and the waiting trays outside the oven. This was close to the actual baking scenario. Dough started being baked after entering the oven and finished when exiting the oven. Conductive heat transfer inside the dough can be determined by qd ¼ kd Tdough
surface
Tdough
center
=thicknessdough
(11:4)
The initial condition was Tdough center ¼ Td0 at t ¼ 0. Therefore, heat transfer at the dough surface can be estimated by qd A ¼ mCdTdough =dt
(11:5)
The initial condition was Tdough ¼ T0 at t ¼ 0. 11.3.4.4.5
Exhaust Box
Normally an exhaust is installed to suck cold air from the front door out of the oven chamber. To simulate the exhaust, one section of the bottom floor was set up as a flow outlet with fixed flow velocity. This boundary allowed air to be removed from the oven with a constant flow rate. 11.3.4.5
Solving the Model
Together with the initial and boundary conditions, the continuity, Navier–Stokes, and energy conservation equations were solved by a CFD-ACEþ (V2002) code. The program discretized the differential equations to produce a numerical solution. CFD-ACEþ uses an iterative, segregated solution procedure. Two nonlinear equation solvers including the conjugate gradient squared (CGS) plus preconditioning solver and the algebraic multigrid (AMG) solver were applied. The first-order upwind spatial differencing scheme was used. The relevant set of linear finite difference equations was solved sequentially and repeatedly until a converged solution was obtained.
11.3.5 MODEL VALIDATION Although the oven geometry was simplified in the model, the prediction of the top temperature profile was reasonably accurate. However, overprediction in the bottom and side temperature profiles appeared in zones 3 and 4 (Figure 11.6). The model performance could be described by the values of correlation coefficient (R) and mean square error (MSE) between the model predicted values and the values measured during industrial production, as shown in Table 11.3. For the velocity profile, as shown in Figure 11.7, a few undesired peaks and valleys appeared. The most severe peaks were around the U-turn. This could be due to the simplification of the model configuration at the U-turn area. As mentioned earlier, the present model could not simulate the real U-turn movement due to the limitation in the software’s capability. As a result, some errors could be produced from the simplification of the tray moving direction. According to Table 11.4, in comparison of the predicted velocity with the measured velocity, a relative error of 37.31% was observed for the whole oven. The error was mainly
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250
200
200 Temperature (⬚C)
Temperature (⬚C)
Three-Dimensional CFD Modeling of a Continuous Industrial Baking Process
150 100
150 100 50
50 0
0 0
375
750
1125
0
1500
375
Top temperature
750
1125
1500
Baking time (s)
Baking time (s)
Bottom temperature
Modeled top temperature
Modeled bottom temperature
250
Temperature (⬚C)
200
150
100
50
0 0
375
750
1125
1500
Baking time (s) Side temperature
Modeled side temperature
FIGURE 11.6 Top, side, and bottom surface temperature profiles. (Reprinted from Therdthai, N., Zhou, W., and Adamczak, T., J. Food Eng., 65, 599, 2004. With permission from Elsevier.)
TABLE 11.3 Model Performance Performance R MSE
Top Temperature
Bottom Temperature
Side Temperature
Velocity
0.9132 141.19
0.9065 276.77
0.9096 281.99
0.6019 0.0336
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0.9 0.8
Velocity (m s−1)
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
375
750
1125
1500
Baking time (s) Actual velocity
Modeled velocity
FIGURE 11.7 Velocity profile. (Reprinted from Therdthai, N., Zhou, W., and Adamczak, T., J. Food Eng., 65, 599, 2004. With permission from Elsevier.)
from the U-turn area in zones 2 and 3. Due to the simplification of tray movement at the U-turn at the end of zone 2 and the beginning of zone 3, a large relative error was found in a high proportion to the measured velocity. A previous study [51] observed an error of 26%–28.5%, using a CFD model to simulate the airflow pattern in a cold store with palloxes. In addition, an error of 40% to predict the airflow pattern in a chiller with objects was reported in Ref. [52]. By comparing the difference between measured velocity and predicted velocity relative to the velocity at the flow source, the error was 4.29%. Due to a much lower flow rate in zones 1 and 2, the relative error to the velocity at the flow source in these two zones was significantly lower than that in zones 3 and 4. In one of the earlier studies, an error of 5% in simulating the airflow pattern in a mechanically ventilated livestock building (the bulk jet velocity was 6:1 m s1 ) without object was also observed [53]. TABLE 11.4 Relative Error Compared to Measured Velocity and Flow Source Relative Error Zone 1 Zone 2 Zone 3 Zone 4 Whole oven
Compared to Measured Velocity (%)
Compared to Velocity at Flow Source (3 m s21) (%)
37.69 39.69 39.16 32.29 37.31
2.35 2.85 5.84 5.26 4.29
Source: Reprinted from Therdthai, N., Zhou, W., and Adamczak, T., J. Food Eng., 65, 599, 2004. With permission from Elsevier.
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TABLE 11.5 Weighting Factors for the Top, Side, and Bottom Tin Temperatures Weight Factor WTi WSi WBi
Zone 1
Zone 2
Zone 3
Zone 4
0.7500 0.4453 0.1953
1.4000 0.4219 0.8219
1.0811 0.4516 0.5328
1.7889 0.3518 1.1406
Overall, the model presented an acceptable performance in predicting the airflow velocity compared to other related works [51–53], although its performance was not as good as that in predicting the temperature profiles. With the good performance in predicting the top temperature profile and reasonable performance in predicting the bottom and side temperatures, the model could be used to predict the corresponding bread quality attributes by utilizing the mathematical models developed by [54] as follows: xi ¼ WTi Ti þ WSi Si þ WBi Bi
(11:6)
where xi (i ¼ 1 4) are the weighted temperatures in the four zones. WTi , WSi , and WBi , are weighting factors whose values are given in Table 11.5. Using Equation 11.6 and Table 11.5, the average weighted temperature profiles were 1168C, 1308C, 1728C, and 1708C for zones 1, 2, 3, and 4, respectively. The corresponding quality attributes were then predicted by using the following equation [54]: yi ¼ fi (x) ¼ bi0 þ
5 X j¼1
bij xj þ
5 X
bijk xj xk þ
j,k¼1, j6¼k
5 X
bijj x2j
(11:7)
j¼1
where yi (i ¼ 1 6) are the quality attributes: percent weight loss ( y1 ), internal temperature ( y2 ), side crust color ( y3 ), top crust color ( y4 ), bottom crust color ( y5 ), and average crust color ( y6 ): xi (i ¼ 1 4) are the tin temperatures in the four zones, respectively: x1 , x2 , x3 , and x4 : x5 is the baking time. bi0 , bij , bijk , and bijj (i ¼ 0,1 5; j ¼ 1 5; k ¼ 1 5; j 6¼ k) are model parameters. As shown in Table 11.6, by using the temperature profiles obtained from the CFD model [55] and the mathematical models [54], the predicted quality attributes were in good agreement with the measured values.
TABLE 11.6 Comparison of the Measured Bread Quality Attributes with Those Predicted from the CFD Model and Mathematical Models Quality Attributes Measured value Predicted value
Weight Loss (%)
Internal Temperature (8C)
Top Crust Color (L-Value)
Side Crust Color (L-Value)
Bottom Crust Color (L-Value)
Average Crust Color (L-Value)
9.10 9.36
98.41 97.86
49.93 48.81
70.47 71.15
50.57 49.80
56.99 56.82
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11.4 APPLICATIONS OF CFD MODEL 11.4.1 SIMULATION
OF
OVEN OPERATION
UNDER INCREASING
OVEN LOAD
During a continuous baking process, baking trays were continually delivered into the oven. Each step of the tray movement increased the oven load unless the oven load already reached its maximum (i.e., a full oven). The change of oven load could affect the temperature gradient; as a result, the convective flow was simultaneously changed. This led to the change of overall airflow pattern. At the same time, the tray movement directly forced the airflow to change its pattern. The variation of airflow pattern could be simulated throughout the whole baking time, using the three-dimensional CFD model. Each traveling tray experienced different airflow and thereby different temperature profiles. From the simulation results by the CFD model, the average temperature profiles of the earlier tins were slightly higher than those of the later tins, as shown in Figure 11.8.
Temperature (8C)
Top temperature 240 220 200 180 160 140
Tray 4 Tray 8 Tray 12 Tray 16
120 100 1
2
Zone
3
4
Temperature (8C)
Bottom temperature 240 220 200 180 160 140 120 100
Tray 4 Tray 8 Tray 12 Tray 16
1
2
3
4
Zone Side temperature Temperature (8C)
240 220 200
Tray 4
180
Tray 8
160
Tray 12
140
Tray 16
120 100 1
2
Zone
3
FIGURE 11.8 Effect of the oven load on the temperature profiles.
4
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Together with the mechanistic models developed earlier in Ref. [54], the simulated temperature profiles could be used to estimate the product quality attributes influenced by the change of oven load. The estimated weight loss of the moving tray No. 4, No. 8, No. 12, and No. 16 was 9.71%, 9.56%, 9.49%, and 9.45%, respectively (Figure 11.9, Part a). At the beginning (i.e., less number of trays was inside the oven), the variation of weight loss between the trays was significant, due to the significant difference in the corresponding crust temperature. However, the variation was reduced and became nonsignificant when the number of trays increased. Similarly, the significant decrease of temperature profile at the beginning made the crust color lighter (i.e., higher L-value) as the number of trays in the oven increased (Figure 11.9, Part c). This was due to the slowing down of browning reactions on the surface. Although the variation of the crust temperature was significant, there was no significant difference in the internal temperature among the different trays (Figure 11.9, Part b). These simulated phenomena were consistent with the observations on the actual baking in industry during a start-up period as well as when there was a production gap in the oven chamber.
Effect of oven load on weight loss
Effect of oven load on internal temperature 100
(a)
Tray 4 Tray 8 Tray 12 Tray 16
9.6
9.4 9.2 9
Temperature (8C)
Weight loss (%)
9.8
(b)
99 Tray 4 Tray 8 Tray 12 Tray 16
98 97 96 95
Effect of oven load on average crust color 60
L-value
59 58 57 56
Tray 4 Tray 8 Tray 12 Tray 16
55
(c) FIGURE 11.9 Effect of the oven load on the quality attributes of the final bread. (a) weight loss, (b) internal temperature, and (c) crust color. (Reprinted from Therdthai, N., Zhou, W., and Adamczak, T., J. Food Eng., 65, 599, 2004. With permission from Elsevier.)
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11.4.2 SIMULATION
OF
BAKING INDEX
Baking index is an indicator of the degree of baking that is related to the starch gelatinization rate. By integrating a kinetic model of starch gelatinization in Ref. [56] with the CFD model in Ref. [55], the baking index for bread baked in the traveling-tray oven could be simulated [57]. Normally an industrial baking tray was composed of four tins. Tin No. 2 had two tins on its right and one tin on its left. To study the extent of starch gelatinization within a loaf, bread baked in the tin No. 2 was taken. As shown in Figure 11.10, at positions of 40, 35, 25, 20, 10, and 0 mm from the center to the left and right sides, there was significant variation in the starch gelatinization rate. In the outer crumb layers (40 mm from the center) on the left and right sides of the loaf, the gelatinization process started in zone 1 and reached the
Top half
Bottom half Zone 4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
Zone 1 Zone 2 Zone 3 Zone 4
Extent of gelatinization
Extent of gelatinization
Zone 1 Zone 2 Zone 3
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
375 750 1125 1500 Baking time (s) +40 mm +35 mm +30 mm +25 mm +20 mm +10 mm 0 mm (a)
0
375 750 1125 1500 Baking time (s) −40 mm −35 mm −30 mm −25 mm −20 mm −10 mm 0 mm (b) Right half
Zone 1 Zone 2 Zone 3 Zone 4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
Extent of gelatinization
Extent of gelatinization
Left half
0
375 750 1125 1500 Baking time (s) +40 mm +35 mm +30 mm +25 mm +20 mm +10 mm 0 mm
0
375 750 1125 1500 Baking time (s) −40 mm −35 mm −30 mm −25 mm −20 mm −10 mm 0 mm (c)
Zone 1 Zone 2 Zone 3 Zone 4
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
(d)
FIGURE 11.10 Variation of starch gelatinization within a loaf. (Reprinted from Therdthai, N., Zhou, W., and Adamczak, T., J. Food Eng., 65, 543, 2004. With permission from Elsevier.)
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maximum extent (i.e., baking index ¼ 1) within 10 min. In zone 1 only the outer crumb layer (40 mm from the center) started the gelatinization process. When baking time was increased, heat penetrated to the inner crumb layer. Other layers towards the center started and finished the gelatinization process later. Due to the position of loaf No. 2 that had two tins on its right and one tin on its left, the gelatinization rate of the left side layer was faster as a consequence of the temperature gradients within the tray. The difference in the gelatinization rate between the left and right sides became more obvious in zone 3, where the airflow pattern was changed due to the U-turn movement. In zone 4, the variation of the gelatinization rate was not significant, because the gelatinization process nearly reached the maximum extent. Considering the variation of the gelatinization rate from the top to bottom of the loaf (0–40 mm away from the loaf center), the bottom crumb layer tended to have a faster gelatinization rate. This was due to more radiation heat from the heating ducts to the bottom of the loaf. The temperature gradient made the loaf temperature on the bottom higher and thereby increased the gelatinization rate. However, the variation in the gelatinization extent decreased in the area near the loaf center (0–20 mm away from center vertically and horizontally), possibly due to the condensation of water vapor. Condensation maintained the temperature at the loaf center region below 1008C [16]. In addition, the moisture content of crumb at the loaf center region was at the same level as that of dough. Therefore, the starch gelatinization, a thermal reaction, could be nearly uniform at the loaf center. In addition to the variation among the traveling trays, variation within the same traveling tray was also found (Figure 11.11). When a tray moved from left to right along the top traveling track (Figure 11.1 and Figure 11.2), tin No. 4 was generally the hottest compared to the other three tins in the same tray. After the direction of the tray changed to the left-to-right movement in zones 3 and 4 (i.e., along the bottom traveling track), tin No. 1 became the hottest. In zones 1 and 2, the gelatinization was just activated, therefore the corresponding variation was not significant. Significant variation in the gelatinization extent was found in zone 3. In zone 4, variation became nonsignificant again, as the gelatinization already reached Zone 1
Zone 2
Zone 3
Zone 4
1 0.9
Extent of gelatinization
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
375 Tin 1
750 1125 Baking time (s) Tin 2
Tin 3
1500 Tin 4
FIGURE 11.11 Variation of the gelatinization extent among tins in the same tray. (Reprinted from Therdthai, N., Zhou, W., and Adamczak, T., J. Food Eng., 65, 543, 2004. With permission from Elsevier.)
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Zone 1
Zone 2
Zone 3
Zone 4
1 0.9 Extent of gelatinization
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
375
750 Baking time (s)
1125
1500
Current operating condition Modified operating condition
FIGURE 11.12 Comparison of the starch gelatinization profiles during baking under the current and modified conditions. (Reprinted from Therdthai, N. Zhou, W., and Adamczak, T., J. Food Eng., 65, 543, 2004. With permission from Elsevier.)
the maximum extent. Although the starch gelatinization extent was taken as the baking index, the effect of starch gelatinization rate and profile during baking on the final product quality attributes has not been studied yet.
11.4.3 DESIGN OF OPERATING CONDITION TO ACHIEVE TIN TEMPERATURE PROFILES
THE
OPTIMUM
According to the three-dimensional CFD simulation results [55], the current oven operating condition resulted in a temperature profile of 1168C, 1308C, 1718C, and 1708C for zones 1, 2, 3, and 4, respectively. Using the mechanistic models in Ref. [54], the consequent weight loss was 9.35% after baking for 25 min. To reduce the weight loss without changing the baking time, the duct temperatures and=or airflow volume needed to be adjusted. The optimum average weighted temperature profile for a total baking time of 25 min was found to be at 1068C, 1308C, 1668C, and 1788C for zones 1, 2, 3, and 4, respectively [54]. Compared to the current profile, there was some significant difference. Under the current operating condition, the average weighted tin temperatures in zones 1 and 3 were too high, whereas the average weighted tin temperature in zone 4 was too low. According to the simulation results from a two-dimensional CFD model [58], the most efficient way to manipulate the baking condition was to adjust the airflow pattern. Increasing the volume of airflow tended to increase the baking temperature profiles. Therefore, heat supply to the oven could be reduced. To obtain the optimal temperature profile which reduced the weight loss, the three-dimensional CFD model was used to simulate the oven operating condition with various airflow volume and heat source temperatures. Due to the temperature profiles in zones 1 and 3 being too high, the duct temperature in zones 1, 3, and 4 was reduced by approximately 108C in order to decrease the tin
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temperature in zones 1 and 3. By only reducing the duct temperatures in some zones, the temperature profiles in zones 2 and 4 might become too low. Therefore, at the same time as decreasing the duct temperatures, the flow volume applied to the convection fan in zone 3 should be increased by doubling its speed, in order to maintain the tin temperatures in zones 2 and 4. By increasing the flow volume supplied to zone 3, the difference between the top, side, and bottom tin temperatures in zone 4 also became less. From the simulation results, by integrating the CFD model with the mechanistic models in Ref. [54], the proposed new operating condition would produce a weight loss of 7.95% with the lightness values of the crust color on the top, bottom, and side of the loaf being around 50.68, 55.34, and 72.34, respectively. Although heat supply was reduced, the obtained bread still had a completed baking inside the loaf, with its internal temperature being 98.698C. Based on the simulation results utilizing the kinetic model of starch gelatinization, the gelatinization rate of dough baked under the proposed operating condition was slower than that baked under the current operating condition, especially in zone 3. This was due to the reduction in energy supply in zone 3, which was the major factor causing high weight loss. However, the gelatinization was speeded up in zone 4 and finally reached the maximum gelatinization extent at the end of the proposed baking process, as shown in Figure 11.12. Therefore, by adjusting the oven operating condition as proposed, the energy supply could be reduced, while the yield could be increased and the quality attributes were within an acceptable range. The proposed oven operating condition is highly recommended for industrial process operations.
11.5 CONCLUSIONS Baking is a complex process due to many thermal reactions involved, including starch gelatinization and nonenzymatic browning reactions, which are coupled with heat and mass transportation. To obtain the best quality bread, temperature profiles should be optimized in accordance with the required thermal reactions. However, to operate an industrial continuous baking oven to achieve the optimum temperature profile is a challenge, because of the complexity of the oven. Both heat supply and airflow in the oven have to be adjusted. Adjusting the oven operation through an online trial-and-error process would not be practical, as it is very time consuming and costly. This chapter has presented the capability of CFD modeling and simulation for optimizing an industrial continuous traveling-tray bread-baking oven. A three-dimentional CFD model with moving grids was established to specially simulate the tin temperature profiles and airflow patterns during the continuous baking process. The CFD model demonstrated reasonably good performance through model validation, where the predicted temperature profiles and airflow profiles were compared to those measured during industrial operations. The model was subsequently used to estimate the effect of oven load on airflow pattern, temperature profiles, and the corresponding bread quality attributes. The CFD simulation results demonstrated a dynamic change in the tin temperature profiles at the beginning of the baking process. However, the change became nonsignificant when the oven was filled with more trays with dough. By integrating the CFD model with other mathematic models for the quality attributes, variations in the weight loss and crust color of bread among different trays and among different tins within the same tray could be estimated. The CFD model was also used to study how the oven operating condition should be adjusted to achieve the optimum tin temperature profile. Based on the prediction, the weight loss and energy consumption could both be reduced while the product quality attributes were maintained in an acceptable range. The obtained information from the CFD simulations would be very useful to further modifying the oven design and the control system for industrial continuous baking ovens.
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NOMENCLATURE C T h k q x a s «
specific heat (J kg1 8C1 ) temperature convective heat transfer coefficient (W m2 8C1 ) thermal conductivity ðW m1 8C1 ) heat flux (W m2 ) distance (m) degree of gelatinization Stefan–Boltzmann constant emissivity
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12
Computation of Airflow Effects in Microwave and Combination Heating Pieter Verboven, Bart M. Nicola¨l , and Ashim K. Datta
CONTENTS 12.1 12.2
Introduction ............................................................................................................. 314 Modeling of the Electromagnetics of Microwave Heating....................................... 315 12.2.1 Governing Equations .................................................................................. 315 12.2.2 Boundary Conditions.................................................................................. 316 12.2.3 Excitation.................................................................................................... 316 12.2.4 Power Loss Calculation .............................................................................. 317 12.3 Modeling of Heat Transfer and Its Coupling with the Microwaves ........................ 317 12.3.1 Governing Equations .................................................................................. 317 12.3.2 Boundary Conditions.................................................................................. 317 12.3.3 Electromagnetics–Heat Transfer Coupling ................................................. 317 12.3.4 Numerical Solution ..................................................................................... 318 12.3.5 Experimental Approaches ........................................................................... 318 12.4 Modeling of Airflow Effects .................................................................................... 318 12.4.1 Governing Equations .................................................................................. 319 12.4.2 Boundary Conditions.................................................................................. 319 12.4.3 Numerical Solution ..................................................................................... 320 12.4.4 Experimental Approaches ........................................................................... 320 12.5 Airflow in a Domestic Microwave Oven.................................................................. 320 12.5.1 Oven Description ........................................................................................ 320 12.5.2 Computational Mesh .................................................................................. 321 12.5.3 Natural and Forced Convection Heating Modes........................................ 322 12.5.4 Flow Patterns and Heat Transfer Coefficients in a Microwave Oven ........ 322 12.6 Combined Airflow and Microwave Heating in a Jet Impingement Oven................ 324 12.6.1 Oven Description ........................................................................................ 325 12.6.2 Computational Mesh .................................................................................. 325 12.6.3 Effect of Impingement Heating................................................................... 327 12.7 Conclusions .............................................................................................................. 329 Nomenclature ..................................................................................................................... 329 References .......................................................................................................................... 330
313
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12.1 INTRODUCTION Food in a microwave oven absorbs the microwaves and thus is directly heated by the microwaves. Dry air does not absorb microwaves and therefore stays cold. The air in the cavity tends to cool the food surface while warming up in the process. The eventual increase of food surface temperature from absorbed microwave energy also increases evaporation of water from it into the air. The airflow pattern inside the microwave oven determines the rates of surface heat and moisture transfer and the distributions of temperature and moisture in the food, thus determining its final quality from the heating process. For example, surface moisture accumulation in microwave heating that often leads to an undesirable soggy food product can be significantly reduced by increasing the airflow rate over the food [1]. In turn, the evaporated water is convected away by the air and may reduce the oven efficiency due to microwave absorption when accumulated in the cavity. A good air exchange is required to prevent such effects. Combination heating couples convection heating with hot air to microwave heating. Such combination can be beneficial to prevent surface cooling and moisture accumulation. In addition, combination heating is believed to improve uniformity of food heating. The chapter will present modeling of microwaves, airflow, and heat transfer inside an oven. Moisture transport in the food, which can be important to both food quality and safety, will not be included here to keep the focus of this chapter to the effect of flow on heat transfer and the reader is referred to articles [1–3] for further information on moisture transport. For simplicity, Figure 12.1 provides an overview of the modeling process involved in microwave heating in presence of air. The microwave energy is deposited volumetrically in the food and is therefore treated as a heat source term. This couples microwave fields to heat transfer. Since heating changes dielectric properties which, in turn, changes microwave fields, consideration of dielectric property changes with temperature leads to a two-way coupling between microwaves and heat transfer. The airflow modeling, like microwave modeling, can couple one-way if the velocities are high and natural convection effects can be ignored. On the other hand, at low velocities as when no blowing device is present inside the oven, natural convection effects are important and the coupling between heat transfer and airflow is two-way. The chapter is organized as follows. First, microwave field modeling is described using Maxwell’s equations. Next heat transfer is described using the energy equation. Coupling of the heat transfer with microwaves is described next. Then, airflow modeling in oven cavities is presented, with focus on low velocities inside a domestic microwave oven. Experimental
Microwaves depositing thermal energy in the food volumetrically
Coupling from temperature dependence of dielectric property
Combined effect determines the temperature distribution in the food Airflow at the surface of food modifies the thermal boundary condition
Coupling from natural convection effects at low airflow rates
FIGURE 12.1 An overview of the microwave heat transfer process in the presence of airflow.
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approaches and results for heat transfer coefficient in case of high airflow rates (as in jet impingement heating) are also discussed. Numerical aspects of the modeling process are presented. Results in terms of velocity profiles and temperature patterns are presented, demonstrating the effects of airflow in microwave and combination heating.
12.2 MODELING OF THE ELECTROMAGNETICS OF MICROWAVE HEATING A microwave oven is a 3D cavity, as illustrated in Figure 12.2. Microwaves are reflected from inside the cavity walls. Inside this cavity, the incoming electromagnetic waves from the magnetron and the reflected waves from the cavity walls form resonant patterns. The qualitative pattern and the magnitude of electric fields inside the food are quite different from that in the air. There is no easy and universal solution to obtain the electric field inside a food placed in such a cavity, as can be shown for a plane wave [4]. Over the years, exponential decay inside a food has been used in a lot of oven heating situations, but for most of the situations this is essentially a qualitative assumption and can be completely wrong depending on size of the food and its dielectric properties. The right way to obtain the electric field patterns inside a food is to solve the Maxwell equations of electromagnetics for the oven and obtain the volumetric rate of heating. This is now described.
12.2.1 GOVERNING EQUATIONS The electromagnetic fields that are responsible for the heating of the food material inside a microwave oven (Figure 12.2) are described by the Maxwell equations @ (mH) @t
(12:1)
@ 0 (« «0 E) þ «00eff «0 vE @t
(12:2)
rE¼ rH¼
FIGURE 12.2 Thermador dual microwave jet oven showing openings for jet impingement at the bottom.
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r («E) ¼ 0
(12:3)
r H ¼ 0
(12:4)
where E and H are the electric and magnetic field vectors, respectively. In food materials, heating is done by the electric field primarily through its interaction with water and ions. The complex permittivity, « is given by « ¼ «0 þ j «00eff
(12:5)
where the properties «0 and «00eff are functions of position in the food due to temperature (and moisture) variations. These properties also vary with frequency of the microwaves; but generally speaking in food applications, the microwave frequency is fixed. In the above equations, «0 is the permittivity of free space (8:86 1012 F m1 ) and ˆ ¼ 2pf is the angular frequency of the microwaves. For a short discussion of Maxwell’s equations and their solution in heating applications, see Ref. [4]. The Maxwell equations are to be solved to obtain the electric field E as a function of position in the food and heating time. The rate of volumetric heat generation is calculated from this electric field.
12.2.2 BOUNDARY CONDITIONS Boundary conditions for the electromagnetic modeling of a cavity are set on the walls of the cavity, which are considered to be perfect conductors. The entire cavity interior is treated as a dielectric, with appropriate dielectric properties of air and food in the regions that they occupy. Note that in modeling of the entire cavity, the food–air interface does not have to be treated in any special way by the modeler as this is built into Maxwell’s equations. In the interior of a perfect electrical conductor, the electric field is zero. This condition, together with Maxwell’s equations, leads to the boundary condition at the air–wall interface as Et,air ¼ 0
(12:6)
Bn,air ¼ 0
(12:7)
Here the subscripts t and n stand for tangential and normal directions, respectively. These conditions are necessary to determine the solution. The input parameters needed for solution are the geometry of the food, inside geometry of the oven, the dielectric properties of the food material, and the magnitude of the excitation. In most cases, the magnitude of the excitation is obtained by matching experimental data on temperature rise.
12.2.3 EXCITATION The excitation for the microwave oven is through a horn waveguide. The shape of the waveguide is designed to transmit maximum possible power from the magnetron to the cavity. From the shape of the antenna projected into the waveguide, it can be safely assumed that the electromagnetic field distribution can be approximated by TE10 mode. The transverse component of the electric field in TE10 mode can be given by the function Em,y (x,y,z;t) ¼
px vm p sin H sin (vt bm z) 0 h2m a a
(12:8)
But due to the reflection of waves back from the cavity, Equation 12.8 may not represent the exact electric field distribution inside the waveguide.
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12.2.4 POWER LOSS CALCULATION Electromagnetic waves carry energy within themselves and this gets absorbed in the dielectric material. Power input in any volume V enclosed by surface S can be given by þ
@ Pin ¼ ðEm HÞ ds ¼ @t
ð V
1 2 2 «m Em þ mH dV 2
(12:9)
Power absorbed by the dielectric food then can be written down in a simple form as 1 P(x,t) ¼ v«0 «00eff E2m 2
(12:10)
12.3 MODELING OF HEAT TRANSFER AND ITS COUPLING WITH THE MICROWAVES 12.3.1 GOVERNING EQUATIONS The governing equation for conduction heat transfer in the food is given by rs cps
@T ¼ ks r2 T þ qgen @t
(12:11)
where qgen is the microwave power density, with units as J m3 obtained from Equation 12.10 of the electromagnetic model. Initial temperature is considered constant in the entire domain.
12.3.2 BOUNDARY CONDITIONS The convective boundary condition on the food surface is given by ks rT ¼ h(T Ta )
(12:12)
where h is the surface heat transfer coefficient over a surface and Ta the air temperature. As described below, the surface heat transfer coefficient will be obtained in two different ways. In case of low and indirect airflow, the complete flow equations will be solved to obtain h. For high-velocity jet impingement heating, h will be obtained experimentally.
12.3.3 ELECTROMAGNETICS–HEAT TRANSFER COUPLING The approach used in coupling the microwaves with heat transfer is to solve Maxwell’s equations inside a microwave cavity and couple the solution with the thermal module to solve for temperature. The flowchart of the numerical solution is shown in Figure 12.3. The flowchart shows the two-way coupling between the electromagnetic and the thermal physics. With change in temperature, the dielectric properties change, this in turn changes the electromagnetic field and therefore the rate of heating. But since the dielectric properties of many high moisture foods are fairly constant in the temperature range of operation, a twoway coupled simulation typically produces a solution that was less than 3% off in the total power loss in the food item. Hence to reduce the computational time, the final solution incorporates only one-way coupling from electromagnetics to the thermal module.
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Thermal module Input power loss as the source term. Jet impingement is accounted by a convection boundary condition
Electromagnetics module calculate power loss in the food material
Electromagnetics module solve for electric and magnetic fields
Yes
Is the change in dielectric properties greater than 10%
No Thermal module solve for temperature
Start Calculate properties at the new temperature
FIGURE 12.3 Flowchart of the electromagnetics–heat transfer coupling mechanism.
12.3.4 NUMERICAL SOLUTION There are a number of commercial software products based on various computational methods, such as the finite difference time domain method and the finite element method (see http:==www.emclab.umr.edu=csoft.html). Many of these codes are not particularly efficient for cavity heating applications where the electromagnetics has to be solved for high frequencies and coupled with heat transfer. Two of the codes that have such coupling capabilities for cavity heating applications are ANSYS and COMSOL. An example of using ANSYS in microwave heating of food can be seen in Ref. [5].
12.3.5 EXPERIMENTAL APPROACHES Direct experimental verification of electric field is difficult since few, if any, sensors are available for this purpose. Typically, the temperature measurements serve as indirect validation of the electric field distributions.
12.4 MODELING OF AIRFLOW EFFECTS Airflow in microwave ovens originates from different actions. First, low-velocity cooling air of the microwave generator is often guided into the cavity to provide air refreshment. Second, the hot and moist food surface heats the surrounding air and results in buoyancy flow. These first two mechanisms may be of similar strengths, resulting in complex cavity airflow. The third airflow mode results, if jet impingement or forced air circulation fans is present. If active, this airflow mode will overrule the other two modes, resulting in turbulent airflow patterns similar to impingement ovens or forced air circulation ovens [6,7]. In any case, the airflow effect cannot be approximated by simple formulas or relationships and a computational fluid dynamics (CFD) approach is mandatory.
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12.4.1 GOVERNING EQUATIONS Assuming the Boussinesq approximation for natural convection airflow valid, the governing equations for airflow and heat transfer in steady-state conditions can be written as r u ¼ 0
(12:13)
ra u ru ¼ rp þ ha r2 u ra gb(T Tref )
(12:14)
u rT ¼ aa r2 T
(12:15)
where u is the Cartesian air velocity vector (m s1 ), p is the pressure (Pa), T is the temperature (8C), and g is the gravity vector (m s2 ). The parameters in the equations are the density ra at 1 reference temperature Tref , the viscosity ha , and the thermal diffusivity aa (m2 s ). When the airflow is turbulent (due to impingement or forced convection at high air velocity), a turbulence component may be added to the parameters viscosity and thermal diffusivity, e.g.,
ht ¼ r a C h at ¼
k2t «t
ht st
(12:16) (12:17)
Additional transport equations need then be solved for the turbulence variables kt , the turbu2 3 lent energy (m2 s ), and «t the turbulence energy dissipation rate (m2 s ). Ch and st are adjustable turbulence model parameters.
12.4.2 BOUNDARY CONDITIONS To solve the above system of equations, boundary conditions are required. At the smooth cavity walls, the air velocity is 0 (no-slip). When air enters the cavity (inlets), the velocity or airflow rate must be specified. When air leaves the cavity (outlets), generally a reference pressure condition is applied together with the condition of global mass conservation. For heat transfer, the temperature or heat flux can be specified at the surface boundaries. At inlets, temperature is required and at outlets, a zero heat flux condition holds. In general the airflow equations can thus be used to calculate the surface heat transfer coefficients on the food surface, which are then used to evaluate the internal heat transfer in the food [8]. A fully coupled analysis of internal and external heat transfer is also possible. In this case, continuity of the heat flux and temperature apply at the air–food interface [9]. The latter approach is more realistic and accurate but requires a transient version of the above model equations and more computational resources. Instead, the former approach suffices to quantify the magnitude of airflow effects. In this case, the surface heat transfer coefficient h is calculated as h¼
qs Ts Ta
(12:18)
where qs is the surface heat flux, Ts is the surface temperature, and Ta is the air temperature.
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12.4.3 NUMERICAL SOLUTION The governing equations for airflow are solved by means of a general purpose CFD code, e.g., ANSYS–CFX (ANSYS Inc., Canonsburg, PA) or Fluent (Fluent, Lebanon, NH) that use the finite volume method (FVM) of discretization. The FVM starts from the integral form of the governing equations. The computational domain is subdivided into a number of interconnected but nonoverlapping subdomains called control volumes. Computational nodes are usually situated at the centroid of the control volumes. By application of the equations to the control volumes, the conservation form of the equations is transferred from the original infinitesimal scale to the discrete scale. Surface integrals and volume integrals are approximated in terms of values of the variables at the cell face and nodes, respectively. Cell face values are themselves expressed in terms of nodal values by means of interpolation. As a result, algebraic equations are obtained for all nodes that can be solved by well-known solution methods. The FVM can be easily applied to any geometry, as the mesh only defines the control volume boundaries. The combination of integration and interpolation, however, makes it difficult to apply higher order approximations on nonstructured grids. On nonstructured meshes control volumes cannot be reordered into a rectangular lattice.
12.4.4 EXPERIMENTAL APPROACHES Airflow during microwave heating could not be measured. A first study case was therefore performed under similar operating conditions for which experimental data were available to demonstrate the performance of the CFD model. The model was then used to investigate the mixed convection conditions that prevail in household microwave ovens. Details are given in Ref. [10]. A combination oven was also studied (Figure 12.2). In this study, the heat transfer coefficients were experimentally evaluated on each surface of the food and jet impingement heating was included as a convective boundary condition. Heat flux on the surface was measured by heat flux sensors (HFS) provided by Omega Engineering (model HFS-3). Simultaneously temperature of the food surface was also calculated using a fiber optic system (Fiso Technologies, Quebec, Canada). Given the ambient temperature of the oven (as set by the user), the flux and the surface temperature of the food, the heat transfer coefficient h was calculated for each surface of the food.
12.5 AIRFLOW IN A DOMESTIC MICROWAVE OVEN CFD was applied to study the mixed convection in a typical oven cavity of a domestic microwave oven [10]. The airspace in the microwave oven having a cylindrical food placed in the center of the oven was a 3D model. The governing airflow equations outlined above were solved numerically using the ANSYS–CFX code for laminar buoyant flow with typical positions of one inlet and one outlet. Natural, laminar forced, and combined convection modes were studied.
12.5.1 OVEN DESCRIPTION Figure 12.4 shows the household microwave oven cavity that was considered. The size of the cavity is 280 mm wide by 280 mm deep by 200 mm high. At low velocity, air enters the cavity from a screen of 150 mm wide and 40 mm high (the inlet) on the left hand side wall. Air leaves the cavity from a 950 mm wide and 850 mm high screen (the outlet) on the opposite wall through suction. A disk-shaped food product of 100 mm diameter and 25 mm thickness is
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Outlet
Inlet
(a)
Food Cavity wall
(b)
Food surface
FIGURE 12.4 Geometry model of a microwave oven with (a) a cylindrical food and (b) computational mesh. (From Verboven, P., Datta, A.K., Nguyen, T.A., Scheerlinck, N., and Nicolaı¨, B.M. J. Food Eng., 59, 181, 2003. With permission from Elsevier.)
positioned on the turntable, which rotates at 6 rev min1 . In case of pure natural convection, only a quarter of the oven needed be modeled due to symmetry. The full cavity was modeled for the forced convection and mixed convection cases. The thermal performance of the oven was investigated from two perspectives: (a) the magnitude and distribution of the surface heat transfer coefficient on the food surface, and (b) the airflow patterns in the cavity. In this modeling study, the food surface was set at a constant temperature.
12.5.2 COMPUTATIONAL MESH A block-structured mesh was used on the oven geometry, with refinements near the surfaces of the food and the cavity walls in order to accurately resolve the velocity and thermal
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Average h (W m–2 ⬚C–1)
8 Natural convection
7
6
5
Forced convection
4
3 0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Average grid size (mm)
FIGURE 12.5 Mesh convergence graph. (From Verboven, P., Datta, A.K., Nguyen, T.A., Scheerlinck, N., and Nicolaı¨, B.M. J. Food Eng., 59, 181, 2003. With permission from Elsevier.)
boundary layers. A typical mesh consisted of 236,000 control volumes (Figure 12.4). A mesh refinement study was performed with mesh sizes ranging from 0.33 mm down to 0.04 mm at the food surface. Figure 12.5 shows how convergence was achieved as the mesh was refined. Solutions on three successively refined meshes display convergence for natural and forced convection separately. The use of the higher order discretization schemes results in an excellent mesh dependence reduction. Using the Richardson extrapolation method, the 1 convergence error was 0:005 W m2 C (<0:1%) on the finest mesh for natural convection 2 1 and 0:04 W m C (<1%) for forced convection, the latter on a coarser mesh [10].
12.5.3 NATURAL AND FORCED CONVECTION HEATING MODES The flow patterns and surface heat transfer coefficients for the natural and low-velocity forced convection modes were analyzed [10]. Totally different airflow exists for the two operational modes (Figure 12.6). In natural convection, a plume establishes due to the microwave heating of the food, while the air stays colder. In forced convection, air travels from inlet to outlet with secondary airflow around the food. It was demonstrated by CFD computation that for a typical refreshment airflow of 0:1 m s1 through the inlet, the surface heat transfer coefficients of natural convection (211 W m2 C1 ) will be in the same range 1 as forced convection conditions (17 W m2 C ).
12.5.4 FLOW PATTERNS
AND
HEAT TRANSFER COEFFICIENTS
IN A
MICROWAVE OVEN
Due to the similar strength of natural and forced convection airflow, mixed convection will exist in the cavity, resulting in complex flow patterns such as those in Figure 12.7. Computations were performed with increasing air velocity magnitude at the inlet of the cavity. In the range from 0.1 to 0:5 m s1 it is shown in the figure that the effect of natural convection gradually disappears. At 0:1 m s1 , the incoming air is immediately drawn towards the food by the downward buoyant flow near the cavity walls. At 0:2 m s1 , this effect is less pronounced and the penetration of the forced flow in the space around the food occurs further into the cavity. At 0:5 m s1 , the dominating effect of the natural convection has completely disappeared and a forced flow from inlet to outlet is established, without fresh air penetrating
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0.3 m s–1
(a)
(b)
0.1 m s–1
FIGURE 12.6 Velocity patterns in the cavity for (a) natural convection and (b) forced convection. (From Verboven, P., Datta, A.K., Nguyen, T.A., Scheerlinck, N., and Nicolaı¨, B.M. J. Food Eng., 59, 181, 2003. With permission from Elsevier.)
the food zone directly. The corresponding effects on the thermal field are considerable as shown in Figure 12.7. The average surface heat transfer coefficient on the top surface for 0.1, 1 0.2, and 0:5 m s1 were respectively 3.0, 4.7, and 4:4 W m2 C . On the side surface of 2 1 the foods, the values were 6.7, 6.4, and 7:8 W m C . It is evident from this study that the surface heat transfer coefficient does not simply scale with air velocity magnitude, since the flow patterns are considerably different for each case. Model-based design of the cavity can therefore only rely on distributed approaches such as CFD.
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Z
Z Y
Y
X
X
Inlet air velocity 0.1 m s–1
Z Y
Z X
Y
X
Inlet air velocity 0.2 m s–1
Z Y
Z X
Y
X
Inlet air velocity 0.5 m s–1
FIGURE 12.7 Airflow pattern (left) and temperature field (right) in a microwave cavity for different air velocity magnitudes. Temperatures are plotted for range from 208C (white) to 408C (black) on a vertical cross section through the cavity.
Furthermore, significant variation of the surface heat transfer exists along the individual surfaces of the food (Figure 12.8). It was shown, however, that the observed simulated heating rate distribution is in reality reduced significantly by the effects of thermal radiation [10].
12.6 COMBINED AIRFLOW AND MICROWAVE HEATING IN A JET IMPINGEMENT OVEN The airflow in forced convection ovens has been studied by CFD and was first achieved by Verboven et al. [6,7]. The combination of high-velocity forced airflow and microwaves could be useful for optimal control of the food temperature and quality [1]. Combined jet impingement and microwave heating was studied in a Thermador dual microwave jet oven. A model was solved combining heat transfer and Maxwell’s equations. To solve Maxwell’s equations, a finite element software, ANSYS version 7.0 (Canonsburg, PA) was used. The thermal
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Air inlet side 8
Air outlet side Combined convection
7
h (W m−2 ⬚C−1)
6 5 4 3
Natural convection
2
Forced convection
1 0 0.050
0.025
0.000
0.025
0.050
Radial distance on top surface of food (m)
FIGURE 12.8 Distribution of the surface heat transfer coefficient on the food surface in a microwave cavity, CFD calculation at air velocity of 0.1 m s1. (From Verboven, P., Datta, A.K., Nguyen, T.A., Scheerlinck, N., and Nicolaı¨, B.M. J. Food Eng., 59, 181, 2003. With permission from Elsevier.)
problem was solved using another finite element code FIDAP version 8.62 (Fluent Inc., Lebanon, NH).
12.6.1 OVEN DESCRIPTION The schematic of the Thermador dual microwave jet oven is given in Figure 12.9. Microwaves are launched from the top and the forced air enters through holes distributed throughout the bottom floor. A rectangular food item is considered at the center of the cavity.
12.6.2 COMPUTATIONAL MESH The finite element mesh of the oven cavity is given in Figure 12.10. Past studies [11] suggest a minimum of seven elements per wavelength for convergence of the electromagnetic
x
FIGURE 12.9 Schematic of the Thermador dual microwave jet oven.
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FIGURE 12.10 Finite element mesh for electromagnetic computations.
simulation. The actual wavelength inside the microwave cavity is not known and depends not only on the dielectric properties but also on the cavity dimensions. A detailed convergence study was done to select the appropriate number of finite elements. The seven elements per wavelength were used only as a guiding figure. The microwave oven is symmetric about a vertical plane passing through the center of the oven (left and right symmetry). So, only half the cavity, half the food, and half the waveguide are modeled in ANSYS. Because of the symmetry, there would be no normal component of the magnetic field on this imaginary middle plane, and that forms the new boundary condition for the model. Figure 12.11 shows the convergence study on the total number of elements in this half cavity and can be considered a good representation of convergence. A total of 120,000 elements were used for the final simulation.
Total power absorbed (Normalized)
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
60,000 75,000 90,000 105,000 120,000 135,000
Total number of elements
FIGURE 12.11 Convergence graph of electromagnetics computation.
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12.6.3 EFFECT
OF IMPINGEMENT
HEATING
Jet impingement heating is modeled as a surface convection phenomenon, with a constant surface heat transfer coefficient on each of the food surfaces and a constant ambient temperature. The flux measurement for each food surface is given in Figure 12.12 and illustrates significant variation. Figure 12.13 shows a comparison between the measured and simulated temperatures for hot spot heating at power level 1 (of the microwave oven) of microwave only heating. The figure also shows very distinctly the power cycling of the magnetron for power level 1. The match between the two temperature graphs is great at lower temperatures, but can be seen to be deteriorating as temperature rises above 508C, due to moisture loss becoming a more significant player at higher temperatures. At the bottom of Figure 12.13 the hot spot temperature variation with time for combined microwave and air jet impingement heating is shown. The hot spot for combination heating is different from that of MW only in the heating process. It is also interesting to note that the temperature in combination heating follows that of jet impingement heating during the initial times (not shown here) and then tends towards that of microwave heating. This is because the location of the point is just under the surface and hence the jet heating is very dominant during the initial times. But as the temperature rises and the flux decreases, the effect of microwave heating becomes more prominent. Figure 12.14 shows temperature distributions after 2 min of heating along a section cut through the middle of the half food. Figure 12.14a shows the contour plots for microwave only heating (power level 1). The combination heating temperature contour plot (Figure 12.14b) clearly depicts the advantages of the combination oven. There is volumetric heating of microwaves along with higher surface temperature of jet impingement that can reduce sogginess and provide browning.
7000
Surface heat flux (W m−2)
6000
5000
4000
3000 Top surface Front/back Bottom surface Right surface Left surface
2000
1000
0
0
15
30
45
60 Time (s)
75
90
105
120
FIGURE 12.12 Surface heat flux on the food during jet impingement heating as measured by heat flux sensors.
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60 Experimental Simulation
Temperature (⬚C)
55 50 45 40 35 30 25 0
20
40
60 Time (s)
80
100
120
80
100
120
90 Simulation Experimental
Temperature (⬚C)
80 70 60 50 40 30 0
20
40
60 Time (s)
FIGURE 12.13 Food temperature at the hot spot during microwave only heating (top) and jet impingement-microwave combination heating (bottom).
FIGURE 12.14 Temperature profiles in a food section during (a) microwave only heating and (b) combination jet impingement-microwave heating.
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12.7 CONCLUSIONS The use of modeling was demonstrated for the purpose of heating efficiency, temperature uniformity, and food quality in microwave ovens. The multiphysics problem (airflow, heat transfer, and electromagnetics) was dealt with by different modeling approaches, using CFD, CHT, and electromagnetic calculations. The complete solution of the transient multiphysics problem has today not been achieved and remains a challenge to the food engineer. Finally, the important issue of moisture transport in combination heating should also be considered.
NOMENCLATURE B cpa cps Ch E g H h Ks K Pin P P qs qgen T U aa b « «0 «0 «00eff «t h ht m ra rs st ˆ
magnetic flux density (T) 1 air specific heat (J kg1 C ) 1 food specific heat (J kg1 C ) constant electric field (V m1 ) gravity vector (m s2 ) magnetic field (A m1 ) surface heat transfer coefficient (W m2 C1 ) food thermal conductivity (W m1 8C1) 2 turbulence kinetic energy (m2 s ) 3 input power (W m ) absorbed power (W m3 ) pressure (Pa) surface heat flux (W m2 ) volumetric heat generation (W m3 ) temperature (8C) air velocity vector (m s2 ) 1 air thermal diffusivity (m2 s ) air volumetric expansion coefficient (K1 ) permittivity (F m1 ) permittivity of the free space (F m1 ) component of permittivity (F m1 ) component of permittivity (F m1 ) 3 turbulence energy dissipation rate (m2 s ) 1 1 air dynamic viscosity (kg m s ) 1 turbulent viscosity (kg m1 s ) 2 magnetic permeability (N A ) air density (kg m3 ) food density (kg m3 ) constant angular frequency of the microwaves (s1 )
SUBSCRIPTS a m n s t t
air magnetron normal food surface turbulence tangential
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REFERENCES 1. A.K. Datta, and H. Ni. Infrared and hot air assisted microwave heating of foods for control of surface moisture. Journal of Food Engineering, 51: 355–364, 2002. 2. H. Ni, A.K. Datta, and K.E. Torrance. Moisture transport in intensive microwave heating of biomaterials: A multiphase porous media model. International Journal of Heat and Mass Transfer, 42(8): 1501–1512, 1999. 3. H. Ni, A.K. Datta, and R. Parmeswar. Moisture loss as related to heating uniformity in microwave processing of solid foods. Journal of Food Process Engineering, 22(5): 367–382, 1999. 4. C. Saltiel and A.K. Datta. Heat and mass transfer in microwave processing. Advances in Heat Transfer, 32: 1–94, 1998. 5. A.K. Datta, S.S.G. Geedipalli, and M. Almeida. Microwave combination heating. Food Technology, 59(1): 36–40, 2005. 6. P. Verboven, N. Scheerlinck, J. De Baerdemaeker, and B.M. Nicolaı¨. Computational fluid dynamics modeling and validation of the isothermal airflow in a forced convection oven, Journal of Food Engineering, 43(1): 41–53, 2000. 7. P. Verboven, N. Scheerlinck, J. De Baerdemaeker, and B.M. Nicolaı¨. Computational fluid dynamics modeling and validation of the temperature distribution in a forced convection oven, Journal of Food Engineering, 43(2): 61–73, 2000. 8. P. Verboven, B.M. Nicolaı¨, N. Scheerlinck, and J. De Baerdemaeker. The local surface heat transfer coefficient in thermal food process calculations: A CFD approach. Journal of Food Engineering, 33: 15–35, 1997. 9. F. Tanaka, P. Verboven, N. Scheerlinck, K. Morita, K. Iwasaki, and B. Nicolaı¨. Investigation of far infrared radiation heating as an alternative technique for surface decontamination of strawberry. Journal of Food Engineering, 79(2): 445–452, 2007. 10. P. Verboven, A.K. Datta, T.A. Nguyen, N. Scheerlinck, and B.M. Nicolaı¨. Computation of airflow effects on heat and mass transfer in a microwave oven. Journal of Food Engineering, 59: 181–190, 2003. 11. H. Zhang and A.K. Datta. Coupled electromagnetic and thermal modeling of microwave oven heating of foods. The Journal of Microwave Power and Electromagnetic Energy, 35(2): 71–85, 2000.
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Thermal Sterilization of Food Using CFD A.G. Abdul Ghani and Mohammed M. Farid
CONTENTS 13.1
Introduction ............................................................................................................. 331 13.1.1 CFD and the Food Industry....................................................................... 333 13.2 Simulations of Thermal Sterilization in a Vertical Can ........................................... 333 13.2.1 Computational Grid ................................................................................... 333 13.2.2 Physical Properties ...................................................................................... 334 13.2.3 Assumptions Used in the Numerical Simulation ........................................ 335 13.2.4 Governing Equations and Boundary Conditions........................................ 336 13.2.5 Results of Simulation.................................................................................. 336 13.3 Simulations of Thermal Sterilization in a Top Insulated Can ................................. 337 13.3.1 Results of Simulation.................................................................................. 337 13.4 Simulation of Bacteria Deactivation and Vitamins Destruction during Sterilization ............................................................................... 339 13.4.1 Convection and Temporal Discretization ................................................... 339 13.4.2 Governing Equations for Heat, Mass, and Momentum Transfer............... 340 13.4.3 Kinetics of Bacteria Deactivation and Vitamin Destruction ...................... 340 13.4.4 Results of Simulation.................................................................................. 341 13.5 Simulation of a Horizontal Can during Sterilization ............................................... 343 13.6 Conclusions .............................................................................................................. 344 Nomenclature ..................................................................................................................... 344 References .......................................................................................................................... 345
13.1 INTRODUCTION Conventional canning processes extend the shelf life of food products and make the food safe for human consumption by destroying the pathogenic microorganisms. Despite the significant advances made in the techniques used for food preservation, canning is still the most effective method. Sterilization of canned food is usually done by steam heating to a temperature sufficient to kill the microorganisms. The time required for the sterilization process depends on the product specifications, container type and size, and its orientation, as well as the heating medium characteristics. Excessive heating will affect food quality and its nutritive properties. Most mathematical models available for the analysis of thermal sterilization of food in cans are based on conduction heating, which has simplified analytical and numerical
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solutions. However, detailed analysis of convection heating in the liquid that is heated in a can is important. During the natural convection heating, the velocity in the momentum equations is coupled with temperature in the energy equation, because the movement of fluid is solely due to buoyancy force. Because of this coupling, the energy equation needs to be solved simultaneously with the momentum equations. Estimation of the heat transfer rate to the food in the can is essential to optimize processing conditions and improve product quality. Also a better understanding of the mechanism of the heating process will lead to an improved performance in the process and may be to some energy savings. Basic principles for determining the performance of different, but related processes have been presented [1,2]. The numerical predictions of the transient temperature and velocity profiles during natural convection heating of canned liquid foods in a still retort have been carried out [3]. Water was used to simulate liquid food, which was heated in a cylindrical can using steam. The water in the can was found stratified with an increasing temperature toward the top of the can. They predicted significant internal circulation of the fluid at the bottom of the can and showed that the slowest heating zone (SHZ) is doughnut shaped and is lying close to the bottom of the can at about one-tenth of the can height. Sterilization of a viscous liquid food in a metal can positioned upright and heated from all sides (Tw ¼ 1218C) in a still retort was simulated [4]. The equations of continuity, momentum, and energy conservation for an axisymmetric case were solved to provide plots of temperature, velocity, and streamlines for natural convection heating and the results were compared with pure conduction contour plots. They also presented a simulation for the same can when its bottom and top surfaces were insulated [4]. The model liquid food was assumed to have viscosity varying with temperature but having constant specific heat and thermal conductivity. The results indicated that natural convection tends to push the slowest heating region to the bottom of the can. Sterilization of a can filled with a viscous liquid sodium carboxymethyl cellulose (CMC), heated by condensing steam on all sides and also with a top insulated (i.e., the presence of an air gap), was recently simulated [5]. The temperature difference from top to bottom of the can at the end of 2574 s of heating was 128C for the can with top insulated whereas it was 108C for the case of can heated from all sides. The results also show that the locations of the SHZ for both cases are similar. This is due to the strong effect of the natural convection current, even when the liquid was highly viscous. In some of the simulations, the wall was not assumed to be at a constant temperature and instead a convective boundary was implemented [5]. The results of such simulations showed very little difference from those predicted for constant wall temperatures, which is attributed to the large heat transfer coefficient of the condensing steam. In the work presented in this chapter, sterilization of canned liquid food in a still retort was numerically studied and analyzed using computational fluid dynamics (CFD). Natural convection heating within a can of liquid food during sterilization is simulated by solving the governing equations for continuity, momentum, and energy conservation for an axisymmetric case using a commercial CFD package (PHOENICS). The results were presented in the form of transient temperature, concentration profiles, velocity profiles, and flow patterns. Different liquid foods were used in the simulations; sodium carboxymethyl cellulose, carrot–orange soup, and concentrated cherry juice were used as the model liquids. Density variations are governed by the Boussinesq approximation (a commonly used assumption for buoyancy problems, whereby the density variations are not explicitly modeled but their effect is represented by a buoyancy force that is proportional to temperature gradient). Specific heat, thermal conductivity, and volume expansion coefficient were all assumed constants, while viscosity was assumed function of temperature.
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13.1.1 CFD AND THE FOOD INDUSTRY Computational fluid dynamics offers process engineers a powerful design and investigative tool. Its application would assist in a better understanding of the complex physical mechanisms that govern the thermal, physical, and rheological properties of food materials. CFD has recently been applied to food processing applications. It has seen applications in many different processing industries, including airflow in clean rooms, ovens, and chillers; flow of foods in continuous-flow systems; and convection patterns during thermal processing [6]. When considering the flow of food products, it is often necessary to take the rheological nature of a food into account because this will dictate its flow behavior. Most foods exhibit some form of non-Newtonian behavior and many different flow models have been used to describe such behavior. As for turbulence problems, the inclusion of a non-Newtonian flow model requires the solution of an extra equation. However, it should be noted that the current state of CFD does not permit the prediction of turbulent flow for non-Newtonian fluids; this is at the forefront of numerical non-Newtonian rheology research [7]. The PHOENICS code used in our simulations is based on the finite volume method, as developed by Patankar and Spalding [8]. The key characteristic of this method is the immediate discretization of the integral equation of flow into the physical 3D space, i.e., the computational domain covers the entire can, which is divided into a number of divisions in the three dimensions. The details of this code can be found in the PHOENICS manuals, especially the PHOENICS input language (PIL) manual [9]. The observation of the movement of the SHZ is a difficult task and requires knowing detailed transient flow patterns and temperature profiles, due to the complex nature of heat transfer in natural convection heating. For this purpose, the partial differential equations, governing such a system, need to be solved in their entirety using numerical techniques. The results were compared with those obtained by Kumar and Bhattacharya [10] for the viscous liquid, and with Datta and Teixeira [3] for water as a liquid food. The following four case studies are discussed in this chapter.
13.2 SIMULATIONS OF THERMAL STERILIZATION IN A VERTICAL CAN Sterilization of liquid food contained in a metal can positioned upright and heated at 1218C from all sides was simulated and the results were presented. Sodium carboxymethyl cellulose was used as a model liquid. The computations were performed for a can with a radius of 0.0405 m and height of 0.111 m (Figure 13.1). The governing equations for continuity, momentum, and energy conservation were solved using a commercial CFD package (PHOENICS), which is based on finite volume method. Transient flow patterns and temperature profiles within the model liquid (sodium carboxymethyl cellulose) were simulated. The model liquid food was assumed to have constant properties except for the viscosity (temperature dependent) and density (Boussinesq approximation). The action of natural convection forces the SHZ to migrate toward the bottom of the can as expected. The magnitude of the axial velocity was found to be in the range of 105 to 104 m s1 and this magnitude varied with time and position in the can.
13.2.1 COMPUTATIONAL GRID The boundary layer occurring at the heated walls and its thickness are very important parameters to the numerical convergence of the solution. Temperature and velocities have their largest variations in this region. To adequately resolve this boundary layer flow, i.e., to keep the discretization error small, the mesh should be optimized and a large
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Computational Fluid Dynamics in Food Processing T = Tw = 1218C, vr = 0, vz = 0 0.081 m
g
T =Tw = 1218C vr = 0 vz = 0
0.111 m
T = Tw = 1218C, vr = 0, vz = 0 Initial conditions T =T0, vr = 0, vz = 0
FIGURE 13.1 Grid mesh used in the simulations with 3519 cells: 69 in the axial direction and 51 in the radial direction (the mesh is for a full can).
concentration of grid points is needed in this region. If the boundary layer is not resolved adequately, the underlying physics of the flow is lost and the simulation will be erroneous. On the other hand, in the rest of the domain where the variations in the temperature and velocity are small, the use of a fine mesh will lead to increases in computation time without any significant increase in computation accuracy. Thus a nonuniform grid system is needed to resolve the physics of the flow properly. The nonuniform grid system was used in the simulations with 3519 nodal points (Figure 13.1): 69 in the axial direction and 51 in the radial direction, graded in both directions with a finer grid near the wall. The natural convection heating of CMC was simulated for 2574 s. It took 100 steps to achieve the first 180 s of heating, another 100 steps to reach 1000 s, and 300 steps for the total of 2574 s of heating. This required 63 h of CPU time on the UNIX IBM RS6000 workstations at the University of Auckland, New Zealand.
13.2.2 PHYSICAL PROPERTIES In the simulation of water and CMC, the viscosity was assumed to be a function of temperature. A second order polynomial used to define the viscosity as required by PHOENICS was of the form m ¼ a þ bT þ cT 2
(13:1)
Food materials are in general highly non-Newtonian and hence the viscosity is a function of both shear rate and temperature with a flow behavior index typically less than 1. Due to the
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extremely high viscosity of the CMC used in the simulation, which causes liquid velocities to be very low, the shear rate calculated from previous simulation [5] was found to be of the order of 0:01 s1 . Because of the low shear rate the viscosity may be assumed independent of shear rate and hence the fluid will behave as Newtonian fluid. This Newtonian approximation is valid for most liquid food materials such as tomato puree, carrot puree, green bean puree, apple sauce, apricot puree, and banana puree, which are regularly canned and usually preserved by heating [11]. The parameters a, b, and c used to calculate the values of viscosity of CMC at different temperatures were 4:135, 6:219 102 , and 2:596 104 , respectively. The variation of the density with temperature is usually expressed [12] as r ¼ r0 [1 b(T T0 )]
(13:2)
where b is the thermal expansion coefficient of the liquid, and T0 and r0 are the temperature and density at the reference condition [12]. The density was assumed constant in the governing equations except in the buoyancy term (Boussinesq approximation), where Equation 13.2 was used to describe its variation with temperature. For viscous liquids, the viscous forces are high and thus the Grashof number is low. This can be shown clearly for CMC at which Grashof number is in the range 102 –101 (using maximum temperature difference and maximum viscosity). The magnitude of the Grashof number gives a good indication whether the natural convection flow is laminar, transitional, or turbulent.
13.2.3 ASSUMPTIONS USED
IN THE
NUMERICAL SIMULATION
To simplify the problem, the following assumptions were made: . .
. .
Axisymmetry, which reduces the problem from 3D to 2D. Heat generation due to viscous dissipation is negligible; this is due to the use of a high viscous liquid [13]. Boussinesq approximation is valid. Specific heat (CP ), thermal conductivity (k), and volume expansion coefficient ( b) are constants (Table 13.1). TABLE 13.1 Properties of the Liquid Food (CMC) Measured at Room Temperature Used in the Simulation Property Density ( r)a Specific heat (CP ) Thermal conductivity (k) Volumetric expansion coefficient ( b) Consistency index (m0 ) Activation energy (E )
Value 950 kg m3 4100 J kg1 K1 0:7 W m1 K1 0:0002 K1 0:002232 Pa sn 30:74 103 kJ kg mol1
Source: From Kumar, A. and Bhattacharya, M., Int. J. Heat Mass Tran., 34, 1083, 1991. a
r ¼ constant and varies only in the gravitational force term in the momentum Equation 13.5 according to Equation 13.2.
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.
Assumption of no-slip condition at the inside wall of the can is valid. Condensing steam maintains a constant temperature condition at the outer surface of the can. Thermal boundary conditions are applied to liquid boundaries rather than the outer boundaries of the can, because of the low thermal resistance of the can wall.
13.2.4 GOVERNING EQUATIONS
AND
BOUNDARY CONDITIONS
The partial differential equations governing natural convection motion in a cylindrical space are the Navier–Stokes equations in cylindrical coordinates [14]. The boundary conditions used were as follows: At the can boundary, r ¼ R, T ¼ T w , vz ¼ 0
vr ¼ 0
for
0zH
(13:3)
vr ¼ 0
for
0rR
(13:4)
@vz ¼0 @r
vr ¼ 0
for
0zH
(13:5)
@T ¼ 0, vz ¼ 0 @z
vr ¼ 0
for
0rR
(13:6)
At the bottom of the can, z ¼ 0, T ¼ Tw , vz ¼ 0 At symmetry, r ¼ 0, @T ¼ 0, @r At the top of the can, z ¼ H,
Initially the fluid is at rest and is at a uniform temperature T ¼ Tw , vz ¼ 0,
vr ¼ 0
at
0 r R,
0zH
(13:7)
The same set of governing equations describes a wide variety of flow situations in liquids and gases. The boundary and initial conditions (Equation 13.3 through Equation 13.7) are the most important parameters that specify the desired solution among many solutions possible for the set of equations. To obtain a good convergence of the numerical solution to these governing partial differential equations, it was necessary to apply a proper under-relaxation or an overrelaxation. The improper over-relaxation or under-relaxation parameter can easily make the computations impracticably long. Many of these optimum parameters are not known at the initial stage and can only be found through numerical experimentation.
13.2.5 RESULTS
OF
SIMULATION
Figure 13.2 shows the temperature profile, velocity vector, and flow pattern of the CMC in a can heated by steam condensing along its outside surface. Figure 13.2a shows the influence of natural convection current on the movement of the SHZ in the can (i.e., the location of the lowest temperature at a given time). It shows that the location of the SHZ is not at the geometric center of the can as it is in the case of conduction heating. As heating progresses,
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84 87 90 92 95 97 100 103 105 108 111 113 116 118 121
(a)
0.0e+0 3.1e+5 6.2e−5 9.3e−5 1.2e−4 1.5e−4 1.9e−4 2.2e−4 2.5e−4 2.8e−4 3.1e−4 3.4e−4 3.7e−4 4.0e−4 4.3e−4
(b)
(c)
FIGURE 13.2 (See color insert following page 462.) (a) Temperature profile, (b) velocity vector, and (c) flow pattern of CMC in a vertical can heated by condensing steam after 1157 s. The right-hand side of each figure is centerline. (From Abdul Ghani, A.G., Farid, M.M., Chen, X.D., and Richards, P.J., J. Food Eng., 41, 55, 1999.)
the SHZ is pushed more toward the bottom of the can. The SHZ keeps moving during heating and eventually stays in a region that is about 10% –12% of the can height from the bottom. Both Figure 13.2b and Figure 13.2c show the recirculating flow created by the buoyancy force, created by temperature variation (from the wall to the core). The secondary flow formation was evident in the case studied as shown clearly in Figure 13.2b and Figure 13.2c.
13.3 SIMULATIONS OF THERMAL STERILIZATION IN A TOP INSULATED CAN In this section, the effect of the presence of an air gap (i.e., head space) at the top of the can on the heat transfer rate is presented. This is important since it represents a real practical situation. The governing equations, physical properties, size of can, and assumptions used to simplify the problem are the same as those used in the previous case. The boundary conditions used were the same as those used earlier in the previous case except for the top of the can, which was assumed insulated as shown in Equation 13.8. At the top of the can, z ¼ H, @T ¼ 0, vr ¼ 0, vz ¼ 0 @z
at
z ¼ H (can top), 0 r R
(13:8)
The assumption of top insulation was used to represent the case of a can with a head space, which is the common situation for canned foods.
13.3.1 RESULTS
OF
SIMULATION
Figure 13.3 shows the velocity vector in a can filled with CMC and heated at 1218C from the bottom and sides only (i.e., top insulated) after 1157 s of heating. The velocity vector
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0.0e+0 2.5e−5 5.0e−5 7.6e−5 1.0e−4 1.3e−4 1.5e−4 1.8e−4 2.0e−4 2.3e−4 2.5e−4 2.8e−4 3.0e−4 3.3e−4 3.5e−4
FIGURE 13.3 Velocity vector profile (m s1) in a top insulated can filled with CMC and heated by condensing steam after 1157 s. The right-hand side of the figure is centerline.
field shown in Figure 13.2b (for can heated from all sides) is similar to that shown in Figure 13.3 (top insulated) with a slightly higher velocity due to more efficient heating in the former. The major difference between the heating in both cases is discussed in the next paragraph. Figure 13.4 shows the temperature profiles in the top insulated can filled with CMC and heated by condensing steam for different periods of time during thermal sterilization. This figure shows that the SHZ extends from the center of the can to the wall and tends to migrate to the bottom of the can as heating progresses. The results do not show any major difference from that shown for the can heated from all sides. Figure 13.2a and Figure 13.4c show that
40 46 52 57 63 69 75 81 86 92 98 104 110 115 121
(a)
40 46 52 57 63 69 75 81 86 92 98 104 110 115 121
(b)
108 109 110 111 112 113 114 115 116 116 117 118 119 120 121
83 86 88 91 94 96 99 102 105 107 110 113 116 118 121
(c)
(d)
FIGURE 13.4 (See color insert following page 462.) Temperature profiles in a can filled with CMC and heated by condensing steam (top insulated) after periods of (a) 54 s, (b) 180 s, (c) 1157 s, and (d) 2574 s. The right-hand side of each figure is centerline. (From Abdul Ghani, A.G., Farid, M.M., Chen, X.D., and Richards, P.J., J. Food Eng., 41, 55, 1999.)
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the temperature difference from top to bottom of the can at the end of 1157 s is almost the same. These two figures show that the location of the SHZ and its shape for both cases are similar. The observed difference in the temperature contour at the top of the can between the two cases is not sufficient to make a major change in the heating process. The convection currents are strong enough to minimize this difference even for such a viscous fluid as the one used in the current simulation.
13.4 SIMULATION OF BACTERIA DEACTIVATION AND VITAMINS DESTRUCTION DURING STERILIZATION The objective of this part of the work is to provide an improved quantitative understanding of the effect of natural convection upon bacteria inactivation and vitamins destruction during thermal sterilization of canned liquid foods. A computational procedure was developed for predicting the changes in live bacteria concentration and in vitamins such as vitamins C (ascorbic acid), B1 (thiamin), and B2 (riboflavin) during sterilization processing of canned food. The numerical approximations and model parameters were the same as those used in the previous simulations.
13.4.1 CONVECTION
AND
TEMPORAL DISCRETIZATION
An important consideration in CFD is the discretization of the convection terms in the finite volume equations. The accuracy, numerical stability, and the boundedness of the solution depend on the numerical scheme used for these terms. The central issue is the specification of an appropriate relationship between the convected variables, stored at the cell center, and its value at each of the cell faces [16]. The convection discretization scheme used for all variables in our simulations is the hybrid-differencing scheme (HDS). The HDS of Spalding [17] used in PHOENICS switches the discretization of the convective terms between central differencing scheme (CDS) and upwind differencing scheme (UDS) according to the local cell Peclet number. The cell Peclet number Pe (ratio of convection to diffusion) for bacteria and vitamins within the flow domain in the z-direction is Pe ¼
vz Dz a
(13:9)
where v and Dz are respectively the typical velocity and typical distance of the cell in the z-direction. The mass diffusivity a of the bacteria and vitamins in the fluid may be described by Stokes–Einstein equation: a¼
KT 6pma
(13:10)
where K is the Boltzman constant, T is the temperature, m is the apparent viscosity, and a is the radius of the particle. The calculated cell Peclet numbers within the flow domain in this study are of the order of 104 for bacteria and vitamins, and hence it is reasonable to ignore the diffusion of bacteria and vitamins, thereby reducing computation time. Within PHOENICS, the temporal discretization is fully explicit.
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13.4.2 GOVERNING EQUATIONS
FOR
HEAT, MASS, AND MOMENTUM TRANSFER
The governing equations of continuity, momentum, and energy are the same as those used in the previous section. In addition to these equations, the following equations for concentrations of bacteria and vitamins are introduced: Mass balance on bacteria @Crb @Crb @Crb 1 @ @Crb @ 2 Crb r þ vr þ vz ¼ Db kb Crb þ r @r @t @r @z @r @z2
(13:11)
Mass balance on vitamins @Crv @Crv @Crv 1 @ @Crv @ 2 Crv r þ vr þ vz ¼ Dv kv Crv þ r @r @t @r @z @r @z2
(13:12)
The relative concentrations of bacteria and vitamins (Crb and Crv) in Equation 13.15 and Equation 13.16 are taken as a dimensionless species concentrations, which are defined as the ratio of real time concentrations (Cb and Cv) to the initial concentrations (Cbo and Cvo) multiplied by 100. The boundary conditions used for bacteria deactivation and vitamins destruction are: At the can boundary, r ¼ R,
@Crb ¼0 @r
At the bottom of the can, z ¼ 0, At symmetry, r ¼ 0,
@Crb ¼0 @z
@Crb ¼ 0 and @r
At the top of the can, z ¼ H,
@Crb ¼0 @z
and and
@Crv ¼0 @r @Crv ¼0 @z
@Crv ¼0 @r and
@Crv ¼0 @z
(13:13) (13:14) (13:15) (13:16)
Other boundary conditions for temperature and velocities are the same as those used in Section 13.2.4 (Equation 13.3 through Equation 13.6). The initial conditions used are: T ¼ T0, Crb ¼ 100, Crv ¼ 100, vr ¼ 0, and vz ¼ 0. The model liquid is assumed to have constant properties except for viscosity (temperature dependent) and density (Boussinesq approximation). The simplifications used in the simulation are the same as those used in Section 13.2.3. Further, the effect of molecular diffusion of bacteria and vitamin C is neglected due to the relatively strong influence of the convection motion. This assumption has been verified by Ghani et al. [18], which allows omitting the diffusion terms in Equation 13.11 and Equation 13.12.
13.4.3 KINETICS
OF
BACTERIA DEACTIVATION AND VITAMIN DESTRUCTION
The rate of bacteria deactivation and vitamin destruction is usually assumed to follow first order kinetics [19]. It is known that the reaction rate constants are functions of temperature and are usually described by Arrhenius equation: For bacteria:
Eb kb ¼ Ab exp Rg T
(13:17)
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TABLE 13.2 Kinetic Data for Some Reaction Processes in the Concentrated Cherry Juice Used in Our Simulations D 121 (min) Reported
Property For bacteria deactivation Clostridium botilinum For vitamins destruction Ascorbic acid (C) Thiamin (B1) Riboflavin (B2)
D 121 (min) Used
0.1–0.3
0.2
245 38–380 2800
245 38 2800
Ea (kJ mol1 ) Reported
Ea (kJ mol1 ) Used
265–340
300
65–160 90–125 100
100 90 100
Source: From Fryer, J.P., Pyle, D.L., and Rielly, C.D., in Chemical Engineering for the Food Industry, Blackie Academic and Professional, London, 1997.
For vitamins: kv ¼ Av exp
Ev Rg T
(13:18)
where Ab and Av are the reaction frequency factors, Eb and Ev are the activation energies for the two processes, respectively, Rg is the universal gas constant, and T is the temperature. Accurate kinetic parameters such as reaction rate constants and activation energy are essential to predict quality changes during food processing [20]. In food process engineering, the decimal reduction time (D) is used more often. The relationship between the reaction rate constant and the decimal reduction time is [21] kT ¼
2:303 DT
(13:19)
The decimal reduction times and activation energies of bacteria inactivation and destruction of vitamins C, B1, and B2 are represented in Table 13.2. The reaction rate constants kb and kv at 1218C for bacteria and different types of vitamins are calculated using Equation 13.19 and the reported values of D. Equation 13.17 and Equation 13.18 are then used to calculate the constants of Arrhenius equation Ab and Av. They were 2.5 1011 s1 for bacteria, 2.85 109, 8.5 108, and 2.48 108 s1 for vitamins C, B1, and B2, respectively. The magnitude of Grashof number for the viscous liquid used in our simulation is in the range of 102–103 (using maximum temperature difference and maximum viscosity), which gives a good indication that natural convection flow is laminar. The Arrhenius equation, used to describe the kinetics of the biochemical changes, is introduced to the existing software package using a FORTRAN code.
13.4.4 RESULTS
OF
SIMULATION
As discussed earlier, the effects of the temperature distribution in the can on bacteria inactivation and the destruction of different types of vitamins are studied by introducing their kinetics in the heat transfer analysis. Figure 13.5 represents the results of the simulation
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0 7 14 22 29 36 43 50 57 64 72 79 86 93 100
(a)
0.0e+0
0 6 12 17
8.8e −5 1.8e −4 2.6e −4 3.5e −4 4.4e −4
23 29 35 40 46 52
5.3e −4 6.2e −4 7.0e −4 7.9e −4 8.8e −4
57 63 69 75
9.7e −4 1.1e −3 1.1e −3 1.2e −3
80
(b)
(c)
FIGURE 13.5 (See color insert following page 462.) Deactivation of bacteria in a can filled with CMC and heated by condensing steam after (a) 180 s, (b) 1157 s, and (c) 2574 s, respectively. The right-hand side of each figure is centerline. (From Abdul Ghani, A.G., Farid, M.M., Chen, X.D., and Richards, P.J., J. Food Eng., 42, 207, 1999.)
for a metal can filled with CMC, steam heated from all sides (at 1218C). Figure 13.5a shows that during the early stage of heating, the bacteria are killed only at locations close to the wall of the can, and live bacteria concentration is not influenced by the flow pattern shown in Figure 13.2c. Figure 13.5b and Figure 13.5c show the results of the simulation after much longer time periods of 1157 and 2574 s, respectively. The bacteria concentration profiles are very different from those observed at the beginning of the heating. The liquid and thus the bacteria carried with it at the SHZ locations are exposed to much less thermal treatment than the rest of the product [22]. Figure 13.5b and Figure 13.5c show that bacteria inactivation is influenced significantly by both the temperature and the flow pattern observed in Figure 13.2. Profiles of temperature distribution, bacteria concentration, and concentrations of vitamins C (ascorbic acid), B1 (thiamin), and B2 (riboflavin) in a can filled with cherry juice during thermal sterilization were obtained through numerical simulations. These profiles are presented in Figure 13.6. The properties of concentrated cherry juice used in the current simulations are: r ¼ 1052 kg m3 , CP ¼ 3500 J kg1 K1 , k ¼ 0:554 W m1 K1 , and b ¼ 0:0002 K1 as reported by Hayes [23]. The simulation highlights the dependency of the concentration of vitamins on both temperature distribution and flow pattern as sterilization proceeds (Figure 13.6). The relative bacteria concentration in the SHZ shown in Figure 13.5 is a good measure of food sterility. However, in the case of vitamin destruction, it is necessary to calculate the vitamin average concentration in the whole can, which is calculated as the weighted average of the local concentrations as follows [24]:
Cave ¼
L X R 2 X rCDzDr R2 L Z¼0 r¼0
(13:20)
The average percentage destruction of the relative concentration of vitamin C is found to be about 25%. The corresponding concentrations for vitamins B1 and B2 are 70% and 3%, respectively, which show the strong influence of sterilization temperature on vitamin B1. Fellows [25] has reported a percentage loss of 50%–75% of vitamin B1 (Thiamin) in canned and bottled foods, which is in agreement with the results obtained from our simulation.
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Residual vitamin C (%)
Residual vitamin B1 (%)
Residual vitamin B2 (%)
FIGURE 13.6 (See color insert following page 462.) Vitamins C, B1, and B2 destruction in a can filled with concentrated cherry juice and heated by condensing steam after 1640 s. The right-hand side of each figure is centerline. (From Abdul Ghani, A.G., Farid, M.M., Chen, X.D., and Richards, P.J., 10th World Congress of Science and Technology, 1999.)
13.5 SIMULATION OF A HORIZONTAL CAN DURING STERILIZATION In this part of the work, sterilization of a canned liquid food in a metal 3D can lying horizontally and heated at 1218C from all sides was predicted and analyzed. Carrot–orange soup was used as a model liquid food. The properties of carrot–orange soup used in the current simulation were: r ¼ 1026 kg m3 , CP ¼ 3880 J kg1 K1 , k ¼ 0:596 W m1 K1 , and b ¼ 0:0002 K1 . The properties were calculated from the values reported [23,26] for all the food materials used in the soup, using their known mass fractions. A nonuniform grid system was used in the simulation with 105,000 cells: 50 in the radial direction, 70 in the vertical direction, and 30 in the angular direction, graded with a finer grid near the wall in radial and vertical directions. The natural convection heating of carrot–orange soup was simulated for 3000 s. It took 10 steps to achieve the first 200 s of heating, another 10 steps for the next 800 s, and the last 10 steps for the remaining 2000 s. This required 17 h of CPU time on the UNIX IBM RS6000 workstations at the University of Auckland. For the horizontal cylinder, the analysis must be based on 3D [27]. The buoyancy force caused by density variation with temperature was governed by the Boussinesq approximation shown in Equation 13.2, which was used in the body force term of the momentum equation in the radial direction. Figure 13.7 shows the radial–angular temperature profile of carrot–orange soup in a 3D cylindrical can lying horizontally and heated by condensing steam after 600 s at two different planes in the direction of (a) radial–angular plane; (b) radial–vertical plane. The can shown in this figure is in the horizontal position. The inclination shown is only to provide more clearly a 3D image. This figure shows the actual shape of the SHZ, which is settled toward the bottom surface of the can. The effect of natural convection in the horizontal can was found smaller than that in the vertical can due to the can having height greater than its diameter.
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(a)
(b)
FIGURE 13.7 (See color insert following page 462.) Radial–angular plane temperature profile of carrot– orange soup in a 3D cylindrical can lying horizontally and heated by condensing steam after 600 s at two different planes in the direction of (a) radial–angular plane and (b) radial–vertical plane. (From Abdul Ghani, A.G., Farid, M.M., and Chen, X.D., J. Food Eng., 51, 77, 2002.)
13.6 CONCLUSIONS CFD is a powerful tool for simulating a large number of food process operations such as thermal sterilization in cans. The CFD analysis presented in this chapter shows that the coldest region in a can during sterilization is influenced significantly by the free convection of the liquid food, which is induced by the heating at the can’s wall. This causes the coldest region of minimum bacteria inactivation to be pushed toward the bottom of the can, unlike conduction heating of solids where it usually lies at the geometric center of the can. A similar conclusion was reached for food sterilization in a horizontal can but with lower influence of the free convection. The simulations also show that the location of minimum damage to vitamins does not necessary coincides with the location of the slowest heating region due to the continuous free convection motion of the liquid.
NOMENCLATURE Ab Av a Cave Cb Cv Cbo Cvo Crb Crv CP DT Db Dv Eb Ev Gr
reaction frequency factor for bacteria (s1 ) reaction frequency factor for vitamins (s1 ) radius of the particle (m) weighted average local concentration of vitamins (kg m3 ) concentration of bacteria in food liquid (number of bacteria m3 ) concentration of the vitamins in food liquid (kg m3 ) initial concentration of bacteria (number of bacteria m3 ) initial concentration of vitamins (kg m3 ) relative bacteria concentration (Cb =Cbo ) relative vitamin concentration (Cv =Cvo ) specific heat of liquid food (J kg1 K1 ) decimal reduction time (min) diffusion coefficient of bacteria (m2 s1 ) diffusion coefficient of vitamins (m2 s1 ) activation energy of bacteria deactivation (kJ (kg mol)1 ) activation energy of vitamins destruction (kJ (kg mol)1 ) gbDTL3 r2 Grashof number, Gr ¼ m2
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g H K k kb kv L Pe p r R Rg t T Tw T0 vz vr vu z
345
acceleration due to gravity (m s2 ) height of the can (m) Boltzman constant thermal conductivity of liquid being heated (W m1 K1 ) reaction rate constant of bacteria at temperature T (s1 ) reaction rate constant of vitamin at temperature T (s1 ) height of the can (m) uDz Peclet number, Pe ¼ a pressure (Pa) radial position from center line (m) radius of the can (m) gas constant (kJ (kg mol)1 K1 ) heating time (s) temperature (8C) wall temperature (8C) initial temperature (8C) velocity in vertical direction (m s1 ) velocity in radial direction (m s1 ) velocity in angular direction (m s1 ) distance in vertical direction from the bottom (m)
GREEK SYMBOLS a b m r r0
thermal diffusivity (m2 s1 ) thermal expansion coefficient (K1 ) apparent viscosity (Pa s) density (kg m3 ) initial density (kg m3 )
REFERENCES 1. N. May. Guidelines No. 13, 16, and 17, the Campden and Chorleywood Food Research Association, 1997. 2. A. Wilbur. Unit operation for the food industries, Food Processing and Technology, Ohio State University, 125–136, 1996. 3. A.K. Datta and A.A. Teixeira. Numerically predicted transient temperature and velocity profiles during natural convection heating of canned liquid foods. Journal of Food Science 53(1): 191–195, 1998. 4. A. Kumar, M. Bhattacharya, and J. Blaylock. Numerical simulation of natural convection heating of canned thick viscous liquid food products. Journal of Food Science 55(5): 1403–1411, 1990. 5. A.G. Ghani, M.F. Mohammed, and X.D. Chen. A CFD simulation of the coldest point during sterilization of canned food. The 26th Australian Chemical Engineering Conference, Port Douglas, Queensland, 28–30 September 1998, No. 358. 6. G. Scott and P. Richardson. The application of computational fluid dynamics in the food industry. Trends in Food Science and Technology 8: 119–124, 1997. 7. S.D. Holdsworth. Rheological model used in the prediction of the flow properties of food products, a literature review. Transaction of Institute of Chemical Engineers 71(C4): 139–179, 1993. 8. S.V. Patankar and D.B. Spalding. A calculation procedure for heat, mass and momentum transfer in three dimensional parabolic flows. International Journal of Heat and Mass Transfer 15(10): 1787–1806, 1972. 9. PHOENICS Reference Manual, Part A: PIL, Concentration Heat and Momentum Limited, TR 200 A, Bakery House, London SW 19 5AU, UK.
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10. A. Kumar and M. Bhattacharya. Transient temperature and velocity profiles in a canned non-Newtonian liquid food during sterilization in a still-cook retort. International Journal of Heat and Mass Transfer 34(4=5): 1083–1096, 1991. 11. J.F. Steffe, I.O. Mohamed, and E.W. Ford. Rheological properties of fluid foods: data compilation. In M.R. Okos (ed.), Physical and Chemical Properties of Foods. St. Joseph, MI: Transaction of American Society of Agricultural Engineers, 1986. 12. B. Adrian. Heat Transfer. New York: John Wiley and Sons, 1993, pp. 339–340. 13. A.F. Mills. Basic Heat and Mass Transfer. New York: Irwin, 1995. 14. R.B. Bird, W.E. Stewart, and E.N. Lightfoot. Transport Phenomena. New York: John Wiley and Sons, 1976. 15. A.G. Ghani, M.M. Farid, X.D. Chen, and P.J. Richards. Numerical simulation of natural convection heating of canned food by computational fluid dynamics. Journal of Food Engineering 41(1): 55–64, 1999. 16. M.R. Malin and N.P. Waterson. Schemes for convection discretization on PHOENICS. The PHOENICS Journal 12(2): 173–201, 1999. 17. D.B. Spalding. A novel finite-difference formulation for differential expressions involving both first and second derivatives. International Journal of Numerical Methodology Engineering 4: 551, 1972. 18. A.G. Ghani, M.M. Farid, X.D. Chen, and P. Richards. A computational fluid dynamics study on the effect of sterilization temperatures on bacteria deactivation and vitamin destruction. Journal of Process Mechanical Engineering 215(Part E): 1–9, 2001. 19. H. Reuter. Aseptic Processing of Foods. Lancaster, PA: Technomic Publishing Company Inc., 1993. 20. S. Ilo and E. Berghofer. Kinetics of color changes during extrusion cooking of maize gritz. Journal of Food Engineering 39: 73–80, 1999. 21. D.R. Heldman and R.W. Hartel. Principles of Food Processing. New York: Chapman and Hall, 1997. 22. A.G. Ghani, M.M. Farid, X.D. Chen, and P.J. Richards. An investigation of deactivation of bacteria in canned liquid food during sterilization using computational fluid dynamics (CFD). Journal of Food Engineering 42: 207–214, 1999. 23. G.D. Hayes. Food Engineering Data Handbook. New York: John Wiley and Sons, 1987. 24. A.G. Ghani, M.M. Farid, X.D. Chen, and P.J. Richards. Numerical simulation of biochemical changes of canned food during sterilization of viscous liquid using computational fluid dynamics. 10th World Congress of Science and Technology, Sydney, Australia, 3–8 October 1999. 25. P.J. Fellows. Food Processing Technology, Principles and Practice. Cambridge: Woodhead Publishing Series in Food Science and Technology, 1996. 26. M.S. Rahman. Handbook of Food Preservation. Food Science and Technology. A series of monographs, textbooks, and reference books. New York: Marcel Dekker Inc., 1995. 27. A.G. Ghani, M.M. Farid, and X.D. Chen. Numerical simulation of transient temperature and velocity profiles in a horizontal can during sterilization using computational fluid dynamics. Journal of Food Engineering 51: 77–83, 2002. 28. J.P. Fryer, D.L. Pyle, and C.D. Rielly. Chemical Engineering for the Food Industry. Blackie Academic and Professional, London, 1997.
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CFD Analysis of Thermal Processing of Eggs Siegfried Denys, Jan Pieters, and Koen Dewettinck
CONTENTS 14.1 14.2
Introduction ............................................................................................................. 347 Egg Geometry Analysis............................................................................................ 349 14.2.1 Egg Shape ................................................................................................... 349 14.2.2 Yolk Shape and Position ............................................................................ 351 14.2.3 Eggshell Thickness ...................................................................................... 352 14.3 CFD Grid Design .................................................................................................... 352 14.4 Boundary Conditions ............................................................................................... 353 14.4.1 Combined CFD and Experimental Approach for Determination of the Surface Heat Transfer Coefficient .................................................... 353 14.4.2 Experimental Design ................................................................................... 354 14.4.3 Surface Heat Transfer Coefficient at the Egg Surface ................................ 356 14.5 CFD Analysis for Combined Conductive and Convective Heat Transfer in Eggs ....................................................................................................... 360 14.5.1 CFD Modeling of Convective Heat Transfer ............................................. 360 14.5.2 Model Eggs ................................................................................................. 361 14.5.2.1 Thermal and Physical Properties ................................................ 361 14.5.2.2 CFD Analysis ............................................................................. 362 14.5.3 Intact Eggs .................................................................................................. 364 14.6 CFD Analysis for Assessment of Egg Pasteurization Processes .............................. 368 14.6.1 Salmonella enteritidis Inactivation Kinetics ................................................ 371 14.6.2 Process Assessment ..................................................................................... 373 14.6.3 Process Design ............................................................................................ 374 14.7 Conclusions .............................................................................................................. 377 Nomenclature ..................................................................................................................... 378 References .......................................................................................................................... 378
14.1 INTRODUCTION Like several other areas of food research, where CFD finds its way as a powerful and promising tool for process design, process analysis, and process assessment, the egg-processing sector also can profit from the flexibility offered by CFD. Eggs are one of the few foods that are consumed in all countries of the world and they have always been recognized as an important and nutritive food. Today, the egg industry is an important segment of the world food industry. In the Western world, the egg industry is almost exclusively based on the production and treatment of chicken eggs. One segment where CFD can be of great value is in the assessment of the 347
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performance of pasteurization processes. Since the 1960s, pasteurization of derived (liquid) egg products became virtually mandatory in Europe and the US to ensure against the presence of any pathogenic bacteria. Mostly, thermal energy is used for this purpose since temperatures around 608C cause dramatic reductions in the number of vegetative cells. Liquid egg products like whole egg, egg yolk, and egg white are routinely pasteurized, mostly by continuous process methods such as plate or tubular heat exchangers. The application and use of CFD for analysis and assessment of continuous process methods using heat exchangers are comprehensively dealt with in other chapters (e.g., Chapter 15 through Chapter 17) and are not the scope of this chapter. Instead, this chapter concentrates on recent advances in the application of CFD for assessing batch pasteurization processes for intact eggs. Although an ever-increasing part of the egg production is presented to the consumer in the form of (liquid) egg products or formulated foods, eggs are usually marketed as shell eggs (or consumer eggs). Consumers have always preferred intact eggs to liquid egg products, since they offer some benefits as an ingredient in recipes. While pasteurization of liquid egg products became common practice and egg products were pasteurized on a large scale, the contents of intact shell eggs were considered to be essentially free of pathogenic microorganisms. Until the early 1990s, pasteurizing intact eggs was therefore not considered. However, in the 1990s reports indicated that intact, clean, fresh shell eggs are perishable and may contain salmonella bacteria. While the number of eggs affected was quite small, cases of foodborne illness were reported every year both in Europe and the US, caused by the consumption of recipes in which the egg ingredients were not cooked (‘‘health food’’ milk shakes made using raw eggs, Caesar salad, Hollandaise sauce, homemade mayonnaise, ice cream, eggnog, etc.) [1]. Today, eggborne salmonellosis is most frequently caused by Salmonella enteritidis (SE). Since the early 1990s, both in Europe and the US high research priority has been directed at the reduction of salmonellae in the egg supply chain. As a result, from the mid-1990s pasteurization of intact eggs has been proposed as an appropriate way to eliminate SE. Some research already showed that foodborne illness-related salmonellae can be adequately killed in raw eggs by thermal pasteurization [2–5]. Nowadays, in-shell pasteurized eggs are available only at a small scale in some countries. In the same way like CFD can be used for analyzing and improving the performance of the continuous processes used for liquid egg product pasteurization, CFD has also a great potential for the design and assessment of processes for intact egg pasteurization. In general, process assessment and design of pasteurization processes are of utmost importance to guarantee food safety. Such assessment should be based on (a) a detailed theoretical or experimental analysis of the heat transfer within the food (and the temperature in the slowest heating zone) and (b) an accurate kinetic thermal inactivation model for the particular target microorganism. For liquid egg products, a complete process assessment system has been developed through the years and inactivation models for SE in egg white and egg yolk have been thoroughly studied and validated in the literature (e.g., Ref. [5]). The main difference between pasteurization processes of intact eggs as compared to liquid egg products is that batch or semicontinuous processes are required for intact eggs. Until recent years no information was available as to what temperatures and process times should be applied in order to obtain safely pasteurized intact eggs without loss of functional properties. Considering the complexity of intact eggs, a CFD analysis is the obvious approach to follow, as it enables to account for complex geometries and to handle nonhomogeneous initial temperature distributions, variable boundary conditions, and nonlinear and nonisotropic thermal and physical properties. A CFD approach would constitute a solid basis for predicting the transient temperature and velocity profiles in shell eggs during pasteurization processes. Moreover, the flexibility of incorporating user-defined procedures and functions in a CFD analysis allows the engineer to predict the impact of processes in terms of surviving microorganisms.
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As mentioned before, the use of CFD for designing and improving continuous processes in heat exchangers is the focus of other chapters and this chapter mainly concentrates on batch pasteurization of intact eggs. The chapter starts with a discussion of how the geometry of eggs can be accurately determined and described in order to obtain useful CFD meshes. Next, a method is presented for obtaining the surface heat transfer coefficient acting at the egg surface during a batch pasteurization process. A combined CFD and experimental approach is suggested for this. After explaining how the boundary conditions can be characterized, the chapter focusses on the possibilities of CFD for modeling combined conductive and convective heat transfer in eggs. Finally, the applicability of CFD for assessing and designing egg pasteurization processes is illustrated.
14.2 EGG GEOMETRY ANALYSIS Obviously, the accuracy of a CFD analysis largely depends on the accuracy to which the studied geometry is described. One could define an ‘‘average’’ egg (e.g., an average-sized egg with a typical yolk location, yolk size, etc.) and perform a CFD analysis for this ‘‘model egg.’’ However, taking into account the variability of egg shapes and the specific geometrical features of individual eggs will obviously lead to more useful results. For example, considering the specific geometrics of individual eggs allows for a more reliable validation for a CFD analysis. This section focusses on how the geometry of individual eggs (egg size and shape, yolk size, shape and location, and eggshell thickness) can be accurately determined and described in order to obtain CFD meshes that provide reliable results.
14.2.1 EGG SHAPE The high variability of egg shapes creates difficulties in their description. In the past, a number of authors have tried to derive mathematical equations that express the contour of an individual egg. References to these descriptions can be found in Ref. [6]. Most of them assume the egg profile to be an ellipsoid or use modified ellipse equations to describe it. For illustration, four mathematical equations of different complexity describing the contour of eggs are included in Table 14.1, together with the corresponding geometrical parameters used in the selected methods. Based on a popular approach that uses two half-ellipses of unequal major half-diameter (e.g., Ref. [7]), Carter [8] modified the ellipse equation in such a way that the scale of the long axis is pulled out towards one pole and compressed towards the other. He defined an egg-shaped body mathematically in terms of three geometric parameters: its length along the axis of symmetry, the ratio of its maximum width and its length, and the distance from the narrow pole to the plane of maximum width (Table 14.1). In a later paper, the same author presented an improved method for estimating the curvature of shell egg profiles based on four measurements [9]. This improved method made provision for variation in the degree of plumpness (‘‘marilynia’’) of the egg at levels between the plane of maximum width and the poles (Table 14.1). The four measurements are length L, maximum width B, and the distances, x1 and x2 , at which the poles project into an annulus of radius r. In an attempt to limit the number of measurements and indices used for the description of egg shape, Narushin [10,11] deduced two mathematical equations for a ‘‘general’’ egg profile, adequately defined by only two geometrical parameters: length L and maximum width B (Table 14.1). When determining the necessary parameters, the methods described by Carter suffer from disadvantages: they entail measuring the distance from the plane of maximum width to a pole [8] or the distances by which the poles project into an annulus of radius r [9]. Obviously, such parameters are difficult to measure accurately. To overcome these difficulties, computer image analysis can give consolation. This was illustrated by Denys et al. [12] who developed a computer application that allows the user to accurately determine the necessary dimensional
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TABLE 14.1 Mathematical Description of the Methods, Selected for Describing Egg Contours Mathematical Description sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 1 x p 1 2 y ¼ B 4 L 2 log(1=2) logðxm =LÞ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x p m B m y ¼ 1 1 2 2 L
Geometrical Parameters L, B, xm
Method Reference Carter [8]
with p ¼
x p x p 1 2 L L rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x p mffi B m 1 and r ¼ 1 1 2 2 L B pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi y ¼ 1:5396 L0:5 x1:5 x2 L pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2=nþ1 x2n=nþ1 x2 y¼ L 2:372 L with n ¼ 1:057 B
y
L, B, (x1 , r), (x2 , r)
Carter [9]
r B (0,0)
with 0 ¼ 1
L, B
Narushin [10]
L, B
Narushin [11]
x1
xm
x2
x
L
Source: From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Sci., 68, 943, 2003. With permission. Note: The geometrical parameters are shown in the inserted figure.
properties of eggs from digital photographs. The application requires one measured dimension (the egg length L, measured with vernier calipers), and calculates any user-defined distance on a digital egg photograph from the derived number of pixels per unit length. Based on a user-defined 2D cartesian coordinate system, the coordinates of the required points (the parameters included in Table 14.1) are defined in a plane of symmetry. Based on the determined geometry parameters, the application allows calculating and plotting the egg contour according to the four equations given in Table 14.1. After this, visual inspection allows evaluating the agreement between the calculated contour and the photograph. To illustrate the method, Figure 14.1 shows sample screen shots of typical outputs for one egg. The straight lines on the figures represent the user-defined egg boundaries, and all lines Narushin (1997)
Narushin (2001)
Carter (1968)
Carter (1974)
FIGURE 14.1 Typical results of the egg geometry analysis using computer image analysis. (From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Sci., 68, 943, 2003. With permission.)
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0.5 0 −0.5 −1 −1.5 0 10 20 30 40 50 60 Longitudinal coordinate x (mm)
Deviation of y-coordinate (mm)
Deviation of y-coordinate (mm)
1
1.5 1 0.5 0 −0.5 −1 −1.5
0 10 20 30 40 50 60 Longitudinal coordinate x (mm)
Extra large Deviation of y-coordinate (mm)
Large
Medium 1.5
1.5 1 0.5 0 −0.5 −1 −1.5
0 10 20 30 40 50 60 Longitudinal coordinate x (mm)
FIGURE 14.2 Results of the egg geometry analysis from two pictures taken from perpendicular directions. The lines give the differences of the obtained ordinates along the longitudinal coordinate of the eggs. (From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Sci., 68, 943, 2003. With permission.)
necessary for determining the coordinates of the required parameters. The egg contours, calculated according to the four mathematical equations given in Table 14.1, are shown as dotted curves. From the analysis of several hundreds of eggs of different sizes and shapes, it was concluded that the three- or four-parameter models of Carter [8,9] resulted in an accurate description of the egg profile. The two-parameter models of Narushin [10,11] were unable to describe the egg contour to an acceptable degree of accuracy. In many cases, these models underestimated the plumpness of the narrow pole (the one opposite to the air cell) (Figure 14.1). In order to obtain good agreement, three or four geometrical parameters had to be used. The four-parameter equation of Carter [9] was selected as the most accurate way of describing egg profiles and was used for routinely generating CFD meshes for CFD analysis of intact eggs [12]. When the egg profile analysis is performed on two photographs of the same egg, taken from perpendicular positions, only minor differences in the obtained egg contours are observed. Figure 14.2 shows the deviation of the y-coordinates against the longitudinal coordinate x for 24 eggs of three weight classes (medium, large, and extra large). Each line represents the difference between the y-coordinates obtained from photographs of the same egg taken from perpendicular positions. Maximum deviations of about 1 mm were observed. This means that eggs are reasonably axisymmetric and 3D egg geometries can easily be generated by revolution of the obtained profiles about the longitudinal axis (see below).
14.2.2 YOLK SHAPE
AND
POSITION
During thermal processing of intact eggs, not only the size and shape of the egg but also the size, shape, and location of the yolk affect the transient heat transfer pattern observed in the egg. Egg white and egg yolk have slightly different thermal properties (see below). Besides, egg yolk consists of concentric layers of light and dark yolk, surrounded by a vitelline membrane, which separates it from the albumen. In fresh eggs, the yolk location is central in the egg, but in older eggs, denaturation of the chalazae and density differences often force the egg yolk to move upward. CFD allows taking into account the diversity in egg yolk shape and position, provided that this geometrical data can be determined by some means. Contrary to the shape of the eggshell, accurate measurements of the geometric parameters of the yolk are difficult and require noninvasive techniques. In the study of Denys et al. [12], a simplified
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z y
(a)
y
(b)
FIGURE 14.3 (a) Geometry analysis of the yolk size, shape, and location in hard-boiled eggs and (b) corresponding computational 3D mesh. (From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Protect., 68, 366, 2005. With permission.)
method using the above described computer application was applied. Basically, the yolk size, shape, and position were determined from evaluation of digital photographs of boiled eggs that were cut into two halves (Figure 14.3a). For the mathematical description of the egg yolk contour, the authors used a simple elliptical equation. Because the yolk is only visualized in one plane, the suggested method only gives a rough estimate of the yolk size, shape, and location.
14.2.3 EGGSHELL THICKNESS The eggshell thickness determines the resistance to heat transfer at the egg boundary. Micrometer measurements of eggshell thickness for some hundreds of eggs showed a variation between 0.36 and 0.58 mm. Within one particular egg, typically variations of about 0.02 mm were observed. No particular trend can be observed over the eggshell surface [12].
14.3 CFD GRID DESIGN Using their specific geometrical features, accurate 3D meshes can be generated for individual eggs. For example, in the work of Denys et al. [12–14], the CFD grid generation was done in Gambit (Fluent Inc., Lebanon, NH), the preprocessor and mesh generator for the CFD solver Fluent. Using the determined geometrical information and parameters (eggshell size and shape, location, size and shape of the yolk, eggshell thickness), 3D egg shapes could be obtained by revolving egg and yolk profiles 1808 about the axis of symmetry. Hereto, the equations obtained with the above described image processing application were used appropriately and each individual egg was reconstructed according to its specific shape profile. Considering the fact that eggs are reasonably axisymmetric, as formerly mentioned, the method allows for accurate modeling of the shape and size of individual eggs. However, some uncertainties on the exact location, size, and shape of the yolk should be kept in mind. After generating the egg geometry, a CFD grid can be developed by discretizing the obtained volumes. To adequately resolve the CFD problem and to keep discretization errors small, grid elements must be sufficiently small [15]. Furthermore, mesh properties such as
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skewness can greatly affect the accuracy and robustness of the CFD solution. Gambit provides several quality attributes to assess the quality of the obtained mesh. For studying heat transfer in eggs, distinction can be made between cases where only conductive heat transfer is considered (such as for hard-boiled eggs or for cases where a conductive model substance was used, see below) and cases where convective heating is taken into consideration. In the work of Denys et al. [12–14], larger elements were used when only conductive heat transfer was included. To adequately resolve the CFD problem for modeling the movement of egg substances caused by natural convection (e.g., in real eggs or eggshells filled with a convective model system, see below), finer computational meshes should be defined. In cases where the criteria for mesh quality are not met, smaller grid elements should be defined. An example of a computational mesh for a typical egg is shown in Figure 14.3b. When generating the CFD grid, several possibilities exist for treating the eggshell. A simple approach is to consider the eggshell as a single wall surrounding the geometry [12–14]. In such approach, instead of defining and discretizing a separate volume, the thermal resistance offered by the eggshell is modeled as a 1D conduction problem. Hereby, the associated (measured) eggshell thickness is assumed to be constant over the complete surface of an individual egg.
14.4 BOUNDARY CONDITIONS For modeling transient heat transfer during thermal processing of intact eggs, some boundary conditions must be defined. Considering the egg as the system under investigation, the thermal resistance at the system boundary is determined by the surface heat transfer coefficient h (W m2 K1 ) acting at the outer shell surface. This parameter is related to the thermal and physical properties of the heating medium used for processing and some physical characteristics of the eggshell surface. In most cases, the surface heat transfer coefficient is estimated from empirical equations, correlating the dimensionless Nusselt number to the variables of the flow in which the body is immersed. The Whitaker equation, for example, relates flow characteristics with the average Nusselt number in case of flows past immersed spheres (e.g., Ref. [16]). Other ways to determine the surface heat transfer coefficient include the lumped capacitance method (e.g., Ref. [17]), where a body with a very high thermal diffusivity (e.g., a metal body) is immersed in the flow, and its temperature is recorded until equilibrium is reached. In the work of Denys et al. [12–14], a combined CFD and experimental approach was followed to determine the thermal resistance at the egg boundary. The advantage of such an approach is that the flow in which the body is immersed does not need to be fully characterized. This section concentrates on the approach published by Denys et al. [12].
14.4.1 COMBINED CFD AND EXPERIMENTAL APPROACH FOR DETERMINATION HEAT TRANSFER COEFFICIENT
OF THE
SURFACE
Thermal resistance at the egg surface depends neither on the properties of the egg contents, nor on the heating regime observed in the egg (conduction or convection). As a consequence, the value of the surface heat transfer coefficient can be derived, provided that the thermal resistance of the egg contents is known. A straightforward procedure for determining the surface heat transfer coefficient was published by Denys et al. [12], who used the predictive capacity of CFD for thermal processing of eggs filled with a conductive heating material with known thermal properties. A combined CFD and experimental approach was followed to determine the surface heat transfer coefficient for specific processing conditions. The general strategy of the procedure is outlined hereafter.
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Empty eggshells were filled with a conductive heating medium with known thermal and physical properties. Thermal processes were then carried out by immersing a single sample egg filled with test material in a water bath. During the process, temperatures were recorded in predetermined positions in the egg (see below). Based on the geometrical analysis of the egg contour, a CFD grid was generated for the particular egg. Using the appropriate initial condition (the initial product temperature), temperature profiles for the locations of the thermocouples in the processed egg were generated by means of a simple CFD model, taking only conductive heating into account. In the CFD analysis, the temperature of the water was used as the boundary temperature. Besides, an initial value for the surface heat transfer coefficient h was defined. The estimation of h resulted from a least sum of squares optimization routine, in which the objective was to find the best fitting surface heat transfer coefficient. In this routine, the sum of the squared differences (SSD) of the experimentally measured and CFD-simulated temperatures in the eggs was calculated over the complete process. The process was repeatedly simulated with the CFD model, using increasing h-values, and the surface heat transfer coefficient resulting in the least sum of squares was retained as the best fitting value. As an initial step in the optimization routine, a ‘‘search area’’ was defined. In order to be useful for this approach, a test material should be used with accurately known thermal and physical properties, so as to give reproducible results. For ordinary liquid water, internationally accepted formulations for all thermodynamic and transport properties in a large range of temperatures are developed and maintained by the International Association for the Properties of Water and Steam (IAPWS). This organization recently released a new international formulation for thermodynamic properties of ordinary water for general and scientific use [18]. Software implementations of these international formulations are available (e.g., the NIST=ASME Steam Properties Database). However, liquid water suffers from the disadvantage that convective currents occur when applying temperature gradients. To overcome this problem, agar gel (2% agar in distilled water) was used as a substitute. The advantage of this water-based homogeneous gel is that convection currents are absent when heating or cooling it. Considering its composition, thermal properties of this substance are expected to be reasonably close to those of water. The temperature dependences of the thermal conductivity and the specific heat capacity of water were calculated from the NIST=ASME Steam Properties Database, and were used in the CFD model. For density, a constant value was considered, since this considerably reduced computation time. The thermal property values used for agar are included in Table 14.2. The optimization procedure for estimating the egg surface heat transfer coefficient was applied to a data set of 24 agar-filled eggs, each one processed at a temperature of 608C. In 12 cases, three thermocouple probes were inserted in the egg (in the geometrical center, near the eggshell, and in a position between the latter two). In the other cases, only one probe was used, at a position near the geometrical center. This was done to find out whether the use of three stainless steel thermocouple probes affected the heat flux entering the egg. Given the relatively high thermal conductivity of the stainless steel probes, their presence in the system could cause an additional inward heat flow, and this could manifest itself in faster heating at the measuring points.
14.4.2 EXPERIMENTAL DESIGN Thermal processes were simulated using eggs of three weight classes (‘‘extra large’’: þ73 g, ‘‘large’’: 63–73 g, and ‘‘medium’’: 53–63 g). Small holes were drilled at each egg pole and the egg content was forced out using pressurized air. After emptying the shells, the inner surface was washed with tap water. The bottom hole of each shell was sealed with universal silicone sealant and the shells were filled with test material. Agar gel was prepared by suspending
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TABLE 14.2 Thermal Properties of the Model Systems and Egg Products Used in the CFD Models Value Agar gel Thermal conductivity (W m1 K1 ) Specific heat capacity (J kg1 K1 ) Density (kg m3 ) CMC suspension Thermal conductivity (W m1 K1 ) Specific heat capacity (J kg1 K1 ) Density (kg m3 ) Viscosity (kg m1 s1 ) Boussinesq parameters: T0 (K) r0 (kg m3 ) b (K1 )
0:7316528 þ 0:007321898 T 9:492 106 T 2 a 3:991225 104 423:1844 T þ 1:879953 T 2 0:00371639 T 3 þ 2:761713 106 T 4 a 998.2
Source
[18] [18] [18]
0.7 4100 950 5:72 4:96 102 T þ 1:45 104 T 2 1:41 107 T 3 a
[23] [23] [23] Provider
288.16 950 0.0003
[23] Provider
Egg white Thermal conductivity (W m1 K1 ) Specific heat capacity (J kg1 K1 ) Density (kg m3 ) Viscosity (kg m1 s1 )
0:43 þ 5:5 104 T a 3560 1048 3:12 8:9 103 T a
[30] [30] [30] [30]
Yolk Thermal conductivity (W m1 K1 ) Specific heat capacity (J kg1 K1 ) Density (kg m3 ) Viscosity (kg m1 s1 )
0.34 3560 1035 1:6 4:8 103 T a
[30] [30] [30] [30]
0.4560 2.25
[30] [12]
Eggshell Thermal conductivity (W m1 K1 )
a
T represents temperature in Kelvin.
nutrient agar in distilled water in the appropriate concentration and bringing this suspension to the boiling point to dissolve completely. After preparation, the solution was cooled down to 608C and then poured into the empty eggshells. To avoid cracking due to a sudden temperature shock, the empty shells were equilibrated at 608C in a convective oven before filling them with warm agar suspension. After filling, the top hole of each egg was sealed with sealant and the agar suspension was allowed to solidify as the eggs cooled down. Eight eggs were used from each of the three different weight classes. Before processing, the eggs were provided with T-type needle thermocouples (length 57 mm, diameter 0.9 mm) (Metrohm, Berchem, Belgium), inserted into small drill holes, and sealed with contact glue. Three thermocouple probes were used. The eggs were then fixed in a vertical position in a holder, shown in Figure 14.4 [12,13], and a geometry analysis was performed using the above described computer application. Besides geometry analysis, the application was also used for accurate determination of the Cartesian coordinates of the thermocouple hot junctions in the eggs. Knowledge of the hot junction coordinates was
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FIGURE 14.4 Picture of the egg holder showing the locations of the inserted thermocouple probes. (From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Sci., 68, 943, 2003. With permission.)
necessary to allow accurate validation of the temperature profiles obtained by the CFD model. Hereto, the exact length of a probe was plotted along its visible part on the digital picture (Figure 14.4), and the coordinates of the hot junction were defined in the Cartesian coordinate system used for the egg contour determination. Batch thermal processes and pasteurization processes were simulated in a simple water bath (basis 200 mm 150 mm, height 400 mm). The eggs were equilibrated at room temperature prior to processing and then immersed into the water at a constant process temperature of (56 + 1)8C. The thermocouples were connected to a data acquisition unit (Agilent 34970A Switch Unit, Agilent Technologies, Melrose, MS), and temperature data was recorded at regular time intervals (5 or 10 s). Water circulation was forced along the long axis of the egg, in a vertical direction from bottom to top, by the pump of a thermostatic unit (Haake F3, Haake GmbH, Germany). The speed of circulation was 15 L=min, which corresponded to an average water velocity of 0.01 m=s. The end of the process was reached when a new state of equilibrium resulted.
14.4.3 SURFACE HEAT TRANSFER COEFFICIENT
AT THE
EGG SURFACE
To illustrate the procedure for estimating the boundary condition at the egg surface, typical experimental time–temperature profiles for a thermal process of an agar-filled egg are shown in Figure 14.5. The processed egg was initially at a uniform temperature (19.4 + 0.2)8C.
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h = 2000 W m–2 K–1
70
60
Temperature (⬚C)
60
Temperature (⬚C)
h = 1000 W m–2 K–1
70
50 Probe 1
40
Probe 2 Probe 3
30
Ambient Predictions
20
50 40 30 20 10
10 0
500
1000 1500
2000
0
2500
500
Time (s)
20 30 40 50
60
60
50 40 30
60
20
70
10
2500
h = 400 W m–2 K–1
70
Temperature (⬚C)
10
2000
Time (s)
h = 500 W m–2 K–1
70
10 20 30
Temperature (⬚C)
–30 –20 –10 0
1000 1500
50 40 30 20 10
0
500
1000 1500
Time (s)
2000
2500
0
500
1000 1500
2000
2500
Time (s)
FIGURE 14.5 Experimental and simulated temperature profiles for a thermal process of an agar-filled egg, showing the effect of varying the surface heat transfer coefficient. Positions of the thermocouple probes are indicated in the inserted figure. (From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Sci., 68, 943, 2003. With permission.)
Temperature profiles in three locations are shown. The egg contour and the positions of the thermocouple probes are indicated in the inserted figure. Using the appropriate initial condition and the prevailing boundary conditions (average temperature of the water bath during the holding period), predicted temperature profiles for three positions corresponding to the locations of the thermocouples in the processed egg were generated by means of the CFD model, using different surface heat transfer coefficients. The effect of changing the h-value is clearly shown in Figure 14.5, where the predicted temperature profiles are included (full lines). The obtained SSD of the experimentally measured and CFD-simulated temperatures at the thermocouple locations are indicated in Figure 14.6. For the particular egg shown in the figure, a good fit was obtained for a surface heat transfer coefficient h of 600 W m2 K1 . For this value, the ‘‘total SSD,’’ defined as the sum of the SSD’s over the three positions, was minimized, and a very accurate prediction was made. However, it was observed that in many cases the minimized SSD, obtained for the thermocouple position near the eggshell, deviated from the values obtained for the other thermocouple positions. Because of the vicinity of the boundary, changing the surface heat transfer coefficient affected the agreement of the prediction to a higher extent at this position. However, given the rather low accuracy to which the thermocouple locations could
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SSD Σ (Texperimental − T predicted)2
1000 900
Probe 1
800
Probe 2
700
Probe 3 Sum
600 500 400 300 200 100 0 200
400 h
600
800
1000
(W m−2 K−1)
FIGURE 14.6 SSD of the experimentally measured and CFD-simulated temperatures at the thermocouple locations, for the particular egg in Figure 14.5. (From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Sci., 68, 943, 2003. With permission.)
be determined (presumably about 1–2 mm), this thermocouple location was not considered in the optimization procedure, and the SSD was calculated by adding the values obtained for the other two thermocouple locations. Following this approach, a surface heat transfer coefficient of 500 50 W m2 K1 resulted for the particular egg shown in Figure 14.5. Using the aforementioned procedure, Denys et al. [12] reported an ‘‘optimized’’ surface heat transfer coefficient of (906 335) W m2 K1 for a data set of 24 eggs. At first sight, a very large variation between the different processes was obtained and the method does not seem to deliver very accurate results. Besides, when the obtained optimized heat transfer coefficients were plotted against the width of the corresponding processed eggs, no clear correlation was observed (black dots in Figure 14.7a). Yet, the diameter of the egg affects the Reynolds number of the water flow past the egg and according to the empirical Whitaker equation, which relates the average Nusselt number to the variables of a flow passing a sphere [16], a slightly negative correlation between the surface heat transfer coefficient and the egg width is expected. For the particular flow variables and egg widths used in the experiments, this ‘‘expected’’ correlation is indicated in Figure 14.7a (dotted line). Another odd observation is shown in Figure 14.7b, where a positive relation appears to exist between the optimized surface heat transfer coefficient and the thickness of the eggshell. The value of the heat transfer coefficient is normally not affected by the eggshell thickness. More likely, the value for thermal conductivity of eggshell found in the literature and included in Table 14.2 was incorrect, resulting in an error that increased for increasing eggshell thickness. Considering the composition of eggshell, a thermal conductivity value of 0:456 W m1 K1 seems quite inconsistent. Indeed, when the complete optimization approach was repeated using a thermal conductivity value of 2:25 W m1 K1 for eggshell an optimized surface heat transfer coefficient of (490 + 82) W m2 K1 was obtained for the same data set of eggs. The variation obtained was much smaller. Besides, its value was independent of the shell thickness as indicated by the open circles in Figure 14.7b and the obtained values were closer to the ‘‘expected’’ values according to the Whitaker equation: a slightly negative correlation with
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Optimized surface heat transfer coefficient (W m−2 K−1)
Thermal conductivity shell = 0.456 W m−1 K−1 Thermal conductivity shell = 2.25 W m−1 K−1 Whitaker approximation 2100 1900 1700 1500 1300 1100 900 700 500 300 100 40
41
42
43
44
45
46
47
48
49
50
Egg width (mm)
(a)
Optimized surface heat transfer coefficient (W m−2 K−1)
Thermal conductivity shell = 0.456 W m−1 K−1 Thermal conductivity shell = 2.25 W m−1 K−1
(b)
2100 1900 1700 1500 1300 1100 900 700 500 300 100 0.35
0.4
0.45
0.5
0.55
0.6
Eggshell thickness (mm)
FIGURE 14.7 Effect of (a) egg width and (b) eggshell thickness on the optimized surface heat transfer coefficients obtained through the optimization procedure. For clarity, error bars were only included for one data point. The error bars for the other points are equal. (From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Sci., 68, 943, 2003. With permission.)
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egg width was found as shown in Figure 14.7a. The particular thermal conductivity value of 2:25 W m1 K1 was found for calcium carbonate, the major constituent of the spongy layer, which comprises two-thirds of the shell thickness [19]. Likely, it represents a more plausible value for the thermal conductivity of eggshell. Increasing the eggshell thermal conductivity to even higher values had only little additional impact on the obtained values for the optimized surface heat transfer coefficient. A higher thermal conductivity for eggshell indicates that the convective surface heat transfer coefficient contributes more to the heat resistance, conditioning the heat flux entering or leaving the egg. Using the suggested approach, an average surface heat transfer coefficient of (490 82) W m2 K1 was obtained through the optimization procedure [12]. Obviously, this value only applies to heat treatments, conducted in the same or very similar experimental conditions as for this study. In cases where other heating media are used for batch thermal processes, like steam or still water, another surface heat transfer coefficient value is expected. Therefore, the optimization procedure should be repeated using the appropriate heating media and conditions in order to obtain useful estimates. On the other hand, the results agree quite well with the empirical Whitaker equation, indicating that an empirical equation can provide at least a good estimate of the surface heat transfer coefficient.
14.5 CFD ANALYSIS FOR COMBINED CONDUCTIVE AND CONVECTIVE HEAT TRANSFER IN EGGS In the previous section, conductive heat transfer in model eggs containing a solid gel was considered for the determination of the surface heat transfer coefficient at the egg boundary. In another recent study, Sabliov et al. [20] developed an axisymmetric transient finite element heat transfer model for cryogenic cooling of shell eggs, also based on conductive heat transfer. Considering the relatively low viscosity of albumen, the major egg component (Table 14.2), it is expected that natural convection can add to the heating or cooling rate when processing eggs. Natural convection is caused by density differences within fluids due to local temperature gradients. When pasteurizing intact eggs using a heating medium like water or steam, temperature gradients cause local convective currents, which can have an important impact on the temperature distribution. Unlike conduction, natural convection heating is not amenable to simple analytical solutions. For modeling this behavior, the energy equation should be solved simultaneously with the equations for conservation of mass and momentum and the gravity force, driving the convective currents, should be taken into consideration. Numerical prediction of transient temperature and velocity profiles in canned liquid foods processed in a still retort has been carried out by Datta and Teixeira [21]. After the introduction of commercial CFD codes, similar approaches were followed by other authors to predict natural convection heating within cans or pouches of food [22–26]. In general, the results of these studies indicated that convection currents tend to push the slowest heating zone towards the bottom of cans or pouches. For process assessment (see further), the location of the slowest heating zone must be known, as this is the zone for which the processing criteria (i.e., the integrated effect of temperature over time) must be established in order to assure consumer safety. In this section, the basic equations for modeling convective heat transfer are outlined and some results for model and real eggs are discussed.
14.5.1 CFD MODELING OF CONVECTIVE HEAT TRANSFER The partial differential equations governing natural convection of a fluid in a 3D geometry are the mass, momentum, and energy conservation equations. In many cases, these equations are simplified by assuming constant thermal and physical properties (i.e., the variation of
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fluid properties with temperature is neglected), and by considering an incompressible flow. Besides, in most cases where natural convection occurs, fluid velocities and shear rates are rather low. Consequently, heat generation due to viscous dissipation can be neglected. In cases where temperature-dependent properties or buoyancy forces are assumed, the flow and energy equations are coupled and should be solved simultaneously. For modeling natural convection, some temperature dependency of the fluid density should be included in the solution. A very popular approach is the Boussinesq approximation. This approach was also used by authors for modeling natural convection in cans or pouches during sterilization processes [24–26]. The principle of this approximation is that there are flows in which temperature varies little, and therefore the density varies little, yet the buoyancy drives the motion. Thus, in the Boussinesq approximation, density differences are considered sufficiently small to be neglected (i.e., the fluid is assumed to be incompressible), except where they appear in terms multiplied by g, the acceleration due to gravity. In the buoyancy term appearing in the momentum equation, the variation of the density with temperature is expressed according to the Boussinesq approximation as (r r0 )g ffi r0 b(T T0 )g
(14:1)
where T0 and r0 are the reference temperature and the corresponding density, respectively, and b is the volumetric thermal expansion coefficient of the liquid.
14.5.2 MODEL EGGS Before focussing on real eggs, it makes sense to develop and test a CFD model for convective heat transfer in some model system. If a CFD model could be validated for a model system with known thermal and physical properties, it would increase confidence in the method and would constitute a solid basis for treating real intact eggs by means of CFD. In a study presented by Denys et al. [13], transient temperature and velocity profiles during thermal processes of eggshell bodies filled with a viscous fluid were studied. As a model system for validation purposes, sodium carboxymethyl cellulose (CMC) suspension was used. CMC suspension is comparable to egg white in terms of properties, but it has the advantage that its thermal and physical properties are fully documented. A wide range of viscosities of water solutions can be obtained by selecting the suitable CMC-type, concentration, and temperature. For the above mentioned study, Blanose refined low-viscosity type 7LF CMC (Hercules Inc., Wilmington, NC) was stirred in cold distilled water until a viscous suspension of 2% was obtained. The viscosity of this suspension was well documented and only slightly lower than that of egg white. Values are given in Table 14.2. After preparation, the CMC suspension was poured into empty eggshells which were used for validating the CFD model. 14.5.2.1
Thermal and Physical Properties
In order to obtain accurate results, correct thermal and physical properties of the test material should be used in the CFD model. When modeling natural convection, viscosity is an important property. For a suspension of 2% Blanose refined low-viscosity type 7LF CMC, detailed viscosity data is provided by the distributor. The viscosity of 7LF CMC shows a rather low dependence on the applied shear rate and thus the suspension behaves as a Newtonian fluid. When shear rates are low (e.g., due to low fluid velocity or high viscosity), most liquid food products can be approximated by Newtonian behavior, although in reality, they are often pseudoplastic. In the present work, the temperature dependence of
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the viscosity followed a third-order polynomial (Table 14.2). Considering its composition, the other thermal and physical properties of the CMC suspension were expected to be reasonably close to those of water. The values presented by Kumar and Bhattacharya [23] were used in the CFD model (Table 14.2). Also the parameters used for the Boussinesq approach are included in Table 14.2. In natural convection, the Rayleigh number Ra takes into account the strength of the buoyancy-induced flow: Ra ¼
gb(DT)L3 r ma
(14:2)
where g (m s2 ) is the gravitational acceleration, L is a characteristic dimension (m), m the dynamic viscosity (N s m2 ), and a (m2 s1 ) is the thermal diffusivity. Using the maximum temperature difference, observed during a typical process, and average egg dimensions, Rayleigh numbers for the CMC used were in the range 106 –107 , indicating buoyancy-induced laminar flow (i.e., no turbulence occurs). Considering the properties of egg albumen, Rayleigh numbers for egg albumen are expected to be in the same range for similar experimental conditions. 14.5.2.2
CFD Analysis
In order to increase confidence in the use of CFD for egg processing, a CFD analysis should be validated by comparison with experiments. Hereto, Denys et al. [13] treated eggs filled with CMC suspension in the same way as described for processing the agar-filled eggs in Section 14.4. Processes were conducted at 408C and 608C. At both conditions, six eggs were treated: two for each of the three weight classes (medium, large, and extra large). In total, 12 heat treatments were performed. Figure 14.8 shows the CFD-simulated temperature distribution in a symmetry plane of a large-sized egg, at different periods of heating during a typical heating process. The processed egg was initially at a uniform temperature of (24:5 0:2)8C and was subjected to a temperature of (59:4 0:2)8C. For comparison purposes, the 538C temperature contour and the location of the coldest point were also included. Figure 14.9a shows the flow pattern and velocity contour plot of the CMC in the same plane of symmetry, after 30 s process time. The figures show that the CMC adjacent to the eggshell receives heat from the surrounding heating medium. Due to the resulting temperature gradient, a buoyancy force is created and the flow moves upwards near the inner shell surface. Flows are deflected at the top and travel radially towards the geometric center. The CMC at the geometric center is at lower temperature and thus heavier, resulting in a downward movement towards the bottom of the egg. The maximum velocity at 30 s process time was 1:5 mm s1 . Very similar results were obtained for the eggs of the other weight classes. Therefore, results for other weight classes are not shown here. It can be seen that, unlike for pure conductive heating, the cold spot (i.e., the location where the temperature is the lowest at a given time) is not a stationary point in the case of natural convection. For comparison, the temperature contours resulting from pure conductive heat transfer were included in Figure 14.10. The same thermal properties were used for the simulation where only conduction was considered, but density was assumed constant and the Boussinesq approximation was not used. Whereas in pure conductive heat transfer the cold spot is located in the geometrical center at any time; in the case of natural convection, the cold spot moves during the process towards the bottom of the egg. It should be mentioned that during the first minute of the process, no distinct cold spot could be determined.
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62 58
1
1
1
54 2 50
2 3
2 3
3
46 42 38
(a)
(b)
(c)
1
1
1
34 2
2
2
30 3
3
3
26 22°C (d)
(e)
(f)
FIGURE 14.8 CFD-calculated temperature contours in the cross-section of an egg filled with CMC and heated in a water bath after periods of (a) 5 s, (b) 10 s, (c) 30 s, (d) 80 s, (e) 150 s, and (f) 300 s. Process conditions: Ti ¼ (24:5 0:2) C; T1 ¼ (59:4 0:2) C. 1, 2, 3: thermocouple hot junction locations. The white line represents the 538C temperature contour, the cross is the coldest point. (From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Eng., 63, 281, 2004. With permission.)
Ghani et al. [24,25] observed a similar behavior for convection in cans and pouches filled with viscous products. They reported the presence of a ‘‘slowest heating zone’’ rather than a single cold spot. Figure 14.11 shows typical experimental and CFD predicted time–temperature profiles for thermal processes at 608C and 408C of a CMC-filled egg. Temperature profiles, measured at three locations, are shown. The egg contour and the locations of the thermocouple probes are indicated in the inserted figures. For the process at 608C, thermocouple locations are also included in Figure 14.8 and Figure 14.10. Using the appropriate initial condition and the prevailing boundary conditions (average temperature of the water bath during the holding period), predicted temperature profiles for three positions corresponding to the locations of the thermocouples in the processed egg were generated by means of the CFD model. The results of the simulation were found to be in good agreement with the experimentally measured temperature profiles. For comparison, predicted time–temperature profiles for pure conductive heating were included in Figure 14.11 (dotted lines). It can be seen that natural convection currents improved the heating rate considerably. Besides, whereas probe 3 indicates the lowest temperatures during the process, in the case of pure conduction this thermocouple probe would measure the highest temperatures (Figure 14.11), since it is located near the eggshell. This illustrates the effect of natural convection on the location of the cold spot. Similar results were obtained both for processes conducted at 408C and 608C.
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0.001650 0.001370 0.001100 0.000825 0.000550 0.000275 0 m/s (a)
(b)
(c)
FIGURE 14.9 CFD-calculated velocity vector plots and velocity contours in a plane of symmetry of an egg filled with CMC and heated in a water bath after 30 s processing: (a) no yolk present, (b) conductive heating yolk present in the egg center, (c) yolk shifted towards the top of the egg. Process conditions for all cases were: Ti ¼ (24:5 0:2) C; T1 ¼ (59:4 0:2) C. (From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Eng., 63, 281, 2004. With permission.)
In general, CFD seems to be able to accurately predict the transient thermal behavior for eggs filled with model suspension. As shown in Figure 14.11, CFD can give a good indication of what happens when a yolk is present in the egg. Here, a sphere-shaped geometry of 27 mm diameter (a typical yolk size, as determined from geometry analysis) was included in the computational grid. In the CFD analysis, only conductive heat transfer was considered in the yolk. Properties for egg yolk used in the analysis are shown in Table 14.2 and the same initial and boundary conditions are considered as for the egg shown in Figure 14.8 and Figure 14.10. The effect on the convection currents is clearly illustrated in Figure 14.11 for two locations of the yolk. For a centrally located yolk, the cold spot is located in the yolk, at a position slightly below its geometrical center (Figure 14.12). Obviously, this is due to the slower conductive heat transfer. However, the location of the cold spot depends on the yolk position. When the chalazae are denatured, the egg yolk often moves to the top of the egg due to density differences (Figure 14.11b). Figure 14.13 shows results for a process where the yolk was positioned at the top of the egg. Also in such case, the cold spot was located at a position near the geometrical center of the yolk.
14.5.3 INTACT EGGS The primary objective of a CFD model for combined conductive and convective heat transfer occurring in eggs is to predict the temperature distribution during thermal processing of real,
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62 58
1
1
1
54 2 50
2 3
2 3
3
46 42 38
(a)
(b)
(c)
1
1
1
34 2
2
2
30 3
3
3
26 22°C (d)
(e)
(f)
FIGURE 14.10 CFD-calculated temperature contours in the cross-section of an egg filled with CMC and heated (conduction only) in a water bath after periods of (a) 5 s, (b) 10 s, (c) 30 s, (d) 80 s, (e) 150 s, and (f) 300 s. Process conditions: Ti ¼ (24:5 0:2) C; T1 ¼ (59:4 0:2) C. 1, 2, 3: thermocouple hot junction locations. The white line represents the 538C temperature contour, the cross is the coldest point. (From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Eng., 63, 281, 2004. With permission.)
intact eggs. Since CFD proved very useful for modeling the thermal behavior of a food simulator in eggs, processes were conducted with intact eggs and the performance of the CFD model was further tested by Denys et al. [14]. Hereto, eggs were processed in the same way as the model eggs using a warm water bath and constant process temperatures of (56 1)8C. For determination of the yolk location and size, the egg holder containing the egg and thermocouples was then immersed for 20 min in a water bath containing water of 1008C. After this boiling process, the egg was re-equilibrated at room temperature and a pasteurization process at (56 + 1)8C was repeated. In this way, temperature data could be obtained for both raw and boiled eggs at identical thermocouple locations. After the second pasteurization process, the hard-boiled egg was cut into two halves for the geometry analysis of the yolk (as explained above). For the CFD study of heat transfer in intact eggs, properties given in Table 14.2 were used. For a detailed description of the procedures, the reader is referred to Denys et al. [14]. For illustration, some results are discussed here. Typical experimental and CFD-simulated time–temperature profiles for thermal pasteurization processes of intact eggs of different sizes are shown in Figure 14.14. Results for both the raw and (hard) boiled state are included in the figure. Temperature profiles, measured at two locations, are shown. Experimental measurements are included, as well as CFD predictions for the same spot. The egg contours and the locations of the thermocouple probes are indicated in the inserted figures.
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65 60 1
Temperature (8C)
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3 2
50 1
45 40
2
1
35
2
30
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25 20 0
200
400 Time (s)
Probe 1 Probe 3 Prediction (convective)
(a)
600
800
Probe 2 Heating medium Prediction (conductive)
45
Temperature (8C)
40 1
3
2 3
35 1 2
30
1 2
25
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20 0
(b)
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Time (s)
FIGURE 14.11 Experimental and simulated temperature profiles for thermal processes of CMC-filled eggs at (a) 608C and (b) 408C. Positions of the thermocouple probes are indicated in the inserted figure. Dotted lines represent predicted time–temperature profiles for pure conductive heating. (From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Eng., 63, 281, 2004. With permission.)
In the boiled state, when the egg proteins are denatured and the egg content is coagulated, convection currents are obstructed by the gel that is formed and heat transfer is driven by conduction only. For such cases, the temperature profiles can be modeled very accurately as shown in Figure 14.14. The experimental time–temperature profiles for raw eggs indicate a slight increase of the heat transfer rate at the points where temperatures were measured compared to the corresponding results for hard-boiled eggs (Figures 14.14b through
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62 58 54 50 46 42
(a)
(b)
(c)
(d)
(e)
(f)
38 34 30 26 228C
FIGURE 14.12 CFD-calculated temperature contours in the cross-section of an egg filled with CMC and containing a conductive heating yolk (indicated by the dashed line), heated in a water bath after periods of (a) 5 s, (b) 10 s, (c) 30 s, (d) 80 s, (e) 150 s, and (f) 300 s. Process conditions: Ti ¼ (24:5 0:2) C; T1 ¼ (59:4 0:2) C. The white line represents the 538C temperature contour, the cross is the coldest point. (From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Eng., 63, 281, 2004. With permission.)
Figure 14.14d). As can be seen in the figures, considering only conductive heating in the CFD model resulted in a consistent underestimation of the heat transfer rate, especially in the yolk (Figure 14.14b). On the other hand, when convection was taken into account, the results yielded an overestimation of the heat transfer rate in the yolk (Figure 14.14c), while the agreement between measured and predicted temperatures was improved in the egg white. This was consistently observed for the majority of experiments, as shown in Table 14.3. In this table, the predictive capacity of the CFD model is expressed by means of the sum of the squared residuals (SSR) of experimentally measured and CFD-simulated temperatures, at time intervals of 20 s over the complete process. SSR calculated for both the egg white and yolk profiles are included in the table. The reported values are average values and corresponding standard deviations for eight processes. SSR and standard deviation values clearly show that the capacity of the CFD model for predicting the temperatures, measured by the thermocouple in the egg white fraction of the egg, improved when convection is taken into account. Whereas the performance of the CFD model for predicting the temperatures in the egg white fraction could be improved by considering convective heat transfer, Denys et al. [14] did not observe improvement for the temperature profiles in the yolk. In its native state, egg yolk consists of concentric layers of light and dark yolk, surrounded by a vitelline
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62 58 54 50 46 42
(a)
(b)
(c)
(d)
(e)
(f)
38 34 30 26 228C
FIGURE 14.13 CFD-calculated temperature contours in the cross-section of an egg filled with CMC and containing a conductive heating yolk (positioned at the top of the egg and indicated by the dashed line), heated in a water bath after periods of (a) 5 s, (b) 10 s, (c) 30 s, (d) 80 s, (e) 150 s, and (f) 300 s. Process conditions: Ti ¼ (24:5 0:2) C; T1 ¼ (59:4 0:2) C. The white line represents the 538C temperature contour, the cross is the coldest point. (From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Eng., 63, 281, 2004. With permission.)
membrane [19]. Very likely, the layered yolk structure obstructs natural convection currents that are expected based on the properties of egg yolk. This assumption was supported by the results of CFD simulations, in which natural convection was considered only in the egg white fraction while heat transfer in the yolk was assumed to be driven by conduction only (Figure 14.14d). These results showed a far better agreement with the experimental profiles in all of the cases under investigation, as shown in Table 14.3. Therefore, Denys et al. [14] concluded that no natural convection occurs in egg yolk when pasteurizing fresh eggs.
14.6 CFD ANALYSIS FOR ASSESSMENT OF EGG PASTEURIZATION PROCESSES As already mentioned in the introduction, the design of egg pasteurization processes should be controlled and processes should be assessed in order to guarantee product safety. Cunningham [27] provides an excellent review of pasteurization methods used by the egg industry, while the International Egg Pasteurization Manual [28] reviews research available to assess present pasteurization requirements. Although liquid egg products are routinely pasteurized (mostly by continuous process methods such as plate or tubular heat exchangers), and although a complete process assessment system for liquid egg products has been developed over the years, no information is available as to what temperatures and process times
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55
55
Temperature (8C)
Medium 53−63 g
Temperature (8C)
Hard boiled—conductive heating 60
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Temperature (8C)
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(a)
800 1000 1200
20
20
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Extra large +73 g
400
Time (s)
Temperature (8C)
Large 63−73 g
Temperature (8C)
Time (s)
50 45 40 35 30 25
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800 1000 1200
Time (s)
20
(b)
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FIGURE 14.14 Experimental and CFD-simulated temperature profiles for thermal processing of (a) hard-boiled and (b–d) raw eggs. Positions of the thermocouple probes are indicated in the inserted figures. (From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Protect., 68, 366, 2005. With permission.) (continued )
should be applied in order to obtain safe, pasteurized, intact eggs, without loss of functional properties. The main difference between pasteurization processes of intact eggs as compared to liquid egg products lays in the fact that batch or semicontinuous process methods are required for intact eggs. As the experimental and CFD results discussed in the previous section indicate, batch or semicontinuous thermal processing of egg-shaped bodies causes convective heat transfer, affecting the temperature distribution inside the product. When assessing pasteurization processes of intact eggs, the temperature distribution should be known as it determines the transient and spatial distribution of microbiological inactivation. Assessment of batch pasteurization and sterilization processes can be based on (a) theoretical or experimental analysis of the heat transferred within the food and (b) kinetic thermal inactivation models
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Raw—convection in egg white only 60
55
55
Temperature (8C)
Medium 53−63 g
Temperature (8C)
Raw—convection 60
50 45 40 35 30 25
50 45 40 35 30 25
20
20 0
200
400
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800 1000 1200
0
200
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60
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200
Time (s) 60
60
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55
50 45 40 35 30
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800 1000 1200
Time (s)
Temperature (8C)
Temperature (8C)
600
25
25
Extra large +73 g
400
Time (s)
Temperature (8C)
Large 63−73 g
Temperature (8C)
Time (s)
25
50 45 40 35 30 25
20
20 0
200
(c)
400
600
800 1000 1200
Time (s)
0
(d)
200
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Time (s)
FIGURE 14.14 (continued)
for the particular target microorganism. For good practice, processes should be evaluated in the cold spot or slowest heating zone (i.e., the point that has the lowest temperature during a thermal process). For conductively heating products, this location is generally the geometrical center of the product but when convection occurs, experimental or other methods are required to establish its location. Besides the safety concerns, pasteurization of eggs or egg products adversely affects the functional properties of the egg components, depending on the time and temperatures used. Therefore, egg pasteurization requires low temperatures and comprehends a complex optimization problem. Basically, operators should be able to define process conditions that guarantee safe eggs, but at the same time loss of functional properties should be avoided or minimized. Considering the flexibility of CFD in generating time and space depending on solutions of the equations, governing conductive and convective heat transfer, CFD offers a very useful tool for assessing pasteurization processes of intact eggs. By including kinetic
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TABLE 14.3 Average (SD) Sum of Squared Differences of Experimentally Measured and CFD-Simulated Temperatures for Eight Processes Medium
Large
Extra Large
Egg Sample, Process
White
Yolk
White
Yolk
White
Yolk
Hard boiled, conductive heating
23.49 (15.07) 106.54 (49.21) 24.98 (12.51) 16.73 (8.32)
50.57 (16.48) 906.89 (370.40) 866.00 (235.60) 58.04 (20.33)
22.84 (14.05) 153.25 (68.54) 32.19 (15.27) 35.16 (16.42)
51.67 (23.79) 856.34 (300.05) 468.45 (201.65) 69.25 (30.04)
26.35 (16.52) 149.36 (75.64) 43.68 (20.46) 34.56 (10.84)
62.07 (24.06) 798.24 (326.14) 805.55 (465.32) 85.37 (34.12)
Raw, no convection Raw, convection Raw, convection in white only
Source: From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Protect., 68, 366, 2005. With permission.
models, describing thermal inactivation of the relevant target microorganisms, CFD can allow processors to gain more insight into processes and to establish process conditions leading to consumer-safe eggs. This section focusses on the procedures presented by Denys et al. [14], who incorporated a widely accepted kinetic inactivation model for SE in a CFD analysis. It will be shown that from such approach, minimum process times and temperatures to provide equivalent pasteurization effectiveness can be obtained.
14.6.1 SALMONELLA
ENTERITIDIS INACTIVATION
KINETICS
Inactivation models for SE have been thoroughly studied and validated in the literature and are extensively used for assessing and designing pasteurization processes for liquid egg products. For a detailed review on the research available for establishing present pasteurization requirements, the reader is referred to the International Egg Pasteurization Manual [28]. Usually a first-order kinetic approach is used to describe the rate of thermal microbial inactivation. In the thermal death time (TDT) approach, generally accepted and widely used by food engineers, the decimal reduction time or D-value is mostly used as a means to describe the inactivation rate [29]. Another kinetic parameter, the z-value, is used to describe the temperature dependency of the inactivation rate. Effects of time and (time-varying) temperatures on the survival of the target microorganism can then be quantified by means of the process value F (min): ðt
F ¼ DTref ½log (N0 ) log (N) ¼ 10(TTref )=z dt
(14:3)
0
where DTref (min) is the D-value at reference temperature, Tref is a constant reference temperature, and N0 and N are the initial and final microbial load, respectively (g mL1 or any appropriate unit). The process value represents the process time of an equivalent process (meaning a process with the same impact in terms of microbial inactivation), conducted at a constant reference temperature Tref . Using the concept of the process value, process engineers and operators are able to quantitatively compare different thermal processes (processes characterized by different and=or time-varying temperatures) in terms of impact or microbial
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load. Furthermore, the concept enables the operator to establish process conditions leading to the required microbial inactivation. For good practice, the F-value should always be evaluated in the cold spot or the slowest heating zone of the product. When conduction is the only heat modus, the cold spot is located at the geometrical center and the problem reduces to finding the time–temperature profile in this location. As explained in the previous section, when processing eggs, convection affects the temperature distribution inside the product and changes the location of the cold spot during the process. In such cases, numerical methods including CFD are the most suitable approach to follow for process assessment, since they allow calculation of spatial distributions of temperature. A kinetic model for thermal destruction of SE was incorporated in a CFD model by Denys et al. [14] and this approach will be discussed here for illustration. SE heat destruction had been thoroughly studied and kinetic models were evaluated by other researchers. Therefore, validation of the predicted Salmonella inactivation is not aimed at here. Instead, a conventional kinetic inactivation model is used to illustrate the applicability of the approach on a theoretical basis. Conventional first-order inactivation kinetics were used for simplicity, since there is growing evidence that Salmonella heat destruction does not necessarily follow first-order kinetics. In cases where tailing is observed in the temperature dependency of the D-value, assuming first-order thermal destruction could lead to underestimation of the process time required for adequate inactivation, especially when process temperatures are low. However, recent re-evaluation studies indicate that the conventional approach where simple kinetic models are considered appears to be adequate for the whole range of egg products [28]. The D- and z-values used in the study of Denys et al. [14] were obtained from the International Egg Pasteurization Manual [28]. In this manual, process times required for pasteurization of derived egg products (liquid egg white and egg yolk) are suggested based on experimentally obtained D- and z-values. The values used are included in Table 14.4. In general, SE is less heat sensitive in the yolk as compared to egg white. This is reflected in higher D-values for SE in yolk. The flexibility of a CFD approach, however, allows allocating different kinetic parameters to different regions of the computational mesh. This is an important advantage of CFD. In general, the safety criterion for egg product pasteurization is to obtain 5 log reductions of the initial SE load. As a result of the higher D-values, the F-value required to obtain 5 log reductions of SE in the yolk is higher than in egg white. For the purpose of comparison, the number of SE log reductions was also included in the CFD calculations discussed here. Both F-value and number of log reductions were incorporated in the CFD model as user-defined functions. Their values were allocated to user-defined memories and updated after each time step (typically 1 s).
TABLE 14.4 Kinetic Parameters Used in the CFD Model Egg Part
DTref (min)
z-Value (8C)
Required F-Valuea (min)
0.57 0.25
4.37 3.29
2.87 1.25
Yolk White
Source: From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Protect., 68, 366, 2005. With permission. a
For 5 log reductions.
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14.6.2 PROCESS ASSESSMENT As explained above, natural convection in the egg white fraction determines the transient and spatial temperature distribution and will have an unnegligible impact on the SE inactivation during intact egg pasteurization processes. Furthermore, since the heat sensitivity of SE is product dependent, inactivation should be followed both in the yolk and the egg white to assure the desired SE reduction and to guarantee consumer-safe eggs. It should be clear that, given the complex interaction between all factors determining the process impact, process design is a complex task. Yet, processes should be assessed and process parameters optimized in order to obtain the desired degree of pasteurization in an acceptable time. Numerical methods and CFD analysis in particular seem to be the most promising technique for reaching these objectives. This section will show that combining the CFD model with a kinetic inactivation model for SE allows for process assessment and process design optimization. For illustrating the method of incorporating SE inactivation kinetics in the CFD analysis, Figure 14.15 shows the spatial distribution of the predicted SE inactivation (expressed in log reductions) on a symmetry plane of an egg during a typical pasteurization process (at 578C), at regular time steps. It can be seen that, in the particular case shown, the inactivation occurs slowest in the yolk, slightly below its geometrical center. The pasteurization criterion (5 log reductions in the cold spot) was reached after 39 min for this particular case. From a practical point of view, lower temperatures would require much longer processes, while temperatures above 608C could affect the functional properties of the egg contents. A process temperature of 578C enabled obtaining 5 log reductions within 40 min, which is a reasonable process time. Again, it should be stressed that the results were obtained on a theoretical basis only, by
5
4
3 5 min
10 min
15 min
20 min
25 min
30 min
2
1
0 SE inactivation (log reductions)
FIGURE 14.15 Spatial distribution of SE inactivation (expressed in log reductions) during a typical pasteurization process, calculated by the CFD-model at regular time steps. Process conditions: initial temperature 208C, ambient temperature 578C. (From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Protect., 68, 366, 2005. With permission.)
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combining conventional inactivation kinetics with a CFD model. In order to further test the reliability of the suggested approach, comprehensive SE inoculation experiments could be performed. However, the SE inactivation predicted by the authors was in the same range as the ones published by Schuman et al. [5]: they performed Salmonella inoculation tests and observed a 3.9–5.0 log reduction after 35 min at 588C, and a 5.6–5.9 log reduction after 42.5 min at the same temperature. Besides optimizing process parameters, CFD can also be very useful to investigate the effect of geometrical parameters. Obviously, the distribution of the predicted SE inactivation depends on the location of the yolk. In fresh eggs, the yolk location is central in the egg, but when the chalazae are denatured, density differences often force the egg yolk to move upward. To illustrate the use of CFD in establishing the effect of the yolk location on the predicted inactivation of SE, three CFD simulations were performed with a virtual egg of average size, in which an average-sized yolk was located at different positions (at the top, in the geometrical center, and at the bottom of the egg). The initial temperature was 208C and the process temperature was 578C in each case. Figure 14.16 shows the egg contour and yolk position for the three cases and the transient cold spots in yolk and egg white, simulated by the CFD model and projected on a plane of symmetry after each time step (uppermost figures). Through CFD simulation, the temperature profiles in the transient cold spots and the corresponding SE reduction (in log units) were simulated and were also included in Figure 14.16 (bottommost figures). The minimal process times required to obtain a 5 log reduction of SE in both transient cold spots were determined and the results were included in Table 14.5. Important conclusions can be drawn from the CFD results. Since longer process times are required to assure the desired reduction in the cold spot of the yolk, process assessment in the yolk should be considered the criterion to obtain a commercially safe product. In practice, the location of the yolk is not known, but according to the CFD analysis, assuming a central position of the yolk would comprise a ‘‘worst-case scenario.’’ Such assumption should lead to good practice when assessing and designing pasteurization processes. Obviously, other geometrical factors like shape and contour of egg and yolk will also contribute to the required process time.
14.6.3 PROCESS DESIGN Besides process assessment, CFD can also be very useful for designing egg pasteurization processes. Process design involves selecting appropriate process parameters to achieve the pasteurization criterion within an acceptable process time and for a range of product dimensions. To illustrate this, CFD simulations were conducted for virtual intact eggs of different sizes. Egg volumes between 45 and 70 cm3 were considered in the procedure. In the simulations, a worst-case scenario was assumed, meaning that SE reduction was calculated in the transient cold spot of the yolk and the yolk was considered to be located at the center. According to the process assessment study described above, such conditions would lead to a conservative and safe approach. The equation of Carter [9] was used for the egg contour description and ‘‘typical’’ egg and yolk geometries were considered based on average geometry parameters p and m (Table 14.1) for eggs of different sizes and shapes, obtained in the work of Denys et al. [12–14]. It was observed that the value of these geometrical parameters was independent of egg size and varied only very little with egg shape, as can be seen from the low standard deviations for 60 eggs of a range of sizes and shapes ( p ¼ 1:096 0:04, m ¼ 2:022 0:07). The geometrical parameters used here are included in Table 14.6. Figure 14.17 shows minimum process times and temperatures to provide equivalent pasteurization effectiveness at 5 log reductions of SE both for derived egg products (according to the parameters used in the International Egg Pasteurization Manual [28]) and for intact eggs. The graphical presentation of Figure 14.17 is
10
20
40 10
20
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20
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30
Temperature (8C)
0
2
4
6
8
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14
SE reduction (log units)
Temperature cold spot egg white SE reduction cold spot egg white
Time (min) Temperature cold spot yolk SE reduction cold spot yolk
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SE reduction (log units) Temperature cold spot egg white SE reduction cold spot egg white
Time (min) Temperature cold spot yolk SE reduction cold spot yolk
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Yolk at center −10
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−30 0
CFD Analysis of Thermal Processing of Eggs
FIGURE 14.16 Top: Transient cold spots in yolk and egg white, projected after each time step (5 s) on a symmetry plane, for three virtual eggs with different yolk locations. Bottom: temperature profiles in the transient cold spots and corresponding SE inactivation (in log reductions). Process conditions: initial temperature 208C, ambient temperature 578C. (From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Protect., 68, 366, 2005. With permission.)
Temperature cold spot egg white SE reduction cold spot egg white
Time (min)
0
15 30
2
4
6
8
10
12
14
20
25
30
35
40
45
50
16
55
Egg white cold spot
18
0
30
Yolk cold spot
20
20
10
60
60
50
40
30
20
0
Yolk at top
−10
Temperature cold spot yolk SE reduction cold spot yolk
Temperature (8C)
10
−20
SE reduction (log units)
−30 0
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TABLE 14.5 Minimal Process Times Required to Obtain 5 Log Reductions of Salmonella enteritidis for the Eggs Shown in Figure 14.16 Yolk Position
Yolk Cold Spot (min)
White Cold Spot (min)
32.2 37.0 35.4
28.7 31.1 29.5
Top Center Bottom
Source: From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Protect., 68, 366, 2005. With permission.
similar to the one published in Ref. [28] for liquid egg products. In an analogous way as suggested in the referred work, the graphic presentation should enable processors to estimate times and temperatures for any selected process. Whereas the process times recommended in the International Egg Pasteurization Manual are for processes at constant temperature and can be used for continuous pasteurization processes in heat exchangers (where uniform temperatures are generally aimed at), the guidelines suggested here take into account the time and spatial variation of temperature, due to conductive and convective heat transfer, simulated by the CFD model. Furthermore, the pasteurization requirements are based on 5 log reductions of SE in the transient cold spot of the yolk. As a result, minimum pasteurization times are much longer than the required process times according to the International Egg Pasteurization Manual (Figure 14.17). The results of the CFD analysis as presented in Figure 14.17 provide very useful information for egg processors aiming at pasteurizing intact eggs. Processors can select appropriate process times and temperatures to obtain the desired pasteurization criterion, for a selected egg size. It should be stressed however that the process times reported in the figure are only valid for a specific surface heat transfer coefficient of 490 W m2 K1 . This value resulted from the combined CFD and experimental approach for the determination of surface heat transfer coefficient for specific experimental conditions, which was explained earlier. Obviously, the surface heat transfer coefficient h depends on the fluid dynamics properties of
TABLE 14.6 Geometrical Parameters for Virtual Eggs Used for the Design of Pasteurization Processes for Intact Eggs Egg No. 1 2 3 4 5 6
Egg Volume (cm3)
L (mm)
B (mm)
p
m
Yolk Diameter (mm)
Shell Thickness (mm)
45 50 55 60 65 70
54.99 56.17 57.35 58.53 59.71 60.89
40.34 41.70 43.07 44.43 45.79 47.16
1.096 1.096 1.096 1.096 1.096 1.096
2.022 2.022 2.022 2.022 2.022 2.022
32 32 32 32 32 32
0.45 0.45 0.45 0.45 0.45 0.45
Source: From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Protect., 68, 366, 2005. With permission.
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Required process time (min)
70 60 50
Egg 70 cm3
40 30 Egg 45 cm3 20
Liquid egg yolk
10
Liquid egg white
0 54
55
56
57
58
59
60
61
Process temperature (⬚C)
FIGURE 14.17 Minimum process times and temperatures to provide equivalent pasteurization effectiveness at 5 log reductions of SE, for liquid egg products (source: egg pasteurization manual), and for virtual intact eggs of volumes 45, 50, 55, 60, 65, and 70 cm3 . (From Denys, S., Pieters, J.G., and Dewettinck, K., J. Food Protect., 68, 366, 2005. With permission.)
the heating media and the geometry under study. If other heating media are used, the value of h should be redetermined or estimated and the results adapted accordingly. Considering the flexibility of CFD, adapting solutions in terms of process conditions or geometrics is very straightforward.
14.7 CONCLUSIONS In this chapter, recent advances in the application of CFD for analyzing, assessing, and designing batch pasteurization processes for intact eggs were illustrated. The general conclusion is that like in other food engineering areas, CFD can be a valuable and promising tool for analysis, design, and assessment of batch processes aimed at the pasteurization of intact eggs. Like for all CFD analyses, the model accuracy largely depends on the accuracy to which the egg geometry can be described. Typically, eggs show a high variability in their size and shape, and some method should be used to take this into account. Simple computer image analysis and mathematical equations available in the literature can be successfully used to this end. Besides geometry analysis, boundary conditions should be established from empirical equations correlating the dimensionless Nusselt number to the flow properties and thermal=physical properties of the heating medium in which the eggs are processed. As an alternative, such boundary conditions can also be determined based on the combination of CFD analysis and experiments using a conductive heating test material with known properties. The latter method can be used when empirical Nusselt relations are not available (e.g., when processing a large amount of eggs where the local heating medium velocities are unknown). When appropriate geometries and boundary conditions are used, CFD can deliver accurate transient temperature and velocity profiles during thermal processing. This was illustrated for both model eggs (egg-shaped bodies filled with a viscous test medium) and intact eggs. CFD analysis furthermore shows that in the case of liquid or semiliquid products, natural convection tends to force the slowest heating zone towards the bottom of the egg. For intact eggs, the most
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accurate results were obtained when considering convective heat transfer in the egg white fraction, but apparently conduction is the dominating heat transfer mode in the yolk. The most promising application of CFD lies in its great potential for assessing and designing intact egg pasteurization processes without the need for extensive experimental work. CFD offers the possibility of incorporating kinetic models describing thermal inactivation of SE through user-defined functions and procedures, allowing the food engineer to predict the impact of processes in terms of surviving microorganisms. Combining CFD and inactivation kinetics seems to be the obvious approach to follow for assessing and designing egg pasteurization processes in terms of consumer safety and process efficiency, as illustrated in the final section of the chapter. In such an approach, geometrical factors contributing to the required process time (like shape and contour of egg and yolk) can be taken into account. In such way, a complete process assessment and design system can be developed for intact eggs based on worst-case conditions. One can imagine that loss of functional properties of egg products could also be included in a profound CFD analysis if useful models are available. This would allow food engineers and operators to design processes that are fully optimized in terms of both consumer safety and functional properties. To date, there has been no intention to include models for loss of functional properties in a CFD analysis.
NOMENCLATURE DTref F G H L N N0 Ra t T T1 T0 Ti Tref z
D-value at reference temperature (min) process value (min) gravitational acceleration (m2 s2 ) surface heat transfer coefficient (W m2 K1 ) characteristic dimension (m) final microbial load (g mL1 or any appropriate unit) initial microbial load (g mL1 or any appropriate unit) Rayleigh number heating time (s) temperature (K) ambient temperature (K) reference temperature (K) initial temperature (K) reference temperature (K) z-value (K)
GREEK SYMBOLS a b r r0 m
thermal diffusivity (m2 s1 ) volumetric thermal expansion coefficient (K1 ) density (kg m3 ) reference density (kg m3 ) dynamic viscosity (N s m2 )
REFERENCES 1. T.J. Humphrey. Contamination of eggs with potential human pathogens. In: R.G. Board and R. Fuller (Eds.). Microbiology of the Avian Egg. London: Chapman & Hall, 1994, pp. 93–116. 2. W.J. Stadelman, R.K. Singh, P.M. Muriana, and H. Hou. Pasteurization of eggs in the shell. Poultry Science 75: 1122–1125, 1996.
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3. H. Hou, R.K. Singh, P.M. Muriana, and W.J. Stadelman. Pasteurization of intact shell eggs. Food Microbiology 13: 93–101, 1996. 4. J.M. Vandepopuliere and J. Owen II. Cotterill egg and egg products symposium—Introduction to egg pasteurization. Poultry Science 75: 1121, 1996. 5. J.D. Schuman, B.W. Sheldon, J.M. Vandepopuliere, and H.R. Ball Jr. Immersion heat treatments for inactivation of Salmonella enteritidis with intact eggs. Journal of Applied Microbiology 83: 438–444, 1997. 6. V.G. Narushin. Nondestructive measurements of egg parameters and quality characteristics. World’s Poultry Science Journal 57: 141–153, 1997. 7. Y. Bonnet and P. Mongin. Mesure de la surface de l’œuf. Annales de Zootechnie 14: 311–317, 1965. 8. T.C. Carter. The hen’s egg: A mathematical model with three parameters. British Poultry Science 9: 165–172, 1968. 9. T.C. Carter. The hen’s egg: Estimation of shell superficial area and egg volume from four shell measurements. British Poultry Science 15: 507–511, 1974. 10. V.G. Narushin. The avian egg: Geometrical description and calculation of parameters. Journal of Agricultural Engineering Research 68: 201–205, 1997. 11. V.G. Narushin. Shape geometry of the avian egg. Journal of Agricultural Engineering Research 79(4): 441–448, 2001. 12. S. Denys, J.G. Pieters, and K. Dewettinck. Combined CFD and experimental approach for determination of the surface heat transfer coefficient during thermal processing of eggs. Journal of Food Science 68(3): 943–951, 2003. 13. S. Denys, J.G. Pieters, and K. Dewettinck. Computational fluid dynamics analysis of combined conductive and convective heat transfer in model eggs. Journal of Food Engineering 63: 281–290, 2004. 14. S. Denys, J.G. Pieters, and K. Dewettinck. Computational fluid dynamics analysis for process impact assessment during thermal pasteurization of intact eggs. Journal of Food Protection 68(2): 366–374, 2005. 15. G. Scott and P. Richardson. The application of computational fluid dynamics in the food industry. Trends in Food Science and Technology 8: 119–124, 1997. 16. W.S. Janna. Engineering Heat Transfer, 2nd ed. New York: CRC Press, 2000, pp. 396–397. 17. F.P. Incropera and D.P. DeWitt. Fundamentals of Heat and Mass Transfer, 5th ed. New York: John Wiley and Sons, 2002, pp. 240–254. 18. W. Wagner and A. Pruß. The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. Journal of Physical and Chemical Reference Data 31: 387–535, 2002. 19. W.J. Stadelman. Quality identification of shell eggs. In: W.J. Stadelman and O.J. Cotterill (Eds.). Egg Science and Technology. London: Macmillan, 1986, pp. 37–62. 20. C.M. Sabliov, B.E. Farkas, K.M. Keener, and P.A. Curtis. Cooling of shell eggs with cryogenic carbon dioxide: A finite element analysis of heat transfer. Lebensmittel-Wissenshaft und-Technologie 35: 568–574, 2002. 21. A.K. Datta and A.A. Teixeira. Numerically predicted transient temperature and velocity profiles during natural convection heating of canned liquid foods. Journal of Food Science 53(1): 191–195, 1988. 22. A. Kumar, M. Bhattacharya, and J. Blaylock. Numerical simulation of natural convection heating of canned thick viscous liquid food products. Journal of Food Science 55(5): 1403–1411, 1990. 23. A. Kumar and M. Bhattacharya. Transient temperature and velocity profiles in a canned nonNewtonian liquid food during sterilization in a still-cook retort. International Journal of Heat and Mass Transfer 34(4=5): 1083–1096, 1991. 24. A.G. Ghani, M.M. Farid, X.D. Chen, and P. Richards. Numerical simulation of natural convection heating of canned food by computational fluid dynamics. Journal of Food Engineering 41: 55–64, 1999. 25. A.G. Ghani, M.M. Farid, X.D. Chen, and P. Richards. Thermal sterilization of canned food in a 3-D pouch using computational fluid dynamics. Journal of Food Engineering 48: 147–156, 2001.
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26. A.G. Ghani, M.M. Farid, and X.D. Chen. Numerical simulation of transient temperature and velocity profiles in a horizontal can during sterilization using computational fluid dynamics. Journal of Food Engineering 51: 77–83, 2002. 27. F.E. Cunningham. Egg-product pasteurization. In: W.J. Stadelman and O.J. Cotterill (Eds.). Egg Science and Technology. London: Macmillan, 1986, pp. 243–272. 28. G.W. Froning, D. Peters, P. Muriana, K. Eskridge, D. Travniceck, and S.S. Summer. International Egg Pasteurization Manual. Alpharetta, GA: United Egg Association, 2002. 29. C.O. Ball and F.C.W. Olson. Sterilization in Food Technology. Theory, Practice, and Calculations. New York: McGraw-Hill, 1957. 30. A.L. Romanoff and A.J. Romanoff. The Avian Egg. New York: John Wiley and Sons, 1949.
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CFD Simulation of Stirred Yoghurt Processing in Plate Heat Exchangers Joa˜o M. Maia, Joa˜o M. No´brega, Carla S. Fernandes, and Ricardo P. Dias
CONTENTS 15.1 15.2 15.3
Introduction ............................................................................................................. 381 Geometry of PHE Channels .................................................................................... 383 Hydraulic Performance of Plate Heat Exchangers with Yoghurt and Newtonian Fluids..................................................................................................... 385 15.4 Thermal Performance of Plate Heat Exchangers with Yoghurt............................... 392 15.5 Conclusions .............................................................................................................. 399 Nomenclature ..................................................................................................................... 399 References .......................................................................................................................... 400
15.1 INTRODUCTION Yoghurt is a dairy food obtained by promoting the growth of the lactic acid bacteria Streptococcus salivarius subsp. thermophilus and Lactobacillus delbrueckii subsp. bulgaricus in milk at a temperature between 408C and 438C until a desired acidity level is reached. These bacteria are responsible for the production of lactic acid from milk lactose. The manufacturing methods employed vary considerably depending, for instance, on the type of product being manufactured and raw materials used; but there are some common principles that determine the nature and quality of the final product. Among these are the fortification of milk solids, the thermal treatment of the milk, the inoculation of the thermally treated milk with the bacterial culture, the incubation of the inoculated milk, and the cooling of the coagulum and the packaging, and chilled storage [1–3]. Yoghurt is usually classified as set yoghurt or stirred yoghurt depending on its physical state in the retail container. Set yoghurt is fermented in a retail container, which is filled after milk inoculation and is incubated for approximately 2.5 to 4 h at a temperature around 408C to 438C. In the manufacturing process of stirred yoghurt, milk is inoculated and incubated in a fermentation tank and the gel of yoghurt is broken up during the stirring, cooling, and packing stages [3]. The rheology of stirred yoghurt is complex and depends on some physical properties of the raw material such as the solids concentration and the physical state of fats and proteins present in the milk and type of starter culture and, at the same time on some process conditions-related, such as homogenization, thermal pretreatment of the milk, and postincubation.
381
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Milk homogenization is characterized by the breaking up of the milk fat globules into smaller ones, which improves the consistency and viscosity, mainly because it prevents the rise of milk fat to the surface in the incubation tanks or in the retail container. Thermal treatment of milk induces the main changes in the manufacture of the yoghurt since it denatures the whey proteins and induces interactions between the k-casein, b-lactoglobulin, and a-lactalbumin, thus increasing the hydrophilic properties of the coagulum and the stability of the yoghurt gel [1,3,4]. After inoculation of thermally treated milk, the bacterial culture begins to produce lactic acid and subsequently a decrease of pH occurs. This effect lowers the negative net charge of the casein particles and the colloidal calcium, which binds the casein micelles together, and is leached out into the serum. Therefore, the micelles begin to aggregate and eventually coagulate into a network of small chains as the casein is precipitated. At a certain pH, coagulation is initiated and as pH approaches the isoelectric point of the casein, maximum curd firmness is obtained, entrapping the fat globules and residual serum. The coagulum of stirred yoghurt has spaces containing the liquid phase and some starter cultures. After inoculation, the coagulum of stirred yoghurt is broken up mechanically before cooling and packing, thus inducing considerable changes in the rheological characteristics. For the consumer acceptability of food products, four quality attributes of food material are crucial—texture, flavor, appearance, and nutrition. Among the four attributes, texture and appearance are strongly dependent on product rheology [5]. The rheology of stirred yoghurt has been studied by several authors [3,6–12]. Stirred yoghurt is characterized as a material with shear thinning, thixotropic, viscoelastic, and yield stress properties. One of the most used models to describe the steady-shear rheological behavior of yoghurt is the Herschel–Bulkley model: s ¼ s0 þ K g_ n ,
(15:1)
where s is the shear stress, s0 is the yield stress, K is the consistency factor, g_ is the shear rate, and n is the flow behavior index. Fangary et al. [5] studied three commercial yoghurts differing mainly in the type of starter culture and found that s0, K, and n varied in the range 6.1–14.9 Pa, 3.4–9.5 Pa sn, and 0.33–0.46, respectively. Henningson et al. [12] introduced three different salt concentrations in a commercial yoghurt and found that s0 and K varied in the range 5.3–6.7 Pa and 3.6–3.7 Pa sn, respectively, assuming the n value of 0.37. Afonso et al. [10] produced a stirred yoghurt and found that, after the cooling in a plate heat exchanger, s0 ¼ 6.7 Pa, K ¼ 3.65 Pa sn, and n ¼ 0.42. Afonso and Maia [3] studied the influence of temperature on viscosity of stirred yoghurt using three samples collected in different stages of the production and identified two regions with different temperature dependencies. Above 258C there was a highly pronounced dependency of viscosity on temperature that could be described mathematically by an Arrhenius-type equation [3,10,13]. For the stirred yoghurt produced by Afonso et al. [10] the activation energy assumed a value of 3394.3 J mol1 for temperatures below the 258C and 94,785 J mol1 above. The authors also found different activation energies in different stages of the yoghurt manufacturing. The breakdown processes that arise during the motion of a fluid are known to have an effect on the rheological properties of nearly all the fluids in the food industry [14]. Physical process brings about irreversible changes in the yoghurt textural properties but a partial structure recovery can be observed upon the cessation of flow due to yoghurt viscoelasticity [3,5]. Plate heat exchangers (PHEs) are commonly used on food and dairy industries for tasks including the high-temperature short time pasteurization of milk, beer, and fruit juices [15,16]
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as well as the cooling of stirred yoghurt, in the laminar regime, to stop lactic fermentation when a desired acidity is reached [10]. This type of equipment is often used due to its advantages namely, easy disassembly of the heat exchanger for cleaning and sterilization, low space requirement, low fouling tendency, and high efficiency [15,17–19]. Process fluid media generally have non-Newtonian characteristics and the shear thinning or thickening behavior of these fluids greatly affects the thermal–hydraulic performance of the production process [20,21]. Due to the broad range of application of this heat transfer equipment, several experimental and modeling studies have been performed in order to evaluate the thermal and hydraulic performance of different plate patterns, fouling tendency, corrosion mechanisms, and the optimization of different arrangements and configurations, when dealing with Newtonian and non-Newtonian fluids [10,15,19,22–38]. However, the data present in literature is very ambiguous in what concerns the geometric properties of the plates used in the studies and usually the rheological properties of the fluids are omitted. Fernandes et al. [36,37] studied numerically the cooling of stirred yoghurt in plate heat exchangers using the commercial package POLYFLOW. The computational fluid dynamics (CFD) results were compared with the experimental data from Afonso et al. [10] and a good agreement was found. The results obtained in the CFD calculations allowed a deep insight of the main phenomena involved in thermal–hydraulic problem than was possible with experimental work.
15.2 GEOMETRY OF PHE CHANNELS The thermal–hydraulic performance of a PHE is strongly dependent on geometrical properties of the chevron plates [18,39,40], namely on corrugation angle, b, area enlargement factor, f, defined as the ratio between the effective plate area and projected plate area, and channel aspect ratio (Figure 15.1). The channel aspect ratio, g, is commonly defined as in Figure 15.1a
z x Pc
L b b w
y x
Px
Symmetry axis (a)
(b)
FIGURE 15.1 (a) Schematic representation of a chevron plate and (b) corrugation dimensions.
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g¼
2b , pc
(15:2)
where b is the interplates distance and pc is the corrugation pitch. The area enlargement factor can be estimated with precision by [41] ( ) 2 0:5 2 0:5 1 p p 1þ 1þ f¼ g þ 4 1 þ 3=2 g : 6 2 2
(15:3)
Equation 15.2 and Equation 15.3 predict that as pc ! 0, the area enlargement factor will achieve very large values. Small values of pc will lead to the formation of microchannels in the PHE passages. For the construction of the computational domain used on the CFD calculations, the corrugations of a chevron plate can be described by a sine curve [29,36]: pc b 2p b y(x) ¼ sin x þ : pc 2 4 2
(15:4)
Assuming that the PHE has a parallel arrangement [10,36] and admitting a uniform distribution of the total flow rate in the various channels, the flow simulations can be carried out in a single channel. If a uniform flow is considered inside each channel, a symmetry axis can be established (Figure 15.1) simplifying the geometrical domain to half of a channel, as is shown in Figure 15.2. Although the computational domain of the PHE passages is highly complex due to the multiple contractions and expansions along the channel, a mesh composed by tetrahedral, hexahedral, prismatic, and pyramidal elements was found to be adequate for the calculations [33–36].
y z
x
FIGURE 15.2 Geometry of half of a PHE channel.
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Grid independency tests have to be performed in order to evaluate the influence of the mesh in the obtained results. The influence of mesh on Fanning friction factors and mean velocities is commonly used for this purpose [29,31,36,37]. Fernandes et al. [36] carried out the grid independence test performing simulations for the same operation conditions and geometry (Figure 15.2), using the same kind of meshes, i.e., meshes constituted by the same type of elements, differing between them in the size of the element only. For that purpose, four meshes with distinct nodal distance were used: 2, 1.5, 1.2, and 1 mm. To evaluate the influence of the mesh in the obtained results, Fernandes et al. [36] used the results of the mean velocities. The obtained results were compared and it was concluded that the values obtained with the two finest grids were very similar (mean deviation of 0.02%) and distinct from those obtained with the others. Since computational time when using the finest grid (1 mm) is about 50% higher than the time spent on the calculations using the mesh with the nodal distance of the 1.2 mm, all simulations shown below were performed using the latter mesh.
15.3 HYDRAULIC PERFORMANCE OF PLATE HEAT EXCHANGERS WITH YOGHURT AND NEWTONIAN FLUIDS Fernandes et al. [36,37] studied numerically the non-Newtonian and nonisothermal laminar flow of stirred yoghurt in a PHE with a chevron angle of 308, which had been the subject of a previous experimental work performed by Afonso et al. [10]. Numerically, Fernandes et al. [36,37] solved the problem using the commercial finite element method package POLYFLOW and all the simulations were performed in the range of Reynolds numbers (0.28 Re 11.25) and temperatures that Afonso et al. [10] have used in their study. Fourier’s law (Equation 15.5) was assumed to model the heat conduction in the plates of the PHE, q ¼ lp rT,
(15:5)
where q is the heat flux vector, lp the thermal conductivity of the plates, and T the absolute temperature. The equations required to describe the laminar flow were the Navier–Stokes equations. This set of equations composes the conservation equations for mass, linear momentum, and energy [42]. Considering stationary flow of incompressible fluid, the equations above assume, respectively, the form div(u) ¼ 0,
(15:6)
div T þ r b r div(uu) ¼ 0,
(15:7)
Tru þ r h div q ¼ 0,
(15:8)
where u is the velocity vector, T the total stress tensor, and h refers to the heat supply or strength of an internal heater. To describe the rheological behavior of stirred yoghurt during cooling treatment on this PHE, the experimental and computational results from Afonso et al. [10], that found the behavior to be of the Herschel–Bulkley type, were used on the numerical study: s ¼ s0 þ K1 g_ s ¼ K2 g_ n
for for
with K1 and K2 being the consistency factors.
s < 6:7 Pa, s 6:7 Pa,
(15:9a) (15:9b)
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Under the operating conditions in the PHE, the referred authors found that the fluid had a predominant shear thinning behavior and for all conditions, values of s 6.7 Pa were obtained. Thus, the constitutive equation employed was exclusively based on Equation 15.9b. The influence of temperature in the material viscosity was introduced by a term of the Arrhenius type: h(T ) / eE=RT ,
(15:10)
where E is the activation energy and R the ideal gas constant. In Equation 15.9b, K2 ¼ 3.65 Pa s0.42, n ¼ 0.42, and E ¼ 94,785 J mol1 [10]. Since experimental data was available [10], Fernandes et al. [36] established the boundary conditions based on that data, taking into account that the PHE studied on their work operates with parallel arrangement and in counterflow. Yoghurt volumetric flow rate per channel, mv, was given by mv ¼
Mv , Nc
(15:11)
where Mv is the total volumetric flow rate of yoghurt and Nc the number of channels, Nc ¼
Np 1 , 2
(15:12)
with Np the total number of plates. The inlet temperature of yoghurt was established according to the experimental data and a variable heat flux was imposed along the plates of the PHE. The profile of heat flux along the plates, q(x), for the case of counterflow could be mathematically expressed by [36]
q(x) ¼ UF Tyogin Twatout
"
1 1 exp 2ULF fx Mwat Cpwat Myog Cpyog
!# ,
(15:13)
where x is the dimension on the main flow direction (0 x L), U is the overall heat transfer coefficient, F the correction factor, M the mass flow rates per channel, and Cp the specific heat from the fluid. Since POLYFLOW only allows the use of a constant or linear heat flux as thermal boundary conditions, Equation 15.13 had to be transformed to a linear form: q(x) ¼ q(0) þ
q(L) q(0) x, L
(15:14)
the average deviation between Equation 15.13 and Equation 15.14, considering all the simulations, being 1.39%. Pressure drops in PHEs passages are usually estimated resorting to Fanning friction factors correlations. In laminar regime these correlations assume the form [18,36]: f ¼
a , Re
(15:15)
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where a is a constant and f and Re are given by f ¼
DPDH , 2Lru2
(15:16)
ruDH : h
(15:17)
Re ¼
In the above equations, DP is the pressure drop, h is the fluid viscosity, r is the fluid density, L is the effective length of the channel, u is the average velocity, and DH is the hydraulic diameter given by u¼ DH ¼
mv , wb
4 channel flow area 2b ffi : wetted surface f
(15:18) (15:19)
Simulations considering and discarding the effect of the temperature on the yoghurt viscosity were performed by Fernandes et al. [36] and the obtained f–Re expressions took the form f ¼
26:740 , Re
(15:20)
f ¼
37:246 , Re
(15:21)
respectively. Equation 15.20 and Equation 15.21 evidence the importance of the activation energy on the pressure drop estimation by CFD calculations and also the laminar flow of the yoghurt under the studied operating conditions. The value of a in the above expressions is clearly inferior to 50, i.e., the typical value for Newtonian fluids and a chevron angle of 308 [18,39,43]. Concerning the isothermal flow of Newtonian fluids in laminar regime from Equation 15.15 through Equation 15.17, it follows that DP 2a u h ¼ : L D2H
(15:22)
The pressure drop in a channel with a shape factor a, can be calculated by the Hagen–Poiseuille equation [44]: DP ¼
ahLav v , D2H
(15:23)
where Lav is the average travel distance of a fluid element in the channel and v the average interstitial velocity of the fluid. The average or apparent velocity, u, and v can be related by v¼u
Lav ¼ ut, L
(15:24)
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Contact point z z (a)
x x
Contact point
(b)
FIGURE 15.3 Velocity vectors for PHE with gx ¼ 0.76: (a) b ¼ 308 and (b) b ¼ 758.
with t being the tortuosity of the 3D fluid flow in the corrugated passage. From Equation 15.22 through Equation 15.24 a mathematical expression that relates the constant a from the f–Re relation, the shape of the channel and the tortuosity of the flow could be obtained by a ¼ a t2 : 2
(15:25)
In plates with b ¼ 908, straight double-sine ducts [45] are observed and the tortuosity assumes the value of 1 (the minimum possible value). With the decrease of the corrugation angle the tortuosity will increase, since this will lead to a higher component of the velocity in the z-direction. This fact can be observed in Figure 15.3, where it is shown the velocity fields, in the plane of contact between the plates, for corrugation angles of 308 and 758. If the ratio gx is defined , gx ¼ 2b px
(15:26)
where px is the pitch on the main flow direction (x-axis), Figure 15.1b, being related with the standard corrugation pitch by the expression px ¼
pc : cos (b)
(15:27)
It is clear that with the increase of gx, Figure 15.1b, the flow will present a more pronounced waving behavior (larger velocities component on the y-direction) and thus a larger tortuosity (see Figure 15.4). In these figures the corrugation angle is the same (308), the waving behavior being larger in the channel with higher gx (Figure 15.4b). The referred quantity gx, defined on the main flow direction, is a useful tool to an easier understanding of the fluid flow in the 3D PHE passages and for that reason we will work with gx instead of g. To study the influence of the corrugation angle on the hydraulic performance of PHEs passages, Fernandes et al. [35] performed a numerical analysis with Newtonian fluids in the laminar regime, considering gx ¼ 0.76. In Figure 15.5, a similar analysis is presented, in
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y x (a)
y
x (b)
FIGURE 15.4 Velocity vectors for a plane perpendicular to the z-axis (z ¼ constant) for PHE channels with b ¼ 308: (a) gx ¼ 0.39 and (b) gx ¼ 0.76.
isothermal conditions, but for gx ¼ 0.52, i.e., the same gx from the PHE studied by Afonso et al. [10] and Fernandes et al. [35,36]. The values of a obtained by CFD calculations, on hydraulic fully developed flows [30], agree reasonably well with the experimental data from Kumar [39] (Figure 15.5). Comparing the present results with that from Fernandes et al. [35] it can be concluded that for the same corrugation angle the constant a increases with gx, which is explained by the increase of the tortuosity (Equation 15.25). 90 CFD calculations
Constant a
75
Kumar [39]
60 45 30 15 0
15
30
45
60
75
90
Corrugation angle b (8)
FIGURE 15.5 Values of constant a for Newtonian fluids and different corrugation angles, with gx ¼ 0.52.
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1.5
45
1.4
40
Shape factor a / 2
Tortuosity t
390
1.3 1.2 1.1 1 10
20
30
40
50
60
70
80
35 30 25 20 15 10 10
90
20
Corrugation angle b (8) (a)
30 40 50 60 70 Corrugation angle b (8)
80
90
(b)
FIGURE 15.6 Tortuosity and shape factor variation with the corrugation angle for gx ¼ 0.52: (a) tortuosity and (b) shape factor.
The estimated contribution of tortuosity and shape factor to the value of the constant a can be evaluated from Figure 15.6 for gx ¼ 0.52. The average interstitial velocity in the PHE channels can be calculated by the CFD, and the results expressed in terms of the tortuosity are given by Equation 15.24, since u is known (Equation 15.18). With the values of the tortuosity and constant a, the shape factors can be estimated by Equation 15.25. As expected, and shown in Figure 15.6a, the tortuosity becomes closer to 1 as the corrugation angle approaches 908. Near this angle (858) the shape factor (Figure 15.6b) is on the range predicted by Ding and Manglik [45] for double-sine ducts with different aspect ratio (29.2–34.2). Besides the importance on pressure drop estimations and the contribution to a better understanding of the fluid flow in PHE passages, the development of Fanning friction factor expressions with Newtonian fluids can be useful in other areas. One of them is the prediction of maldistribution in PHEs. It is known that after the inlet of the fluid in a PHE with a parallel arrangement, the flow rate is hardly equally distributed to the different passages, the nonuniformity of the flow rate distribution in the different parallel channels being inversely proportional to the Fanning friction factors of the passages and directly proportional to the number of passages [22]. This unequal flow rate distribution leads to unequal convective heat transfer coefficients and pressure drops in the different PHE ducts [22,46]. Another area where Newtonian Fanning friction factor correlations can be useful is on the prediction of shear rates in channels with complex geometries. When studying the flow of power-law fluids in different channels, Delplace and Leuliet [27] proposed for the calculation of wall shear rate, g_ w , in a generic duct: g_ w ¼ j
yn þ 1 u : (y þ 1)n DH
(15:28)
For infinite parallel plates, the coefficients j and y assume the value of 12 and 2, respectively. In complex ducts, as in PHEs passages, the analytical deduction of the referred coefficients is not possible and the authors propose that they be given by j¼
f Re, 2
(15:29)
24 , j
(15:30)
y¼
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Wall shear rate gω (s−1)
2000 1
1500
2
⋅
1000
4 3
500 5 0 0
0.05
0.1
0.15
Velocity u (m
0.2
0.25
s−1)
FIGURE 15.7 Wall shear rate prediction using Equation 15.28, for PHEs with gx ¼ 0.52. Line 1 corresponds to b ¼ 308 [10,36,37]; line 2 to b ¼ 608 [33,34]; line 3 to b ¼ 858; line 4 to parallel plates; and line 5 for cylindrical ducts.
where f is the Fanning friction factor of the duct, determined with a Newtonian fluid, in laminar regime and isothermal conditions. The results of this methodology, developed in laminar isothermal conditions, can be then applied also to nonisothermal situations and turbulent flows [27]. The referred authors found a good agreement with the data available in the literature for complex ducts and Fernandes et al. [36] accordingly found good agreement between the yoghurt CFD wall shear rates and Equation 15.28. PHEs develop high shear rates close to the wall, as shown in Figure 15.7, the shear rates being much higher than the observed in infinite parallel plates or cylindrical ducts with the same hydraulic diameter. The laminar isothermal CFD values of a from Figure 15.5 can be used to estimate the wall shear rates developed during the flow of yoghurt (n ¼ 0.42), resorting to Equation 15.28 through Equation 15.30, in a broad range of corrugation angles (Figure 15.7). The low viscosity of yoghurt is one of the most common manufacturing defects of yoghurt, one of the remedies being the improvement of the dispensing assembly [5,47]. During the flow through the cylindrical filling nozzles the yoghurt is subjected to high wall shear rates (typical values are between 800 and 1250 s1) and this may lead to an irreversible breakdown of yoghurt viscosity [5]. Besides the magnitude of the shearing the extent of the viscosity breakdown depends also on the exposing time, 5 s being a typical value for the flow of the yoghurt through the filling head [5]. In the manufacturing process of stirred yoghurt, the gel is broken up during the stirring, cooling, and packing stages but the extension of the structure degradation of the coagulum must be controlled. In Figure 15.7, curve 1, it can be seen that for the PHE (with 0.19 m length) and yoghurt studied by Afonso et al. [10] and Fernandes et al. [36], wall shear rate goes up to a value around 1800 s1 the residence time (L=u) being near 1 s for the correspondent velocity. In the same figure it can be observed that PHEs with the same hydraulic diameter and higher corrugation angle can provide smaller wall shear rates for a certain velocity. Since high shear rates can be also obtained with these higher corrugation angles, by varying the velocity, they seem to be a more flexible solution from the single point of view of the desired gel structure breakdown. Simultaneously, high corrugation angles will provide lower Fanning friction factors (see Figure 15.5).
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0.8
Viscosity h (Pa s−1)
Shear rate g (s−1)
200
150
⋅
100
50
0.6
0.4
0.2
0
0 0
0.05 0.1 0.15 Distance x (m)
0
0.2
0.05
0.1 0.15 Distance x (m)
0.2
(b)
(a)
FIGURE 15.8 (a) Shear rate and (b) viscosity of yoghurt profiles along the intersection of the planes; y ¼ 0 and z ¼ 0.009 for Re ¼ 1.81.
On the other hand, as the Fanning friction factors decrease, the maldistribution effect can increase mainly if a large number of plates are used and a point where no flow is observed in some of the PHE channels [22] can be reached. It is clear in this extreme case that in the channels available to the flow the average velocity (and wall shear rate) will be higher than that predicted by admitting a uniform flow distribution to all the channels. So, the extent of the structure breakdown obtained with a PHE presenting a good flow distribution will not be the same to that obtained with a PHE presenting serious problems of maldistribution. As shown in Figure 15.4, PHEs present a complex geometry the fluid being subjected to periodic contractions and expansions. As a consequence, the shear rate shows a sinusoidal behavior along the channels (Figure 15.8a); this, in turn, induces a similar behavior in the viscosity (Figure 15.8b), which increases along the channel during yoghurt cooling. Resorting to the average values of viscosity and shear rate, the numerical simulations showed, in the operating conditions used by Fernandes et al. [36], that the average values of shear stress ranged from 20 to 46 Pa, which are clearly higher than 6.7 Pa, i.e., the apparent yield stress from the yoghurt experimentally studied by Afonso et al. [10]. Despite the complex 3D flow observed in PHEs, Fernandes et al. [36] found for the PHE and yoghurt under study that wall shear rate and average, or bulk, shear rate were closely related by an expression usually employed in infinite parallel plates: g_ ¼
n g_ : nþ1 w
(15:31)
The majority of the velocity profiles, acquired in different points of the PHE, presented a parabolic-conical shape and this can be an explanation to the observed relation. The maximum velocities of the referred profiles were however very different, due to the variations of cross-sectional area offered to the fluid.
15.4 THERMAL PERFORMANCE OF PLATE HEAT EXCHANGERS WITH YOGHURT Thermal performance of PHEs is normally evaluated resorting to the Nusselt number, Nu, usually described by empirical correlations, the most common being the Dittus–Boelter type [48]:
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Nu ¼ c Rem Pr0:3 ,
393
(15:32)
where Pr is the Prandtl number and defined as Pr ¼
Cph , k
(15:33)
with k the thermal conductivity of the fluid. For Newtonian fluids, c and m are constants dependent on the flow regime and geometrical characteristics of the PHE plates [18,43]. However, when the processed fluids exhibit a strong dependence of viscosity with temperature, the PHE induces changes in velocity fields and normally a Sider and Tate correction is introduced in the Dittus–Boetler correlation to describe this effect [23,43,48]: 0:14 h Nu ¼ c Rem Pr0:3 h , w
(15:34)
with h and hw being the apparent viscosity of fluid in the bulk and on the wall of the channel, respectively. Local Nusselt numbers along the PHE channels can be determined taking into account the following definition: Nu(x) ¼
h(x)DH , k
(15:35)
where h(x) is the local convective heat transfer coefficient. Using the thermal boundary condition employed, h(x) can be determined by h(x) ¼
q(x) : (Tyog Tw )(x)
(15:36)
When studying the yogurt cooling in a PHE with b ¼ 308 and gx ¼ 0.52, Fernandes et al. [37] did the Tyog and Tw estimation, resorting to POLYFLOW (Figure 15.9). In each plane x ¼ constant, Tyog was the average temperature of the fluid in the channel, and Tw was computed as the average temperature of the stainless steel plates. Figure 15.9 shows the irregularity of the temperature in the channel. Due to the complexity of the plates and flow, elements of fluid with lower temperature coming from the walls mix with hot fluid in the bulk and vice versa, which explains the observed irregularity. The average temperatures of yoghurt and wall along the PHE presented by Fernandes et al. [37] for Re ¼ 0.28 are shown in Figure 15.10. As the conclusion was already made for
323.42 319.80 316.17 312.55 308.93 305.30 301.68 298.05
y
z Plates
Channel
FIGURE 15.9 Temperature distribution in the plane x ¼ 0.03 for Re ¼ 1.81.
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7
Temperature T (K)
315
6 310
5 4
305
3
300
2 295
Temperature Tyog − Tw (K)
8
320
1 0
290 0
0.05
0.1
0.15
0.2
Distance x (m)
FIGURE 15.10 Average temperatures along the channel for Re ¼ 0.28. ( ) yoghurt; ( ) wall; and ( ) difference between wall and yoghurt temperatures.
shear rate and viscosity [36], in reality the yoghurt temperature presents a sinusoidal profile along the plates (Figure 15.11). Fernandes et al. [36,37] studied the average temperature of the wall and yoghurt along the PHE and estimated the respective local convective heat transfer coefficients and Nusselt numbers. In Figure 15.9, it is clear that the difference between wall and yoghurt temperature also varies in the z-direction and therefore Nusselt numbers will also vary in this direction. It seems reasonable to assume, as in other areas [44], a dependency between transversal thermal dispersion and the PHEs tortuosity, which will be studied in future studies. After the calculation of the local heat transfer coefficients by Equation 15.36, local Nusselt numbers can be estimated by Equation 15.35, some of the results being shown in Figure 15.12. It can also be observed in Figure 15.12 that with the employed operating conditions (Reynolds numbers between 0.28 and 11.25), thermal fully developed flows are achieved at a distance from the inlet of about 5 cm. For the referred operating conditions, in the region of
Temperature Tyog (K)
320
315
310
305
300 0
0.05
0.1
0.15
0.2
Distance x (m)
FIGURE 15.11 Temperature profile along the intersection of the planes y ¼ 0 and z ¼ 0.009 for Re ¼ 1.81.
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75
Re = 5.14 Re = 11.25
60 45 30 15 0
0
0.05
0.1 Distance x (m)
0.15
0.2
FIGURE 15.12 Local Nusselt numbers for different Reynolds numbers.
the thermal fully developed flows, Nusselt numbers varied between 10 and 40 (Figure 15.12). For Reynolds numbers between 0.28 and 11.25, the Nusselt numbers for water and a PHE with a chevron angle of 308 can be estimated by Kumar correlations [39] to vary between 0.81 and 2.94, or between 0.94 and 3.68 by Wanniarachchi et al. correlations [49]. Therefore, due to the higher Prandtl numbers and shear thinning effects, yoghurt provides Nusselt numbers, on thermal fully developed flows, more than 10 times higher than those of water. The large magnitude of the thermal entry effects can be clearly identified in Figure 15.12. Thermal entry lengths depend not only on Reynolds numbers but also on Prandtl numbers. In the present analysis low Reynolds numbers were used, but due to the high Prandtl numbers of yoghurt (between 581 and 1867 in all the simulations) important thermal entry effects were obtained. Since the used PHE [10,37] presents a short length (19 cm), the impact of this effect on average Nusselt numbers is considerable. The average Nusselt numbers for each Reynolds number as well the correspondent Prandtl numbers allowed the determination of the adequate Dittus–Boetler correlation: Nu ¼ 1:718 Re0:449 Pr0:3 , R2 ¼ 0:987:
(15:37)
This correlation differs from the one presented by Fernandes et al. [37] due to the definition used for the hydraulic diameter. For the present correlation the area enlargement factor is taken into account (Equation 15.19) since it is consensual that this geometrical parameter influences the performance of the PHEs [18,39,43,49]. Fernandes et al. [37] and Afonso et al. [10] used a hydraulic diameter defined as 2b in their analysis for a PHE with corrugation angle 308. PHEs with this corrugation angle can have different area enlargement factors, the thermal correlations being distinct for each one of these different PHEs, if a hydraulic diameter 2b is considered. If the area enlargement factors are included in the hydraulic diameter the obtained thermal correlations should be similar. Data from literature is many times ambiguous due to absence of the main geometrical parameters of the plates, which leads to difficulties on the comparison of results from different sources. Although the viscosity of the stirred yoghurt is dependent on temperature, Fernandes et al. [37] performed simulations disregarding this influence in order to analyze the impact of this simplification on the thermal correlations, obtaining the expression: Nu ¼ 1:787 Re0:462 Pr0:3 , R2 ¼ 0:985:
(15:38)
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The correlations (Equation 15.37 and Equation 15.38) above are similar, the maximum deviation between them being smaller than 7.6%. Both of the results reported above compare also well with the experimental correlation presented by Afonso et al. [10] which can be written as Nu ¼ 1:673 Re0:455 Pr0:3 ,
(15:39)
when the hydraulic diameter is considered as defined by Equation 15.18. The best agreement with the latter correlation was achieved taking into account the effect of the temperature on viscosity (maximum deviation of 3.6%), as shown in Figure 15.13. However, the results without this effect are still quite satisfactory (maximum deviation of 9.0%), which indicates that the influence of temperature on the yoghurt viscosity can be neglected for the estimation of the thermal correlation since the improvements in precision, when the dependence of viscosity on temperature is taken into account, are small when compared with the decrease of the computational time when the simulations are performed disregarding this effect. Both of the problems (considering and neglecting the effect of temperature on viscosity) presented convergence difficulties due to the low value of the flow behavior index (0.42). When the simulations were performed considering the influence of temperature on viscosity the high value of E brought about additional convergence difficulties. So, the numerical resolution had to be divided into two steps. First, the problem was solved without the influence of temperature on viscosity, that is, the constitutive equation was reduced to the power-law part, h(g_ ) ¼ K g_ n1 ,
(15:40)
and Picard’s iteration method was used to solve the initial value problem associated with it. Subsequently, these results were used as an initial condition for the problem with temperature variable viscosity effects. During this phase, an evolution process had to be 10
Nu/Pr 0.3
1
2
3 1 0.1
1
10
100
Reynolds number Re
FIGURE 15.13 Thermal correlations of convective heat transfer coefficient for stirred yoghurt. Line 1 represents Equation 15.38, line 2 represents Equation 15.37, line 3 represents Equation 15.39. (~) are the numerical results for stirred yoghurt with E ¼ 94,785 J mol1 and () numerical results for stirred yoghurt with E ¼ 0 J mol1.
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implemented due to the high value of E. In this process, a sequence of new problems were generated and the activation energy value raised from one problem to another until the real value was achieved (E ¼ 94,785 J mol1). As a consequence, the computational time for the problem where E was discarded was about one-third of that when the effect of temperature on viscosity was considered. For laminar flows of Newtonian and non-Newtonian fluids, an m of about one-third, i.e., lower than that obtained in the study performed by Fernandes et al. [37], can be found in the literature [18,25]. This fact could be related with the impact of the entry effects (Figure 15.12) on the average Nusselt numbers determined on a short length PHE. In order to further clarify the exponent m, additional simulations were performed by Fernandes et al. [37] considering the rheological parameters of a power-law fluid similar to a cloudy apple juice [50]: K ¼ 0.0499 Pa sn, E=R ¼ 3065 K, and n ¼ 0.5. The obtained correlation was Nu ¼ 1:703 Re0:346 Pr0:3 , R2 ¼ 0:993:
(15:41)
Since the cloudy apple juice had a lower consistency index than yoghurt, the Prandtl numbers obtained (between 45 and 106) were lower than that obtained by Afonso et al. [10] and in consequence the constant m decreased due to the lower thermal entry effects. The order of magnitude of the constant c is confirmed since n is similar in the two cases. Constant c is higher than the typical values (0.718 [39]) for Newtonian fluids and this is related with the shear thinning behavior of the fluids [21]. Although the correlations from Kumar [39] include a Sider and Tate correction and Equation 15.41 does not, it will be shown below that this correction does not require a drastic change in the parameter c. Since laminar flow was observed and yoghurt exhibits a viscosity dependency on temperature, a Sider and Tate correction [23,48] on the Dittus–Boetler correlation should be included in the analysis. For the case where the effect of temperature on viscosity was considered, (h=hw) was given by h ¼ hw
! E Tyogw Tyog n þ 1 1n exp , n RTyogw Tyog
(15:42)
since g_ and g_ w can be related by Equation 15.30 in the present case. Neglecting the effect of temperature on yoghurt viscosity implies that the viscosity variations are due to the shear thinning behavior of yoghurt only, Equation 15.42 being reduced to h ¼ hw
n þ 1 1n : n
(15:43)
Considering in Equation 15.42 that the temperature of the yoghurt at the wall is equal to the wall temperature, (h=hw) was analyzed along the PHE (Figure 15.14). The inlet temperature of yoghurt was similar in all simulations and is the typical yoghurt fermentation temperature (around 438C). After the zone where entry effects are clear, for the higher Reynolds numbers the ratio (h=hw) had approximately a constant sinusoidal behavior and remained at a value around 1.6–1.7. For lower Reynolds numbers, where higher variations of yoghurt temperature occur and higher viscosities are obtained, this ratio had a similar sinusoidal behavior but with a tendency to increase along the channel.
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2 Re = 1.32 Viscosity ratio h / hw
1.9
Re = 6.65 Re = 11.25
1.8 1.7 1.6 1.5
0.05
0
0.1
0.15
0.2
Distance x (m)
FIGURE 15.14 Ratio between mean and wall viscosity of yoghurt for different Reynolds numbers.
Resorting to the local values of (h=hw), average values of the referred ratio were calculated for different Reynolds numbers (Figure 15.15). In this figure, the good agreement between numerical calculations and Equation 15.43 is evident in the present case. Taking into account the average values of (h=hw) for different Reynolds numbers, the following correlation, considering the effect of temperature on viscosity, was found: Nu ¼ 1:605 Re
0:448
Pr
0:3
h hw
0:14 ,
R2 ¼ 0:988:
(15:44)
4
4
3
3
2
2
1
0
2
4
6
8
10
. . Shear rate ratio gw/g
Viscosity ratio h/h w
Comparing these correlations, with Equation 15.37 and Equation 15.38, it can be observed that m is similar and that the constant c slightly decreases, as expected. The thermal–hydraulic performance enhancement of a heat exchanger can be evaluated by the concept of area goodness factor, this factor being defined as the ratio between the Colburn factor and Fanning friction factor [21,31]. For a PHE with b ¼ 308 and in laminar regime, the area goodness factor obtained with yoghurt is four to five times higher than
1 12
Reynolds number Re
FIGURE 15.15 Average values of (&) (h=hw) and () g_ w =g_ for different Reynolds numbers. Line () represents Equation 15.43.
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the obtained with a Newtonian fluid. This comparative increase of the area goodness factor is obtained with a concomitant enhancement of the thermal and hydraulic performance, with similar contributions.
15.5 CONCLUSIONS In this chapter it has been shown that the shear thinning effects observed during the flow of stirred yoghurt in a PHE give raise to a substantial thermal–hydraulic performance enhancement in comparison with that from Newtonian fluids. Additionally, it was shown that PHEs with high corrugation angles are more flexible concerning the extension of the gel structure breakdown desired for this stirred yoghurt production stage. Due to the good agreement found between numerical results and different experimental data, CFD calculations can be useful to aid process optimization, indicating the best operating conditions and PHEs for the stirred yoghurt processing, which is a very complex problem since hydraulic performance, thermal performance, PHEs maldistribution, and the quality of the final product are all closely related.
NOMENCLATURE a b c Cp DH E f F h k K, K1, K2 L Lav m M mv Mv n Nc Np Nu pc px Pr q q R Re T T
constant interplates distance (m) constant specific heat of fluids (J kg1 K1) hydraulic diameter (m) activation energy (J mol1) Fanning friction factor correction factor convective heat transfer coefficient (W m2 K1) thermal conductivity of the fluid (W m1 K1) consistency index (Pa sn) effective length (m) average travel distance (m) constant mass flow rate per channel (kg s1) volumetric flow rate per channel (m3 s1) total volumetric flow rate (m3 s1) flow behavior index number of channels number of plates Nusselt number corrugation pitch (m) corrugation pitch on the main flow direction (m) Prandtl number heat flux vector (W m2) heat flux (W m2) ideal gas constant (R ¼ 8.3145 J mol1 K1) Reynolds number total stress tensor (Pa) absolute temperature (K)
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u u U v w x, y, z
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velocity vector (m s1) mean velocity (m s1) overall heat transfer coefficient (W m2 K1) average intersticial velocity (m s1) effective width (m) spatial coordinates (m)
GREEK SYMBOLS a b DP f g gx g_ g_ h lp r s s0 t y j
shape factor corrugation angle (8) pressure drop (Pa) area enlargement factor channel aspect ratio channel aspect ratio on the main flow direction shear rate (s1) mean shear rate (s1) fluid viscosity (Pa s) thermal conductivity of the plates (W K1 m1) fluid density (kg m3) shear stress (Pa) yield stress (Pa) tortuosity parameter geometrical parameter
SUBSCRIPTS w wat yog
wall cooling water yoghurt
REFERENCES 1. A.Y. Tamine and R.K. Robinson. Fermented milks and their future trends. Part II. Technical aspects (review). Journal of Dairy Research 55: 281–307, 1988. 2. M.C. Staff. Cultured milk and fresh cheeses. In: R. Early (ed.) The Technology of Dairy Products. London: Blackie Academic and Professional, 1998, pp. 123–144. 3. I.M. Afonso and J.M. Maia. Rheological monitoring of structure evolution and development in stirred yoghurt. Journal of Food Engineering 42: 183–190, 1999. 4. A.Y. Tamine and H. Deeth. Yoghurt: technology and biochemistry. Journal of Food Protection 43: 939–977, 1980. 5. Y.S. Fangary, M. Barigou, and J.P.K. Seville. Simulation of yoghurt flow and prediction of its end-of-process properties using rheological measurements. Transactions of the Institution of Chemical Engineers 77 (part C): 33–39, 1999. 6. T. Benezech and J.F. Maingonnat. Flow properties of stirred yoghurt: structural parameter approach in describing time dependency. Journal of Textures Studies 24: 455–473, 1993. 7. H. Rohm and A. Kovac. Effects of starter cultures on linear viscoelastic and physical properties of yoghurt gels. Journal of Structure Studies 25: 311–329, 1994. 8. H. Rohm and A. Kovac. Effects of starter cultures on small deformation rheology of stirred yoghurt. Lebensmittel-Wissens chaft und-Technologie-Food Science and Technology 28: 319–322, 1995.
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9. E. Ro¨nnega˚rd and P. Dejmek. Development of breakdown of structure in yoghurt studied by oscillatory rheological measurements. Le Lait 73: 371–379, 1993. 10. I.M. Afonso, L. Hes, J.M. Maia, and L.F. Melo. Heat transfer and rheology of stirred yoghurt during cooling in plate heat exchangers. Journal of Food Engineering 57: 179–187, 2003. 11. G. Mullineux and M.J.H. Simmons. Effects of processing on shear rate of yoghurt. Journal of Food Engineering 79: 850–857, 2007. ¨ stergren, and P. Dejmek. Plug flow of yoghurt in piping as determined by 12. M. Henningsson, K. O cross-correlated dual-plane electrical resistance tomography. Journal of Food Engineering 76: 163–168, 2006. 13. Y. Lee, S. Bobroff, and K.L. McCarthy. Rheological characterization of tomato concentrates and the effect of uniformity of processing. Chemical Engineering Communications 189: 339–351, 2002. 14. P. Perona, R. Conti, and S. Sordo. Influence of turbulent motion on structural degradation of fruit purees. Journal of Food Engineering 52: 397–403, 2002. 15. J.A.W. Gut and J.M. Pinto. Modeling of plate heat exchangers with generalized configurations. International Journal of Heat and Mass Transfer 46: 2571–2585, 2003. 16. H.B. Kim, C.C. Tadini, and R.K. Singh. Heat transfer in a plate heat exchanger during pasteurization of orange juice. Journal of Food Engineering 42: 79–84, 1999. 17. M. Reppich. Use of high performance plate heat exchangers in chemical and process industries. International Journal of Thermal Sciences 38: 999–1008, 1999. 18. S. Kakac¸ and H. Liu. Heat Exchangers Selection, Rating, and Thermal Design, 2nd ed. Boca Raton, FL: CRC Press, 2002, pp. 373–412. 19. J.A.W. Gut and J.M. Pinto. Selecting optimal configurations for multisection plate heat exchangers in pasteurization processes. Industrial and Engineering Chemistry Research 42: 6112–6124, 2003. 20. R.M. Manglick and J. Ding. Laminar flow heat transfer to viscous power-law fluids in double-sine ducts. International Journal of Heat and Mass Transfer 40(6): 1379–1390, 1997. 21. C.S. Fernandes, R.P. Dias, J.M. No´brega, and J.M. Maia. Influence of geometry on the thermal–hydraulic performance of plate heat exchangers. In: Proceedings of the International Symposium on Food Rheology and Structure. Switzerland, 2006, pp. 465–469. 22. M.K. Bassiouny and H. Martin. Flow distribution and pressure drop in plate heat exchangers—I. Chemical Engineering Science 39(4): 693–700, 1984. 23. G. Antonini, O. Franc¸ois, and X.S. Shuai. Corre´lations transfert=facteur de frottement por le chauffage=refroidissement d’un fluide visqueux a` forte de´pendance thermorhe´ologique en e´coulement de conduite en re´gime laminaire. Revue Ge´ne´rale de Thermique 308–309: 427–431, 1987. 24. J.C. Leuliet, J.F. Maigonnat, and M. Lalande. Etude de la perte de charge dans de e´changeurs de chaleur a` plaques traitant des produits nonNewtoniens. Revue Ge´ne´rale de Thermique 308–309: 445–450, 1987. 25. J.C. Leuliet, J.F. Maigonnat, and M. Lalande. E´coulement et transferts de chaleur dans les e´changeurs a` plaques traitant des produits visqueux newtoniens et pseudoplastiques. The Canadian Journal of Chemical Engineering 68: 220–229, 1990. 26. J.C. Leuliet, J.F. Maigonnat, and M. Lalande. Thermal behavior of plate heat exchangers with Newtonian and nonNewtonian fluids. In Congre´s Eurotherm 5 et 1er Colloque TIFAN, Compie`gne, France, 1988. 27. F. Delplace and J.C. Leuliet. Generalized Reynolds number for the flow of power law fluids in cylindrical ducts of arbitrary cross section. The Chemical Engineering Journal 56: 33–37, 1995. 28. M. Ciofalo, J. Stasiek, and M.W. Collins. Investigation of flow and heat transfer in corrugated passages—II. Numerical simulation. International Journal of Heat and Mass Transfer 39: 165–192, 1996. 29. M.A. Mehrabian and R. Poulter. Hydrodynamics and thermal characteristics of corrugated channels: computational approach. Applied Mathematical Modelling 24: 343–364, 2000. 30. M. Ciofalo, J. Stasiek, and M.W. Collins. Investigation of flow and heat transfer in corrugated passages—II. Numerical simulations. International Journal of Heat and Mass Transfer 39(1): 165–192, 1996. 31. H.M. Metwally and R.M. Manglick. Enhanced heat transfer due to curvature–induced lateral vortices in laminar flows in sinusoidal corrugated-plate channels. International Journal of Heat and Mass Transfer 47: 2283–2292, 2004.
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32. T. Kho and H. Mu¨ller–Steinhagen. An experimental and numerical investigation of plate heat transfer fouling and fluid flow in flat plate heat exchangers. Transactions of the Institution of Chemical Engineers 77 (part A): 124–130, 1999. 33. C.S. Fernandes, R.P. Dias, J.M. No´brega, and J.M. Maia. Effect of corrugation angle on the hydrodynamic behavior of power-law fluids during a flow in plate heat exchangers. In: Proceedings of 5th International Conference on Enhanced, Compact and Ultra-Compact Heat Exchangers: Science, Engineering and Technology. Canada, 2005, pp. 491–495. 34. C.S. Fernandes, R.P. Dias, J.M. No´brega, and J.M. Maia. Effect of corrugation angle on the thermal behavior of power-law fluids during a flow in plate heat exchangers. In: Proceedings of 5th International Conference on Enhanced, Compact and Ultra-Compact Heat Exchangers: Science, Engineering and Technology. Canada, 2005, pp. 496–501. 35. C.S. Fernandes, R.P. Dias, J.M. No´brega, J.M. Maia, and V.V. Wadekar. Numerical analysis of nonisothermal Newtonian flows in plate heat exchangers. In: Proceedings of Chempor 2005, ISBN: 972-8055-13-7. Portugal, 2005. 36. C.S. Fernandes, R.P. Dias, J.M. No´brega, I.M. Afonso, L.F. Melo, and J.M. Maia. Simulation of stirred yoghurt processing in plate heat exchangers. Journal of Food Engineering 69: 281–290, 2005. 37. C.S. Fernandes, R.P. Dias, J.M. No´brega, I.M. Afonso, L.F. Melo, and J.M. Maia. Thermal behavior of stirred yoghurt during cooling in plate heat exchanger. Journal of Food Engineering 76: 433–439, 2006. 38. P.J. Heggs, P. Sandham, R.A. Hallam, and C. Walton. Local transfer coefficients in corrugated plate heat exchanger channels. Transactions of the Institution of Chemical Engineers 75 (part A): 641–645, 1997. 39. H. Kumar. The plate heat exchanger: construction and design. First UK National Conference on Heat Transfer, University of Leeds, Inst. Chem. Symp. Series No. 86, 1984, pp. 1275–1288. 40. D.-H. Han, K.-J. Lee, and Y.-H. Kim. Experiments on the characteristics of evaporation of R410A in brazed plate heat exchangers with differnt geometric configurations. Applied Thermal Engineering 23: 1209–1225, 2003. 41. H. Martin. A theoretical approach to predict the performance of chevron-type plate heat exchangers. Chemical Engineering and Processing 35: 301–310, 1996. 42. D.S. Chandrasekharaiah and L. Debnath. Continuum Mechanics. London: Academic Press, 1994, pp. 325–362. 43. Z.H. Ayub. Plate heat exchanger literature survey and new heat transfer and pressure drop correlations for refrigerant evaporators. Heat Transfer Engineering 24(5): 3–16, 2003. 44. J. Du, X. Hu, W. Wu, and B.-X. Wang. A thermal dispersion model for single phase flow in porous media. Heat Transfer—Asian Research 32(6): 545–552, 2003. 45. J. Ding and R.M. Manglik. Analytical solutions for laminar fully developed flows in double-sine shaped ducts. Heat and Mass Transfer 31: 269–277, 1996. 46. B.P. Rao, P.K. Kumar, and S.K. Das. Effect of flow distribution to the channels on the thermal performance of a plate heat exchanger. Chemical Engineering and Processing 41: 49–58, 2002. 47. A.Y. Tamine and R.K. Robinson. Yoghurt: Science and Technology. Oxford: Pergamon Press, 1985. ´ changeur de chaleur a` plaques et joints. Re´solution nume´rique 48. F. Rene´ and M. Lalande. E des e´quations d’e´change thermique entre les diffe´rents canaux. Revue Ge´ne´rale de Thermique 311: 577–583, 1987. 49. A.S. Wanniarachchi, U. Ratnam, B.E. Tilton, and K. Dutta-Roy. Approximate correlations for chevron-type plate heat exchangers. In: Proceedings of 30th National Heat Transfer Conference. US, 1995, pp. 145–151. 50. J.F. Steffe. Rheological Methods in Food Process Engineering, 2nd ed. East Lansing: Freeman Press, 1996, pp. 350–384.
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CFD Modeling of the Hydrodynamics of Plate Heat Exchangers for Milk Processing Koen Grijspeerdt, Dean Vucinic, and Chris Lacor
CONTENTS 16.1 16.2
Introduction ............................................................................................................. 403 Hydrodynamic Modeling ......................................................................................... 405 16.2.1 1D Modeling ............................................................................................... 405 16.2.2 2D Modeling ............................................................................................... 406 16.2.3 3D Modeling ............................................................................................... 406 16.3 Case Study ............................................................................................................... 407 16.3.1 Methods ...................................................................................................... 407 16.3.2 2D Model .................................................................................................... 408 16.3.3 3D Model .................................................................................................... 408 16.3.4 Temperature Influence ................................................................................ 410 16.3.5 Experimental Verification of the Flow Field Simulations ........................... 411 16.4 Conclusions .............................................................................................................. 414 Acknowledgments .............................................................................................................. 414 References .......................................................................................................................... 414
16.1 INTRODUCTION The heat treatment or pasteurization of milk derives its principles from the work of Louis Pasteur (1822–1895). In 1864 he developed a method to prevent an abnormal fermentation in wine by destroying the responsible organisms by heating the wine to 608C. Today, the heat treatment of milk and milk products is one of the most important operations in the dairy industry. It is done to ensure safety from microbes and to increase the shelf life of the end product. In addition, the heat treatment has an effect on the final product in terms of chemical, physical, and organoleptic properties. The kinetics of these processes are an order of magnitude lower than the bacterial inactivation, keeping these undesirable changes minimal [1,2]. The mentioned effects depend on the combination of temperature and time
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to which the product is subjected. The higher the temperature, the shorter the required time to obtain a sufficiently safe product. In the dairy industry, the basic heat treatments can be classified by four main types: 1. 2. 3. 4.
Thermization for inactivation of psychrotrophic microorganisms (e.g., 20 s at 658C). Low pasteurization for inactivation of pathogenic microorganisms (e.g., 20 s at 728C). High pasteurization for inactivation of all microorganisms (e.g., 20 s at 858C). Sterilization (e.g., 30 min at 1108C) and ultrahigh temperature (UHT) treatment (e.g., 5 s at 1408C) to destroy spores, such as Bacillus stearothermophilus and Bacillus sporothermodurans spores [3]. Recent research indicated that B. stearothermophilus spores attach better to stainless steel walls than vegetative cells, stressing the need for high processing temperatures [4,5].
The effect of a milk heat treatment is not limited to the product quality. An important drawback effect is the fouling of the heat equipment by the deposit formation on the heat exchanger walls, as a result of the heat-induced reactions of the milk components. The deposit formation leads to an additional heat and transport resistance and it consequently reduces the effective heat transfer coefficient, increasing the pressure drop of the heat treatment equipment. In order to maintain a safe product, a higher temperature is required for the heat-exchanging medium to compensate for the lower heat transmission and reduced residence time, thus resulting in higher energy costs. Ultimately, if the fouling is high enough that it would compromise the product safety, the undergoing production needs to be stopped prematurely, resulting in higher operating costs. The result is that the equipment has to be cleaned with a special cleaning agent, which additionally increases the operating costs and has a nonnegligible environmental impact [6,7]. The heat treatment equipment can be divided into two major types: direct and indirect systems. This classification is based on the way the high temperatures are obtained within the heat treatment process. In direct systems, the heating is achieved by mixing the milk product with the steam under pressure. Compared to indirect systems, the heat transfer is typically much higher; the residence time is very short and such systems are less prone to fouling [8]. However, they are more difficult to control, and consequently, less used in practice [1]. In the indirect systems, solid walls separate the heat transfer medium (typically water or steam) and the dairy product. In addition, the indirect systems can be further subdivided in two types: the plate heat exchangers and the tubular heat exchangers. Due to the fouling, the common practice for the indirect heat exchangers is that they are cleaned at least once a day. For such required cleaning process, the extra costs can be subdivided into [9]: . . . .
Increased capital costs Increased energy costs High maintenance costs Costs for production losses
Visser and Jeurnink [10] give an overview of the economic aspects of fouling and cleaning for heat exchangers in the dairy industry. The yearly fouling costs in the UK are estimated to be between e400 and e700 million, that is 0.3% of the UK gross national product (GNP). In the US, the heat exchanger fouling costs are estimated to be e3.5–8.3 billion. In France the costs amounted to e150 million and in the Netherlands e40 million=year was reported. Besides the economic impact, there is also the issue of the environmental problems due to the use of aggressive cleaning agents [6,7]. The mentioned numbers illustrate that the fouling effects are
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very costly and give rise to different environmental problems. Therefore, it would be beneficial to diminish the occurrence of fouling in the dairy industry. The mechanism and the kinetics of the underlying processes of fouling have received considerable attention in the literature. There are ongoing debates, but there seems to be a consensus that the denaturation of the whey protein b-lactoglobulin is a key process in the formation of fouling components, at least when the temperature is below 908C [11–16]. With increasing temperature level and depending on pH, mineral precipitation (particularly calcium phosphate) gradually becomes more and more important [16–18]. Besides the influence of the product composition, temperature, and pH, aspects like plate geometry [16], the presence of air bubbles [15], and to a lesser extent surface material [16,19] affect the fouling rate. Of utmost importance is the mixing intensity [16,20], which depends on the fluid flow rate and the plate corrugation. Recently, the link between fouling models and the detailed heat exchanger design is receiving more attention [21–23]. Especially, significant progress has been made in the detailed description of the hydrodynamics of the heat exchangers [24,25]. An adequate hydrodynamic model for the heat exchanger is the basis for the simulation of the other processes occurring during the thermal treatment, the most important one being the inactivation of pathogenic microorganisms. When an adequate model is available, the process can be optimized to obtain the best operating conditions to minimize the undesirable side effects of heating, while protecting the microbiological quality of the milk. According to de Jong et al. [26], such an optimization could potentially reduce the operating cost of a typical system by more than 50%. Given the fact that plate geometry has a significant effect on fouling, it is suggested that during the heat exchanger design an analysis of its hydrodynamic model would be potentially very beneficial [27–29].
16.2 HYDRODYNAMIC MODELING 16.2.1 1D MODELING Until recently the flow in milk treating heat exchangers was generally modeled by a one-dimensional (1D) plug flow model. Such model is generally quite suited for tubular heat exchangers with a high length=diameter ratio in combination with the high fluid speed. The drawback of these models is that they are not able to take into account the influence of turnings and connected regions where the plug flow assumption is not valid anymore. De Jong [30] has combined a kinetic fouling model with a plug flow model for the tubular heat exchangers. It is claimed that the reparameterization of the heat exchanger dimensions could justify the use of such model for plate heat exchangers as well. However, this has not been rigorously validated and data from Delplace and Leuliet [31] and Kho and Mu¨ller-Steinhagen [32] show a difference in the fouling behavior between plate heat exchangers configured with plates of different profiles. This clearly indicates the importance of the hydrodynamic analysis during the equipment design, also confirmed by Jun and Puri [33] who compared a 1D model with a 2D model for a plate heat exchanger and found the predicting capacity of the former to be inferior to the latter. There are numerous other examples of the coupling of a protein fouling model to the operation of an indirect heat exchanger but they are all based on 1D flow [21,23,31,34–36]. Less work is done for direct heat exchanger systems. De Jong [30] made an attempt to simulate fouling in a direct infuser heating system, but the agreement between the model results and experimental data was not very good, probably due to invalid kinetic data and deviations under assumed hydrodynamic conditions.
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10
T
Cooling 4 Cooling 3 Homogenization (CO3) (HOM)
Cooling 2 (CO2)
Cooling 1 (CO1)
Steam
8
1
Heating 1 (HE1)
2
Heating 2 (HE2) 3
Heating 3 (HE3) 4 Holding 1 (HO1)
Heating 4 (HE4)
5
Holding 2 (HO2)
FIGURE 16.1 A schematic layout of a typical temperature treatment in the dairy industry. (From Grijspeerdt, K., Mortier, L., De Block, J., and Van Renterghem, R., Food Control, 15, 117, 2004. With permission from Elsevier.)
Georgiadis et al. [37–40] adapted the 1D plug flow model and added axial convection and radial dispersion effects. From the point of view of operational optimization, this seems to be the most sensible approach. Heat exchanger systems for milk treatment typically include heat recouplings (Figure 16.1). Once included in an optimization scheme the simulation becomes computationally very challenging [21,41] and it is currently not possible to combine it with the full-fledged hydrodynamic models.
16.2.2 2D MODELING In order to assess the influence of the corrugation profiles on the flow characteristics Jun and coworkers [42–44] developed a 2D model using computational fluid dynamics (CFD). A similar exercise was carried out by Grijspeerdt et al. [25]. A 2D model is useful for assessing the impact of the shape of the profile of the plate on the flow and could assist in locating hot spots. But it falls short when trying to obtain an overall picture of the flow behavior in between the plates and cannot describe the detailed influences of inlet and outlet positions. In a sense we can conclude that these models fall between two stools: they are too complex to be integrated in an optimization scheme, but they are not sophisticated enough to assist in an optimal design of the plate profiles and orientation.
16.2.3 3D MODELING There are examples of 3D modeling of plate heat exchangers [24,25,32,45,46], illustrating different approaches to improve the plate design. The mentioned models show the capability of assessing the detailed influence on the flow taking into account the corrugation shape and the orientation and in addition the inlet and outlet configuration. Kho and Mu¨ller-Steinhagen [32] investigated the impact of the inlet flow distributors by simulating flat plate heat exchangers. Jun and Puri [24] implemented a 3D model coupled with the fouling model of Petermeier [47,48]. They applied the 3D model to investigate the difference between different plate designs, typically used in a dairy industry, while others are typical design for automobile air conditioners. This model predicted the alternative plate to be more effective in terms of heat transfer, while allowing for a lower deposition rate. It has to be noted that for such intrinsically dynamic model, the deposition scheme did not include a recalculation of the heat exchanger area, the plate dimensions and the heat transfer characteristics, although, strictly speaking, this would be necessary. Usually the validation of a 3D model is done indirectly by measuring the outlet temperature and=or the flow depositions in pilot-scale equipment.
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16.3 CASE STUDY To illustrate the potential of CFD for modeling plate heat exchangers in the dairy industry, we will discuss in closer detail the modeling exercise described in Grijspeerdt et al. [25]. In this study, the plates of the pilot-scale indirect plate heat exchanger were used as the basis for the CFD simulation. The profile of the corrugated plate was optically measured along the corrugation direction (normal to the flutes). This was done using a micrometer tool, by measuring specific corrugation points, selected optically (by eye) and placing the tool by hand to take the various distances. The flutes are inclined at a 568 angle to the primary flow direction of the heat exchanger element. The irregularity of the measured geometry was eliminated during the grid generation by definition of a smooth curve, which fitted the measured points. The curve normal to the flute has a unit length (peak to peak distance) of 7.64 mm and amplitude of 1.08 mm. The flow channel was simulated by considering two plates parallel to each other (Figure 16.2). The minimum and maximum gaps between the plates were 5.6 and 9.2 mm, respectively. The width of the flow passage between the plates was 50 mm. Both numerical and experimental simulations were done for this test case. The numerical simulation was used to simulate the flow field hydrodynamics and the heat transfer processes. The experimental simulation of the flow was conducted on a transparent model constructed with off-the-shelf elements. The aim was to compare the experimental results with the numerical simulation results.
16.3.1 METHODS The simulations were carried out in the FINE-Turbo software environment (Numeca International, Belgium), an integrated CFD environment based on the EURANUS CFD code [49]. For all computations, a turbulent Navier–Stokes simulation applying the Baldwin–Lomax turbulent stress model was used [50]. The Baldwin–Lomax turbulence model is an algebraic eddy viscosity, zero-equation model. Several advantages of the model are its computational efficiency and robustness. This model works best in wall-bounded flows with favorable pressure gradients, as is the case here. As the flow physics become more complicated,
Y
X
Z
FIGURE 16.2 The heat exchanger plates grid. (From Grijspeerdt, K., Hazarika, B., and Vucinic, D., J. Food Eng., 57, 237, 2003. With permission.)
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FIGURE 16.3 2D vector flow field. (From Grijspeerdt, K., Hazarika, B., and Vucinic, D., J. Food Eng., 57, 237, 2003. With permission.)
as well as the geometry of the model being tested, the performance of this turbulence model greatly decreases. The applied Reynolds number for the simulations was 4482 (corresponding to a characteristic velocity of 1 m=s) and the Prandtl number 6.62.
16.3.2 2D MODEL In a first stage, as a ‘‘natural’’ extension of a plug flow approximation, a 2D model was implemented. The 2D geometry was considered with the flow direction perpendicular to the flutes, one inlet velocity was used. A grid of the geometry was constructed using the FINE-Turbo preprocessor (IGG). The grid consisted of a total of 33,150 points. The system was assumed to be at steady-state conditions at the start of the simulation. The simulation results show that the main flow is relatively straightforward in the center of the flow channel. Within the corrugations the flow separates at the beginning of the diverging portion and recirculation bubbles are present (Figure 16.3). These recirculation regions cover the whole additional area provided by the corrugations making it unavailable for through flow. Therefore, the primary flow in the largest cross section has approximately the same velocity as in the smallest cross-sectional area. This is illustrated by the particle traces shown in Figure 16.3. Obviously, the 2D model results show that the reverse flow regions within the corrugations are the most sensitive spots with respect to fouling. The residence time of particles in these regions and the temperature to which they are subjected will be on average higher. On the other hand, particles flowing through the center run the risk of being subjected to lower temperatures in combination with lower residence times. This example shows that 2D modeling can be useful to bring more insight regarding the applied plate geometry. However, the simulation does not teach us about the influence of the inlet and the orientation of the corrugations, which can only be accomplished using 3D modeling.
16.3.3 3D MODEL The 3D flow geometry was simulated using 25 complete flutes giving a parallelogram-shaped exchanger (Figure 16.2). Three different uniform velocity fields were employed at the inlet so the effect of the inlet conditions could be assessed. Again, we assumed that at the start of the
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CFD Modeling of the Hydrodynamics of Plate Heat Exchangers for Milk Processing Vx 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0
FIGURE 16.4 Only velocities higher than 1 m=s in the x-direction are shown in this figure. The influence of the corrugations is clear. (From Grijspeerdt, K., Mortier, L., De Block, J., and Van Renterghem, R., Food Control, 15, 117, 2004. With permission.)
simulation the system is operating under steady-state conditions. A grid of the geometry was constructed using the FINE-Turbo preprocessor (IGG) with a total of 551,265 points. From the preliminary simulations, while constructing and testing the model, it was observed that the inlet velocity influences the flow in a very short region near the entrance only. Therefore, the results of the simulation with the inlet vector having all the three components are the only ones presented in this section. It is obvious that the 3D simulation gives a more detailed picture than the 2D simulation. As can be seen from Figure 16.4, the plate profile has a profound impact on the flow velocity. In Figure 16.5, the flow traces for three flow particles are followed along the flutes. At first sight, the backflows in the corrugations seem similar to the 2D simulation. But this figure shows a reverse flow because of the angle at which the field is viewed. In reality, it is a spiral motion along a flute. In the mainstream direction (x), the flow advances by 4 units (flutes) by the time the particles traverse from one wall to the opposite wall. The curvature of the traces at the start is due to the vy component of velocity. Within a distance of 2 flutes, the influence of the inlet becomes negligible. Once the particles approach the wall they gradually move toward the wavy walls. The particles trapped in the flutes move downstream along the flutes
FIGURE 16.5 A complete view and a zoom of the flow traces for three flow particles for the 3D simulation, as seen along the flutes. (From Grijspeerdt, K., Hazarika, B., and Vucinic, D., J. Food Eng., 57, 237, 2003. With permission.)
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FIGURE 16.6 Particle trace and velocity vector profile for the 3D simulation, as seen along the y-axis. (From Grijspeerdt, K., Hazarika, B., and Vucinic, D., J. Food Eng., 57, 237, 2003. With permission.)
until they are close to the opposite wall where they gradually move toward the center plane and then to the opposite plane wall. This phenomenon is clearly visible when the flow traces are plotted along the y-axis (Figure 16.6). This view is oriented along the y-axis (at the top of the plate) and the velocity vectors are plotted along the central plane (y ¼ constant) traversing 4 flutes in the width of the heat exchanger. In the plane of symmetry, a strong velocity component is present in the positive z-direction. At the wall the particles move toward the wavy walls. The particles trapped in the flutes flow along the flutes to the opposite wall. Again, the curvature at the beginning of the traces (left side) is due to the vz component of velocity. This view obviously illustrates the need for 3D modeling, as there are strong 3D velocity components present. A final view is oriented from the exit end of the flow domain along the z-axis (Figure 16.7). The traces on the right side near the center are the starting point. The velocity vector near the right side wall has a much higher magnitude than that near the left side where the low-velocity fluid coming along the flutes converge. The flow along the flutes has a spiral motion. For the case examined here, 2D simulations were not capable of providing a complete picture as shown by the 3D simulation result in the 3D space. The simulations indicate that the inlet configuration of the plates has only limited importance; the influence of a different inlet velocity component can only be felt up to three corrugations. Furthermore, the simulations show that the average particle only gets trapped in a corrugation once after which it will remain in the bulk flow.
16.3.4 TEMPERATURE INFLUENCE Two scenarios were simulated. First, the incoming fluid flow was assumed to have a uniform temperature of 1008C and the plates a uniform temperature of 1108C. A second simulation was carried out for a uniform plate temperature of 1408C. The temperature differential (DT )
FIGURE 16.7 Particle trace and velocity vector profile for the 3D simulation, as seen along the z-axis. (From Grijspeerdt, K., Hazarika, B., and Vucinic, D., J. Food Eng., 57, 237, 2003. With permission.)
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Temperature (⬚C) 110
105
100
FIGURE 16.8 Temperature profile as viewed from the side of the plates. (From Grijspeerdt, K., Hazarika, B., and Vucinic, D., J. Food Eng., 57, 237, 2003. With permission.)
between the heating medium and the milk has been reported to have an influence on fouling formation [16]. In particular, Hiddink et al. [51] suggested that the temperature differential influences fouling when it exceeds 108C158C. The temperature profile at low DT as viewed from the side of the plates is shown in Figure 16.8. Obviously, the inlet temperature effect stretches quite far, as opposed to the flow field influence. As could be expected from the flow field simulations, the highest temperature regions are located at the downside of the corrugations. These will be the spots that will be the most prone to fouling. For the case of the high DT, the temperature profile essentially has the same outlook with a different temperature scale. The difference between the wall temperature and the bulk temperature is higher for this case (Figure 16.9), making it more prone to fouling. Clearly, a DT of 408C will not likely occur in practice, but the results could be useful to indicate trends and amplify weaker spots in the plate design.
16.3.5 EXPERIMENTAL VERIFICATION
OF THE
FLOW FIELD SIMULATIONS
An attempt was made to obtain a proof of concept of the 3D simulations by using experimental fluid dynamics (EFD). EFD allows for an instantaneous measurement of the whole ∆T = 10°C
∆T = 40°C
112
Temperature (°C)
Temperature (°C)
140
Outlet Inlet
110 108 106 104 102 100 98 0.0
Outlet Inlet
130 120 110 100
0.2
0.4
0.6
Dimensionless distance
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
Dimensionless distance
FIGURE 16.9 The temperature profile between the plates for the two DT cases. (From Grijspeerdt, K., Hazarika, B., and Vucinic, D., J. Food Eng., 57, 237, 2003. With permission.)
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FIGURE 16.10 Model used for flow visualization experiment. (From Grijspeerdt, K., Hazarika, B., and Vucinic, D., J. Food Eng., 57, 237, 2003. With permission.)
flow field and consequently can be of great assistance in understanding the physics of the flows before applying more traditional point measurement experiments (e.g., hot wire anemometers, laser doppler anemometers, pressure probes, and thermocouples). These point measurements deliver quantities that are necessary for the numerical solvers. In complex flows, flow field visualization is necessary to interpret the results and to decide what quantities are important for the flows, and to identify the spatial locations for investigation with point measurement [52]. A model was constructed from transparent roofing material readily and available at low cost. The best compromise was to construct a model of 3.8 times the size of the prototype that led to a limited geometrical nonsimilarity of 9% between the model and the prototype. The CFD simulations indicated that the influence of the inlet is prevalent only for a short distance. Therefore, the length of the test section could be shorter than that used for the grid. The model constructed had 21 complete flutes in its test section. Along the centerline the model was 80 cm long with 20 cm lengths of straight walls upstream and downstream of it giving a total length of 120 cm for the test bed. The width of the test section was 20 cm and the gap between the plates was adjustable. For this particular set of tests the minimum and maximum gaps between the corrugated sections were adjusted to 2 and 3.5 cm, respectively. The straight portions had 3.5 cm gaps. Figure 16.10 shows two views of the test section. The experiments were conducted with water that was supplied by a two-stage evacuation pump. The water entered the test section from the upstream flow regulator. The regulator, which was 20 cm wide, 40 cm long, and 40 cm high, had two compartments separated by screens. The pumps delivered water to the upstream compartment and the exit from the regulator enters the test bed through a honeycomb sandwiched between screens. The flow from the test bed enters a downstream head-controlling chamber, which was 20 cm long, 20 cm wide, and 20 cm high. The water from this chamber flowed out to the reservoir where the two pumps were submerged. The total length of the test setup was 180 cm. The test bed was made suitable for conducting particle image velocimetry (PIV) measurements. The PIV measurement technique is based on the extraction of specific images from the video recording of a suitably seeded flow, illuminated by a laser light sheet. Cross-correlation velocimetry is applied to these images and the planar velocity field is obtained for plane where the laser sheet is placed. Figure 16.11 shows the PIV visualization setup. Laser light sheet flow visualization was conducted in this test rig. The light sheet used had a thickness of 2 mm. The visualization was conducted for Reynolds numbers varying between very low to the operating condition value. The top view of the test section and the side view with the laser sheet are shown in Figure 16.12.
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Laser
Experiment
Storage
Computation
Video camera Computer for recording and postprocessing images
Database
Seeding Flow field visualization
Database administration and post analysis
Video Recording
Quantifying moving images
Velocity field manipulation
Illumination
FIGURE 16.11 The PIV setup components.
The flow visualization showed results that are similar to those obtained by the simulation, operating at the same Reynolds number. At low Reynolds numbers large eddies are visible in the central plane. Two images from the visualization are shown in the figure. In these two photographs, the flow is in the general direction from left to right as in the flow field figures shown before. The photograph on the left shows the traces in the center plane near the flat edge wall where the flow is pointed toward the wall and then traverses into the flutes. The general trend of the flow is toward the flat wall at a small angle at the upper edge of Figure 16.12 and at the right edge of Figure 16.12. The second photograph shows the traces in the center plane where the flows coming along the flutes converge toward the centerline and leave the flat side wall at a large angle because of the small axial velocity (at the lower edge of Figure 16.12 and at the left edge of Figure 16.12). The similarity between the simulated flow in CFD and the EFD visualization illustrate that the numerical simulation produced reliable results.
FIGURE 16.12 Photographs from flow visualization at high Reynolds numbers (flow is from left to right). (From Grijspeerdt, K., Hazarika, B., and Vucinic, D., J. Food Eng., 57, 237, 2003. With permission.)
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16.4 CONCLUSIONS The use of CFD for the design and optimization of plate heat exchangers in the dairy industry is starting to grow to maturity. There have been several studies in the past few years illustrating the potential of CFD in this field. The case study that was discussed in more detail in this chapter shows the potential of CFD as a tool to model the detailed flow patterns in plate heat exchangers. Although this example is limited to the hydrodynamics only, it already allows drawing some relevant conclusions with respect to the layout and design of the plates used in a pilot-scale heat exchanger. In order to simulate the fouling process itself, it will be necessary to incorporate a model for the denaturation of b-lactoglobulin and mineral precipitation on the one hand, and a model for the wall adhesion of the fouling components in the CFD code. This will make the computations much more complex because fouling renders the process intrinsically dynamic, whereas the current practice is generally steady state. When applying CFD modeling, the verification of the modeling results by detailed comparison of simulation results with real-life experiments is too often neglected and consequently deserves more attention.
ACKNOWLEDGMENTS Figure 16.1 is reprinted from Food Control, 15, Grijspeerdt, K., Mortier, L., De Block, J., and Van Renterghem, R., Applications of modeling to optimise ultra high temperature milk heat exchangers with respect to fouling, 117–130, 2004, with permission from Elsevier. Figure 16.2, Figure 16.3, Figure 16.5 through Figure 16.10, and Figure 16.12 are reprinted from Journal of Food Engineering, 57, Grijspeerdt, K., Hazarika, B., and Vucinic, D., Application of computational fluid dynamics to model the hydrodynamics of plate heat exchangers for milk processing, 237–242, 2003, with permission from Elsevier.
REFERENCES 1. Burton, H., Ultra-high Temperature Processing of Milk and Milk Products, Elsevier Applied Science, London, 1988. 2. Walstra, P., Geurts, T.J., Noomen, A., Jellema, A., and van Boekel, M.A.J.S., Dairy Technology: Principles of Milk Properties and Processes, Marcel Dekker, New York, 1999. 3. Herman, L., Vaerewijck, M., Moermans, R., and Waes, G., Identification and detection of Bacillus sporothermodurans spores in 1, 10, and 100 milliliters of raw milk by PCR, Applied and Environmental Microbiology 63: 3139, 1997. 4. Flint, S., Palmer, J., Bloemen, K., Brooks, J., and Crawford, R., The growth of Bacillus stearothermophilus on stainless steel, Journal of Applied Microbiology 90(2): 151, 2001. 5. Kusumaningrum, H.D., Riboldi, G., Hazeleger, W.C., and Beumer, R.R., Survival of foodborne pathogens on stainless steel surfaces and cross-contamination to foods, International Journal of Food Microbiology 85(3): 227, 2003. 6. Graßhoff, A., Cleaning of heat treatment equipment, Bulletin of the IDF 328: 32, 1997. 7. Jeurnink, T.J.M. and Brinkman, D.W., The cleaning of heat exchangers and evaporators after processing milk or whey, International Dairy Journal 4: 347, 1994. 8. de Jong, P., Waalewijn, R., and Van der Linden, H.J.L.J., Performance of a steam-infusion plant for heating milk, Netherlands Milk Dairy Journal 48: 181, 1994. 9. Sandu, C. and Singh, R.K., Energy increase in operation and cleaning due to heat exchanger fouling in milk pasteurization, Food Technology 45: 84, 1991. 10. Visser, H. and Jeurnink, T.J.M., General aspects of fouling and cleaning, Bulletin of the IDF 328: 5, 1997.
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415
11. Lalande, M., Tissier, J.P., and Corrieu, G., Fouling of a plate heat exchanger used in ultra-high-temperature sterilization of milk, Journal of Dairy Research 51: 557, 1984. 12. Roefs, S.P.F.M. and de Kruif, C.G., A model for the denaturation and aggregation of b-lactoglobulin, European Journal of Biochemistry 226: 883, 1994. 13. Jeurnink, T.J.M., Milk fouling in heat exchangers, Ph.D. thesis, Wageningen Agricultural University, The Netherlands, 1996. 14. de Jong, P., Impact and control of fouling in milk processing, Trends Food Science and Technology 8: 401, 1997. 15. Tirumalesh, A., Ramachandra Rao, H.G., and Jayaprakash, H.M., Fouling of heat exchangers, Industrial Journal of Dairy Bioscience 8: 41, 1997. 16. Visser, H., Jeurnink, T.J.M., Shraml, J.E., Fryer, P., and Delplace, F., Fouling of heat treatment equipment, Bulletin of the IDF 328: 7, 1997. 17. Foster, C.L. and Green, M.L., A model heat exchange apparatus for the investigation of fouling of stainless steel surfaces by milk. II. Deposition of fouling material at 1408C, its adhesion and depth profiling, Journal of Dairy Research 57(3): 339, 1990. 18. Belmar-Beiny, M.T. and Fryer, P., Preliminary stages of fouling from whey protein solutions, Journal of Dairy Research 60: 467, 1993. 19. Jeurnink, T.J.M., Verheul, M., Cohen, S.M., and de Kruif, C.G., Deposition of heated whey proteins on a chromium oxide surface, Colloids Surfaces B: Biointerfaces 6: 291, 1996. 20. Delplace, F., Leuliet, J.C., and Levieux, D., A reaction engineering approach to the analysis of fouling, Journal of Food Engineering 34(1): 91, 1997. 21. Grijspeerdt, K., Mortier, L., De Block, J., and Van Renterghem, R., Applications of modelling to optimize ultra high temperature milk heat exchangers with respect to fouling, Food Control 15(2): 117, 2004. 22. Jun, S. and Puri, V.M., Fouling models for heat exchangers in dairy processing: a review, Journal of Food Process Engineering 28(1): 1, 2005. 23. Gut, J.A.W. and Pinto, J.M., Modeling of plate heat exchangers with generalized configurations, International Journal of Heat and Mass Transfer 46(14): 2571, 2003. 24. Jun, S. and Puri, V.M., 3D milk-fouling model of plate heat exchangers using computational fluid dynamics, International Journal of Dairy Technology 58(4): 214, 2005. 25. Grijspeerdt, K., Hazarika, B., and Vucinic, D., Application of computational fluid dynamics to model the hydrodynamics of plate heat exchangers for milk processing, Journal of Food Engineering 57(3): 237, 2003. 26. de Jong, P., te Giffel, M.C., Straatsma, H., and Vissers, M.M.M., Reduction of fouling and contamination by predictive kinetic models, International Dairy Journal 12(2–3): 285, 2002. 27. Kenneth, J.B., Heat exchanger design for the process industries, Journal of Heat Transfer 126(6): 877, 2004. 28. Wilson, D.I., Progress towards the antifouling heat exchanger: developments in fouling and cleaning, in International Dairy Federation World Dairy Summit, Melbourne, Australia, 2004. 29. Park, K., Choi, D.-H., and Lee, K.-S., Optimum design of plate heat exchanger with staggered pin arrays, Numerical Heat Transfer Part A: Applications 45(4): 347, 2004. 30. de Jong, P., Modeling and optimization of thermal processes in the dairy industry, Report no. V341, NIZO, Ede, The Netherlands, 1996. 31. Delplace, F. and Leuliet, J.C., Modeling fouling of a plate heat exchanger with different flow arrangements by whey protein solutions, Transactions of IchemE Part C 73: 112, 1995. 32. Kho, T. and Mu¨ller-Steinhagen, H., An experimental and numerical investigation of heat transfer fouling and fluid flow in flat plate heat exchangers, Special issue: Heat Mass Transfer 77(A2): 124, 1999. 33. Jun, S. and Puri, V.M., Dynamic modeling of thermal performance of multichannel plate heat exchangers, Paper no. 036188, 2003 ASAE Annual Meeting. American Society of Agricultural and Biological Engineers, St. Joseph, MI, 2003, www.asabe.org. 34. Paterson, W.R. and Fryer, P.J., A reaction engineering theory for the fouling of surfaces, Chemical Engineering Science 43: 1714, 1988. 35. Fryer, P.J., The use of fouling models in the design of food process plant, Journal of the Society of Dairy Technology 42(1): 23, 1989.
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36. Grijspeerdt, K., Mortier, L., De Block, J., and Van Renterghem, R., Modeling heat exchangers for the thermal treatment of milk, Mededelingen Faculteit Landbouwwetenschappen Universiteit Gent 64=5b: 477, 1999. 37. Georgiadis, M.C. and Macchietto, S., Dynamic modeling and simulation of plate heat exchangers under milk fouling, Chemical Engineering Science 55(9): 1605, 2000. 38. Georgiadis, M.C., Rotstein, G.E., and Macchietto, S., Modeling and simulation of complex plate heat exchanger arrangements under milk fouling, Computers and Chemical Engineering 22 (Suppl. 1): S331, 1998. 39. Georgiadis, M.C., Rotstein, G.E., and Macchietto, S., Modeling and simulation of shell and tube heat exchangers under milk fouling, AIChE Journal 44(4): 959, 1998. 40. Georgiadis, M.C., Rotstein, G.E., and Macchietto, S., Optimal design and operation of heat exchangers under milk fouling, AIChE Journal 44(9): 2099, 1998. 41. Georgiadis, M.C. and Papageorgiou, L.G., Optimal energy and cleaning management in heat exchanger networks under fouling, Chemical Engineering Research and Design 78(A2): 168, 2000. 42. Jun, S. and Puri, V.M., A 2D dynamic model for fouling performance of plate heat exchangers, Journal of Food Engineering 75(3): 364, 2005. 43. Ozden, H.O., Jun, S., and Puri, V.M., Sensitivity analysis of plate heat exchangers using FLUENT, Paper number NABEC-04-0019, 2004 Special Meeting Papers. American Society of Agricultural and Biological Engineers, St. Joseph, MI, 2004, www.asabe.org. 44. Jun, S. and Puri, V.M., A 2D dynamic model for fouling performance of plate heat exchangers, Journal of Food Engineering 75(3): 364, 2006. 45. Patankar, S.V. and Prakash, C., An analysis of the effect of plate thickness on laminar flow and heat transfer in interrupted-plate passages, International Journal of Heat and Mass Transfer 24(11): 1801, 1981. 46. Zhang, Z. and Li, Y., CFD simulation on inlet configuration of plate-fin heat exchangers, Cryogenics 43(12): 673, 2003. 47. Petermeier, H., Benning, R., Delgado, A., Kulozik, U., Hinrichs, J., and Becker, T., Hybrid model of the fouling process in tubular heat exchangers for the dairy industry, Journal of Food Engineering 55(1): 9, 2002. 48. Petermeier, H., Benning, R., Becker, T., and Delgado, A., Numero-fuzzy hybrid for modelling and simulation of the fouling of milk heat exchangers, Proceedings in Applied Mathematics and Mechanics 3(1): 470, 2003. 49. Hirsch, C., Rizzi, A., Lacor, C., Eliasson, P., Lindblad, I., and Hauser, J., A multiblock=multigrid code to simulate complex 3D Navier–Stokes flows on structured meshes, in Proceedings of the 4th International Symposium on Computational Fluid Dynamics, University of California Davis, Davis, CA, 1991. 50. Baldwin, B. and Lomax, H., Thin-layer approximation and algebraic model for separated turbulent flows, in 16th Aerospace Sciences Meeting American Institute of Aeronautics and Astronautics, Huntsville, AL, 1978, p. 9. 51. Hiddink, J., Lalande, M., Maas, A.J.R., and Streuper, A., Heat treatment of whipping cream. I. Fouling of the pasteurization equipment, Milchwissenschaft 41: 542, 1986. 52. Vucinic, D. and Hazarika, B.K., Integrated approach to computational and experimental flow visualization of a double annular confined jet, Journal of Visualization 4(3): 245, 2001.
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Plate Heat Exchanger: Thermal and Fouling Analysis Soojin Jun and Virendra M. Puri
CONTENTS 17.1 17.2
Introduction ............................................................................................................. 417 CFD Modeling......................................................................................................... 418 17.2.1 Fouling Model ............................................................................................ 418 17.2.2 CFD Simulation.......................................................................................... 420 17.2.3 Model Validation ........................................................................................ 422 17.2.3.1 PHE Configurations ................................................................... 422 17.2.3.2 Measurements ............................................................................. 423 17.3 Results and Discussion............................................................................................. 423 17.4 Conclusions .............................................................................................................. 429 Nomenclature ..................................................................................................................... 429 References .......................................................................................................................... 430
17.1 INTRODUCTION Heating of liquids is a common unit operation in food industry such as pasteurization and sterilization of dairy products. Thermal instability of food components results in the formation of fouling layers within food processing equipment. Fouling increases thermal and electrical energy usage by decreasing the heat transfer coefficient. Additionally, fouling results in a significant downside associated with microbiological problems of pasteurized food products [1]. Due to the fouling, cleaning at least once-a-day, i.e., every 5–10 h, is a common practice for widely used plate heat exchangers (PHEs). This gives rise to extra processing costs in terms of capital, energy, maintenance, water, and production losses. In 1991, it was estimated that the heat exchanger fouling costs the entire US industrial community about $4.2–10 billion=per year, with the US dairy industry contributing one of the largest fractions [2]. Besides the economic impact, there are also the environmental problems due to excessive water usage, and the use of aggressive cleaning agents, which might remain in, and thereby contaminate the pasteurized product. Also, the fouling deposits provide favorable growth conditions for pathogens, which are attributed to the entrapment of bacteria in or attachment of bacteria onto the fouled heat transfer surfaces. It is therefore beneficial and timely to rationally address and minimize the problem of fouling in the dairy industry, and by extension to the food industry. Accurate prediction and analysis of fouling dynamics based on an understanding of chemistry and fluid mechanics are very useful in predicting how real process equipment is likely to respond. There has been a considerable amount of literature available on the modeling of the fouling process [3]. There seems to be an agreement that the thermal
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denaturation of the whey protein—b-lactoglobulin (b-LG) plays a major role in the fouling process, certainly when the temperature is below 908C [4,5]. Georgiadis and Macchietto [6] presented mathematical modeling for complex PHE arrangements subjected to milk fouling by adapting a plug flow model with added axial convection and radial dispersion effects. However, the presented models were based on 1D hydrodynamic performance of the PHE, which is a considerable simplification of the effect of plate geometry used in the industry. In our previous study, a 2D fouling model that accounts for the hydrodynamics and thermodynamics of fluid flow and the reaction scheme of milk protein under fouling was capable of predicting milk deposition with higher accuracy than a 1D model [7]. The 2D dynamic model could identify zones most prone to milk deposits, thus enabling the quantitative analysis of milk fouling. However, the 2D simulation could rarely provide a complete picture of the PHE performances with corrugation profiles, which would cause undesired flow maldistribution in the channel. Since the hydrodynamic characteristics of fluid flow are mostly governed by the corrugation geometry in PHEs, the predictive errors of fouling model can be minimized using only 3D computational fluid dynamics (CFD), which can readily take into account the detailed geometry of the plates. From our knowledge, there has been no study on 3D fouling model for PHEs in food industry, probably due to its complexity and computational efforts. Availability of such a model can optimize the process to obtain the best operating conditions while minimizing undesirable side effects associated with heating such as fouling. The operating conditions are, for example, temperature, residence time, and flow rate. If the control is applied incorrectly, for instance, having wall temperature that is too high or product flow rate that is too low, fouling may become more severe [8]. The aim of this research was to implement the hydrodynamic and thermodynamic models in 3D for precise prediction of flow and temperature profiles in the channel using CFD, which were coupled with a milk fouling model. Incorporating a physicochemical model for the denaturation of b-LG to the 3D dynamics requires the knowledge of wall adhesion of the fouling components. The developed and validated model can permit the dairy process scientists and engineers to predict the likely profile of milk deposition in a plate and furthermore, design the plate shape and corrugation profile optimized for reducing the extra cost involved in fouling. Such an optimization could potentially reduce the operating cost of a typical system by more than 50% [9].
17.2 CFD MODELING 17.2.1 FOULING MODEL For the thermal process dominated by the precipitation of minerals, the interaction of minerals with the intermediate unfolding state (or active) of b-LG before being aggregated should be considered. Unfolded protein reacts through a heat-induced interaction with k-casein at the casein–micelle surface, to which the micellar calcium phosphate binds [10]. The formed particles may be subsequently bound to the surface through mediation of the attached whey protein molecules. Therefore, the fouling model is closely related to a mass transfer or surface reaction process [11]. de Jong et al. [12] and de Jong [9] have developed a mathematical fouling model wherein both surface and bulk reactions are considered. The denaturation of b-LG was described as a consecutive reaction kinetics of unfolding and aggregation [13]. The model with the empirical kinetic data of the unfolding and aggregation of b-LG was applied to PHEs:
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N!U!A # D
419
(17:1)
where N, U, A, and D are the native, unfolded, aggregated, and deposited b-LG, respectively. The fouling reaction scheme of Petermeier et al. [14] is essentially the one presented by de Jong et al. [12], and de Jong [9]. However, there exists a different reaction order for the deposition of unfolded b-LG:
@CN ¼ kU CN @t
(17:2)
@CU ¼ kU CN kA CU2 kD CU @t
(17:3)
@CA ¼ kA CU2 @t
(17:4)
@CD ¼ kD CU @t
(17:5)
where C is the protein concentration, t is the time, and k is the reaction constant. It is observed that the second reaction equation reflects the conservation of protein mass balance due to the loss of unfolded b-LG involved in deposition process. Also by use of the last equation form, the deposited b-LG can be directly obtained as a concentration before it is converted to the deposited mass. The reaction rate constant k is related to the absolute temperature according to the Arrhenius equation: Eai k ¼ k0 exp , i ¼ N, U, A, and D (17:6) RTk where Eai is the activation energy, R is the gas constant, Tk is the temperature in K, and k0 is the preexponential factor. Of interest is the assumption that only the aggregated protein is deposited on the wall and is not functional for the model of de Jong et al. [12,15] and de Jong [9], which hypothesized that the main mechanism in fouling process is a reaction-controlled adsorption of unfolded b-LG. The information on kinetics data for b-LG can be found in publications, as shown in Table 17.1. The governing 3D flow equations in the FLUENT software (v. 6.0, Fluent Inc., Lebanon, NH) include the continuity and the momentum equations in Cartesian coordinates, as given by @u @v @w þ þ ¼0 @x @y @z 2 @u @u @u @u 1 @P @ u @2u @2u þu þv þw ¼ þ x-Momentum: þ þ @t @x @y @z @x @x2 @y2 @z2 2 @v @v @v @v 1 @P @ v @2v @2v þu þv þw ¼ þ þ þ y-Momentum: @t @x @y @z @y @x2 @y2 @z2 2 @w @w @w @w 1 @P @ w @2w @2w þu þv þw ¼ þ þ þ z-Momentum: @t @x @y @z @z @x2 @y2 @z2 Continuity:
(17:7) (17:8) (17:9) (17:10)
where y is the kinematic viscosity, r is the density, P is the pressure, t is the time, and u, v, and w are the velocity components along with x, y, and z directions.
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TABLE 17.1 Kinetic Parameters for the Fouling Reaction Scheme Unfolding Aggregation
EN (kJ mol1) K0N (s1) EU (kJ mol1) K0U (s1)
Deposition
EN (kJ mol1) K0N (s1)
261 3.371037 312 56 1.361043 1.83106 45.1 0.51
708C–908C 908C–1508C 708C–908C 908C–1508C
de Jong et al. [12,15], Toyoda and Fryer [18]
Petermeier et al. [14], Grijspeerdt et al. [3]
The transient energy equation for a 3D constant property, incompressible flow is as follows:
Energy:
@T @T @T @T k @2T @2T @2T þu þv þw ¼ þ þ @t @x @y @z Cp @x2 @y2 @z2
(17:11)
where T is the temperature and Cp is the specific heat.
17.2.2 CFD SIMULATION The PHE system (Junior s=s, APV, Tonawanda, NY) from a HTST milk pasteurizer in Creamery Research Pilot Plant (Penn State University, PA) was used as the basis for the simulation. Figure 17.1 shows the computational domain and coordinate system which has two plates parallel to each other. The profile of the corrugated plate was normal to the primary flow direction. The minimum and maximum gaps between the plates were 2 and 6 mm, respectively. A regular, structured grid of hexahedral mesh elements was created to discretize the domain using 88,000 elements.
Outlet
Inlet
Y X Z
FIGURE 17.1 The computational PHE domain and grids.
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The simulation was carried out using the FLUENT software (v. 6.0). A grid of the geometry was constructed using the GAMBIT 2.0 preprocessor. The Reynolds number used in the simulation ranged between 0.7 and 302, which could be treated as laminar flow. The FLUENT software can model the mixing and transport of chemical species, i.e., native, unfolded, aggregated, and deposited proteins, by solving the conservation equations describing convection, diffusion, and reaction sources for each component species. Multiple simultaneous chemical reactions can be modeled with reactions occurring in the bulk phase (volumetric reactions) and=or wall or particle surfaces. Species transport modeling capabilities, both with and without reactions, are available and the inputs are provided. The approach is based on the solution of transport equations for species mass fractions, with the defined chemical reaction mechanism. The reaction rates that appear as source terms in the species transport equations are computed from Arrhenius rate expressions [16]. The principle of fouling model can be described by using a flow chart (Figure 17.2). Given initial and boundary conditions, the FLUENT calculates the flow and temperature profiles. The temperature profiles along the heat transfer surface enable the calculation of the unfolding and aggregation rates of b-LG in bulk layer and the deposition rates on wall surface. All reaction rates are recalculated at a determined time t þ Dt until the time t reaches the end point. The deposited mass can be calculated as a sum of an integral of the deposition rate (g m2 s1) with respect to the heat transfer area (m2) at each time step Dt. The time step Dt is set to be 0.1 s, which is small enough to satisfy the stability criterion [17].
t = t0
FLUENT
Flow field
Temperature field
Native protein, CN Volumetric reactions
Unfolded protein, CU
t = t + ∆t
Aggregated protein, CA
Milk deposition, CD
No
t = tend?
Wall surface reactions
Yes
End
FIGURE 17.2 The flow chart of FLUENT for the simulation of milk fouling on the surface.
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17.2.3 MODEL VALIDATION 17.2.3.1
PHE Configurations
The PHE system, used in dairy pasteurization process, has three different sections, i.e., cooling, regeneration, and heating. The heating section of PHE, where heat transfer occurs between the supersaturated hot water and raw dairy products, consists of 19 plates and 2 end plates. Flow patterns comprising both countercurrent and cocurrent have five channels per pass with a total of two passes for raw milk, and 10 channels per pass with a total of one pass for hot water (Figure 17.3). The key geometrical specifications and operating conditions for the PHE system are listed in Table 17.2. CH1
End
1
CH2
2
CH6
10
11
CH3
3
4
CH7
12
13
5
CH4
6
CH8
14
15
7
CH5
8
CH9
16
17
9
CH10
18
19
End
Hot water Milk
FIGURE 17.3 Flow configuration for PHE system.
TABLE 17.2 Geometrical Specifications and Operating Conditions for the PHE System Plate model Material Actual heat Transfer area Thickness, dp (mm)
Junior s=s, APV Stainless Steel 316Ti Height, H (mm) Width, W (mm)
Conditions Inlet temperature (8C) Inlet flow rate (m s1) Flow pattern Total number of plates a
400 60 0.6
Cold Stream (Raw Milk)
Hot Stream (Water)
63 0.655=5a Both countercurrent and cocurrent 19 þ 2 end plates
100 0.655=10a
Number of channels per pass.
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17.2.3.2
Measurements
For model validation, temperature values were measured for the first pass of fluid milk and fouling measurement for the second pass of fluid milk in PHE system. It was intended to avoid the possible interference between two measurements, for example, the thermocouple might affect the adhesion of aggregate protein into the plate surface. To measure the flow temperature, temperature sensors (T-type thermocouple, #36) were installed at five different locations of the plate 2 along with the vertical centerline, similar to our previous work [17]. The data acquisition unit (Agilent 39704A) used to record the measured temperature data was controlled by a personal computer (PC) with RS232C serial communication. A computational program developed using LabView v. 6.0 (National Instruments, Austin, Texas) was designed to monitor the dynamic temperature profiles of the fluid at different locations. For the quantitative analysis of milk deposits, the PHE system with raw milk (Creamery, Penn State University, Pennsylvania) was operated for 20 h. After the system was shut down, the array of plates was disassembled. As representative of the system, plate 18 was chosen to collect the fouled mass by a scraper and weigh them. The measured value was compared with the simulated data obtained using 3D fouling model.
17.3 RESULTS AND DISCUSSION Figure 17.4a shows the cross-sectional view of velocity profiles at various locations in the channel. The most intensive flow stream is clearly formulated in the right side of channel at which the inlet port is located (circle area). The flow is relatively straightforward in the center of flow channel. Within the corrugations the flow separates at the beginning of the diverging portion and recirculation zones are present (Figure 17.4b). These recirculation zones, in other words, eddy flows cover the whole additional area provided by the corrugations. The reverse flow regions could be the most prone to fouling since the longer residence time of the milk components would cause more heating and consequently more fouling.
2.42e−01
Velocity (m s−1)
2.27e−01 2.12e−01 1.97e−01 1.82e−01 1.67e−01 1.52e−01 1.36e−01
Inlet
1.21e−01 1.06e−01 9.09e−02 7.58e−02 6.06e−02 4.55e−02 3.03e−02
Y
1.52e−02 0.00e+00
Z
X
(a)
FIGURE 17.4 (a) The cross-sectional view of velocity profiles at various locations in the channel. (continued )
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Y X
Z
(b)
FIGURE 17.4 (continued) (b) A closer view of cross-sectional velocity distribution.
The simulation provides the transient patterns of temperature and fouling of fluid milk on plate 2 in the PHE system (Figure 17.5 and Figure 17.6). The amount of heat flux as boundary conditions of wall surfaces was 20.6 (kW m2), as calculated from our previous work [17]. As time progressed, a uniform initial surface temperature (608C) at the onset of heating became uneven and the developed hot areas were geometrically skewed to the right side of plate surface primarily due to the flow maldistribution. The localized hot zones can be identified readily at the bottom area near the outlet port and the corner opposite to the inlet port, with the temperature reaching up to 908C. The predicted temperature values of fluid milk were close to the measurement with a maximum prediction error of 1.68C or 2.1%. The initial mass fraction of native protein was 0.01, as referred in the work of Georgiadis and Macchietto [6].
Temperature (K) 3.73e+02 3.71e+02 3.69e+02 3.67e+02 3.65e+02 3.63e+02 3.61e+02 3.59e+02 3.57e+02 3.55e+02 3.53e+02 3.51e+02 3.49e+02 3.47e+02 3.45e+02 3.43e+02 3.41e+02 3.39e+02 3.37e+02 3.35e+02 3.33e+02
(a) t = 0.3 s
(b) t = 6.4 s
(c) t = 9.1 s
Y X Z
(d) t = 29.8 s
FIGURE 17.5 Simulated temperature profiles of fluid milk under the unsteady-state conditions.
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Plate Heat Exchanger: Thermal and Fouling Analysis Deposition rate (kg m−2 s−1) 6.25e−07 5.94e−07 5.62e−07 5.31e−07 5.00e−07 4.69e−07 4.37e−07 4.06e−07 3.75e−07 3.44e−07 3.12e−07 2.81e−07 2.50e−07 2.19e−07 1.87e−07 1.56e−07 1.25e−07 9.37e−08 6.25e−08 3.12e−08 0.00e+00
(a) t = 0.3 s
(b) t = 6.4 s
(c) t = 9.1 s
Y Z
X
(d) t = 29.8 s
FIGURE 17.6 Simulated fouling profiles of fluid milk under the unsteady-state conditions.
The calculated fouling map (Figure 17.6) clearly shows the increment of milk fouling on the plate surface as a function of time. Most plate area keeps the surface relatively free of foulants; however, as time progresses, there is an increase in the deposition rate around the bottom near the outlet port. Figure 17.7 shows a closer view of the area most prone to fouling in the channel. Since it is known that milk deposition occurs not in the bulk layer but in the thermal boundary layer [18], the corresponding chemical reaction has been coded under the wall surface reactions. The figure shows that there occurs less fouling when the flow stream passes through the
Deposition rate (kg m−2 s−1) 6.23e−07 5.92e−07 5.61e−07 5.30e−07 4.99e−07 4.67e−07 4.36e−07 4.05e−07 3.74e−07 3.43e−07 3.12e−07 2.80e−07 2.49e−07 2.18e−07 1.87e−07 1.56e−07 1.25e−07 9.35e−08 6.23e−08 3.12e−08 0.00e+00
Y Z
X
FIGURE 17.7 Simulated fouling profiles of fluid milk in the corner of channel.
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Deposition rate (g s−1)
1.40e−05 1.20e−05 1.00e−05 8.00e−06
Plate 18 Plate 2
6.00e−06 4.00e−06 2.00e−06 0.00e+00 0
20
40
60
80
100
Time (s)
FIGURE 17.8 The deposition rate profiles of milk protein for plates 2 and 18.
narrow gap between two corrugated plates. This is due to the increase of flow rate, which is governed by the Bernoulli equation. However, thicker layer of potential milk fouling can be observed inside the corrugation where there might occur the entrapment of milk proteins due to eddy or reverse flows. Figure 17.8 shows the graphs of deposition rates of milk protein versus the operating times for plates 2 and 18. The plate 2 is located in the first pass, which has raw milk input with cocurrent flow pattern, whereas the plate 18 has inlet temperature and fouling components, which are the mean outlet values of the channels belonging to the previous pass. The inlet temperature of milk measured in channel 10 including plate 18 was 76.68C. The initial mass fractions of protein components numerically determined based on the validated 2D simulation results are 0.0072, 0.0028, and 1.78105 for native, unfolded, and aggregated proteins, respectively. For the plate 2, the deposition rate curves reach steady state (within a steadystate error of 3%) after 29.8 s whereas the plate 18 has the steady-state value after 17.9 s. The area below the graph denotes for the total mass of potential milk foulant. Over a period of operation of 20 h, the total deposit on the plate 18 is calculated to be 1.00 g, which is close to the experimentally measured data, 1.01 g with 1% error. Although the experimental data was not collected for plate 2, the expected fouling mass on the plate 2, 0.092 g is very close to that of the validated 2D model, 0.09 g. Compared to 2D model, the 3D model can permit not only the consideration of the corrugation profiles of plates but also the design of plate geometry for the enhancement of PHE performance in terms of fouling. Special attention was paid to the design of a new plate shape and corrugation profile, which is aimed at minimizing milk fouling with enhanced efficiency. The new grid of the plate domain in a 3D environment was designed and meshed using the GAMBIT, a preprocessor of FLUENT, as shown in Figure 17.9. This is one of the typical designs of compact PHE evaporator for automobile air conditioners. The 3D numerical simulation was intended to verify that the plate shapes and corrugation profiles used for nonfood industry could be functional for thermal processing in food industry. The domain was meshed using tetrahedral scheme with 831,169 elements. The plain top plate is facing the bottom plate, which has two corrugated guidelines on each left and right sides. The flow is directed by guidelines to pass though the zone 1 and curve round the U-shaped zone 2, and then head toward the outlet (the zone 3), which is adjacent to inlet port (Figure 17.9).
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Top plate
Y
X Z
Bottom plate
Zone 3
Zone 2 Zone 1
Outlet
Inlet Y
X Z
FIGURE 17.9 The computational domain of new PHE system.
It should be noted that the zone 2 provides for mixing of three main flow streams out of the zone 1 and then split it into three flow streams along with the embossed guidelines. Table 17.3 shows the comparison of system specifications between the current PHE and new PHE. For even comparison, the area-weighted average values of temperature for both systems, as defined in Equation 17.9, are controlled to be identical, i.e., 350 K:
TABLE 17.3 Comparison of Simulation Results for the Current and New PHEs
Area (m2) Inlet temperature (K) Outlet temperature (K) Area-weighted average (K) Mass flow rate (kg s1) Linear flow rate (m s1) Heat flux (kW m2) Heat transfer rate (W) Deposition rate (mg m2 s1)
Current PHE
New PHE
Differences (%)
0.026 333 351.4 350.5 0.0156 0.13 20.6 537.5 0.049
0.024 333 342.8 351.1 0.0072 0.13 30.6 745.3 0.0036
6.5 0 2.4 0.2 53.8 0 48.6 38.6 92.6
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1 A
ð
fdA ¼
n 1 X f jA i j A i¼1 i
(17:12)
where f is the variable, i.e., temperature, A is the total area, and i is the element number. It should be noted that the total heat transfer area of the new PHE is smaller than the current PHE by 30% so a larger amount of heat flux needs to be set on the boundary. Figure 17.10 shows the temperature and fouling profiles of milk flow in the channel of new PHE system. Since the flow stream is uniformly distributed over the whole area, there occurs little recirculation zone, unlikely to cause serious milk deposition. As shown in Table 17.3, the milk deposition rate in the new PHE is about 10 times smaller than the current PHE system, which leads to a marked reduction of potential milk fouling on the plate surface. The antifouling performance of new PHE system could be further improved by optimizing the plate shape and corrugation profile, which is, however, beyond the scope of our research. The chemical reaction scheme used in FLUENT is not perfect to fully describe the fouling phenomena. The final step for milk deposition from unfolded protein can be explained not
Temperature (K) 3.71e+02 3.69e+02 3.67e+02 3.64e+02 3.62e+02 3.59e+02 3.57e+02 3.55e+02 3.52e+02 3.50e+02 3.47e+02 3.45e+02 3.43e+02 3.40e+02 3.38e+02 3.35e+02
Y
X
3.33e+02
Z Deposition rate (kg m−2 s−1) 3.70e−08 3.46e−08 3.23e−08 3.00e−08 2.77e−08 2.54e−08 2.31e−08 2.08e−08 1.85e−08 1.62e−08 1.39e−08 1.15e−08 9.24e−09 6.93e−09 4.62e−09 2.31e−09 0.00e+00
Y
X
Z
FIGURE 17.10 Simulated temperature and fouling profiles of milk flow in new PHE system.
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only by the mass transfer based on the chemical reaction but also by the surface chemistry and surface finish. Indeed, the surface chemistry needs to be coupled with the conventional reaction scheme for the precise analysis of fouling kinetics. According to Na and Webb [19], the embryo formation rate on a unit surface area for nucleation, in other words, induction stage of fouling can be estimated using the equation given by Gc I ¼ I0 exp kTK
(17:13)
where I is the embryo formation rate, I0 is the kinetic constant dependent on the matter of parent phase, k is the Boltzmann constant (1.38066 1023 J K1), Tk is the surface temperature given in Kelvin, and Gc is the critical Gibbs energy. Equation 17.10 implies that the nucleation or induction process requires that the foulant embryo should overcome a critical Gibbs energy barrier. The embryo formation rate increases as the critical Gibbs energy decreases. The change of critical Gibbs energy is dependent on the interfacial energy at each interface, i.e., between milk foulant and stainless steel surface. For example, the critical Gibbs energy change of the embryo can be reduced with a lowered interfacial energy, in other words, increased contact angle [19]. Since the surface energy of the base substrate affects the initial fouling kinetics to a great extent, needs for further fouling study exist on integration of the significant effect of surface energy into the current 3D fouling model.
17.4 CONCLUSIONS Milk fouling process in PHE system was simulated based on the hydrodynamic and thermodynamic principles using the CFD code. The 3D fouling model permits the influence of corrugation shapes and orientations, which is not feasible by 2D model. A quantitative validation of the model shows that the predicted fouling distribution and the amount of milk deposits in each channel were in good agreement with the experimental observation (prediction error <1%). The approach shows that the 3D fouling model coupled with CFD software in FLUENT can be used for design of new plates with shapes and corrugation profiles aimed to inhibit foulant absorption onto the surface. The simulation results based on new PHE system show it could decrease the deposited mass by a factor of 10, compared to the current system under the identical energy basis. It will ensure the efficiency of the milk pasteurizing system for minimizing fouling, with the potential and promise to pave the way for new processing protocols in the dairy industry. Most of the fouling models have theoretically dealt with the deposition process of b-LG as the mass transfer governed by the chemical reaction; however, the absorption of the milk foulant onto the surface can be overlooked without consideration of the surface energy and finish conditions.
NOMENCLATURE A C Cp Ea
total area (m2) protein concentration in bulk (kg m3) specific heat (J kg1 8C1) activation energy (J mol1)
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Gc i I I0 k k0 k P R Re T Tk t u v w r f y
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critical Gibbs energy (J) facet number embryo formation rate kinetic constant for embryo formation thermal conductivity (W m1 8C1) preexponential factor Boltzmann constant, 1.38066 1023 (J K1) pressure (Pa) gas constant (J mol1 8C1) Reynolds number temperature (8C) temperature (K) time (s) velocity vector in x-direction (m s1) velocity vector in y-direction (m s1) velocity vector in z-direction (m s1) density (kg m3) variable kinematic viscosity (m2 s1)
REFERENCES 1. J. Verran. When is a biofilm not a biofilm—and does it really matter? In: D.I. Wilson, P.J. Fryer, and A.P.M. Hasting (eds.). Fouling, Cleaning and Disinfection in Food Processing. Cambridge, UK: Department of Chemical Engineering, University of Cambridge, 2002, pp. 49–56. 2. C. Sandu and R.K. Singh. Energy increase in operation and cleaning due to heat exchanger fouling in milk pasteurization. Food Technology 32: 84–91, 1991. 3. K. Grijspeerdt, L. Mortier, J. de Block, and R. van Renterghem. Applications of modeling to optimize ultra high temperature milk heat exchangers with respect to fouling. Food Control 15(2): 117–130, 2004. 4. P. de Jong. Impact and control of fouling in milk processing. Trends in Food Science and Technology 8: 401–405, 1997. 5. H. Visser, T.J.M. Jeurnink, J.E. Shraml, P. Fryer, and F. Delplace. Fouling of heat treatment equipment. Bulletin of the International Dairy Federation 328: 7–31, 1997. 6. M.C. Georgiadis and S. Macchietto. Dynamic modeling and simulation of plate heat exchangers under milk fouling. Chemical Engineering Science 55: 1605–1619, 2000. 7. S. Jun, V.M. Puri, and R.F. Roberts. A dynamic 2D model for thermal performance of plate heat exchangers. Transactions of the ASAE 47(1): 213–222, 2004. 8. P.J. Fryer. The use of fouling models in the design of food process plant. Journal of the Society of Dairy Technology 42: 23–29, 1989. 9. P. de Jong. Modeling and optimization of thermal processes in the dairy industry. The Netherlands: NIZO Research Report V341, 1996, p. 165. 10. H.J.M. van Dijk. On the structure of casein micelles. In: E. Dickinson and P. Walstra (eds.). Food Colloids and Polymers: Stability and Mechanical Properties. Cambridge, UK: Royal Society of Chemistry, 1993, pp. 165–166. 11. V. Visser and T.J.M. Jeurnink. Fouling of heat exchangers in the dairy industry. Experimental Thermal and Fluid Science 14(4): 407–424, 1997. 12. P. de Jong, S. Bouman, and H.J. van der Linder. Fouling of heat transfer equipment in relation to the denaturation of b-lactoglobulin. Journal of the Society of Dairy Technology 45: 3–8, 1992. 13. J.N. de Wit and G. Klarenbeek. Technological and functional aspects of milk proteins. In: Milk Proteins in Human Nutrition. Germany: Steinkopff Darmstadt, 1989, pp. 211–222.
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14. H. Petermeier, R. Benning, A. Delgado, U. Kulozik, J. Hinrichs, and T. Becker. Hybrid model of the fouling process in tubular heat exchangers for the dairy industry. Journal of Food Engineering 55: 9–17, 2002. 15. P. de Jong, R. Waalewijn, and H.J.L.J. van der Linden. Validity of a kinetic fouling model for heattreatment of whole milk. Lait 73: 293–302, 1993. 16. FLUENT Inc. 6.0 User’s Guide, Chapter 13, Lebanon, NH: Fluent Inc. 17. S. Jun and V.M. Puri. A 2D dynamic model for fouling performance of plate heat exchangers. Journal of Food Engineering 75: 364–374, 2006. 18. I. Toyoda and P.J. Fryer. A computational model for reaction and mass transfer in fouling from whey protein solutions. In: C.B. Panchal (ed.). Fouling Mitigation of Industrial Heat Exchange Equipment. New York: Begell House, 1997, pp. 589–600. 19. B. Na and R.L. Webb. A fundamental understanding of factors affecting frost nucleation. International Journal of Heat and Mass Transfer 46: 3797–3808, 2003.
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CFD Applications in Membrane Separations Systems Sean X. Liu
CONTENTS 18.1 18.2 18.3
Introduction ............................................................................................................. 434 Implementation of CFD Modeling and Simulation................................................. 435 Applications of CFD in Membrane Separations ..................................................... 439 18.3.1 Membrane Separation by Hydrostatic Pressure Difference—Membrane Filtration............................................................... 441 18.3.2 Membrane Separations by Electrical Potential Difference—Electrodialysis ......................................................................... 442 18.3.3 Membrane Separations by Partial Vapor Pressure Gradient ...................... 443 18.3.3.1 Pervaporation .............................................................................. 443 18.3.3.2 Membrane Distillation................................................................. 445 18.3.4 Membrane Modules .................................................................................... 446 18.3.4.1 Spiral Wound .............................................................................. 446 18.3.4.2 Hollow Fiber ............................................................................... 448 18.3.4.3 Plate and Frame .......................................................................... 448 18.3.4.4 Tubular ........................................................................................ 448 18.4 CFD Modeling and Simulations .............................................................................. 450 18.4.1 Solving Fluid Flow and Mass Transfer in a Membrane Channel with CFD .................................................................................................... 450 18.4.2 Predicting Flow Behaviors in the Membrane Channel ............................... 451 18.4.2.1 CFD Simulations of Membrane Systems under Laminar Conditions ................................................................................... 452 18.4.2.2 CFD Simulations of Membrane Systems under Turbulent Conditions ................................................................................... 453 18.4.3 Predicting Concentration Polarization ........................................................ 453 18.4.4 Predicting Effects of Spacers on Flow Behaviors........................................ 456 18.4.5 Predicting Flow Behaviors and Mass Transfer of Novel Membrane and Module ................................................................................................. 461 18.5 Conclusions .............................................................................................................. 462 Nomenclature ..................................................................................................................... 462 References .......................................................................................................................... 463
433
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18.1 INTRODUCTION Membrane separations, like liquid food processing technologies, have been around for some time now, with the dairy industry taking the lead—membrane processes for fractionation of milk such as cold pasteurization of skim milk (bacterial removal), concentration of casein micelles from skim milk, and recovery of serum proteins from cheese whey. Today, membrane-based food processing technologies have extended beyond whey protein recovery, fruit juice concentration, and cold pasteurization; and depectinization-related processes and have found new niches in diverse areas of food and postharvest processing [1,2]. Emerging membrane-based processes, such as dealcoholization of wine (and beer), either with pervaporation [3] or with reverse osmosis [4], membrane emulsification [5], hydrolysis of lactose with membrane bioreactor [6], and aroma compound recovery [7–11] from fruit juices or food or agricultural wastes, have the potential to go mainstream in the near future [1,12–14]. Foods by nature are a complex biopolymer mixture comprised of carbohydrates, lipids, minerals, and proteins. These components of foods have broad particle size distribution ranging from 1 nm to 1 mm, not counting coarse particles that settle quickly over time. This broad size distribution of particulates in liquid foods combining with natural variations among the same category of foods poses a very serious challenge since the separation capability and selectivity of a membrane are based on pore size of the membrane and its distribution for separations. New development in ceramic membranes, track etched membranes, silicon microsieves, and metal microfilters has somewhat addressed the size distribution issue; however, there is another more prominent issue resulting from process conditions, which adversely affects the membrane performance. Many membrane processes are hindered in various degrees by process phenomena of concentration polarization and membrane fouling [15–17]. Concentration polarization, a significant concentration gradient between the solute in the bulk and the membrane surface, reduces process performance in the form of reduced permeation flux. It is an unavoidable common reversible process phenomenon innate in all membrane-based processes. In membrane-based food processing, concentration polarization also contributes to irreversible membrane fouling and even formation of scale on the membrane surface, as certain scaling minerals in the feed stream exceed their solubility limits at the membrane surface. The occurrences of these adverse process phenomena in pressure-driven membrane processes such as ultrafiltration and reverse osmosis follow a familiar pattern: during the initial cycles (permeation followed by membrane cleaning), the concentration polarization is the main culprit for permeation flux decline, and as the solutes accumulate on the surface, the permeation flux reduction can be clearly, at least partly, attributed to the irreversible membrane fouling [18]. Pervaporation, another emerging membrane-based food processing technology, also suffers from concentration polarization infliction, although its manifestation is different from those in pressure-driven membrane separations as illustrated in Figure 18.1. Concentration polarization in pervaporation is formed as a result of different mass transfer rates of the solute species in the membrane matrix and in the liquid boundary layer. Membrane fouling affects not only permeation flux but also selectivity of the membrane in terms of species separations. Since the main aim in optimal designing and controlling of all membrane processes is to ensure maximum permeate flux while retaining maximum less-permeable species rejection with minimum capital and operating costs, any improvement in permeation flux and membrane lifetime as a result of less severe concentration polarization (and membrane fouling) would bring about significant gain in process economics. In order to reduce concentration polarization the detailed information about flow velocity field and solute concentration distribution in the membrane system needs to be known before and after the concentration polarization reduction technique is applied. Methods of controlling or alleviating membrane fouling have been developed, but some of the approaches to alleviate membrane
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UF/RO Feed in
Retentate out
PV Feed in
Retentate out
FIGURE 18.1 Concentration polarization in reverse osmosis=ultrafiltration (RO=UF) and in pervaporation (PV).
fouling inevitably increase the complexity in equipment and operations. Additionally, the complexity also complicates the task of process optimization and performance enhancement. In all likelihood, experimental measurements of velocity and concentration profiles of the solute are preferred methods for process assessment and improvement. The difficult experimental environment in the narrow membrane flow channel of common membrane modules (e.g., spiral wound module) and implementations of strategies of controlling membrane fouling has stimulated development of models that could simulate and predict the characteristics of the boundary layer mass transfer, or concentration polarization using computational fluid dynamics (CFD) approaches. By having fundamental understanding of flow dynamics and mass transfer in membrane channels, it will substantially reduce the cost of process design and improvement of membrane systems in the food industry. It is also possible for the designer and operator of the membrane system in an industrial operation to operate the system just below the optimal performance calculated with CFD simulations.
18.2 IMPLEMENTATION OF CFD MODELING AND SIMULATION CFD modeling and simulation is a powerful computer-based tool that analyzes systems involving fluid, heat and mass transfer, and associated phenomena such as chemical reactions, ion exchange, and adsorption and is being increasingly applied in the membrane field [19]. It allows an in-depth analysis of fluid mechanics in the membrane flow channel and local effects of momentum and mass transfers. CFD can produce extremely large amounts of results at virtually no added costs to the user after the user acquires the necessary computer software and hardware. The principle of CFD is simple: first, the region of interest of an engineering problem (e.g., a rectangular membrane flow channel) is divided into a large number of cells or control volumes (the mesh or grid). In each of these cells, the partial differential equations (the Navier– Stokes equations) describing the fluid flow are reformulated as algebraic equations that relate the pressure, velocity, temperature, and other variables, such as species concentrations, to the corresponding values in the neighboring cells. The algebraic equations are then solved numerically, generating a complete picture of the flow down to the resolution of the grid. In general, CFD provides better performance predictability and accuracy than those semiempirical correlations in many food engineering problems [20,21]. The cost of CFD simulation, despite the high costs of computer hardware and software license fees and steep learning curve, is still far below the cost of a full-scale experiment, in terms of facility use and man-hour costs on a comparable number of data points obtained.
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CFD codes are structured around the numerical algorithms that solve engineering problems involving fluids and aiding in designing process equipment for fluid flows [22,23]. Earlier, CFD applications were performed by engineers using the computer codes they developed numerically in FORTRAN language and some of those individuals still are doing their own coding, sometimes with the help of one of those excellent ‘‘recipe’’ books [24,25]. By and large, most researchers use one of many publicly available CFD codes today; some are free and some cost tens of thousands of dollars annually, to predict the flow behaviors and associated phenomena. The free and low-cost CFD codes can be found in the Web site (http:==www.cfd-online.com=Links=soft.html), while the available commercial CFD software packages can also be found on the Web (http:==www-berkeley.ansys. com=cfd=CFD_codes_c.html). As one can intuitively recognize, free and low-cost CFD codes have some drawbacks when compared to the commercial ones, even though some of the free and low-cost codes can be more efficient and accurate than commercial codes in some situations. First of all, free and low-cost CFD code owners do not provide any training or even detailed documentation to users. Second, there is no technical support whatsoever with free and low-cost codes—you are on your own. Third, the majority of free and low-cost CFD codes were designed to solve one particular flow-related problem, so unless you have a similar problem at hand or if you are proficient with FORTRAN or C programming and numerical analysis (most of them provide source codes with the software), these codes may prove to be of little usefulness. Many commercial codes are general-purpose CFD codes with add-ons for specific engineering problems; some of the commonest commercial CFD codes that have been widely used in membrane community are listed in Table 18.1. Finally, commercial CFD codes provide excellent postprocessing capabilities with top-notch graphical display and GUI and multiple-platform support. Commercial CFD codes, of course, have their share of TABLE 18.1 List of Commercial General-Purpose CFD Software Packages Used in Membrane Research CFD Code
Company Contact Information
FLUENT
Fluent, Inc., www.fluent.com
STAR-CD
CD-ADAPCO, www.cd-adapco.com Concentration Heat and Momentum Ltd., www.cham.co.uk AEA Technology, www. waterloo.ansys.com CFD Research Corporation, www.cfdrc.com COMSOl, www.comsol.com
PHOENICS
CFX CFD-ACEþ
FEMLAB
Applications in Membrane Separations
Numerical Method FLUENT (Finite Volume Method), POLYFLOW (Finite Element Method), FIDAP (Finite Element Method) Finite Volume Method
FLUENT: [28,31,59,77,88,91,92,94] FIDAP: [58,50]
Finite Volume Method
[83]
Finite Volume Method
[49,51,60,73–76,84–87,90,95,96]
Finite Volume Method
[97]
Finite Element Method
[6]
[19]
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FIGURE 18.2 Discretization by quadrilateral and triangular elements. (From Peng, M., Ph.D. dissertation, The State University of New Jersey, Rutgers, New Brunswick, 2004.)
shortcomings in addition to high cost. The very nature of general-purpose commercial CFD codes virtually guarantees that there will be occasions when a specifically designed CFD code outperforms a general-purpose commercial code in terms of efficiency and accuracy. It should also be borne in mind that the learning curve for a commercial CFD code is rather steep. Most commercial CFD codes contain three main elements: preprocessor, solver, and postprocessor. Preprocessing is the first stage in any CFD model to create a geometry that represents the object being modeled. A grid (or mesh) of nonoverlapping cells (or controlled volumes or elements) is generated with a meshing program similar to a computeraided design (CAD) program within the geometrical domain of the object. Figure 18.2 shows two 2D mesh schemes for a membrane channel [26] and Figure 18.3 illustrates a 3D meshing of a cylindrical membrane module [27]. Some commercial CFD software packages can automatically optimize the mesh to concentrate analysis on points of interest. Once the mesh is complete, the physical and chemical phenomena that need to be modeled are specified and the definition of fluid properties as well as the boundary conditions of the cells that coincide with or touch the domain boundary are set. A solver in a CFD code is a numerical algorithm that employs one of the four common discretization methods that approximate partial differential equations to the corresponding algebraic equations: the
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Reject
Permeate
Feed in
Grid points
Reject
z=0
z = L + Ix
y z
x
Permeate Feed Central feeder Bulk stream
z=L
Permeate stream
FIGURE 18.3 A 3D finite difference meshing of a hollow fiber membrane module. (From Chatterjee, A., Ahluwalia, A., Senthilmurugan, S., and Gupta, S.K., J. Membr. Sci., 236, 1, 2004.)
finite volume, the finite difference, the spectral methods, and the finite element. The finite volume method is the commonest method used by commercial CFD code developers. The solutions to the algebraic equations at cells when an acceptable convergence is achieved are the results of a numerical simulation of a CFD code. When the model has been solved, the results can be analyzed both numerically and graphically. A crucial aspect of a successful implementation of a solver for the underlying fluid-related problem is the understanding of three mathematical concepts in the numerical analysis: convergence, consistency, and stability [22]. Convergence is the property of a numerical algorithm to produce a solution of the algebraic equation that approaches the exact solution as the size of the cell is reduced to zero. Consistency requires that the numerical algorithm produces the system of algebraic equations that can be proved to be identical to the original governing equations. Stability is the measure of how well a numerical scheme can damp the errors generated as a result of discretization as the calculation proceeds through the mesh. It is difficult to satisfy convergence, consistency, and stability requirements simultaneously for the numerical schemes in CFD simulations. The delicate balancing act of solution accuracy (convergence and consistency) and stability in a CFD computation is challenging and attributes to the steep learning curve for commercial CFD operators. The computed data after passing the tests of solution accuracy and stability will be channeled to a postprocessor. A postprocessor consists of the visualization tools capable of displaying the solution data in a variety of ways ranging from simple 2D graphs to 3D representations of particle tracks, vectors, and gradients. Figure 18.4 is an example of a 2D presentation of CFD
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2.68e-01 2.51e-01 2.34e-01 2.18e-01 2.01e-01 1.84e-01 1.67e-01 1.51e-01 1.34e-01 1.17e-01 1.00e-01 8.37e-02 6.70e-02 5.02e-02 3.35e-02 1.67e-02
2.88e-04 2.70e-04 2.52e-04 2.34e-04 2.16e-04 1.98e-04 1.80e-04 1.62e-04 1.44e-04 1.26e-04 1.08e-04 9.00e-05 7.20e-05 5.40e-05 3.60e-05 1.80e-05 0.00e+00
FIGURE 18.4 (See color insert following page 462.) Velocity and concentration profile of membrane flow channel with a baffle. (From Liu, S.X., Peng, M., and Vane, L.M., J. Membr. Sci., 265, 124, 2005.)
simulations of a slit (narrow or flat sheet) type of pervaporation membrane channel with a baffle using commercial FLUENT CFD code [28].
18.3 APPLICATIONS OF CFD IN MEMBRANE SEPARATIONS Membrane processes in the food industry are primarily used to concentrate or fractionate a liquid to generate two liquids or one liquid and one solid that differ in their compositions. The concentration or fractionation is achieved by diffusion of some components of the liquid feed across thin membranes that sometimes produce chemical and physical separations at lower costs. The advantages of membrane technology are as follows: . .
.
. .
Most systems are simple, modular in nature, and can be retrofit into existing processes. Membrane processes are nondestructive for thermally labile foods and flavors, and are able to recover valuable products from waste streams and by-products. Most membrane processes do not involve a phase change and are therefore energy efficient, and for those membrane processes that do involve phase changes, the energy requirement is still far less than that of a typical conventional separation technology. Membrane systems can be operated either continuously or batchwise. Membranes can be used to improve food product quality or achieve separations that were previously impossible or uneconomical.
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Potential disadvantages are as follows: .
.
.
Concentration polarization and fouling result in various degree of performance reduction. Most polymeric materials cannot maintain mechanical stability under conditions of high temperature, high pH, chlorine, and organic solvents. In some cases, sufficient separations cannot always be achievable.
It should be noted that membrane separation is not an ideal new technology, but just another type of unit operation, whose attractiveness must be weighed against other separation technologies. Thus it is imperative to have a reliable physical model that permits sufficiently accurate estimation of the technical and economical feasibility. Such a model also provides the basis for process optimization and development of new membrane materials and modules when evaluating the advantages and disadvantages of membrane applications in a particular food-processing operation. Membrane-based technologies are a category of a promising separation technology, and because of its multidisciplinary characteristics it can be used to perform a large number of separations in food processing. The membrane processes that are commonly found in food processing plants or research laboratories include microfiltration (MF), reverse osmosis (RO), ultrafiltration (UF), nanofiltration (NF), electrodialysis (ED), membrane reactor (MR), membrane distillation (MD), membrane emulsification (ME), and pervaporation (PV). Membrane processes are based upon different separation principles or mechanisms, and their applications in food processing range from concentration of food fluids to aromatic flavor recovery. Despite these differences, all membrane processes have one thing in common—they all have a membrane that acts as a permselective barrier segregating permeate from feed. The membrane is at the center of every membrane process. This is because the membrane not only functions as a gatekeeper to the retained species and at the same time allows one or more components to transport across it in a liquid feed stream, but also provides a large contacting area in which mass transfer can take place. However, membrane separation can only be achieved when a driving force is applied to the underlying membrane process. In assessing membrane systems two experimental parameters that determine the overall performance of membrane processes should be the main focus of the designers’ attention. The first one is selectivity, the other permeation flux. The selectivity of a membrane toward a mixture, which characterizes the extent of separation, is customarily expressed by one of the two quantities: the retention, R, and the separation factor, a. The retention, R, is more suitable for the membrane separations of a dilute binary system and given by R¼
Cf Cp Cf
(18:1)
where Cf is the solute concentration in the feed stream and Cp is the solute in the permeate. The value of R varies between 100% (complete rejection or retention) and 0% (complete permeation). For most mixtures, however, selectivity factor is more adequate: aij ¼
(Ci =Cj ) p (Ci =Cj ) f
(18:2)
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where Ci and Cj are the concentrations of components i and j in the permeate and in the feed. The value of a is greater than 1 if the component i is more readily permeable than component j and if the separation occurs. The other parameter, permeation flux, takes many forms depending upon the underlying membrane processes. It is normally expressed as Ji ¼ K
dg dz
(18:3)
where K is the phenomenological coefficient and dg=dz is the driving force expressed as the gradient of g (concentration, temperature, and pressure) in the z-direction toward the membrane. The phenomenological coefficient K is strongly related to the driving force, module configuration, and operating conditions. Membrane processes can be classified according to the nature of their driving forces and pore size of the membrane. Although all membrane processes are driven by electrochemical potential gradient, one particular driving force is usually dominant in a membrane process. Three types of membrane separation processes relevant to the food industry can be considered: those that are driven by hydrostatic pressure difference, by partial vapor pressure gradient, or by electrical potential differences. A brief general description of the membrane processes used or potentially usable in various operations of food industry is provided as follows.
18.3.1 MEMBRANE SEPARATION FILTRATION
BY
HYDROSTATIC PRESSURE DIFFERENCE—MEMBRANE
Membrane filtration is represented by MF, UF, NF, and RO. Membrane performance of a pressure-driven system is usually described by the flow rates of water (solvent) and solute (permeate). The flow of water (volume flux) through a membrane without considering concentration polarization and fouling (or gel layer) is expressed by Jw ¼ Kw (DP sDP)
(18:4)
where Kw is water permeability, DP is the applied pressure, DP is the osmotic pressure difference, and s is the reflection coefficient of the membrane toward the solute, which is a measure of degree of solute rejection. The driving force is DP DP as dq=dz in Equation 18.3. Since there is no perfect membrane, we may suspect (can be verified) that some solutes, including those undesirable, also transport across the membrane though less freely than water (solvent): Js ¼ Ks (Cm Cp )
(18:5)
where Ks is the solute permeability and Cm and Cp are concentrations on the upstream side of the membrane and on the permeate side, respectively. Note that Ks has a different unit from that of Kw because the driving force in Equation 18.5 is expressed as the solute concentration difference. While Equation 18.4 and Equation 18.5 are generally considered as valid phenomenological expressions, the true meanings of Cm and Cp are not what they seem to be. This is because, in a pressure-driven membrane process, the retained solutes transported by convective transmembrane flux can accumulate at the membrane surface, leading to a high concentration of solutes near the membrane. This concentration gradient is encompassed in a region
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designated as the boundary layer (velocity has its own gradient due to the viscous effect at the water–membrane interface for a common cross-flow membrane configuration; thus a velocity boundary layer). In a steady-state situation, the concentration polarization is the result of solute build-up counterbalanced by the solute flux through the membrane plus the diffusive flux of solute at the membrane surface toward the bulk flow on the upstream side of the membrane. The magnitude of the concentration polarization is expressed by the following equation as a result of the solute mass balance: Cm Cp Js ¼ exp Cb Cp k
(18:6)
where Cb is the concentration of the solute in the bulk flow and k is the mass transfer coefficient that is the ratio of diffusivity of the solute in the solvent to the thickness of the concentration boundary layer, which can be interpreted as the mass transfer coefficient when the permeation flux approaches zero [1]. The cause of concentration polarization phenomenon is different in RO as in MF or UF. In RO, as the low molecular weight material is retained on the membrane surface, the increase in the solute concentration causes the osmotic pressure to rise, which decreases the water flux as illustrated in Equation 18.4. In UF, the high concentration of larger molecules accumulated on the membrane surface does not result in significant osmotic pressure increase. However, these retained molecules may lead to precipitation and possibly formation of a gel layer on the membrane surface. The mass transfer coefficient, k, in Equation 18.6 has to be determined experimentally since the thickness of the concentration boundary layer is usually an unknown quantity that is strongly influenced by hydrodynamics of the system. The mass transfer coefficient, k, however, can often be related to the semiempirical Sherwood number correlations with the following form of expression: kdh rudh b V c b c Sh ¼ ¼ aRe Sc ¼ a D D m
(18:7)
where Re is Reynolds number, Sc is Schmidt number, and Sh is Sherwood number, and a, b, and c are all constants. In Equation 18.7, m and V are dynamic viscosity and kinematic viscosity, respectively, while r is density, D diffusivity, and dh hydrodynamic diameter. It is clear that the mass transfer coefficient k is mainly a function of the feed flow velocity, the density, the viscosity, the diffusivity of the solute, and the membrane module type. Many Sherwood relationships for different flow regimes and membrane module shape and dimensions available in the literature [1–3,14].
18.3.2 MEMBRANE SEPARATIONS
BY
ELECTRICAL POTENTIAL DIFFERENCE—ELECTRODIALYSIS
Electrodialysis (ED) is an electrically driven membrane-separation process that is capable of separating, concentrating, and purifying selected ions from aqueous solutions (as well as some organic solvents). The process is based on the property of ion exchange membranes to selectively reject anions or cations. If membranes are more permeable to cations than to anions or vice versa, the concentration of ionic solutions increases or decreases, so that concentration or depletion of electrolyte solutions is possible. Since in ED only ionic species are transferred directly, removal of ionic species from nonionic products can be accomplished, so that purification is possible. Electrodialysis reversal (EDR) is an ED process in which the polarity of the electrodes is reversed on a prescribed time cycle, thus
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reversing the direction of ion movement in a membrane stack. The advantage of EDR is that it mitigates some of the concentration polarization and membrane fouling problems [1,2]. The largest application of ED is the production of potable water from brackish water. Electrodialysis can remove salts from food, dairy, and other products, as well as concentrate salts, acids, or bases. It also finds applications in wine and juice stabilization and in removing unwanted total dissolved solids that can build up in product streams [1]. Faraday’s law supplies the basis to model ion transport and affirms that the total current in an electrolytic cell is equal to the sum of the electricity conveyed by each ion species: DCi I ¼ f ðJi Zi Þ ¼ fQ Zi (18:8) ei where I is the current density, f is the Faraday’s constant, Q is the flow rate, DCi is the concentration difference, Ji is the molar flux, ei is the current efficiency, and Zi is the valence of ion i. Concentration polarization also severely affects the current density, and the diffusive flux (the current density) through the concentration gradient over the boundary layer for a univalent ionic solution (Z ¼ 1) is I¼
Df (Cb Cm ) dc (tm tbl )
(18:9)
where D is the diffusivity, Cm and Cb are concentrations at the membrane surface and in the bulk, respectively, dc is the thickness of the concentration boundary layer, and tm and tbl are the transport numbers of the ion in the membrane and in the solution, respectively. The transport number of the ion is defined as ti ¼
18.3.3 MEMBRANE SEPARATIONS 18.3.3.1
BY
(Ji Zi ) (Ji Zi )
(18:10)
PARTIAL VAPOR PRESSURE GRADIENT
Pervaporation
Pervaporation is the separation of liquid mixtures by partial vaporization through a dense permselective membrane. Unlike the other membrane processes, a phase change occurs when the permeate changes from liquid to vapor during its transport through the membrane. PV in fact is an enrichment technique similar to distillation; however, unlike distillation, PV is not limited by the vapor–liquid equilibrium. As a matter of fact, PV has been commercially applied to the separation of azeotropic mixtures (dehydration of alcohol). The heart of the PV is a nonporous membrane, which either exhibits a high permeation rate for water but does not permeate organics, or vice versa. A gradient in the chemical potential of the substances on the feed side and the permeate side is the driving force for the process, which can be represented by partial vapor pressures on both sides of the membrane. The driving force is kept at a maximum by applying low pressure (vacuum or sweep gas) to the permeate side of the membrane, combined with immediate condensation of permeated vapors. Pervaporation processes have found use in the chemical industry to break azeotropic water–alcohol mixtures and to perform separations that are highly energy-intensive when distillation is used.
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The performance of PV is commonly evaluated by two experimental parameters, namely, the permeation flux and the selectivity. The performance of a PV process is assessed by the flux of the permeating species and the selectivity of the species [14]: 0 L v Ji ¼ kov i r [Ci Ci ]
(18:11)
0 L v where kov i , r , Ci , Ci are the overall mass transfer rate constant, molar density of feed, bulk liquid phase concentration (mole fraction), and bulk vapor phase concentration, respectively, for component i. The most commonly used selectivity parameter is the separation factor shown in Equation 18.2. Sometimes, however, the enrichment factor, bi, is used as an indication of the separation selectivity for component i:
bi ¼
(Ci )v (Ci )L
(18:12)
As the concentration of component i is reduced, the concentration of component j will approach 1. The separation factor will therefore be close to the value of the enrichment factor, bi, for dilute solutions: aij bi
(18:13)
Pervaporative transport process follows the solution-diffusion model that is also the transport mechanism of RO and NF, which consists of the following steps: . . . . .
Diffusion through the liquid boundary layer next to the feed side of the membrane Selective partitioning of molecules of components into the membrane Selective transport (diffusion) through the membrane matrix Desorption into vapor phase on the permeate side Diffusion away from the membrane and into the vapor boundary layer on permeate side of the membrane
Often each step can be modeled with different approaches and fundamental assumptions; however, as with all mass transfer operations, the slowest step in this sequence will limit the overall rate of mass transfer and will be the center of research focus. Naturally, these steps are conveniently expressed in the form of the resistance-in-series model, which is expressed with mathematical symbols as 1 1 1 1 ¼ þ þ kov kbl km kv
(18:14)
The k’s appearing in the equation are mass transfer coefficients and their reciprocals represent the mass transfer resistance at each step. For many PV processes, the mass transfer resistance in the vapor boundary layer tends to be small enough to be ignored. This leaves only the liquid boundary layer (1=kbl) and membrane (1=km) resistances to deal with. Membrane resistance is strongly determined by polymer properties, the thickness of the membrane, and chemical structures of the components in the liquid. In situations where hydrophobic aroma compounds being removed from orange juice by PV, the mass transfer rate is often limited by diffusion of the compound in the liquid boundary layer, i.e., kov kbl. This situation arises because nowadays the membrane can be made in such a way that the membrane provides minimal mass transfer resistance to the aroma compounds, almost to the point of being absent. This situation manifests itself as concentration polarization,
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i.e., the steep discrepancy in aroma compound concentrations between the bulk and the membrane surface. When concentration polarization is severe, the function of the membrane is to minimize the solvent flux, thereby maximizing the selectivity of the intended separation. The analysis of the liquid boundary layer mass transfer resistance is very important to the process designers and operators alike. One common approach to the analysis is to find out the correlation between mass transfer coefficient and process parameters. It is recommended that the boundary layer theory would have to be adopted to provide more robust analysis that has broader application and scalability [14]. However, in reality, it is exceedingly difficult to do so. Instead the semiempirical correlations that have the form of Sherwood number correlations shown in Equation 18.7 are commonly employed. Among these correlations is the frequently cited Le´veˆque’s correlation: kbl ¼ 1:6
1=3 D 1=3 1=3 d h Re Sc dh L
(18:15)
The only new parameter in this correlation is L, the length of the membrane channel. This correlation indicates that the mass transfer coefficient is mainly dependent upon flow conditions on the feed side and the shape and dimensions of the module. Temperature has a substantial impact upon the mass transfer coefficient through the diffusivity of the solute and viscosity. Nevertheless, temperature is not a commonly manipulated parameter due to the issues of membrane stability and the vapor pressure of the volatile solute since the feed has to be kept in the liquid phase. Flow velocity (flow rate) is the parameter that can be adjusted to minimize the liquid boundary layer resistance for a fixed membrane module (configuration). 18.3.3.2
Membrane Distillation
Membrane distillation is a type of low temperature, reduced pressure distillation using porous hydrophobic (water hating) polymer materials. It is a process that separates two aqueous solutions at different temperatures and has been developed for the production of high-purity water, and for the separation of volatile solvents such as acetone and ethanol. MD can achieve higher concentration than RO. In MD, the membrane must be hydrophobic and microporous. The hydrophobic nature of the material prevents the membrane from being wetted by the liquid feed and hence liquid penetration and transport across the membrane is avoided, provided the feed side pressure does not exceed the minimum entry pressure for the pore size distribution of the membrane. The driving force of MD is temperature gradient and the two different temperatures produce two different partial vapor pressures at the solution–membrane interface, which propels consequent penetration of the vapor through the pores of the membrane. The vapor is condensed on the chilled wall by cooling water, producing a distillate. This process usually takes place at atmospheric pressure and at a temperature that may be much lower than the boiling point of the liquids (e.g., solvents). It is commonly observed that the effect of the osmotic pressure from the permeate to the feed solution will be prominent when the high solute concentrations of feed liquids are processed. A variation of MD is sometimes called ‘‘low pressure membrane distillation’’ or ‘‘osmotic distillation,’’ which uses an auxiliary device to condense the vapor coming out of the membrane. The driving force for vapor transport in this case is the pressure differential. Alternatively, the auxiliary cooling device can be replaced by using an inert sweep gas or absorbing strip liquid to remove the vapor permeate and maintain the pressure differential. The MD is very similar to a single-stage distillation and thus unable to achieve a high separation factor. The primary advantage of MD is high surface area to volume ratio available,
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thus the high permeation rates. And most food applications of MD are concentrated upon dehydration of liquid foods. The performance of an MD can be evaluated by a phenomenological equation: J ¼ F DP
(18:16)
where the flux is related to two parameters; one is pressure difference and the other proportionality factor (membrane permeability) F. DP is mainly determined by the temperature difference DT, which can be related to the Clausius–Claperyron relationship: ln P ¼
DHvap þc RT
(18:17)
where Hvap is the enthalpy of the vapor of permeating species, T is the absolute temperature, and c is a constant. MD sometimes experiences temperature polarization phenomenon due to the difference in heat transfer rate between the heat conduction in the membrane and the heat transfer in the bulk fluid. In each of the membrane processes mentioned above, the membrane is arranged in an enclosure so that the membrane may function properly with the highest ratio of membrane surface versus enclosure volume. The enclosure is called module—recognition of its selfcontaining and modular nature. For pressure-driven membrane processes, MD, and PV, there are four primary configurations (modules), each with inherent advantages and weaknesses. These four are: spiral wound, hollow fiber, plate and frame, and tubular.
18.3.4 MEMBRANE MODULES 18.3.4.1
Spiral Wound
A spiral wound module is a logical step from a flat-sheet membrane. In spiral wound modules, a flat membrane envelope or set of envelopes is rolled into a cylinder as shown in Figure 18.5a. The envelope is constructed from two sheets of membrane, sealed on three edges. The inner surface of the envelope is the permeate side of the membrane. A thin porous spacer inside the envelope keeps the two sheets separated. The open end of the envelope is sealed to a perforated tube (the permeate tube) with a proper glue so that the permeate can pass through the perforations and, for PV, it is also the place to which the vacuum or sweep gas is applied. Another spacer is laid on top of the envelope before it is rolled, creating the flow path for the feed liquid. This feed spacer generates turbulence due to the undulating flow path that disrupts the liquid boundary layer, thereby enhancing the feed side mass transfer rate. It is because the envelopes and spacers are wrapped around the permeate tube that gives the module its name, spiral wound module. The spiral wrapped envelopes and spacers are then wrapped again with tape or glass or net-like sieve before fitting into a pressure vessel. In this way, a reasonable membrane area can be housed in a convenient module, resulting in a very high surface area to volume ratio. One noticeable drawback lies in the permeate path length. A permeating component that enters the permeate envelope farthest from the permeate tube must spiral inward several feet. Depending upon the path length, permeate spacer design, gel layer, and permeate flux, significant permeate side pressure drops can be encountered. The other disadvantage of this module is that it is a poor choice for treating fluids containing particulate matter.
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Residual Feed
Permeate Residual Feed spacer Membrane Permeate spacer Membrane Feed spacer
(a)
Bundle of silicone coated hollow fibers
Feed
Residual
Permeate
Epoxy seal
(b)
Permeate collection manifold Permeate
Feed
Feed flow channel (c)
Outer housing tube
Residual
Membranes permeate zone
Porous substrate tube
Retentate
Feed
(d)
Membrane
Permeate
FIGURE 18.5 A schematic illustration of (a) a spiral wound module (courtesy of Dr. Leland Vane of USEPA), (b) a hollow fiber tube (courtesy of Dr. Leland Vane of USEPA), (c) a plate and frame module (courtesy of Dr. Leland Vane of USEPA), and (d) a tubular module.
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Hollow Fiber
In a hollow fiber configuration, small diameter polymer tubes are bundled together to form a hollow fiber module like a shell and tube heat exchanger (Figure 18.5b). These modules can be configured for liquid flow on the tube side, or lumen side (inside the hollow fibers), or vice versa. These tubes have diameters on the order of 100 mm. As a result, they have a very high surface area to module volume ratio. This makes it possible to construct compact modules with high surface areas. The drawback is that the liquid flow inside the hollow fibers is normally within the range of laminar flow regime due to its low hydraulic diameter. The consequence of prevalent laminar flows is high mass transfer resistance on the liquid feed side. However, because of laminar flow regime, the modeling of mass transfer in a hollow fiber module is relatively easy and the scale-up behavior is more predictable than that in other modules. One noticeable problem with a hollow fiber module is that a whole unit has to be replaced if failure occurs. 18.3.4.3
Plate and Frame
Plate-and-frame configuration is a migration from filtration technology, and is formed by the layering of flat sheets of membrane between spacers. The feed and permeate channels are isolated from one another using flat membranes and rigid frames (Figure 18.5c). This configuration was an early favorite, it is a natural scale-up from bench-scale laboratory membrane cells that have one feed chamber and one permeate chamber separated by a flat sheet of membrane. A single plate and frame unit can be used to test different membranes by swapping out the flat sheets of membrane. Further, it allows for the use of membrane materials that cannot be conveniently produced as hollow fibers or spiral wound elements. The disadvantages are that the ratio of membrane area to module volume is low compared to spiral wound or hollow fiber modules, dismounting is time consuming and labor intensive, and higher capital costs are associated with the frame structures. 18.3.4.4
Tubular
Polymeric tubular membranes are usually made by casting a membrane onto the inside of a preformed tube, which is referred to as the substrate tube. The tube is generally made from one or two piles of nonwoven fabric such as polyester or polypropylene. The diameters of tubes range from 5 to 25 mm (Figure 18.5d). A popular method of construction of these tubes is a helically wound tape that is welded at the edges. The advantage of the tubular membrane is its mechanical strength if the membrane is supported by porous stainless steel or plastic tubes. Tubular arrangements often provide good control of flow to the operators and are easy to clean. Additionally, it is the only membrane format for inorganic membranes, particularly ceramics. The disadvantage of this type of modules is mainly higher costs in investment and operation. The arrangement of tubular membranes in a housing vessel is similar to that of a hollow fiber element. Tubular membranes sometimes are arranged helically to enhance mass transfer by creating a second flow (Dean vortex) inside the substrate tube. The interests in CFD applications in membrane separations have grown, spurred by the growths in membrane-based processes in various industries and computing power of modern computers. The CFD applications in current membrane-based processes are mainly used in testing new membranes and module designs, refining new membrane processes (e.g., membrane emulsification), optimizing operating conditions of existing processes, and devising strategies for fouling abatement. The role of CFD in the above activities comes naturally as
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all aspects of the development of membrane technologies involve some sort of modeling as the full-scale trial-and-error experimentation becomes less financially attainable in current technology-driven and competitive industrial operations. Generic models for membrane material development and specific models for module development and process optimization or fouling reduction, if applied successfully, can shorten the development cycle and reduce the cost of experimentation and testing by minimizing the number of experiments needed to explore a wide array of variables; CFD, in many cases, brings the power of the modeling process to full fruition. The popularity of applying CFD simulations in membrane processes is due partly to the fact that newly developed membrane modules tend to have complex geometries and contain turbulent promoters and inserts in the membrane channels. This complexity of membrane channels in modern membrane modules makes simple analytical analysis of flow and mass transfer situations in membrane modules impossible without introducing a large amount of error and uncertainty. CFD, on the other hand, relies on brutal power of modern computers and advanced numerical schemes and algorithms to calculate flow velocities and mass concentrations at large number of points in the channel. The widely available computation power and development in numerical and mathematical methods today also contribute to the popularity of CFD. Additionally, CFD can perform some tests and evaluations that cannot be easily and accurately conducted with experiments at the current stage of instrument and detecting device development; examples include concentration distribution near the membrane surface and velocity gradient in the membrane channel. Although great strives have been made in the area of laboratory instrumentation, there is no technique that can be readily employed to quantitatively and reliably measure concentration polarization and fouling; CFD offers real possibilities to appraise these situations quantitatively once the CFD model in question has been verified by either analytical solutions or benchmark ordinary differential equations or partial differential equations [29,30]. Fluid transport in membrane modules or channels has significant impact on the mass transfer of membrane-based processes. Since almost all membrane processes (with the exception of MD and, to a lesser extent, pervaporation) are purely mass transfer phenomena in the fluid flow, the performance of a membrane system is therefore strongly tied to the fluid movement in the system. As such, CFD is a very useful tool for predicting the performance of the membrane system characterized by the presence of interdependent and often nonlinear transport phenomena. General-purpose commercial or free or low-cost CFD codes available are attractive CFD simulation tools; however, they are not always readily useable in solving underlying fluid flow problems intertwined with mass transfers, because majority of them are designed for fluid flow or heat transfer. It is true that the analogy between heat transfer and mass transfer does permit migrating the CFD code for a set of the governing equations of a heat transfer problem to a mass transfer-based fluid flow problem as long as the governing equations of the mass-transfer problem is mathematically similar to the equations of the heat transfer problem. Such an analogy is not always applicable in membrane processes since transmembrane permeation across the membrane is different from the heat conduction at the membrane–water interface. This difference stems mainly from the fact that the heat conduction at the interface transfers heat, which causes little or no change in fluid dynamics near the membrane (negligible natural convection), and the membrane permeation at the interface loses mass of the bulk fluid (sometimes it could be substantial in pressure-driven membrane processes), which could affect fluid pattern and velocity distribution near the membrane [31]. Some approximations can be made to certain membrane-based processes involving low flux rates; examples include PV, dialysis, and low-concentration electrodialysis.
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18.4 CFD MODELING AND SIMULATIONS 18.4.1 SOLVING FLUID FLOW
AND
MASS TRANSFER
IN A
MEMBRANE CHANNEL WITH CFD
It should be borne in mind that many combined flow and mass transfer problems in membrane systems involve complex physics and the simulation results of a CFD code are as good as the model the CFD operator designs. This puts tremendous burden on the operator of the CFD simulations on membrane separations. The operator needs to go through an unremitting mental laboring in identifying and formulating the flow and associated mass transfer (and heat transfer) problem in terms of the physical and chemical phenomena that underwrite the problem. The person has to first determine whether two or three dimensions are needed to model the problem, whether exclusion of certain temperature and solute concentration variations on density of a liquid food feed is warranted, whether a specific turbulent model is needed to solve the problem, and whether other minor effects of the flow at certain localities may be neglected. These decisions have to be made in the form of assumptions in order to reduce the complexity of the problem to a manageable level without sacrificing the fundamental characteristics of the problem. This calls for considerable modeling skill in CFD modeling and simulations in addition to solid understanding of the problem at hand. A superior understanding of the numerical algorithm for CFD calculations is also required. There are three essential issues related to numerical computations, which determine the quality and accuracy of the CFD work: convergence, consistency, and stability [22]. However, in reality these mathematical concepts are difficult to establish theoretically, so the common alternatives to these concepts in practice are long-established methods: conservativeness, boundedness, and transportiveness. In CFD codes using the finite volume method, a numerical scheme that possesses conservativeness ensures a local conservation of fluid property of F for each control volume; numerical algorithms that hold the conservativeness property also guarantee global conservation of the fluid property over the entire physical domain of a membrane flow channel. The boundedness property is analogous to stability and can be achieved by placing boundaries on the magnitude and signs of the coefficients of the algebraic equations. The transportiveness property accounts for effects due to convection and diffusion in all directions. Conservativeness, boundedness, and transportiveness are built-in for all commercial CFD codes employing the finite volume method and have been proven to be reasonably accurate in producing CFD simulations. Even with thorough knowledge of the extent of conservativeness, boundedness, and transportiveness requirements in the CFD code, an operator still needs skills to decide the grid design and how the grid design can lead to successful CFD simulations because the convergence of iterative process (in terms of the magnitude of residuals) and grid independence of the meshing or grid scheme determine the appropriateness of the meshing scheme in describing the specific domain geometry of the membrane system (usually a module). Grid independence is a process of gradually applying and refining grid-rendering to a geometrical domain starting with coarse meshing until certain key results of interest do not change [26]. The CFD simulations result after grid independence testing are considered robust computations. Since all commercial CFD codes follow certain algorithms, some innate errors associated with the algorithms will show up in the CFD simulation results at some points or some time. The key to this issue is to have a thorough understanding of the algorithms and to be mindful of what it may cause. However, the only way of knowing whether a particular CFD study is ‘‘good enough’’ is through well-designed experiments and highly accurate analytical solutions [29,30].
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18.4.2 PREDICTING FLOW BEHAVIORS
IN THE
451
MEMBRANE CHANNEL
The fundamental fluid transport equations that govern the flow in a membrane channel are derived from the law of momentum conservation, the law of mass conservation, and the law of energy conservation. For laminar flows with a local Reynolds number less than 2100, the governing equations can be expressed mathematically in terms of instantaneous variables in the form of the Navier–Stokes equations: Equation of continuity: (r v) ¼ 0
(18:18)
r[v rv] ¼ rp þ mr2 v
(18:19)
Equation of motion:
Equation of continuity for solute 1: rv rv1 ¼ (r j1 )
(18:20)
where v is velocity vector, P is pressure, r is density, j is flux vector, m is viscosity, and v is concentration. These equations can be solved numerically with appropriate initial and boundary conditions that characterize the system under the operating conditions and material properties. For turbulent flows, the Navier–Stokes equations still apply; however, the variables in the equations are not instantaneous entities, but rather time-averaged values reflecting the chaotic nature of turbulence. The simulations of turbulent flows in membrane systems are different from the laminar flows because of the existence of eddies and the wide range of length scales that are usually 103 times smaller than that of a typical flow field in the membrane module geometry thus making meshing of these length scales in the turbulent flow impossible with current computer capabilities. There are several ‘‘shortcut’’ turbulent models for CFD computations that have found some successes in various flow arrangements and characteristics: mixing length, Balwin–Lomax, Apallart– Almaras, k–«, RNG k–«, k–v, Reynolds stress, large eddy, and algebraic stress models. In turbulent flow situations, the capabilities of CFD models in quantitatively predicting flow behaviors are more limited. The several common turbulent models used in the past CFD computations in the other applications have registered conflicting pros and cons. The venerable two-equation k–« model (or RNG k–«) has proven to offer an interesting compromise between computation resources and usefulness of simulation data in membrane systems. It is believed that any attempt of using other turbulent models for simulating turbulence in membrane modules accurately without resorting to adjustable parameters (which has to be obtained from experimental data) now would entail nothing so much as floccinaucinihilipilification of time. Multiphase flows present another formidable challenge for CFD simulations in membrane systems; for example, the use of air bubbles to enhance mass transfer in the membrane processes will complicate the quantitative predictions of multiphase flows using CFD [32,33]. For dilute multiphase flows, it may be possible to develop appropriate closure models for Eulerian–Eulerian approaches [23]. In response to development of new types of durable MF membranes with narrow pore size distribution such as silicon or silicon nitrile microsieves [34] and metal microfilters [35], a lattice-Boltzmann CFD model has been developed to optimize the pore design of micromachined membranes [36].
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CFD Simulations of Membrane Systems under Laminar Conditions
The majority of CFD work in the membrane area involves laminar flow, because many membrane processes work under the laminar flow conditions [37]. For single-phase or pseudo-single-phase Newtonian flows, advanced CFD models can usually predict quantitatively the laminar flow and mixing of the fluids in the complex industrial process equipment such as membrane modules. Composition-dependent material properties can usually be accounted for in the models; the end effects of membrane modules and of spacers or inserts in the membrane flow channels on the velocity and concentration distributions as well as scale-up issues can be addressed adequately by CFD simulations. The recent development in addressing the role of fluid dynamics in pressure-driven membrane filtration under laminar flow condition has been reviewed by Belford [38]. These laminar models are based on laminar flow in a porous pipe or rectangular slit (narrow channel) that has either variable wall suction or variable transmembrane (wall) mass flux. These models have been verified with the analytical solution to a very similar problem described in Berman’s classic paper [39]. Many authors have successfully used these models to optimize various membrane-based processes and systems [40–43]. Note that the papers cited here include some new improvements in CFD simulations of laminar flows in membrane systems; the commonest approach in these new studies was the use of both Navier–Stokes and Darcy’s equations (Darcy’s equation is J ¼ K dh=dd, where K is hydraulic conductivity; h is the hydraulic head; d is the thickness of the membrane wall). Darcy’s equation is mathematically similar to Fourier’s law of thermal conduction and often used to set up the porous wall (membrane) conditions whereas the hydrodynamic landscape in the membrane channel is captured with the Navier–Stokes equations and equations of continuity. However, the implementations of the two-pronged approach to the coupled hydrodynamics-mass transfer are often the sources of much complication, since pressure drops in membrane processes are substantial in terms of the fraction of the total inlet pressure and affect the transmembrane mass permeation flux. In contrast, one of the highly simplified cases of describing flows and mass transfer in membrane systems would be the use of the Darcy law for depicting transmembrane mass transfer, implying that flow conditions under consideration are the same as those at the inlet. Another highly simplified case would involve the Navier–Stokes equations with constant wall (membrane) concentration or constant wall (membrane) flux for describing the hydrodynamics in the membrane channel unaffected by the transmembrane mass transfer. Obviously, both simplistic treatments of laminar flows in membrane channels are inadequate for dealing with the real membrane systems. In modeling pressure-driven membrane filtration processes for CFD simulations, many used the average inlet and outlet pressures as the feed side transmembrane pressure in applying the Darcy equation; however, Rahimi and others [44] employed the predicted pressure distribution in the Darcy equation to determine the local permeation flux and the total flux across the membrane area was calculated by summing the local permeation fluxes over the entire membrane area. They claimed that their approach was superior to the method of averaging of inlet–outlet pressures without further elaboration. There were many CFD studies on flows in thin rectangular membrane channels that were used for membrane filtration or PV [37,42,45–50]. And far fewer studies of CFD simulations of tubular modules (including hollow fiber type) were conducted [33,41,42,51]. This is possibly due to the fact that the spiral wound modules (depending on the area of interest, they could be straight slits or curvilinear slits formed by two membrane walls) are popular in various industries due to their efficiency and scalability, and rectangularshaped laboratory modules are widely used in the bench-scale testing of the membrane and fundamental aspects of the process. In contrast, the number of papers in the literature on
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CFD simulations of tubular membrane modules is far smaller; this is in part due to the fact that the spiral wound modules often contain spacers, and therefore the subject of the intensive CFD studies is on the roles of these inserts in changes in hydrodynamics in the membrane channels. It should be pointed out that inserts or turbulence promoters in tubular membrane modules, though a novelty, do exist [52]. Other notable examples of CFD simulations on tubular membrane modules can be found in Refs. [32,33,41,51,53]. The paper authored by Cui’s group [32] had to do with gas-sparged membrane filtration processes, where tubular membrane module is the norm. Other more exotic membrane modules such as Dean vortex [54–56], vibrating [57], and rotating disk [58] are the variations of basic flat-sheet and tubular modules with Dean vortex modules being coiled tubular membranes causing secondary flow (Dean vortices) and vibrating or rotating disk being mechanized flat-sheet modules causing shears at the surfaces in order to reduce concentration polarization, fouling, and possible scaling. 18.4.2.2
CFD Simulations of Membrane Systems under Turbulent Conditions
The major difference between turbulent flow and laminar flow in terms of CFD simulations is the occurrence of eddy motions that appear in a wide range of length scales. In order to use CFD simulations to describe flows in certain membrane modules that are clearly turbulent, one has to choose a model from several numerical turbulent models that may be used to solve the time-averaged Navier–Stokes equations. It is claimed that for membrane channels with spacers, the RNG k–« is better than plain k–« model due to its analytically derived differential formula for effective viscosity at low-Reynolds number regions [59,60]. Other turbulent models available in several commercial CFD packages require substantial computing time even though they may be slightly more accurate, thus unsuitable for large-scale CFD simulations. Despite challenges with CFD simulations of turbulent flows in membrane modules, the knowledge and insight of the turbulent hydrodynamics are important since some membrane modules are operated under turbulent conditions to reduce the concentration polarization and membrane fouling. Several CFD simulations of turbulent flows in membrane systems have varied degree of successes in certain cases [61–63] and none of these studies have ever been validated with experiments. The much smaller number of papers of CFD simulations of turbulent flows in membrane systems illustrates the difficulty of applying CFD techniques to predict flow behaviors and mass transfer under turbulent conditions.
18.4.3 PREDICTING CONCENTRATION POLARIZATION The complications of the boundary layer mass transfer modeling and estimations stem from the fact that quantitative information regarding velocity profile and concentration distribution in the layer is notably incomplete. Several experimental techniques such as light deflection, magnetic resonance imaging, direct pressure measurements, laser triangulometry, and optical laser sensors were tried in membrane filtration setups and the information gained from these tests was not quite quantitative. One group [51] has, over the years, developed an ultrasound computer tomography technique (UCT) for a tubular PV setup; however, their technique was limited in temperature profile and density change of the mixture fluid, thus providing insufficient information regarding concentration polarization in a typical membrane module. Conventionally, semiempirical correlations in the form of the common Sherwood correlations are used for calculating mass transfer coefficient in concentration boundary layer in several common circumstances. Although this approach allows a general and rough judgment of mass transfer efficiency under different membrane modules,
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its capability is limited in handling complex module and filtration cake or fouling, and providing insight into the mass transfer process. Thus there is a need for developing boundary layer mass transfer models that are beyond curve fitting of experimental data to fit adjustable parameters in the Sherwood correlations. Investigations of flow dynamics in relation to concentration polarization in membrane channels with CFD have been emerging since the late 1990s. There are several impetuses that drive this phenomenon: cheaper and better computer hardware and software, the dissatisfaction with the results from mass transfer modeling using semiempirical correlations, the difficult implementation of experiments in the narrow membrane channel, and the inability of the conventional modeling approaches to account for spacers and other flow mixing promoters residing in the membrane channel in modeling and simulation. The first comprehensive attempt to model concentration polarization in membrane filtration was carried out by Blatt and others [64]. The model is subsequently called the ‘‘gel-polarization model.’’ The first of the underlying assumptions of the gel-polarization model is the presence of a gel layer on the surface; and once it is formed, the applied pressure will not affect the permeation flux rate. The second assumption claims negligible osmotic pressure once the macromolecules accumulate on the surface of the membrane forming the gel. The second assumption is not always valid as later studies made it known. The gelpolarization model, however, is still widely used in many fields using membrane filtration, particularly in UF and MF. Several individual groups have used CFD techniques to understand the gel layer or cake formation [45,65]. The importance of osmotic pressure in modeling concentration polarization phenomena in NF and RO can be appreciated in the popularity of the osmotic pressure models; one of the models is widely adopted in modeling of these membrane processes: J ¼ Lp(DP sDp) R¼
s(1 F ) (1 sF )
where DP is the transmembrane pressure, Lp is membrane permeability, Dp is osmotic pressure, R is true rejection, F ¼ exp(J a), a ¼ (1 s)=Pm; Pm is the overall permeability coefficient, and s is the reflection coefficient [66]. This is a combined Spiegler–Kedem and film theory model. Many studies of NF and RO module simulations using CFD focused on the split-type of membrane modules with spiral wound and plate-and-frame module as its most prominent representatives. This fascination with slit-type membrane modules reflects the wide acceptance of spiral wound modules in various industries. This membrane configuration tends to generate laminar flow and a number of CFD simulations have been conducted to understand the mass transfer processes in the modules and their optimization [37,47,49,50,60,67–76]. For PV, the concentration polarization is often formed as a result of the different mass transfer rates between the boundary layer and the membrane itself [77]. Unlike pressure-driven membrane filtration processes, the concentration boundary layer in a PV module is only a fraction of the velocity boundary layer [78]. The application of CFD codes in PV membrane modules, which are similar to those for membrane filtration, is not much different from that in membrane filtration, with the exception of the region near the membrane surface called boundary layer region. Peng and others [77] developed a CFD model for a laboratory-scale slit type of membrane unit assuming negligible membrane resistance that led to a mass transfer coefficient in the concentration boundary layer under an idealized situation, i.e., total mass transfer resistance came from the boundary layer.
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By this assumption, target solutes would be able to diffuse fast enough from the membrane surface into downside vapor side; therefore mass transfer at the membrane surface could be taken as a pseudochemical reaction happening on the membrane surface. This can be expressed as a first order reaction, which is similar to the expression of Henry’s law: Solute in solution ! solute in membrane
(18:21)
Henry’s law constant for the target solute partitioning between water and the membrane phases was said to describe the equilibrium state, i.e., the concentration in the membrane varied linearly with solute concentration in water where the solution was dilute. In essence, they claimed, the introduction of reaction constant k would help define the overall effects of all boundary conditions starting from the membrane to the permeate (vapor) side. d[solute in water] d[solute in membrane] ¼ dt dt
(18:22)
d[solute in water] ¼ kS[solute in water] dt
(18:23)
The right-hand-side term in Equation 18.22 is the transmembrane flow rate of the permeate. The time derivative in the above equations indicates that for a batch PV operation the whole process will be an unsteady process, i.e., permeate of the organic compound through the membrane will cause a concentration decrease in the feed tank. When the PV operation is carried out in continuous steady state with constant feed concentration, a balance will be established between diffusion of solute compounds with the amount expressed by the chemical reaction mechanism. This approach took analogy to the kinetics of heterogeneous processes in the literature [79] where a mass delivery coefficient was used to describe the kinetics of a dissolving process. The reaction rate constant observes the Arrhenius relationship:
Ea k ¼ A exp RT
(18:24)
where Ea is the reaction activation energy (kJ=kmol), R is the universal gas constant, and T is the absolute temperature (K). When this reaction rate constant decreases, it will correspond to a certain increase in the membrane resistance. The concentration profile near the membrane surface and permeation flux corresponding to different membrane resistance could therefore be predicted. As PV separation is mostly used in separating solutes from dilute solutions, water flux is usually relatively constant and not subject to concentration polarization. Its flux can either be deduced with a similar Arrhenius equation or by using available experiment data. Peng and others [77] used this approach to model the boundary layer polarization and found that the mass transfer coefficient values from CFD simulations were consistently larger than those obtained by using Leveque’s equation under the same operating conditions. Marriott and others [41] described the detailed modeling of parallel-flow hollow fiber PV modules for removing organics with focus on concentration profiles inside the hollow fibers. They noticed a significant radial concentration polarization in addition to axial concentration variations. Their 2D simulation results were compared to the experimental
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data of Tsuyumoto and others [80] and found to be very close to each other [42]. Although it is acceptable in many cases to ignore the effect of heat transfer in membrane PV, it is widely acknowledged that heat transfer is present in all membrane PV processes and may exert some influence on permeation flux rate. A research group in the Netherlands has been developing experimental techniques (e.g., UCT) as well as CFD modeling to predict the temperature and velocity distributions in a tubular laboratory membrane module [51,81].
18.4.4 PREDICTING EFFECTS
OF
SPACERS ON FLOW BEHAVIORS
Over the years, different techniques for enhancing mass transfer in membrane modules have been investigated; they are either passive or active. The active techniques often involve external power to improve targeted mixing and reduction in concentration polarization near the membrane surface. Examples include stirrers, rotating disk-shaped module [58], rotating module [82], vibrating module [57], and air bubbling [33]. Although laboratory-scale or even pilot-scale studies showed promises for the active techniques, the difficulties associated with large-scale manufacturing, maintenance, and high extra energy consumption hamper the techniques from being widely accepted in many industries. The passive implementation of mass transfer enhancement relying on membrane module configurations (e.g., Dean vortex), inserts, and spacers in the membrane channels, on the other hand, has enjoyed wide acceptance. In fact, all commercial spiral wound type membrane modules contain passive mass transfer enhancer such as turbulent promoters or spacers. Majority of turbulent-promoting spacers are found in spiral wound modules or other flatsheet or slit types of membrane configurations. As noted previously, screw-type inserts have been tested in the tubular membrane modules; their future in commercialization is still uncertain. Spacers in many ways are double-edged swords: the presence of these spacers promotes turbulence and eddy mixing and reduces concentration polarization near the membrane wall, but the presence of these spacers also leads to increased pressure drop and the formation of localized ‘‘dead zones,’’ where momentum and mass transfers are minimal. This apparent contradiction has attracted many CFD studies in order to understand and optimize the impact of spacers on membrane process performance and efficiency. The focus of CFD studies on spacer effects in membrane channels is primarily on narrow channels or slits— the type of membrane configuration to which spiral wound membrane modules belong, as spiral wound modules are the commonest commercial units available. The recent surge of CFD simulations of spacer-filled narrow membrane channels corresponds to the new development of computing techniques and computer hardware and improvement in commercial CFD codes, enabling researchers to investigate the flow pattern and experiment with the new designs of spacers as well as their layouts in the spacer-filled membrane channels. Since nettype spacers are the commonest for commercial spiral wound membrane modules, it is no surprise that early CFD studies on the role of spacers in hydrodynamics and mass transfer in the narrow membrane channels concentrated on this type of spacers. Karode and Kumar [83] employed CFD codes to investigate the pressure drop and shear rate in a laboratory test cell filled with 10 net-type commercial spacers. The test cell schematic layout and the typical visual presentation of flow velocity profile in the membrane channel are shown in Figure 18.6. They were able to validate total drag coefficient dependence of Reynolds from the CFD simulations with the experimental data in the literature and arrived at a tentative conclusion on effectiveness of turbulence-promoting and enhancing shear rate of these spacers in the test cell. Since the CFD simulations of Karode and Kumar [83] were strictly in the laminar flow, they could not determine whether the fluid flow across the spacers was actually ‘‘steady.’’ Similarly, Cao and others [59] used a commercial CFD package, FLUENT, to
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Outlet
Channel axis (overall bulk fluid flow direction) y z x=0 y=0 (a) z = 0
x
FIGURE 18.6 (a) Schematic of rectangular cell and grid in the X–Y plane, and (b) velocity vectors. (From Karode, S.K. and Kumar, A., J. Membr. Sci., 193, 69, 2001.)
study the net-type spacers in narrow channels focusing on the arrangements of individual transverse (the flow direction and the main axle of the cylindrical filament are perpendicular to each other) filaments (three in total); each filament was considered as a cylinder. Unlike Karode and Kumar [83], they did not restrict themselves to the commercial net-type spacers, which enabled them to ‘‘play around’’ with the cylindrical filaments in terms of distance between the filaments, distance between the membrane wall (top or bottom) and the filament, and various filament arrangements in relation to the membrane walls (they later named the arrangements ‘‘cavity,’’ ‘‘zigzag,’’ and ‘‘submerged’’). More importantly, Cao and others [59] deployed the RNG k–« scheme in FLUENT to probe the eddy activities in the vicinity of the spacers and concluded the ‘‘suspended’’ transverse filaments (submerged spacer) of the nettype spacers would be the best arrangement for enhanced mass transfer because they produced the most active eddy activities (Figure 18.7). Schwinge and others [84,85] further
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Velocity (m/s) 1.490 1.320 1.160 1.000 0.840 0.680 0.520 0.360 0.200 0.036 –0.130 (a) Velocity (m/s) 2.910 2.580 2.260 1.930 1.610 1.290 0.962 0.639 0.315 –0.009 (b)
–0.333
FIGURE 18.7 Velocity distributions in the channel—two opposing cylinders. (From Cao, Z., Wiley, D.E., and Fane, A.G., J. Membr. Sci., 185, 157, 2001.)
expanded their group’s CFD [59] by investigating flow distributions around the spacers and pressure drop and the effects of Reynolds number, mesh length, and filament diameter on mass transfer for three filament arrangements (cavity, zigzag, and submerged spacer) as illustrated in Figure 18.8. Other researchers turned their attention to commercial spacers in order to figure out a way of improving the design of spacers for spiral wound membrane modules. Li and others [86] investigated the commercial net-type spacers based on their fundamental arrangements: woven and nonwoven (Figure 18.9); the simulation results were validated with a well-crafted experiment [87]. Koutsou and others [88] focused on the transverse cylindrical filaments in 2D geometry and applied periodic boundary conditions to save computing time. Their work was intended to get a better understanding of momentum and mass transfers in the narrow flow channels. Liu and others [28] investigated the effects of rectangular filament spacer on PV mass transfer and hydrodynamics in the slit-type membrane module as shown in Figure 18.10. They found that CFD numerical
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Inlet length l in > 10 d f
Cavity type lm df lm
hch
Submerged type
df lm
Exit length l ex > 2 l in
hch
Zigzag type df
hch
FIGURE 18.8 Channel geometry and spacer types used for CFD simulation. (From Schwinge, J., Wiley, D.E., and Fletcher, D.F., Ind. Eng. Chem. Res., 41, 2977, 2002.)
simulation results indicated 14%, 24%, and 34% improvements of the average mass transfer coefficient within the concentration boundary layer with the increase in the height of the filament for 10%, 30%, and 50% of the slit height of the module, reaching 1.25 105, 1.35 105, and 1.44 105 m=s, respectively, as compared with 1.08 105 m=s where there was no filament. The impacts of several arrangements of these rectangular filaments on pressure drop and mass transfer can be found in Figure 18.11. The Geraldes group from Portugal also studied extensively on the effects of various spacers on the hydrodynamics and mass transfer in the narrow membrane channels. Their spacers were described as ‘‘ladder type’’ (rectangular-shaped filaments transverse to the flow), which were placed in the membrane channel [70]. By altering the distance between neighboring transverse filaments (as changing ‘=h ratio where ‘ is the distance between the filaments and h is the height of the filament), they were able to examine the effects of the different arrangements of the ‘‘ladder’’ on flow patterns and they found there was a good agreement between the numerical and experimental values of the friction factor. Some of the above mentioned studies assumed either impermeable walls or constant wall concentrations or fixed permeate velocities in their respective CFD simulations; this may not be realistic in spiral wound NF and RO modules. Song and Ma [89] used a fully coupled streamline upwind Petrov=Galerkin finite element model to better link hydrodynamics to wall concentrations in the presence of net-type spacers in a slit membrane channel.
Nonwoven
Woven
FIGURE 18.9 The basic patterns of commercial net spacers. (From Li, F., Meindersma, W., de Haan, A.B., and Reith, T., J. Membr. Sci., 208, 289, 2002.)
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FIGURE 18.10 (See color insert following page 462.) Concentration contour and flux distribution for baffle distance of 5.7 mm. (From Liu, S.X., Peng, M., and Vane, L.M., J. Membr. Sci., 265, 124, 2005.)
1.8E−05 1.59E−05
20.0 1.47E−05
1.60E−05 1.6E−05
1.47E−05
1.4E−05 1.2E−05 1.0E−05 10.0
8.0E−06
k (m s−1)
Flux (g h−1m−2)
15.0
1.09E−05
6.0E−06 5.0
4.0E−06 2.0E−06 0.0E+00
0.0 No baffle
1 baffle
2 baffles-a
2 baffles-b
2 baffles-c
Baffle type
FIGURE 18.11 Modeling result: overall flux and mass transfer coefficient for different baffle types. Note: the distance between two baffles in ‘‘2 baffles-a’’ is 5.7 mm; the distance between two baffles in ‘‘2 baffles-b’’ 8.0 mm; the distance between two baffles in ‘‘2 baffles-c’’ 15.4 mm. (From Liu, S.X., Peng, M., and Vane, L.M., J. Membr. Sci., 265, 124, 2005.)
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As these CFD studies on the impact of spacers on hydrodynamics and mass transfer, which can subsequently affect concentration polarization and fouling in membrane processes, become increasingly detailed and more in-depth, it is no coincidence that some researchers employed CFD techniques to virtually test and optimize new types of spacers: different shapes and other geometrical features of spacers and forming angles of transverse and longitudinal filaments in ‘‘net-type’’ or ‘‘ladder-type’’ spacers [86,90–92]. These latest publications further show that CFD is without doubt a very important tool for understanding hydrodynamics and mass transfer in the membrane processes and modules. Opportunities for developing new spacers as well as modules are numerous, and CFD will be the key enabling tool to conduct virtual experimentation on these new designs before any prototype is put out for testing.
18.4.5 PREDICTING FLOW BEHAVIORS AND MASS TRANSFER OF NOVEL MEMBRANE AND MODULE Membrane emulsification has been demonstrated in the laboratory for years [5,93] and recently, CFD simulations were used to aid membrane design [95,97]. Membrane emulsification is a unique membrane-based technology in which separation is not the goal. The membrane functions not as perm-selective barrier but rather as oil or water droplet former. The advantages of ME over traditional emulsification are low energy, because only low shear needed at the surface; control of size of droplet and size distribution; and scalability [95]. The focus of CFD studies on ME is on the droplet formation under the hydrodynamic shear near the pores. For example, Abrahamse and others [95] used a commercial CFD package, CFX 4.2, to calculate the shape of the oil droplet formed when oil is pushed through a cylindrical pore of the membrane and the deformity of the droplet. The simulation was two dimensional and not validated by any experiment. Nakajima group in Japan [97] have been developing the emulsification technology using straight-through microchannel for years. Their recent fray into the CFD study on simulation and analysis of emulsion droplet formation from the straight-through microchannel illustrated the important role of CFD simulations in equipment design and process improvement. Their goal was to gain insight into the droplet formation phenomena from the microchannel and to pave the road for future improvements in microchannel design. CFD study of rotating disk membrane modules is another common research topic among membrane scientists and engineers. Because of the movement of the membrane in rotating disk membrane modules and the centrifugal force generated, CFD studies on flow behaviors and mass transfer in rotating disk membrane modules are quite unique. Wiesner group at Rice University investigated the performance of a rotating membrane filter with a commercial CFD package [58,98]. They examined the effects of shears (in the form of rotating speed of the disk), permeabilities of membrane and its support, as well as the gap between the disk and the wall of the module on performance of the membrane module, and due to local turbulence near the disk, the turbulent model was used. They found that in some localities of the rotating membrane disk, the transmembrane pressure gradient was actually reversed, resulting in negative permeation flux in these localities due to the centrifugal force acting upon the fluid permeating through the membrane. This was an important insight into this type of membrane module; future designs of the rotating membrane disk modules need to take this abnormal behavior into account. The benefits of rotating disk membrane modules are many, and not the least is its ability to reduce concentration polarization and membrane fouling due to centrifugal force and shear force on the disk surface without introducing high pressure. This feature of a rotating disk filter is particularly favorable for bioseparations using membrane technologies. Castilho and Anspach [99] employed CFD techniques to aid in designing a rotating disk filter to separate mammalian cells. They developed a dynamic rotating disk filter
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with the help of CFD, statistical experiment design and analysis, and geometry optimization; they claimed the filter did not damage the cells and fouled the membrane. However, the future of rotating disk membranes for bioseparations and food processing is still being explored and CFD is a vital tool to help its development and perfection.
18.5 CONCLUSIONS The recent surge in the number of publications of CFD applications in membrane processes and modules illustrates the important role of CFD simulations in membrane process and module development. This phenomenon is also a result of greater accessibility of everincreasing computing power by the membrane researchers and food engineers. New and innovative numerical and mathematical models also help along the way. This chapter showed the importance of coupled hydrodynamics and mass transfer in CFD simulations of membrane modules. In the majority of the cases, CFD studies were designed to better understand hydrodynamics in membrane channels and mass transfer across the membranes in order to minimize the concentration polarization and to a lesser extent, membrane fouling, thus enhancing membrane system performance. The ability of CFD to predict concentration polarization of a membrane flow channel has important implications and significance. Membrane channels are commonly very narrow and are difficult to set up in experimental measurements. As a result, the prediction of membrane performance with ‘‘black-box’’ type of overall mass balance measurements or semiempirical correlations tends to be indirect and unreliable despite the best efforts to setting up creative experiments. The CFD could change this situation and would help establish strong footholds for membrane separations in the food industry. The challenge of the current application research of CFD in the food processing and preservation needs to focus on development of new modules with the help of CFD simulations for membrane separations and other membrane-based processes (e.g., membrane emulsification) and the reliable experimental verification of CFD simulation data (therefore ensuring confidence in the predictions). As with all modeling techniques, a model is as good as the data it uses; the reliability and availability of the data for CFD simulation in foodrelated membrane processes are unsatisfactory at best. The property data of certain food materials needed for CFD simulations needed to be compiled and provided for general uses. The most challenging issue in regard to the data for CFD models is the availability of useful membrane material data. Since the membrane materials are most probably developed in a business other than food-related enterprise, and the membranes are probably designed for general-purpose applications, the scarcity of the data needed for CFD models compounds the problem of lack of appropriate data for CFD application. It is predicted that commercial CFD codes will become easier to use and have enhanced self-meshing capabilities; it is also possible in the near future that customized CFD codes will be made available for membrane processes involving foods with an expansive property database. As the benefits of CFD techniques are made known to the food industry, we will see more people in membrane separation areas embrace CFD simulations in their engineering operations and process improvement.
NOMENCLATURE C Ea h j
solute concentration (mol m3 or kg m3) activation energy (J) height of the narrow channel or hydraulic head (m) flux (kg m2 s1)
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K k Lp Pm P R S T t
463
hydraulic conductivity (m s1) or phenomenological constant or permeability mass transfer coefficient (kg m2 s1) membrane permeability (mol s1 m1) overall permeability in the osmotic model pressure (N m2) universal gas constant (J mol1 K1) or true rejection in the osmotic model surface area (m2) thermodynamic absolute temperature (K) time (s)
GREEK SYMBOLS d s p n m v
thickness of the membrane wall (m) reflection coefficient in the osmotic model (mol s1 m1) osmotic pressure in membrane filtration (N m2) velocity (m s1) viscosity (kg m1 s1) solute concentration (mol m3)
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Applications of CFD in Jet Impingement Oven Dilek Kocer, Nitin Nitin, and Mukund V. Karwe
CONTENTS 19.1 19.2
Introduction ............................................................................................................. 469 Jet Impingement Ovens ............................................................................................ 471 19.2.1 Classification of Jets ................................................................................... 471 19.2.2 Flow Field and Heat Transfer in Jet Impingement Ovens.......................... 471 19.2.2.1 Flow Field in Jet Impingement Ovens ........................................ 471 19.2.2.2 Experimental Characterization of Flow Field in Jet Impingement Ovens........................................................... 473 19.2.2.3 Heat Transfer in Jet Impingement Ovens ................................... 473 19.2.2.4 Experimental Characterization of Heat Transfer in Jet Impingement Ovens........................................................... 474 19.3 Applications of CFD in Jet Impingement Ovens ..................................................... 475 19.3.1 Turbulence Models ..................................................................................... 475 19.3.2 Applications ................................................................................................ 476 19.3.2.1 Fluid Flow and Thermal Transport for a Single Jet Impingement.......................................................................... 476 19.3.2.2 Fluid Flow and Thermal Transport for a Multiple Jet Impingement.......................................................................... 480 19.4 Conclusions .............................................................................................................. 482 Nomenclature ..................................................................................................................... 482 References .......................................................................................................................... 482
19.1 INTRODUCTION Air impingement oven technology is a relatively new and promising commercial development to increase the efficiency, uniformity, and energy savings. Jet impingement ovens represent a special class of forced convection ovens, which were first designed by Smith [1]. In these ovens, high velocity (5–50 m s1) jets of hot air (1008C–2508C) impinge on a food product. A schematic diagram of a jet impingement oven is shown in Figure 19.1, with multiple jets impinging on a food product. The use of jet impingement oven by applying high velocity jets of hot air on a food product has substantially reduced the disadvantages of conventional ovens such as long processing time, energy inefficiency, and nonuniform heating. Impinging high velocity jets on the product surface removes the cool, moist stagnant air layer just above the product surface and improves the moisture removal with increased heat and mass transfer rates at the surface. Higher rate of surface moisture removal under hot air jet impingement results in a
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Nozzles Hot air jets
Conveyor belt or turn table
Nozzles
FIGURE 19.1 A schematic diagram of multiple jet impingement oven.
quick crust formation. Since the crust has lower moisture diffusivity, the product retains more moisture inside which can enhance the perceived quality of the processed food [2], including increase in shelf life as well as retention of some key health-promoting nutraceutical compounds such as Omega-3 fatty acids in products such as fish cakes [3]. Food industry has been using the jet impingement oven technology for baking of tortilla, potato chips, pizza crust, pretzels, crackers, cookies, breads, and cakes for faster processing rates or reduced cooking times [3–10]. Table 19.1 shows the comparison of product baking times and air temperatures for products baked in conventional vs. jet impingement oven. Numerous
TABLE 19.1 Comparison of Product Baking Times and Air Temperatures for Products Baked in Conventional vs. Jet Impingement Oven Conventional Oven Product Muffins Layer cake Devil’s food cake Pound cake Dinner rolls Pan bread Quiche Frozen fruit pie Croissant Puff pastry Cheese Danish Apple Danish Cherry turnovers Raisin oatmeal cookies Raisin nut oatmeal cookies
Jet Impingement Oven
Time (min)
Air Temperature (8C)
Time (min)
Air Temperature (8C)
26 26 29 75 22 20.5 48 60 18 22 16 20 28 15 16
174 159 159 134 171.5 206.5 159 184 171.5 166.5 171.5 171.5 171.5 166.5 169
12 16 18 55 12 17 23 22 12 13 7 10 14 12 12
154 149 149 124 146.5 159 129 174 154 159 146.5 149 154 159 154
Source: Adapted from Walker, C.E. and Sparman, A.B., Am. Inst. Baking Tech. Bull., XI(11), 1, 1989.
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perceived advantages of jet impingement oven technology in the food industry have created a need for investigation of detailed transport phenomena associated with multiple jet impingement oven systems. Understanding the interaction of the jet flow pattern with the product, measurement, and prediction of heat and mass transfer coefficients, understanding the effect of nonuniform heating of the product due to spatial variation of heat transfer coefficients around the product, and developing optimal design parameters for equipment design are critical to predict and evaluate the baking process, and to achieve better design of the oven [11]. Application of computational fluid dynamics (CFD) in jet impingement oven systems provides detailed understanding of the fluid flow and heat transfer, which reduces the cost and time involved in experimentation. Using CFD simulation tools in jet impingement oven systems, the effect of different oven geometries as well as objects subjected to jet impingement can be studied with less effort. In addition, CFD simulation can provide information on local velocity and temperature values where it is almost impossible to conduct such detailed experimental measurements. This chapter summarizes the studies in the field of jet impingement oven systems, which include the description of jet impingement ovens, applications of jet impingement oven systems in food applications, and discussion of experimental measurements and numerical predictions of flow and heat transfer in jet impingement ovens.
19.2 JET IMPINGEMENT OVENS 19.2.1 CLASSIFICATION
OF JETS
In jet impingement ovens heated air is directed toward a food product using nozzles. The distance between nozzles and the product surface, nozzle diameter=width, and spacing between the nozzles are important factors that have to be considered in the oven design [12]. Nozzles can be round holes in a plate, short nozzles, or long thin tubes. Depending on nozzle geometry, the jets can be classified as slot or circular jets. Jets can be further classified as submerged or nonsubmerged jets. For submerged jets, the jet fluid is the same as the surrounding medium while for nonsubmerged jets, the jet fluid is different from the surrounding medium. Nonsubmerged jets are not used in jet impingement oven technology to heat or bake food products. Submerged jets can be further divided into two categories, i.e., free jets and impinging jets. In free jets, there is no target surface for impingement. In impinging jets, a jet of liquid or gas coming from a nozzle impinges on a desired surface. Another classification is based on the flow characteristic of the jets such as turbulent or laminar jets. For example, submerged round jets become turbulent jets when the Reynolds number based on the nozzle diameter exceeds 3000.
19.2.2 FLOW FIELD 19.2.2.1
AND
HEAT TRANSFER
IN JET IMPINGEMENT
OVENS
Flow Field in Jet Impingement Ovens
The flow of an impinging jet has been classified into three regions, i.e., the free jet region, the stagnation region, and the lateral spread region (Figure 19.2) [13,14]. The free jet region is further classified into three subregions: the potential core region, the developing flow region, and the developed flow region. There is little or no vorticity in the flow in the potential core region due to the free shear between the impinging jet and the stagnant air. The rate of energy dissipation and the length of the potential core are largely dependent on the shape and configuration of the nozzle [15]. However, the nozzle edges cause mixing in the periphery of
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Nozzles Free jet region
Lateral spread region
Stagnation region
Plate
FIGURE 19.2 Regions of impinging jet flow.
the jet and significant energy dissipation from the jet occurs. This region of mixing is called the developing flow region, which eventually leads to developed flow region (Figure 19.3). The turbulence level and the width of mixing region increase with increase in jet length, i.e., the downstream distance. The characteristics of turbulence in the free jet region have been shown by various researchers [16,17] to be affected by nozzle geometry, exit velocity, length of nozzle, and the sharpness at nozzle exit. Impinging jet enters into the stagnation region within 1–1.5 nozzle diameters distance from the impinging surface [14]. In the stagnation region the axial velocity decreases rapidly, the static pressure rises. In lateral spread region, the radial velocity rapidly increases near the stagnation region due to negative pressure gradient and later drops away due to wider area available for the same mass of material to flow and the viscous drag at the wall [18,19]. In case of confined jet flow the radial flow zone eventually develops into a recirculation region [15]. Flow field in multiple impinging jets also consists of free jet, stagnation, and lateral spread regions like a single impinging jet. However, there can be possible interactions between
Nozzle
Fully developed turbulent flow region Developing flow region
Potential core region
FIGURE 19.3 Diagram illustrating the transition from laminar region to a turbulent region in a flow from round submerged single jet of 6.35 mm diameter (Reynolds number ~ 30,000). (Adapted from Landis, F. and Shapiro, A.H., An Album of Fluid Motion, The Parabolic Press, Stanford, 1982.)
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surrounding jets, which depend on nozzle-to-nozzle spacing. Interactions can also occur in the lateral spread region of two adjacent jets. In the case of lateral exit in ovens, a cross flow is observed in which jet flow can sweep against its surrounding jets in lateral spread region, while moving toward lateral exit. This interaction disrupts the stagnation region of adjacent jets and leads to reduction in the rate of heat transfer. The cross flow effect can be controlled by the location of exit ports in a multiple jet impingement system. In closed systems, interactions between the lateral jets can lead to strong up flows or ‘‘upward jet fountains,’’ which can create high level of turbulence in lateral spread region and result in secondary heat transfer maxima on the impinging surface [20,21]. 19.2.2.2
Experimental Characterization of Flow Field in Jet Impingement Ovens
Experimental investigation of flow field has been carried out by many researchers to understand the characteristic of jet impingement flow. This section summarizes the experimental methods that have been used to characterize the fluid flow in jet impingement systems. The use of smoke wire method based on the flow pattern is a qualitative approach [22,23] for flat surfaces. Similar approach has been used to study the flow pattern of a circular jet impinging on concave and convex surfaces [24], which can be useful in understanding the flow characteristics in food applications, e.g., baking or roasting of hot dogs. Quantitative experimental determination of the flow field has been carried out by several researchers. Hot wire anemometry [14,25] and Pitot tube [26,27], which measure point velocity of impinging jets, are invasive techniques and likely to induce changes in the flow field. Laser Doppler anemometry (LDA) [18,19,28] and particle imaging velocimetry (PIV) [29] are noninvasive techniques which have been developed to quantitatively measure the flow field. Compared to an LDA system which gives point measurement, PIV technique allows the study of flow field in a plane if suitable tracer particles and light sources are available. The contours of axial velocity for three-jet configuration obtained using LDA technique are shown in Figure 19.4 [18]. The measured velocity profiles show negative (upward) velocity regions in the lateral flow regime due to the interaction between the adjacent jets. These negative velocity regions are important in describing the heat transfer characteristics of multiple jets due to increased turbulence in the jets near the plate [18]. Recently, a study was done using helium-filled bubbles as tracer particles for visualizing flow field and the results gave an insight into features such as free jet turbulence, boundary layer growth, and the presence of stagnation [30]. 19.2.2.3
Heat Transfer in Jet Impingement Ovens
In general, for a single jet impinging on a flat surface, the heat transfer coefficient is high at the stagnation region. As the flow develops downstream, the heat transfer coefficient decreases along radial direction due to growing boundary layer, resulting in relatively milder temperature gradients at the flow–wall interface. The value of heat transfer coefficient at the stagnation point and its decline along radial surface are shown to be a function of Reynolds number and nozzle to plate spacing [14,16]. The optimum z=d (z is nozzle-to-plate distance and d is hydraulic diameter of jet at inlet) ratio for high and uniform heat transfer (which is of greatest importance for food processing) is achieved for z=d ratios in the range of 6–8. If z=d ratio is less than 6, the jet is not fully developed and the flow near the stagnation point may be laminar, which causes lower heat transfer. Heat flux associated with turbulent impinging jet is significantly higher than those associated with laminar flow for same jet exit conditions [31,32]. On the other hand, if z=d ratio is greater than 8 the energy of the jet decays due to the turbulence in free jet region, causing lower heat transfer coefficient. In addition to z=d ratio and Reynolds number, the
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60
uz (m s−1)
40
23.94 20.16
Y (mm)
16.38
20
12.61 8.83 5.05
0
1.28 −2.50 −6.27 −10.05
−20
−40 −80
−60
−40 −20 X (mm)
0
20
+X
+Z
10 mm
FIGURE 19.4 Contours of constant axial (uz) velocity for three jets impinging on a flat plate. Measurements made in a plane 10 mm from flat plate. (From Marcroft, H.E., Chandrasekaran, M., and Karwe, M.W., J. Food Process. Pres., 23, 235, 1999.)
geometry of the nozzle and jet outlet conditions have also been shown to affect the heat transfer coefficient [33,34]. Higher rates of heat transfer for nozzle (long nozzles) jet geometry have been reported as compared to orifice jets (short nozzles) at stagnation point due to the difference in the jet velocity profile at the nozzle exit [33]. Heat transfer during multiple jet impingement is also affected by Reynolds number, nozzle-to-plate spacing as in the case of a single jet. Besides, jet–jet mixing, wall jet interactions, cross flow, nozzle-to-nozzle spacing, and nozzle array geometry affect the heat transfer rate for multiple jets. The formation of secondary maxima is observed between the jets [21,35], which can be correlated to increase in local turbulence due to mixing and in some cases due to the formation of upward fountain. The formation of secondary peaks in heat transfer reduces with an increase in nozzle-to-plate spacing [36]. Cross flow has detrimental effect on the magnitude and uniformity of heat transfer [37]. 19.2.2.4
Experimental Characterization of Heat Transfer in Jet Impingement Ovens
Different techniques have been used to study the heat transfer associated jet impingement flows. Heat transfer measurements for jet impingement systems have been carried out to develop empirical correlations under different jet geometries, exit conditions, and
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nozzle-to-plate spacing. A method using microcalorimeters was developed [31] to measure the surface heat transfer coefficient. Lumped capacitance technique has been used to determine average heat transfer coefficient [8] during jet impingement. As this technique gives average estimate for heat transfer coefficient values, it has limitations in food processing applications because spatial variations of heat transfer coefficients have an effect on the uniformity of the heating=cooling process. Liquid crystals have been used to study the spatial variation of heat transfer coefficient under impinging jets [35,39–41]. Liquid crystals are not suitable for many food processing applications due to its low working temperature range (108C to 1108C). A two-dimensional (2D) infrared radiometer has been used to study local heat transfer [42,43]. Naphthalene film has been used as an indirect approach to measure the spatial variation of surface heat transfer for a model object [44,45]. Over and above the empirical correlations, numerical simulations are needed to predict heat transfer rates during jet impingement processing under a variety of operating conditions and oven geometries. Numerical simulations have to be validated with experiments. A validated simulation technique allows one to explore in a broader range of operating parameters for optimization purposes.
19.3 APPLICATIONS OF CFD IN JET IMPINGEMENT OVENS 19.3.1 TURBULENCE MODELS The flow and heat transfer in a jet impingement system is essentially turbulent and described by conservation of mass, momentum, and energy. Due to fluctuating velocity components in turbulent flow, velocity and temperature terms are time-averaged and divided into mean and fluctuating values to obtain following time-averaged continuity, Navier–Stokes and energy equations for incompressible flow of a jet: Conservation of mass (continuity): @Ui ¼0 @xi
(19:1)
@Ui @Ui Uj 1 @P @ @Ui @Uj þ ¼ þ n þ ra ui uj ra @xi @xj @t @xj @xj @xi
(19:2)
Conservation of momentum:
Conservation of energy: ra Cva
@T @T @ @T þ ra Ui Cpa ¼ ka þ ra Cpa ui u @t @xi @xi @xi
(19:3)
Time-averaged turbulent flow equations contain additional unknown variables known as Reynolds stresses (ui uj ) and Reynolds heat fluxes (uj u). These additional variables cause the problem of closure that has been investigated over the last 50 years [11,46–48] because the number of unknowns (velocity components, pressure, stress components, and temperature) is more than the number of equations. Therefore, several turbulence models (algebraic, one-equation, two-equation, and Reynolds stress model) have been suggested to solve these time-averaged turbulent flow and heat transfer equations based on derived equations for Reynolds stresses and Reynolds heat fluxes [49]. In this section, we explain the turbulence models that are appropriate to use for jet impingement systems.
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One of the most popular models is the two-equation k–« model [50] based on turbulence kinetic energy (k) and turbulence kinetic energy dissipation rate («). The model transport equations can be derived from averaged turbulent flow and heat transfer equations without introducing additional variables [46]. Various researchers have used k–« model to compute the flow field and heat transfer for impinging jet flow [51–53]. For food processing applications, the standard k–« model has been used to solve problems related to meat chilling, blast freezing, convection, and jet impingement ovens [27,54–57]. Another two-equation model is the k–v model based on turbulence kinetic energy (k) and specific dissipation rate (v) [58]. k–v model predicts free shear flow spreading rates that have been shown to be in close agreement with measurements for far wakes, mixing layers, and plane, round, and radial jets, and is thus applicable to wall-bounded flows and free shear flows. The shear-stress transport (SST) model combines the k–v model near the surface and the k–« model at the boundary layer edge and outside the boundary layer [59]. SST model is more accurate and reliable for adverse pressure gradient flows, airfoils, and transonic shock waves. SST model was used to study heat transfer from a slot jet impinging on a circular cylinder placed on a solid surface and it predicted heat transfer more accurately than other models [47]. Using renormalization group theory (RNG), the standard k–« model was modified in order to improve its performance [60]. The RNG k–« model improves the accuracy for rapidly strained and swirling flows, provides variable turbulent Prandtl numbers, and accounts for low Reynolds number effects depending on the treatment of the near-wall region [61]. The RNG k–« model gives reasonably good results for impingement applications in cases of rough walls [41,62]. Another modification to the k–« model is realizable k–« model, which contains a new formulation for turbulent viscosity and dissipation rate. The realizable k–« model predicts the spreading rate of both planar and round jets more accurately [61]. The choice of turbulence model depends on the physics involved in the flow, the level of accuracy required, the available computational resources, and the amount of time available for the simulation [61]. Different models result in significantly different predictions for fluid flow and heat transfer. Therefore, it is a big challenge to choose a turbulence model that accurately predicts fluid flow, heat transfer, and heat transfer coefficients [11]. Numerical approaches to study the complex flow field and heat transfer associated with turbulent jet impingement flow have been the subject of investigation for some research groups [51–53]. Most of these studies have been limited to 2D turbulent impinging jets on a flat surface, whereas for food applications, the prediction of flow field and heat transfer for impinging jet on a defined geometry object is of importance. Modeling the flow field and surface heat transfer for a given geometry provides the understanding of the surface variation of heat transfer and is critical in baking and similar applications. The following section is focused on the numerical simulation of fluid flow and thermal transport for a single or multiple jets impinging on an object of given geometry=shape.
19.3.2 APPLICATIONS 19.3.2.1
Fluid Flow and Thermal Transport for a Single Jet Impingement
Numerical simulation of flow field and thermal transport processes for 2D axisymmetric turbulent jet impinging on a cylindrical model cookie and on the surface of a cylindrical object (e.g., hot dog) has been modeled using the standard k–« model [57,63]. For both cases, thermal transport in the fluid (air) and in the solid (model cookie) was included to model the
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Jet inlet U max = 40 m s−1 T jet = 298 K
3.94e+01 3.55e+01 3.15e+01
Jet direction
2.76e+01 2.36e+01 1.97e+01
Potential core
1.58e+01 1.18e+01 7.88e+00
Stagnation point
3.94e+00
Axis
Model aluminum cookie
0.00e+00 m s−1
FIGURE 19.5 Contour plot of total velocity in a turbulent round impinging jet at z=d ¼ 3. (From Nitin, N. and Karwe, M.V., J. Food Sci., 69, 59, 2004.)
conjugate heat transfer between the impinging jet and the model cookie. Governing mass, momentum, and energy equations were solved using a commercial CFD software FLUENT (Version 6.0, Fluent, Inc., Lebanon, NH). The numerical simulation of fluid flow and heat transfer for a 2D axisymmetric turbulent jet impinging on a cylindrical model cookie showed the formation of potential core region along the centerline and stagnation point at the center (Figure 19.5). Maximum heat transfer coefficient was observed at the stagnation point while at higher jet velocities (30 and 40 m s1), the local maximum shifted away from the stagnation point for high z=d ratios (Figure 19.6) due to radial acceleration of the impinging jet and simultaneous decrease in the jet centerline velocity with increased entrainment. The comparison of numerically predicted and experimentally measured heat transfer coefficient values showed a good agreement with a +15% error. This study also showed that the surface heat transfer coefficient values were independent of the thermophysical properties of the object. Numerical analysis showed that the surface heat transfer coefficient values for an aluminum model cookie and a food material are the same (Figure 19.7a), although the surface temperature values for the two cookies are vastly different (Figure 19.7b). A recent study reported results from the numerical simulation of a turbulent jet impinging on the surface of a cylindrical object (e.g., hot dog). In this study, the variation of temperature along the axis of the cylindrical object was ignored considering that heat transfer coefficient is fairly uniform under each jet and also between the jets [63]. The numerically predicted flow field of a 2D slot jet impinging on a model cylindrical geometry with a slot-to-plate spacing of z=d ¼ 3 showed a stagnation region at the point of impingement and a flow separation zone (Figure 19.8). The existence of separation zone can have significant effect on the uniformity of heat transfer for a cylindrical object in a jet impingement oven leading to nonuniform baking or drying, which can be prevented by impinging jets on both sides of the product (top and bottom) or by rotation of the product. As predicted, the local heat transfer coefficient values vary along the surface of cylindrical hot dog with a maximum at the stagnation point and decrease rapidly along the surface (Figure 19.9a) away from the
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350 300 250
40 m s −1
200 30
m s −1
150 20 m s −1
100
10 m s −1
50 0 0
0.01 0.02 0.03 Radial position on cookie top surface (m)
Surface heat transfer coefficient h (W m −2 K −1)
Surface heat transfer coefficient h (W m −2 K −1)
478
(a)
350 300 250 40 m s−1
200 30 m s−1
150 20 m s−1
100 10 m s−1
50 0 0
0.01 0.02 0.03 Radial position on cookie top surface (m)
(b)
FIGURE 19.6 Variation of local surface heat transfer coefficient as a function of position on top surface of cookie at different jet inlet velocities at jet temperature of 450 K for (a) z=d ¼ 2 and (b) z=d ¼ 5. (From Nitin, N. and Karwe, M.V., J. Food Sci., 69, 59, 2004.)
stagnation point. The comparison of numerically predicted average surface heat transfer coefficient values with experimentally measured values indicated a fair agreement with a +20% error, which includes +10% systematic error in measurement [63]. The surface heat transfer coefficient increases with increase in diameter of cylinder due to decrease in the distance between the impinging jet and the target cylinder as well as decrease in the curvature of the cylindrical surface, resulting in more uniform surface heat transfer over larger area
Top surface temperature (K)
Surface heat transfer coefficient h (W m−2 K −1)
120
100 80 60 40 20 0 0
(a)
0.005 0.01 0.015 0.02 0.025 0.03 Position on cookie top surface (m) Food system Aluminum
400 395 390 385 380 375 370 0
0.01
0.02
0.03
Radial position on cookie top surface (m) Aluminum Food system (b)
FIGURE 19.7 Numerically obtained (a) variation of local surface heat transfer coefficient and (b) surface temperature, for cookies with thermophysical properties of aluminum and typical food material. (From Nitin, N. and Karwe, M.V., J. Food Sci., 69, 59, 2004.)
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Top wall
2.20e+01 2.07e+01 1.94e+01 1.81e+01 1.68e+01 1.55e+01 1.42e+01 1.29e+01 1.17e+01 1.04e+01 9.05e+00 7.77e+00 6.47e+00 5.18e+00 3.88e+00 2.59e+00 1.29e+00 0.00e+00
Line of symmetry
Stagnation point
m s−1
Bottom wall Separation zone
FIGURE 19.8 Velocity contours of an impinging jet on a 10 mm diameter cylinder with an inlet velocity of 22 m s1. (From Nitin, N., Gadiraju, R.P., and Karwe, M.V., J. Food Process Eng., 29, 386, 2006.)
(Figure 19.9b). The correlation for average Nusselt number (Nu ¼ hR=ka) for a turbulent jet impinging on the surface of a cylindrical object based on Reynolds number (Re ¼ raUmaxd=ma) indicated a strong dependence of the surface heat transfer coefficient on the diameter of the cylinder: Nu ¼ 0:000348 Re0:78 ðd=DÞ0:65
600
Local heat transfer coefficient h (W m−2 K−1)
Average heat transfer coefficient h (W m−2 K−1)
300
500
250 200
400
150
300
100
200 100 0 0.038
0.043
0.048
0.053
0.058
0.063
50 0 0
Projected distance (m) along the z-direction Inlet velocity = 42 m s−1 Inlet velocity = 22 m s−1 (a)
(19:4)
30 40 10 20 Velocity at jet inlet (m s−1)
50
10 mm 15 mm 20 mm (b)
FIGURE 19.9 (a) Variation of local surface heat transfer coefficient as a function of distance along the surface of a 20 mm diameter cylinder at two different jet velocities; (b) variation of average surface heat transfer coefficient as a function of velocity of jet at inlet for three cylindrical diameters (10, 15, and 20 mm) at jet air temperature of 1488C. (From Nitin, N., Gadiraju, R.P., and Karwe, M.V., J. Food Process Eng., 29, 386, 2006.)
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Another study covers the investigation of heat transfer from a slot air jet impinging on a cylindrical food product using k–«, k–v, and SST model using CFX 5.5 (ANSYS Inc., Canonsburg, PA) [47]. The results of this study showed that SST model is the best model compared to other models. In this study, the flow from an impinging jet was divided into free jet, stagnation point (at the top of the cylinder), cylinder flow, wake recirculation (at two sides of the cylinder), and wall jet regions. This study also showed that the heat transfer coefficient has the highest value at the stagnation point due to higher degree of turbulence and it was low in the separation region. Similarly, the study showed that the Nusselt number distribution around the cylinder and at the stagnation point was affected by the surface curvature but had little dependency on the jet-to-cylinder distance. The interaction between the cylinder and the wall in the wake recirculation region created an increase in velocity and heat transfer. Therefore, it can be concluded that for a slot air jet impinging on a cylinder-shaped product, the heat transfer is higher at the stagnation point and in the wake, lower at the separation point and the back of the cylinder. SST model gives good predictions of heat transfer in the stagnation region and the point of separation; however, it overpredicts the heat transfer in the wake recirculation region due to anisotropy of the flow. The existence of heat transfer coefficient maximum at the stagnation point and reduction of heat transfer coefficient away from the stagnation point was also proved by a study in which local heat and mass transfer in food slabs under jet impingement was modeled using k–v model with FLUENT 6.1 [64]. In this study, additional modeling for watervapor transfer and interpolation across the food interface was incorporated. Likewise, this study also showed that the heat and mass transfer rates were nonuniform along the exposed surface; the evaporation and depletion of liquid water was evident in the stagnation region, directly under the jet, where the temperature was the highest. The location where the wall jet region starts to form, the surface vapor is blown away by the airflow, inducing more diffusion within the food. However, the study failed to predict the duration of the process. All the above studies were focused on the numerical simulation of fluid flow and heat transfer for a single jet impinging on an object. In the following section, the numerical simulation results for fluid flow and heat transfer in a multiple jet impingement ovens are briefly described. 19.3.2.2
Fluid Flow and Thermal Transport for a Multiple Jet Impingement
A 3D numerical simulation of fluid flow and heat transfer around a cylindrical model cookie in a multiple jet impingement oven (Fujimak SuperJet, Enersyst Corporation, Dallas, TX) was studied using the k–« model for turbulence assuming that inherent design of the oven causes turbulent flow of the air in the oven [27]. The air impingement in the oven was achieved by forcing outside and partially recirculated heated air through 1 cm diameter jet orifices at the bottom (33 jet orifices) and top (31 jet orifices) of the oven cavity. The computational mesh covering the oven cavity was generated using a commercial mesh generating software (Gambit, Fluent Inc., Lebanon, NH) and governing mass, momentum, and energy equations were solved using FLUENT. The conduction heat transfer inside the model cookie was coupled with the convection heat transfer at the surface of the model cookie. Although jets entered the oven cavity vertically (along +Y-direction) from the bottom and the top (Figure 19.10), velocity vectors for flow near a model cookie were parallel to the top and bottom surfaces of the cookie due to recirculation of air caused by an exhaust fan at the back of the oven. The jets were not impinging the cookie surface normally. Heat transfer analysis showed that there was a good agreement between experimentally measured (25–42 W m2 K1) and
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(a)
Model cookie
Y X Z
1.06e+01 1.00e+01 9.52e+00 8.99e+00 8.46e+00 7.93e+00 7.41e+00 6.88e+00 6.35e+00 5.82e+00 5.30e+00 4.77e+00 4.24e+00 3.71e+00 3.19e+00 2.66e+00 2.13e+00 1.60e+00 1.07e+00 5.47e−01 Z m s−1 1.99e−00
Model cookie
Y
X
(b)
FIGURE 19.10 Velocity vectors in (a) middle plane (XY) and (b) middle plane (YZ) around a model cookie at air temperature of 300 K, air velocity of 10 m s1. (From Kocer, D. and Karwe, M.V., J. Food Process Eng., 8, 378, 2005.)
numerically predicted (11–66 W m2 K1) average value of the heat transfer coefficient values around the surface of the cookie with a +10%–15% error. Numerical results also showed that the average value of the surface heat transfer coefficient on the side of the cookie was higher than the bottom and top surfaces of the cookie due to the characteristic of the flow around the cookie. The correlation for the average Nusselt number (Nu ¼ haveL=ka) in terms of Reynolds number (Re ¼ raUad=ma) for multiple jets impinging on the surface of a cylindrical model cookie indicated the strong dependence of surface heat transfer coefficient on velocity of the jet: Nu ¼ 0:58(Re)0:375
(19:5)
Another study investigated the flow and heat transfer from multiple slot air jets impinging on circular cylinders by SST model using CFX 5.5 [65]. The flow characteristics and the heat transfer distribution around the cylinders were found to be dependent on the distance and opening between the jets. This study showed that, at larger distances between the jets, more entrainment of air between the jets occurred, whereas for smaller spacing between the jets, the entrainment was suppressed, almost no air exited through the opening between the jets and the flow between the cylinders was almost stagnant. It was concluded that the spacing between the jets should be high enough to achieve desired entrainment and recirculation of air between the jets, which in turn can achieve the desired high heat transfer. If the distance between the jets is too large, a larger recirculation zone is created between the jets leading to more kinetic energy loss and lower rate of heat transfer. This study also showed that for multiple jets impinging on several cylinders, the heat transfer was comparable to a single cylinder, which should be considered during the geometric design of the oven. In another study, an isothermal airflow in a forced convection oven was modeled using RNG k–« model where CFX 4.1 commercial code was used [54]. Since swirls created by the fan strongly influenced airflows in the oven, the characteristics of the fan were incorporated in the commercial code. The average error for predicted velocity was 22% of the actual velocity, which was measured using hot-film velocity sensor. It was concluded that this study should be further developed to study the effect of food in the oven, which will change the airflow pattern in the oven.
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19.4 CONCLUSIONS The main advantage of jet impingement ovens is higher rates of heat and mass transfer coefficients around the food product, which allows jet impingement ovens to be used successfully in processes where rapid external thermal transport is desired. A detailed study of fluid flow and heat transfer in jet impingement oven systems is very critical to increase the product quality and process efficiency. CFD can be successfully used as a tool to predict fluid flow and heat transfer in jet impingement oven systems to understand the fluid flow and heat transfer as well as spatial variations of heat transfer coefficients around the food product leading to better design of jet impingement oven systems. CFD simulation of jet impingement oven systems requires solution of time-averaged turbulent flow and heat transfer equations with appropriate turbulence modeling. With CFD modeling, we can investigate and optimize the effect of jet-to-jet spacing, orifice design, oven cavity size, product shape, and product-to-product spacing on the heat transfer between the jets and the products.
NOMENCLATURE n u ra ma Cpa Cva d D h have ka L P R t T Ua Ui ui Uj uj Umax xi xj z
kinematic viscosity of the air (m2 s1) turbulent temperature fluctuation (K) density of air (kg m3) viscosity of air (Pa s) specific heat of air at constant pressure (J kg1 K1) specific heat of air at constant volume (J kg1 K1) hydraulic diameter of jet (m) diameter of the cylindrical geometry (m) surface heat transfer coefficient (W m2 K1) average heat transfer coefficient (W m2 K1) thermal conductivity of air (W m1 K1) thickness of cylindrical geometry (m) mean pressure component (Pa) radius of cylindrical geometry (m) time (s) mean air temperature (K) inlet velocity magnitude (m s1) mean velocity component (m s1) turbulent velocity fluctuation component (m s1) mean velocity component (m s1) turbulent velocity fluctuation component (m s1) maximum jet velocity (m s1) directional component (i ¼ 1, 2, 3) (m) directional component ( j ¼ 1, 2, 3) (m) nozzle-to-plate distance (m)
REFERENCES 1. D.P. Smith. Cooking Apparatus. U.S. Patent #3,884,213, 1975. 2. C.E. Walker. Impingement oven technology—Part I: Principles. AIB Research Department Technical Bulletin Volume XI, Issue 11, November, 1987. 3. R. Borquez, W. Wolf, W.D. Koller, and W.E.L. Spie. Impinging jet drying of pressed fish cake. Journal of Food Engineering 40: 113–120, 1999.
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4. C.E. Walker and A.B. Sparman. Impingement oven technology—Part II: Applications and future. AIB, Research Department, Technical Bulletin Volume XI, Issue 11, 1989. 5. Y. Yin and C.E. Walker. A quality comparison of breads baked by conventional versus nonconventional ovens: A review. Journal of the Science of Food and Agriculture 67: 283–291, 1995. 6. A. Li and C.E. Walker. Cake baking in conventional, impingement and hybrid ovens. Journal of Food Science 61: 188–197, 1996. 7. J. Lujan-Acosta and R.G. Moreira. Reduction of oil in tortilla chips using impingement drying. Lebensmittel-Wissenschaft und-Technologie 30: 834–840, 1997. 8. N. Nitin and M.V. Karwe. Measurement of heat transfer coefficient for cookie-shaped object in a hot air jet impingement oven. Journal of Food Process Engineering 24(1): 51–69, 2001. 9. R. Moreira. Impingement drying of foods using hot air and superheated steam. Journal of Food Engineering 49: 291–295, 2001. 10. A.T. Caixeta, R. Moreira, and M.E. Castell-Perez. Impingement drying of potato chips. Journal of Food Process Engineering 25: 63–90, 2002. 11. A. Sarkar, N. Nitin, M.V. Karwe, and R.P. Singh. Jet impingement technology in food processing: A review. Journal of Food Science 69(4): 113–122, 2004. 12. D.Z. Ovadia and C.E. Walker. Directing jets of fluid such as air against the surface of food provides advantages in heating, drying, cooling, and freezing. Food Technology 52(4): 46–50, 1998. 13. R. Gardon and J.C. Akfirat. Heat transfer characteristics of impinging two-dimensional air jets. ASME-Heat Transfer 20l: 410–414, 1964. 14. R. Gardon and J.C. Akfirat. The role of turbulence in determining the heat transfer characteristics of impinging jets. International Journal of Heat and Mass Transfer 8: 1261–1272, 1965. 15. K. Jambunathan, E. Lai, M.A. Moss, and B.L. Button. Review of heat transfer data for single circular jet impingement. International Journal of Heat and Fluid Flow 13(2): 106–115, 1992. 16. H. Martin. Heat and mass transfer between impinging gas jets and solid surfaces. Advanced Heat Transfer 13(1): 1–60, 1977. 17. S. Polat, B. Huang, A.B. Majumdar, and W.J.M. Douglas. Numerical flow and heat transfer under impinging jets: A review. In: C.L. Tien (ed.), Annual Review of Numerical Fluid Mechanics and Heat Transfer, Vol. 2. Washington, DC: Hemisphere Publishing Corporation, 1989, pp. 157–197. 18. H.E. Marcroft and M.V. Karwe. Flow field in a hot air jet impingement oven—Part I: A single impinging jet. Journal of Food Processing and Preservation 23: 217–233, 1999. 19. H.E. Marcroft, M. Chandrasekaran, and M.W. Karwe. Flow field in a hot air jet impingement oven—Part II: Multiple impingement jets. Journal of Food Processing and Preservation 23: 235–248, 1999. 20. K.R. Saripalli. Visualization of multijet impingement flow. American Institute of Aeronautics and Astronautics Journal 21(4): 483–484, 1983. 21. A.M. Huber and R. Viskanta. Impingement heat transfer with a single rosette nozzle. Experimental Thermal and Fluid Science 9: 320–329, 1994. 22. C.O. Popiel and O. Trass. Visualization of a free and impinging round jet. Experimental Thermal and Fluid Science 4(3): 253–264, 1991. 23. R. Viskanta. Heat transfer to impinging isothermal gas and flame jets. Experimental Thermal and Fluid Science 6: 111–134, 1993. 24. C. Cornaro, A.S. Fleischer, and R.J. Goldstein. Flow visualization of a round jet impinging on cylindrical surfaces. Experimental Thermal and Fluid Science 20(2): 66–78, 1999. 25. Y. Sugiyama and Y. Usami. Experiments on flow in and around jets directed normal to a cross flow. Bulletin of Japan Society of Mechanical Engineers 22: 1736–1745, 1979. 26. R.L. Stoy and Y. Ben-Haim. Turbulent jets in a confined crossflow. Journal of Fluids Engineering— Transactions of ASME 95(4): 551–556, 1973. 27. D. Kocer and M.V. Karwe. Thermal transport in a multiple jet impingement oven. Journal of Food Process Engineering 8: 378–396, 2005. 28. F. Durst, B. Lehmann, and C. Tropea. Laser Doppler system for rapid scanning of flow fields. Review of Scientific Instruments 52(11): 1676–1681, 1981 29. R.J. Adrian. Particle-imaging techniques for experimental fluid mechanics. Annual Review of Fluid Mechanics 23: 261–304, 1991.
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30. A. Sarkar and R.P. Singh. Spatial variation of convective heat transfer coefficient in air impingement applications. Journal of Food Science 68(3): 910–916, 2003. 31. C. duP. Donaldson, R.S. Snedeker, and D.P. Margolis. A study of free jet impingement. Part 2. Free jet turbulent structure and impingement heat transfer. Journal of Fluid Mechanics 45(3): 477–512, 1971. 32. A. Khan, M.M. Hirata, N. Kasagi, and N. Nishiwati. Heat transfer augmentation in an axisymmetric impinging jet. International Heat Transfer Conference 3: 363–368, 1982. 33. D.W. Colucci and R. Viskanta. Effect of nozzle geometry on local convective heat transfer to a confined impinging air jet. Experimental Thermal and Fluid Science 13: 71–80, 1996. 34. B.R. Hollworth and R.D. Berry. Heat transfer from arrays of impinging jets with large jet-to-jet spacing. Journal of Heat Transfer 100: 352–357, 1978. 35. R.J. Goldstein and J.F. Timmers. Visualization of heat transfer from arrays of impinging jets. International Journal of Heat and Mass Transfer 25(12): 1857–1868, 1982. 36. R.J. Goldstein and A.I. Behbahni. Impingement of a circular jet with and without cross flow. International Journal of Heat and Mass Transfer 25: 1377–1382, 1982. 37. D.E. Metzger and R.J. Korstad. Effects of cross flow on impingement heat transfer. ASME Journal of Engineering Power 94: 35–42, 1972. 38. L.W. Florscheutz, C.R. Truman, and D.E. Metzger. Streamwise flow and heat transfer distributions for jet array impingement with cross flow. Journal of Heat Transfer 102: 337–342, 1981. 39. J.W. Baughn. Liquid crystal methods for studying turbulent heat transfer. International Journal of Heat and Fluid Flow 16(5): 365–375, 1995. 40. M. Mesbah, J.W. Baughn, and C.W. Yap. The effect of curvature on the local heat transfer to an impinging jet on a hemispherically concave surface. In: Proceedings of the Ninth International Symposium on Transport Phenomena in Thermal Fluids, Singapore, 1996. 41. J. Lee and S.J. Lee. Effect of nozzle configuration on stagnation region heat transfer of axisymmetric jet impingement. International Journal of Heat and Mass Transfer 43(18): 3497–3509, 2000. 42. Y. Pan, J. Stevens, and B.W. Webb. Effect of nozzle configuration on transport in the stagnation zone of axisymmetric, impinging free-surface liquid jets: Part 2: Local heat transfer. Transactions of the ASME, Journal of Heat Transfer 114: 880–886, 1992. 43. Y. Pan and B.W. Webb. Heat transfer characteristics of arrays of free-surface liquid jets. Transactions of the ASME Journal of Heat Transfer 117: 878–883, 1995. 44. E.M. Sparrow and B.J. Lovell. Heat transfer characteristics of an obliquely impinging circular jet. Journal of Heat Transfer 102: 202–209, 1980. 45. M. Angioletti, R.M. Di Tommaso, E. Nino, and G. Ruocco. Simultaneous visualization of flow field and evaluation of local heat transfer by transitional impinging jets. International Journal of Heat and Mass Transfer 46: 1703–1713, 2003. 46. C.J. Chen and S.Y. Jaw. Fundamentals of Turbulence Modeling. Washington, DC: Taylor & Francis, 1998, pp. 21–59. 47. E.E.M. Olsson, L.M. Ahrne´, and A.C. Tra¨ga˚rdh. Heat transfer from a slot air jet impinging on a circular cylinder. Journal of Food Engineering 63: 393–401, 2004. 48. H. Tennekes and J.L. Lumley. A First Course in Turbulence, 1st edn. Cambridge, MA: MIT Press, 1972, 300 pp. 49. S.B. Pope. Turbulent Flows. New York: Cambridge University Press, 2000, 771 pp. 50. B.E. Launder and D.B. Spalding. Mathematical Models of Turbulence. New York: Academic Press, 1972, 169 pp. 51. S.V. Patankar, D.K. Basu, and S.A. Alpay. Prediction of the three dimensional velocity field of a deflected turbulent jet. Journal of Fluids Engineering 99: 758–762, 1977. 52. G.D. Catalano, K.S. Chang, and J.A. Mathis. Investigation of turbulent jet impingement in a confined crossflow. American Institute of Aeronautics and Astronautics Journal 27(9110): 1530–1535, 1989. 53. S. Polat and W.J.M. Douglas. Heat transfer under multiple slot jets on a permeable moving surface. American Institute of Chemical Engineers Journal 36(9): 1370–1378, 1990. 54. P. Verboven, N. Scheerlinck, J. De Baerdemaeker, and B.M. Nicolai. Computational fluid dynamics modeling and validation of the isothermal airflow in a forced convection oven. Journal of Food Engineering, 43: 41–53, 2000.
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55. Z. Hu and D.-W. Sun. Effect of fluctuation in inlet airflow temperature on CFD simulation of air blast chilling process. Journal of Food Engineering 48(4): 311–316, 2001. 56. P.S. Mirade, A. Kondjoyan, and J.D. Daudin. Three-dimensional CFD calculations for designing large food chillers. Computers and Electronics in Agriculture 34(1–3): 67–88, 2002. 57. N. Nitin and M.V. Karwe. Numerical simulation and experimental investigation of conjugate heat transfer between a turbulent hot air jet impinging on a cookie. Journal of Food Science 69(2): 59–65, 2004. 58. D.C. Wilcox. Turbulence Modeling for CFD. DCW Industries, Inc., La Canada, California, 1998. 59. F.R. Menter. Two-equation eddy-viscosity turbulence models for engineering applications. American Institute of Aeronautics and Astronautics Journal 32(8): 1598–1605, 1994. 60. V. Yakhot and S.A. Orzag. Renormalization group analysis of turbulence. I. Basic theory. Journal of Scientific Computing 1(1): 3–51, 1986. 61. Fluent 6.1 User’s Guide. Fluent Inc., Lebanon, NH, 2003. 62. H. Laschefski, T. Cziesla, G. Biswas, and N.K. Mitra. Numerical investigation of heat transfer by rows of rectangular impinging jets. Numerical Heat Transfer 30(A): 87–101, 1996. 63. N. Nitin, R.P. Gadiraju, and M.V. Karwe. Numerical simulation and experimental investigation of conjugate heat transfer between turbulent hot air jet impinging on a hot-dog-shaped objects. Journal of Food Process Engineering 29: 386–399, 2006. 64. M.V. De Bonis and G. Ruocco. Modelling local heat and mass transfer in food slabs due to air impingement. Journal of Food Engineering 78(1): 230–237, 2005. 65. E.E.M. Olsson, L.M. Ahrne´, and A.C. Tra¨ga˚rdh. Flow and heat transfer from multiple slot air jets impinging on circular cylinders. Journal of Food Engineering 67: 273–280, 2005. 66. F. Landis and A.H. Shapiro. An Album of Fluid Motion. Assembled by Milton Van Dyke, Stanford, California: The Parabolic Press, 1982.
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CFD Modeling of Jet Impingement during Heating and Cooling of Foods Eva E.M. Olsson and Christian Tra¨ga˚rdh
CONTENTS 20.1 20.2
Introduction ............................................................................................................. 487 Jet Impingement Heat Transfer ............................................................................... 488 20.2.1 Principles of Jet Impingement..................................................................... 488 20.2.2 Flow Characteristics ................................................................................... 489 20.2.3 Heat-Transfer Characteristics ..................................................................... 490 20.3 CFD for Jet Impingement Heat Transfer ................................................................ 491 20.3.1 Introduction ................................................................................................ 491 20.3.2 Governing Equations .................................................................................. 491 20.3.3 Turbulence Models for Jet Impingement .................................................... 492 20.3.3.1 Jet Flow Characteristics .............................................................. 492 20.3.3.2 Heat-Transfer Characteristics ..................................................... 494 20.3.4 Wall Treatment ........................................................................................... 496 20.4 Applications of Jet Impingement Modeling............................................................. 496 20.4.1 Influence of Important Parameters ............................................................. 496 20.4.2 Industrial Impingement Equipment ............................................................ 497 20.4.3 Quality Aspects — Effects on Food Properties ........................................... 498 20.5 Conclusions .............................................................................................................. 500 Acknowledgments .............................................................................................................. 501 Nomenclature ..................................................................................................................... 501 References .......................................................................................................................... 502
20.1 INTRODUCTION Heating and cooling are important processes in the food industry. Rapid heat-transfer methods can be used to shorten the process time and increase the production rate. Jet impingement is a rapid convective heat-transfer method, which consists of directed jets that impinge on the surface of the product. It can be used to speed up thermal processes in the food industry as well as in other applications. Impinging jets have been widely used and developed to increase heat and mass transfer in areas such as cooling gas turbines, drying paper and textiles, and cooling electronic components, and in anti-ice systems on aircraft. Impingement systems designed for food applications can be used for heating=baking [1–5], drying [6,7], cooling [8], and freezing [9,10]. The first impingement oven was patented by
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Smith in 1975 [11]. Several reviews and surveys on impingement heat transfer can be found in the literature [12–16]. Impingement in the food industry has been reviewed by Ovadia and Walker [17] and Sarkar et al. [18]. Cooling precooked food is necessary to avoid quality degradation. Rapid cooling can be used to decrease the risk of growth of thermophilic and many mesophilic microorganisms, and increase the quality of the food. In baking and heating, rapid heat transfer can be used to reduce the baking temperature, baking time, and the total moisture loss, which in turn may increase the shelf life. In convective heating, the heating rate affects the food product in several ways, not only surface properties such as color and crust thickness, but also properties that affect the entire food product, such as the rate of water loss. The effect of heating using different methods can also be taken into consideration when developing new products. The total energy consumption may be reduced by using jet impingement compared with conventional techniques. The heat transfer from the jet to the product in impingement techniques is dependent on the design of the equipment and process conditions, and the product characteristics, including product geometry. In designing equipment and in the choice of optimal process conditions, it is important to have a complete understanding of the airflow and the heat-transfer characteristics from the impinging jets to the product. By using computational fluid dynamics (CFD), the fluid flow, turbulence, and the heat transfer from the impinging jets to the food product can be predicted. CFD modeling is a powerful tool in studying complex flow and heat transfer. It can be used to investigate the effect of various parameters on the flow pattern and the heat-transfer distribution on the surface of the product, leading to a reduction in the experimental tests required, and=or greater knowledge in general. The first and most important factor in successful CFD modeling is to determine the most suitable turbulence model, as all impinging jets in food-processing applications operate under turbulent conditions. The second, also very important, factor is the development of a good mesh to ensure that the capabilities of the turbulence model are not impaired. A good numerical mesh is one that gives final results, which are in principle independent of the distance between the mesh points. This chapter focuses on that task. In addition, it should quantitatively and qualitatively describe the flow and heat-transfer characteristics of impinging jets with special emphasis on cases where they impinge on curved surfaces. It should also give some insight into how the heat-transfer characteristics can be utilized in food-processing applications and equipment and process design to achieve the desired product properties.
20.2 JET IMPINGEMENT HEAT TRANSFER 20.2.1 PRINCIPLES
OF JET IMPINGEMENT
Jet impingement is a convective heat-transfer method in which the energy is transported by the bulk motion of the air. A jet impingement system may consist of a single jet or multiple jets of high velocity that are directed (orthogonally or at another angle) toward the surface of the product. A schematic figure of a single orthogonal slot jet impinging on a cylindrical product is shown in Figure 20.1. A velocity boundary layer develops as the air jet approaches the solid surface. The air in contact with the surface has zero velocity, which retards the fluid in the fluid layer on the surface. The development of the velocity boundary layer depends on the flow conditions and the surface friction. A thermal boundary layer is developed in the same way as for the velocity boundary layer. The heat transfer is related to the velocity boundary layer since the heat transfer is controlled by the mechanisms of turbulence and molecular diffusion (corresponding to viscosity and thermal diffusivity, respectively).
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W
H
D
FIGURE 20.1 Impinging air jet on a cylindrical product. (From Olsson, E., PhD dissertation, Lund University, Lund, Sweden, 2005.)
The great advantage of jet impingement is that when the high-velocity jet impinges on the surface, a velocity boundary layer starts to develop between the surface and the bulk flow, which is thin compared with the fully developed boundary layer in more conventional crossflow techniques. An impinging jet is a stream of air exiting from a nozzle at a velocity high enough to entrain the surrounding air on its way toward a surface, with enough energy to impinge onto the surface and increase the heat transfer through the high turbulence levels in the vicinity of the stagnation point of the impinging jet [19]. The velocity field, the turbulent diffusion, and the thickness of the thermal boundary layer determine the heat-transfer rate. Variations in velocity and thermal boundary layer thickness between the air and the product result in a variation in heat transfer around the product. A higher velocity or higher Reynolds number generally results in a thinner boundary layer and greater turbulence, which enhances the transport of momentum, heat, and mass.
20.2.2 FLOW CHARACTERISTICS The typical flow characteristics of a jet impinging on a flat surface (Figure 20.2a) can be divided into the following regions: free jet, stagnation point, and wall jet (I, II, III in Figure 20.2). In the case of a jet impinging on a solid object (e.g., a cylinder or a sphere) the flow will generally separate (IV in Figure 20.2) from the curved object (Figure 20.2b). A wake (V in Figure 20.2) is formed in the region downstream of the separation point. The presence of a solid supporting plate under the object affects both the location of the separation point and the appearance of the wake compared to the case when no solid plate is used.
I. II. III. IV. V.
I
Free jet Stagnation point Wall jet Flow separation Wake recirculation
I
II IV II (a)
V
III
III
(b)
FIGURE 20.2 Schematic diagram of a jet impinging on (a) a flat plate and (b) a cylindrical object.
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Entrainment of the air from the surroundings will take place as the free jet meets the stagnant air. A potential core is formed, in which the jet centerline velocity is the same as the exit velocity. The kinetic energy is high in the shear layers where the jet meets the surrounding air due to the high-velocity gradients and resulting shear stresses. As the jet approaches the surface, there is a rapid increase in static pressure and the velocity approaches zero at the stagnation point with high turbulence intensity as the high kinetic energy in the jet is transferred into turbulent kinetic energy. The impinging object redirects the flow and a wall jet is formed. The flow pattern will be different for a jet impinging on an object placed on a supporting surface. The flow of a jet impinging on a cylinder placed on a flat surface follows the curvature of the cylinder after the stagnation point until the point of separation. The separation point is strongly affected by the transition of the boundary layer from laminar to turbulent flow, which in turn depends on the Reynolds number. The separation point is earlier for turbulent flow than for the laminar flow. The flow is reversed after the separation point due to the viscous and inertial interaction with the cylinder and, when applicable, the supporting plate. Separation occurs much earlier and the wake recirculation zone is smaller when there is a supporting plate under the cylinder than in a simulation case of a free-standing cylinder. The flow pattern is also dependent on several other factors that influence the behavior of the jet and the resulting heat transfer, such as the nozzle geometry (round or slot nozzles have most frequently been studied), nozzle-to-surface distance (H=W ), jet orientation, and Reynolds number. Downs and James [14] reviewed the characteristics of heat transfer from round and slot jets. They summarized the impact of geometry and temperature, interference and cross flow, turbulence levels, and incidence and surface curvature. Jambunathan et al. [15] reviewed experimental data on heat-transfer rates in the case of circular jets impinging on a flat surface. Jets with a Reynolds number in the range of 5000–124,000 and jet-to-surface distances of 1.2–16 were investigated. In the design of industrial impingement equipment, it is important to understand the behavior and interaction of multiple jets. The flow pattern and the heat transfer to the product will be different from that of a single jet if the jets are close enough to interact with each other. A number of studies on multiple jets can be found in the literature [20–24].
20.2.3 HEAT-TRANSFER CHARACTERISTICS The heat transfer in convective heating is closely related to the airflow due to the analogy between momentum and heat transfer. The heat transfer is determined by the velocity field, the turbulent diffusion, and the velocity and thermal boundary layers. Variations in the boundary layer properties will result in variations in the heat-transfer rate. The heat transfer is highest at the stagnation point as the impinging jet disrupts the velocity boundary layer and a thin boundary layer results in high heat transfer. After the stagnation point the air follows the surface, and in the case of a jet impinging on a flat surface, the boundary layer grows and the heat transfer decreases. Heat transfer from a jet impinging on a flat surface has been studied by several authors [25–29]. In the case of a jet impinging on a cylindrical object the heat transfer around the cylinder surface is affected by the point of boundary layer separation. The heat transfer around a cylinder due to an impinging jet has been studied by Olsson et al., Kang and Greif, Tawfek, McDaniel and Webb, and Gori and Bossi [8,30–33]. The heat transfer was also found to be affected by the supporting plate and the recirculation zone that is formed due to the flow separation. The recirculation region is larger in the case of a free-standing cylinder. The nozzle geometry, the Reynolds number, the nozzle-to-surface distance, and, in the case of a cylinder, the surface curvature are important in achieving optimal heat transfer.
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The heat transfer increases with the Reynolds number, approximately by the square root of the Reynolds number. The nozzle-to-surface distance has an optimal value at which the heat transfer is maximum. This optimal distance coincides with the length of the potential core, which is about 6–7 jet diameters or 4–7 slot widths [14].
20.3 CFD FOR JET IMPINGEMENT HEAT TRANSFER 20.3.1 INTRODUCTION Flow and heat transfer involve nonlinear transport equations of momentum, energy, and mass. In complex flow situations, geometries, and boundary conditions, a CFD program can be used to solve the governing equations in a computational domain describing the flow situation using various discretization techniques. A turbulence model is usually required to solve the chaotic motion of turbulent flows in a reasonable amount of time and computer power. There is no single turbulence model that is best in all flow situations; the turbulence model must be chosen and tested for each flow system studied. The use of CFD in the food industry is increasing and has been reviewed by Scott and Richardson [34] and Xia and Sun [35]. Fundamental aspects of CFD flow are described by, for example, Versteeg and Malalasekera [36].
20.3.2 GOVERNING EQUATIONS To solve flow and heat-transfer problems, the governing equations used are transport equations for momentum and energy, developed from the conservation laws of physics. The fluid flow is described by the conservation of mass (the continuity equation) and momentum (the Navier–Stokes equations). The energy equation is based on the first law of thermodynamics, which is rewritten in a form suitable for temperature. The time-dependent Navier–Stokes equations describe the fluid motion. Reynolds reformulated the equations by dividing each term into a mean and a fluctuating value: ui(t) ¼ Ui þ ui0 and T(t) ¼ T þ T 0 . In most situations the time-averaged properties of the flow are sufficient. Together with accurate boundary conditions, the governing equations for an incompressible Newtonian fluid with negligible external and viscous forces are the Reynolds-averaged equations: @Uj ¼0 @xj
(20:1)
@ Ui Uj @Ui @P @ @Ui @Uj þr ¼ þ t ij þ t turb ¼ m þ ¼ ru0i u0j (20:2) r ; t ; t turb ij ij ij @xi @xj @t @xj @xi @xj rcp
@ Uj T mcp @T @T @ þ rcp ¼ qj þ qturb ; ; qj ¼ j @xj @t @xj Pr @xj
qturb ¼ rcp u0j T 0 j
(20:3)
where Uj and uj0 are the mean and fluctuating velocity components for each direction xj, i is the index for the equation in each direction, r is the density, t the time, P the total pressure, m the dynamic viscosity, cp the specific heat, T and T 0 the mean and fluctuating temperatures, and Pr the dimensionless Prandtl number. The additional terms that appear on the right-hand side of the time-averaged equations are the turbulent stresses, that is, the Reynolds stresses t turb ¼ ru0i u0j and the turbulent heat fluxes qturb ¼ rcp u0j T 0 . The modeling of these stresses is ij j
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known as the closure problem of turbulence. The Reynolds stresses can be described as the average value of the extra flow of momentum out of the control volume caused by the turbulence.
20.3.3 TURBULENCE MODELS
FOR JET IMPINGEMENT
The important issue here is to choose a suitable turbulence model as well as appropriate wall treatment. This can mean the difference between success and failure. The most commonly used turbulence models in general, as well as in this application, are the two-equation models, for example, the k–«, k–v, and the shear stress transport (SST) models. They are based on the assumption that there is an analogy between the viscous stresses and the Reynolds stresses, also known as the Boussinesq assumption. The analogy is formulated as a turbulent viscosity, which is related to the Reynolds stresses and the mean velocity gradients. The turbulent transport of heat is described as a Fourier law expression with a turbulent Prandtl number, defined as the ratio between the turbulent viscosity and the turbulent (eddy) diffusivity. The standard k–« model is robust, economic, and reasonably accurate for a wide range of turbulent flow conditions, but the assumption of an isotropic turbulent viscosity is often too coarse and leads to inaccurate predictions in nonisotropic flow. The k–v model is applicable to wall-bounded flows where modifications are made for low-Reynolds-number effects, compressibility, and shear flow spreading, but has strong freestream sensitivity. The SST model is a turbulence model that combines the advantages of the k–« and the k–v models. It combines the k–v model near the wall and the k–« model outside the boundary layer. The SST model can be more accurate and reliable for a broader class of flows than the standard k–v and k–« models. The Reynolds stress model (RSM) does not assume isotropic turbulent viscosity. It accounts for the directional effects of the Reynolds stress field by describing the individual Reynolds stresses by transport equations. Another six Reynolds stress equations t turb ¼ ru0i u0j ij have to be solved since the tensor is symmetric. The advantage of the RSM is that it accounts for anisotropic flow, such as the effects of streamline curvature, swirl, rotation, and rapid changes in the strain rate in a better way than the two-equation models [37]. However, because of the extra transport equations, the RSM requires greater computer power, and difficulties with convergence are sometimes encountered. In the literature, various turbulence models have been described for modeling impingement flows. A jet impinging on a surface has several features, such as the perpendicular flow at the stagnation point that changes the direction and the flow at curved boundaries on a cylindrical surface, which are difficult to reproduce with most turbulence models. Craft et al. [28] used experimental data to evaluate the k–« model and three second-moment closure models. Angioletti et al. [38] used different k–« models, the SST model, and an RSM for comparison with experimental data, and Olsson et al. [8,24] used the SST model for modeling of single and multiple jets after evaluating the k–«, k–v, and SST models. Olsson et al. [24] compared the performance of the RSM with that of the SST model. 20.3.3.1
Jet Flow Characteristics
To determine the heat transfer from convective airflow, it is necessary to have knowledge of the flow pattern and the velocity boundary layer formed between the bulk flow and the solid surface. The flow from a single slot jet impinging on a circular cylinder was studied by Olsson et al. [8]. The airflow from the jet around the cylinder was simulated in two dimensions, using the SST turbulence model, and compared with data obtained by particle image velocimetry (PIV). In particular, the mean velocity and the turbulence intensity were studied and the
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PIV
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
(a)
(b)
FIGURE 20.3 Comparison between mathematical modeling using the SST model (a) and PIV measurements (b) of the mean and normalized velocity, U=Umax, of an impinging jet on a cylinder. ReW ¼ 11,500 and H=W ¼ 8. (Adapted from Olsson, E., PhD dissertation, Lund University, Lund, Sweden, 2005.)
results for the mean and normalized velocity are shown in Figure 20.3. As the air exited the slot nozzle, the velocity decreased due to entrainment of the surrounding flow. The simulations of the mean velocity of the jet were in good agreement with the PIV measurements. The velocity close to the nozzle exit was predicted well with both the RSM and SST turbulence model. As the jet developed and came closer to the cylinder, the RSM gave a greater overprediction of the velocity than the SST model. The centerline velocity was better predicted in relation to experimental data by the SST model than by the RSM (see Figure 20.4a). In the simulations, the boundary conditions (k, v, and «) in the jet exit were specified based on the PIV data. The simulations were slightly sensitive to the boundary value of the kinetic dissipation rate, but less sensitive to the other boundary conditions, for example, the kinetic energy and the specific energy dissipation rate. The CFD simulations did not predict the turbulence intensity as well as the mean velocity, compared with the PIV measurements (see Figure 20.4b). Both the SST and the RSM models underpredicted the turbulence intensity on the centerline, but the RSM underpredicted to a
U/Umax
0.8
Turbulence intensity (%)
PIV SST RSM
1.0
0.6 0.4 0.2 0.0 0
(a)
1
2
3
4 y /W
5
6
7
PIV SST RSM
30 25 20 15 10 5 0 0
8 (b)
1
2
3
4
5
6
7
8
y /W
FIGURE 20.4 Jet centerline velocity (a) and turbulence intensity (b) for H=W ¼ 8. Comparison between the RSM and the SST model, and PIV measurements. y=W is the dimensionless distance from the nozzle to the cylinder. (Adapted from Olsson, E., PhD dissertation, Lund University, Lund, Sweden, 2005.)
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greater extent than the SST model. The SST model predicted first an increase in turbulence intensity and then a slow decrease, starting at the end of the potential core and ending before impact on the cylinder. Close to the cylinder, both turbulence models predicted an increase, but the RSM predicted an initial decrease in turbulence intensity and a fairly constant intensity from the end of the potential core to the increase close to the cylinder. The turbulence intensity at the nozzle exit is usually reported to be low (a few percent) until the end of the potential core, where it increases [39–41]. More active momentum exchange with the surrounding air occurs after the potential core, leading to an increase in the turbulence intensity. The turbulence intensity was found to be more sensitive to the boundary conditions than was the mean velocity in the simulations. The potential core was found to be short, about 1–2 slot jet widths (see Figure 20.3 and Figure 20.4). Other authors have found the potential core to be longer, about 4 slot jet widths [13], or 5.7–6.5 jet widths [39]. The degree of confinement influences the flow entrainment in the jet [40]. The nozzle in the impingement system in Figure 20.3 and Figure 20.4 was constructed as a slit at the bottom of the plenum chamber, which resulted in a flow entrainment of air different from those in other investigations, and may explain the observed difference [19]. As expected, the turbulence intensity was high in the shear layers. The jet lost kinetic energy to the surroundings before impinging on the cylinder. The point of flow separation affects the heat-transfer distribution around the cylindrical surface. The heating or cooling of a food product will thus not be uniform around the surface. The flow separation is important for the heat-transfer distribution around the cylinder since the heat transfer falls close to the separation point. The point of flow separation is dependent on the Reynolds number of the jet flow, whether the boundary layer is laminar or turbulent, the shape of the object on which the jet impinges, and the presence of a supporting plate or bars under the cylinder. The point of separation was predicted by both the SST and the RSM models to be at about u ¼ 608–708 [19] (see Figure 20.5); the PIV measurements indicated a slightly larger angle on the cylinder. The RSM performed slightly better than the SST model in the nonisotropic flow regime. 20.3.3.2
Heat-Transfer Characteristics
Heat transfer is dependent on the airflow that creates the velocity boundary layer between the stagnant surface and the high velocity of the impinging jet, in analogy with the heat and momentum exchange, which is also used in the heat-transfer model. The heat-transfer PIV
(a)
SST
(b)
RSM
(c)
FIGURE 20.5 Velocity vectors in the impingement region and flow separation at the cylinder, ReW ¼ 11,500. Comparison between PIV measurements (a), CFD using the SST (b) and the RSM models (c). (Adapted from Olsson, E., PhD dissertation, Lund University, Lund, Sweden, 2005.)
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Re = 23,000
h (W m−2 K−1)
350
Re = 50,000
300
Re = 70,000
250
Re = 100,000
200 150 100 50 0 0
45
90
135
180
q (⬚)
FIGURE 20.6 Heat transfer around the cylinder for different Reynolds numbers, H=d ¼ 4 and d=D ¼ 0.86. (Adapted from Olsson, E.E.M., Ahrne´, L.M., and Tra¨ga˚rdh, A.C., J. Food Eng., 63, 393, 2004. With permission.)
distribution around a cylinder on which a jet impinges has been found to be nonuniform [8]. Different Reynolds numbers (23,000–100,000) were investigated and the Nusselt number, based on the jet width, was predicted using the SST turbulence model (see Figure 20.6, replotted into heat-transfer coefficients). The heat transfer was highest at the stagnation point due to the thin boundary layer and the high turbulent fluctuations normal to the wall caused by the impinging jet. The heat transfer decreases as the boundary layer grows on the side of the cylinder to the separation point, where the heat transfer falls more rapidly. Behind the cylinder, the recirculation of the airflow increases the heat transfer; the heat transfer shows a maximum at about u ¼ 1308. The heat transfer increases with increasing Reynolds number. Olsson et al. [8] found that the heat transfer was not dependent on the nozzleto-surface (H=W) distance probably due to the small potential core. Maximum heat transfer was found when H=W ¼ 5–8 [32,33,39,41]. These studies involve a wide range of Reynolds numbers (600–87,000) and both round and slot jets. CFD simulations using the SST and the RSM models were compared with experimental data by Olsson [19]. The distribution of heat-transfer coefficients around the surface of the cylinder was determined (see Figure 20.7) (NB: not the same impinging jet as in Figure 20.6).
SST
200
h (W m−2 K−1)
RSM IHTM
150 100 50 0 0
45
90
135
180
q (⬚)
FIGURE 20.7 Comparison of heat-transfer coefficients around the cylinder using the inverse heattransfer method (IHTM), and CFD simulations with the SST and RSM models. (Adapted from Olsson, E., PhD dissertation, Lund University, Lund, Sweden, 2005.)
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The RSM generally predicted a slightly lower heat transfer on the upper part of the cylinder than the SST model. The RSM is theoretically a better turbulence model for flow with high anisotropy, which is the case in the recirculation zone. Two-equation models are known to overpredict the dissipation in these areas. The increase in heat transfer at the back of the cylinder (u ¼ 1808) is the result of the cylinder placed a few millimeters above the supporting plate. The heat-transfer distribution around a cylinder in cross flow without a supporting plate has been modeled using the two-equation k–v, k–«, and SST turbulence models, and compared with experimental data [8]. It was found that the most-appropriate turbulence model for these flow conditions was the k–v-based SST model with a low-Reynolds-number model. Turbulence models based on the k–v model are well suited for wall-bounded flows [42].
20.3.4 WALL TREATMENT When modeling heat transfer from the fluid flow to a solid surface, good modeling of the flow near the wall is very important to achieve accurate predictions. The two most common ways are to use a wall function or to resolve the boundary layer in a very fine mesh close to the surface, that is, a low-Reynolds-number model approach. A wall function that uses a logarithmic function to relate the wall shear stress to the conditions in the fully turbulent region is frequently used in many engineering applications. It is then possible to reduce the number of nodes in the mesh and thereby reduce the amount of computer capacity and time. As mentioned above, these wall functions were derived for fully developed boundary layer flows and are thus not expected to perform well for a developing boundary layer, as is the case here. The accuracy of near-wall modeling may also be reduced. In a low-Reynolds-number model approach, the fine mesh near the surface allows the computations to be extended through the dominantly viscous sublayer close to the wall, allowing more accurate predictions of the heat transfer. The heat transfer around a free cylinder in cross flow using different grids close to the cylinder was studied by Olsson et al. [8]. Compared to the literature data, the low-Reynoldsnumber model using a fine grid close to the surface (yþ < 1–2) gave, as expected, better results than using a wall function (2 < yþ < 25). The k–v and SST models preformed well using a resolved boundary layer, but performed poorly using wall functions. The standard k–« model using wall functions did not perform well, also as expected. The simulations are also dependent on the mesh, and it is important to make sure that this effect is negligible.
20.4 APPLICATIONS OF JET IMPINGEMENT MODELING 20.4.1 INFLUENCE
OF IMPORTANT
PARAMETERS
Mathematical modeling using CFD is a powerful tool for predicting the airflow and the heat transfer in the design of efficient convective cooling or heating equipment. The effect of important parameters can be studied by reducing the amount of expensive and timeconsuming experimental work required. Simulations can be made to identify the optimal process conditions. Modeling cannot completely replace experimental measurements, but it can be used to gain a better understanding of the flow and the heat-transfer processes. The heat transfer from an impinging jet has been widely studied, and several relationships have been developed to describe it. The relationship between the heat-transfer coefficient or the Nusselt number and the Reynolds number is dependent on several factors, including the choice of characteristic length, the turbulence level, the surface curvature, and the geometry
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of the nozzle. The heat transfer increases with increasing Reynolds number (Figure 20.6). The relationship between the heat transfer in terms of the Nusselt number (Nu) and the Reynolds number (Re) is Nu C Rem [15], where m is about 0.5. As discussed above, a specific nozzle-to-surface distance (H=W ) has been found by several authors to give a heat transfer maximum. For slot jets, this distance has been reported by many investigators to be 5–8 [29,32,33,39] for a wide range of Reynolds numbers. Downs and James [14] reported that an H=W distance of 6–7 jet diameters gave maximum heat transfer for round jets. Olsson et al. [8], however, found no heat-transfer maximum. For a jet impinging on a cylindrical surface, the heat transfer has been found to increase with greater surface curvature (ratio of jet width to cylinder diameter) [8,41].
20.4.2 INDUSTRIAL IMPINGEMENT EQUIPMENT Industrial impingement equipment usually consists of multiple jets in different configurations. When designing industrial ovens using multiple jets, it is important to evaluate the interaction and behavior of the jets. The flow field resulting from multiple, round impinging jets in an impingement oven has been studied by Marcroft et al. [20]. Nitin and Karwe´ [43] studied the average heat-transfer coefficient for single and multiple biscuit-shaped objects in a hot air impingement oven. Numerical studies of heat transfer from multiple slot jets impinging on a flat surface have been made by Seyedin et al., Yang and Shyu, and Tzeng et al. [21–23]. Olsson et al. [24] studied the interaction and resulting heat transfer beneath each jet from two and three jets impinging on a cylinder using the k–v SST turbulence model. Multiple jets that were close enough to interact with each other strongly affected the flow pattern and the heat-transfer rate from the airflow to the cylinders. It was found that the distance between the jets and the size of the opening between them were very important. A small distance between the jets removes the normal entrainment of the jet and they merge into a single jet. The pressure conditions in the plenum chamber were also important as the flow takes the paths that are most favorable. The heat transfer around the cylinder was highest for the case with two jets impinging on two cylinders, when the distance between them was two jet widths (see Figure 20.8). The streamlines of the velocity in this case are shown in Figure 20.9. In the case of three jets, the heat-transfer distribution around the center cylinder was different from the outer cylinders. The air from the center jet also ‘‘stroked’’ the outer cylinders after impinging on the center cylinder. L /d = 1
300
L /d = 2
h (W m−2 K−1)
250
L /d = 4
200
Single jet
150 100 50 0
−180
−135
−90
−45
0
45
90
135
180
q (⬚)
FIGURE 20.8 Heat-transfer distribution around the right cylinder for two jets, impinging on two cylinders at different separations. (Adapted from Olsson, E.E.M, Ahrne´, L.M., and Tra¨ga˚rdh, A.C., J. Food Eng., 67, 273, 2005.)
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FIGURE 20.9 Streamlines of the velocity for two jets, separated by a distance of two jet widths, impinging on two cylinders. (Adapted from Olsson, E.E.M, Ahrne´, L.M., and Tra¨ga˚rdh, A.C., J. Food Eng., 67, 273, 2005.)
Double impingement, that is, jets directed both from above and below, is common in industrial heating-and-cooling equipment using impinging jets. The products are then placed on a conveyor belt made of a net or bars that allows air to pass through without disturbing the large-scale flow pattern. Olsson et al. [44] found that the use of two rectangular bars or a net of parallel bars did not interfere with the airflow in the domain, compared with a cylinder without any support. The flow was disturbed only on a local scale close to the bars supporting the cylinder. The separation point was earlier, as a result of the jet from below, which affected the distribution of heat transfer around the cylinder (Figure 20.10). The heat transfer to the cylinder in contact with the supporting bars was decreased. To minimize this heat-transfer loss, the supporting bars should be placed where heat transfer is already low. The heat transfer around the cylinder is lowest just after the flow has separated from the cylinder.
20.4.3 QUALITY ASPECTS — EFFECTS
ON
FOOD PROPERTIES
Impingement systems designed for food applications can be used to create rapid heat transfer. Several authors have studied the effect of impingement heat transfer on food quality, for Two bars No plate
h (W m−2 K−1)
100
Net
80 60 40 20 0 0
45
90
135
180
q (⬚)
FIGURE 20.10 Heat-transfer distribution around a cylinder placed on different surfaces in double impingement, Re ¼ 23,000. (Adapted from Olsson, E.E.M., Ahrne´, L.M., and Tra¨ga˚rdh, A.C., Proceedings of the 9th International Congress on Engineering and Food (ICEF 9), Montpellier, France, 2004.)
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499
Temperature (⬚C)
250 200 150 100 50
IM crust HO crust
0 0
2
IM crumb HO crumb
4
6
Time (min)
FIGURE 20.11 Temperatures in the crust and the crumb during heating using impingement (IM) and heating in a conventional household oven (HO). (Adapted from Olsson, E.E.M., Tra¨ga˚rdh, A.C., and Ahrne´, L.M., J. Food Sci., 70, E484, 2005.)
example, the effects of heating [2,4,7,45] and freezing food products [46]. The quality of impingement-baked products relative to conventional oven-baked products was studied by Ovadia and Walker, and Li and Walker [47,48]. The effect of impingement heating on crust formation on part-baked minibaguettes was studied by Olsson et al. [5] and compared with infrared heating and conventional heating. The baguettes were partially baked so as to have a ready-baked crumb and a very thin, colorless crust. The effect of postbaking using several heating techniques including impingement was studied. Parameters such as color, crust thickness, and total water loss were investigated at different temperatures, air velocities, and heating times. The temperature was measured in the crust and in the crumb during heating. Figure 20.11 shows the time–temperature profiles for impingement heating and heating in a conventional household oven for the same air temperature (2508C). The mean air velocity in the impinging jet was about 7.5 m s1. The crust and crumb temperature in impingement heating increased rapidly compared with heating in the household oven [5]. The rapid impingement heating resulted in high heat- and mass-transfer rates. The water loss during heating was strongly related to the heat flux, crust temperature, and heating time. The impingement-baked baguettes were exposed to high heat-transfer rates, which resulted in high rates of water loss, but because of the shorter baking time, the total water loss was reduced when compared with conventional heating (Figure 20.12). Bread baked in
14 Water loss (%)
12 10 8 6
IM 2508C IM 1808C HO 2508C HO 1808C
4 2 0 0
1
2
3
4
5
6
7
8
9 10
Time (min)
FIGURE 20.12 Water loss during impingement (IM) heating and a conventional household oven (HO). (Adapted from Olsson, E.E.M., Tra¨ga˚rdh, A.C., and Ahrne´, L.M., J. Food Sci., 70, E484, 2005.)
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70 60 50 40 30 20 10 0
IM 2508C IM 1808C HO 2508C HO 1808C
0
1
2
3
4 5 6 7 Time (min)
8
9 10
FIGURE 20.13 Color development during impingement (IM) heating and heating in a conventional household oven (HO). (Adapted from Olsson, E.E.M., Tra¨ga˚rdh, A.C., and Ahrne´, L.M., J. Food Sci., 70, E484, 2005.)
impingement ovens has a higher moisture content, which results in a softer crumb and longer shelf life [49]. The heating of bread results in browning of the surface due to the Maillard reactions between the sugar and the proteins in the crust. The color development is strongly dependent on the crust temperature, which rises as the crust dries. Surface browning has been found to start at about 1308C–1408C [19]. The color development rate was high in impingement heating because of the high heat transfer. The air temperature in convective heating limits the final color. A rapid convective method, such as impingement, achieves the final color faster than baking in a conventional household oven (Figure 20.13). Crust formation starts during heating as the drying zone moves toward the interior of the bread. High heat-transfer rates and high temperatures in the crust are associated with a high dehydration rate, which, in combination with a long heating time, results in a thick crust. In general, a rapid heat-transfer method requires less time than a conventional, slower heattransfer method, for the desired color to be reached, resulting in a thinner crust.
20.5 CONCLUSIONS Jet impingement is a rapid heat-transfer method that can be used to speed up heating or cooling in the food industry. In order to design industrial equipment and process conditions that give optimal heat transfer and a high, uniform product quality, it is necessary to understand and to be able to predict the heat-transfer distribution around the product. Computational fluid dynamics is well suited for predicting flow and heat transfer. The main drawback is that it is necessary to choose a suitable turbulence model. Common models are the two-equation k–«, k–v, and SST models. An RSM is often recommended for predicting wall-bounded flow and heat transfer. The velocity obtained by CFD modeling is generally in good agreement with experimental data. In impingement flows, turbulence models based on the k–v approach (the k–v and the SST models) using a low-Reynolds-number model close to the surface predict the heat transfer better than the k–« model. In the case of a jet impinging on a cylinder, the SST model predicted the velocity and turbulence intensity in the jet more accurately than the RSM. The RSM gave a somewhat better prediction than the SST model in the anisotropic flow region close to the back of the cylinder. However, the RSM requires more computer time and has greater problems with convergence. The heat-transfer rate and distribution around the product are closely related to the airflow from the impinging jet. The SST model predicted the heat transfer better on top of the cylinder, but the RSM gave a better prediction close to the recirculation zone than measuring the heat transfer using an inverse heat-transfer method.
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Thus, it is strongly recommended that model predictions be validated against relevant experimental data. Both the turbulence model itself and the conditions need to be carefully assessed. The required data are the flow field, including turbulence statistics, and local heattransfer coefficients. The initial choice of models and wall treatment can be based on principles and theoretical considerations. It is also worth mentioning the importance of appropriate meshing in the near-wall region, for example, a suitable distance from the wall to the first mesh point and an appropriate expansion ratio of the mesh outward from the wall. It is important to investigate the interaction between multiple jets when designing and optimizing equipment using multiple jets. The distance between the jets strongly affects the flow pattern and the heat transfer around the product. To achieve high, uniform heat transfer a suitable jet configuration and distances between the jets are necessary. Double impingement, that is, jets from both above and below, alters the heat transfer around the cylinder compared to the use of only one jet from above. The heat transfer is higher at the bottom of the cylinder and the separation point is also earlier because of the jet from below. Rapid heating affects the food product. In the case of bread products, characteristics such as the color and crust development and the total water loss are affected. The rapid heat transfer achieved with air jet impingement increases the rate of color development and shortens the total heating time, but the temperature of the air limits the final color of the bread. The high heattransfer rate also results in high mass-transfer rates but the total water loss is reduced because the total heating time is shorter. A short heating time also results in a thin crust.
ACKNOWLEDGMENTS The authors would like to acknowledge Dr. Lilia Ahrne´ at SIK, The Swedish Institute for Food and Biotechnology, Go¨teborg, Sweden, for her contribution to the work on which this chapter is based.
NOMENCLATURE cp H H=W i k L P Pr q qturb Re ReW t T T0 u Uj uj0 W yþ
specific heat (J kg1 8C1) distance between nozzle exit and cylinder (m) nozzle-to-surface distance coordinate index for the governing equations (turbulent) kinetic energy (m2 s2) characteristic length (m) total pressure (Pa) Prandtl number heat flux (W m2) turbulent heat flux (W m2) Reynolds number Reynolds number based on slot jet width time (s) temperature (8C) fluctuating temperature (8C) velocity (m s1) mean velocity component for each direction xj (m s1) fluctuating velocity component for each direction xj (m s1) jet width (m) dimensionless distance
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GREEK SYMBOLS « u m r t tturb v n
dissipation rate (m2 s3) angle on the cylinder (8) dynamic viscosity (Pa s) density (kg m3) shear stress (N m2) turbulent stress (N m2) specific dissipation rate (s1) kinematic viscosity (m2 s1)
REFERENCES 1. T.M. Midden. Impingement air baking for snack food. Cereal Foods World 40 (8): 532–535, 1995. 2. I.S. Dogan and C.E. Walker. Effects of impingement oven parameters on high-ratio cake baking. Cereal Foods World 44 (10): 710–714, 1999. 3. H.E. Marcroft and M.V. Karwe´. Flow field in a hot air jet impingement oven. Part I: A single impinging jet. Journal of Food Process and Preservation 23: 217–233, 1999. 4. U. Wa¨hlby, C. Skjo¨ldebrand, and E. Junker. Impact of impingement on cooking time and food quality. Journal of Food Engineering 43 (3): 179–187, 2000. 5. E.E.M. Olsson, A.C. Tra¨ga˚rdh, and L.M. Ahrne´. Effects of near infrared radiation and jet impingement heat transfer on crust formation of bread. Journal of Food Science 70 (8): E484–E491, 2005. 6. R. Borquez, W. Wolf, W.D. Koller, and W.E.L. Spiess. Impinging jet drying of pressed fish cake. Journal of Food Engineering 40 (1–2): 113–120, 1999. 7. R.G. Moreira. Impingement drying of foods using hot air and superheated steam. Journal of Food Engineering 49: 291–295, 2001. 8. E.E.M. Olsson, L.M. Ahrne´, and A.C. Tra¨ga˚rdh. Heat transfer from a slot air jet impinging on a circular cylinder. Journal of Food Engineering 63: 393–401, 2004. 9. V.O. Salvadori and R.H. Mascheroni. Analysis of impingement freezers performance. Journal of Food Engineering 54 (2): 133–140, 2002. 10. A. Sarkar and R.P. Singh. Modeling flow and heat transfer during freezing of foods in forced airstreams. Journal of Food Science 69 (9): 488–496, 2004. 11. D.P. Smith. Cooking apparatus, U.S. patent 3884213, May 20, 1975. 12. R. Gardon and J.C. Akfirat. The role of turbulence in determining heat-transfer characteristics of impinging jets. International Journal of Heat and Mass Transfer 8: 1261–1272, 1965. 13. H. Martin. Heat and mass transfer between impinging gas jets and solid surfaces. Advances in Heat Transfer 13 (1): 1–60, 1977. 14. S.J. Downs and E.H. James. Jet impingement heat transfer—A literature survey, American Society of Mechanical Engineers, Paper 87, HT-35, 1–11, 1987. 15. K. Jambunathan, E. Lai, M.A. Moss, and B.L. Button. A review of heat transfer data for single circular jet impingement. International Journal of Heat and Fluid Flow 13 (2): 106–115, 1992. 16. R. Viskanta. Heat transfer to impinging isothermal gas and flame jets. Experimental Thermal and Fluid Science 6: 111–134, 1993. 17. D.Z. Ovadia and C.E. Walker. Impingement in food processing. Food Technology 11(6): 1147–1176, 1998. 18. A. Sarkar, N. Nitin, M.V. Karwe´, and R.P. Singh. Fluid flow and heat transfer in air jet impingement in food processing. Journal of Food Science 69 (4): 113–122, 2004. 19. E. Olsson. Jet impingement and infrared heating of cylindrical foods. Flow and heat transfer studies. PhD dissertation, Lund University, Lund, Sweden, 2005. 20. H.E. Marcroft, M. Chandrasekaran, and M.V. Karwe´. Flow field in a hot air jet impingement oven. Part II: Multiple impinging jets. Journal of Food Processing Preservation 23: 235–248, 1999. 21. S.H. Seyedin, M. Hasan, and A.S. Mujumdar. Turbulent flow and heat transfer from confined multiple impinging slot jets. Numerical Heat Transfer, Part A. Applications 27: 35–51, 1995.
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22. Y.-T. Yang and C.-H. Shyu. Numerical study of multiple impinging slot jets with an inclined confinement surface. Numerical Heat Transfer, Part A. Applications 33: 23–37, 1998. 23. P.Y. Tzeng, C.Y. Soong, and C.D. Hsieh. Numerical investigation of heat transfer under confined impinging turbulent slot jets. Numerical Heat Transfer, Part A. Applications 35: 903–924, 1999. 24. E.E.M. Olsson, L.M. Ahrne´, and A.C. Tra¨ga˚rdh. Flow and heat transfer from multiple slot air jets impinging on circular cylinders. Journal of Food Engineering 67: 273–280, 2005. 25. J. Baughn and S. Shimizu. Heat transfer measurements from a surface with uniform heat flux and an impinging jet. Journal of Heat Transfer 111: 1096–1098, 1989. 26. X. Yan, J.W. Baughn, and M. Mesbah. The effect of Reynolds number on the heat transfer distribution from a flat plate to an impinging jet. American Society of Mechanical Engineers, Heat Transfer Division (Publication), HTD 226: 1–7, 1992. 27. D. Cooper, D.C. Jackson, B.E. Launder, and G.X. Liau. Impinging jet studies for turbulence model assessment—I. Flow-field experiments. International Journal of Heat and Mass Transfer 36 (10): 2675–2684, 1993. 28. T.J. Craft, L.J.W. Graham, and B.E. Launder. Impinging jet studies for turbulence model assessment—II. An examination of the performance of four turbulence models. International Journal of Heat and Mass Transfer 36 (10): 2685–2697, 1993. 29. J. Lee and S.-J. Lee. Stagnation region heat transfer of a turbulent axisymmetric jet impingement. Experimental Heat Transfer 12 (2): 137–156, 1999. 30. S.H. Kang and R. Greif. Flow and heat transfer to a circular cylinder with a hot impinging air jet. International Journal of Heat and Mass Transfer 35 (9): 2173–2183, 1992. 31. A.A. Tawfek. Heat transfer due to a round jet impinging normal to a circular cylinder. Heat and Mass Transfer 35: 327–333, 1999. 32. C.S. McDaniel and B.W. Webb. Slot jet impinging heat transfer from circular cylinders. International Journal of Heat and Mass Transfer 43: 1975–1985, 2000. 33. F. Gori and L. Bossi. On the cooling effect of an air jet along the surface of a cylinder. International Communications in Heat and Mass Transfer 27 (5): 667–676, 2000. 34. G. Scott and P. Richardson. The application of computational fluid dynamics in the food industry. Trends in Food Science and Technology 8 (4): 119–124, 1997. 35. B. Xia and D.-W. Sun. Applications of computational fluid dynamics (CFD) in the food industry: A review. Computers and Electronics in Agriculture 34: 5–24, 2002. 36. H.K. Versteeg and W. Malalasekera. An Introduction to Computational Fluid Dynamics. The Finite Volume Method. Essex, England: Longman Scientific and Technical, 1995. 37. Fluent 6.0 User’s Guide. Fluent Inc., 2001. 38. M. Angioletti, E. Nino, and G. Ruocco. CFD turbulent modeling of jet impingement and its validation by particle image velocimetry and mass transfer measurements. International Journal of Thermal Science 44: 349–356, 2005. 39. T.L. Chan, C.W. Leung, K. Jambunathan, S. Ashforth-Frost, Y. Zhou, and M.H. Liu. Heat transfer characteristics of a slot jet impinging on a semi-circular convex surface. International Journal of Heat and Mass Transfer 45: 993–1006, 2002. 40. S. Ashforth-Frost, K. Jambunathan, and C.F. Whitney. Velocity and turbulence characteristics of a semiconfined orthogonally impinging slot jet. Experimental Thermal and Fluid Science 14: 60–67, 1997. 41. D.H. Lee, Y.S. Chung, and M.G. Kim. Turbulent flow and heat transfer measurements on a curved surface with a fully developed round impinging jet. International Journal of Heat and Fluid Flow 18: 160–169, 1997. 42. F.R. Menter. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal 32 (8): 1598–1604, 1994. 43. N. Nitin and M.V. Karwe´. Heat transfer coefficient for cookie shaped objects in a hot air jet impingement oven. Journal of Food Process Engineering 24: 51–69, 2001. 44. E.E.M. Olsson, L.M. Ahrne´, and A.C. Tra¨ga˚rdh. Prediction of optimal heat transfer from slot air jets impinging on cylindrical food products using CFD. In: Proceedings of the 9th International Congress on Engineering and Food (ICEF 9), Montpellier, France, 2004.
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45. U. Wa¨hlby and C. Skjo¨ldebrand. Reheating characteristics of crust formed on buns, and crust formation. Journal of Food Engineering 53: 177–184, 2002. 46. V. Soto and R Bo´rquez. Impingement jet freezing of biomaterials. Food Control 12: 515–522, 2001. 47. D.Z. Ovadia and C.E. Walker. Opportunities for impingement technology in the baking and allied industries. American Institute of Baking Technology Bulletin 19: 1–8, 1997. 48. A. Li and C.E. Walker. Cake baking in conventional, impingement and hybrid ovens. Journal of Food Science 61 (1): 188–191, 197, 1996. 49. Y. Yin and C.E. Walker. A quality comparison of breads baked by conventional versus nonconventional ovens: A review. Journal of the Science of Food and Agriculture 67: 283–291, 1995.
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Use of CFD for Optimization, Design, and Scale-Up of Food Extrusion Bharani K. Ashokan, Jozef L. Kokini, and Muthukumar Dhanasekharan
CONTENTS 21.1 Introduction ............................................................................................................. 505 21.2 Numerical Simulation of Extrusion ......................................................................... 506 21.3 Modeling of Single-Screw Extruders........................................................................ 511 21.4 Modeling of Twin-Screw Extruders ......................................................................... 517 21.5 Optimization of Extruders ....................................................................................... 520 21.6 Extruder Scaling....................................................................................................... 528 21.7 Conclusions .............................................................................................................. 533 Nomenclature ..................................................................................................................... 534 References .......................................................................................................................... 534
21.1 INTRODUCTION Harper defined extrusion as the continuous formation of plastic or soft materials through a die, often after a previous heating of the material, and an extruder as a machine that shapes materials by the process of extrusion [1]. Principally, common extruders used in food and plastics industries are screw extruders (as opposed to ram or piston extruders) consisting of flighted screws rotating within a sleeve or barrel. Such extruders can be subdivided into two broad classes—single- and twin-screw extruders. The single-screw extruder is regarded as a shear flow pump. It relies on the shear properties between the material and the barrel surface [2]. Twin-screw extruders are further subdivided into corotating and counter-rotating based on the relative direction of rotation of the screws and also as intermeshing or nonintermeshing twin-screw extruders. The screws in a twin-screw extruder are usually assembled using screw elements that can be flighted conveying screws or kneading blocks with staggered disks or even specialized elements (with ridges on the conveying elements or other such modifications) that are customized for certain processing operations. Early efforts at understanding the transport phenomena in an extruder and in optimizing extruder operations used empirical and trial-and-error approaches at each step in process and product development. For example, scaling an extruder to different sizes without compromising product quality has remained a challenge in extrusion processing. The fundamental challenge is the squared dependence of heat transfer to length and the cubic dependence of
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flow rate on length creating a dimensional inconsistency for scaling. Analytical scaling relationships have failed in the literature and scaling remained a trial-and-error process. A trial-and-error approach requires extensive experimentation and may not allow for an optimum, efficient, appropriately scaled extruder. Therefore, understanding the basic transport phenomena in an extruder and developing broad principles to match key operating parameters linked to quality is the key for successful scale-up or scale-down. Computational fluid dynamics (CFD) modeling and numerical simulation of extrusion processes have since been used to improve the comprehension of the transport phenomena in extruders. However, even with CFD, there are still challenges in being able to rationally choose the process conditions to obtain final product quality, to predict the most efficient control variables, and to scale up laboratory experimentation to the industrial level [3]. Such challenges in addressing the heat and mass transport processes in extruders have been numerically modeled and analyzed by various researchers for both single- and twin-screw extruders [4 –34] and will be the focus of this chapter. Extrusion in the synthetics polymer industry relies mainly on the melting of the polymers at high temperatures followed by subsequent shaping of the melted extrudate in a die. In food extrusion, heating the food to high temperatures is almost always accompanied with cooking, leading to reaction extrusion; and when modeling food extrusion processes, these reactions need to be taken into account. Numerical simulation of the flow and heat transfer in a food extruder requires the coupling between the momentum (flow) and the energy balance equations. Food materials have thermal diffusivities that are extremely small (of the order of 105 to 106 m2=s), resulting in large Peclet numbers of the order of a few hundred thousand to millions, and convective heat transport problems are numerically difficult to solve. Such problems have in the past limited the ability of numerical simulations to aid in successful design and optimization of food extruders. There are only a few examples of CFD studies that have successfully applied advances in numerical modeling of extrusion of synthetic polymers to food extrusion with the associated complexities in modeling reactions and complex rheology [13,17]. In this chapter, the numerical techniques commonly used to solve extrusion problems will be first discussed. This will be followed by a summary of the advances in food extrusion numerical simulation that address design, optimization, and scaling of extruders using CFD modeling.
21.2 NUMERICAL SIMULATION OF EXTRUSION Numerical simulation of extrusion is conducted by simultaneously solving the equations of the conservation of momentum and energy, with a rheological equation of state (constitutive models) of the food material to be extruded, along with boundary or initial conditions. Because food materials are reactive in nature and the rates of reactions depend on both shear and temperature, kinetic models are needed, which link the change in state and chemistry to physical properties such as viscosity, elasticity, heat capacity, density, and thermal conductivity. For an incompressible fluid, the stress tensor s is given as the sum of the isotropic pressure ( p) component and an extra-stress tensor (T). The extra-stress tensor is described using an appropriate constitutive model: s ¼ pI þ T
(21:1)
The momentum equation is a statement of conservation of momentum in the coordinate space and describes momentum transport by convection, diffusion, and other sources.
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Let r be the fluid density and f be the external body force per unit mass. The conservation of linear momentum is then given by r s þ rf ¼ r
@v þ v rv @t
(21:2)
Here the first term on the left hand side of Equation 21.2, the divergence of the stress tensor, is responsible for the diffusion of momentum. The second term accounts for external forces, such as gravitational forces that impart momentum, whereas the terms on the right hand side of the equation describe the momentum transport by convection. For an incompressible fluid rv¼0
(21:3)
Finally, the equation for conservation of energy is given as rC(T)
@T þ v rT ¼ T : rv þ r r q @t
(21:4)
where C(T ) is the heat capacity as a function of temperature, r is the given volumetric heat source, and q is the heat flux. Viscous heating is described through the term T : rv. These equations, together with viscous or viscoelastic constitutive models, form a complete set of governing equations whose solutions give velocity and temperature profiles for a particular problem. In most cases, these equations cannot be solved analytically and, therefore, the use of numerical methods is very common. One of the most successful numerical methods widely employed in solving flow problems is the finite element method (FEM). This method is characterized by three features [35]: 1. The domain of the problem is represented by a collection of simple subdomains called finite elements. The collection of finite elements is called the finite element mesh. 2. Over each finite element, polynomial functions and algebraic equations relating physical quantities at the corners of elements called nodes approximate the physical process. 3. The element equations are assembled using continuity and ‘‘balance’’ of physical quantities. Common finite element formulations make use of the weak form of the equations of motion (Equation 21.2), and the incompressibility equation 21.3 to solve such problems [36]. Consider a domain V over which the velocity field and pressure, together with the extrastress tensor, T, are required. For illustration assume the inertia terms are zero. Let V and P denote the function spaces of the velocity and pressure fields, respectively. Then the finite element formulations are given by ð (rp þ r T þ f) u dV ¼ 0 8u 2 V (21:5) V
ð V
(r v)q dV ¼ 0
8q 2 P
(21:6)
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where u and q are weighting functions. By setting the weighted integrals of the error in the governing equations to be zero, it is ensured that there are required numbers of independent linear algebraic equations. In order to transfer some of the differentiability requirements from the approximate solutions to the weight functions, integration by parts is performed to obtain the ‘‘weak’’ form of the governing equations. Integrating Equation 21.5 using integration by parts ð
ð ð ( pI þ T) ru dV ¼ f u dV þ t u d T
V
V
8u 2 V
(21:7)
@V
where t denotes the surface traction on the boundary @V of V. The traction is the natural boundary condition and contains the pressure. The essential boundary condition is the velocity at the boundary. The essential boundary condition is applied by replacing the velocity approximation with the exact value at the nodes that fall on the boundary. By creating a weak form, the continuity conditions on the basis functions are reduced and the natural boundary conditions in the problem statement are explicitly included. Other formulations have been based on the fourth-order stream function formulation that uses the combined continuity and momentum equations and the second-order stream function or vorticity formulation [37]. Equation 21.6 and Equation 21.7 constitute the weak forms of Equation 21.2 and Equation 21.3, respectively. The domain V is now discretized using finite elements covering a domain, Vh, on which the velocity field and pressure fields are approximated using vh and ph. The approximations are obtained using vh ¼
X
Vi ci , ph ¼
X
pi p i
(21:8)
where Vi and pi are nodal variables and ci and pi are finite element basis functions also known as shape functions. To calculate the unknowns Vi and pi, the weak forms of the equation of motion and the continuity equation as given by Equation 21.6 and Equation 21.7 are solved along with the formulations for the constitutive models. Two basic approaches are used to solve the system of equations from Equation 21.6 through Equation 21.8. The first approach is referred to as the coupled method, or the mixed or the stress–velocity–pressure formulation. In this approach the extra-stress tensor becomes a primary unknown along with the velocity and pressure fields. The stress tensor is formulated using an approximation Th with Th ¼
X
Ti fi
(21:9)
where Ti are nodal stresses while fi are shape functions. This procedure is normally used with differential models. The advantage of this method is the possibility of utilizing Newton– Raphson’s technique to solve for the primary variables in the nonlinear problem. However, the disadvantage is the large number of unknowns and hence high computational costs for typical flow problems. The second approach, known as the decoupled scheme, uses an iterative method. The computation of the viscoelastic extra stress is performed separately from that of flow kinematics. From known kinetics the stress field is calculated. The kinematics is then iterated typically using Picard’s iterative algorithm. The number of variables is much smaller than in the mixed method, but the number of iterations is much larger.
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A straightforward implementation of these approaches often gives an instability and divergence of the numerical algorithms for viscoelastic problems. A variety of numerical methods are used to circumvent convergence problems for viscoelastic flows. For flow problems of viscoelastic fluids of the differential type, a mixed Galerkin formulation of the governing equations is first developed. The viscoelastic extra-stress, velocity, and pressure are approximated by the means of the finite element expansions as described before (Equation 21.8 and Equation 21.9). Substituting the approximation into the isothermal governing equations using Galerkin’s method, the following set of equations is obtained: ð
fi A(Ta1 ,
l)
Ta1
dTa1 a 2h1 D dV ¼ 0 þ l(g_ ) dt
(21:10)
V
ð
ð a Dva T a a f þ rcj p I þ 2h2 D þ T1 dV ¼ cj s n ds cj r Dt
V
(21:11)
@V
ð
pk ½r va dV ¼ 0
(21:12)
V
where Equation 21.11 and Equation 21.12 represent the discretized forms of conservation of momentum and mass, respectively. Equation 21.10 is the discretized form of the viscoelastic constitutive equation which is dTa1 z D z r ¼ T1 þ 1 T1 2 2 dt
(21:13)
The values of the functions A and l and the variable z depend on the particular constitutive model. For example, when A is equal to the unit tensor and l vanishes, the constitutive equation reduces to the generalized Newtonian case. Due to the hyperbolic r nature of lrv T1 originating from the upper-convected derivative of the extra-stress T1 , the accuracy and stability of the mixed Galerkin formulation deteriorates as the elasticity number (the ratio of elastic forces to inertial forces) increases in flows with boundary layers or singularities. In such cases, the numerical results are stabilized by the use of viscoelastic extra-stress interpolations. The most robust extra-stress interpolation technique, streamline upwinding (SU), consists of applying an artificial diffusivity, K ¼ k(vv=v v) to the hyperbolic term only in the streamwise direction. The discrete constitutive equation then becomes ð V
ð
dTa lk fi A Ta1 , l Ta1 þ l(g_ ) 1 2h1 Da dV þ a a va rTa1 va rfi dV ¼ 0 v v dt
(21:14)
V
where k is a scalar of O(h) and is equal to (v2h þ v2j )1=2 =2. A drawback of this technique is that it gives rise to artificial extra-stress diffusion along the streamlines whose importance decreases when the finite element mesh is refined. In order to eliminate the effects of artificial diffusivity, at least three meshes of decreasing size are used to verify all results. In contrast, streamline upwinding=Petrov–Galerkin (SUPG) applies K to all the terms in the discrete constitutive equation, eliminating the artificial diffusion. This method is considered more accurate compared to the SU method. Other viscoelastic extra-stress field
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interpolation techniques available include biquadratic, 2 2 bilinear subelements, 4 4 bilinear subelements, and extra viscous stress splitting (EVSS). EVSS is one of the stable techniques available for use in 3D or with multiple relaxation times. In EVSS, the stress tensor is split into elastic and viscous components as T ¼ T1a þ
hp D h0
(21:15)
When this form of the stress tensor is used, the convected derivative of the rate of strain emerges, which requires a second-order derivative of the velocity field. To overcome this, D is considered an unknown and is obtained by an L2-projection of the velocity gradient as D 1=2[(rv) þ (rv)T]. The modified discrete constitutive equation and strain rate equation are as follows: ð
a r dT a a a þ 2h1 D dV ¼ 0 fi AðT , lÞ T þ l(g_ ) dt
(21:16)
V
and ð
jl Da rva þ rT va =2 dV ¼ 0
(21:17)
V
This discretization is much more computationally intensive compared to previous approaches, but that is offset by the tremendous increase in the robustness of the algorithm. The use of the polymer viscosity in the formulation of T instead of the solvent viscosity as is done in the viscous formulation effectively under-relaxes the stress in the calculations and causes the solution to be less sensitive to the gradual loading of elasticity. This technique remains effective even when the solvent viscosity goes to zero, whereas the viscous formulation requires a viscosity ratio of at least 1=9 for most differential models. The quality of the finite element mesh is very crucial in the success of the FEM. One of the crucial quality metrics is the equiangle skew. Equiangle skew is a normalized measure of skewness of an element which is defined as follows:
QEAS
umax ueq ueq umin ¼ max , 180 ueq ueq
(21:18)
where umax and umin are the maximum and minimum angles in degrees between the edges of the element, and ueq is the characteristic angle corresponding to an equilateral cell of similar form, which would be 608 for a triangular or tetrahedral cell and 908 for a quadrilateral or hexahedral element. By definition, therefore, the equiangle skew is between 0 (quadrilateral element) and 1 (degenerate element). In 3D flow problems, an average skewness value of 0.4 is considered excellent. Skewness values up to 0.6 are considered good, and fair to poor elements are up to 0.9. Skewness values greater than 0.9 are usually not acceptable. Other mesh quality indicators include the degree of stretch, aspect ratio, taper, and warpage among others. The use of these various mesh quality indicators depends on geometrical considerations (for instance, if the geometry is predominantly curved or rectangular) and has to be appropriately chosen.
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21.3 MODELING OF SINGLE-SCREW EXTRUDERS Using the FEM techniques described above, many attempts were made to numerically model an extruder. The first extrusion processes to be studied were the simpler single-screw extruder geometries. Most numerical simulation based modeling studies of single-screw extruders used a moving barrel formulation [2,17,18] with a stationary screw. The rheological models used were either simple Newtonian or power-law models. Since single-screw extruders had been used in the plastics industry for a much longer time than in foods, most modeling studies were directly derived from plastics processing literature and did not incorporate the reaction kinetics of food materials or the physical and rheological properties of foods. Plastics are relatively homogeneous polymeric materials that can be chemically and physically characterized with relatively simple material equations. In contrast, food extrusion uses a large variety of food ingredients as feed materials and requires quite complex material characterization techniques. In plastics extrusion, melting of the polymer is a major change in the extrusion process. In food extrusion, there can be many simultaneous chemical reactions such as starch gelatinization and melting, protein–starch interactions, and lipid–carbohydrate and lipid–protein interactions during cooking, which cause extensive alterations in the chemical and physical nature of the extruded materials. For successful design, optimization, and operation of extrusion unit operations, prediction of the nonlinear rheological properties of the dough is required. Specifically, because the strains and strain rates encountered during these processes are very large and rheological properties of doughs at those strains and strain rates strongly depend on the magnitude of the applied strains and strain rates, the models required to describe the flow behavior of doughs must be nonlinear in nature. Process design is accomplished by solving flow equations in conjunction with a constitutive equation. Scaling principles need to follow from design principles by matching key processing parameters such as residence time distribution (RTD) and specific mechanical energy (SME), and finding sets of geometrical and operating conditions that give isoresidence time distributions and isospecific mechanical energy conditions. Some of the basic ideas originating from plastics extrusion can be applied to extrusion of foods using simplistic generalized Newtonian models. The assumptions usually made in solving the flow in an extruder are that the flow is laminar and fully developed [1]. Early modeling studies such as those of Griffith [18], Zamodits and Pearson [33], and Fenner [15] obtained numerical solutions based on 2D flow geometries and assumed fully developed flow in an infinitely wide rectangular screw channel while ignoring effects of curvature and leakage across the flights. This is acceptable in most cases as food doughs are highly viscous and the screw turns relatively slowly. If the flow is steady, then the velocity profiles remain constant with time and location. For modeling purposes, the screw is considered stationary and the barrel is imagined rotating in the opposite direction. This situation is identical to the actual, but reverse situation, assuming the centripetal forces are small because the screw turns slowly. Ignoring the effects of curvature by assuming shallow channels, the ratio of the channel depth (H) to the channel width (W ) is much smaller than 1 allowing the use of the so-called lubrication approximation. Consider that the channel width was along the x–z plane and the flight height was along the y-direction, with u, v, and w being the velocity components in the x, y, and z directions, respectively. Physically, the lubrication assumption implies that the effect of the velocity components u and w will be functions of y only, and v ¼ 0. Other assumptions include that gravity effects and inertia effects are negligible and also that the fluid is incompressible.
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Therefore, the governing flow equations for this specific problem are @P @ @u ¼ h @x @y @y @P @ @w ¼ h @z @y @y
(21:19) (21:20)
where P is the pressure developed. The h in the equation can be a constant (Newtonian material) or described by a power-law model. In addition to the above equations, the leakage flow is neglected by imposing that there is no net transfer of melt perpendicular to the channel walls: H ð
u dy ¼ 0
(21:21)
0
The boundary conditions are No-slip conditions on screw surface and barrel w(x, 0) ¼ w(0, y) ¼ w(W, y) ¼ 0; u(x, 0) ¼ 0 w(x, H) ¼ Vz ; u(x, H) ¼ Vx where Vx and Vz are imposed velocity components due to rotation of the barrel. These equations can be further coupled with the energy equation for nonisothermal analysis as @T @T @ @T þw k rCp u (21:22) ¼ þ hg 2 @x @z @y @y where the shear rate is given by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 @u @w g¼ þ @y @y .
(21:23)
and r, Cp, and k are the density, specific heat, and thermal conductivity of the material, respectively. The equations above describe a general problem description for the single-screw extruder. Building on these solutions, Elbirli and Lindt [14] presented a new solution for thermally developing flows in a single-screw extruder for power-law fluids. They showed that a transformation to a Lagrangian frame enables one to extend the solution to extrusion situations where appreciable ‘‘pressure back flow’’ exists. This in mathematical terms translates to reformulating the energy Equation 21.22 as rCp
@T @ @T k ¼ þ hg 2 @tR @y @y
(21:24)
where tR is the residence time of a fluid particle along a streamline. This novel treatment of the energy equation enabled the researchers to determine the performance of a screw pump by coupling the heat transfer and residence-time characteristics of the melt flow. The mathematical model was developed using standard lubrication approximations as described before. The utility of the model was demonstrated using polystyrene as a model fluid.
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Further advances were made when Meijer and Verbraak [25] modeled extrusion using slip boundary conditions. This can be mathematically described using conventions as u(x, 0) ¼ u0 such that t ¼ c0u0 u(x, H) ¼ Vx us such that t ¼ chus where c0 and ch are slip coefficients and u0 and us are slip velocities. These slip coefficients were made dimensionless by defining, B0 ¼ c0H=h and Bh ¼ chH=h. Their calculations were based on 2D Newtonian isothermal conditions with constant boundary layer parameters. A strong dependence of pumping characteristics and efficiency on the slip boundary conditions and also on the extruder length in the case of friction was found especially when slip was only allowed for at the screw surface. Thibault et al. [31] proposed a new computational model to simulate the behavior of molten polymer such as LDPE and PVC resins in the melt-conveying zone of extruders. They used a hybrid finite difference and finite element scheme for solving the equations of change governing momentum and heat transfer. The algorithm can be described as follows: Set the initial conditions Ti and Pi. For i ¼ 1 to N 1 (N ¼ number of cross sections): Calculate the cross-channel and down-channel flow profiles and the corresponding pressure gradient components. Estimate the Nusselt number at Ti. Determine viscous dissipation. Compute the temperature and pressure at the flow section (i þ 1). This algorithm is explicit and, therefore, the quality of the results depends directly on the number of cross sections used. The numerical results were validated using LDPE and PVC. As mentioned before, most of the modeling studies in single-screw extruders were performed with synthetic polymers. In food extrusion, among the first notable pieces of work is that of Gopalakrishna and Jaluria [17]. They modeled the gelatinization of starch in a singlescrew extruder using the conventional moving-barrel approach and unwinding the screw. In addition to the classical formulation, they considered the mass diffusion equation, which is written as w
@cm @ 2 cm ¼ þ S0 (cm )m , S 0 ¼ 0 for T < Tgel @z @y2
(21:25)
The last term in the above equation represents a source–sink for the diffusing species due to reaction. This term applies only when the temperature exceeds the gelatinization temperature. The authors considered the reaction to be zero order, m ¼ 0. For significant viscous dissipation within the material, the material temperature rises above the imposed barrel temperature by as much as 100%. The flow field was not affected by this change. Moisture removal and bonding due to gelatinization were observed to take place first at the screw root for higher reaction rate. Gelatinization increases the viscosity significantly, which in turn causes larger viscous heating and consequently cooking of food material. While the above work was done in single-screw extruders that were geometrically modified to be in 2D, more recently, complete 3D models have been studied. Syrjala [30] proposed a 3D fluid flow and heat transfer model that utilized a series of 2D cross sections in the crosschannel direction of an unwound single-screw to build a 3D picture of the overall flow in the axial (down-channel) direction. The authors argued that even for a large (but finite) channel width to channel depth ratio, the effects of the cross-channel circulation play an important
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FIGURE 21.1 Screw geometry and FEM mesh used for simulation using the Phan–Thien–Tanner (PTT) differential viscoelastic model. (From Dhanasekharan, M. and Kokini, J.L., J. Food Process Eng., 23, 237, 2000. With permission.)
role in the overall pressure developed in the downstream direction, and in the temperature profiles in each cross-channel plane. Using a comparison between the traditional 2D unwound model and the 3D model that they proposed, they showed the importance of velocity components across the screw channel and the role they play in convective heat transport. This in turn led to wide variations in the predicted temperature profiles, which then led to changes in viscosity and hence the associated pressure drop. This new scheme also had the advantage of modeling a high Peclet number problem without upwinding. Dhanasekharan [38] modeled Newtonian and power-law fluids in a complete 3D representation of the single-screw geometry (Figure 21.1). The author validated the simulation with available analytical results and extended the model to a dough-like rheology using the modified Morgan et al. model [39]. Profiles for velocity, temperature, pressure, and shear rates were predicted (Figure 21.2 through Figure 21.5, respectively). The predicted down-channel velocity profile is shown in Figure 21.2 at different axial locations. Vz=Vbz is the ratio of the downchannel velocity to the velocity at the barrel. The profile shows the imposed zero velocity at the screw root and the velocity of the barrel on the barrel surface. Y=H ¼ 0 indicates screw root and Y=H ¼ 1 indicates the barrel. Similarly, Z=L ¼ 0 indicates the inlet into the metering section and Z=L ¼ 1 indicates the outlet of the metering section. The flow is almost fully developed in the down-channel direction as indicated by little variation of the profile with Z=L. Figure 21.3 shows the temperature profile as a function of Y=H for different values of Z=L. In the initial portion when Z=L ¼ 0.08, the temperature at the barrel is highest (408C imposed) and the bulk of the fluid is close to 308C (imposed). As one progresses down the channel, viscous dissipation raises the temperature of wheat dough higher than the barrel temperature. Eventually, beyond a certain downstream location, heat flows from wheat dough to the barrel because of the generation of heat due to viscous dissipation. This also implies that initial heat input at the barrel is followed by heat removal beyond a particular location downstream.
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Dimensionless flight height Y/H
0.9 0.8 0.7 0.6 0.5 0.4 0.3
Z /L = 0.08 Z /L = 0.25 Z /L = 0.42 Z /L = 0.58 Z /L = 0.75 Z /L = 0.92
0.2 0.1 0 0
0.2 0.4 0.6 0.8 Dimensionless axial velocity Vz /Vbz
1
FIGURE 21.2 Prediction of the down-channel velocity profile under nonisothermal conditions. (From Dhanasekharan, M. and Kokini, J.L., J. Food Eng., 60, 421, 2003. With permission.)
The pressure distribution along the axial direction at Y=H ¼ 0.5 is shown in Figure 21.4. The pressure in the pushing flight is higher than that in the trailing flight. The observation can be translated that wheat dough flows from the pushing flight toward the trailing flight in the screw channel and wheat dough leaks from the pushing flight backward the trailing flight in the flight lands. 1 Z/L = 0.08 Z/L = 0.25 Z/L = 0.42 Z/L = 0.58 Z/L = 0.75 Z/L = 0.92
Dimensionless flight height Y/H
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 300
305
310
315
320
325
330
Temperature (K)
FIGURE 21.3 Prediction of temperature versus Y=H at different axial locations. (From Dhanasekharan, M. and Kokini, J.L., J. Food Eng., 60, 421, 2003. With permission.)
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Pressure (Pa)
1.0E+06
0.0E+00
−1.0E+06
−2.0E+06
−3.0E+06 0
0.2
0.4
0.6
0.8
1
Dimensionless axial length Z/L
FIGURE 21.4 Prediction of pressure versus axial distance. (From Dhanasekharan, M. and Kokini, J.L., J. Food Eng., 60, 421, 2003. With permission.)
The shear rate profile along the axial direction is also shown for Y=H ¼ 0.96 in Figure 21.5. The reason for the choice of Y=H ¼ 0.96 is to observe the shear rates in the flight lands. The shear rate profile shows large shear rates occurring in the flight lands compared to the shear rates in the channel. The large shear rates cause a higher power dissipation, which appears as a larger SME. The SME was predicted as 104.85 kJ=kg. Although 3D modeling of single-screw extruders with generalized Newtonian models was shown to be possible, it was not attempted in the synthetic polymers or food literature 70 60
Shear rate (s–1)
50 40 30 20 10 0 0
0.2
0.4
0.6
0.8
1
Dimensionless axial length Z/L
FIGURE 21.5 Prediction of local shear rate versus axial distance. (From Dhanasekharan, M. and Kokini, J.L., J. Food Eng., 60, 421, 2003. With permission.)
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1.1e+08 PTT Model 1.0e+08
Newtonian Model
Pressure (dyne cm–2)
9.0e+07 8.0e+07 7.0e+07 6.0e+07 5.0e+07 4.0e+07 3.0e+07 2.0e+07 0
0.2
0.4
0.6
0.8
1
Dimensionless axial length Z/L
FIGURE 21.6 Comparison of pressure profile of PTT model prediction with the Newtonian model. (From Dhanasekharan, M. and Kokini, J.L., J. Food Process Eng., 23, 237, 2000. With permission.)
with a viscoelastic constitutive model. However, as discussed before, to simulate the behavior of dough and other important biopolymers in an extruder, viscoelasticity is very important. In the only study of its kind, Dhanasekharan and Kokini [13] simulated in 3D a singlescrew extruder with the viscoelastic Phan–Thien–Tanner (PTT) constitutive model with simplified model parameters using the mesh in Figure 21.1. Even with the low degree of viscoelasticity modeled, the authors showed that the pressure developed in the PTT case was lesser than the pressure for the Newtonian case (Figure 21.6). This was attributed to the shear-thinning nature of the PTT fluid. The chosen flow conditions and extruder geometry implied a Deborah number (De) ¼ 0.001 and Weissenberg number (We) ¼ 5.22. Although this was not a high enough De to see the complete effects of viscoelasticity (which happen at a De ~ 1), the Weissenberg number was quite high for such a complex geometry and was one of the successful examples of a solution at such high Weissenberg numbers. These deviations of the viscoelastic model from a comparable non-Newtonian model that ignored the elastic effects demonstrate the compelling need for solving viscoelastic models for food extrusion.
21.4 MODELING OF TWIN-SCREW EXTRUDERS The twin-screw extruder is utilized in different configurations based on the position of the screws (intermeshing or not) and the relative direction of rotation of the screws (corotating or counter-rotating). Early numerical modeling studies of the twin-screw extruder concentrated on the melt conveying section of the screws that was modeled as 2D cross sections in a direction perpendicular to the flow. An example of such work is the studies by Janssen and coworkers [29] that discusses the relationship among the extrusion rate, the shear-thinning effect of viscosity, and the circulation flow utilizing FEM to analyze the non-Newtonian flow in twinscrew extruder. Using a similar technique, Sastrohartono et al. [27] analyzed the flow in a
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corotating partially intermeshing extruder and reported the effects of flow rate, pressure gradient, and power-law index on the flow field. Kalyon et al. [23] then worked on a nonisothermal non-Newtonian flow in a corotating intermeshing extruder and studied the mixing performance while also considering the viscous heating in the nip region. However, these 2D studies neglected leakage flow and could not take into account the helix angles in the translational region while assuming that the melt conveying regions were fully filled. The kneading block section of the screws could not be modeled at all using these techniques as the flow geometry is complex and does not lend itself suitable for 2D cross-sectional analysis as in the melt conveying section. The next advances were made by Sastrohartono et al. [28,40] who considered a 212 -D model in which the translational and intermeshing regions were solved separately and the two domains were coupled to get the final solution. Velocity, pressure, shear rate, and temperature results were obtained and the velocity results were validated with experimental data providing acceptable agreement. Although this technique provided an improved understanding, it was still not entirely accurate as the boundaries between the translational and intermeshing region were not very clear and constituted an approximation in the solution. Full 3D modeling of the real geometry is required to address these deficiencies. Initial steps in 3D to tackle the changing screw geometry as they rotated were made by meshing the discrete screw positions at different rotational positions and modeling each step as a quasi-steady-state solution. Mours et al. [26], Bravo et al. [9,41], and the research group led by Funatsu have all utilized this approach to model either the melt conveying or kneading block sections of a twin-screw extruder. While Mours et al. [26] utilized an automatic grid generator to create meshes at each step, Funatsu’s group used a coordinate system that moved in the axial direction parallel to the flights to fix the geometry of the analysis domain [22,32]. Later work by Funatsu’s group [19–21] and also by Bravo et al. [9,41] used a quasi-steady-state analysis with the mesh at each step manually generated at given increments. Funatsu and coworkers have used Bird–Carreau and cross generalized Newtonian constitutive models that fit polypropylene steady shear experimental data to numerically solve twin-screw extrusion problems under nonisothermal conditions using a quasi-steady-state approach. They modeled individual geometries with meshes for each discrete position of the screws (at every 158 rotation, Figure 21.7) [19,21]. The pressures and temperatures predicted by the simulation results were experimentally validated with measurements taken far away from the nip at the top of the barrel using polypropylene melts in several fully filled twin-screw extruder configurations with a range of operating conditions and showed good agreement for lower screw speeds (Figure 21.8 and Figure 21.9) [19,21]. Using the validated solutions from their previous studies, they then went on to solve particle marker tracking problems to obtain mixing performance indices that included RTD, stress distribution, mean nearest distance between markers, backward flow mixing index, area stretch, strain history, and SME [21]. Similarly, Bravo et al. [9] simulated the intermeshing corotating and counter-rotating kneading block section of a twin-screw extruder using a similar quasi-steadystate approach to obtain experimentally validated pressure results that were in close correlation with available data. Recently, Zhu et al. [34] simulated the reaction extrusion of e-caprolactone in a twin-screw extruder using a finite volume and quasi-steady-state technique. They used the Yasuda– Carreau equation to model for viscosity changes and incorporated a rate of reaction heat generation term into the energy conservation equation. A first-order reaction term was used for the kinetic polymerization during extrusion. The influence of screw geometry (screw pitch), screw speeds, initial conversion of the material at the inlet, and the (material viscosity dependent) viscous dissipation on the conversion rate of e-caprolactone was studied. It was concluded that all the variables studied played a significant role and had a complex
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a = 0⬚ Y a
a = 15⬚
X
a = 30⬚
a = 45⬚
a = 60⬚
a = 75⬚
FIGURE 21.7 Sequential geometries of a twin-screw extruder representing a quarter of rotation cycle. (From Ishikawa, T., Kihara, S.I., and Funatsu, K., Poly. Eng. Sci., 40, 357, 2000. With permission.)
interdependence on each other in influencing the final conversion rate. This study is a significant improvement in modeling reactions during extrusion and similar examples in twin-screw food extrusion modeling are not available. With the development of techniques like the fictitious domain method and mesh superposition technique (MST) (described in detail in Chapter 23), full 3D transient simulations of the twin-screw geometry were made possible. To validate these new techniques, Avalosse and Rubin [6] modeled the flow and mixing in a complete 3D single-screw extruder using the MST 3.0 Measured Calculated
Pressure (MPa)
2.5
2.0
1.5
1.0 0
60 120 Rotational degree a (°)
180
FIGURE 21.8 Comparison between calculated and experimental value of pressure profiles at a point on the upper left part of a twin-screw barrel; rpm ¼ 200. (From Ishikawa, T., Kihara, S.I., and Funatsu, K., Poly. Eng. Sci., 40, 357, 2000. With permission.)
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250 100 rpm 200 rpm 400 rpm
240 Temperature (⬚C)
Calculated 230
220
210
200 0
0.02
0.04
0.06
0.08
0.1
Axial distance (m)
FIGURE 21.9 Comparison between calculated and experimental value of temperature profiles in the axial direction at different rotational speeds. (From Ishikawa, T., Kihara, S.I., and Funatsu, K., Poly. Eng. Sci., 40, 357, 2000. With permission.)
with a Bird–Carreau viscous fluid model for HDPE and compared the results to those obtained with a rotating reference frame and obtained a good match. They then evaluated different types of finite elements in improving accuracy of the MST simulation and concluded that the mini-element velocity and constant pressure elements for the interpolation provided the best results. Avalosse et al. [7] then conducted a transient 3D simulation of the kneading block section of an intermeshing corotating twin-screw extruder using MST. They used the same model geometry as that used by Ishikawa et al. [19] and further verified MST with the experimental and quasi-steady-state numerical results provided in Ishikawa et al. [19]. After achieving good correlation with published data (Figure 21.10), they extended the same simulation to a counter-rotating geometry to observe the differences. They concluded that the counterrotating geometry achieved lesser shear rate and pressures than the corotating geometry and reduced torque requirements by about 20%. To further improve the accuracy of numerical simulations in the critical shear regions in the intermeshing region and in the gaps between the barrel and screws, Bertrand et al. [8] implemented an adaptive meshing strategy that is based on mesh refinement of a reference mesh which is refined at each time-step to adapt locally to the position of the gaps in the computational domain (Figure 21.11). The method was utilized with flow in a twin-screw extruder in 2D. When the accuracy of the simulations was compared to the experimental values (Figure 21.12), it was observed that there was a good agreement between the two, with less than 7% relative error.
21.5 OPTIMIZATION OF EXTRUDERS Design changes such as the ratio of the length of the screw over its diameter (L=D) in a single-screw extruder or the stagger angle of kneading blocks in a twin-screw extruder are used to optimize the design of an extruder for a chosen operation (typically a mixing operation). An example of such an optimization in a single-screw extruder is a recent study by Manas-Zloczower and coworkers
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3.00e+06
Pressure (Pa)
Num. (Funatsu)
2.00e+06
Exp. (Funatsu) 1.00e+06 MST
0.00e+00 0
25
50
75
100
Rotational degree (°)
FIGURE 21.10 Comparison of pressure profiles generated by MST and quasisteady techniques with experimental data. (From Avalosse, T., Rubin, Y., and Fondin, L., J. Reinf. Plast. Comp., 21, 419, 2002. With permission.)
[42] that modeled an unwound single-screw extruder with diagonal ridges or pins on the surface of the screw (Figure 21.13), and studied the effects of these design changes on the mixing efficiency of the extruder. They concluded that the pin geometry was more efficient at dispersive mixing than the ridged or plain screw geometries. Dhanasekharan and Kokini [43] also developed design charts that accounted for the influence of design variables such as screw pitch, flight height, screw and barrel diameter, flight width, and L=D ratio on SME and RTD (Figure 21.23 and Figure 21.24). While their design charts were subsequently used for a scaling analysis, they could also be used effectively in optimizing a single-screw extrusion process with specific process targets. However, such studies on single-screw extruders are less common and design optimization is more prevalent in the screw design of twin-screw extruders—especially the kneading and mixing section of the twin screw. Reference mesh
Two-level refinement
FIGURE 21.11 Two-level adaptive mesh refinement procedure in the vicinity of the gaps. (From Bertrand, F., Thibault, F., Delamare, L., and Tanguy, P.A., Comput. Chem. Eng., 27, 491, 2003. With permission.)
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4.00e+03
Pressure (kPa)
3.75e+03 3.50e+03 3.25e+03 3.00e+03 Experimental Numerical
2.75e+03 2.50e+03 0
(a)
50
100
150 200 Screw rotation (°)
250
300
350
(b)
FIGURE 21.12 Variation of pressure with screw position. Simulated values from adapted mesh. (From Bertrand, F., Thibault, F., Delamare, L., and Tanguy, P.A., Comput. Chem. Eng., 27, 491, 2003. With permission.)
FIGURE 21.13 Different geometries for unwound channel of single-screw extruder: (a) simple channel, (b) channel with diagonal ridges, and (c) channel with pin. (From Camesasca, M., Manas-Zloczower, I., and Kaufman, M., Plast. Rubber Compos., 33, 372, 2004. With permission.)
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Manas-Zloczower’s research group has worked for several years on numerically simulating various twin-screw configurations and optimizing these configurations to improve the twin-screw extruder’s distributive and dispersive mixing capabilities. Cheng and ManasZloczower [11] used a quasi-steady-state approach and a finite volume method to analyze the dispersive mixing efficiency of the kneading block section of two twin-screw extruders with different screw diameters. A three-lobed kneading disk was employed in the larger ZSK-53 twin-screw extruder, whereas the smaller ZSK-30 used a two-lobed kneading disk (Figure 21.14). This difference in the kneading blocks allowed the ZSK-53 to provide better flow-field characteristics for dispersive mixing while concurrently extracting a higher penalty in terms of the torque or power used. This study was followed by another on the distributive mixing efficiency of the ZSK-53 twin-screw extruder [12]. In this second study, the authors explored the effect of screw speed on distributive mixing in the conveying elements of the extruder. They concluded that distributive mixing improved with higher screw speeds and also that the frequent folding and reorientation of the material when it is transferred from one screw to the other improved distributive mixing.
FIGURE 21.14 Mesh design (a) ZSK-53 forward configuration and (b) ZSK-30 forward configuration; rotors rotating clockwise. (From Cheng, H.F. and Manas-Zloczower, I., Polym. Eng. Sci., 37, 1082, 1997. With permission.)
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FIGURE 21.15 Disk surface of three-tip kneading blocks (a) neutral, (b) L30, and (c) R30 types. (From Yoshinaga, M., Katsuki, S., Miyazaki, M., Liu, L.J., Kihara, S.I., and Funatsu, K., Polym. Eng. Sci., 40, 168, 2000. With permission.)
Later, Funatsu’s group conducted similar research on the effects of various geometrical design parameters on the operation of the extruder. Yoshinaga et al. [32] studied a three lobed kneading disk with three disks at different stagger angles (Figure 21.15) to evaluate their effect on distributive mixing and concluded that a neutral stagger angle provided the best mixing using a form of segregation scale as the criterion. This was followed by a study conducted by Ishikawa et al. [20] on kneading disks with different thicknesses and stagger angles (Figure 21.16) and their effect on temperature and pressure distributions using nonisothermal simulations. The disk width was shown not to have any effect in pressure or temperature distributions in the axial direction. They showed that the pressure gradient was small when the kneading blocks were arranged in a forward (pumping) stagger (FFF) and larger for the backward (reverse flow) stagger (BBB) (Figure 21.17). When the influence of stagger angle on the
y
x
Transport direction
z FFF (L /D = 0.5 ⫻ 3)
FNB (L /D = 0.5 ⫻ 3)
NNN (L /D = 0.5 ⫻ 3)
BBB (L /D = 0.5 ⫻ 3)
NNW (L /D = 1.0 ⫻ 1.5)
NWW (L /D = 1.5 ⫻ 1)
FIGURE 21.16 Screw configurations used in numerical analysis. (From Ishikawa, T., Kihara, S.I., and Funatsu, K., Polym. Eng. Sci., 41, 840, 2001. With permission.)
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1.0 FFF NNN
0.8
BBB
Pressure (MPa)
FNB 0.6
0.4
0.2
0.0
0
0.01
0.02
0.03
0.04
0.05
Axial distance (m)
FIGURE 21.17 Pressure distributions in the axial direction with different stagger angles. (From Ishikawa, T., Kihara, S.I., and Funatsu, K., Polym. Eng. Sci., 41, 840, 2001. With permission.)
axial temperature distribution was observed, it was once again seen that the backward flow caused by the BBB configuration increased the temperature higher than the FFF configuration (Figure 21.18) They also showed that the FNB configuration provided the highest dispersive and 270
Temperature (⬚C)
260
250
FFF NNN BBB FNB
240
230
220 0
0.01
0.02
0.03
0.04
0.05
Axial distance (m)
FIGURE 21.18 Temperature distributions in the axial direction with different stagger angles. (From Ishikawa, T., Kihara, S.I., and Funatsu, K., Polym. Eng. Sci., 41, 840, 2001. With permission.)
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FIGURE 21.19 (a) SME: right handed screw with left handed slots, (b) right handed full flight screw, and (c) right handed kneading block with 458 stagger. (From Ishikawa, T., Amano, T., Kihara, S.I., and Funatsu, K., Polym. Eng. Sci., 42, 925, 2002. With permission.)
distributive mixing as the number of particles passing through the highest stress regions and those experiencing high area stretches is highest in this configuration. Ishikawa et al. [21] then conducted simulations on a new type of screw mixing element (Figure 21.19) whose performance was numerically compared to a full-flighted conveying screw and a 458 staggered kneading block. Comparison of pressure profiles between the fully flighted conveying screw (FF) and the screw mixing element (Figure 21.20) showed significant leakage flow in the screw mixing element through the slots in its design while establishing good correlation with experimental results. The authors showed that this backflow or leakage flow in the screw mixing element (SME) screw design caused it to broaden the residence time distribution and improve dispersive and distributive mixing capabilities at high screw speeds. These studies [16,21] showed the degree of maturity in CFD work that could comprehensively compare different screw elements in their distributive and dispersive mixing abilities and enabled design and optimization decisions using CFD. However, these simulations were still time consuming due to the nature of the quasi-steady-state simulations—namely using different meshes for each new position of the screws.
2.0e+06
Pressure (Pa)
1.5e+06
1.0e+06
SME 200 rpm calc. SME 200 rpm exp. FF 200 rpm calc. FF 200 rpm exp. KB 200 rpm calc. KB 200 rpm exp.
5.0e+05
0.0e+00
0
0.01
0.02
0.03
0.04
Axial distance (m)
FIGURE 21.20 Effect of screw element type on pressure developed across the extruder. (From Ishikawa, T., Amano, T., Kihara, S.I., and Funatsu, K., Polym. Eng. Sci., 42, 925, 2002. With permission.)
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Type of kneading block
Base view
Side view
Natural elements 10 ds r = 90° length = 40 mm (kb 90/10/40)
Natural elements 9 ds r = 90° length = 40 mm (kb 90/8/40)
Pump elements 6 ds r = 45° length = 40 mm (kb 90/5/40)
Reverse elements 5 ds r = −45° length = 40 mm (kb −45/6/40)
FIGURE 21.21 Element configuration of kneading blocks investigated by Alsteens and co-workers. (From Alsteens, B., Legat, V., and Avalosse, T., Int. Polym. Process., 19, 207, 2004. With permission.)
Further advances in numerical simulation techniques using MST and fictitious domain methods have since been employed to optimize extruder design. Alsteens et al. [5] have successfully used MST to simulate kneading blocks with different lengths and stagger angles (Figure 21.21) and evaluated their suitability for distributive and dispersive mixing. The authors conducted simulations having finite elements with different degrees of freedom to test for improvement in accuracy while not significantly affecting the computational costs. They chose the mini-element for velocity with constant pressure element as the best compromise. Using distributions of residence time, pressure drops across the screw, shear rates experienced in different areas of the extruder, and also a global stretching efficiency, they concluded that a reverse flow configuration with larger disk widths provides the most mixing (Table 21.1). But this configuration carries a heavy penalty in power consumption (Table 21.1) and they recommended the neutral configuration as the best compromise.
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TABLE 21.1 Characteristic Values of Process Indicators for Different Kneading Block Configurations Element Property Power (W) Pressure drop (Pa) Residence time 75% (s) Percent of fluid mass with shear rate >50 s1 >150 s1 >300 s1 50th percentile of the maximum of shear rate on the exit plane (s1) Total shear 75% at the exit plane Global stretching efficiency at the exit plane
Neutral 10 Discs 602 3e5 10.4
Neutral 5 Discs
Pump 5 Discs
Reverse 5 Discs
548 2,5e5 2.96
582 5e5 2.69
618 10e5 6.67
79 29.6 7.9 706
80.7 22.2 6.5 492
78 30 5.97 431
59.7 22.2 6 841
716 4.9e 3
402 1.3e 2
377 5.8e 3
629 5.6e3
Source: From Alsteens, B., Legat. V., and Avalosse, T. Int. Polym. Process, 19, 207, 2004. With permission.
21.6 EXTRUDER SCALING Extrusion scaling has remained only a partially solved problem over the years. Most scaling principles developed thus far are based on dimensional analysis relationships. If all dimensions of the extruder were increased by a factor f, flow and power requirements would theoretically increase by a factor of f3. However, the heat transfer for heating the barrel and also the viscous dissipation of mechanical energy will increase as f2, because they are related to surface area. For proper scaling of an extruder it is essential to change the screw diameter, channel depth, and screw speed in such a manner that the heat transfer area, flow rate, and mechanical energy input also change approximately at the same rate, while keeping the residence times and shear rates constant. One of the early scale-up theories for polymer extrusion was derived by Carvey and McKelvey [44] and subsequently followed by several workers [45,46]. However, these theories were not general enough to apply for both low and high Brinkman numbers and in particular could not be applied directly to food materials whose rheology is strongly affected by moisture, temperature, and shear rate. Rauwendaal [47] conducted a fundamental analysis of scale-up in plasticating singlescrew extruders using solids conveying, mixing, residence time, heat transfer, power consumption, and specific energy consumption as evaluation tools for extrusion performance. Two theories were developed by Rauwendaal [47] and were based on ideas of constant SME and high throughput rates. The first method, valid for high Brinkman numbers, kept the specific surface area constant, whereas the second method, which can be used for low Brinkman numbers, kept the melting rate equal to pumping rate (Table 21.2). Yacu [2] provided a good review of existing analytical scale-up theories for thermoplastic single- and twin-screw extruders. The review primarily focussed on Rauwendaal [48] and three methods were discussed. The scaling charts for the three methods are shown in Table 21.3. In the first method, scale-up factors are defined such that the output capacity is increased in relation to surface area while maintaining constant shear rate in the channel. From this scale-up
0 0 3
3 3 0 0 3 0
v
1þvh
hþ2þv
1 þ 1=2v þ l
2 þ v þ 1=2nv þ l
hþ2þv
l1v
lh
l þ n þ 2 þ nv þ v nh
l h þ n þ nv nh
lh1v
Screw speed
Shear rate
Pumping rate
Melting ratea
Melting rateb
Solids conveying rate
Residence time
Shear strain
Power consumption
Specific energy const.
Area=Throughput
b
a
At low Brinkman numbers. At high Brinkman numbers.
Source: From Rauwendaal, C., Polym. Eng. Sci. 27, 1059, 1987. With permission.
1
2
1
l
Axial length
1
H
Carley=McKelvey
Channel depth
Basic Relationships
TABLE 21.2 Scaling Relationships of Different Theories
0
0.5
2.5
0.5
0.5
2
2.51=4n
1.75
2
0
0.5
1
0.5
Maddock
Pearson
3 þ 7n 2 þ 4n n2 þ 9n þ 6 2 þ 4n
1 þ 5n 1 þ 3n n2 þ 6n þ 1 1 þ 3n 1 þ 5n 1 þ 3n
0
0
2
n 1 þ 2n
2n 1 þ 3n 1 þ 5n 1 þ 3n 0 1þn 1 þ 3n
1þn 1 þ 2n
2 þ 2n 1 þ 3n
2
2
1 þ 5n 1 þ 3n
1 þ 2n 2n 0 1 2
1 2
1þn 2n
n2 þ 3n þ 1 4n 1 þ 2n 2n
1 þ 2n 2n
1 þ 2n 2n
1 2n
1 1 þ 2n
2 1 þ 3n
1 1þn 1 þ 2n
1 2 þ 2n 1 þ 3n
Rauwendaal (II) 1 2n 1þn 2n 1
Rauwendaal (I) 1þn 1 þ 2n
1þn 1 þ 3n
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TABLE 21.3 Results of Common Scale-Up Factors Large Extruder
Parameter Diameter Channel Width Channel Depth Screw Speed Screw Tip Speed Shear Rate Residence Time Solid Conveying Rate Melting Capacity Melting Conveying Rate Specific Energy Consumption
Small Extruder
Common Scale-Up Factors
Scale-Up for Heat Transfer
Scale-Up for Mixing
D1 W1 H1 N1 Vb1 g1 t1 Ms1
D2 W2 ¼ W1(D2=D1) H2 ¼ H1(D2=D1)0.5 N2 ¼ N1(D1=D2)0.5 Vb2 ¼ Vb1(D2=D1) g2 ¼ g1 t2 ¼ t1(D2=D1)0.5 Ms2 ¼ Ms1(D2=D1)2
D2 W2 ¼ W1(D2=D1) H2 ¼ H1(D2=D1)0.5 N2 ¼ N1(D1=D2) Vb2 ¼ Vb1 g2 ¼ g1(D1=D2)0.5 t2 ¼ t1(D2=D1) Ms2 ¼ Ms1(D2=D1)1.5
D2 W2 ¼ W1(D2=D1) H2 ¼ H1(D2=D1) N2 ¼ N1 Vb2 ¼ Vb1(D2=D1) g2 ¼ g1 t2 ¼ t1 Ms2 ¼ Ms1(D2=D1)3
Mp1 V1
Mp2 ¼ Mp1(D2=D1)1.75 V2 ¼ V1(D2=D1)2
Mp2 ¼ Mp1(D2=D1)1.5 V2 ¼ V1(D2=D1)1.5
Mp2 ¼ Mp1(D2=D1)2 V2 ¼ V1(D2=D1)3
Z1
Z2 ¼ Z1(D2=D1)0.5
Z2 ¼ Z1
Z2 ¼ Z1
Source: From Rauwendaal, C., in Polymer Extrusion, Hanser Publications, New York, 1986. With permission.
method it can be seen that the larger extruder will provide longer residence time and higher specific energy input. The second method is used primarily for plastics processing where heat convection, heat conduction, and viscous dissipation all play significant roles in the melting process. In this method the residence time increases and the shear rate decreases with diameter. The third method needs the residence time and shear rate to remain constant in the two extruders. This can be achieved by maintaining geometric similarity in the two extruders while operating at the same screw speed. However, the melting capacity does not match the increased output capacity and this is undesirable in thermoplastic extrusion. Extruder scaling through CFD was done in the past using simplistic dimensionless equations obtained by solving a 2D flow problem using Newtonian or power-law fluids [4,24,33]. These equations considered an isothermal flow while neglecting leakage flow between the flights and curvature in the screw geometry [18]. The inaccuracy of such dimensionless equations made the scaling laws less practical. Dhanasekharan and Kokini [43] were the first to successfully demonstrate the simultaneous scale-up of mixing and heat transfer using a full 3D FEM simulation of the flow in a single-screw extruder. They utilized a rotating barrel technique with a modified Morgan et al. [39] fluid rheology to model the flow of dough-like material in the extruder. SME and RTD were used to scale-up heat transfer and mixing, respectively. Several design variables such as screw pitch, flight height, screw and barrel diameter, flight width, and L=D ratio were varied (Table 21.4) and a series of screw geometries were developed (Figure 21.22) [38]. SME and RTD results were obtained for changes in each of these design parameters and design charts were constructed that showed the influence of each of these design parameters on SME (Figure 21.23) and RTD (Figure 21.24) [43]. Figure 21.23 shows that increasing the screw diameter while keeping the channel depth and helix angle constant increases SME. The authors explained this with the fact that when D=H is increased, H=W decreases. In the current case when D=H ¼ 3.33, H=W ¼ 0.374 and
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TABLE 21.4 Design Variables Used in the Development of Trend Charts and Their Values Variable D=H at two different values of H Helix angle Clearance L=D
Limits 3.33, 5, 6.5, 8 17.668–408 0–0.3 mm 3–6
Source: From Dhanasekharan, M. and Kokini, J.L., J. Food Eng. 60, 421, 2003. With permission.
when D=H ¼ 8, H=W ¼ 0.156. A shallower channel causes higher shear rates due to higher velocity gradients. Therefore, the SME increases with D=H at constant helix angle. An increase in the helix angle keeping D=H and L=D constant decreases SME because of less number of turns. The number of turns in the screw when u ¼ 17.668 is 6, while the number of turns when u ¼ 408 is 2.3 keeping D=H constant. This reduction in the number of turns while keeping the other parameters constant also results in a reduction of local shear rates and therefore produces a smaller SME. Similarly, the effects of channel depth, L=D and clearance on SME were also evaluated and conclusions were drawn on the changes in the screw design, which would keep the SME constant as shown below: 1. Decrease H and increase D=H while keeping tan u constant. 2. Decrease H and increase D=H and increase tan u. 3. Decrease clearance or L=D or both and increase D=H.
a) D/H = 3.33, q = 17.66⬚, H = 0.381 cm, e = 0.3 mm, L/D = 6
b) D/H = 3.33, q = 17.66⬚, H = 0.381 cm, e = 0.3 mm, L/D = 3
c) D/H = 3.33, q = 40⬚, H = 0.381 cm, e = 0.3 mm, L/D = 6
d) D/H = 5, q = 17.66⬚, H = 0.381 cm, e = 0.3 mm, L/D = 3
FIGURE 21.22 Examples of screw geometries used to produce design charts. (From Dhanasekharan, M., Ph.D. dissertation, Rutgers, The State University of New Jersey, New Brunswick, New Jersey, 2001.)
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450 q = 17° q = 40° H=1 e=0 L/D = 3
400
SME (kJ/kg−1)
350 300 250 200 150 100 50 3
4
5
6
7
8
9
Dimensionless distance D/H
FIGURE 21.23 Hybrid SME trend chart with screw geometry parameters. When not mentioned, the parameters are u ¼ 17.668, « ¼ 0.3 mm, H ¼ 0.381 cm, and L=D ¼ 6. (From Dhanasekharan, M. and Kokini, J.L., J. Food Eng., 60, 421, 2003. With permission.)
However, all these changes may not allow for the RTD to remain constant. Hence, a detailed analysis of the RTD curves was also performed and an example is shown in Figure 21.24. Using a strategy of keeping the SME and RTD constant between two extruders for scaleup, the authors suggested two geometries—geometry 1 (Figure 21.25) with a high throughput 0.2 D/H = 5; L /D = 3 D/H = 5; L /D = 6 D/H = 3.33; L /D = 3 D/H = 3.33; L /D = 6
Residence time distribution E(t)
0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0
20
40
60
Time (s)
FIGURE 21.24 Effect of L=D on RTD for D=H ¼ 3.33 and 5. Other screw parameters are « ¼ 0.3 mm, H ¼ 0.381 cm, and u ¼ 17.668. (From Dhanasekharan, M. and Kokini, J.L., J. Food Eng., 60, 421, 2003. With permission.)
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FIGURE 21.25 Screw geometry and FEM mesh for D ¼ 3.5 cm, H ¼ 1 cm, D=H ¼ 3.5, u ¼ 17.668, « ¼ 0.03 cm, and L=D ¼ 6—Geometry 1. (From Dhanasekharan, M. and Kokini, J.L., J. Food Eng., 60, 421, 2003. With permission.)
of 17.39 kg=h and geometry 2 (Figure 21.26) with a lower throughput of 1.63 kg=h as two extruders of different sizes that could provide similar performance. They then went on to demonstrate this idea by numerically simulating the two extruders and verifying that the SME and RTD in the two extruders were similar. The SME in geometry 1 and geometry 2 was 164.42 and 152.57 kJ=kg, respectively, while the average residence time was 31.16 and 31.81 s, respectively. These simulations are a valuable indicator of the progress that can be made through numerical modeling of extrusion and its practical significance.
21.7 CONCLUSIONS Recent advances in modeling complex intermeshing geometries with constantly changing boundaries have successfully allowed sophisticated CFD modeling of various transport phenomena during extrusion processing. The current state-of-the-art allows for a geometrically accurate 3D numerical simulation of a section of an extruder with realistic rheological and boundary conditions. Such simulations have allowed for improved design and optimization decisions, particularly in synthetic polymer processing that have simple rheology with few or no reactions during extrusion. Although some progress has been made in incorporating complexities such as reactions during extrusion and viscoelastic rheology to account for food extrusion, future work should address these issues in greater depth for true applicability to food extrusion. Progress also needs to be made in comprehensively extending the work done on optimizing extruders to address scale-up of twin-screw extruders. In addition, more experimental data is needed in food extruders to validate the CFD simulations and for more accurate definitions of fluid models and boundary conditions. In spite of all the issues, CFD modeling of food extrusion has indeed made rapid advances in the recent past and tremendous insights have been gained and will continue to be made in the design, optimization, and scale-up of extruders.
FIGURE 21.26 Screw geometry and FEM mesh for D ¼ 1.6 cm, H ¼ 0.381 cm, u ¼ 408, « ¼ 0.03 cm, and L=D ¼ 6—Geometry 2. (From Dhanasekharan, M. and Kokini, J.L., J. Food Eng., 60, 421, 2003. With permission.)
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NOMENCLATURE A C(T ) c 0, c h D De El f H I i,j K k k p ph q QEAS r RTD SME T T t T1 T2 u, v, w u0, u s v vh Vx Vz W g_ l s D r h h1 h2 r ci, pi, fi
generalized differential viscoelastic extra-stress multiplier heat capacity as a function of temperature (J kg1) slip coefficients rate of strain tensor (s1) Deborah number elasticity number body force (dyne or newton) flight height (cm) unit tensor index variables artificial diffusivity applied by streamline upwinding (SU) unit vector in the z direction SU artificial diffusivity constant pressure (Pa or dyne cm2) pressure field heat flux (J m2 s1) equiangle skew volumetric heat source (W m3) residence time distribution specific mechanical energy extra-stress tensor (Pa or dyne cm2) temperature (K) time (s or min) viscoelastic solute stress tensor T generalized Newtonian solvent stress tensor T velocity components (m s1) slip velocities (cm s1) velocity vector (cm s1 or m s1) velocity field imposed velocity in the x-direction (cm s1) imposed velocity in the z-direction (cm s1) flight width (cm) strain rate or shear rate (s1) relaxation time (s) total stress tensor viscous dissipation (Pa s1 or dyne cm2 s1) differential operator viscosity or partial viscosity (Pa s or poise) viscoelastic solute viscosity generalized Newtonian solvent viscosity density (kg m3 or g ml1) shape functions
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25. H.E.H. Meijer and C.P.J.M. Verbraak. Modeling of extrusion with slip boundary conditions. Polymer Engineering and Science 28: 758–772, 1988. 26. M. Mours, D. Reinelt, H.G. Wagner, N. Gilbert, and J. Hofmann. Melt conveying in co-rotating twin screw extruders—experiment and numerical simulation. International Polymer Processing 15: 124–132, 2000. 27. T. Sastrohartono, M. Esseghir, T. Kwon, and V. Sernas. Numerical and experimental studies of the flow in the nip region of a partially intermeshing co-rotating twin-screw extruder. Polymer Engineering and Science 30: 1382–1398, 1990. 28. T. Sastrohartono, Y. Jaluria, and M.V. Karwe. Numerical coupling of multiple-region simulations to study transport in a twin-screw extruder. Numerical Heat Transfer Part A—Applications 25: 541– 557, 1994. 29. J.A. Speur, H. Mavridis, J. Vlachopoulos, and L.P.B.M. Janssen. Flow patterns in the calender gap of a counter-rotating twin screw extruder. Advances in Polymer Technology 7: 39–48, 1987. 30. S. Syrjala. On the analysis of fluid flow and heat transfer in the melt conveying section of a singlescrew extruder. Numerical Heat Transfer, Part A—Applications 35: 25–47, 1999. 31. F. Thibault, P.A. Tanguy, and D. Blouin. A numerical-model for single-screw extrusion with poly(vinyl chloride) (Pvc) resins. Polymer Engineering and Science 34: 1377–1386, 1994. 32. M. Yoshinaga, S. Katsuki, M. Miyazaki, L.J. Liu, S.I. Kihara, and K. Funatsu. Mixing mechanism of three-tip kneading block in twin screw extruders. Polymer Engineering and Science 40: 168–178, 2000. 33. H.J. Zamodits and J.R.A. Pearson. Flow of polymer melts in extruders—1. Transactions of the Society of Rheology 13: 357–385, 1969. 34. L.J. Zhu, K.A. Narh, and K.S. Hyun. Investigation of mixing mechanisms and energy balance in reactive extrusion using three-dimensional numerical simulation method. International Journal of Heat and Mass Transfer 48: 3411–3422, 2005. 35. J.N. Reddy. An Introduction to the Finite Element Method. Singapore. McGraw-Hill, 1993, pp. 13–14. 36. M.J. Crochet. Numerical simulation of viscoelastic flow: a review. Rubber Chemistry and Technology 62: 426–455, 1989. 37. K.H. Huebner. The Finite Element Method for Engineers. New York: John Wiley, 1975. 38. M. Dhanasekharan. Dough rheology and extrusion: design and scaling by numerical simulation. Ph.D. dissertation, Rutgers, The State University of New Jersey, New Brunswick, New Jersey, 2001. 39. R.G. Morgan, J.F. Steffe, and R.Y. Ofoli. A generalized viscosity model for extrusion of protein doughs. Journal of Food Process Engineering 11: 55–78, 1989. 40. T. Sastrohartono, Y. Jaluria, and M.V. Karwe. Numerical-simulation of fluid-flow and heattransfer in twin-screw extruders for non-Newtonian materials. Polymer Engineering and Science 35: 1213–1221, 1995. 41. V.L. Bravo, A.N. Hrymak, and J.D. Wright. Study of particle trajectories, residence times and flow behavior in kneading discs of intermeshing co-rotating twin-screw extruders. Polymer Engineering and Science 44: 779–793, 2004. 42. M. Camesasca, I. Manas-Zloczower, and M. Kaufman. Influence of extruder geometry on laminar mixing: entropic analysis. Plastics Rubber and Composites 33: 372–376, 2004. 43. M. Dhanasekharan and J.L. Kokini. Design and scaling of wheat dough extrusion by numerical simulation of flow and heat transfer. Journal of Food Engineering 60: 421–430, 2003. 44. J.F. Carley and J.M. McKelvey. Extruder scale-up theory and experiments. Industrial and Engineering Chemistry Research 45: 989–992, 1953. 45. R.T. Fenner and J. Williams. Some experiments on polymer melt flow in single screw extruders. Journal of Mechanical Engineering Science 13: 65–74, 1971. 46. B.H. Maddock. Extruder scale-up by computer. Polymer Engineering and Science 14: 853–858, 1974. 47. C. Rauwendaal. Scale-up of single screw extruders. Polymer Engineering and Science 27: 1059– 1068, 1987. 48. C. Rauwendaal. Polymer Extrusion. New York: Hanser Publications, 1986.
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Modeling of High-Pressure Food Processing Using CFD A.G. Abdul Ghani and Mohammed M. Farid
CONTENTS 22.1
Introduction ............................................................................................................. 537 22.1.1 High-Pressure Processing of Food .............................................................. 537 22.1.2 High-Pressure Processing Applications....................................................... 538 22.1.3 Combined Effect of Temperature and Pressure .......................................... 539 22.1.4 Analysis of High-Pressure Processing Using CFD ..................................... 539 22.1.5 HPP Research Work and the Current Study .............................................. 540 22.2 Simulations of Solid–Liquid Food Mixture in High-Pressure Processing................ 540 22.2.1 Numerical Approximations and Model Parameters ................................... 540 22.2.2 Computational Grid ................................................................................... 541 22.2.3 Governing Equations and Boundary Conditions for the Liquid ................ 542 22.2.4 Governing Equations for the Solid ............................................................. 543 22.2.5 Compression Steps ...................................................................................... 543 22.2.6 Physical Properties ...................................................................................... 543 22.2.7 Results and Discussions .............................................................................. 545 22.2.7.1 Compression of Liquid Food...................................................... 546 22.2.7.2 Compression of Mixture of a Liquid and Solid.......................... 546 22.2.7.3 Experimental Validations............................................................ 548 22.3 A Simulation to Study the Convection Currents of Liquid Food in a Nonadiabatic High-Pressure Processing ........................................................... 548 22.3.1 Numerical Approximations and Model Parameters ................................... 548 22.3.2 Results and Discussions .............................................................................. 549 22.3.3 Experimental Validation ............................................................................. 551 22.4 Conclusions .............................................................................................................. 553 Nomenclature ..................................................................................................................... 553 References .......................................................................................................................... 553
22.1 INTRODUCTION 22.1.1 HIGH-PRESSURE PROCESSING
OF
FOOD
High-pressure processing (HPP) is a nonthermal sterilization of liquid and solid food by the application of high pressure of the order 3000–8000 atm. The process retains the food’s quality of freshness and nutrient such as vitamins. HPP of foods is of increasing interest because it permits microbial inactivation at low or moderate temperature with minimum degradation.
537
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HPP can be applied to a large number of food products ( juices, milk, meat, and other solid foods) using batch or continuous treatment units. It has become clear in the last decade that HPP may offer major advantages to the food preservation and processing industry [1,2]. Next to the inactivation of microorganisms and spoilage enzymes [3,4], promising results have been obtained with respect to the application on gelation of food proteins [5,6], improving digestibility of proteins and tenderization of meat products [7,8]. During compression, the liquid food is pumped to the treatment chamber using a highpressure pump followed by an intensifier. Liquids at extreme high pressure are compressible requiring extra fluid to be pumped to the treatment chamber. The increase in temperature due to compression induces heat transfer within the liquid and heat exchange with the treatment chamber’s walls. As a consequence, fluid density differences occur, which lead to free convection motion of the fluid. The fluid motion generated by forced and free convection strongly influences the temporal and spatial distribution of the temperature, which has already been observed using experimental techniques [9]. The adiabatic heating caused by the fluid compressing (or solid–liquid) can lead to significant temperature distribution throughout the treated food. The inaccurate evaluation of this temperature variation would lead to incorrect scale-up of the HPP units from laboratory size to industrial size. In this chapter, the effects of transient pressure and the temperature distribution are analyzed and studied.
22.1.2 HIGH-PRESSURE PROCESSING APPLICATIONS HPP can be used not only for preservation but also for modifying the physical and functional properties of foods and can be applied to a large number of food products ( juices, milk, meat, and other solid foods) using batch or continuous treatment units. Some HPP-treated commercial food products such as juices, jams, jellies, yogurts, meat, and oysters, which are treated by HPP, are already available in the market in US, Europe, and Japan. Some of the features of HPP are .
.
.
.
. .
HPP can work without significant heating that can damage the taste, texture, and nutritional value of the food. Since spoilage organisms can be destroyed, foods will actually stay fresher. HPP is based on ‘‘hydrostatic pressure,’’ which is equal from every direction. It does not create shear force to distort food particles. Thus, any moist food such as a whole grape can be exposed to these very high pressures without being crushed. One of the unique advantages of HPP is that pressure transmission is instantaneous and uniform. Pressure transmission is not controlled by product size and no edge or thickness effect takes place. It is effective throughout the food items, from the surface through the center. The ‘‘mechanism’’ of HPP does not promote the formation of unwanted new chemical compounds, ‘‘radiolytic’’ by-products, or free-radicals. Vitamins, texture, and flavor are basically unchanged. For example, enzymes can remain active in high-pressure produced orange juice. HPP is an all-natural process. The amount of energy needed to compress food is relatively low. HPP is more energy efficient than many other food production methods that require heat.
The limitation of the HPP lies in the high cost of the equipment needed for processing. Alsofood with limited moisture content cannot be treated as they will shrink during compression.
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22.1.3 COMBINED EFFECT
OF
539
TEMPERATURE AND PRESSURE
There is a growing interest in the combined effect of temperature and pressure as an effective means of inactivation of microorganisms. Bacterial spores have more resistance to temperature and pressure than vegetative bacteria, and the combined pressure–temperature effect is very efficient for their treatment. Also, it is known that food undergoes minimal nutrients destruction at temperatures below 1008C. Hence the HPP can be applied at moderate temperatures to a large number of food products, especially those contaminated with spores, which are usually sterilized thermally at a temperature above 1218C [10]. At low temperature, excessive pressure of the order of 1000 MPa is required to treat spores. However, only moderate pressure (<600 MPa) and temperature (>708C) are required for pressure–temperature treatment. It is known that food undergoes minimum nutrient destruction at temperatures below 1008C. Hence the application of HPP at moderate to high temperatures can be applied to a large number of food products, especially those contaminated with spores, which need severe thermal treatment.
22.1.4 ANALYSIS
OF
HIGH-PRESSURE PROCESSING USING CFD
Computational fluid dynamics (CFD) models have been used since long time in different applications, such as aerospace, automotive, nuclear industries, and food processing [11]. Advances in computational speed and memory capacity of computers are allowing ever more accurate and rapid calculations to be performed, and a number of commercial software packages of practical use to the food industry have now become available, such as CFX, PHOENICS, FLUENT, FLOW 3D, and FIDAP. PHOENICS is used in the simulations presented in this chapter. CFD models can provide much useful information in a variety of food engineering applications; it is only recently applied in the applications of HPP of foods. There is a growing interest toward the use of mathematical models to predict the food temperature during the nonthermal treatment of foods such as HPP. A numerical conductive heat transfer model for calculating the temperature evolution during batch HPP of foods was analyzed and tested for two food systems—apple sauce and tomato paste [12]. Uniformity of inactivation of Bacillus subtilis a-amylase and soybean lipoxygenase during HPP was evaluated. The residual enzyme activity distribution appeared to be dependent on the inactivation kinetics, which is pressure–temperature dependent. A detailed numerical simulation of HPP of fluid food systems is studied by Hartmann [9]. In this work of thermofluid dynamics, effect of high-pressure treatment is analyzed by means of numerical solution. Pure water is compressed up to 500 MPa in a 4 ml chamber at different compression rates by enforced mass flow. The spatial and temporal evolution of temperature fields and fluid velocity fields is analyzed. The work shows that the temperature difference occurring in the high-pressure volume depends strongly on the pressure ramp during pressurization. The influence of heat and mass transport effects on the uniformity of a high-pressure induced inactivation is investigated by Hartmann et al. [13] based on computer simulation. The inactivation of Escherichia coli suspended in packed ultrahigh temperature (UHT) milk carried out in a batch process with water as pressure medium is taken as a model process. The results show that the effective inactivation rate increases with the geometrical scale of the high-pressure vessel. Significant nonuniformities of more than one log reduction in the residual surviving cell were observed depending on package material used, and the position of the packages in the vessel [13]. Hartmann et al. [14] studied the thermofluid dynamics and process uniformity of HPP in a laboratory scale autoclave size using experimental and numerical simulation techniques. In this work, direct treatment of water at pressure levels of 500 and 300 MPa is considered.
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It was found that the temperature level in the chamber is only roughly influenced by the tempering device due to thermal inertia of the solid structure of the chamber. The PHOENICS code used in our simulations is based on the finite volume method, as developed by Patankar and Spalding [15]. The key characteristic of this method is the immediate discretization of the integral equation of flow into the physical three-dimensional space, i.e., the computational domain cover the entire treated space, which is divided into a number of divisions in the three dimensions. The details of this code can be found in the PHOENICS manuals, especially the PHOENICS input language (PIL) manual [16].
22.1.5 HPP RESEARCH WORK
AND THE
CURRENT STUDY
Already, the extensive research has been done worldwide to process large varieties of liquid and solid food using HPP. However, most of the work was based on experimental observation and over simplified calculations based on the assumptions of uniform temperature throughout the treatment chamber. Such models can be used only for small HPP. The adiabatic heating caused by the fluid compression at high pressure can cause significant temperature distribution throughout the treated food. Ignoring such temperature variation would lead to incorrect scale-up of the laboratory HPP units to the industrial size units. The temperature distribution in the treatment chamber, which is caused by the adiabatic heating due to compression, complicates the mathematical analysis of the system. The requirement of cooling or heating the food during the HPP and the effects of gradual increase and decrease of pressure (come-up time and depressurization rate) at the beginning and the end of the process would add further complications. The analysis is further complicated by the presence of two phases such as solid and liquid food with different physical properties [17], which vary with both the temperature and pressure. To date, a heat transfer model for HPP that includes most of the above-mentioned effects is not yet available. The development of such model is very important, as experimental testing of every single food product at different operating conditions can be very time consuming. In the mean time, the lack of understanding of the HPP as an efficient sterilization process when compared to thermal sterilization may have limited its commercial applications. In this chapter, the following different case studies are analyzed using CFD: 1. A model to study the temperature distribution, velocity, and pressure profiles during high-pressure compression of solid–liquid food mixture (beef fat and water), within a three-dimensional cylinder basket (Figure 22.1). This model has not been investigated before. 2. A model to study the effect of compression come-up time and the effects of natural and forced convection heating within a three-dimensional cylinder filled with liquid during HPP. Measurements were conducted to validate some of the simulations.
22.2 SIMULATIONS OF SOLID–LIQUID FOOD MIXTURE IN HIGH-PRESSURE PROCESSING 22.2.1 NUMERICAL APPROXIMATIONS
AND
MODEL PARAMETERS
In the simulation presented here, the computations are performed for a three-dimensional pressure cylinder basket similar to that used in the experimental work. The use of a threedimensional analysis is due to the presence of the solid food and the inlet hole of the pressure cylindrical basket used in this simulation. The high pressure cylinder outer surface temperature (top, bottom, and side) is assumed to be compressed to a constant pressure of 500 MPa
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38 mm
225 mm
290 mm
6.5 mm
FIGURE 22.1 Geometry of the high-pressure vessel shows the configuration of the solid food pieces.
throughout the treating period. The effect of natural convection at the early stage of compression was also simulated. This required 3 h of CPU time on the Compaq laptop Evo N1000v—Pentium 4 Intel Inside, 768 MB RAM. The solutions have been obtained using a variety of grid sizes and time steps and the results showed that the solutions reported in this study are almost time-step independent and weakly dependent on grid size. Different commercial packages are available, which could solve the governing partial differential equations. A computational fluid dynamics package (PHOENICS) was used in these simulations. It is a general purpose software that uses the finite-volume method to simulate many classes of fluid flows, and has been used in a variety of fields. The convection discretization scheme used for all variables in the simulations is the hybrid-differencing scheme (HDS). The HDS used in PHOENICS switches the discretization of the convective terms between the central differencing scheme (CDS) and the upwind differencing scheme (UDS) according to the local cell Peclet number.
22.2.2 COMPUTATIONAL GRID A uniform grid system in angular, radial, and vertical directions is used in the simulation to improve the computation. The whole domain was divided into 100,000 cells: 20 in angular direction, 50 in radial direction, and 100 in the vertical direction, distributed equally in each direction as shown in Figure 22.2. The computations domain was performed for a cylinder with a diameter (D) of 38 mm and height (H ) of 290 mm. Water was used as a model liquid food, compressed to 500 MPa in the 300 ml chamber for a total period of 1000 s. Different computational grid refinement has been done during the numerical solution of the governing equation to provide a mesh independent solution.
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Grid in r–z plane
Grid in r–q plane
Solid pieces grid
FIGURE 22.2 The three-dimensional grid meshes of the high-pressure vessel. The arrow shown in the figure is just for a point in the computation process. (From Abdul Ghani, A.G. and Farid, M.M., Journal of Food Engineering, in press.)
The geometry of high-pressure chamber is not axisymmetric due to the presence of the solid, which required the treatment chamber to be considered as a three-dimensional geometry for the solution domain in the computation of the simulation as shown in Figure 22.2. The temperature of the incoming fluid is assumed to be 258C during the whole period of compression.
22.2.3 GOVERNING EQUATIONS
AND
BOUNDARY CONDITIONS
FOR THE
LIQUID
The partial differential equations governing natural convection of the fluid (water) being compressed and heated in a cylinder are the Navier–Stokes equations [18]. The boundary conditions used were as follows: At the cylinder boundary, r ¼ R, vr ¼ 0,
vu ¼ 0, vz ¼ 0,
@T ¼0 @r
At the bottom and top of the cylinder, z ¼ 0 and z ¼ H,
for
0zH
(22:1)
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vr ¼ 0, v ¼ 0, At t ¼ 0, At
T ¼ 25 C
P ¼ 0:1 MPa,
30 > t 0,
@T ¼0 @z
vz ¼ 0,
for
P ¼ 16:663t þ 0:1 MPa At
for
for
0rR
0rR 0rR
and
0zH
and
t > 30 s, P ¼ 500 MPa
0zH
(22:2) (22:3) (22:4) (22:5)
At the walls of the pressure chamber, the kinematic boundary condition requires zero fluid velocity, which implies a no slip condition. This assumption is valid except at the inlet.
22.2.4 GOVERNING EQUATIONS
FOR THE
SOLID
The beef fat pieces are assumed as an impermeable solid, and heat is transferred through them only by conduction. In this case, the three convection terms in the energy conservation equation can be omitted, reducing the governing equation to the well-known diffusion equation: @T 1 @ @T 1 @2T @2T Q ¼ m r þ þ 2 þ @t r @r @r r @2 @z2 rCP
(22:6)
22.2.5 COMPRESSION STEPS The pressure generated by the high-pressure pump and intensifier of the HPP machine was found to increase with time linearly as shown in Equation 22.4. After a compression time of 30 s, the pressure remains constant at 500 MPa. Simulations were conducted for treatment time of 1000 s and the results were presented when pressure reached 100, 200, 300, 400, and 500 MPa after 6, 12, 18, 24, and 30 s, respectively. This was based on the performance of the HPP unit available at the University of Auckland, New Zealand. The pressure level of 500 MPa is reached within 30 s. When the pressure reached 500 MPa, it was held at that pressure until decompression starts. Reynolds number of the water flowing through the inlet hole is found small; therefore, the flow can be assumed laminar even at the beginning of the compression.
22.2.6 PHYSICAL PROPERTIES An equation of state accounting for the compressibility of pure water under high pressure is implemented in the program to describe the variation of the density with pressure and temperature. This equation was taken from the study of Ref. [19] as implemented in one of the PHOENICS subroutines used. The properties of the model liquid food (water) at atmospheric pressure and ambient temperature of 208C are r ¼ 998.23 kg m3, CP ¼ 4181 J kg1 K1, k ¼ 0.597 W m1 K1. For the solid pieces (beef fat), the properties of the solid model at atmospheric pressure are r ¼ 900 kg m3, CP ¼ 3220 J kg1 K1, k ¼ 0.43 W m1 K1 [20,21]. As the pressure and temperature change during compression, the program calculates the new values of physical properties with the aid of FORTRAN statements written, as discussed below. The properties of water are calculated based on the updating values at every time step, which is done using the subroutines in PHOENICS, named CHEMKIN. A call is made to the CHEMKIN routine CKHMS to calculate these properties using the appropriate formula. Both solid (beef fat) and liquid (water) are compressible under high pressure. Appropriate equations of state describing the density as a function of pressure and temperature have to be added to the equation set. For water, these equations are already available in the PHOENICS
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subroutines. For solid, there are no thermophysical data available at high pressure. Therefore, the following equations have been incorporated in the software to take into account the pressure dependency of the physical properties, following the same approach adopted by Hartmann et al. [13]:
rBeef (T) rBeef (P,T) ¼ r (P,T) rWater (T) atm P Water CPBeef (T) CPBeef (P,T) ¼ : CPWater (P,T) CPWater (T) atm P kBeef (T) kBeef (P,T) ¼ kWater (P,T) kWater (T) atm P
(22:7) (22:8) (22:9)
The CHEMKIN system used for the liquid is supplied by Sandia National Laboratories and consists of 1. Thermodynamics database 2. Library of FORTRAN subroutines which the user may call from his application programs to supply thermodynamic data 3. ‘‘Stand-alone’’ interpreter program that reads a ‘‘plain language’’ file that specifies the thermodynamic data for the thermochemical system under investigation Associated with CHEMKIN, and also supplied by Sandia National Laboratories, is a further system that supplies transport data. The transport properties system consists of the following: 1. Transport database 2. Library of FORTRAN subroutines which the user may call from his application programs to supply viscosities, thermal conductivities, diffusion coefficients, and thermal diffusion ratios or coefficients calculated according to two approximations 3. Fitting program that generates polynomial fits to the detailed transport properties in order to make the calculations performed by the subroutine library more efficient Another built-in subroutine used in the simulation is named PRESS0, which is the parameter representing the reference pressure, to be added to the pressure computed by PHOENICS in order to give the physical pressure needed for calculating density and other physical properties. The use of this variable is strongly recommended in cases in which the static component of the pressure is much greater than the dynamic head. The reason is that the static component can be absorbed in PRESS0 leaving the stored pressure field to represent the dynamic variations, which otherwise may be lost in the round off, according to the machine precision and the ratio of dynamic pressure to the static head. Several built-in subroutines are used as well in this simulation: .
.
DVO1DT, used to calculate the volumetric coefficient of thermal expansion of phase 1 of the material used (water). It is useful for the prediction of natural convection heat transfer. DRH1DP, which is used to calculate the compressibility
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dr1 . d( ln r1) r1, i:e:, dP dP .
(22:10)
If DRH1DP is given a positive value used for the dependence of the first-phase density on pressure, recourse to GROUND is necessary when density is a nonlinear function of pressure, or a function of other variables. The following options have been provided in subroutine in PHOENICS called GXDRDP.
22.2.7 RESULTS
AND
DISCUSSIONS
The temperature distribution and the location of the hottest zone (HZ) during the process are analyzed for the two cases below: 1. Compression of liquid (water) 2. Compression of mixture of a liquid (water) and solid (beef fat) In order to minimize numerical errors, the pressure is calculated relative to that fixed at the inlet, which was increasing from atmospheric pressure to 500 MPa. Hence, the calculated pressure field (Figure 22.3) primarily shows the hydrostatic gradient (2.94 kPa at the base). The kinetic head is negligible due to the extremely low liquid velocity (3 1084 107m s1) in the high-pressure (HP) cylinder after such long time of 1000 s.
Pressure 2.902e+04 2.709e+04 2.515e+04 2.322e+04 2.128e+04 1.935e+04 1.741e+04 1.548e+04 1.354e+04 1.161e+04 9.673e+03 7.739e+03 5.804e+03 3.869e+03 1.935e+03
FIGURE 22.3 Pressure variation in the fluid along the cylinder height (t ¼ 1000 s, P ¼ 500 MPa). The arrow shown in the figure is just for a point in the computation process. (From Abdul Ghani, A.G. and Farid, M.M., Journal of Food Engineering, in press.)
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Velocity
Temperature
4.347e−07
4.052e+01
4.058e−07
3.077e+01
3.769e−07
3.902e+01
3.480e−07
3.827e+01
3.191e−07
3.752e+01
2.902e−07
3.677e+01
2.613e−07
3.602e+01
2.324e−07
3.527e+01
2.036e 07
3.451e+01
1.747e−07
3.376e+01
1.458e−07
3.301e+01
1.169e−07
3.226e+01
8.799e−08
3.151e+01
5.910e−08
3.076e+01
3.021e−08
3.0001e+01
1.320e−09
2.926e+01
Velocity profile
Temperature profile
FIGURE 22.4 Velocity and temperature profile of the fluid due to adiabatic compression (t ¼ 30 s, P ¼ 500 MPa). The arrow shown in the figure is just for a point in the computation process.
22.2.7.1
Compression of Liquid Food
Figure 22.4 shows velocity and temperature profiles of the fluid due to adiabatic compression of 500 MPa after 30 s, which is the end of compression period. Figure 22.4a shows the velocity profile of the compressed fluid in the cylinder. The fluid adjacent to it will have higher density causing it to flow downward. At all other locations in the bulk of the cylinder, the liquid will flow upward as shown in this figure. The velocity is in the range of 107–109 m s1 only after 30 s. Due to the high hydrostatic pressure, the velocities are very small (Figure 22.4), and hence the effect of free convection heat transfer is expected to be very small in this situation. This is confirmed by the temperature profile in the liquid food shown. The hottest region (40.528C) after 30 s of adiabatic compression is almost at the center of the cylinder, with only very little shift toward the top of the cylinder. The increase of 158C due to compression at 500 MPa is the same as the value usually reported in the literature due to adiabatic heating (38C per 100 MPa). However, the increase in the fluid average temperature in the cylinder is significantly less than 38C. 22.2.7.2
Compression of Mixture of a Liquid and Solid
The temperature distribution during heating of solid and liquid food is presented in the form of isotherms in Figure 22.5 for different periods of compression (12, 24, and 30 s). The isotherms shown in the figure are for compression pressures of 200, 400, and 500 MPa, respectively. Figure 22.5 shows that the solid (beef fat) is heated much more than the fluid (water), which is due to its larger heat of compression. This figure shows clearly how the fluid enters the cylinder through the hole in the top (cold) then deviates when it hits the two pieces of solid. Figure 22.6 shows that the HZ in the cylinder (the location of the highest temperature at a given time) remains in the middle of the solid food (beef fat) due to the higher heat of compression of the beef fat and due to the fact that heat is transferred by conduction only. Due to the higher temperature of the solid, heat is transferred from the solid to the water by free and forced convection heat transfer. As pressure increases to 500 MPa, the temperature profile (Figure 22.5) becomes very different from that observed at the beginning of the compression. The figure shows that the temperature profile is influenced by the cooling caused by the pumped water through the hole
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Temperature
Temperature
Temperature
3.032e+01
5.610e+01 5.470e+01 5.330e+01 5.190e+01 5.050e+01 4.910e+01 4.770e+01 4.630e+01 4.490e+01 4.350e+01 4.211e+01 4.071e+01 3.931e+01 3.791e+01 3.651e+01 3.511e+01
6.150e+01 5.995e+01 5.841e+01 5.686e+01 5.532e+01 5.377e+01 5.223e+01 5.068e+01 4.914e+01 4.759e+01 4.605e+01 4.450e+01 4.296e+01 4.141e+01 3.987e+01 3.032e+01
Solid−liquid at 200 MPa after 12 s
Solid−liquid at 400 MPa after 24 s
4.000e+01 3.935e+01 3.871e+01 3.806e+01 3.742e+01 3.677e+01 3.613e+01 3.548e+01 3.484e+01 3.419e+01 3.355e+01 3.290e+01 3.226e+01 3.161e+01 3.097e+01
Solid−liquid at 500 MPa after 30 s
FIGURE 22.5 (See color insert following page 462.) Radial–vertical temperature profile of the solid– liquid food mixture (beef fat and water) at compression rates of 200, 400, and 500 MPa, respectively. The red arrow shown in the figure is just for a point in the computation process. (From Abdul Ghani, A.G. and Farid, M.M., Journal of Food Engineering, in press.)
5.610e+01 5.470e+01 5.330e+01 5.190e+01 5.050e+01 4.910e+01 4.770e+01
12 mm
60 mm
150 mm
4.630e+01 4.490e+01 4.350e+01 4.211e+01 4.071e+01 3.931e+01 3.791e+01 3.651e+01 3.511e+01
240 mm
261 mm
276 mm
FIGURE 22.6 Radial–angular temperature profile of the solid–liquid food mixture due to compression rate of 400 MPa at different heights of 12, 60, 150, 240, 261, and 276 mm from the bottom. The arrow shown in the figure is just for a point in the computation process. (From Abdul Ghani, A.G. and Farid, M.M., Journal of Food Engineering, in press.)
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at the top of the cylinder (inlet). The velocity of the cold water entering the inlet hole is 102–103 m s1 as calculated which is much higher compared to the velocity inside the cylinder (107–109 m s1) shown in Figure 22.4. At this stage, the buoyancy force also starts to play a role due to temperature variation of the liquid from outside to the core of the cylinder. Under adiabatic compression heating conditions, the sample temperature at process pressure is dictated by the sample’s thermodynamic properties and the heat transfer between the sample and the pressure-transmitting fluid. Also the fluid as it enters the pressure vessel during the come-up time would likely influence the sample temperature [22]. Some of the commonly used pressure-transmitting fluids are water, food-grade glycol–water solutions, silicone oil, sodium benzoate solutions, ethanol solutions, and castor oil. In the simulation used in this work, water was assumed as the pressure-transmitting fluid. 22.2.7.3
Experimental Validations
In order to validate the results of the simulations for the two cases (liquid and solid–liquid), experimental data are obtained from measurements conducted on the HPP machine at the Food Laboratory at the Chemical Engineering Department, University of Auckland. The maximum operating pressure of the unit is 900 MPa and the temperature range is 208C to þ908C. Pressure is controlled by electronic control module with integral digital display, with a programmable logic controller (PLC) (Mitsubishi ‘‘F’’ series). The cylinder, used in the measurements has the same size as those used in theoretical analysis. The cylinder’s internal diameter is 38 mm and the inner height is 290 mm. Direct processing of water at pressure level of 500 MPa and within a pressure holding phase ending at 1000 s is conducted. The measurements were found in excellent agreement with the numerically simulated temperature fields for the two cases and as reported by Abdul Ghani and Farid [17].
22.3 A SIMULATION TO STUDY THE CONVECTION CURRENTS OF LIQUID FOOD IN A NONADIABATIC HIGH-PRESSURE PROCESSING In these second case studies, temperature, velocity, and pressure profiles during the early stages of high-pressure compression of liquid food (water) within a three-dimensional cylinder basket are simulated. The computations domain was performed for a cylinder with same dimensions as those used in the previous section. Direct processing of water at pressure level of 500 MPa and a pressure holding time of 970 s is simulated. Pressure is assumed to rise from the atmospheric pressure to the treatment pressure linearly by enforced mass flow. The simulation for the liquid food shows, for the first time, the effect of forced and free convection flow, on the temperature distribution in the liquid at the early stages of compression. This is due to the difference between the velocity of the pumping fluid as it enters the inlet of the cylinder hole (102–103) m s1 and the velocity in all other locations in the treatment chamber (108–109) m s1.
22.3.1 NUMERICAL APPROXIMATIONS
AND
MODEL PARAMETERS
In order to analyze the temperature distribution in a liquid food in a high-pressure treatment, the following process is considered: A high-pressure chamber of 300 ml volume (Figure 22.7) is filled with liquid food (pure water). The liquid food is compressed from ambient pressure to a maximum pressure of 500 MPa. The inflow of water is stopped when the maximum pressure is reached. The pressure level is held at 500 MPa for up to 1000 s. During the holding phase, the pressure remains constant. The initial temperature of the fluid and the wall temperature of the treatment chamber were assumed to be at 208C during the whole period.
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Ø 38 mm
75 mm
175 mm
290 mm
Thermocouple
FIGURE 22.7 Geometry of the high-pressure vessel.
The computation grid, governing equations, and compression steps were same as those used in Section 22.2.2, Section 22.2.3, and Section 22.2.5, respectively. An equation of state accounting for the compressibility of pure water under high pressure is implemented in the program to describe the variation of the density with pressure and temperature. This equation was taken from the study of Saul and Wagner [19] as was implemented in one of the PHOENICS subroutines used. The properties of the model liquid food (water) were same as those used in Section 22.2.6.
22.3.2 RESULTS
AND
DISCUSSIONS
During HPP of food, an increase of temperature due to compression is observed as a result of partial conversion of mechanical work into internal energy. This is known as adiabatic heating. In reality the situation is much more complex. In the simulation presented here, heat exchange between the treated fluid and the cylinder wall, as well as the cooling effect caused by the entering fluid during compression is included in the analysis. Temperature distribution, location of the HZ, velocity profile, and pressure profile during the process are compared and analyzed based on the simulations conducted. Experimental measurements are used to validate these simulation results. The change in the temperature profile at early stages of compression is due to compression heating and cooling caused by the pumped water through the hole at the top of the cylinder (inlet). The velocity of the cold water through the inlet hole is much higher than the velocity inside the cylinder. At this stage, the buoyancy force starts to be also effective due to temperature variation of the liquid from outside to the core of the cylinder. Figure 22.8 and Figure 22.9 show the temperature and velocity profiles at the early stages of compression after periods of 12 and 24 s at nonadiabatic compression pressures of 200 and 400 MPa, respectively. In Figure 22.8, the fluid velocity at the top (location of the inlet) of the cylinder is large. It is in the range of 102–103 m s1 at the top (at location close to the inlet) of the cylinder, while it is very small (107–109 m s1) in the rest of the cylinder as shown in Figure 22.4. This is due to the liquid being pumped through the inlet at the top of the cylinder
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Velocity 1.998e−02 1.864e−02
Temperature 2.559e+01 2.522e+01
1.731e−02
2.485e+01
1.598e−02
2.449e+01
1.465e−02
2.412e+01
1.332e−02
2.375e+01
1.199e−02
2.339e+01
1.065e−02
2.302e+01
9.322e−02
2.265e+01
7.990e−03
2.229e+01
6.659e−03
2.192e+01
5.327e−03
2.155e+01
3.995e−03
2.119e+01
2.663e−03
2.045e+01
1.332e−03
2.082e+01
2.177e−10
2.008e+01
FIGURE 22.8 Temperature and velocity profiles of the fluid at the early stage (t ¼ 12 s) of compression rate of 200 MPa. (From Abdul Ghani, A.G. and Farid, M.M., Journal of Food Engineering, in press.)
Velocity
Temperature
1.998e−03
3.303e+01
1. 864e−03
3.217e+01
1.731e−03
3.131e+01
1.598e−03
3.045e+01
1.465e−03
2.958e+01
1.332e−03
2.872e+01
1.199e−03
2.786e+01
1.065e−03
2.700e+01
9.322e−04
2.614e+01
7.990e−04
2.527e+01
6.659e−04
2.441e+01
5.327e−04
2.355e+01
3.995e−04
2.269e+01
2.663e−04
2.182e+01
1.332e−04
2.096e+01
3.539e−11
2.010e+01
FIGURE 22.9 Temperature and velocity profiles of the fluid at the early stage (t ¼ 24 s) of compression rate of 400 MPa. (From Abdul Ghani, A.G. and Farid, M.M., Journal of Food Engineering, in press.)
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in order to fill the shortage of water caused by the effect of compression. This has pushed the HZ more toward the bottom of the cylinder as it is clearly seen in the figure. Without this effect, the HZ will move more toward the top due to buoyancy effect. In Figure 22.9, the fluid velocity is decreased to 103104 m s1 at the top of the cylinder and remained very small in the rest of the cylinder, while the HZ is pushed even further toward the bottom of the cylinder. Figure 22.8 through Figure 22.10 show for the first time the effects of forced and natural convection current at early stages of compression during HPP. At later stages of compression (Figure 22.11), the fluid flow diminishes and the liquid velocity drops to very low values. Under such a condition heat transfer is dominated more by conduction and to a lesser extent by free convection in the liquid. Figure 22.11 shows temperature profile of the fluid due to nonadiabatic compression of 500 MPa after 1000 s of starting the compression. Due to the high hydrostatic pressure, the velocities are very small, and hence the effect of free convection heat transfer is expected to be very small in this situation. The HZ (35.558C) after 30 s of nonadiabatic compression, which represents 158C per 500 MPa, is almost at the center of the cylinder, with a slight shift toward the top of the cylinder. This figure shows that the increase in the fluid average temperature in the cylinder is significantly less than 38C, usually reported in adiabatic compression. The nonadiabatic condition occurred due to two factors: (a) cooling caused by the lower temperature of the wall of the cylinder; (b) cooling caused by the incoming fluid through the inlet of the cylinder during compression. Due to the external cooling at the wall, the fluid adjacent to it will have higher density causing it to flow downward (Figure 22.4). At all other locations in the bulk of the cylinder, the liquid will flow upward as shown in this figure. The velocity is in the range of 107–109 m s1 at the end of the process. However, at early stages of compression, the calculated liquid velocity was as high as 102–104 m s1, as shown in Figure 22.8 and Figure 22.9, after compression periods of 12 and 24 s, respectively.
22.3.3 EXPERIMENTAL VALIDATION Experimental measurement was used to validate the results of the simulation presented using the equipment available at the University of Auckland, New Zealand. The HPP unit used in the experimental measurements is same as those used above. The measurements at Velocity
Temperature
1.858e−03
3.589e+01
1.734e−03
3.484e+01
1.610e−03
3.379e+01
1.486e−03
3.274e+01
1.362e−03
3.169e+01
1.238e−03
3.064e+01
1.115e−03
2.959e+01
9.908e−04
2.853e+01
8.669e−04
2.748e+01
7.431e−04
2.643e+01
6.192e−04
2.538e+01
4.954e−04
2.433e+01
3.715e−04
2.328e+01
2.477e−04
2.223e+01
1.238e−04
2.118e+01
3.629e−12
2.013e+01
FIGURE 22.10 (See color insert following page 462.) Temperature and velocity profiles of the fluid at the early stage (t ¼ 30 s) of compression rate of 500 MPa. (From Abdul Ghani, A.G. and Farid, M.M., Journal of Food Engineering, in press.)
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Temperature 3.555e+01 3.454e+01 3.352e+01 3.250e+01 3.149e+01 3.047e+01 2.946e+01 2.844e+01 2.743e+01 2.641e+01 2.540e+01 2.438e+01 2.337e+01 2.235e+01 2.134e+01 2.032e+01
FIGURE 22.11 Temperature profile of the fluid due to nonadiabatic compression at t ¼ 1000 s and P ¼ 500 MPa. (From Abdul Ghani, A.G. and Farid, M.M., Journal of Food Engineering, in press.)
two different locations at the axis of the cylinder are found in excellent agreement with the numerically simulated temperature fields as reported by Abdul Ghani and Farid [23]. The effect of cooling by the fluid which enters during compression is shown more clearly in Figure 22.12. The temperature at the higher location is about 28C lower than the center of the cylinder at the end of compression. If the cooling effect is ignored, the temperature at the higher location would experience higher temperature due to buoyancy. At the center 75 mm apart from the top At the center 175 mm apart from the top
Temperature (8C)
35
30
25
20
15 100
200
300
400
500
Pressure (MPa)
FIGURE 22.12 Comparison between two theoretically predicted points at different heights; top point located at the center of the pressure vessel 75 mm apart from the top (the highest location of convection currents).
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In reality, a true isothermal operation is difficult to achieve. For HPP experiment at elevated temperatures, it is important to recognize that an externally delivered pressure-transmitting fluid may enter the system at a much lower temperature than the pressure-transmitting fluid already in the pressure vessel. The temperature of this fluid should be monitored and reported where possible [22].
22.4 CONCLUSIONS In this chapter, HPP of food is introduced and analyzed with emphasis on the mathematical analysis of HPP using CFD. The analysis is conducted for liquid food (water) as well as combined solid–liquid food (meat) compressed to 500 MPa. A three-dimensional analysis was necessary for the solid–liquid food case and the properties of the solid and liquid were assumed pressure and temperature dependent. The simulation for the liquid food shows that the temperature profile in the treatment cylinder is influenced significantly by the cooling caused by the pumped liquid through the hole at the top of the cylinder, especially at the early stages of compression heating. Simulations were conducted for both adiabatic and nonadiabatic compressions. For solid–liquid, the simulation shows excessive heating within the solid (beef) due to the fat having higher heat of compression. Conduction heating was found to dominate all cases studied except at early stages of compression heating. Such analysis will be very valuable for the next generation pressure-assisted thermal sterilization.
NOMENCLATURE CP D g H k P Q r r, u, z t T Tref vr vu vz z a b m r rref
specific heat of liquid food (J kg1 K1) diameter of cylinder (mm) Acceleration due to gravity (m s2) height of the cylinder (mm) thermal conductivity of liquid food (W m1 K1) pressure (Pa) volumetric generation (W m2) radius of the cylinder (mm) radial, angular, and vertical direction of the cylinder compressing time (s) temperature (8C) reference temperature (8C) velocity in radial direction (m s1) velocity in angular direction (m s1) velocity in vertical direction (m s1) Distance in vertical direction from the bottom (m) thermal diffusivity (m2 s1) thermal expansion coefficient (K1) apparent viscosity (Pa s) density (kg m3) reference density (kg m3)
REFERENCES 1. G.V. Barbosa–Canovas, U.R. Pothakamury, E. Paulo, and B.G. Swanson. Non-Thermal Preservation of Foods. New York: Dekker, pp. 9–52, 1997. 2. L. Ludikhuyze, I. Indrawati, C. Van der Broeck, C. Weemens, and M.E. Hendrickx. Effect of combined pressure and temperature on soybean lipoxygenase. 2. Modeling inactivation kinetics under static and dynamic conditions. Journal of Agricultural Food Chemistry 46: 4081–4086, 1998.
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3. I. Seyderhelm, S. Bogulawiski, G. Michaelis, and D. Knorr. Pressure induced inactivation of selected food enzymes. Journal of Food Science 61(2): 308–310, 1996. 4. G.C. Yen and H.T. Lin. Comparison of high pressure treatment and thermal pasteurization on the quality and shelf life of guava puree. International Journal of Food Science and Technology 31: 205–213, 1996. 5. A. Richwin, A. Roosch, D. Teichgraber, and D. Knorr. Effect of combined pressure and temperature on the functionality of egg-white proteins. European Food Science 43(7=8): 27–31, 1992. 6. T. Ohshima, H. Ushio, and C. Koizumi. High pressure processing of fish and fish products. Trends in Food Science and Technology 4: 370–375, 1993. 7. P.E. Bouton, A.L. Ford, P.V. Harris, J.J. Macfarlane, and J.M. O’Shea. Pressure treatment of post rigor muscle: effects on tenderness. Journal of Food Science 42: 132–135, 1997. 8. T. Ohmori, T. Shigehisa, S. Taji, and R. Hayashi. Effect of high pressure on the protease activities in meat. Bio Chemistry 55(2): 357–361, 1991. 9. C. Hartmann. Numerical simulation of thermodynamic and fluid-dynamic processes during the high-pressure treatment of fluid food systems. Innovative Food Science and Emerging Technologies 3: 11–18, 2002. 10. D. Knorr. Effects of high hydrostatic pressure processes on food microorganism, Trends in Food Science and Technology 4: 370–375, 1993. 11. G. Scott and P. Richardson. The applications of computational fluid dynamics in the food industry. Trends in Food Science and Technology 8: 119–124, 1997. 12. S. Denys, A.M. Van Loey, and M.E. Hendrickx. A modeling approach for evaluating process uniformity during batch high hydrostatic pressure processing: combination of a numerical heat transfer model and enzyme inactivation kinetics. Innovative Food Science and Emerging Technologies 1: 5–19, 2000. 13. C. Hartmann, A. Delgado, and J. Szymczyk. Convective and diffusive transport effects in a highpressure induced inactivation process of packed food. Journal of Food Engineering 59: 33–44, 2003. 14. C. Hartmann, J.P. Schuhholz, P. Kitsubun, N. Chapleau, A.L. Bali, and A. Delgado. Experimental and numerical analysis of thermo fluid dynamics in a high-pressure autoclave. Innovative Food Science and Emerging Technologies 5: 399–411, 2004. 15. S.V. Patankar and D.B. Spalding. A calculation procedure for heat, mass and momentum transfer in three dimensional parabolic flows. International Journal of Heat and Mass Transfer 15(10): 1787–1806, 1972. 16. PHOENICS Reference Manual, Part A: PIL, Concentration Heat and Momentum Limited, TR 200 A, Bakery House, London SW 19 5AU, UK. 17. A.G. Abdul Ghani and M.M. Farid. Use the computational fluid dynamics to analyze the thermal sterilization of solid–liquid food mixture in cans. Innovative Food Science and Emerging Technologies 7: 55–61, 2006. 18. R.B. Bird, W.E. Stewart, and E.N. Lightfoot. Transport Phenomena. New York: John Wiley and Sons, 1976. 19. A. Saul and W. Wagner. A fundamental equation for water covering the range from the melting line to 1273 K at pressures up to 25,000 MPa. Journal of Physical and Chemical Reference Data 9: 1212–1255, 1989. 20. M.S. Rahman. Handbook of Food Preservation. Food Science and Technology. A series of monographs, textbooks, and reference books, New York: Marcel Dekker, 1995. 21. G.D. Hayes. Food Engineering Data Handbook. New York: John Wiley, 1987. 22. V.M. Balasubramaniam, E.Y. Ting, C.M. Stewart, and J.A. Robbins. Recommended laboratory practice for conducting high pressure microbial inactivation experiments. Innovative Food Science and Emerging Technologies 5: 299–306, 2004. 23. A.G. Abdul Ghani and M.M. Farid. Numerical simulation of solid-liquid food mixture in a high pressure processing unit using computational fluid dynamics. Journal of Food Engineering, in press.
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Analysis of Mixing Processes Using CFD Robin K. Connelly and Jozef L. Kokini
CONTENTS 23.1 23.2
Introduction ............................................................................................................. 555 Approaches for Using CFD to Simulate Mixing Flows .......................................... 556 23.2.1 Techniques to Handle Moving Parts .......................................................... 556 23.2.2 Techniques to Handle Turbulent Flow ....................................................... 559 23.3 Analysis of Mixing Using CFD Results................................................................... 559 23.4 CFD Analysis of Motionless Mixers........................................................................ 564 23.5 CFD Analysis of Helical Ribbon Mixers................................................................. 564 23.6 CFD Analysis of Mixing Processes in Stir Tanks .................................................... 564 23.6.1 CFD Simulation of Mixing in a Stir Tank ................................................. 564 23.6.2 CFD Simulation of Crystallization Processes ............................................. 565 23.7 CFD Analysis of Dough Mixing Processes.............................................................. 568 23.7.1 CFD Simulation of Viscoelastic Behavior in Simplified Dough Mixing Geometries...................................................................................... 568 23.7.2 CFD Analysis of Mixing in Dough Mixers Using Generalized Newtonian Fluid Models ............................................................................ 571 23.8 Conclusions .............................................................................................................. 581 Nomenclature ..................................................................................................................... 581 References .......................................................................................................................... 583
23.1 INTRODUCTION Mixing is an important unit operation in processing operations, which is used for purposes that include blending of ingredients, improvement of the rate of heat transfer, facilitation of chemical reactions, creation of structure, the addition of energy to create or break molecular bonds, etc. Turbulent mixing of low-viscosity liquids and gases works quickly because it mainly uses the mechanisms of distributive mixing and molecular diffusion in chaotic turbulent eddies. These eddies are superimposed on the mean flow pattern and scale from the size of the mixing element down to the molecular level [1,2]. The mixing of highly viscous fluids is more difficult because it generally takes place only in the laminar regime and mainly involves the mechanisms of laminar shear, elongational flow, and distributive mixing to reduce the scale of segregation, whereas molecular diffusion (which occurs very slowly) and dispersion act to reduce the intensity of segregation [2,3]. Due to the complexity of both the geometry and the flow patterns in commercial mixers, the use of CFD simulation to determine flow profiles, stress and strain rate distributions, and mixing efficiency during mixing has been slow to develop. In addition, the inherent error
555
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caused by the time and space discretization, numerical integration, and the finite accuracy of any computational device increases exponentially in many of the common mixing measures such as circulation time and length of stretch [4]. However, as the speed of computer processors and available memory resources have grown in combination with a greatly increased efficiency and accuracy for FEM and FVM solvers, it has become possible to use CFD to simulate and analyze the flow and mixing in more realistic mixing geometries, especially when using Newtonian and generalized Newtonian fluid models.
23.2 APPROACHES FOR USING CFD TO SIMULATE MIXING FLOWS 23.2.1 TECHNIQUES
TO
HANDLE MOVING PARTS
The most difficult aspect of the numerical simulation of almost any process that involves mixing is the time-dependent nature of the flow domain due to the motion of the mixing elements. For systems where there is only a single rotating part in a cylindrical vessel with no baffles or other elements whose position moves relative to the mixing element, the most obvious way to handle the motion is to use a rotating reference frame such that the mixing element is stationary and the vessel walls are rotating, as seen in Figure 23.1. This fixes the flow domain in time, which allows for a simpler and more accurate steady-state solution. With a steady-state problem, it is then possible to use complex models to describe the flow response of the fluids including those that model the viscoelastic behavior. In order to compensate for the effect of the rotating reference frame on the flow, rigid rotation of the entire system can be defined so that the centrifugal and Coriolis forces are taken into account, which becomes significant particularly in situations where viscoelastic flow models are used [5]. The calculated velocity components can then be converted back to the stationary or inertial reference frame using the equation: virf ¼ vrrf Vk r where k is the unit vector in the z-direction [6]. However, when there are separately moving mixing elements, baffles, noncircular vessel geometries, or nonsymmetrical elements such as inlets and outlets, then the time-dependent aspects of the flow field geometry must be addressed.
FIGURE 23.1 1480 element mesh for a rotating reference frame simulation of a single paddle in a cylindrical mixing tank. (From Connelly, R.K. and Kokini, J.L., Adv. Polym. Tech., 22, 22, 2003. With permission from Elsevier.)
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When there is a single rotating mixing element in a time-dependent geometry or multiple, noninteracting moving parts, the simplest approach is to use a domain decomposition method where one or more local rotating reference frames are used to contain the moving parts, while the rest of the flow domain remains in the inertial reference frame. With this multiple reference frame (MRF) technique [7–9], each rotating frame is contained within a grid that has a perfect surface of revolution on the outside. Then the momentum equations for the parts of the flow domain inside the surface are solved in a rotating reference frame while those outside are solved in the ordinary stationary reference, with information shared at the boundary between the two frames in a steady-state, time-independent fashion. As the mixing element remains in one position, its orientation to any baffles or other nonsymmetrical elements is constant. However, in cases when the interaction between the moving elements and the time-dependent elements is minimal, such as when there is a draft tube between baffles and the mixing element as seen in Figure 23.2, this technique is an effective way to handle the moving parts in a manner that still allows for a steady-state solution. In cases where there is significant interaction between time-dependent elements but no intermeshing of moving parts, a time-dependent sliding mesh technique [9,10] is an approach of choice. With this technique, the grid surrounding the moving part moves with it in a discrete, time-stepping manner and slides relative to the mesh of the stationary domain. Then the cell faces on one side of the interface surface exchange information with the closest cell face on the other side of the interface. Interpolation is used as needed to properly match the information that is passed back and forth. This technique is the most rigorous and informative way available to handle noncircular flow domain mixing simulations. Transient simulations using this technique have been shown to capture low-frequency oscillations in the flow field that are well below the blade rotation frequency [11].
Z X
Y
FIGURE 23.2 Mesh for a multiple reference frame (MRF) simulation of a propeller mixing with a draft tube in a baffled tank. The local rotating reference frame is highlighted in gray. (From Connelly, R.K., Dhanasekharan, K., and Hartel, R., Institute of Food Technologists Annual Meeting, Las Vegas, NV, July 12–16, 2004.)
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In order to model the flow in mixers that contain more than one interacting mixing element, some type of remeshing or moving-mesh technique is required. Some authors have actually created new meshes for each time-step that are solved as sequential steady-state problems [12–15], but this technique is time consuming and labor intensive. It also does not allow for start-up effects. A simpler way to approach the remeshing problem is to mesh the flow domains and moving elements separately, and then superimpose the meshes as they would be positioned at any given time, as seen in Figure 23.3. A technique introduced by Bertrand et al. [16] superimposes the moving part geometry on the meshed flow domain using Lagrangian multipliers with a velocity constraint and has been dubbed the fictitious domain method. A similar technique is the mesh superposition technique (MST) of Avalosse and Rubin [17,18], which uses a penalty force term, H(v vp), where H is either zero outside the moving part or 1 within the moving part and vp is the velocity of the moving part. The term is used by modifying the equation of motion as follows: Dv H(v vp ) þ (1 H) rp þ r T þ rf r ¼ 0: Dt
(23:1)
When H ¼ 0 the normal Navier–Stokes equations are left, but when H ¼ 1 the equation degenerates into v ¼ vp. The value of H is determined by the generation of an ‘‘inside’’ field that depends on the position of the moving part. When an element or node is greater than 60% within the moving part, H is given a value of 1. The threshold of the ‘‘inside’’ field can be modified with a larger value equivalent to a ‘‘thinner’’ moving part. Due to the modification of the velocity in the regions of the flow domain covered by the moving part, mass conservation cannot be completely satisfied, leading to the need of a very small compression
FIGURE 23.3 Mesh superposition farinograph blade meshes superimposed on the mixing bowl mesh 1808 from the initial position. (From Connelly, R.K., PhD dissertation, Rutgers University, New Brunswick, NJ, 2004.)
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factor ( b0 ), and the possibility of a small amount of leakage of mass being observed. That modifies the conservation of mass equation as follows: rvþ
b0 : rp ¼ 0, m(g)
(23:2)
where b0 is the relative compression factor that is recommended to be of a value of 0.01. If the value for this is chosen too low, false pressure peaks appear in regions of high geometrical constraint or in meshes so coarse that there is only one element between the wall and the moving part. However, if the value is too high, the fluid is made unphysically compressible and the legitimate pressure gradients are smoothed out. An additional drawback of both mesh superposition and the fictitious domain method is a loss of sensitivity in the velocity profiles at the moving part boundaries, although use of adaptive remeshing [19,20] to temporarily refine the flow domain mesh at the moving part boundaries can alleviate this drawback substantially. Unfortunately, the use of adaptive remeshing is frequently incompatible with material point tracking, which is needed for a full mixing analysis. However, these drawbacks are balanced by the ease in creating meshes and the robustness of the method due to the avoidance of remeshing or sliding-mesh schemes.
23.2.2 TECHNIQUES
TO
HANDLE TURBULENT FLOW
Turbulent flows at high Reynolds numbers such as those found during mixing of lowviscosity fluids at high speed in a stir tank are highly unsteady, with velocity fluctuations on a broad range of length and timescales that make direct numerical simulation difficult. They also mix all of the transported properties and cause them to fluctuate [21]. In order to reduce the computational cost, the classical approach to accounting for turbulence is through an averaging process in the governing equations where, for example, the velocity is considered to be the sum of an equilibrium velocity and fluctuating component, v ¼ v þ v0 . Inserting this type of variable representation into the Navier–Stokes equations produces the Reynoldsaveraged Navier–Stokes (RANS) equations and generates a set of new time-averaged unknowns that are called the Reynolds stresses. The Reynolds stresses are related to other variables using turbulence models [11]. The most common approach to developing turbulence models for the Reynolds stresses starts by expressing the Reynolds stresses in terms of the mean velocity gradients using a new constant called the turbulent or eddy viscosity (mt). When these representations of the Reynolds stresses are substituted into the RANS equations and the terms are collected, a new effective viscosity term can be introduced, meff ¼ m þ mt. The most widely used and validated turbulence model is the k–« model [22], which provides rapid, stable calculation and reasonable results, especially for high Reynolds-number flows [11,23]. This model solves the semiempirical transport equations using constants based on experimental observations of high Reynolds number flows for air and water that provide the kinetic energy of turbulence (k) and the rate of dissipation of turbulence («), which are used to calculate the turbulent viscosity. A variation of the k–« model useful for mixing applications is the RNG k–« model [24], which is based on statistical renormalization group theory and is applicable to transitional as well as high Reynolds number flows [11].
23.3 ANALYSIS OF MIXING USING CFD RESULTS Many ways of characterizing mixing have been proposed over the years, with no single method being able to quantify all aspects of mixing for every process. The practical problem with using any of these methods of characterizing mixing has been measurement. The results
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from the proposed methods tend to be highly dependent on the limit of resolution of the measurement technique and difficult to relate directly to fluid mechanics. Instead, properties such as rheology, color, chemical analysis, and electrical conductivity are frequently used to estimate the values of the mixing measures [3,25]. However, the advent of CFD applied to mixing, especially when combined with material point tracking, has offered an opportunity to better utilize these methods to characterize the mixing effectiveness of a mixing process. In particular, the precise tracking of the positions of a large number of material points that can be assigned specific concentration values allows for the use of statistical techniques to evaluate distributive mixing indices, while the knowledge of the velocity profile and material point paths allow analysis of the effectiveness of the flow for dispersive mixing and the efficiency with which the mixing energy is used to deform rather than displace fluid elements. In order to calculate statistical mixing measures and efficiencies, as well as to get visual indications of local mixing flaws and the overall mixing effectiveness of a mixing process, it is necessary to follow the trajectories of a large number of material points. The initial positions of the material points are generated by randomly distributing a set of material points throughout the flow domain or in clusters in the flow domain. Then a typical approach is to calculate the trajectories by the time integration of the equation x_ ¼ v using a fourth-order explicit Runge–Kutta scheme within an element with local rather than global coordinates. The time-step is sized such that the final position in crossing an element is always on the element boundary so that the element coordinates may be transformed to the local coordinates of the next element to be crossed before continuing the integration. The sum of the steps when transformed to global coordinates gives the successive positions of the material points in real space [15,26]. This then allows the calculation of the kinematic parameters for each material point along its trajectory such as stretching, rate of stretching, and rate of dissipation, which are recorded as required. One of the oldest measures of distributive mixing is the scale of segregation, Ls [2,27], which is a measure of the binomial distribution and is defined as ðz
Ls ¼ R(jrj)djrj,
(23:3)
0
where M P
R(jrj) ¼
j¼1
(c0j c) (c00j c) MS 2
,
(23:4)
where R(jrj) is the Eulerian coefficient of correlation between concentrations of pairs of points in the mixer separated by jrj where R(0) ¼ 1 for points having the same correlation and R(z) ¼ 0 where there is no correlation. S2 is the sample variance and the number of pairs separated by jrj is M. The concentration of the points in the jth pair is c0j and c00j , while c is the average concentration. The value of Ls is an indication of the average size of segregated regions and is a global measure that is not able to identify local defects in the flow. The quality of distributive mixing of a cluster of a minor ingredient into the bulk can also be analyzed statistically by the use of the discrete pairwise correlation function [13,28,29]. The discrete pairwise correlation function is defined as f (r) ¼
X 2 d(r0i þ r) d(r0i ) c(r)Dr, N(N 1) i
(23:5)
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where d() ¼ 1 if a material point is present and 0 if absent in the shell of radius r + Dr=2 around the point i located at ri0 , N is the number of material points, and c(r) is the coefficient of the probability density function. The area under the curve of c(r) is a constant, independent of the shape of the distribution, therefore, r¼r max X
c(r)Dr ¼ 1,
(23:6)
r¼0
where rmax is the largest dimension of the system such that c(r > rmax) ¼ 0. An ideal c(r) can be defined for a system in which the minor component is randomly distributed. A cluster distribution index («) that measures the difference between an actual distribution and the ideal case is then given as 1 Ð
«¼
½c(r) c(r)ideal 2 dr
0 1 Ð
,
(23:7)
2
c(r)ideal dr
0
which is the normalized deviation of the density of probability function for the cluster at a given time from the density of probability function of the optimal random distribution [13,29]. It varies between 1, where all the points are in the same position, and 0, where there is an ideal distribution. Although this parameter is independent of the size of the flow domain, it is very much dependent on the initial position of the cluster. It is also dependent on the number of material points in the cluster as it cannot measure deviation of the distribution for distances less than mean distance between neighboring points in the optimal case and there is an increase in error when there are fewer points used in the simulation. Using the concepts of interfacial area between two components in a mixture [30] and the distance between interfaces or striation thickness [31], Ranz, Ottino and coworkers [32–36] developed a kinematic approach to modeling distributive mixing that used a lamellar model to track the amount of deformation experienced by fluid elements. Given a motion x ¼ x (X,t) where initially X ¼ x (X,0) for an infinitesimal material line segment dx ¼ F dX located at position x at time t where the deformation tensor is F ¼ =x, the length of stretch of a material line is defined as l ¼ jdxj=jdXj and the area stretch of a material surface as h ¼ jdaj=jdAj where da ¼ dx1 dx2. The arithmetic and geometric means of the length of stretch can be represented as l a eQn
and
hli a eLn ,
(23:8)
where n is the number of periods (or revolutions) in a time-periodic flow and the coefficients, and L, are the growth rates of the arithmetic and geometric averages of the ln l and are known as the topological entropy exponent and the Lyapunov exponent, respectively [37–39]. The arithmetic mean of the length of stretch l has been shown to be directly related to the geometric mean striation thickness and is a measure of the growth of the interfacial area where the topological entropy exponent can be regarded as mixing rate in the global sense, and also in the local sense in chaotic regions of the flow [37–39]. The geometric mean is a measure of the stretching rate and captures the most probable rate of elongation, with the Lyapunov exponent shown to be less than the topological entropy exponent, both experimentally and numerically [37–39].
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The local efficiency of mixing is defined as el ¼
^m ^ D ln l=Dt D : m l_ =l ¼ ¼ , 1=2 1=2 (D : D) (D : D)1=2 (D : D)
(23:9)
^ is the current orientation unit vector, and (D : D)1=2 is where D is the rate of strain tensor, m ^m ^ according to Cauchy–Schwarz’s inequality the magnitude of D and is the limit of D : m [33,34]. It falls in the range of [1,1]. A value of 1 (l_ < 0) would indicate that all the energy dissipated was used to shorten the length of the material line, in effect unmixing it. A value of 1 (l_ > 0) indicates that all the energy dissipated was used to stretch the material line. The maximum efficiency for simple shear flows corresponds to when a material line that was initially oriented perpendicular to the direction of flow is oriented at a 458 angle to the direction of flow with a value of el ¼ (2)1=2=2 0.707, which is the upper bound for 2D flows [34,36]. Likewise, the upper bound for 3D flows is found as t!1 for 3D axisymmetric elongational flow and is el ¼ (2=3)1=2 0.816 [34,36]. This efficiency can be thought of as the fraction of the energy dissipated locally that is used to stretch a fluid element at a given instant in a purely viscous fluid [36]. This physical understanding is based on the fact that the viscous dissipation is defined as D ¼ T : D [40,41]. Then when the generalized Newtonian definition of the stress is used such that T ¼ 2h(g_ )D, the viscous dissipation is D ¼ T : D ¼ 2hD : D, which is always positive and represents an irreversible conversion of mechanical energy into internal energy. Then (D : D)1=2 ¼ (D=2h)1=2. However, when T is defined in such a way that energy can be stored as in viscoelastic fluids, the viscoelastic dissipation is somewhat reversible and can be negative [41]. Therefore, interpretation of the meaning of the efficiency for other than generalized Newtonian fluids becomes nontrivial [34]. The time-averaged efficiency is defined as 1 hel i ¼ t
ðt el dt
(23:10)
eh dt:
(23:11)
0
and
heh i ¼
1 t
ðt 0
Typical behavior of the time-averaged mixing efficiency ranges from the decay of the efficiency with time as t1 for flows with no reorientation such as the simple shearing flow described earlier, to flows with some periodic reorientation but still decaying on average with time as t1, and finally flows with strong reorientation with an average constant value of the efficiency [36]. Elongational flow has been shown to be more effective than simple shear flow for dispersive mixing of clumps [42,43] and breaking of immiscible bubbles and droplets [44,45], especially at high viscosity and low interfacial tension. The Manas-Zloczower mixing index, lMZ [46], which is also known in some contexts as the flow number [47,48], can be considered a mapping of the mechanism of dispersive mixing within the mixer. It is defined as lMZ ¼
jDj , (jDj þ jVj)
(23:12)
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where D is the rate of strain tensor and V is the vorticity tensor, which are the symmetric and asymmetric components of the velocity gradient tensor. It has a range of 0 to 1 with 0.5 being shear flow and 1 being pure elongational flow. The mixing index is not frame invariant [49], and the magnitude of the shear stress must be considered when interpreting it in relation to dispersive mixing [12]. The use of histograms and mappings of lMZ is much more informative than the global volumetric averages. Histograms give a picture of the distribution of lMZ and an indication of the amount of volume that is experiencing the elongational flow conditions necessary for dispersive mixing, while mappings show where in the flow the elongational conditions are found and can be compared with mappings of the stress magnitude in order to get an indication of where the conditions are sufficient for good dispersive mixing. Because the stresses are highly responsive to changes in the operating conditions and geometry, they will dictate how much of the flow indicated as dispersive by the lMZ will actually be effective at dispersive mixing. A criterion of flow classification similar to the Manas-Zloczower mixing index is used in Jongen [50]: Z¼
1 <2 , 1 þ <2
(23:13)
tr(V2 ) tr(D2 )
(23:14)
where <2 ¼
and <2 is the kinematical vorticity number. Pure rotational flow gives a Z value of 1, pure shear flow gives a Z value of 0, and pure extensional flow gives a Z value of 1. This flow parameter has the same nonobjectivity flaw as the Manas-Zloczower mixing index and is used for a similar purpose in examining the mixing ability of a series of 2D mixing geometries. It can be related to the Manas-Zloczower mixing index lMZ by the expression [51]: 2
< ¼
1
lMZ
2 1
:
(23:15)
The classification of the nature of the flow inherent in the Manas-Zloczower mixing index and the criteria used by Jongen [50] has been described as the flow strength [52]. A strong flow is described as the one in which the material lines grow exponentially with time and includes elongational flow [52] and=or flows with hyperbolic streamlines [53]. A strictly weak flow has sinusoidally oscillating material lines and includes those with elliptic streamlines [53] with the outer boundary being rigid-body motion [54]. A marginally weak flow has material lines that are increasing, but not exponentially, and includes flows with straight streamlines [53] and=or shearing and viscometric flows [54]. A flow type criterion that is frame invariant has been introduced by Larson [53] as Sf ¼ o
2(trD2 )2 o
,
(23:16)
tr(D)2
where D D VT D D V is the Jaumann derivative of the rate of strain tensor. Values for this criteria have Sf ¼ 1 for a steady simple-shearing flow and Sf ¼ 1 for a steady
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extensional flow. A normalized version of Larson’s criteria, Ns ¼ Sf=(1 þ Sf), with values ranging from 0 for solid body rotation to 1 for pure elongation has been used with CFD mixing simulations [55–57]. However, since it requires computation of the second derivative for the velocity, high density meshes are needed to minimize the numerical error. This leads to computational facility limitations and limited the ability of the authors to use it extensively in power law simulations of 2D roller mills, 3D kneading disks of corotating twin screw extruders, and 3D axial discharge continuous mixers. Since it was found to give similar information to the Manas-Zloczower mixing index in mixing simulations [56], it is generally not necessary to use the frame invariant normalized version of Larson’s criteria unless comparing mixers simulated in different reference frames.
23.4 CFD ANALYSIS OF MOTIONLESS MIXERS One of the most accurately studied mixing geometries is the motionless or static mixer, because the mixing is achieved by multiple flow division, rather than moving mixing elements that require special treatment. While the geometry is complex, and therefore challenging to properly mesh, the flow is continuous and steady state with easy to define inlet and outlet conditions for velocity and pressure. The resulting CFD simulations are also particularly amenable to validation using pressure drop measurement, as well as flow visualization and laser Doppler anemometry (LDA) velocity measurement. The flow patterns and mixing performance of commercial static mixers have been analyzed in detail with CFD using a combination of the mixing measures listed earlier. Rauline et al. [58,59] studied the mixing performance of several commercial static mixers with a viscous Newtonian fluid using 3D simulations performed by the commercial CFD FEM program POLY3D. They calculated many of the common mixing measures and developed evaluation criteria for the performance of the mixers. CFD has also been used to aid in the design of improved static mixing element configurations for Newtonian fluids [60].
23.5 CFD ANALYSIS OF HELICAL RIBBON MIXERS Tanguy et al. used the agitator as the viewpoint to calculate the flow in a helical ribbon mixer [61] and used a domain decomposition method to calculate the flow in a dual impeller mixer that is composed of a disk turbine and a helical ribbon impeller mounted on the same axis but turning at different speeds [20,62], in which the cylindrical domain surrounding the turbine was meshed separately and the mesh was allowed to slide within the domain that contains the rest of the flow field with the equations of change resolved on the boundaries. The numerical simulations, which used both Newtonian and shear thinning fluid models, accurately predicted experimental power data and allowed comparison of the effectiveness and efficiency of the two mixers.
23.6 CFD ANALYSIS OF MIXING PROCESSES IN STIR TANKS 23.6.1 CFD SIMULATION
OF
MIXING IN
A
STIR TANK
The MST with particle tracking as implemented by Polyflow (Fluent Inc., Lebanon, NH) was used to calculate in 3D the velocity profile, distributive mixing efficiency, and cluster distribution index in a stir tank with and without baffles for a range of Reynolds numbers [17]. Lamberto et al. [63,64] used the FVM Fluent CFD program of Fluent, Inc. using the rotating reference frame technique to explore laminar mixing of a Newtonian fluid
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in an unbaffled stir tank with one impeller and obtained results that were in good agreement with particle image velocimetry (PIV) experiments on seeded glycerin solutions and showed minimal exchange of material between the upper and lower sections of the mixer. Zalc et al. [39] introduced CFD results for a three-impeller unbaffled stir tank with the rotating reference frame technique using the ORCA (Dantec Dynamics, Mahwah, NJ) package that features a FEM parallel solver, acuSOLVE (ACUSIM Software, Saratoga, CA), with eight processors. The results were validated using PIV experiments on a water=glycerine solution with a viscosity of 0.4 Pa s at Re ¼ 20–200. They included an analysis of the calculated magnitude of the deformation tensor, which concluded that the magnitude of the deformation tensor increased nonlinearly with Re. They also analyzed the chaotic versus regular mixing areas by comparing the CFD calculated results with experimental PLIF (PIV=laser-induced fluorescence) results and the circulation velocity. Later results [37] using computational material point tracking results to create Poincare´ sections were able to reveal the segregated regions identified in the experiments and follow their change in shape with changing impeller velocity. These CFD results also revealed the temporal mixing structures by plotting all the points visited by 30,000 material points initially placed in a vertical line from the top to the bottom of the shaft, in a similar fashion to the experiments. Analysis of the arithmetic and volume averages of the length of stretch and the distribution over time of clusters and lines lead to the observation that the mixing does not necessarily improve with increasing Reynolds number, and the positioning of the optimal injection points and other important process parameters is a nontrivial and nonintuitive function of the Reynolds number [39,64]. Kelly and Gigas [65] were able to detect the reason for errors when using the Metzner– Otto approach in transitional flow to predict the power number during mixing of shear thinning power law fluids using CFD with a local rotating reference frame for the stirrer combined with LDA experiments and propose an alternative approach. Choi et al. [66] accurately predicted the mean residence time of an injected inert tracer in viscous Newtonian fluids with a CFD approach that modeled the stirrer as being in a local rotating reference frame.
23.6.2 CFD SIMULATION
OF
CRYSTALLIZATION PROCESSES
The abilities of CFD finite volume method numerical simulation techniques have been coupled with particle population balance theory to predict the crystal size distribution (CSD) in a variety of crystallization processes using multipurpose commercial CFD packages that include Fluent (Fluent Inc., Lebanon, NH) and CFX (ANSYS Inc., Canonsburg, PA). Modeled crystallization processes included crystallization caused by precipitation of the product of a chemical reaction [67–70] and cooling crystallization [71–73]. There have been three main approaches used for incorporating the population balance equation into CFD simulations: discretized population balance [71,72], standard method of moments [67,68,70], and quadrature method of moments [69]. Wei et al. [67] modeled a semibatch crystallizer using a transient expression of the moment transport equations, while the other studies were at a steady state in continuous crystallizers. Marchisio et al. [69] introduced the quadrature method of moments, which was able to simulate aggregation=breakage problems. To predict the crystal size distribution, it becomes necessary to solve the particle population balance equation [74]: @nðv;x,tÞ þ r ve nðv;x,tÞ þ r vi nðv;x,tÞ ¼ Bðv;x,tÞ Dðv;x,tÞ, @t
(23:17)
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where n(v;x,t) represents the number density function; x refers to spatial coordinates that are x,y,z; and v represents particle size. This could be particle volume or a characteristic length dimension of the particle. Consider the number density function as a probability function that tells us the number of particles of a particular size per unit volume. In other words, it represents the size distribution. The first term in the equation is a time-dependent term that describes the evolution of size distribution with time. The second term with ve represents the convection with respect with external coordinates, which is the velocity vector and is the link to fluid mechanics of the system. The velocity field comes into the equation through this term. Traditionally, people assumed plug flow or well-mixed condition or sometimes even a network of zones approach. However, CFD provides the velocity field and thus can be naturally linked with this equation for size distribution. The next term with vi represents the convection with respect to the internal coordinate, particle size (v), typically referred to as the growth rate (G) of the particle. On the right-hand side, we have birth and death terms. The method of moments transforms the population balance equation to reduce its dimensionality to that of a transport equation. The moments can be inverted to obtain the ‘‘most probable’’ size distribution [74]. An alternative to the standard method of moments uses a quadrature approximation [69,74]. The general conclusion was that CFD offered an effective way to study the particular aspect of the crystallization process of interest to the author. For example, Rousseaux et al. [68] found the best agreement between the experiments and simulations when they used a growth rate dependent on particle size for precipitation of pseudoboehmite. Likewise, Mori et al. [72] found their assumption of a diffusional model for crystal growth rates calculate an overall growth rate that was in close agreement with their experiments. As seen in Figure 23.4a through Figure 23.4c, preliminary work by Connelly et al. [73] was able to use the FVM
80 76 72 68 64 60 56 52 48 44 40 36 32 28 24 20 16 12 8 4 0
Z X
Y
(a)
FIGURE 23.4 Results of the numerical simulation of lactose crystallization in an MSMPR crystallizer: (a) constant size velocity vectors on a vertical plane that are shaded by magnitude in cm s1. (Note that vectors that appear smaller are actually pointing into or out of the plane of the page.)
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(b)
0.222 0.222 0.221 0.221 0.22 0.22 0.219 0.219 0.218 0.218 0.217 0.217 0.216 0.216 0.215 0.215 0.214 0.214 Z 0.213 0.213 X Y 0.212
1.00e+20
Length number density (# m−3 m−1)
1.00e+19 MSMPR model Fluent simulation 1.00e+18
1.00e+17
1.00e+16
1.00e+15
1.00e+14
1.00e+13 0.00000 0.00001 0.00002 0.00003 0.00004 0.00005 0.00006 0.00007 0.00008 0.00009
(c)
Particle diameter (m)
FIGURE 23.4 (continued) (b) (See color insert following page 462.) Volume fraction of lactose crystals on a horizontal plane. (Note that the two shaded boxes in flow domain are the inlet and outlet positions. The lowest volume fraction of crystals is located near the inlet.) (c) Lactose crystal size distributions predicted by the MSMPR lactose crystallization model and the CFD Fluent simulation. (From Connelly, R.K., Dhanasekharan, K., and Hartel, R., Institute of Food Technologists Annual Meeting, Las Vegas, NV, July 12–16, 2004.)
CFD code Fluent (Fluent Inc., Lebanon, NH) with the mesh, shown in Figure 23.2, to recreate a crystal size distribution similar to that predicted by a mixed-suspension, mixedproduct-removal (MSMPR) model for lactose crystallization [75]. They were also able to identify evidence of short-circuiting, as well as stagnation behind the baffles that can be seen in Figure 23.4b. Now that the population balance module is publicly available in Fluent 6.3, work on simulation of lactose crystallization is continuing.
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23.7 CFD ANALYSIS OF DOUGH MIXING PROCESSES 23.7.1 CFD SIMULATION OF VISCOELASTIC BEHAVIOR DOUGH MIXING GEOMETRIES
IN
SIMPLIFIED
Due to the complexity of both dough mixers and the viscoelastic rheological behavior of dough materials, much of the application of CFD to simulate and analyze dough mixers has been done using simplified representative geometries and fluid models. In order to systematically study the effect of shear thinning and viscoelasticity on mixing flows, Connelly and Kokini [76] used representative series fluid models that include the viscous Newtonian and shear thinning Carreau models, as well as the differential viscoelastic Oldroyd-B and PhanThien–Tanner (PTT) models. The viscosity of the Newtonian and Oldroyd-B models were identical, whereas the steady shear viscosity profiles of the Carreau and PTT fluid models were nearly identical and of the same magnitude as the Newtonian viscosity in the shear rate range of interest. The models’ mixing geometry consisted of a simplified model 2D mixer consisting of a paddle in a rotating cylindrical barrel shown in Figure 23.1, which is based on the geometry of the 2’’ Readco Continuous Processor (Readco Manufacturing Inc., York, PA). This simple 2D case can be considered a batch simulation of a paddle in a cylindrical tank [77]. The FEM techniques described in Connelly and Kokini [5] were used to generate flow profiles and then to calculate trajectories for material points with random initial positions. The mapping of the shear stress in the gap in Figure 23.5 shows that shear thinning reduces the magnitude of stresses generated, with the generalized Newtonian fluid models showing a symmetric pattern at this low speed, whereas viscoelastic fluid models show asymmetry. The asymmetry seen in the viscoelastic results appears to be driven by the way each of the viscoelastic fluid models respond to a step change in the shear rate, which is effectively what we have in the entrance and exit to the gap [51]. The two viscoelastic fluid models used here respond to a step change in the shear rate in very different ways, with the Oldroyd-B model experiencing a significantly delayed relaxation response and the PTT model experiencing a delayed response followed by moderate stress overshoot. These different responses are reflected in the different patterns seen in the two fluid shear stress results.
1.0e+06 8.0e+05 6.0e+05 4.0e+05 2.0e+05 0.0e+00 –2.0e+05 –4.0e+05 –6.0e+05 –8.0e+05
(a)
–1.0e+06
Y Z
X
FIGURE 23.5 Shear stress generated in the gap for (a) constant viscosity Newtonian.
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5.0e+04 3.5e+04 2.0e+04 5.0e+03 –1.0e+04 –2.5e+04 –4.0e+04 –5.5e+04 –7.0e+04
Y –8.5e+04
(b)
–1.0e+05
X
Z
1.0e+06 8.0e+05 6.0e+05 4.0e+05 2.0e+05 0.0e+00 –2.0e+05 –4.0e+05 –6.0e+05
Y –8.0e+05
(c)
–1.0e+06
Z
X
5.0e+04 3.5e+04 2.0e+04 5.0e+03 –1.0e+04 –2.5e+04 –4.0e+04 –5.5e+04 –7.0e+04 –8.5e+04
(d)
–1.0e+05
Y Z
X
FIGURE 23.5 (continued) (b) Shear thinning Carreau, (c) constant viscosity, differential viscoelastic Oldroyd-B, and (d) shear thinning, differential viscoelastic Phan-Thien–Tanner fluid models. (From Connelly, R.K., PhD dissertation, Rutgers University, New Brunswick, NJ, 2004.)
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0.25
Time-averaged efficiency
0.20
0.15
Mean, Newt. SD, Newt. Mean, BC
0.10
SD, BC Mean, OB SD, OB Mean, PTT
0.05
SD, PTT
0.00 −0.05
0
60
120
180
240
300
360
420
480
540
600
Time (s)
FIGURE 23.6 Effect of rheology on the mean and standard deviation of the time-averaged efficiency during mixing in the single-paddle mixer. (Reprinted from Connelly, R.K. and Kokini, J.L., J. NonNewton. Fluid, 123, 1, 2004. With permission from Elsevier.)
In particular, behind the trailing edge of the paddle (the right edge in Figure 23.5), a small region of low shear stress is seen in the PTT model likely due to stress overshoot, whereas the stress remains much higher for a wider range behind the trailing edge of the paddle in the Oldroyd-B model than in its Newtonian counterpart, as the stress lags in relaxing with the fast reduction in shear rates that occur after the material exits the gap. The subtle effects of the rheology on the secondary velocity profiles translated into obvious differences in the mixing effectiveness, especially in the areas near the gap and in the period of the circulation. For example, the circulation pattern seen in the secondary flow profiles described in Connelly and Kokini [5] dominates the mixing effectiveness of this geometry. Material points did not distribute effectively in this simple 2D geometry, but were trapped within the circular streamlines such that they spread out like beads on a necklace as shown in Figure 23.7a, except very near the gap. The mixing measures all showed the cyclic nature of the mixing in this geometry as demonstrated in the oscillations of the length of stretch of the single blade mixer in Figure 23.9, with rheology effecting the circulation time [76]. Since there was no mechanism to reorient the material lines in this geometry, the mean time-averaged efficiency decayed as t1 as shown in Figure 23.6. The effects of energy storage and release in the viscoelastic PTT fluid model were illustrated by the mean time-averaged efficiency of the mixing as it became negative after just five revolutions. A group at the University of Wales used a combination of numerical modeling and experimental results in model mixers to better understand dough kneading in order to improve performance of industrial dough mixers [78–81]. They used single and double concentric cylinder mixers for both modeling and experimental analysis of the flow and mixing in filled and partially filled conditions. In particular, they studied the wetting and peeling of dough and other liquids on solid surfaces and present methods to model the free surfaces. Their simulations were done using a FEM semi-implicit time-stepping Taylor– Galerkin=pressure-correction scheme and their results include viscoelastic Oldroyd-B and PTT fluid models’ simulations of the fully filled wall-driven mixer case with concentric,
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FIGURE 23.7 Particle tracking results showing the distributive mixing of a cluster 100 of noncohesive, material points (a) initially and after 10 revolutions in the single-paddle mixer and (b) initially and after 10 revolutions in the twin-paddle mixer. (Reprinted from Connelly, R.K. and Kokini, J.L., J. Food Eng., Published on-line, 2006. With permission from Elsevier.)
eccentric, and double eccentric rotating pin mixers. They found the asymmetrical stirrer positioning of a single stirrer to provide the best mixing of viscoelastic fluids. Their experimental techniques included laser scatter technology, LDA, and a video capture technique to determine velocity profiles and peeling stresses in a prototype industrial mixer allowing both horizontal and vertical orientations and mixing speeds between 25 and 450 rpm with the cylindrical bowl and stirring rods fashioned from Perspex. Close agreement was found between numerical and experimental flow fields and free surface profiles.
23.7.2 CFD ANALYSIS OF MIXING IN DOUGH MIXERS USING GENERALIZED NEWTONIAN FLUID MODELS Although using fluid models that accurately simulate the complex behavior of dough in CFD simulations of actual dough mixers remains a future goal, the ability to model flow and mixing using the complex motions and geometries generally employed in dough mixers with simpler Newtonian and generalized Newtonian fluid models has become possible. One of the first attempts at simulating the complex flow patterns in more realistic dough mixer geometries was reported by Jongen and coworkers [50,82]. They did 2D numerical simulation of several batch dough mixers with a Newtonian fluid model using the FEM CFD package Fidap (Fluent, Inc., Lebanon, NH). The movement of the mixing elements was taken into account using a variant of the fictitious domain method [16,83]. They evaluated the flow type using a normalized flow strength parameter based on the invariants of the velocity gradient tensor [36,54] and followed the paths of a limited number of material points. Initial comparisons of the oven rise of crispy rolls mixed in the four dough-mixers studied compared with the space- and time-averaged flow type parameter suggested that a deformation combining
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Single screw — b2 Twin screw — b2
Cluster distribution index
0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 0
1
2
3
4
5
6
7
8
9
10
Revolutions
FIGURE 23.8 Variation in the cluster distribution index over 10 revolutions for clusters of 100 noncohesive, material points initially located at the top of the leftmost section of the flow region of the 2D single- and twin-blade mixers. (Reprinted from Connelly, R.K. and Kokini, J.L., J. Food Eng., 79, 956, 2006. With permission from Elsevier.)
shear and elongation as done in the planetary pin mixograph geometry was the most effective. A 3D FEM study that also considered shear thinning fluid behavior found model rotating pin mixers to provide the highest level of elongation and model twin z-blade mixers to provide the highest strain rates, while shear thinning fluids generated larger stagnant zones than the Newtonian fluids [48]. A 2D study comparing the mixing ability of a single-paddle versus a twin-paddle mixer design by Connelly and Kokini [84] using a more representative generalized Newtonian– Carreau dough model [85] showed the much-greater mixing effectiveness of the twinpaddle design, as seen from its ability to distribute a cluster of noncohesive material points in Figure 23.7. The cluster distribution index results generated by that cluster are found in Figure 23.8 and show oscillations that are caused by the stringing out and reforming of the cluster in the single-paddle mixer. The twin-paddle results oscillate at much lower amplitude and are at a lower magnitude that indicates it is closer to an ideal random distribution. A comparison of the mean length of stretch of the two mixers in Figure 23.9 shows that the twin-paddle mixer demonstrates a logarithmic increase in the length of stretch, which is a necessary requirement for effective distributive mixing. The single-paddle mixer values stagnate due to the fact that the particles remain stuck on their streamlines as seen in Figure 23.7a. Connelly and Kokini [51,86,87] have done realistic 3D FEM numerical simulations of the farinograph (C.W. Brabender, S. Hackensack, NJ) using Polyflow (Fluent, Inc., Lebanon, NH). The farinograph is a low shear rate batch dough mixer with two nonintermeshing, asymmetrical sigma blades, where the fast (right) blade turns at 93 rpm counterclockwise and the slow (left) blade turns at 62 rpm clockwise. CAD STEP representations of the blade geometries were provided by C.W. Brabender Instruments, Inc. and transformed into meshes using Gambit (Fluent, Inc., Lebanon, NH). Because the blades turn at different speeds, two revolutions of the slow blade and three revolutions of the fast blade are required before there is repetition of the relative blade positions. The left (slow) blade mesh of 6232 tetrahedral
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16 Single screw—mean Single screw—SD Twin screw—mean Twin screw—SD
ln(length of stretch)
14 12 10 8 6 4 2 0 0
1
2
3
6 4 5 Revolutions
7
8
9
10
FIGURE 23.9 The arithmetic mean and standard deviation of the length of stretch over 10 revolutions of the mixing paddles of the 2D single- and twin-blade mixers. (Reprinted from Connelly, R.K. and Kokini, J.L., J. Food Eng., Published on-line, 2006. With permission from Elsevier.)
elements and the right (fast) blade mesh of 6166 elements were superimposed on the bowl (41,860 hexahedral elements) every 0.027 s, as shown in Figure 23.3, giving a total of 72 positions per blade cycle with 108 between positions for the slow blade and 158 between positions for the fast blade. The simulations were done with rheological fluid models for a high-viscosity Newtonian corn syrup over an entire mixing cycle and at two positions for a shear thinning 2% CMC solution and a highly shear thinning 0.11% Carbopol solution. The fill and boundary conditions matched those used to generate available experimental LDA data [88–90]. The time marching flow simulation results were then used to generate particle tracking data for 10,000 material points initially randomly distributed throughout the flow domain as shown in Figure 23.12a. The concentration was initially assigned as 1 to material points on the left and 0 to those on the right as viewed from the front. As these abstract points were tracked throughout the flow domain, the associated local flow and mixing characteristics were recorded at each time-step, thus providing a spatial and temporal history of phenomena such as stretching and deformation. The effect of varying the rheology is evident in the shear rate and mixing index result maps shown in Figure 23.10 and Figure 23.11, with the areas of high elongation at the top of the mixer shifting closer to the blades as the level of shear thinning increased. This should serve to improve the dispersive mixing in these zones as the shear rate was also intensified by shear thinning. The cost of this was a decrease in the dispersive mixing effectiveness near the top of the mixer, but fortunately this should not be a problem since this zone would not be filled during the normal operation of this mixer. Within the area swept by the blades, the areas of reorientation or rotating flow grew in size with increased shear thinning, but in the regions where the shear rate was already the lowest. The Newtonian fluid material point tracking results showed that the differential in the speed of the two blades in the farinograph caused an occurrence of exchange of material between the blades. The primary circulation pattern, which is evident in Figure 23.12b, consists of material moving from the slow blade up toward the top of the mixer and over
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FIGURE 23.10 Simulated mixing index on a plane across center of bowl ( y ¼ 4.225 cm) for (a) Newtonian corn syrup. (b) shear thinning 2% CMC, and (c) highly shear thinning 0.11% Carbopol. (From Connelly, R.K. and Kokini, J.L., Adv. Polym. Tech., 25, 182, 2006. With permission.)
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FIGURE 23.11 Simulated shear rates on plane across center of bowl ( y ¼ 4.225 cm) for (a) Newtonian corn syrup, (b) shear thinning 2% CMC, and (c) highly shear thinning 0.11% Carbopol. (From Connelly, R.K. and Kokini, J.L., Adv. Polym. Tech., 25, 182, 2006. With permission.)
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FIGURE 23.12 3D positions of 10,000 initially randomly distributed material points (a) with initial concentrations of 1 (light gray) on the left and 0 (dark gray) on the right viewed from the front and (b) after three blade cycles. (From Connelly, R.K. and Kokini, J.L., AIChE J., 52, 3383, 2006.)
toward the fast blade. The fast blade pushes material toward the slow blade near the bottom of the mixer. A slower mixing pattern is also observed where material around the blades moves from the center toward the walls and then up toward the top and back down in the center of the mixer [86]. The zone in the center of the mixer between the two blades is shown to have excellent distributive and dispersive mixing ability with high shear rates and mixing index values [87]. That region also has fast distribution throughout both sides of the lower section of the mixer as shown by material point clusters that travel through it [86]. In contrast, very slow mixing is seen near the top in the area away from the region swept by the blades that is generally not filled during normal use of this mixer (see Figure 23.12b). The evolution of the segregation scale over three blade cycles with this initial concentration profile is shown in Figure 23.13 and indicates that the average size of segregated regions is continuing to drop slowly but steadily, while the values for a front=back initial concentration drops quicker at first but then levels off. A similar 3D FEM study [91,92] has recently been undertaken on the reomixer (Reologica Instruments, Lund, Sweden), which has a revolving planetary pin mixer geometry similar to
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4.5
Scale of segregation (cm)
4.0
Left /right Front /back
3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0
360
720 1080 1440 Rotation of slow blade (°)
1800
2160
FIGURE 23.13 Segregation scale for material points initially segregated between the front and back or the left and the right sides of the mixer over three cycles of the blades. (From Connelly, R.K. and Kokini, J.L., AIChE J., 52, 3383, 2006.)
the mixograph (National Manufacturing, Lincoln, NB) as seen in Figure 23.14. The position of the revolving pairs of planetary pins resets every 2.73 s after three revolutions of the moving pins around their planetary axis and four revolutions of the planetary axis that rotates at 88 rpm. The motion of the pins have been mapped and modeled by Walker and Hazelton [93]. A rotating reference frame was used with mesh superposition of both the stationary (light gray in Figure 23.14) and revolving pairs of planetary pins (dark gray in Figure 23.14). This approach simplified the mapping of the motion of the rotating pairs of planetary pins to two circles on the flow domain with the three stationary pins revolving
FIGURE 23.14 Geometry and mesh superposition mesh in a rotating reference frame for a rotating planetary pin mixograph type mixer. (From Jordan, J.B., MS thesis, University of Wisconsin-Madison, Madison, WI, 2006.)
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FIGURE 23.15 Velocity vectors sized by magnitude on a vertical plane in a reomixer, a revolving planetary pin mixograph type mixer. The maximum velocity magnitude is 0.253 m s1. (From Connelly, R.K., Jordan, J.B., and Kokini, J.L., American Association of Cereal Chemists International, World Grains Summit: Foods and Beverages, San Francisco, CA, September 17–20, 2006.)
around the center of the bowl on a third circle [92]. Then the flow domain mesh was designed to better represent the shape of the superimposed pins with a greatly reduced area in the flow domain that had to be made dense in order to better capture the flow gradients near where the pins passed. A velocity profile at one position of the pins is shown in Figure 23.15 [91]. Note the intense velocity magnitude as the material squeezes between the stationary and planetary pins near the top and the folding motion seen near the lower left stationary pin in Figure 23.15. The effect of these flow patterns on the mixing is demonstrated in Figure 23.16 [92], with the distributive mixing pattern caused by the folding and squeezing still evident after 2 revolutions of the planetary gear and 1.5 revolutions of the pins around their axis, which is a half
FIGURE 23.16 Top view of positions and concentrations of 10,000 material points in the reomixer (a) initially with assigned concentrations of 1 (light gray) on the left and 0 (dark gray) on the right.
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FIGURE 23.16 (continued) (b) After a half geometry reset cycle and (c) after three geometry reset cycles. (From Jordan, J.B., MS thesis, University of Wisconsin-Madison, Madison, WI, 2006.)
geometry reset cycle. After three geometry reset cycles, the initially segregated material points appear to be randomly distributed. However, there is little evidence of vertical motion in Figure 23.15 and this is seen in the mixing pattern in Figure 23.17 [92]. After three complete resets of the geometry, there is very little distributive mixing between the layers, especially near the top, and indicates that 2D simulations of this geometry will provide realistic flow patterns and mixing results. As evident from the preceding discussion, the flow patterns and mixing action of the farinograph and the mixograph are very different even though they are used for similar purposes in the food industry. A direct comparison of the mean of the normalized length of stretch calculated for material points in the Newtonian fluid case in both the farinograph and the mixograph type reomixer in Figure 23.18 [86,91,92] shows that it increased exponentially
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FIGURE 23.17 Side view of positions and concentrations of 10,000 material points in the reomixer (a) initially with assigned concentrations of 1 (light gray) and 0 (dark gray) in horizontal layers and (b) after three geometry reset cycles. (From Jordan, J.B., MS thesis, University of Wisconsin-Madison, Madison, WI, 2006.)
over time in both mixers, indicating effective mixing for the majority of material points. However, the reomixer mean length of stretch increases at a faster rate. In both mixers, the mean time-averaged efficiency plotted in Figure 23.19 [86,91,92] stays above zero while its standard deviation reduces over time, indicating that the majority of the points are continuously experiencing stretching over time. However, while the reomixer is initially more efficient, over time the CFD results indicate that the farinograph maintains a higher level of efficiency with a faster drop in the standard deviation. 12 Reomixer Farinograph Mean of ln(length of stretch)
10 8 6 4 2 0
0
1
2
3
4 Time (s)
5
6
7
8
FIGURE 23.18 Arithmetic mean of the natural log of the length of stretch generated over time by 10,000 infinitesimal material lines in the farinograph and reomixer. (From Connelly, R.K., Jordan, J.B., and Kokini, J.L., American Association of Cereal Chemists International, World Grains Summit: Foods and Beverages, San Francisco, CA, September 17–20, 2006.)
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0.4 Reomixer—mean Reomixer—SD Farinograph—mean Farinograph—SD
Time-averaged efficiency
0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0
1
2
3
4 Time (s)
5
6
7
8
FIGURE 23.19 Evolution of the mean time-averaged efficiency of mixing for 10,000 infinitesimal material lines in the farinograph and reomixer. (From Connelly, R.K., Jordan, J.B., and Kokini, J.L., American Association of Cereal Chemists International, World Grains Summit: Foods and Beverages, San Francisco, CA, September 17–20, 2006.)
23.8 CONCLUSIONS The recent advances in numerical simulation techniques give CFD applications the ability to handle the complex motions of the mixing elements in various types of mixing processes that range from simple model mixing geometries to complex intermeshing mixing geometries, particularly with Newtonian fluids. This in turn has allowed researchers to more effectively use existing mixing measures and develop new mixing measures for analyzing the effectiveness of the mixing under varying conditions and for various purposes. In some cases, CFD simulation and analysis of mixing have advanced to the point where design improvements and optimization of mixing processes is possible. Future work will need to extend existing CFD applications or develop new CFD approaches to handle the more complex fluid rheology that is typical of many fluid foods, particularly those that require highly shear thinning or viscoelastic fluid models. In addition, CFD simulations are only as good as the inputs that are used, so in many cases more accurate fluid and boundary condition models are needed that better represent the actual behavior found in food systems, particularly time and strain dependent or viscoelastic fluid behavior, as well as free surface boundary conditions. As these issues are worked out, the application of CFD to simulate and analyze mixing has the potential to greatly improve the efficiency and effectiveness of food mixing processes as well as aiding in the design, changeover, and scale-up of food mixing equipment.
NOMENCLATURE A, a B(v;x,t) c(r) c0j and c00j c
initial and current positions of infinitesimal material surfaces (cm2 or m2) particle or crystal birth rate (# mL1 min1) coefficient of the probability density function concentration ratio of the points in the jth pair average concentration ratio
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D o D D D(v;x,t) el , eh F f f(r) G H i, j k k Ls M ^ m n n(v;x,t) N Ns p Re R(jrj) < r r, ri0 S Sf T t tr v, ve virf, vrrf vp v, v0 vi v X,x x,y,z Z
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rate of strain tensor (s1) Jaumann derivative of the rate of strain tensor dimensionality particle or crystal death rate (# mL1 min1) length and area efficiency of mixing deformation gradient body force (dyne or newton) pairwise correlation function particle or crystal size growth rate (mm min1) coefficient of the penalty force term index variables unit vector in the z-direction kinetic energy of turbulence (J) scale of segregation number of pairs current orientation unit vector number of periods particle or crystal number density function (# m3) number of points or nodes normalized flow strength number pressure (Pa or dyne cm2) Reynolds number Eulerian coefficient of correlation between concentrations of pairs of points Flow parameter ratio Distance between a pair of points or radius (cm or m) Radial positions of material points and radial position of point i sample variance flow strength extra stress tensor (Pa or dyne cm2) time (s or min) trace or sum of the diagonal elements of a tensor velocity vector (cm s1 or m s1) velocity vectors in the inertial and rotating reference frames (cm s1 or m s1) moving part velocity (cm s1 or m s1) equilibrium and fluctuating velocity components in turbulent flow (cm s1 or m s1) particle or crystal size growth rate due to internal convection (mm s1, cm s1, or m s1) particle or crystal size in either length (mm, cm, or m) or volume (cm3 or m3) initial and current positions of a fluid element (cm or m) position variable for global Cartesian coordinates (cm or m) normalized flow classification measure
GREEK SYMBOLS a b0 x D = d()
scaling constant compression factor flow domain with boundary @x viscous dissipation (Pa s1 or dyne cm2 s1) differential operator Kronecker delta
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« g_ h l l, hli lMZ m, meff, mt L r V V z
583
cluster distribution index or rate of dissipation of turbulence (m2 s3) strain rate or shear rate (s1) area stretch (normalized) or viscosity (Pa s or poise) or partial viscosity length of stretch (normalized) arithmetic and geometric means of the length of stretch Manas-Zloczower mixing index viscosity, effective viscosity, and turbulent or eddy viscosity (Pa s or poise) Lyapunov exponent or growth rate of the geometric average of the ln l topological entropy or growth rate of the arithmetic average of the ln l density (kg m3 or g mL1) vorticity tensor (s1) angular velocity=mixing speed (rpm or s1) or flow domain distance between pair of points where there is no longer any correlation (cm or m)
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64. D.J. Lamberto, M.M. Alvarez, and F.J. Muzzio. Computational analysis of regular and chaotic mixing in a stirred tank reactor. Chemical Engineering Science 56(16): 4887–4899, 2001. 65. W. Kelly and B. Gigas. Using CFD to predict the behavior of power law fluids near axialflow impellers operating in the transitional flow regime. Chemical Engineering Science 58(10): 2141–2152, 2003. 66. B.S. Choi, B. Wan, S. Philyaw, K. Dhanasekharan, and T.A. Ring. Residence time distributions in a stirred tank: Comparison of CFD predictions with experiment. Industrial and Engineering Chemistry Research 43(20): 6548–6556, 2004. 67. H. Wei, W. Zhou, and J. Garside. Computational fluid dynamics modeling of the precipitation process in a semibatch crystallizer. Industrial and Engineering Chemistry Research 40(23): 5255– 5261, 2001. 68. J.-Rousseaux, C. Vial, H. Muhr, and E. Plasari. CFD simulation of precipitation in the slidingsurface mixing device. Chemical Engineering Science 56(4): 1677–1685, 2001. 69. D.L. Marchisio, R.D. Vigil, and R.O. Fox. Quadrature method of moments for aggregation– breakage processes. Journal of Colloid and Interface Science 258(2): 322–334, 2003. 70. Z. Jaworski and A.W. Nienow. CFD modelling of continuous precipitation of barium sulphate in a stirred tank. Chemical Engineering Journal 91(2–3): 167–174, 2003. 71. Z. Sha, P. Oinas, M. Louhi-Kultanen, G. Yang, and S. Palosaari. Application of CFD simulation to suspension crystallization: Factors affecting size-dependent classification. Powder Technology 121(1): 20–25, 2001. 72. Y. Mori, Z. Sha, M. Louhi-Kultanen, and J. Kallas. CFD study of local crystal growth rate in a continuous suspension crystallizer. Journal of Chemical Engineering of Japan 35(11): 1178–1187, 2002. 73. R.K. Connelly, K. Dhanasekharan, and R. Hartel. Crystallization of lactose: Modeling and experiments (abstract and presentation). Institute of Food Technologists Annual Meeting. Las Vegas, NV, July 12–16, 2004. 74. A.D. Randolph and M.A. Larson. Theory of Particulate Processes: Analysis and Techniques of Continuous Crystallization, 2nd ed. San Diego, CA: Academic Press, 1988. 75. B. Liang, Y. Shi, and R.W. Hartel. Growth rate dispersion effects on lactose crystal size distributions from a continuous cooling crystallizer. Journal of Food Science 56(3): 848–854, 1991. 76. R.K. Connelly and J.L. Kokini. The effect of shear thinning and differential viscoelasticity on mixing in a model 2D mixer as determined using FEM with particle tracking. Journal of NonNewtonian Fluid Mechanics 123(1): 1–17, 2004. 77. A. Youcefi, D. Anne-Archard, H.C. Boisson, and M. Sengelin. On the influence of liquid elasticity on mixing in a vessel agitated by a two-bladed impeller. Journal of Fluids Engineering 119: 616–622, 1997. 78. A. Baloch, P.W. Grant, and M.F. Webster. Parallel computation of two-dimensional rotational flows of viscoelastic fluids in cylindrical vessels. Engineering Computations 19: 820–853, 2002. 79. D.M. Binding, M.A. Couch, K.S. Sujatha, and M.F. Webster. Experimental and numerical simulation of dough kneading in filled geometries. Journal of Food Engineering 58: 111–123, 2003. 80. M.A. Couch and D.M. Binding. An experimental study of the peeling of dough from solid surfaces. Journal of Food Engineering 58: 299–309, 2003. 81. K.S. Sujatha, M.F. Webster, D.M. Binding, and M.A. Couch. Modelling and experimental studies of rotating flows in part-filled vessels: Wetting and peeling. Journal of Food Engineering 57: 67–79, 2003. 82. T.R. Jongen, M.V. Bruschke, and J.G. Dekker. Analysis of dough kneaders using numerical flow simulations. Cereal Chemistry 80(4): 383–389, 2003. 83. F. Bertrand, R. Giguere, and P.A. Tanguy. A three-dimensional mesh refinement strategy for the simulation of fluid flow with a fictitious domain method. Computers and Chemical Engineering 30(3): 453–66, 2006. 84. R.K. Connelly and J.L. Kokini. Examination of the mixing ability of single and twin screw mixers using 2D finite element method simulation with particle tracking. Journal of Food Engineering 79(3): 956–969, 2006. 85. M. Dhanasekharan, H. Huang, and J.L. Kokini. Comparison of the observed rheological properties of hard wheat flour dough with the predictions of the Giesekus–Leonov, the White–Metzner, and the Phan-Thien–Tanner models. Journal of Texture Studies 30(5): 603–623, 1999.
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86. R.K. Connelly and J.L. Kokini. Mixing simulation of a viscous Newtonian liquid in a twin sigma blade mixer. AIChE Journal 52(10): 3383–3393, 2006. 87. R.K. Connelly and J.L. Kokini. 3D numerical simulation of the flow of viscous Newtonian and shear thinning fluids in a twin sigma blade mixer. Advances in Polymer Technology 25(3): 182–194, 2006. 88. S. Prakash, M.V. Karwe, and J.L. Kokini. Measurement of velocity distribution in the brabender farinograph as a model mixer, using laser-Doppler anemometry. Journal of Food Process Engineering 22(6): 435–454, 1999. 89. S. Prakash and J.L. Kokini. Determination of mixing efficiency in a model food mixer. Advances in Polymer Technology 18(3): 209–224, 1999. 90. S. Prakash and J.L. Kokini. Estimation and prediction of shear rate distribution as a model mixer. Journal of Food Engineering 44(3): 135–148, 2000. 91. R.K. Connelly, J.B. Jordan and J.L. Kokini. Comparison of the flow and mixing patterns in laboratory flour testing mixers using numerical simulation (abstract and presentation). American Association of Cereal Chemists International, World Grains Summit: Foods and Beverages, San Francisco, CA, September 17–20, 2006. 92. J.B. Jordan. CFD simulation development and mixing analysis of a Newtonian fluid in a 3D mixograph style mixer. MS thesis, University of Wisconsin-Madison, Madison, WI, 2006. 93. C.E. Walker and J.L. Hazelton. Mixograph pin paths and points of minimum clearance. In: C.E. Walker, J.L. Hazelton, and M.D. Shogren (Eds.). The Mixograph Handbook. Lincoln, NE: National Manufacturing, 1998, pp. 33–37.
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CFD Simulation of Multiphysical– Multi(bio)chemical Interactions of Tea Fermentation and Infusion Guoping Lian
CONTENTS 24.1 24.2
Introduction ............................................................................................................. 589 Modeling Tea Fermentation .................................................................................... 590 24.2.1 Biochemical Reactions during Tea Fermentation ....................................... 590 24.2.2 Airflow and Heat Transfer.......................................................................... 591 24.2.3 Integrated Product–Process Design............................................................. 592 24.3 Modeling Tea Bag Infusion ..................................................................................... 594 24.3.1 Tea Bag Brewing Method ........................................................................... 594 24.3.2 Multiphysical Process of Tea Bag Infusion................................................. 595 24.3.3 Integrating Tea Bag Design with In-Use Brewing ...................................... 596 24.4 Conclusion ............................................................................................................... 600 Nomenclature ..................................................................................................................... 600 References .......................................................................................................................... 601
24.1 INTRODUCTION Many agricultural and food products have complex microstructure with multiphase compositions. Processing of agricultural and food products also involves multiphysical and multi(bio)chemical interactions. In order to optimize the delivery of flavor, texture as well as the nutritional and health benefits of agricultural and food products, it is not only necessary to integrate the design of product with process, but also important to understand the interaction of finished product with in-use process. Unfortunately, in agricultural and food industry, the design of both product and process still remains as largely empirical. The physical, chemical, and biochemical interactions taking place during both processing and in-usage are mostly not fully understood. In recent years, computational fluid dynamics (CFD) has found increasing applications in agriculture and food industry. A main advantage of the CFD method is that the multiphysical and multi(bio)chemical interactions can be modeled simultaneously. The method also offers the potential to fully integrate product design with process and in-use delivery. In this chapter, two examples are demonstrated using CFD method to simulate the multiphysical and multi(bio)chemical interactions during tea fermentation and tea bag infusion. In the first
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application of tea fermentation, the enzymatic oxidation of flavonoids interacts with airflow and heat transfer through the porous packed bed of leaf dhool. By predicting the interplay between the heat transfer and enzymatic reactions during tea fermentation, the optimal process conditions for desired flavor generation and functional properties can be obtained. In the second application of tea bag infusion, the release of tea flavor and other soluble solids interacts with the fluid flow through and around the tea bag. The aim is to show that CFD simulation allows the integration of tea bag design with the in-use process of brewing so as to achieve optimal delivery of color, flavor, and health benefits of the tea drink.
24.2 MODELING TEA FERMENTATION 24.2.1 BIOCHEMICAL REACTIONS
DURING
TEA FERMENTATION
Tea fermentation is an important process step of black leaf tea manufacture. The major process steps of black leaf tea manufacture include withering, maceration, fermentation, and drying. Fermentation is the key process stage where the characteristic molecular compounds responsible for the sensorial properties of black tea are produced. During tea fermentation, several physical and biochemical processes interact. The dominant interactions include the complex enzymatic oxidations and the coupling with heat transfer and airflow through the packed bed of porous tea leaf particles. Heat is also generated by enzymatic oxidation of tea polyphenols. The enzymatic oxidation is an important biochemical process for the development of the unique color and flavor of black leaf tea. Initiated by polyphenol oxidase present in tea leaves, the biochemical reactions that take place during fermentation have complex pathways. The major reactions involve the oxidation of four flavanol species of catechins including epicatechin (EC), epicatechin-gallate (ECG), epigallocatechin (EGC), and epigallocatechingallate (EGCG). The reactive quinines of oxidized catechins can be paired to form four dimmers of theaflavin (EC þ EGC), theaflavin-3-gallate (EC þ EGCG), theaflavin-30 -gallate (ECG þ EGC), and theaflavin-3,30 -diggalate (ECG þ EGCG). Collectively, those dimmers are called as theaflavins and contribute to the unique color and taste of black tea. Theaflavins are unstable products and are further oxidized to form a heterogeneous group of compounds called thearubigins [1]. Thearubigins can be also formed from the reactive quinines of oxidized catechins. More details of the biochemistry of tea fermentation can be found elsewhere [2]. To summarize, there are 12 major biochemical reaction pathways: four synthetic reactions for the formation of the four dimmers of theaflavins, four reactions for the direct oxidation of the four major catechin species to thearubigins, and four reactions for the further oxidative transformation of the four theaflavin species to thearubigins. The reaction for the oxidation of the four catechins and four dimmers (theaflavins) is modeled by the Michaelis–Menten equation [3], which is written as
r¼
k[c] s þ [c]
(24:1)
where r is the reaction rate, [c] is the concentration of the reactant, k and s are the Michaelis– Menten constants. For the formation of the four theaflavin species, the following modified Michaelis– Menten equation was used to model the reaction rate:
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rf ¼
kf [ca ][cb ] sf þ [ca ][cb ]
(24:2)
where rf is the rate of theaflavin formation, [ca ] and [cb ] are the concentrations of the two associated catechin species, and kf and sf are the two reaction constants.
24.2.2 AIRFLOW
AND
HEAT TRANSFER
The fermentation process under consideration is an experimental system consisting of a cylindrical glass container with a metal mesh mounted at the bottom. Macerated dhool of tea leaf was evenly placed on a metal mesh to form a packed bed. The packed bed was aerated using saturated air fed from below the metal mesh. Airflow through the packed bed follows porous flow equation and the Forchheimer–Brinkman model was used. Airflow through the packed bed of porous leaf dhool is coupled with enzymatic oxidation through the heat transfer equation. During tea fermentation, heat is generated. The rate of heat generation is found to correlate well with the rate of catechin oxidation as shown in Figure 24.1. The relationship is best fitted by the following equation: Q ¼ kr rcat
(24:3)
where Q is the rate of heat generation, kr is a scaling constant, and rcat is the rate of catechin oxidation. When the rate of catechin oxidation is given in mg s1 , the best fitted value of kr is 360 J mg1 . This value of kr is considered with the rate of heat generation during tea fermentation given in J s1 . The rate of enzymatic oxidation during tea fermentation depends on the temperature. The relationship was described by the following Arrhenius equation for the reaction rate constants of the Michaelis–Menten equation: E 1 1 k ¼ k0 exp R T T0
(24:4)
450
Rate of heat generation (J s−1)
400 350 y = 359.64x
300
R 2 = 0.9676
250 200 150 100 50 0 0
0.2
0.4
0.6
0.8
Rate of catechin oxidation (mg
1
1.2
s−1)
FIGURE 24.1 Heat generation as a function of catechin oxidation during leaf tea fermentation.
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TABLE 24.1 Reaction Rate Constants and Activation Energy for Enzymatic Oxidations during Tea Fermentation Reaction Pathway Formation of TF Formation of TF-3-g Formation of TF-30 -g Formation of TF-3,30 -d Oxidation of EC Oxidation of EGC Oxidation of ECG Oxidation of EGCG Oxidation of TF Oxidation of TF-3-g Oxidation of TF-30 -g Oxidation of TF-3,30 -d
Rate Constant at 208C s21
Activation Energy (kJ mol21)
Michaelis–Menton Constant (mg2 g22)
0.00499 0.00248 0.00251 0.00063 0.00089 0.00371 0.00278 0.00367 0.00023 0.00004 0.00004 0.00006
13.4 27.6 26.3 45.1 43.5 31.0 19.9 37.2 104.9 125.6 124.8 135.5
264 430 342 464 0.44 0.01 5.82 7.52 3.80 0.90 0.77 0.43
where k0 is the reaction rate constant at reference temperature T0 , E is the activation energy, and R is the gas constant. Based on experimental data, the best fitted values of activation energy for the 12 reaction pathways during tea fermentation are obtained as shown in Table 24.1. To summarize, the multiphysical and multi(bio)chemical model of black leaf tea fermentation has three interacting physical and biochemical processes including porous airflow, convective heat transfer, and 12 enzymatic reactions. The two partial differential equations of airflow and heat transfer together with the 12 reaction equations are solved using commercial CFD software FIDAP (Fluent, Inc). More details of the computer simulation scheme were given in Ref. [4].
24.2.3 INTEGRATED PRODUCT–PROCESS DESIGN The system under consideration is a packed bed of radius of 9.25 cm and bed depth of 3.5 cm. The problem is simulated as 2D axisymmetrical. The moisture content of the dhool was kept to about 70% (w=w) and did not change significantly during fermentation. The thermal physical properties of the dhool were as follows: bulk density, 1093 kg m3 ; specific heat capacity, 3570 J kg1 ; and thermal conductivity, 0:321 W m1 K1 . The thermal physical properties of the saturated air were as follows: density, 108 kg m3 ; specific heat capacity, 991 J kg1 ; and thermal conductivity, 0:00145 W m1 K1 . The initial concentrations of the four major catechins in the dhool were measured to be (in dry mass): EC, 5:19 mg g1 ; EGC, 14:54 mg g1 ; ECG, 7:69 mg g1 ; and EGCG, 21:85 mg g1 . Simulations have been performed for superficial airflow velocities of 1.86 and 3:72 cm s1 , respectively. Figure 24.2 shows the predicted temperature distributions in the packed bed for a superficial airflow velocity of 3:72 cm s1 . Predictions of temperature distribution in the packed bed made it feasible to examine the impact of airflow and heat transfer on the enzymatic reaction in terms of the generation of theaflavin and thearubigins. As an example, Figure 24.3 compares the predicted catechin depletion and theaflavin accumulation for two different superficial airflow velocities of 1.86 and 3:92 cm s1 , respectively. At the higher
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Dimensionless temperature (T /T0)
1.25 Top
1.20
Middle
1.15
1.10 Bottom 1.05
1.00 0
0.2
0.4
0.6
0.8
1
1.2
Dimensionless radius (r/R)
Dimensionless temperature (T / T0)
1.25 Top
1.20
Middle
1.15
1.10 Bottom 1.05
1.00 0
2000
4000
6000
8000
Fermentation time (s)
FIGURE 24.2 Predicted radial distribution (above) and history (below) of temperature at the inlet (bottom), middle, and outlet (top) of the packed bed of leaf dhool during tea fermentation at a superficial airflow velocity of 3:72 cm s1 . All temperatures are made dimensionless to the initial temperature of 248C.
airflow rate of 3:72 cm s1 , the rate of catechin oxidation is slower due to faster heat removal. The rate of theaflavin accumulation is also slower initially. However, at the later stage of fermentation, theaflavin accumulation caught up with that of the lower airflow rate of 1:86 cm s1 : During tea fermentation, theaflvins are subjected to further oxidation. The accumulation of theaflavins is the net result between the synthesis of oxidized catechin quinones and further oxidation. As a result, the effect of temperature on theaflavin accumulation becomes complex. Theaflavins are important markers of black leaf tea and contribute to the brightness and astringency of tea liquor. They also possess a wide range of health properties. By modeling the coupling of airflow and biochemical reaction pathways, it is feasible to integrate the process and product design to achieve optimal color, taste as well as health benefits of black leaf tea.
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0.08 0.07
1
0.06 0.8
−1
Catechins, 3.72 cm s −1 Catechins, 1.86 cm s −1 Theaflavins, 3.72 cm s −1 Theaflavins, 1.86 cm s
0.6
0.05 0.04 0.03
0.4
0.02 0.2 0
0.01 0
2000
4000
6000
Dimensionless total theaflavins (c /c0)
Dimensionless total catechins (c /c0)
1.2
0 8000
Fermentation time (s)
FIGURE 24.3 Predicted depletion of total catechins and accumulation of total theaflavins during tea fermentation at a superficial airflow velocity of 1.86 and 3:72 cm s1 , respectively. The concentrations area made dimensionless to the initial concentration of total catechins of 49:27 mg g1 leaf.
24.3 MODELING TEA BAG INFUSION 24.3.1 TEA BAG BREWING METHOD For food products, their property and functionality (i.e., nutrition and flavor) depend not only on the finished products, but also their in-use process of preparation, cooking, and consumption. Integrating product design with in-use delivery has been a main challenge for food product innovation. Multiphase and multiscale modeling can provide valuable tools for integrating product design with the in-use interaction. In this section, we demonstrate such integration by the example of tea bag infusion. Since tea drinking became a global phenomenon, there are wide variations in both the type of tea product consumed in different cultures and the way tea is prepared. In general, people in the Western countries drink black tea, made by infusing a quantity of black leaf, usually contained in a tea bag, in boiling water. The infusion time is generally short and the beverage is usually consumed hot (often with added milk and=or sugar). Brewing habits not only vary between countries, but also between individuals within countries. Infusion time ranging from less than 30 s to 5 min is commonly observed, with the majority brewing for less than 2 min. Various agitation behaviors have been also observed by consumers in an attempt to speedup the infusion process. While some tea drinkers add boiling water to the tea bag and just leave it float for a given time, others stir the water or move the tea bag up and down. Variations in both the types of tea bag and brewing habits have important effects on the infusion properties in terms of the appearance and flavor as well as the possible health benefits suggested by many recent studies [5–10]. In order to optimize the delivery of the flavor and health properties of tea bags, it is necessary to integrate tea bag design with the in-use process of brewing. However, when one considers the popularity of tea, it is surprising that there have been so very few studies on the in-use process of tea bag infusion. Most of the early studies have considered the infusion kinetics of loose tea leaves under well-controlled experimental conditions rather than in-use conditions. Aqueous extraction of black loose-leaf tea was first studied by Long [11,12] but much work has been conducted by Spiro
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and coworkers [13–23]. Recently, the rate of transfer of aqueous caffeine through a membrane of tea bag paper was measured in a model system by Spiro and Jaganyi [18]. To our knowledge, extraction experiments on tea bags were only recently reported by Jaganyi and Mdletshe [24].
24.3.2 MULTIPHYSICAL PROCESS
OF
TEA BAG INFUSION
Tea bag infusion involves multiphysical process and the major three interacting processes are (a) the release of soluble solids from tea leaf particles to the surrounding fluid, (b) the leaching of the soluble solids through the packed bed of tea leaves due to the porous fluid flow, and (c) the convection and diffusion of soluble solids in the fluid. The theory describing the release of soluble solids from a solid particle immersed in a fluid has been established by Crank [25] and Sherwood et al. [26], respectively. The Crank equation assumes that the mass transfer is rate-limited by the solid particle and the Sherwood approach considers the release as rate-limited by the transfer in the fluid. Under infinite sink condition, the Sherwood equation leads to a first-order kinetics equation. The Crank equation can be also reasonably approximated by the leading term of the first-order kinetics [27]. Previous studies of loose-leaf tea extraction by Spiro and coworkers [19,23] suggested that the infusion kinetics follow the first-order kinetics. In the model, the release of solute from leaf particle to the porous fluid in the packed bed is described by the general equation of interfacial mass transfer: S¼
dmt ¼ A km (cl cp ) dt
(24:5)
where A is the interfacial surface area of the leaf particle, km is the interfacial mass transfer coefficient, mt is the amount of soluble solids released, and cl and cp are the concentrations of the solute in the leaf particle and porous fluid, respectively. The mass transfer coefficient is estimated from loose-leaf tea infusion kinetics using the following relationship (for more details refer to Ref. [28]): km ¼
ke as
(24:6)
where as is the specific surface area per unit weight of tea leaves and ke is the rate constant of loose-leaf tea infusion. The second physical process of tea bag infusion involves the diffusion and advection of the released tea solutes through the packed bed. The packed bed is assumed to be a homogeneous and isotropic porous medium. The fluid flow through the porous bed is described by the Darcy equation [29]: r @^ ui m þ ^ ui ¼ ^p, i þ m(^ui, j þ ^uj,i ), j þ rgi f @t k
(24:7)
where i, j ¼ 1, 2 for two-dimensional or axisymmetric flows, i, j ¼ 1, 2, 3 for three-dimensional flows, k is the permeability of the porous medium, m is the viscosity of the fluid, m is the effective viscosity , and rgi is the body force due to gravity. Note that ^ p and ^ ui are the volume-averaged pressure and velocity components and depend on the porosity of the packed bed.
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The equation describing the mass transfer of the dissolved tea solids in the porous medium may be formulated as follows: @^c þ ^ui ^c,i ¼ (rDe^c, i ), i þ S r @t
(24:8)
where De is the effective diffusion coefficient and S is the source term accounting for the release of the solute from tea leaves. The third important process of tea bag infusion is the fluid flow around the tea bag. This can be described by the classical Navier–Stokes equation of Newtonian fluid flow r
@ui þ uj ui, j ¼ p, i þ m(ui, j þ uj, i ), j þ rfi @t
(24:9)
The corresponding mass transfer equation of the dissolved tea solutes is r
@c þ ui c,i @t
¼ (rDc,i),i
(24:10)
where D is the diffusion coefficient of the tea solutes in water. The bulk density of the fluid depends on the concentration of the dissolved tea solutes and the fluid temperature. As the concentration of the dissolved tea solids is very small (<3%), the bulk density of the tea liquor may be approximated by r ¼ r0 ½1 bT (T 293:15)(1 bc c)
(24:11)
where T is the absolute temperature, r0 is the bulk density of pure water at 20 C, bT (¼ @rw =@T) and bc (¼ 1 þ r0 =bc ) are the temperature- and solute concentration-dependent volume expansion coefficients, respectively. Their values are given as bT ¼ 0:437e3 K1 and bc ¼ 0:375. The buoyancy force due to the density variation of the fluid is approximated by the Boussinesq approximation [31] expressed as ( r ro )gi ¼ ro [bT (T T0 ) þ bc c]gi
(24:12)
where gi is the gravitational constant. In summary, the physical processes for tea bag infusion were described by the kinetic equation of soluble solids dissolution, two partial differential equations for fluid flow and mass transfer in porous media, and the classical Navier–Stokes equation of bulk fluid flow coupled with the diffusion–convection equation of solute. All the equations have been solved numerically using the commercial CFD software FIDAP. Further details of the computer simulation scheme were reported by Lian and Astill [28].
24.3.3 INTEGRATING TEA BAG DESIGN
WITH IN-USE
BREWING
The infusion process under consideration involves the infusion of round tea bags of 50 mm in diameter, infused in 200 ml hot water at 908C in glass beakers of 56 mm in diameter.
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The tea bags were made from Dexter 2049 paper. Each tea bag was loaded with 2.67 g of Indian (Mijicajan) tea leaves, manufactured by the crush–tear–curl (CTC) process and sieved to give a size range from 0.50 to 1.18 mm. In order to mimic the in-use process of tea bag infusion, two scenarios were simulated. The first simulation considers the ‘‘dunking’’ with the tea bag mechanically moved up and down in such a manner that at the highest position the top of the bag was just below the water level. The second simulation considers the static infusion with the tea bag lowered into the beaker just below the water level and held stationary. To validate the computer simulation, the tea bag infusion under the above two conditions was monitored using evolution in the absorbance at 445 nm of the liquor. The relationship between the absorbance and the concentration of tea liquor is shown in Figure 24.4 and best fitted by Beer’s law [30]: Ab ¼ 6:715cs
(24:13)
where Ab is the absorbance at 445 nm wavelength and cs is the concentration (% by weight) of the tea solids. The initial concentration of extractable solutes in the tea leaf is also related to the infusion kinetics of loose-leaf tea infusion by the following equation in terms of absorbance: A0 ¼ xwl Ae
(24:14)
where x w1 is the water–leaf ratio and Ae is the equilibrium absorbance. The best fitted values of the equilibrium absorbance and infusion rate constants were 3.52 and 0:028 s1 , respectively. The problem was simulated as 2D axisymmetrical. For all the simulations, the hydraulic conductivity (permeability) of the packed bed of tea leaf is assumed to be
3.0
Absorbance at 445 nm
2.5 2.0 1.5 1.0 0.5 0.0 0
5
10
15
20
25
30
35
40
Concentration of tea solids (%)
FIGURE 24.4 Correlation of tea solid concentration with UV absorbance at 445 nm. The data (D) is best fitted by Beer’s law (solid line).
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isotropic. It is expressed as a function of the packing density using the following empirical relationship: kx ¼ ky ¼ kz ¼ ka
f3 (1 f)2
(24:15)
with ka ¼ 3:66e6 m2 s1 . The diffusion of tea solids in water was set to 2:0 109 m2 s1 around the tea bag and 1:0 109 m2 s1 in the packed bed of tea leaves. The viscosity of water was set to 0:32 103 pa s in the bulk and 0:64 103 pa s in the packed bed to account for the tortuisity effect. More details of both the experimental set-up and computer simulation can be found in Ref. [28]. Computer-simulated fluid flow and contours of tea solid concentration are presented in Figure 24.5 for static infusion. The results for the dynamic infusion are presented in Figure 24.6. Here to be consistent with the experimental study, the concentration is expressed in absorbance. Under the static infusion condition, there was a rapid build-up of a relatively high concentration of tea solutes within the tea bag. As the infusion proceeds, the concentration of tea solutes within the tea bag remained constantly higher than that in the surrounding bulk fluid. The high concentration of tea solids within the tea bag resulted in fluid convection around the tea bag. The circulation of the fluid was initiated in a small region near the tea bag and propagated to a larger region as infusion proceeded. The fluid flow Absorbance 3.0
0.0
t = 20 s
40 s
60 s
120 s
t = 20 s
40 s
60 s
120 s
FIGURE 24.5 (See color insert following page 462.) Computer-simulated contours of tea solid concentration (above, expressed in absorbance) and velocity fields (below) during the static infusion of a round tea bag.
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Absorbance 3.0
0.0
t = 20 s
40 s
60 s
120 s
FIGURE 24.6 (See color insert following page 462.) Computer-simulated contours of tea solid concentration (above, expressed in absorbance) and velocity fields (below) during the dynamic infusion of a round tea bag. The velocity fields are presented for a cycle of dunking.
reached a maximum velocity of 0:012 m s1 at approximately 60 s of infusion and gradually decreased afterwards. Clearly, the formation of the convection eddies has a significant effect on the infusion rate of statically infused tea bags and is the dominant factor that controls the infusion rate. For tea bags infused dynamically by dunking, the distribution of soluble solids predicted by the computer simulation was much more homogeneous. The concentration within the bag was very similar to that in the bulk fluid. As the infusion proceeded, the concentration of tea solids in both the tea bag and the bulk fluid increased rapidly. The infusion rate was much faster due to increased fluid flow through the tea bag. Fluid flow during a cycle of dunking is shown to be much more intense and the maximum velocity reached 0:104 m s1 , which is one order of magnitude greater than that of static infusion. Computer-simulated infusion curves can be compared with experimental data. This is shown in Figure 24.7. The predicted results are in good agreement with the experimental data for both static and dynamic infusions. The different infusion characteristics of statically and dynamic brewed tea bags have important implications for tea bag design. In order to optimize the delivery of flavor and heath benefits of tea liquor, it is desirable to enhance the infusion of tea bags under static brewing conditions. Innovation and optimization of tea bag design is apparent an important step to achieve this. The multiphysical model of tea bag infusion provides a tool for integrating tea bag design with in-use process of brewing.
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Absorbance at 445 nm
2.4 1.9 1.4 0.9 0.4 −0.1
0
50
100
150
200
250
Infusion time (s)
FIGURE 24.7 A comparison of the computer-simulated infusion (solid lines) of round tea bags compared with the experimental data under both static (*) and dynamic (.) brewing conditions.
24.4 CONCLUSION Two examples of CFD simulation of tea fermentation and infusion have been presented. The aim is to demonstrate the advantage of CFD simulation for integrated product–process design as well as integrating product design with in-use delivery of food and drink products. With the first example of tea fermentation, the CFD model simulates the interaction of 12 biochemical reactions of polyphenol oxidation with airflow and heat transfer in the packed bed. Airflow through the packed bed is shown to have complex impact on the accumulation of theaflavins, the dimmers that are characteristic to black leaf tea and important to color, taste, and health benefits. By simulating the multiphysical and multi(bio)chemical interactions during tea fermentation, optimal process conditions for desired black leaf tea property and functionality can be obtained. The second example considers tea bag infusion. By simulating the multiphysical interactions of solute dissolution with porous flow and solute transfer, the impact of in-use brewing on the delivery of soluble solids is investigated. Statically infused round tea bag is shown to greatly reduce the infusion rate, hindering the delivery of color, flavor, and health benefits of black leaf tea. The infusion model offers a tool for integrating tea bag design with in-use brewing so that the optimal delivery of color, flavor, and health benefits of black leaf tea can be achieved.
NOMENCLATURE as A A0 , Ab , Ae [c], [ca ], [cb ] cl , cp , cs D De E k, kf , k0 ke km
specific surface area per unit weight of tea leaves (m2 g1 ) interfacial surface area of the leaf particle (m2 ) UV absorbance of tea liquor at 445 nm wavelength polyphenol concentration in tea leaf (mg g1 ) solid concentration in tea liquor (g m3 ) diffusion coefficient of solute in fluid (m2 s1 ) effective diffusion coefficient of solute in porous leaf (m2 s1 ) activation energy (J) Michaelis–Menten reaction rate constant (mg s1 g1 ) rate constant of loose-leaf tea infusion (s1 ) interfacial mass transfer coefficient (m s1 )
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kr mt p ^ p Q r, rcat , rf R s, sf S T, T0 ui ^ ui bT bc xwl k, ka m m r, r0
601
scaling constant correlating rate of catechin oxidation with heat generation (J mg1 ) amount of soluble solids released from leaf tea (g) fluid pressure (N m2 ) volume-averaged pressure of fluid in packed bed of tea leaves (N m2 ) rate of heat generation (J s1 ) 1 enzymatic reaction rate of polyphenols (mg s1 g ) universal gas constant (K J1 ) Michaelis–Menten constant (mg g1 ) source term for the release of tea solute from tea leaf to fluid (mg s1 g1 ) temperature (K) fluid velocity (m s1 ) volume-averaged velocity of fluid in packed bed of tea leaves (m s1 ) temperature-dependent volume expansion coefficient of fluid (K1 ) solute concentration-dependent volume expansion coefficient (g1 m3 ) water–leaf ratio permeability of fluid in porous tea leaf (m2 s1 ) viscosity of fluid (N m2 s) effective viscosity of fluid in porous tea leaf (N m2 s) bulk density of fluid (kg m3 )
REFERENCES 1. S.C. Opie, M.N. Clifford, and A. Robertson, The role of epicatechin and polyphenol oxidase in the coupled oxidative breakdown of theaflavins. Journal of the Science of Food and Agriculture 63: 435–438, 1993. 2. N. Subramanian, P. Venkatesh, S. Ganguli, and V.P. Sinkar, Role of polyphenol oxidase and peroxidase in the generation of black tea theaflavins. Journal of Agricultural and Food Chemistry 47: 2571–2578, 1999. 3. M.F. Chaplin and C. Bucke, Enzyme Technology, Cambridge University Press, Cambridge, 1990. 4. G. Lian, A. Thiru, and A.P.S. Moore, CFD simulation of heat transfer and polyphenol oxidation during tea fermentation. Computers and Electronics in Agriculture 34: 145–158, 2002. 5. D. Charles, A cup of green tea a day may keep cancer away. New Scientist, 14 September, p. 17, 1991. 6. M.G. Hertog, D. Kromhout, C. Aravanis, H. Blackburn, R. Buzina, F. Fidanza, S. Giampaoli, A. Jansen, A. Menotti, and S. Nedeljkovic, Flavonoid intake and long-term risk of coronary heart disease and cancer in the seven countries study. Archives of Internal Medicine 155: 381–386, 1995. 7. P.C. Hollman, M.G. Hertog, and M.B. Katan, Role of dietary flavonoids in protection against cancer and coronary heart disease. Biochemical Society Transactions 24: 785–789, 1996. 8. A. Jha, R.S. Mann, and C. Balachandran. Tea: A refreshing beverage. Indian Food Industry 15: 22–42, 1996. 9. T. Kada, K. Kaneko, S. Matsuzaki, T. Matsuzaki, and Y. Hara, Detection and chemical identification of natural bio-antimutagens: A case of the green tea factor. Mutation Research 150: 127–132, 1985. 10. L.B.M. Tijburg, T. Mattern, J.D. Folts, U.M. Weisberger, and M.B. Kata, Tea flavonoids and cardiovascular diseases: A review. Critical Reviews in Food Science and Nutrition 37: 771–785, 1997. 11. V.D. Long, Aqueous extraction of black leaf tea. II. Factorial experiments with a fixed-bed extractor. Journal of Food Technology 13: 195–210, 1978. 12. V.D. Long, Aqueous extraction of black leaf tea. III. Experiments with a stirred column. Journal of Food Technology 14: 449–462, 1979. 13. W.E. Price and M. Spiro, Kinetics and equilibria of tea infusion: Part 4—Theaflavin and caffeine concentrations and partition constants in several whole teas and sieved fractions. Journal of the Science of Food and Agriculture 36: 1303–1308, 1985.
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14. W.E. Price and M. Spiro, Kinetics and equilibria of tea infusion: Part 5—Rates of extraction of theaflavin, caffeine and theobromine from several whole teas and sieved fractions. Journal of the Science of Food and Agriculture 36: 1309–1314, 1985. 15. W.E. Price and J.C. Spitzer, The temperature dependence of the rate of extraction of soluble constituents of black tea. Food Chemistry 46: 133–136, 1993. 16. W.E. Price and J.C. Spitzer, The kinetics of extraction of individual flavanols and caffeine from a Japanese green tea (Sen Cha Uji Tsuyu) as a function of temperature. Food Chemistry 50: 19–23, 1994. 17. M. Spiro, D. Jaganyi, and M.C. Broom, Kinetics and equilibria of tea infusion: Part 9—The rates and temperature coefficients of caffeine extraction from green Chun Mee and black Assam Bukial teas. Food Chemistry 45: 333–335, 1992. 18. M. Spiro and D. Jaganyi, Kinetics and equilibria of tea infusion: Part 15—Transport of caffeine across a tea bag membrane in a modified rotating diffusion cell. Food Chemistry 69: 119–124, 2000. 19. M. Spiro and D.S. Jago, Kinetics and equilibria of tea infusion: Part 3—Rotating-disc experiments interpreted by a steady-state model. Journal of the Chemical Society—Faraday Transactions 78: 295–305, 1982. 20. M. Spiro and W.E. Price, Kinetics and equilibria of tea infusion: Part 6—The effects of salts and pH on the concentrations and partition constants of theaflavins and caffeine in Kapchorua Pekoe Fannings. Food Chemistry 24: 51–61, 1987. 21. M. Spiro and W.E. Price, Kinetics and equilibria of tea infusion: Part 7—The effects of salts and pH on the rate of extraction of caffeine from Kapchorua Pekoe Fannings. Food Chemistry 25: 49–59, 1987. 22. M. Spiro, W.E. Price, W.M. Miller, and M. Arami, Kinetics and equilibria of tea infusion: Part 8—The effects of salts and pH on the rate of extraction of theaflavins from black tea leaf. Food Chemistry 25: 117–126, 1987. 23. M. Spiro and S. Siddique, Kinetics and equilibria of tea infusion: Kinetics of extraction of theaflavins, thearubigins and caffeine from Koonson Broken Pekoe. Journal of the Science of Food and Agriculture 32: 1135–1139, 1981. 24. D. Jaganyi and S. Mdletshe, Kinetics of tea infusion: Part 2—The effect of tea bag material on the rate and temperature dependence of caffeine extraction from black Assam tea. Food Chemistry 70: 163–165, 2000. 25. J. Crank, The Mathematics of Diffusion, Oxford University Press, London, 1956. 26. T.K. Sherwood, R.L. Pigford, and C.R. Wilke, Mass Transfer, McGraw-Hill, New York, 1975. 27. G. Lian, Modeling flavor release from oil-containing gel particles. In D.D. Roberts and A.J. Taylor (Eds.). Flavour Release, ACS Symposium Series 763. 2000, pp. 201–211. 28. G. Lian and C. Astill, Computer simulation of the hydrodynamics of tea bag infusion. Food and Bioproducts Processing 80: 155–162, 2002. 29. J. Bear, Dynamics of Fluids in Porous Media, Dover Publications, New York, 1972. 30. R.C. Weast (Ed.). Handbook of Chemistry and Physics, 54th edn, CRC Press, Boca Raton, FL, 1973. 31. G.K. Batchelor, An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, 1967.
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CFD Prediction of Hygiene in Food Processing Equipment Bo Boye Busk Jensen and Alan Friis
CONTENTS 25.1 25.2 25.3
Introduction ............................................................................................................. 604 CFD for Predicting Hygiene in Food Processing Equipment .................................. 605 Prediction of Cleanability Using CFD..................................................................... 609 25.3.1 Case Study: Prediction of Cleaning Trail Results in a Spherical-Shaped Valve House ............................................................ 609 25.3.1.1 Cleaning Procedure ..................................................................... 609 25.3.1.2 Threshold Value of Wall Shear Stress ........................................ 611 25.3.1.3 Wall Shear Stress Prediction in Complex Equipment................. 613 25.3.1.4 Cleanability Prediction Using Wall Shear Stress ........................ 617 25.3.2 Case Study: Fluid Exchange for Improved Prediction of Cleanability ....... 619 25.3.2.1 Simulation Set-Up for Fluid Exchange Prediction ..................... 620 25.3.2.2 Mesh Description for the Fluid Exchange Simulations .............. 620 25.3.2.3 Fluid Exchange in Sphere-Shaped Valve .................................... 621 25.3.2.4 Fluid Exchange in Upstand ........................................................ 622 25.3.2.5 Prediction of Cleaning Combining Wall Shear Stress and Fluid Exchange .................................................................... 622 25.3.3 Explaining Different Cleaning Characteristics of a Butterfly Valve ........... 623 25.3.3.1 Geometry and CFD Model......................................................... 623 25.3.3.2 Simulation Set-Up....................................................................... 624 25.3.3.3 Prediction of Cleanability ........................................................... 624 25.3.3.4 Verification of Cleanability Prediction ....................................... 625 25.4 Challenges for the Future ........................................................................................ 625 25.4.1 Near-Wall Treatment.................................................................................. 626 25.4.2 Wall Shear Stress Prediction ....................................................................... 626 25.4.3 Fluid Exchange Predictions ........................................................................ 626 25.4.4 Combining Fluid Mechanics with Knowledge of the Structure and the Mechanics of the Soil Itself............................................................ 627 25.4.5 Boundary Layer Thickness Prediction ........................................................ 627 25.5 Conclusion ............................................................................................................... 627 Nomenclature ..................................................................................................................... 628 References .......................................................................................................................... 628
603
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25.1 INTRODUCTION Application of computational fluid dynamics (CFD) in hygienic design has many possibilities at different levels of detail and complexity, from the prediction of adhesion and cleaning based on a hydrodynamic parameter point of view, over the more detailed approach where hydrodynamic parameters from CFD simulations are used as input to mathematical models of adhesion and cleaning, to the use of CFD for predicting pasteurization and sterilization of equipment based on heat transfer due to convection and in some cases also conduction of heat through solid surfaces. The sparse work done so far focuses on applying CFD for prediction of cleaning in closed processing equipment as this provides relatively well-defined boundary conditions. Extending it to open equipment increases the complexity of the modeling, as twophase flow and free surface flows in these cases have to be modeled and this is still a fairly new subject to treat for commercial CFD programs. From this chapter it will be obvious that CFD has a future in predicting and improving hygienic design of processing equipment. Cleaning of closed systems depends on liquid flow as this provides not only the force acting on the soil on a surface, but also, equally important, acts as a carrier for detergent and heat throughout the system. In addition, the flow is also the only means of transporting detached soil and microorganisms out of the system to avoid contamination of already cleaned surfaces. It should be evident that modeling of flow is directly connected to modeling of cleaning for the purpose of identifying areas difficult to clean in closed equipment. Being able to predict hygiene (cleanability, pasteurizability, and sterilizability) by CFD in processing equipment reduces the number of expensive and time-consuming experimental tests for which prototypes of equipment must be present. Hence, it allows equipment manufacturers a unique opportunity to do preprototype evaluation of the hygienic state of new components or the effect of changes to existing components. The effect of small design changes on hygiene can be compared and even uncommon design features can be tested in a virtual environment where additional changes are easy to perform without the expenses of additional prototypes. The information provided by such exercises will not only result in better hygienic designed equipment, but also, in the long term, provide an increased understanding of the important flow parameters on cleaning and the small design features necessary to generate flow conditions (parameters) that are advantageous to hygiene. The validation of hygienic state of equipment by CFD does not have to be an extra expenditure. CFD analyses for optimizing equipment performance might already be done on the equipment. Hence, data for evaluating the hygienic design might already be available. In addition, also the now and then needed compromise between equipment performance (with respect to, e.g., pressure loss, mixing, and careful processing) and the hygienic state can be investigated and good compromises made. Ideally, design features can be implemented that promote both hygiene and other performance demands. In addition to the benefits for equipment manufactures with respect to optimizing equipment, also food producers and teachers of hygienic design can take advantage of the visualization possibilities lying in having a CFD simulation of flow in particular components and fittings in a processing plant. For food manufactures it can be used for in-house training of maintenance staff and operators to explain why certain design features are critical with respect to cleaning. For teachers of hygienic design pictures of flow are now available that show 3D features that can explain why certain designs are better for cleaning than others. This has been difficult to explain to non-fluid-mechanics previously, when only experimental visualization and 2D drawings of flow were available. This chapter focuses on closed equipment cleaned by cleaning in place (CIP) procedures as this is the most obvious use for CFD for evaluating hygienic design. Different aspects of
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cleaning with special focus on the applicability of CFD in predicting hygienic design are presented to justify the use of CFD and to outline the approach for its use in evaluating hygienic design. Work published thus far on CFD in hygienic design of food processing equipment and on identification of important flow parameters for cleaning is discussed with focus on the flow conditions used in the different studies as this could effect the conclusions. Finally, examples are given to illustrate state-of-the-art in this area (the examples are based on the work of the authors of this chapter). Focus is on considerations related to mesh generations (especially near-wall mesh), near-wall treatment, quality of results (hydrodynamics), and finally prediction of cleanability using CFD data.
25.2 CFD FOR PREDICTING HYGIENE IN FOOD PROCESSING EQUIPMENT To justify that CFD is useable for predicting hygienic design, one has to look at the mechanisms of cleaning (i.e., the removal of any adhering substance from a surface). The process of cleaning is influenced by four parameters: time, temperature, detergent, and the mechanical force with each contributing on different levels. Imagine that a certain amount of energy is required to break the bond between (remove) a certain type of soil and a surface. The energy required is applied from the four parameters at different magnitude as illustrated by Sinner [1] (Figure 25.1). The total amount of energy always has to be the same for a certain combination of soil and surface, so a decrease in one has to be compensated for by an increased contribution from one or more of the other parameters. The influence of flow on each parameter is what makes CFD an interesting tool for predicting cleanability (hygienic design) of food processing equipment. The influence of fluid flow on each parameter is: Temperature and detergent: Flow is the most effective method to distribute temperature and detergent (heat and mass transfer by convection) throughout the equipment to be cleaned. Only at the boundary layer dominates diffusion=conduction. The lower the temperature and detergent concentration at the soil the longer it takes to weaken the bond between surface and soil, i.e., two identically soiled surfaces exposed at identical times to
Chem.
Time
Temp.
Mech.
FIGURE 25.1 Sinner’s circle illustrating the energy required to remove soil from a surface with contribution from time, temperature (temp.), detergent (chem.), and mechanical force (mech.).
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two different sets of temperature and detergent (one high and one low) have to be cleaned with different mechanical forces to obtained identical cleaning times. Time: Closely linked to the convection of temperature and detergent as the important aspect of the time is the contact time at the expected=required temperature and concentration. The shorter the time at expected temperature and concentration the longer it takes to weaken the bond between surface and soil, i.e., two identically soiled surfaces exposed to identical temperature and detergent but at two different times have to be cleaned with different mechanical forces to achieve identical cleaning. Mechanical force: This occurs as a direct influence of the flow, because of the force dragging the soil away from the surface (wall shear stress). A lower force requires a longer contact time between flow with correct temperature and detergent concentration and the soil to reduce the bond between surface and soil to a level where the force present at the soil exceeds that of the bond between surface and soil. In well-described flows (fully developed pipe flow and square ducts) time-averaged wall shear stress, convection of heat and mass, and contact time at required temperature and concentration are identical on all surfaces resulting in similar cleaning times in the entire pipe. Having just a small disturbance in the flow, as in more complex equipment and fittings, different wall shear stress, heat and mass transfer, and contact times are found on surfaces compared to the fully developed flow regime. Thus, different levels of cleaning are seen in areas with different flow conditions. Often, this problem is enhanced as areas of low heat and mass transfer are also areas of low velocity, i.e., low wall shear stress (e.g., dead-ends as illustrated in Figure 25.2). From the above it should be clear that knowledge of local hydrodynamics is of extreme importance for the prediction of hygiene in food processing equipment. These local parameters are not all easy to measure without disturbing the flow conditions and impossible to get as continuous data (as opposed to discrete data points) on the entire surfaces to evaluate. This calls for the use of CFD. In addition, CFD is also a requirement for any model of adhesion or cleaning in processing equipment that is based on local flow phenomena. Such models are obtained from adhesion and cleaning test performed under ideal flow conditions where important parameters can be found from analytical or empirical solutions to the
h/D = 1
t w (Pa)
FIGURE 25.2 (See color insert following page 462.) Wall shear stress (left) and fluid exchange in computational cell closets to boundary (right) predicted using Star-CD. For the fluid exchange on the right, blue colors represent the old fluid and red colors the new fluid.
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Complex geometry
Cleaning trials
Identification of zones that are insufficiently cleaned Could insufficiently cleaned zones be predicted using wall shear stress?
CFD simulations
Cleaning trials
Identification of zones expected to be insufficiently cleaned
Critical wall shear stress
Parallel flow
FIGURE 25.3 Procedure for evaluating the use of a threshold wall shear stress for predicting the outcome of a specific cleaning test. (From Jensen, B.B.B., Hygienic design of closed equipment by use of computational fluid dynamics. Lyngby, BioCentrum-DTU Technical University of Denmark, 2003.)
Navier–Stokes equations. If these models can be found (as complex as they may prove to be) there is a need to predict the local flow conditions in any part of the equipment to make a sound judgment of the level of adhesion and the effectiveness of cleaning, as these conditions will be a model variable in complex flows. Here measurements are insufficient as this can only be done in discrete points on a surface, if it is at all possible to measure the required parameters in the complex equipment. Studies in the late 1980s and mid-1990s [2–4] proposed the use of CFD for identifying difficult to clean areas as cleaning is, as explained above, very much dependent on flow in the equipment. These first studies conclude that cleaning was poor in areas of low velocity and low wall shear stress on a qualitative base. Later Jensen at BioCentrum-DTU [5–7] took a more quantitative approach, which combined experimentally obtained threshold values for a specific combinations of soil, surface, and cleaning procedure with CFD-predicted values in complex equipment. The procedure used is shown in Figure 25.3. Jensen and Friis [7] conclude that wall shear stress compared with a threshold value is insufficient for the prediction of cleaning in complex equipment (work described in detail later in this chapter). Some surface areas exposed to wall shear stress below the threshold value were cleaned and surface areas exposed to wall shear stress above the threshold values were not. Even surface areas of identical wall shear stress could be found clean in some areas and in some areas not cleaned. This is not that surprising, as heat and mass transfer has large local differences in complex flows. Work by the authors of this chapter (examples shown later in this chapter) shows that combining knowledge of the wall shear stress threshold value, wall shear stresses predicted using CFD, and qualitative knowledge of local fluid exchange predicted using transient CFD simulations provides very good predictions of areas with different degree of cleaning. The weakness of this, to be applicable to industry, is the fact that no threshold value has yet been
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found for the fluid exchange and an approach to quantify fluid exchange is still work in progress. In addition, transient simulations of flow are a time-consuming exercise, which also has to be taken into consideration. A parallel study to the one of Jensen [8] by Lelie`vre et al. [9] at INRA aimed at measuring wall shear stress in discrete points using electrochemical sensors [10] in geometrical simple equipment and comparing measured values of wall shear stress with microbial counts from cleaning test performed in similar equipment to that used for measuring wall shear stress. Their findings were along the lines of those found by Jensen and Friis [7]. Surface areas of different degree of cleanability were seen in areas exposed to identical, on a time average, wall shear stresses. However, better cleaning was seen on surface areas exposed to low wall shear stresses than in other areas exposed to high wall shear stresses. Lelie`vre explained these differences by the fluctuation of the measured signal from the sensors. High fluctuations provide better cleaning than low fluctuations. What they actually measured was mass transfer of electrodes to the probe. As previously mentioned the influence of different fluid parameters on cleaning is only an interesting finding if the level of the important parameter, in the case of Lelie`vre the fluctuations, can be predicted or measured. Measuring is an option [9], but only in discrete points and only using destructive methods. A collaboration between Jensen and Lelie`vre [11] shows that steady state CFD analysis can be applied to predict areas where surfaces are exposed to high or low fluctuations. The fluctuations are not directly predicted, but visualizing the turbulence intensity (Ti ) (see Equation 25.1) provides a good qualitative prediction: rffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffi ffi u0 2 2 k ¼ Ti ¼ 3 U2 U
(25:1)
where k is the turbulent kinetic energy, U is the velocity, and u0 is the fluctuating component of the velocity. Values of each parameter are taken in the computational cell closets to the wall. At present turbulence intensity can be used to give a qualitative prediction of high and low (relatively) fluctuations in geometry. However, for this parameter to be applicable for actual equipment design a scale defining low and high fluctuations is needed. Prediction of the actual level of fluctuation can turn out to be very difficult as .
.
.
Fluctuation itself is not found from the CFD analysis but the turbulence intensity can be used to produce a qualitative prediction. Calibration of the CFD model is difficult with respect to finding the same levels of turbulence intensity as the level of measured fluctuation. A more obvious approach is to have a conversion constant between turbulence intensity predicted by CFD and the fluctuations found from the electrochemical measurements. Levels of turbulence intensity and turbulent kinetic energy dissipation at the inlet, pressure outlet, and initially in the CFD flow domain might have large influences on not only the magnitude of the predicted turbulence intensity, but also on the location of local extremes.
Having obtained data on important hydrodynamic parameters in cleaning it is possible, not only to evaluate the cleanability of entire pieces of equipment, but also make additional verification of these parameters by comparison between CFD-predicted values and results from cleaning tests such as the European Hygienic Engineering and Design Group (EHEDG)
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test, the TTC agar test, or even discrete enumeration of microorganisms on the surfaces in discrete points. The rest of this chapter focuses on the CFD aspects of using CFD in hygienic design. This is illustrated through examples on how to predict cleanability using CFD based on wall shear stress and fluid exchange.
25.3 PREDICTION OF CLEANABILITY USING CFD There is in fact diverting conclusions on the importance of wall shear stress on removal of soil from a surface. Many published studies have found [12–14] a clear connection between the magnitude and, e.g., the number of microorganisms removed during cleaning while others [7,9] do not see a clear effect of increasing the wall shear stress. However, to find a definite conclusion one also has to look at the conditions (i.e., parameters such as Reynolds number and boundary layer thickness) under which the different experiments have been performed even though they are all performed in pipes or ducts. Most of the work that is pro-wall shear stress as the important factor made their experiments in straight pipes, parallel plate channels, or radial flow cells (RFCs) under laminar flow conditions. Those finding a less importance of wall shear stress did the work using experimental set-ups that allows for more realistic flow phenomena giving highly turbulent flow conditions. Especially during the last couple of years, publications have shown that wall shear stress is important to some extent in turbulent flow, but because of the complexity of the flow, other parameters are equally or even more important (wall shear stress fluctuations, fluid exchange, turbulence, boundary layer thickness—all of them related to mass and heat transfer). This part of the chapter details one of the published studies that show wall shear stress magnitude has to be combined with, in this case, knowledge of local fluid exchange to identify hardest to clean areas. Most of this work was initially published in the three papers [5–7].
25.3.1 CASE STUDY: PREDICTION VALVE HOUSE
OF
CLEANING TRAIL RESULTS
IN A
SPHERICAL-SHAPED
One approach of using CFD for investigating the hygienic design of closed food processing equipment is to compare the important hydrodynamic parameters related to cleaning of surfaces to threshold values found under controlled experiments. The hypothesis of the case given here is that the wall shear stress, which can be used as a threshold value in pipes and ducts, can be used for predicting the cleanability of components typically found in food industry. Here the results for a spherical valve house without seat lifts are used to represent complex flows and the cleaning test methods used are based on the EHEDG test procedure [15]. The procedure for testing the hypothesis is outlined in Figure 25.2 and is based on finding a threshold value for the wall shear stress, comparing this threshold value to wall shear stress in a complex component found by CFD, to predict surface areas expected clean and unclean, and finally comparing the predictions with results from cleaning tests performed in the complex equipment. Here, the focus will be on the CFD aspects in estimating a critical wall shear stress using an RFC and the prediction of cleanability of a mixproof valve (MPV) with spherical values houses. 25.3.1.1
Cleaning Procedure
Since 1992 EHEDG has offered producers of food processing equipment the opportunity to certify closed processing equipment for liquid processing. The cleaning test identifies areas
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potentially difficult to clean, through a challenge test from a qualitative point of view, by comparing the cleanability to that of a straight pipe. If possible to predict the outcome of this test method using CFD, equipment manufacturers can perform prototype testing using CFD, thereby only needing to make EHEDG test on the final version (a positive side effect is that additional knowledge into why certain designs offer better cleaning than others is obtained). The cleaning test is published by EHEDG [15] and based on the work of Shapton and Hindes [16]. The soil used consisted of a 105 spores=mL mixture of commercial sour milk and Bacillus stearothermophilus spores. Prior to soiling, the equipment was autoclaved for 30 min at 1208C to ensure sterility. A test disc designed to fit into the RFC was soiled by smearing the mixture homogenously on the disc. The MPV and the reference pipe were soiled by filling them with a total of approximately 1.5 L of the mixture. In a standard EHEDG test, the component is pressurized to 5 bar three times and movable parts operated a total of 10 times during the three pressure cycles to allow the mixture to enter crevices near gaskets and joints. This was omitted for the purpose of this work, as the areas of interest were the inside surfaces of the valve house, and not the gaskets and crevices. The MPV and the reference pipe were then drained and the mixture that remained on the surfaces was dried for 4 h with air at an average velocity of 1 m=s through the inlet pipe. The test disc for the RFC was dried in a fume cupboard. The air velocity measured 10 mm above the surface was 1 m=s. Measurements were performed with a Testo 400 Robust hot-ball probe with a range from 0 to 10 m=s and an accuracy of +0.03 m=s. The equipment was then assembled and rinsed for 1 min with tap water at 208C, cleaned with a 1% detergent solution (‘‘Lever industrial PD332’’ from Lever Otares, the Netherlands) for 10 min at 638C, and finally rinsed for 1 min with tap water at 208C. All steps were performed at an average velocity of 1.5 m=s through the inlet pipe of the MPV and 10 L=min through the RFC. After cleaning, the equipment was disassembled and incubated in Shapton and Hindes (SH) agar [16] for 20 h at 588C. Under these conditions, germinating B. stearothermophilus spores produce acid that changes the color of the SH agar from purple to yellow. Identification of the yellow zones was done by cutting up the almost spherical-shaped agar clump from the valve house into wedge-shaped slices (pie cutting technique). Each agar wedge was approximately 11.58 in tangential thickness. This ensured that the maximum thickness of a single agar wedge was around 5 mm. Each wedge was then illuminated with backlight from a Kenro light table model KL 003=E. Recordings were made with a Sony Digital Handycam DCR-TRV10E PAL, where the still shots of the wedges had a resolution of 640 480 pixels with 16 million colors. The zones with yellow agar were identified from still shots of each agar wedge using Paint Shop Pro 7 (PSP7) and the results were outlined on hand-drawn sketches. The area where agar was yellow was determined using the grid facility of PSP7. The grid used resolved each wedge in 30–35 boxes with equal height (the number of boxes was not constant due to the fact that it was impossible to produce uniformly sized agar in this type of valve house). The vertical location and size of yellow zones were then determined by visually identifying boxes containing yellow agar. The test discs were removed from the RFC and put into a Petri dish and covered with SH agar to a thickness of 5 mm. The SH agar was removed after incubation and treated as described above (more information on the RFC and additional cleaning trials is given in Ref. [5]). Three cleaning tests were performed. In all tests, the RFC and the MPV were placed in parallel to ensure identical cleaning procedures (except from hydrodynamic effects) in the two pieces of equipment. The results of the three cleaning trials are grouped as surface areas uncleaned in all three tests, surface areas uncleaned in two out of the three tests, and surface
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areas uncleaned in only one of the tests. The EHEDG test defines a surface area as ‘‘difficult to clean’’ if this surface area has yellow agar present in three consecutive tests [15]. 25.3.1.2
Threshold Value of Wall Shear Stress
Estimation of the threshold value for the EHEDG test soil was done using an RFC assay using same surface material, surface properties, and cleaning test procedure as in the complex equipment. The test section of the RFC is the space between two parallel discs (see Ref. [17] for a general description of the RFC principle and Ref. [5] for the RFC used for this work). The RFC has the advantage, compared to pipes and ducts, that the effect of a range of wall shear stresses can be investigated in each experiment. Turbulent flow in the RFC was chosen to obtain flow conditions similar to those present in the MPV. From the cleaning experiments a critical radius for the cleaning can be found and this radius converted into a critical (or threshold) wall shear stress for this particular type of test method and surface. Wall shear stress as a function of radius can be found from analytical equations for the ideal flow (fully developed inlet conditions), however, the 908 turn at the inlet to the test section gives a nonfully developed flow. A CFD simulation was performed for prediction of the wall shear stress as a function of radius in the RFC. Challenges faced in the CFD study carried out by Jensen and Friis [5] was related to the decelerating flow at Reynolds numbers close to the critical Reynolds number. Below is a description of some of the interesting findings of using CFD for predicting wall shear stress in the RFC [5]. Simulations of turbulent flow were carried out for the RFC constructed by use of the commercial package: Star-CD v. 3.100b. The flow domain was resolved with a mesh of hexahedral and wedge-shaped cells. Star-CD offers structured mesh creation with integral and arbitrary couples between cells at nonmatching interfaces, which allow easy local grid refinement. The choice of turbulence model and near-wall treatment is an important factor of mesh creation as these models and treatments provide requirements to the nondimensional distances (yþ ) of the first mesh point normal to the wall: y ut y ¼ n þ
rffiffiffiffiffi tw where ut ¼ r
(25:2)
where y is the normal distance from the wall and ut is the friction velocity. The three general concepts for description of the near-wall flow available in Star-CD v. 3.100b are (yþ requirements in parenthesis): One- and two-equation turbulence models using the wall function that assumes a logarithmic velocity distribution in the near-wall region (30 < yþ < 300); ‘‘Two-layer’’ models that predict flow by two-equation turbulence models in the main flow and a one-equation model in the near-wall region (yþ 3); and a low Reynolds number k–« model, where flow is described by a two-equation turbulence model except in the near-wall cell where dissipation is algebraically fixed (yþ 1). The near-wall treatment best suited for modeling the turbulent flow in the RFC was evaluated by comparing CFD simulations of the idealized flow to wall shear stresses from analytical and empirical solutions. The work was limited to the low Reynolds number k–« and the two-layer model of Norris and Reynolds. To select the best turbulence model an initial study was made comparing analytical and empirical solutions of the wall shear stress with the wall shear stress predicted using different turbulence models. This was performed for a flow cell with a fully developed velocity profile located at the symmetry axis of the RFC (an idealized RFC). It was shown
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Wall shear stress [Pa]
25
20
15
10
5
0 0
10
20
30
40
50
60
70
80
Distance from RFC center [mm]
FIGURE 25.4 Example of cleaning result from cleaning test performed on the RFC. Shown is a black and white photo of the agar. Bright areas are yellow (cleaned) and dark areas are purple (uncleaned). The wall shear stress distribution in the RFC working under turbulent flow conditions is shown above. Added is the analytical solution for the wall shear stress for the ideal flow in the RFC.
that neither of the turbulence models can predict the wall shear stress over the entire range of radii [5]. Close to the turbulence-dominated center, the two-layer approach gives the best prediction. Outside a radius of 27 mm laminar flow takes over and the low Reynolds number k–« approach produces the best match to the wall shear stress given by literature for the ideal flow present here. This is also the case for the real RFC even though the inner most part is highly affected by the flow around the 908 inlet-bend. CFD simulations of flow in the real RFC showed that the prediction of wall shear stress at low radii was difficult due to the complex flow in this region (Figure 25.4). At a radius of approximately 7 mm, the wall shear stress predicted by the two-layer model showed a local
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minimum that indicated the end of the recirculation zone downstream of the inlet (Figure 25.4). The low Reynolds number k–« model did not predict this. This suggested difficulties for this model to predict the complexity of the flow in this region. Downstream of the recirculation zone a large difference is seen between wall shear stresses predicted by the two models. As for the ideal flow the low Reynolds number k–« model predicted wall shear stress values below those predicted by the two-layer model from a radius of approximately 27 mm and outward. The wall shear stresses in the real RFC predicted by CFD only differed from the ideal flow case at radii below 15 mm (Figure 25.4). This indicates that an almost fully developed radial flow is present at radii 15 mm. The findings suggest that the best prediction of wall shear stress in an RFC with transitional flow needs to be done from two simulations. At smaller radii the two-layer approach should be used and at larger radii the low Reynolds number k–« approach. The radius for shifting between curves is where the two curves cross (Figure 25.4). This makes it possible to estimate critical wall shear stress when comparing cleaning test results with the CFD-predicted wall shear stresses. Getting close to the recirculation zone, or being at a radii in the recirculation zone, caution should be taken when concluding on a critical value due to the complexity of the flow in this region (heat and mass transfer is different from the fully developed flow region at larger radii). A critical (threshold) wall shear stress of 3 Pa was estimated based on the experimental data from a number of tests (more information is given in Ref. [5]). Caution for estimating such a value must be made. First of all the cleaning tests involve living microorganisms, which introduce variation between experiments. Furthermore, it is extremely important that information of any critical wall shear stress also includes a detailed description of surface, soil, and cleaning procedure properties as the critical wall shear stress will be dependent on this. 25.3.1.3
Wall Shear Stress Prediction in Complex Equipment
Having obtained a critical wall shear stress for the cleaning procedure under investigation, prediction of wall shear stress distribution in the equipment is necessary in order to make prediction of cleanability. Prediction of wall shear stress in complex equipment requires careful selection of the near-wall treatment used. The normally used law-of-the-wall method will probably not be sufficient as flow in complex equipment has different features close to the surface than what is required for using the law-of-the-wall model: fully developed boundary layer. In the case of recirculating flow and adverse pressure gradients other near-wall treatments are required. In the near-wall region where flow is unidirectional, it is advantageous to have hexahedral or prism-shaped cells. Gradients are easier to obtain with hexahedral or prism cells than tetrahedral cells, as the velocity difference and the height of the cell are the same in the entire cell. With tetrahedral cells near the wall, prediction of nonphysical velocities is possible as parallel flow (streamlines) is represented by tetrahedral cells. The wall function uses the law-of-the-wall method to cover the viscous sublayer, the buffer layer, and part of the logarithmic layer by one cell only. The velocity in this cell is described by
u¼
8 > > <
yþ ut þ uw ,
> > : 1 lnðEyþ Þ ut þ uw , k
yþ yþ m þ 1 yþ m k ln Eym ¼ 0 þ
y >
yþ m
(25:3)
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where u is the fluid velocity parallel to the wall, uw the wall velocity, and k and E empirical coefficients. For a hydraulic smooth pipe, yþ m is approximately 10. In simulations of flows with adverse pressure gradients and recirculation zones or where flow near the walls, heat transfer, wall shear stress, or friction is of special interest, Rodi [18] suggests two-layer models for description of flow in the near-wall layer. In contrary to the wall function, the buffer zone and the logarithmic layer are resolved by a number of cells. A transport equation for turbulent kinetic energy is solved in the near-wall layer and dissipation of turbulent kinetic energy is expressed by an algebraic function. A shift to, for example, the standard k–« turbulence model is done at a distance from the wall where viscous effects become negligible compared to inertia effects. yþ should be around 3 and approximately 15 points should be placed within the near-wall layer [19]. As flow is simulated all the way to the viscous sublayer, wall shear stress is calculated based on the velocity gradient and the viscosity. The last method available is the low Reynolds number k–« model. Here the flow domain down to yþ 1 is treated as if the flow was in the core region. The only difference to the twolayer models is that in the near-wall cell dissipation is correlated to the turbulent kinetic energy [19,20]. Depending on the choice of near-wall treatment, a threshold yþ value shall be obeyed. In complex flows, prediction of the distance from the wall to the first node in advance is difficult, as the friction velocity is unknown. The easiest way to obtain the threshold yþ value is: (1) create a rough mesh near the walls with yþ values above 100, (2) yþ values are estimated from simulations on the rough mesh, and (3) cells with yþ values above the threshold value and their neighboring cells are identified and refined normal to the wall. This procedure is repeated until yþ values below the threshold value is obtained. 25.3.1.3.1
Numerical Set-Up
The commercial CFD-package Star-CD v. 3.100b, from the CD Adapco Group (www.cdadapco.com), was used for simulation of flow in the MPV. The Navier–Stokes equations are discretized in the flow domain and an iterative process is carried out by use of an algorithm (here implicit SIMPLE was used) to couple momentum and conservation of mass to the relative pressure. The second-order self-filtered central difference (SFCD) scheme was chosen for discretization of the Navier–Stokes equations [19]. Turbulence was modeled by the RNG k–« turbulence model and the two-layer method of Norris and Reynolds [21] for description of the near-wall flow. These choices were based on extensive comparison of the schemes and turbulence models available in Star-CD (see Table 25.1 for those tested). Comparison was made between the two-layer model and the TABLE 25.1 Numerical Schemes, Turbulence Models, and Near-Wall Treatments Compared for the Purpose of Modeling Flow in an MPV Using Star-CD Scheme
Turbulence Model
Upwind (UD) Central (CD)
k« High Re k« RNG
Self-filtered (SFCD) Monotone advection and reconstruction scheme (MARS)
k« Chen k« Cubic high Re k« Quadratic high Re
Near-Wall Treatment Wall function—law-of-the-wall Two-layer model of Norris and Reynolds
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2.0 Law-of-the-wall mesh-1 Two-layer model mesh-2 Velocity measured with LDA
1.8
Normalized velocity (Ux/Um)
1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 −0.2 0.2
0.4
0.6
0.8
1.0
Normalized distance to center of valve (r/R)
FIGURE 25.5 Validation of CFD analysis for MPV. Measurement was performed using LDA and is described. (From Jensen, B.B.B. and Friis, A., J. Food Process Eng., 27, 65, 2004.)
commonly used wall function that use the law-of-the-wall. In combination with the mesh presented later, the models chosen produced the best results when compared to the experimental data (Figure 25.5). The relaxation factors given as standard in the CFD code were chosen to damp changes from iteration to iteration. These were 0.7 for momentum and turbulence, and 0.2 for the pressure. Boundary configurations in the CFD model were chosen to represent the physical geometry. All walls were treated as hydraulically smooth, no-slip walls, as it is not possible to specify a roughness to a boundary while modeling the near-wall layer by two-layer models. The fully developed turbulent velocity profile at the inlet was given a turbulence intensity of 5% and a turbulent length scale of 10% of the inlet pipe diameter [22]. Symmetry was applied on the vertical symmetry plane of the geometry. Across the outlet, isotropic conditions (Dirichlet conditions) were assumed for the velocities and pressure. 25.3.1.3.2
Mesh Configuration
In order to find a proper mesh configuration and simulation set-up, it was decided to focus on the upper valve house. The mesh was created as an unstructured hexahedral mesh using integral and arbitrary couples for unmatched faces (integral couples are two or more faces that precisely cover one large neighbor face and arbitrary couples are more faces that overcover one large neighbor face) making mesh generation easy. Using these couples allow meshing of even complex geometries by use of hexahedral cells. Without these couples such complex geometries can only be modeled using many cells (memory demands) or even impossible to model using hexahedral cells. A basic mesh of the MPV was constructed by revolving a 2D surface of cells (mesh-1 shown in Figure 25.6, left) around the center axis of the valve house. The surface represented the cross-sectional area of the upper MPV house. The 2D surface was composed of three rectangles; BCDE, ABEH, and HEFG that consisted of 16 40, 8 40, and 8 6 cells,
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A
H G
B
E F
C
D
FIGURE 25.6 Mesh structure in MPV. On left is initial mesh (mesh-1) with yþ 40 and on right is mesh-2 with yþ 3. (From Jensen, B.B.B. and Friis, A., J. Food Process Eng., 27, 65, 2004.)
respectively (horizontal vertical). Tests were done to prove if this was sufficient for obtaining a good prediction of the flow in the valve (not shown). Revolving the 2D surface 72 times in steps of 2.58 around the rotational axis of symmetry in the center of the valve house generated one half of the valve house. The cell density in the 2D surface and the number of revolutions were chosen based on experience from CFD simulations of similar geometries. Inlet and outlet pipes were made from 2D surface butterfly meshes located 1.5 times the diameter upstream and downstream of the valve house. Simulations with an outlet pipe length of 20 times the diameter downstream showed no difference in results compared to the results from simulations with the outlet length used. The 2D surfaces of the pipes consisted of 10 10 almost quadratic cells in the pipe center, encircled by an almost circular mesh of 40 tangential and 4 radial cells. The outer layers of cells in the pipes were radial refined once to obtain yþ values between 30 and 100. The pipes were generated by extruding the 2D butterfly meshes in the axial direction of the pipe. This was followed by projection of the vertices closest to the valve house onto the valve house. Cells in the inlet and outlet pipes were refined 20 times in the axial direction and the eight layers of cells generated closest to the valve house were refined axially once. Arbitrary couples between pipes and valve house were applied at their common interface. The mesh generated from the above refinements was called ‘‘mesh-1’’ and consisted of 83,000 cells and had yþ values of approximately 40. A mesh appropriate for two-layer models requires substantial refinement of near-wall cells to obtain yþ values in the range of 3. Cells for refinement were identified from a series of simulations that started at mesh-1 where near-wall cells with yþ above 3 and their neighbor cells perpendicular to the wall were collected and refined in that direction. Cells parts of arbitrary couples were not refined. Refinement to yþ 3 was only done in the valve house. In the inlet and outlet pipes, the wall function was still used, as these parts were of no interest to this study. Finally, cells in the valve house part of arbitrary couples and connected to cells near the outer surface of the inlet and outlet pipes were refined radially until momentum and mass conservation residuals dropped below 103 . After refinement, the number of cells was 160,000 (called ‘‘mesh-2’’) and the number of nodes within the near-wall layer differed between four and eight (mesh shown in Figure 25.6, right). This is less than the 15 nodes suggested, hence, a test was carried out to compare wall shear stress and flow patterns predicted by simulation on a mesh with 6 and 11 nodes. Only minor differences were seen for both flow patterns and wall shear stresses [8].
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Laser Doppler anemometry (LDA) measurements were performed to get data for validation of the CFD model set-up [6]. Comparison between measured and simulated velocity profile in the MPV showed that a good prediction was achieved using mesh-2 (Figure 25.5). Small differences are seen close to the valve stem as the mesh in this area was not optimized like the mesh close to the outer surface and also the fact that very complex flow patterns are present at the stem (detachment and reattachment of boundary layers) makes prediction difficult in this area. Separate refinements of mesh-2 were done in the axial, tangential, and radial directions for cells not previously refined in that particular direction to see the isolated effects on mesh independence. For the radial and axial direction, near-wall cells were not refined, as this would change the yþ values. The numbers of cells in the models were: 251,000, 285,000, and 281,000, respectively (results can be seen in Ref. [8]). Constant residuals below 103 were achieved within 3000 s for mesh-1, 103 within 6000 s for mesh-2, and an average of 9000 s for the three independence tests (all simulated on a 1.6 GHz IBM intelli Station with 1 Gb RAM). 25.3.1.4
Cleanability Prediction Using Wall Shear Stress
From the critical wall shear stress of 3 Pa it was predicted that nearly 60% of the outer surface area of the MPV would not be cleaned (the part located in area A in Figure 25.7). The surface area predicted as uncleaned by the critical wall shear stress starts close to the inlet and covers most of the surface down through the valve, with some surface areas predicted as being cleaned in the lower and upper parts of the valve house (area B). Comparing cleanability predicted from the critical wall shear stress to the results obtained from the cleaning trials (Figure 25.8) showed that the surface areas predicted uncleaned by the critical wall shear stress were larger than the surface areas found uncleaned by the cleaning trials. The percentage of uncleaned surface area identified in the same location in all three experiments was 12%, identified uncleaned in the same location in two out of the three experiments was 33%, and uncleaned in just one of experiment was 34%. Some surface areas with wall shear stress well below 3 Pa were in fact cleaned in all three experiments, and some areas with wall shear stress above 3 Pa were in fact not cleaned in at least two of the three experiments. These regions are especially seen in the region near the bottom, from 1=2 of the downstream distance to 3=4 of the downstream distance from the inlet to the outlet. Near the outlet, areas with wall shear stresses above 3 Pa, areas were
B
2.5 A
2.5 B
3.5
3
A
B 3 3.5
FIGURE 25.7 Prediction of cleanability in MPV from the assumption that CFD simulations predict the wall shear stress, and that the wall shear stress is the only controlling hydrodynamic parameter for cleaning. A is areas predicted uncleaned and B cleaned. Included is also the influence from having predicted wall shear stress either too high or too low or estimating a too high or too low critical wall shear stress; curves with 2.5 and 3.5. (From Jensen, B.B.B. and Friis, A., J. Food Process Eng., 28, 89, 2005.)
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FIGURE 25.8 Illustration of results from cleaning trails without seat lifts, which is done in a standard EHEDG test method. Black is uncleaned zones. Dotted lines mark the zones predicted as cleanable from a critical wall shear stress of 3 Pa. (From Jensen, B.B.B. and Friis, A., Foodsim’ 2002 Proceedings, 2002.)
not cleaned, while areas below 3 Pa were cleaned. This demonstrated that cleanability could not be totally well predicted by use of a critical wall shear stress under the assumption that wall shear stress was reasonably well predicted by the CFD simulations. It was only possible to indicate zones potentially difficult to clean. Prediction of cleanability by use of wall shear stress close to the critical value of 3 Pa (2.5 and 3.5 Pa) showed that the area predicted as unclean only changed from 60% to 52% (2.5 Pa) and 67% (3.5 Pa) (Figure 25.7). This strengthens the conclusion of this work. Even if the wall shear stresses predicted in the MPV were too high, or the critical wall shear stress was above or below the predicted of 3 Pa by as much as 20%, the conclusion would still be the same. Thus, a critical wall shear stress was not useful for prediction of cleanability in complex equipment. If wall shear stresses were predicted too high, as compared to real wall shear stresses, the area predicted as uncleaned by CFD would be larger than that presented here. This would mean that the prediction of cleanability by a critical wall shear stress would be even worse than that which is detailed in this chapter. Hence, the conclusion becomes even more evident. Reasons for the better cleaning of the MPV than what was predicted by the critical wall shear stress could be numerous. First of all, fluctuations in the mass transfer of detergent solution to the surface (analogous to wall shear stress) are very likely to have an influence [9]. In a straight duct, Paulsson [23] concludes that fluctuations in wall shear stress are as much as 3.5 times higher, and 0.3 times lower, than the average wall shear stresses measured. Secondly, examination of the flow patterns shown in the MPV [6] could provide a further explanation. It was shown that swirl-like zones of circulating fluid were generated in the MPV as fluid enters the valve house (Figure 25.9). Two vertical swirl zones on top of each other in the section of the valve house closest to the outer walls were observed. Such flow structures are a mechanism that improves mixing of ‘‘old’’ and ‘‘new’’ CIP fluid during cleaning [8]. Enhanced mixing distributes detergent and heat to the soil so it swells and loosens [24], hence, it allows a lower wall shear stress to remove the soil. It could be argued that in a pipe or an RFC, detergent and heat are also transported across the pipe=test surfaces, thereby aiding the loosening of the soil. This is partly true;
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FIGURE 25.9 Flow pattern in MPV illustrated with vectors that represents flow direction. Left is in the upstream part of the valve house, middle is midway between inlet and outlet pipe, and right is in the downstream part of the valve house.
however, in fully developed flow parallel to a surface, the soil is protected from the main flow of detergent and heat by a relatively thick boundary layer where the transport rate of heat and chemicals is diffusion dependent. Hence, transport is reduced by the increased thickness of the boundary layer. Therefore, unless high wall shear stress or sufficiently long CIP times are present, cleaning pipes could actually be more difficult than cleaning well-designed complex equipment.
25.3.2 CASE STUDY: FLUID EXCHANGE
FOR IMPROVED
PREDICTION
OF
CLEANABILITY
In the previous section it has been shown that a critical wall shear stress only gives a limited quality of the prediction of cleanability. Even surface areas exposed to relatively low wall shear stresses could in fact be cleaned. The contrary has been seen for an upstand geometry (cleaning experiments performed by Campden Chorleywood [2] and CFD analysis made by the authors of this chapter [25]). Here surface areas exposed to identical wall shear stress were cleaned to different degrees (in this case relatively large wall shear stresses could clean in some areas but not in others). The CFD simulations of the MPV house and the upstand were extended to transient simulations to predict fluid exchange. In addition to the wall shear stress, others (e.g., Ref. [26]) postulate, but do not prove, that the fluid exchange rate could be correlated to the degree of cleanability. Exchange of fluid serves as a transport mechanism, due to convection of detergent and heat from the mainstream to the near-wall region. These two components weaken the bond between deposit and surface, which allows a lower wall shear stress to remove the deposit [27]. In addition the exchange of fluid also transports the removed deposit away from the near-wall regions enabling decontamination. The need for transporting detergent and heat to surfaces is amplified as surfaces in areas of low fluid exchange very often are exposed to low wall shear stress because of recirculation zones of low fluid velocity. Exchange of fluid can be obtained from experimental methods such as conductive measurements [26] or by discrete sampling in the product stream, both yielding results on a macroscale level. An alternative is transient CFD simulations that provide a tool for prediction and visualization of the exchange of fluid on both micro- and macroscale levels. The method used for predicting the exchange of fluid involves two steps: (1) A steady state solution is carried out to predict the flow field in the geometry using appropriate properties of the CIP fluid of a predefined color. (2) A transient simulation is restarted using the steady state solution as initial conditions with a new fluid with the same properties as the old one but with a different color used as inlet fluid from t ¼ 0 s and onward. Stepping through time in small time steps gives the exchange of old fluid with new fluid.
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Fluid exchange predictions using CFD together with information on wall shear stress can be applied to make very good prediction of areas difficult to clean. The areas in the MPV not directly explainable as cleaned by threshold wall shear stress can in fact be explained by information on the fluid exchange. Additionally, an upstand geometry will also be used for showing the importance of combining fluid exchange information with wall shear stress for predicting cleanability. Hall et al. [2] showed that looking at the velocities in a short upstand geometry one could explain the surface areas cleaned or not. However, focusing on the velocities solely is dangerous as it might become a matter of identifying where the velocity should be low. Moreover, close to walls velocities are always low. It is shown below that by using fluid exchange in the near-wall region and wall shear stress, one can in fact give a good prediction of the cleaning results presented by Hall et al. [2]. 25.3.2.1
Simulation Set-Up for Fluid Exchange Prediction
The simulations are performed using the finite volume based code Star-CD v. 3.100b. The Navier–Stokes equations set up transport equations for momentum, energy, and scalars by use of appropriate parameters. Spatial and temporal discretization of the transport equations is performed using the second-order accurate SFCD and Crank–Nicholson schemes, respectively. The importance of choosing second-order discretization for both dimensions of progress has been shown as numerical diffusion is significant in lower order schemes [22]. A time step of 0.005 and 0.0005 s for the upstand and spherical-shaped valve, respectively, is chosen to obtain Courant numbers below 100 to capture features of the flow [19]. If the Courant number is too high, the risk of losing information convected across cells in the domain is large and thereby information from one cell is likely to be transferred across neighboring cells reducing the accuracy of the solution. The time step used in the simulations of the spherical-shaped valve could have been the same as for the upstand without violating the Courant number of 100. However, with the mesh configuration and models chosen it was impossible to get a converged transient simulation at a time step of 0.005 s. A maximum number of 20 corrector steps are chosen to obtain a physical solution to the fluid exchange in the spherical-shaped valve compared to only 10 in the upstand. The RNG k–« model with the two-layer model of Norris and Reynolds is used for turbulence modeling, with a dynamic estimation of the cells located within the near-wall layer to describe the flow in the near-wall region [18,21]. In both geometries the inlet conditions are described using the Dirichlet method with a fully developed turbulent velocity profile at an average velocity of 1.5 m=s, turbulent kinetic energy of 5%, and turbulent length scale of 1=10 of the inlet pipe diameter. The outlet is described as a pressure outlet with constant pressure on the boundary. Walls are prescribed with no-slip conditions and as hydraulic smooth. 25.3.2.2
Mesh Description for the Fluid Exchange Simulations
For the MPV the mesh used for predicting fluid exchange is identical to the one used for wall shear stress estimation presented earlier. The upstand geometry is modeled using hexahedral cells in an unstructured mesh with integral and arbitrary couplings between cells with unmatched faces. Both pipes are generated from the butterfly method (Figure 25.10). Exploiting the geometric plane of symmetry, a model with 51,000 cells is created for one half of the upstand. The validity of using a symmetry plane as a boundary condition for the flow was tested (not shown) and shown to have only little difference in exchange rates.
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FIGURE 25.10 Mesh created to discretize the flow domain of the upstand. (From Jensen, B.B.B. and Friis, A., Foodsim’ 2002 Proceedings, 2002.)
The mesh is created with a butterfly mesh of 7 7 40 (width height axial) cells in the core region and encircled by a 5 28 40 (radial tangential axial) celled cylindricalshaped mesh. The cells closest to the walls are refined radial to obtain yþ 3 as recommended for the use of two-layer models (Figure 25.10). Cell part of an arbitrary couple is not refined. The upstand pipe positioned between 1.5 times the inlet diameter and 2.5 times the inlet diameter downstream of the inlet consists of 7 7 18 box like mesh and 28 5 18 cylindrical mesh. Refinement is made of the near-wall cells to yþ 3: Ten rows with double axial distance compared to the axial distance in the region of interest are added to the downstream side of the upstand to position the outlet boundary sufficiently far downstream. 25.3.2.3
Fluid Exchange in Sphere-Shaped Valve
The flow pattern in a spherical valve house with inlet and outlet located as shown in Figure 25.11 is very complex because transition from a small circular cross-sectional area to a larger noncircular shape produces two swirl zones on top of each other in the zone seen closest to the outer surfaces (Figure 25.11). Near the cone the flow is almost unidirectional toward the outlet. The swirl zones have a large influence on the exchange of fluid from areas close to the outer walls. As new fluid enters the sphere most of it flows directly through the center of the valve and toward the outlet pipe. Within 0.23 s most of the old fluid is exchanged in the mainstream. As time progresses the old fluid is exchanged in the remaining part of the sphere. The zones with lowest exchange rate are near the equator of the sphere (Figure 25.11) and especially in the area just next to the inlet. The total exchange takes 0.95 s. Wall shear stress is below 3 Pa in large zones on the surfaces (Figure 25.11, right). Only near the outlet
FIGURE 25.11 Predicted fluid exchange in MPV at time from changing fluid of 0.23 and 0.48 s. Dark is new fluid and bright is old fluid. Grayscales between these are mixtures of the two fluids. Right is shown the areas of the surface with wall shear stress below 3 Pa. Flow from left to right.
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pipe, close to the top and bottom and near the inlet, close to the bottom are wall shear stresses above 3 Pa (looking only at the outer surface of the valve). 25.3.2.4
Fluid Exchange in Upstand
In the short upstand investigated the flow is more complicated than in a longer upstand (i.e., H=D ¼ 0.5). A recirculation zone is seen in a longer upstand on a plane coinciding with the symmetry plane. As the space for this recirculation zone is reduced in the short upstand this recirculation zone is suppressed and almost nonexisting. Instead two recirculation zones in the plane perpendicular to the axial direction of the main pipe are formed in the upstand and a recirculation zone is also seen in the horizontal plane. The effect of the nonexisting recirculation zone is seen in the flow downstream of the upstand as flow is pushed away from the wall producing a zone of low exchange rate. This is not seen in the long upstand, as the horizontal recirculation zone does not influence the main flow as much as in the short upstand. In the downstream zone exchange of fluid (Figure 25.12) is approximately three times slower and in the upstand six times slower than in the part located in the ‘‘bulk flow.’’ Investigations of the magnitude of the wall shear stress (Figure 25.12, right) show wall shear stress below the critical value of 3 Pa in the upstand and in a thin streak downstream of the upstand. The zone of low exchange rate downstream of the upstand extends to more than 1.5 times the diameter downstream of the upstand. 25.3.2.5
Prediction of Cleaning Combining Wall Shear Stress and Fluid Exchange
Comparing cleaning results, CFD simulations, and the critical wall shear stress shows that wall shear stress alone is insufficient for approximating problematic areas in the spherical-shaped valve and upstand used in this study. Areas with low wall shear stresses are cleaned (valve) and areas of high wall shear stress are not cleaned (upstand geometry). In the valve areas with wall shear stress below the critical value of 3 Pa are cleaned. The expected area of hygienic problems according to the wall shear stress is outlined in Figure 25.8 as the dotted lines and shows a large area around the equator expected to be uncleaned. Comparing Figure 25.8 to predicted exchange (Figure 25.11) shows that the zone of low exchange rate is decreased into a smaller and smaller zone just above the equator as time progresses.
S I R
FIGURE 25.12 Predicted fluid exchange in upstand at time from changing fluid of 0.15 and 0.25 s. Dark is new fluid and bright is old fluid. Grayscales between these are mixtures of the two fluids. Right is shown the areas of the surface with wall shear stress below 3 Pa. Flow from top to bottom for the fluid exchange figures and bottom to top for the wall shear stress figure.
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The areas cleaned having low wall shear stress have a relatively high exchange rate compared to the exchange in, e.g., the upstand (Figure 25.12) and other places in the valve with the same wall shear stress. From this, zones with low wall shear stress, but clean, can be explained by the relative fast fluid exchange (below 0.3 s). This is in accordance with the mechanisms of cleaning. The higher the fluid exchange the more time soil is exposed to the desired temperature and detergent concentration, hence, a lower wall shear stress is needed to remove the soil (e.g., areas in the valve). On the contrary, it will be difficult to clean surface areas of low fluid exchange even though wall shear stress is relatively high, as the desired detergent concentration and temperature are only present for short periods of time.
25.3.3 EXPLAINING DIFFERENT CLEANING CHARACTERISTICS
OF A
BUTTERFLY VALVE
For designers of closed processing equipment and fittings proof of CFD as a useful tool for prediction of cleanability is very important. Above, it has been shown for two very different components for closed processing lines. An additional example is the widely used butterfly valve. In this example the knowledge presented above is used to predict and explain the differences in cleaning characteristics found for a fully open and half open butterfly valve. The EHEDG test was performed by the accredited testing institute Technological Institute in Denmark. The CFD results presented in this section on the butterfly valve are rough simulations to show that even by such a simulation valuable information is gained in the quest to optimize cleaning of a simple component. This model is generated using the Fluent CFD package using Gambit for the preprocessing that includes geometry creation and meshing. Fluent ver. 6.2.16 and Gambit ver. 2.2.30 were used. 25.3.3.1
Geometry and CFD Model
The butterfly valve used in this example is a typical butterfly valve inserted in a 2 in. pipe. A simplified 3D CFD model of the valve was set up in Gambit and flow was simulated using Fluent. The disc is 2.5 mm thick with a diameter 4.6 mm smaller than the inner pipe diameter and its axis of rotation is located 2 D downstream of the inlet of the geometry. The outlet is located 11 D downstream of the axis of rotation. For the half open valve the plate is turned 458 compared to the fully open state. A critical area during meshing of this type of geometry is the valve seat (where the plate touches the pipe walls). If the plate is inserted in the pipe it will have two areas where it is very close to the pipe wall. This area was difficult to mesh while not generating a huge amount of cells in the rest of the geometry. To simplify this area, the steering rod of the plate was modeled as a 20 mm width and 2.5 mm deep plate at both of the areas where the plate is closest to the pipe wall. The models of the fully open and the half open valve are generated as full 3D models. The volume is decomposed into three main regions; one surrounding the disc, a short region upstream and a longer one downstream. All regions are then split in two down the symmetry plane of the pipe to allow mesh control in the axial direction. A boundary mesh is created on all faces located perpendicular to the axial direction. Then the end faces of the center volume are meshed with a quadratic pave mesh and the center volume is meshed with triangular mesh. Finally, the upstream and downstream volumes are meshed by extruding the endface mesh of the center volume to the inlet and outlet, respectively. This produces a good quality mesh where control of the boundary layer in the downstream pipe is possible, which is crucial for evaluation of wall shear stress. Optimization of yþ values is done by adaptive mesh refinement in Fluent.
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25.3.3.2
Simulation Set-Up
Simulations are done using properties of water at 208C. The discretization is done using second-order upwind for the momentum and first-order upwind for all other equations. For this illustration purpose only, a standard wall function is used to speed up calculations and the RNG k–« was used for turbulence modeling. All the default model parameters were used. The transient simulation is done with a constant time step of 0.01 for the first 0.05 s and 0.001 for the remaining time. Fluid exchange was predicted using the ‘‘mixture’’ method available in Fluent that allows both phases to move with same velocity. A steady state simulation was done first to get a ‘‘moving’’ flow pattern of the ‘‘old’’ fluid. At time 0 s a ‘‘new’’ fluid with identical properties was set at the inlet and fluid exchange is visualized as a function of time. 25.3.3.3
Prediction of Cleanability
Looking at the simulation results from the two simulations (fully open and half open butterfly valve, Figure 25.13) shows that there is a big difference in wall shear stress. For the fully open butterfly valve the wall shear stress is almost the same on the entire surface of the pipe. The only place where lower wall shear stresses compared to the relatively undisturbed parts of the flow are evident is in two thin streaks behind the steering rod of the disc. The wall shear stresses range from around 10 Pa on the leading edge of the disc to approximately 6 Pa in the almost undisturbed flow and around 3–4 Pa in the thin streak region. If the walls were plain stainless steel, cleaning would be assumed possible as wall shear stress is above the critical
0.00e+00
1.50e+00
3.00e+00
4.50e+00
6.00e+00
7.50e+00
9.00e+00
1.00e+01
0.00e+00
2.85e+01
5.70e+01
8.55e+01
1.14e+02
1.43e+02
1.71e+02
1.90e+02
FIGURE 25.13 Wall shear stress close to the plate in a fully open butterfly valve (top) and a half open butterfly valve (bottom). Flow from left to right.
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value of 3 Pa and fluid exchange is acceptable in the straight pipe. However, removing soil and microorganisms from gasket materials is, by experience, found more difficult compared to stainless steel. In this case the gasket circumferences the pipe where the disc closes between itself and the pipe wall. To clean the gasket material a higher wall shear stress might be needed, so this could be a problematic area. Looking at the wall shear stress on the walls for the half opened butterfly valve shows that the reduced cross-sectional area increases velocity in the area where high velocity is needed (at the walls). This gives wall shear stress up to 120 Pa and down to around 5–10 Pa in the part downstream of the steering rod. It is predicted that these high wall shear stresses produce better cleaning than in the fully open valve. One possible problematic area though could be the back side of the disc and the pipe surface in the downstream region of the steering rod. Better cleaning would be expected downstream rather than upstream of the disc because of the higher wall shear stresses. To investigate if the low wall shear stresses in these areas might be problematic, further study is required of the fluid exchange. 25.3.3.4
Verification of Cleanability Prediction
The above predictions have shown that problems with cleanability for the fully opened valve are on and around the big gasket, as gasket material is often more difficult to clean than stainless steel (requiring higher wall shear stress). For the half open valve it was predicted that only the part of the thick gasket located in that half of the pipe where the disc is moved downstream could be a problematic area, as this zone still has low wall shear stress while the other half has very high wall shear stresses. This is because the disc here is turned toward the flow direction creating high wall shear stresses around the gasket. Examining results from a cleaning test performed on a butterfly valve with a wide gasket at Technological Institute, Kolding Denmark shows that a problematic area for the fully opened valve is all around the wide gasket, both on the leading edge, the flat side, and the trailing edge. For the half opened valve only problems are seen on the wide gasket, in the area located in the half of the pipe where the disc is turned downstream and not at all in the area turned upstream. No other problematic areas are seen in the half open and fully open valve—not even on the downstream side of the disc for the half open valve where low wall shear stresses do not result in any poor cleaning. This is an area where low fluid exchange takes place and low wall shear stress is present. The reason for this case in cleaning is probably that the plate itself is made from a very smooth surface compared to the pipe surface and the gasket material. Thus, in this case, the good cleaning is associated with the state of the surface.
25.4 CHALLENGES FOR THE FUTURE It is obvious from the above that it is not straightforward to apply CFD for hygienic design. The quality of the CFD simulations with respect to levels of wall shear stress, fluid exchange, etc. is a key prerequisite if the CFD is not only going to be used for comparison studies. CFD software has proved its worth on simulating parameters for bulk flow, but closer to the walls, prediction of the flow is not straightforward due to the transition from turbulent to laminar flow, the anisotropy of the turbulence in this region, and, as proposed by some, turbulent bursts at the surface [28]—turbulent bursts are randomly occurring lifts of the boundary layer from the surface. This and more challenges for the future for CFD in hygienic design of food processing equipment are discussed below from the point of view of the author of this chapter.
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25.4.1 NEAR-WALL TREATMENT Dealing with CFD for prediction of hygiene in food processing equipment, and in particular the cleaning of surfaces, flow close to the surface is very important. CFD programs have proven valid for predicting bulk flow patterns and also near-wall flow in fully developed pipe and duct flow. The latest generation of CFD programs has seen the implementation of nearwall treatments that allows for an improved description of the flow in the boundary layer. This is particularly useful for flows involving adverse pressure gradients and recirculating flows, but also for CFD investigations where near-wall properties of the flow are of interest, as is the case for cleaning prediction. The near-wall treatments are necessary to use if quantitative values are desired for example, comparison with threshold values of wall shear stress or if boundary layer properties such as thickness, mass transfer (fluid exchange), or fluctuations are of interest. For a rougher comparison on a qualitative basis often a CFD model with law-of-the-wall models for the near-wall flow can be sufficient. However, the choice will often be a compromise between time and detail.
25.4.2 WALL SHEAR STRESS PREDICTION Wall shear stress is a standard parameter in commercial CFD codes predicted based on velocity gradients close to the wall or, as in the case of the law-of-the-wall, on the predescribed velocity profile in the boundary layer. The qualitative prediction of wall shear stress (location) is closely connected to the quality of the CFD simulations to predict the general flow patterns in the geometry. The validity of the magnitude of wall shear stresses is up for discussion when dealing with turbulent flows in geometries, which feature flow structures where the law-of-the-wall model is invalid. For a regular fully developed pipe and duct flow wall shear stress magnitudes are very well predicted using both standard wall-function models and the more sophisticated near-wall treatments or enhanced wall treatments, but for the more complex flows the prediction is difficult to validate as wall shear stress data in such flows are not that common. The electrochemical methods mentioned in this chapter can give the required information. In addition, the wall shear stress is probably not constant due to the turbulent fluctuations in the flow and also the, perhaps existing, turbulent bursts. This means that prediction of the time-dependent fluctuations is needed from transient simulations, or through some other parameter (as shown earlier with the turbulence intensity).
25.4.3 FLUID EXCHANGE PREDICTIONS As shown in the above section, knowledge of wall shear stress combined with the knowledge of fluid exchange can give good prediction of the areas hardest to clean in a piece of complex equipment. For the wall shear stress a critical wall shear stress was found for the EHEDG cleaning test giving a threshold value as input to the CFD program for evaluating what levels of wall shear stress are high and low. For the fluid exchange a critical value has not yet been identified. The fact is that surfaces located in areas of low fluid exchange clean poorer than surfaces located in areas of high fluid exchange. The challenge is to quantify the fluid exchange so a threshold value can be found for combinations of soil and cleaning procedure. This would allow for combinations of wall shear stress and fluid exchange levels to be set up for predicting cleanability. In addition to the challenge of quantifying fluid exchange, validation of predicted exchange has to be performed. Different experimental techniques are available such as conductive measurement and NMR. The conductive measurement method can give the concentrations of two different fluids in a single point. This provides an overall number for the time needed to achieve total fluid exchange in a geometry. For the NMR
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method, a snapshot of the distribution of two different salt concentrations can be obtained giving detailed information for use in validation of CFD data.
25.4.4 COMBINING FLUID MECHANICS WITH KNOWLEDGE OF AND THE MECHANICS OF THE SOIL ITSELF
THE
STRUCTURE
In the early 2000 the group of Prof. Fryer at Birmingham University [30] and the group of Prof. Wilson at Cambridge University [31] started looking into the mechanics of the soil on the surface. They have both shown that the removal of soil from a surface can happen in different modes: (1) as an adhesive soil, where the force between surface and soil is the predominant one, (2) cohesive, where the internal force in the soil is the predominant one, and (3) a combination of the two. In mode (1), the soil will be removed as single particles from the surface, while for mode (2) the soil will be removed in flakes from the surface. The fact that there are different modes of detachment makes it important to characterize one’s soil before starting to consider the use of CFD for predicting cleanability. For the adhesive mode CFD can be used, but for the cohesive mode and the combination the use of CFD will be limited with the knowledge available at present. However, the future could bring knowledge of fracture mechanics and fluid dynamics together to predict the removal of flake-like structures from a surface. This is complicated by the fact that when a flake is partly loosened from the surface, water will go under the flake and give additional forces on this part. Prediction of this using CFD will be a challenge for the future as modeling this will demand for transient solutions of the fluid dynamics and a continuous back-and-forth communication between the mechanical structure of the soil and the flow. This includes changing boundary conditions and dynamic meshing.
25.4.5 BOUNDARY LAYER THICKNESS PREDICTION Timperley and Lawson [29] showed that the boundary layer thickness could be a possible important parameter for the cleaning of surfaces. The thickness of the boundary layer has to be predicted using CFD as estimating boundary layer thickness continuously on all surfaces of a piece of processing equipment is not possible. Instead, e.g., a turbulent parameter could be used to define the boundary between the laminar sublayer and the buffer zone (e.g., turbulence intensity or turbulent length scale). To do this near-wall treatments are essential, as the boundary layer must also be discretized. Furthermore, the influence of wall roughness of these parameters must be taken into consideration.
25.5 CONCLUSION CFD has been around for a substantial amount of time, however, very little work has been done in the area of using it for prediction of cleaning and increasing hygienic design of closed processing equipment. Few attempts have been made all concluding that it is a tool with large potential in this area. The results presented so far, and summarized in this chapter, also show very good results. Areas potentially of becoming a hygienic hazard based on wall shear stress and velocity can be identified. It has also been shown that a more quantitative approach of optimizing equipment from a hydrodynamic point of view with respect to cleaning still is not completely possible, as threshold values for parameters such as fluid exchange and wall shear stress fluctuations are still not known. Threshold values for the parameters controlling cleaning are necessary if sound predictions are to be made. If not, only comparative studies can be carried out, in which suggestions on the relative cleaning difficulties between areas can be made.
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At present CFD can be used to obtain a deeper knowledge into the controlling hydrodynamic mechanisms involved in cleaning and identifying advantageous and disadvantageous flow patterns and thereby geometrical design. A good example is the conclusion that 3D swirl zones improve cleaning compared to stationary 2D recirculation zones, and that in particular we should look at 3D flow patterns when evaluating hygienic design. Still some challenges are present to be able to make very good predictions of cleanability. An important area is the diversity of soil, its attachment to surfaces, and the detachment from the surfaces. This is an area that is having large focus at present and could open for collaboration between fluid mechanics and facture mechanics for implementing the cohesion part of cleaning in CFD models. With this overview of CFD for predicting hygiene in processing equipment we hope that new ideas have appeared, or an interest has been awoken to perform more work in this area in the future. More case studies should be undertaken to prove some of the concepts outlined already.
NOMENCLATURE k U u0 Ti yþ y n ut tw r « uw E k H D
turbulent kinetic energy (m2 s2 ) velocity (m s1 ) fluctuating component of the velocity (m s1 ) turbulence intensity (%) dimensionless distance from wall () distance from wall (m) kinematic viscosity (m2 s1 ) friction velocity (m s1 ) wall shear stress (Pa) density (kg m3 ) dissipation of turbulent energy (m2 s3 ) wall velocity (m s1 ) empirical constant () empirical constant () height (m) diameter (m)
REFERENCES ¨ ber das waschen mit haushaltwaschmaschinen: in welchem umfange erleichtern haushalt1. H Sinner. U waschmaschinen und-gera¨te das wa¨schehaben im haushalt? Hamburg: Haus þ heim verl, 1960. 2. JE Hall, MR Jones, and AW Timperley. Improving the Hygienic Design of Food Processing Equipment Using Modelling Approaches Based on Computational Fluid Dynamics. Chipping Campden: Campden & Chorleywood Food Research Association, 1999. 3. G Hauser and H Kru¨s. Hygienegebrechte gestaltung von bauteilen fu¨r die lebensmittelherstellung— schwachstellenanalyse durch tests und numerische berechungen. Web publication on www. cyclone.nl (23-05-2006), Cyclone Fluid Dynamics, Waalre, 2000. 4. C Karlsson and C Tra¨ga˚rdh. Modelling of Soil Removal Kinetics. In: PJ Fryer, APM Hasting, and ThJM Jeurnink (ed.), Fouling and Cleaning in Food Processing—1994. Luxemburg: European Commission, 1996, pp. 196–200. 5. BBB Jensen and A Friis. Critical wall shear stress for the EHEDG test method. Chemical Engineering and Processing 43(7): 831–840, 2004.
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6. BBB Jensen and A Friis. Prediction of flow in mix-proof valve by use of CFD—validation by LDA. Journal of Food Process Engineering 27: 65–85, 2004. 7. BBB Jensen and A Friis. Predicting the cleanability of mix-proof valves by use of wall shear stress. Journal of Food Process Engineering 28: 89–106, 2005. 8. BBB Jensen. Hygienic design of closed equipment by use of computational fluid dynamics. Lyngby: BioCentrum-DTU Technical University of Denmark, 2003. 9. C Lelie`vre, P Legentilhomme, C Gaucher, J Legrand, C Faille, and T Be´ne´zech. Cleaning in place: effect of local wall shear stress variation on bacterial removal from stainless steel equipment. Chemical Engineering Science 57: 1287–1297, 2002. 10. J Legrand, H Aouabed, P Legentilhomme, G Lefebvre, and F Huet. Use of electrochemical sensors for the determination of wall turbulence characteristics in annular swirling decaying flows. Experimental Thermal and Fluid Science 15: 125–136, 1997. 11. BBB Jensen, A Friis, Th Be´ne´zech, P Legentilhomme, and C Lelie`vre. Local wall shear stress variations predicted by computational fluid dynamics for hygienic design. Transaction of the Institute of Chemical Engineers, Part C. Food and Bioproducts Processing 83(C1): 53–60, 2005. 12. B Bergman and C Tragardh. An approach to study and model the hydrodynamic cleaning effect. Journal of Food Process Engineering 13: 135–154, 1990. 13. JE Duddridge, CA Kent, and JF Laws. Effect of surface shear stress on the attachment of Pseudomonas fluorescence to stainless steel under defined flow conditions. Biotechnology and Bioengineering 24: 153–164, 1982. 14. MS Powell and NKH Slater. Removal rates of bacterial cells from glass surfaces by fluid shear. Biotechnology and Bioengineering 24: 2527–2537, 1982. 15. AW Timperley, F Boution, Th Benezech, B Carpentier, GJ Curiel, K Haugan, J Hofman, J Kastelein, U Ronner, C Tragardh, and G Wirtanen. EHEDG GL 2: A Method for the Assessment of In-Place Cleanability of Food Processing Equipment. EHEDG, 2nd edn. Chipping Campden: Campden & Chorleywood Food Research Association, 2000. 16. DA Shapton and WR Hindes. The standardisation of a spore count technique. Chemistry and Industry 9: 230–234, 1963. 17. HW Fowler and AJ McKay. The measurement of microbial adhesion. In: HW Fowler and AJ McKay (ed.), Microbial Adhesion to Surfaces. Chichester: Ellis Horwood Ltd, 1980, pp. 143–161. 18. W Rodi. Experience with two-layer models combining the k–« model with a one-equation model near the wall, AIAA report (91-0216), American Institute of Aeronautics and Astronautics, Reston, VA, 1991. 19. Anonymous. Methodology Manual (On-Line)—Ver. 3.10a and User Guide (On-line)—Ver. 3.10a, Software Manual, CD Adapco Group, London, 1999. 20. FS Lien, WL Chen, and MA Leschziner. Low-Reynolds-number eddy-viscosity modelling based on non-linear stress–strain=vorticity relations. Turbulence Modelling and Experiments 3: 91–100, 1996. 21. LH Norris and WC Reynolds. Turbulent channel flow with a moving wavy boundary, Scientific report (FM-10), Stanford University, USA, 1975. 22. M Casey and T Wintergerste. ERCOFTAC Special Interest Group on ‘‘Quality and Trust in Industrial CFD’’—Best Practice Guide, 1st edn. Brussels: ERCOFTAC, 2000. 23. B-O Paulsson. Removal of Wall Deposits in Turbulent Pipe Flows. Lund: Department of Food Engineering, Lund University, Sweden, 1999. 24. CR Gillham, PJ Fryer, APM Hastings, and DI Wilson. Cleaning-in-place of whey protein fouling deposits: mechanisms controlling cleaning. Transaction of the Institute of Chemical Engineers, Part C. Food and Bioproducts Processing 77: 127–136, 1999. 25. BBB Jensen and A Friis. Fluid exchange for predicting cleanability using CFD. In: B O’Conner and D Thiel (ed.), FoodSim’ 2002—Second International Conference on Simulation and Modelling in Food and Bio-Industry. Ghent, Belgium: SCS Publishing House, 2002. 26. A GraBhoff. Untersuchungen zum stromungsverhalten von flussigkeiten in zylindrischen totraumen von rorhleitungssystemen. Die Kieler Milchwirtshaftlichen Forschungsberichte 32: 273–298, 1980. 27. PJ Eginton, J Holah, DG Allison, PS Handley, and P Gilbert. Changes in the strength of attachment of micro-organisms to surfaces following treatment with disinfectants and cleansing agents. Letters in Applied Microbiology 27: 101–105, 1998.
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28. JW Cleaver and B Yates. Mechanism of detachment of colloidal particles from a flat substrate in a turbulent flow. Journal of Colloid and Interface Science 44: 464–474, 1973. 29. DA Timperley and GB Lawson. Test rigs for evaluation of hygiene in plant design. In R Jowitt (ed.), Hygienic Design and Operation of Food Plant. Chichester: John Wiley & Sons Limited. 30. W Liu, GK Christian, Z Zhang, and PJ Fryer. Direct measurement of the force required to disrupt and remove fouling deposits of whey protein concentrate. International Dairy Journal 16: 164–172, 2006. 31. JYM Chew, WR Paterson, and DI Wilson. Fluid dynamic gauging for measuring the strength of soft deposits. Journal of Food Engineering 65: 175–187, 2004.
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CFD Design and Optimization of Biosensors for the Food Industry Pieter Verboven, Yegermal T. Atalay, Steven Vermeir, Bart M. Nicolaı¨, and Jeroen Lammertyn
CONTENTS 26.1 26.2
Introduction ............................................................................................................. 631 Mathematical Models of Biosensors ........................................................................ 633 26.2.1 Regime ........................................................................................................ 633 26.2.2 Flow Mechanisms ....................................................................................... 634 26.2.3 Governing Equations.................................................................................. 634 26.2.3.1 Fluid Flow................................................................................... 634 26.2.3.2 Mass Transfer.............................................................................. 636 26.2.3.3 Reaction Kinetics ........................................................................ 636 26.3 A Microcalorimetric Biosensor for Ascorbic Acid Quantification........................... 637 26.3.1 Microplate Differential Microcalorimetry .................................................. 637 26.3.2 Model.......................................................................................................... 638 26.3.3 Oxygen Limited Performance of the Biosensor .......................................... 639 26.4 An Electrokinetic Biochip for Taste Analysis .......................................................... 641 26.4.1 Miniaturization of Enzymatic Kits ............................................................. 641 26.4.2 Lab-on-a-Chip Design ................................................................................ 642 26.5 Conclusions .............................................................................................................. 646 Nomenclature ..................................................................................................................... 647 References .......................................................................................................................... 647
26.1 INTRODUCTION Due to the permanent risk of food crises, with several serious occurrences in the last years, the consumer’s attention is directed toward improved food quality and safety. Where food safety is concerned with the presence of harmful components like toxins and chemicals (PCBs, dioxins, etc.), food quality is determined by sensory properties like taste, aroma, texture, and appearance, and more recently functionality. The determination of many of these quality attributes often requires sophisticated analytical techniques like liquid chromatography and gas chromatography–mass spectrometry. Routine quality measurements on food products, which are hampered by such traditional analytical techniques, are often too costly and timeconsuming to be included. An alternative is provided by biosensors (Figure 26.1). Biosensors are a subgroup of chemical sensors where the detection of a chemical component is based on a
631
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Chemical analyte
Biological detection element
Transducer
Signal
Signal processor
FIGURE 26.1 Principle of a biosensor.
specific interaction of this chemical component with a bio-recognition molecule—being an enzyme, antibody, aptamer, microorganism or even a whole cell. This biological sensing element is integrated with or in intimate contact with a physicochemical transducer [1,2]. A wide range of transducers are available to detect the interaction between the analyte and the bio-recognition molecule and convert it into an electronic signal. Electrochemical, optical, thermal, and mass sensitive transduction mechanisms have been used in biosensor development over the past decade. Biosensors have a great potential not only for monitoring food composition (e.g., carbohydrates and organic acids) and product freshness (e.g., fish, fruits, and vegetables) but also for online process control and fermentation processes. Many food safety applications are reported and discussed in literature, such as rapid detection of pathogenic organisms, pesticides, microorganisms, and toxins. For different food applications, the reader is referred to Refs. [3–7]. Although their potential, commercialization of biosensors has not often been achieved, this is related to factors such as stability (the limited lifetime of the biological component), mass production, storage, and sensitivity (practicality in handling in the real sample), which will have to be further studied before reaching the commercialization stage. A few basic performance criteria in the design of successful biosensors need to be considered. These include calibration characteristics (i.e., sensitivity, detection and quantitative determination limits, operational and linear concentration range), selectivity and reliability, response time, high sample throughput, reproducibility, stability, and lifetime [8]. The resulting biosensor should, in addition, be cheap, small, portable, and capable of being used by semiskilled operators. Miniaturization of biosensors is one of the recent trends aiming not only at an increased performance and portability but also at low-cost mass production. Biosensor technology also benefits from the fast growth of microelectronic developments, which results in advanced biochips by combining the knowledge of microfluidics with microelectronics [9,10]. Optimization of the geometric and operational parameters then becomes a crucial step in the development [9,11]. Numerical prototyping by means of multiphysics computational fluid dynamics meets this need. This chapter will deal with aspects such as fluid flow, mass transfer, and chemical kinetics in biosensors. The main focus will particularly be on miniaturized microfluidic devices (Figure 26.2). Besides the practical advantages such as portability and minimal operation cost, miniaturization has the principal advantage of improving the analytical performance of the process [9,10]. First, for a cylindrical microtube with 50 mm radius, the surface area to
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FIGURE 26.2 Example of a microfluidic chip, containing eight reservoirs for supply of reagents and collection of products and microchannels (red) for transport and mixing (http:==www.chem.agilent. com=cag=feature=8-98=feature_graphics=chip.jpg).
volume ratio reaches 4 104 m1 , which is a huge interface for reactions to take place [12]. Second, because the diffusion time scales with the square of the distance the molecules travels, it is possible to reduce the molecular diffusion time significantly by handling microvolumes of fluids in small channels. These advantages have opened a new field of research and development called microfluidics. Microfluidics is the science of designing, manufacturing, and formulating devices and processes that deal with volumes of fluid in the order of nanoliters (dimensions in the order of micrometers), which will be significantly important when the reagents used are expensive. The fabrication of microdevices is relatively inexpensive and very amenable both to highly elaborate, multiplexed devices, and also to mass production [12,13]. Similar to microelectronics, microfluidic technologies enable the fabrication of highly integrated devices with different functions on one substrate chip. One of the long-term goals in the field of microfluidics is to create integrated, portable diagnostic devices for home and bedside use, thereby eliminating time-consuming laboratory analysis procedures. This chapter will present the state-of-the-art models that are used in biosensor design with two examples: a microcalorimetric biosensor for ascorbic acid (AA) determination and a lab-on-a-chip for taste analysis of fruit juices.
26.2 MATHEMATICAL MODELS OF BIOSENSORS 26.2.1 REGIME The flow of a fluid through a microfluidic channel can be characterized by the Reynolds number. Due to the small dimensions of microchannels, the Reynolds number is usually
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smaller than 100, often much smaller than 1. In this Reynolds number regime, the flow is completely laminar. Furthermore, in long narrow channels, the fluid flows parallel to the channel walls (uniaxial flow). The significance of uniaxial laminar flow is that all transport of momentum, mass, and heat in the direction normal to the flow is by molecular mechanisms: diffusion becomes the main method to move particles, mix fluids, and control reaction rates in biochips [14]. As the channel dimension diminishes the relative importance of surface and interfacial phenomena (such as surface tension, roughness, and electrokinetic effects) increases [11]. Using the latter phenomena as an advantage for fluid transport currently makes microfluidics an interesting field of study [14].
26.2.2 FLOW MECHANISMS Fluid can be transported through a microfluidic device in different ways. One can apply a pressure or a voltage difference over the microchannel or use surface forces like for instance capillarity. Hydrodynamic pressure is customarily used, but for small channels, pressure-driven flow exhibits a parabolic velocity profile resulting in Taylor dispersion of the analyte and reagents, which affects sensor performance in a negative way [1]. Further, the pressure drop is inversely proportional to the second power of the transverse dimension of the channel and will consequently be very large and make the method impractical for some applications. An attractive alternative is provided by electrokinetics [15]. Electrokinetics is a phenomenon that involves the interaction between solid surfaces (such as glass or a polymer-based substrate), ionic solutions, and applied electric fields. Electrokinetic flow can take place by electroosmosis and electrophoresis. Electroosmotic flow (EOF) exhibits a velocity profile that is uniform in the cross section of microchannels, which results in significantly less dispersive effects than pressure-driven flow. With the appropriate application of potentials, the valveless control of fluid flow by electrokinetics is favored in high-performance sample separation techniques. The method is very well suited for miniaturization as the need for additional structures such as pumps and valves becomes less important.
26.2.3 GOVERNING EQUATIONS Here the equations are described that apply to fluid flow and mass transfer in microchannels of biosensors. 26.2.3.1
Fluid Flow
The equation of motion for steady, low-Reynolds number flow in a microfluidic biosensor is 0 ¼ rp þ hr2 u þ rE E
(26:1)
where the last term on the right-hand side represents the body force on the fluid as a result of an applied electric field to a microchannel with an electric double layer (EDL), which requires the solution of the Poisson–Boltzmann equation, which is described below. As most surfaces possess a negative charge, resulting from the ionization of the surface or the adsorption of the ionic species, a layer of cations builds up near the surface when this surface gets in contact with polar liquids to maintain the charge balance. This creates an EDL of ions near the surface and a potential difference between the fixed charges on the wall and the diffuse charges of the mobile ions called zeta potential (z). The EDL is resolved in two regions: a compact and a diffuse layer (Figure 26.3). The compact layer is immobile due to a
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y
Negatively charged surface Compact layer (stern plane) Diffuse layer Shear plane
y0
ζ
Bulk region
0
Distance from the surface
x
FIGURE 26.3 Electrical double layer.
strong electrostatic force whereas the diffuse layer has a net charge different from zero. This layer will move when a longitudinal electric field, E, is applied. As a result of the viscous force on the rest of the fluid, the bulk starts to flow. This collective movement induces fluid motion in the channel, creating what is called EOF. Therefore the magnitude of the EOF depends on the electric field strength and the local net charge density which is a function of the EDL field. For simplified systems, the net charge density in the EDL can be given by Prodromidis and Karayannis [3]:
zec rE ¼ 2zen0 sin h kB T
(26:2)
where kB (J K1 ) is Boltzmann’s constant, T (K) is the temperature, z is the valence number of the ion, F is Faraday’s constant, e (C) is the charge of a proton, n0 (m3 ) is the ionic concentration, and c is the local potential. This charge density can be related to the local potential by the Poisson equation: r2 c ¼
rE «
(26:3)
where « is the permittivity. This results in the Poisson–Boltzmann equation: 2zen0 zec r c¼ sin h kB T « 2
(26:4)
The thickness of the diffuse layer therefore depends on the bulk concentration and the electrical properties of the liquid. The thickness of the EDL is described by the Debye length, given as [16]: rffiffiffiffiffiffiffiffiffiffiffiffiffiffi «RT lD ¼ 2F 2 CB
(26:5)
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with CB the ion concentration in the bulk (mol m3 ) and R the universal gas constant (J mol1 K1 ). In most common cases, the EDL thickness is only a few nanometers. In such a case, the EOF can be described by a slip flow boundary condition at the wall for the standard flow equations [16]. 26.2.3.2
Mass Transfer
Mass transfer is governed by the following convection–diffusion–reaction equation: @Ci þ r ( Di rCi zi mep Ci rc þ Ci u) ¼ Ri @t
(26:6)
where Ci (mol m3 ) is the component concentration in the bulk fluid and Di (m2 s1 ) the diffusivity, Ri (mol m3 s1 ) denotes the reaction term that is discussed in the next section. The velocity vector u is equal to the velocity of the solvent. This can be the result of either or both electroosmosis and pressure-driven flow. The equation also includes a term for electrophoretic transport. Applying electrical fields to ionic solutions induces migration transport in addition to the existing diffusion and convection processes. Migration implies that positive ions migrate from a positive potential to a negative potential along the direction of the electric field and vice versa for negatively charged ions. mep (m2 V1 s1 ) is the ionic mobility or electrophoretic mobility. 26.2.3.3
Reaction Kinetics
We restrict ourselves to enzyme kinetics in this chapter. Recently, interest has also grown in hybridization kinetics, which is useful for antibody–antigen interactions. The interested reader is referred to Refs. [17–20]. In an enzymatic reaction the substrate (S) is converted into a product (P) with the help of the enzyme (E): E
S ! P
(26:7)
The rate of reaction RP can be expressed in terms of either the change of substrate concentration CS or the product concentration CP : RP ¼
dCS dCP ¼ dt dt
(26:8)
It is important to know how the reaction rate is influenced by reaction conditions such as substrate, product, and enzyme concentration. Figure 26.4 shows a typical curve in which the enzymatic conversion rate is depicted as a function of substrate concentration, given a fixed enzyme concentration. It can be observed that the reaction rate is proportional to the substrate concentration (first-order reaction) at low values of substrate concentration, and does not depend on the substrate concentration (zero-order reaction) at high values of substrate concentration which means the reaction goes gradually from first-order to zeroorder as the concentration of the substrate is increased (Figure 26.4). This behavior can be described by V ¼ RP ¼
Vmax CS KM þ CS
(26:9)
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Vmax
V 0.5 Vmax
KM
CS
FIGURE 26.4 Reaction rate of an enzymatic reaction as a function of substrate concentration.
with Vmax (mol m3 s1 ) and KM (mol m3 ) the maximum reaction rate and the Michae¨lis– Menten constant, respectively, which need to be experimentally determined. The maximum reaction rate Vmax is proportional to the enzyme concentration. This equation describes many experimental results well. Leonor Michae¨lis and Maud Menten proposed a quantitative theory to support the observed enzyme kinetics and which is still widely used today under the name Michae¨lis–Menten kinetics [21]. For an in-depth discussion of enzyme kinetics and other possible enzyme kinetic models, the reader is referred to Refs. [21,22].
26.3 A MICROCALORIMETRIC BIOSENSOR FOR ASCORBIC ACID QUANTIFICATION The importance of AA (vitamin C) for the human health is well known, such as its role in biosynthesis of collagen and in the metabolism of amino acids. Fruits and vegetables are the main sources of AA in the human diet. The amount of the vitamin in these products is an important objective parameter for nutritional quality evaluation of the fruits. The development of fast, accurate, and cheap detection methods is requirement for routine large-scale analyses. In the literature, a wide range of analysis methods have been described, such as chromatography, spectrophotometry, and electrochemical methods [23]. Other methods (fluorimetry, titration, UV) are also used [24]. Microcalorimetry has been presented as a method for AA quantification [23,25]. The method uses the measurement of the enzymatic reaction heat of AA with ascorbate oxidase as a detection mechanism and has large potential for high-throughput analyses. The speed of the reaction and the specific sensitivity of the sensor to AA oxidation still require attention. The role of oxygen has not received attention to date. In this section we present a model-based approach to analyze a high-throughput microcalorimetric technique for detection of AA.
26.3.1 MICROPLATE DIFFERENTIAL MICROCALORIMETRY Microcalorimetry has proven in the past to be a successful technique for the enzymecatalyzed measurement of a whole range of analytes but this is the first application of a
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(a)
Temperature compensated Sample well: 10 µL ascorbate oxidase (0.5 U)
Reference well: 10 µL buffer
Simultaneous injection 1 µL sample .
.
(b)
Measure ∆T
FIGURE 26.5 Microplate differential calorimetry by MiDiCaly (Vivactis NV, Belgium).
high-throughput microcalorimetric device using a novel membrane wafer sensor mechanism. The transduction mechanism of the presented method is based on the microplate differential calorimetry (MiDiCaly) technology developed by Vivactis [26]. The microplate contains an array of 96 wells (volume 20 mL), which allow simultaneous AA quantification of 48 samples. The transduction principle is based on the measurement of the difference in heat generation between two microfluidic wells, located at the cold and the hot junctions of a thermopile (Figure 26.5). Initially one well is filled with an enzyme–buffer mixture whereas the other is filled with only buffer. Afterwards the sample (max 4 mL) is injected in both wells with a nanodispenser. The exothermic reaction of AA with ascorbate oxidase AAO (E.C 1.10.3.3) is monitored and the AA-content is estimated by integrating the area under the signal curve. A high correlation (R2 > 0:99) was found between this parameter and the AA concentration in the sample. A linearity of calibration curve was observed between 0.5 and 100 mM with a limit of detection of 0.5 mM corresponding to a total amount of 0.5 nmol AA in the sample.
26.3.2 MODEL A model was solved for the different species involved in the reaction, namely AA and oxygen. The enzymatic reaction was modeled by a modified Michae¨lis–Menten model that included
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Air with 20% oxygen
Liquid drop (max. 20 µL) with 20% oxygen and ascorbate oxidase, ascorbic acid is added Wall of the well Membrane stack with thermopile
FIGURE 26.6 Model of a microcalorimeter well.
the effect of oxygen on the reaction rate by means of the following reaction mediated by ascorbate oxidase AAO [27]: AAO
2AA þ O2 ! 2H2 O þ 2DAA
(26:10)
The equation system is solved for mass transport of the species and heat transfer in a single well of the microplate. The geometry of the system (in 2D axisymmetric formulation) is given in Figure 26.6. The reaction takes place in a microliter drop between the walls of the well. A thermopile in the floor of the well measures the heat generation. The drop is saturated with oxygen in equilibrium with the surrounding air. When the reaction starts, oxygen is consumed and the deficit is supplied by means of diffusion from the surrounding air. Both oxygen and AA move through the drop from regions of high concentration to regions of low concentration. The generated heat diffuses through the drop and the well, and is finally removed by the surrounding air. The model is solved using the finite element method, employing FEMLAB 3.1 (Comsol, Sweden). The mesh consists of 1783 triangular elements and is visible in Figure 26.1. Backward differentiation formulas of fifth order are used for a stable solution of the resulting differential equation system. The transient solution (2000 s) is obtained in less than a minute CPU time on an AMD Athlon 2.41 GHz Windows XP workstation with 2 GB RAM.
26.3.3 OXYGEN LIMITED PERFORMANCE
OF THE
BIOSENSOR
Figure 26.7 shows the simulated profiles of oxygen and AA in the well of the biosensor for a concentration of 500 mM AA and 0.5 U AAO. The available oxygen in the well is consumed very fast and its concentration remains zero in the lower part of the well for most of the process time, while higher values are maintained toward the surface of the drop. During the first period, the oxygen concentration profile remains the same, balancing supply from the air and consumption by the enzyme reaction. At the same time, AA is steadily transformed at the surface of the well without pronounced gradients in the well. Note that no
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0.3 O2 (mM)
0.25 0.2 Time
0.15 2000 s
0.1
1600 s
0.05
50−1400 s
0 0
0.2 0.4 0.6 Height on axis of well (mm)
AA (mM)
(a) 45 40 35 30 25 20 15 10 5 0
0.8
0s 100 s 400 s
600 s Time 1600 s 2000 s 0
0.2 0.4 0.6 Height on axis of well (mm)
(b)
0.8
FIGURE 26.7 Concentration on the height axis of the well during enzyme mediated oxidation of ascorbic acid (1 mL 500 mM AA in a 12:5 mL well): (a) model simulations of oxygen and (b) ascorbic acid.
Signal response
transformation takes place at the bottom of the well because oxygen is not available. The transformation of AA is thus balanced by its diffusion. In the second period, when AA has decreased considerably, the demand for oxygen by the reaction decreases. Oxygen then diffuses further into the well where reaction can now take place locally. Figure 26.8 demonstrates the large effect of oxygen on the reaction. The simulated biosensor response is shown for a reaction that is limited or not by oxygen. In the latter
(a)
(b)
0
500
1000 Time (s)
1500
2000
FIGURE 26.8 Simulated biosensor response as affected by oxygen diffusion (1 mL 500 mM AA in a 12:5 mL well): (a) no oxygen limitation and (b) oxygen limitation.
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0
500
1000 Time (s)
1500
2000
FIGURE 26.9 Model (thin lines) versus experimental (thick lines) microplate calorimeter biosensor response (1 mL 500 mM AA in a 12:5 mL well).
case, it is assumed that the well is continuously saturated with oxygen. Clearly, the reality of oxygen consumption leads to a reaction time that is four times longer. The sensor signal shape is also different. In the presence of oxygen depletion, the response exposes a shoulder or plateau that indicates a limiting effect of oxygen is manifested. The oxygen is indeed a reaction-limiting factor, demonstrated by the validation of the model response, as given in Figure 26.9.
26.4 AN ELECTROKINETIC BIOCHIP FOR TASTE ANALYSIS Driven by the increased awareness for food functionality, quality, and safety, new technologies are required for fast and cheap analysis of food components. Traditional taste analysis techniques like liquid and gas chromatography and sensory panel analysis are expensive and require laborious sample preparation and well-trained operators. On top of that it is often difficult to implement them in high-throughput context to monitor food quality and safety. Furthermore, multicomponent multi-analysis platforms are required to reduce analysis time and improve user-friendliness. The objective of this work was to combine the advanced technologies of microtiter plate enzymatic biosensor assays and microfluidics to develop a lab-on-a-chip device that fulfills the above requirements for analysis of taste components (sugars and acids) of fruit juices.
26.4.1 MINIATURIZATION
OF
ENZYMATIC KITS
Enzymatic kits offer a means to determine the concentration of the taste-active compounds. However, the use of such enzymatic assays can be very costly. A high-throughput enzymatic taste biosensor (ETB) was designed by the miniaturization of existing commercial kits for glucose, fructose, sucrose, sorbitol=xylitol, citric acid, malic acid, succinic acid, oxalic acid, AA, and glutamic acid (R-Biopharm, Germany) in the wells of microtiter plates (96, 384 wells) with the use of an automated liquid handling system. This miniaturization not only reduced the cost of analysis up to 93%–97% (in comparison to analysis in 3 mL cuvettes) but also increased the number of samples which can be analyzed per day without loss of sensitivity and specificity. The linear regression correlation coefficient of the miniaturized
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ETB-analysis (g L−1)
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
0.2
0.4
0.6
0.8
1
HPLC-analysis (g L−1)
(a) 1.2
ETB-analysis (g L−1)
1 0.8 0.6 0.4 0.2 0 0
0.2
(b)
0.4
0.6
0.8
1
1.2
HPLC-analysis (g L−1)
FIGURE 26.10 Validation of the miniaturized enzymatic taste biosensor for (a) glucose in three tomato cultivars and (b) L-malic acid in three apple cultivars.
analysis was higher than 0.99; high-performance liquid chromatography (HPLC) validation showed slope-values around 1 and intercepts close to 0 (Figure 26.10).
26.4.2 LAB-ON-A-CHIP DESIGN Microfluidics allows integrating sample injection, mixing, reaction, and detection of the above analysis on a single device, restricting human intervention. A miniaturized flow system is designed to simulate transport and mixing of the sample and enzymatic kit reagents for different food components and predict the biosensor response. For design and optimization of the system, a model was developed for the microfluidic flow including electroosmotic transport (the Poisson–Boltzmann equation coupled to the Navier–Stokes equations), enzyme kinetics (Michae¨lis–Menten), and mass transfer of the different species involved in the analysis. As an example, here the detection of D-glucose is presented. It involves two enzyme-mediated reaction steps by means of hexakinase, and subsequently, glucose-6phosphate dehydrogenase. The analysis requires ATP and NADPþ in the buffer solution. The transport and depletion or production of a total of seven species therefore needed to be
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Buffer
Injection Channel
Enzymes
Glucose solution
Mixing channel: 150 ⫻ 50 µm Length 14 mm
Spectrophotometric detection
FIGURE 26.11 Lab-on-a-chip for taste analysis.
described. The model was solved by means of the finite element method in the code Comsol Multiphysics 3.2 (Comsol BV, Stockholm, Sweden). The system used a total of 180,724 degrees of freedom and a mesh size of 7922 elements and is solved on a desktop PC. The design of the taste chip is shown in Figure 26.11. Different wells filled with the required reactants were charged with an electrical potential (typically in the kV range). Due to electroosmosis as a consequence of potential gradients, the fluids will move in a plug flow through the microscopic channels at a velocity of a few mm s1 . At the intersection, the three plug streams start to mix and fast reaction takes place. The velocity profile of the EOF in the microchannels is shown in Figure 26.12. It is demonstrated that, compared to pressure-driven laminar flow, EOF results in very flat velocity profiles that result in a plug flow behavior. Consequently, one of the advantages of EOF is its suitability for sample injection. Injection of the sample into the biosensor is one of the key elements in the sample handling process and its characteristics determine the quality of the chemical analysis. Design as well as fabrication of a pressure-driven injection system for limited sample volumes is difficult because of the integration of a valve system into the microfluidic biosensor device. Electrokinetics offers a means for implementing valveless switching—a technique used for introducing precisely metered samples in a microfluidic channel. Design and optimization of the injection process includes a study of the geometry of the channel intersection, the selection of the appropriate voltages as well as a precise timing for switching the electric field [12]. A numerical analysis (Figure 26.13) shows that it is possible to control the volume of loaded sample by adjusting the focusing potential (potential at the reservoirs of the injection channel) during the loading stage: the larger the value of the potential, the smaller the sample volume at the intersection (Figure 26.13).
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(a) ⫻10−4
Electrokinetic flow
Velocity (m s−1)
3 Pressure-driven flow
2
1
0 0 (b)
0.5
1
1.5
2
2.5
3
3.5
Cross channel distance (m)
4
4.5
5
⫻10−5
FIGURE 26.12 Fluid flow in a microchannel of a biochip: (a) typical mesh resolution and (b) computed velocity profile in the microchannel, comparison of pressure-driven and electroosmotic flow.
However, increasing the focusing potential beyond a certain limit (larger than 8.5 V in the case considered, not shown) no sample will reach the cross junction, which will be completely filled with buffer. In this example, the injection phase potential settings are suboptimal to avoid leakage. To reduce the degree of leakage, the electric potential at the vertical ports can be manipulated during the injection stage. By creating a gradient from the cross section to the sample reservoirs at the loading channel it is possible to pinch the sample back toward the reservoirs instead of following the sample in the injection channel. This is achieved by applying a smaller potential or grounding at those ports. In the simulation of the chip design of Figure 26.11, enzymes and glucose were injected with 0.5 s delay for a period of 5 s each. The simulated profiles in the channels are given in Figure 26.14. The resulting transient plots of the concentration of glucose and the product
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6V
10 V
Flow 8.5 V
8.5 V
12 V
0V
Flow
6V
0V
(b)
(a)
10 mM
0
FIGURE 26.13 Simulation of a sample injection process in a microchannel by means of electroosmosis: (a) loading of the sample in the vertical channel with focussing at the channel cross junction and (b) injection of the sample into the horizontal microchannel. The applied voltages are given to control the electrokinetic transport.
nicotinamide adenine dinucleotide phosphate (NADPH) are given in Figure 26.15 for different locations in the mixing channel. Glucose dilutes thrice when flowing from the loading channel into the mixing channel; then the glucose is completely consumed within a period of 10–15 s over a distance of only 14 mm. The remaining peak of 1 mM is due to the fact that enzyme and glucose were injected 0.5 s out of phase. The remaining 0.5 s plug of glucose was therefore not in contact with the enzymes and could not be directly converted, only after slow diffusion into the enzyme plug. The resulting plug of NADPH amounts to the same concentration of the glucose at the start of the mixing channel. Spectrophotometric detection of NADPH will give a linear and fast response of the lab-on-a-chip, suitable for cheap high-throughput analysis of taste components.
0 5.5 mM
0 0.03 mM
0 0.05 mM
0.1 mM
(a)
(b)
(c)
FIGURE 26.14 Simulation of a lab-on-a-chip for measurement of glucose: (a) glucose concentration, (b) hexakinase concentration, and (c) NADPH concentration 2 s after injection of the reactants.
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6 Injection channel Mixing channel 1 mm Mixing channel 10 mm Mixing channel 14 mm
Glucose (mM)
5 4 3 2 1 0 5
0 (a)
10
15
Time (s)
1.8 Mixing channel 1 mm
1.6
Mixing channel 10 mm Mixing channel 14 mm
NADPH (mM)
1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 (b)
10
5
15
Time (s)
FIGURE 26.15 Enzymatic assay of glucose in the lab-on-a-chip. Time plots of (a) glucose depletion and (b) NADPH production in the microfluidic system.
26.5 CONCLUSIONS Biosensors show great potential in food industries as online detection methods. Clear advantages over conventional methods are the high-sampling rates and speed of the process. The effective development and application of biosensors for food quality control depends on the elimination of some of the shortcoming such as short-term stability, low-measurable ranges of analytes, shelf life of the biosensor, and sensitivity to process conditions such as temperature and pH. The role of CFD analysis is important as it reduces the cost for constructing many suboptimal prototypes and provides a tool to determine relevant design parameters to assist the prototyping stage. Different examples in this chapter have demonstrated the importance of transport phenomena, including fluid flow and mass transfer, in the design process.
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NOMENCLATURE Ci Di E E e F KM kB n0 P p Ri S T u V Vmax z « h lD r mep rE s c
concentration of species i (mol m3 ) diffusivity (m2 s1 ) electric field (V m1 ) enzyme charge of a proton (C) Faraday’s constant (C mol1 ) Michae¨lis–Menten constant (mol m3 ) Boltzmann constant (J K1 ) bulk concentration of ion species (mol m3 ) product pressure (Pa) 1 reaction rate (mol m3 s ) substrate temperature (8C) velocity vector (m s2 ) reaction rate (mol m3 s1 ) maximum reaction rate (mol m3 s1 ) ion valence number permittivity (F m1 ) air dynamic viscosity (kg m1 s1 ) characteristic EDL thickness (m) density (kg m3 ) ionic mobility (m2 V1 s1 ) net charge density (C m3 ) constant electrical potential (V)
REFERENCES 1. J. Lammertyn, P. Verboven, E.A. Veraverbeke, S. Vermeir, J. Irudayaraj, and B.M. Nicolaı¨. Analysis of fluid flow and reaction kinetics in a flow injection analysis biosensor. Sensors and Actuators B 114: 728–736, 2006. 2. D.R. The`venot, K.Toth, R.A. Durst, and G.S. Wilson. Electrochemical biosensors: Recommended definitions and classification. Biosensors and Bioelectronics 16: 121–131, 2001. 3. M.I. Prodromidis and M.I. Karayannis. Enzyme based amperometric biosensors for food analysis. Electroanalysis 14(4): 241–261, 2002. 4. S.K. Sharma, R. Singhal, B.D. Malhotra, N. Sehgal, and A. Kumar. Lactose biosensor based on Langmuir–Blodgett films of poly(3-hexyl thiophene). Biosensors and Bioelectronics 20(3): 651–657, 2004. 5. U. Bilitewski and I. Rohm. Biosensors for process monitoring. In E. Kress-Rogers (Ed.). Handbook of Biosensors and Electronic Noses: Medicine, Food and the Environment. Boca Raton: FL: CRC Press, Inc, pp. 435–468, 1997. 6. L.D. Mello and L.T. Kubota. Review of the use of biosensors as analytical tools in the food and drink industries. Food Chemistry 77(2): 237–256, 2002. 7. V. Rajendran and J. Irudayaraj. Detection of glucose, galactose, and lactose in milk with a microdialysis-coupled flow injection amperiometric sensor. Journal of Dairy Science 85: 1357–1361, 2002. 8. D.G. Buerk. Biosensors: Theory and Applications. Lancaseter, PA: Technomic Publishing Company, Inc, 1993.
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9. D. Erickson and D. Li. Integrated microfluidic devices. Analytica Chimica Acta 507: 11–26, 2004. 10. B.H. Weigl, R.L. Bardell, and R.C. Catherine. Lab-on-a-chip for drug development. Advanced Drug Delivery Reviews 55: 349–377, 2003. 11. D. Li. Electrokinetics in Microfluidics. Interface Science and Technology, Vol. 2. Amsterdam: Elsevier Academic Press, pp. 7–29, 2004. 12. M. Koch, A. Evans, and A. Brunnschweiler. Microfluidic Technology and Applications. Baldock, Hertfordshire, England: Research Studies Press, 2000. 13. G. Karniadakis, A. Beskok, and N. Aluru. Microflows and nanoflows: Fundamentals and simulation. In S.S. Antman, J.E. Marsden, and L. Sirovich (Eds.). Interdisplinary Applied Mathematics, Vol. 29. Springer, 2005. 14. T.M. Squires and S.R. Quake. Microfluidics: Fluid physics at the nanoliter scale. Reviews of Modern Physics 77: 977–1026, 2005. 15. N.A. Polson and M.A. Hayes. Microfluidics controlling fluids in small places. Analytical Chemistry 73(11): 312A–319A, 2001. 16. K.V. Sharp, R.J. Adrian, J.G. Santiago, and J.I. Molho. Liquid flows in microchannels. In M. Gad-el-Hak (Ed.). The MEMS Handbook, Boca Raton: FL: CRC Press, 2002. 17. J.H. Kim, A. Marafie, X. Jia, J.V. Zoval, and M.J. Madou. Characterization of DNA hybridization kinetics in a microfluidic flow channel. Sensors and Actuators B: Chemical 113(1): 281–289, 2006. 18. D. Erickson, D. Li, and U.J. Krull. Modeling of DNA hybridization kinetics for spatially resolved biochips. Analytical Biochemistry 317: 186–200, 2003. 19. K.Lebedev, M. Salvador, and P. Stroeve. Convection, diffusion and reaction in a surface-based biosensor: Modeling of cooperativity and binding site competition on the surface and in the hydrogel. Journal of Colloid and Interface Science 296: 527–537, 2006. 20. R.W. Glaser. Antigen–antibody binding and mass transport by convection and diffusion to the surface: A two dimensional computer model of binding and dissociation kinetics. Analytical Biochemistry 213: 152–161, 1993. 21. A. Moser. Rate equations for enzyme kinetics. In H. Brauer (Ed.). Biotechnology Volume 2: Fundamentals of Biochemical Engineering. Weinheim: VCH Verlagsgesellschaft, pp. 199–226, 1985. 22. A.G. Marangoni. Enzyme Kinetics: A Modern Approach. Hoboken, NJ: John Wiley & Sons, pp. 41–60 and pp. 174–192, 2003. 23. M.L. Antonelli, G. D’Ascenzo, A. Lagana`, and P. Pusceddu. Food analyses: A new calorimetric method for ascorbic acid (vitamin C) determination. Talanta 58: 961–967, 2002. 24. W. Zeng, F. Martinuzzi, and A. MacGregor. Development and application of a novel UV method for the analysis of ascorbic acid. Journal of Pharmaceutical and Biomedical Analysis 36: 1107–1111, 2005. 25. R.J. Wilson, A.E. Breezer, and J.C. Mitchell. A kinetic study of the oxidation of L-ascorbic acid (vitamin C) in solution using an isothermal microcalorimeter. Thermochimica Acta 264: 27–40, 1995. 26. MiDiCaly. Microplate Differential High Throughput Calorimeter. Leuven: Belgium, http:==www. vivactis.be, 2005. 27. BRENDA. The Comprehensive Enzyme Information System. Cologne, Germany, http:==www.brenda. uni-koeln.de=, 2005.
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Modeling Airflow through Vented Packages Containing Horticultural Products Maria J. Ferrua and R. Paul Singh
CONTENTS 27.1 27.2
27.3
27.4
Introduction ............................................................................................................. 650 Transport Phenomena in Porous Medium............................................................... 652 27.2.1 Definition and Characteristics .................................................................... 652 27.2.2 Volume-Averaging Technique..................................................................... 652 27.2.3 Fundamental Theory of Laminar Fluid Flow through Porous Media ....... 653 27.2.3.1 Continuity Equation ................................................................... 653 27.2.3.2 Momentum Equation.................................................................. 653 27.2.4 Fundamental Theory of Turbulent Fluid Flow through Porous Media.............................................................................................. 657 27.2.4.1 Transition to Turbulence ............................................................ 657 27.2.4.2 Main Features of Turbulence in Porous Media.......................... 657 27.2.4.3 Theoretical Modeling of Macroscopic Turbulence in a Porous Media....................................................................... 658 27.2.5 Heat Transfer in Porous Media .................................................................. 659 27.2.5.1 Volume-Averaged Models........................................................... 659 Modeling of the Forced-Air Cooling Process Using the Porous Media Approach ...................................................................................................... 661 27.3.1 Review of Numerical Models...................................................................... 661 27.3.2 Limitations of the Porous Media Approach ............................................... 666 Use of CFD as a Design Tool for Individual Horticultural Packages— A Case of Study ....................................................................................................... 667 27.4.1 Use of PIV to Study the Airflow in Packed Structures .............................. 667 27.4.1.1 Transparent Model for PIV Applications ................................... 668 27.4.1.2 Fabrication of a Transparent Fixed Bed of Packaged Products ...................................................................... 668 27.4.1.3 Results......................................................................................... 669 27.4.2 Numerical Modeling of the Experimental Flow Field ................................ 671 27.4.2.1 Computational Model................................................................. 672 27.4.2.2 Numerical Solution ..................................................................... 675 27.4.2.3 CFD Results ............................................................................... 676 27.4.2.4 Validation ................................................................................... 679
649
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27.4.3
Use of Flow Field Model to Predict Heat Transfer Process in Packed Objects........................................................................................ 682 27.4.3.1 Numerical Solution ..................................................................... 684 27.4.3.2 Results......................................................................................... 685 27.5 Conclusions .............................................................................................................. 688 Nomenclature ..................................................................................................................... 691 References .......................................................................................................................... 692
27.1 INTRODUCTION Reducing postharvest losses of fresh horticultural commodities is a topic of major importance around the world. No doubt, numerous researchers are actively engaged in seeking methods to improve postharvest practices. Research conducted during the last several decades in this area has relied on experimental studies and mathematical modeling. Due to the often encountered complexity in mathematical analysis to study such systems, advanced computational procedures are often necessary. With the recent advances in computational resources, there has been considerable interest in developing predictive capabilities for design and analysis of innovative systems. Computational fluid dynamics (CFD) codes are increasingly being used for solving complex engineering problems involving fluid flow and heat transfer. In this chapter, recent research conducted on the topic of forced-air cooling of horticultural commodities is presented. A number of researchers have used the porous media approach to solve this problem. A review of salient concepts of the porous media approach is first presented to obtain an understanding of its relevance to the postharvest-related problems and its key limitations. Major research studies undertaken using porous media approach and CFD modeling are then reviewed. To provide a more comprehensive appreciation of the use of CFD modeling, a detailed case study involving prediction and validation of the flow field and heat transfer in a model representing a package containing berry fruit is presented. To maintain the quality and enhance the shelf life of fresh produce after harvest, suitable postharvest techniques are required. Among these techniques, temperature management is the most important factor in controlling the deterioration rate of fresh horticultural products [1,2]. A proper and rapid postharvest cooling to 08C–38C, along with proper temperature maintenance throughout the marketing distribution, greatly improves the quality and postharvest life of fresh produce by slowing down vital processes (such as respiration), suppressing or stopping the microbial growth, and minimizing the moisture evaporation [3]. Among commercial methods available for precooling (such as hydrocooling and vacuum cooling), the forced-air cooling is the most common and most recommended one, especially in the case of horticultural commodities that are highly perishable or susceptible to waterborne decay organisms [4,5]. Although the forced-air cooling method is commonly used by the industry, an important loss of product quality still occurs due to nonuniform cooling. Temperature differences of as much as 108C in the same pallet load and variations in the product water loss of up to 50% between the coldest and warmest points have been reported by different research groups [6]. Alvarez and Flick [7,8] demonstrated that heterogeneity of the forced-air process is not only generated by an increase in the air temperature as it flows through the produce pallet, but also by the heterogeneity of the airflow behavior within the palletized structure. Under this scenario, it is clear that there is a significant impact of the produce containers and their vent design on the efficiency and homogeneity of the forced-air cooling process.
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Over the years different types of containers and packing structures have been used to store and market horticultural produce. Traditionally, products such as potatoes or oranges have been packed in bulk using wooden boxes or corrugated cartons, while delicate and highly perishable fruits (such as berries) have been packed in individual containers and placed in open-top master trays. During the last decade, new polymeric individual packages have streamlined the distribution and marketing of many horticultural products (strawberries, grapes, cherries, pears, and blueberries). The design of these novel containers is largely based on the criterion of mechanical strength (with minimal consideration of the effect of their venting pattern on the efficiency of the cooling process). Unfortunately, many of the horticultural packages currently used by the industry remain inefficient in promoting rapid and uniform cooling of the packaged products. Several experimental studies are reported in the literature to elucidate the effect of different vent design on the efficiency of the forced-air cooling process [2,9–11]. However, these experimental studies are expensive and involve much time and labor. An alternative approach, pursued by several research groups, has involved the development of mathematical models capable of predicting the airflow field and the heat transfer process within horticultural packages under different conditions and design patterns. The complex and chaotic structure within horticultural produce packages complicates the numerical study of the thermal behavior of each individual product within a pallet load of packages during the forced-air cooling process. The main obstacle that has limited this analysis is the determination of the airflow behavior around particles; information that is required to determine the values of the local heat transfer coefficients. Even in the case of uniformly distributed products in a package, the measure of the fluid flow within individual products, by means of traditional methods, is impossible without disturbing the packaging arrangement itself. In 1988, Talbot [4] introduced the idea of using a porous media approach to numerically predict the pressure and velocity field within a three-dimensional package, and used this information along with a suitable heat transfer model to predict the cooling response of individual products in packages with different vent designs. This alternative approach was based on the feasibility of assuming a heterogeneous system of product and air as a continuous domain. This assumption has been extensively used since 1970 in order to elucidate the relationship between the pressure drop and the rate of airflow forced through a bulk of horticultural products [12–17]. Since then, numerous studies have focused on numerically simulating the flow field and heat transfer process to improve the design and efficiency of the forced-air cooling process [18–26]. In the preceding studies the airflow behavior was modeled using the porous media approach. To model heat transfer two different approaches have been considered. In one of them, the heat transfer process was modeled assuming a porous media approach, the packaged structure was assumed as a unique continuous domain whose thermal behavior depends on a series of effective parameters that are either experimentally or numerically determined. In the other one, the heterogeneous physical domain was divided into a large number of subzones where local energy balances were applied for product and air zones, respectively, by considering as many physical interactions between them as possible. Due to the significant role that the porous media approach has played during the last 30 years in mathematical modeling of the forced-air cooling process of horticultural produce, a general knowledge of the transport phenomena through this type of media is essential to fully understand the accomplishments and limitations of the work done in this area. In the following, a summary of the main concepts involved in the transport of momentum and energy is presented.
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27.2 TRANSPORT PHENOMENA IN POROUS MEDIUM 27.2.1 DEFINITION AND CHARACTERISTICS A porous medium domain is a heterogeneous system composed of an irregular solid matrix with interconnected pores through which a flow field, of at least one type of fluid, is developed. Under the scope of this chapter a porous medium that consists only of two distinct regions will be considered: a rigid, impermeable solid phase (denoted by the subscript s) and a Newtonian fluid (denoted by the subscript f ). In general, the transport of any extensive quantity through a porous medium (momentum, mass, and energy) occurs not only within each phase in the medium but also across the microscopic interface boundary that separates them. Hence in order to model the transport of any quantity within a porous medium, the spatial and temporal distribution of the corresponding state variable (e.g., velocity, pressure, and temperature) must be determined within the complete heterogeneous medium. In principle, the equations that describe the various transport phenomena are known and can be written at the pore scale (microscopic or local level ), where only a unique phase of the porous medium is considered. However, even when the conditions that prevail on the surface that bounds each particular phase at this level may be known, the complexity of the surface geometry that bounds this microscopic domain prevents a general solution of the transport equation. As a consequence, the description and solution of a transport problem at the microscopic level is impractical and perhaps also impossible. In order to model the transport phenomena within a porous media, it is necessary to introduce a new level of description (macroscopic level ), at which measurable, continuous, and differentiable quantities can be determined and boundary value problems can be stated. The macroscopic transport equations are obtained by averaging the standard equations, obeyed at the microscopic level, over a representative elementary volume (REV). This REV must be large enough to smooth out microscopic variations of the quantity and small enough to accurately represent a sufficiently close neighborhood around the point of sampling. In other words, the length scale of the REV (l ) must be much larger than the pore length scale (d ), over which significant variations in the point velocity take place, but considerably smaller than the length scale of the macroscopic flow domain (L), over which significant variations in the volume-averaged velocity take place. All theoretical analysis of the transport phenomena through porous media are based on the possibility of treating the heterogeneous structure as a continuous domain, which requires an overall system dimension (L) much larger than the product or pore dimension (d ). However, there is no clear statement in literature about the relationship that these length scales have to verify. Kaviany [27] indicated that in order to validate the applicability of a single continuum treatment of the heterogeneous porous medium, L should be at least four orders of magnitude larger than d. The generally accepted application of this approach is for L=d > 10, a value that validates the empirical model developed by Ergun [28].
27.2.2 VOLUME-AVERAGING TECHNIQUE To theoretically develop the volume-average form of the transport equations every point in the space domain is associated with an REV and the average quantity value of any variable at each point is defined in terms of that volume. In order to present the basis of the volumeaveraging technique, independent of the type of region within the system, the two distinct regions within the porous media will be referred as the a-phase and the b-phase.
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The volume of the REV, V, can be represented in terms of the volume of the individual phases (Va , Vb ) according to V ¼ Va (x) þ Vb (x)
(27:1)
Based on this REV, two volume-averaged techniques, commonly used in the theoretical description of multiphase transport process, are defined: the superficial average and the intrinsic average. The superficial average of a given function within phase b, cb , is defined according to
ð 1 c dV cb ¼ V Vb b x
(27:2)
The superficial average hcb i is defined at the point location x, the centroid of the REV. The intrinsic average of a given function within phase b, cb , is defined by ð b 1 c dV cb ¼ Vb Vb b x
(27:3)
These two averages are related by the volume fraction of the b-phase according to
b cb ¼ « b cb
(27:4)
where «b is explicitly defined as «b ¼
Vb V
(27:5)
Note that if b refers to the phase that occupies the void space, then «b ¼ « is the porosity of the porous media. When forming the volume average of any transport equation, the average of a gradient or the average of a divergence appear. In order to transform this into the gradient or divergence of an average quantity, the spatial-averaging theorems are used [29].
27.2.3 FUNDAMENTAL THEORY OF LAMINAR FLUID FLOW
THROUGH
POROUS MEDIA
In this section a brief review of the theory of a laminar and incompressible Newtonian fluid flow through a rigid and impermeable solid phase in a porous media is presented. 27.2.3.1
Continuity Equation
The volume-averaged form of the continuity equation for an incompressible fluid has the following expression: r hui ¼ 0 27.2.3.2
(27:6)
Momentum Equation
The development of a mathematical model capable of predicting the transport of momentum through a porous media structure was originally proposed in 1856 when Henry Philibert
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Gaspard Darcy presented an empirical law that revealed the proportionality between the flow rate and the applied pressure difference for a steady and unidirectional flow. Since then, the development of the momentum balance has been a combination of direct empirical relationships and more rigorous theoretical developments aided to support them. In the following sections a historic review of the most relevant advances, which lead to the most recent flow field models through porous media is presented. 27.2.3.2.1
Darcy Equation (Microscopic Viscous Stress Effect)
Based on observations and experiments for a steady, unidirectional, and incompressible creeping flow of a Newtonian fluid through a relative long and isotropic porous medium, Darcy [30] in 1856 proposed a direct relationship between the flow rate and the applied pressure difference: uD ¼
K Dp m Dx
(27:7)
where uD is the Darcy or filtration velocity (flow rate per unit of column cross-sectional area), m is the dynamic viscosity of the fluid, Dp=Dx is the pressure gradient in the flow direction, and K is the specific permeability of the medium. The specific permeability is a measure of the flow conductance of the matrix; it is independent of fluid properties but it depends on the geometry of the medium. For example, in the case of an isotropic porous media, the hydraulic radius theory of Carman–Kozeny leads to a relationship between K, the porosity of the porous media and the particle diameters, for a bed of particles approximately spherical in shape and whose diameters fall within a narrow range [31]. Whitaker [32] improved the empirical relation suggested by Darcy by providing a theoretical derivation of it for the case of a steady, incompressible, creep flow of a Newtonian fluid, by performing volume average of the local governing equations. This theoretical analysis confirmed the fact that Darcy equation represents the pressure drop due to the viscous shear resistance exerted on each small channel within the porous media. In the case of a three-dimensional flow through an anisotropic porous media, the Darcy’s proportionality is nowadays expressed by hui ¼
K r h pi m
(27:8)
where K is a second-order tensor that represents the specific permeability of the medium. In the particular case of an isotropic porous media the permeability tensor becomes a simple scalar. Until 1990, most of the studies carried out in porous media were based on the Darcy flow model, but it is presently known to be limited in several aspects. It neglects the friction due to macroscopic shear (it does not satisfy the nonslip condition on solid boundaries) and it disregards the inertial forces that become significant in the case of fast moving flows. 27.2.3.2.2
Forchheimer Equation (Microscopic Form Effect)
It is nowadays recognized that Darcy equation holds only for filtration velocity small enough to neglect fluid inertia effects, but it was not until 1901 that Forchheimer made a compilation of published experimental results indicating that a quadratic model fits the data more accurately than the linear one [33].
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The first equation of motion proposed to account for nonlinear effects had the following one-dimensional form:
Dp m ¼ uD þ bu2D Dx K
(27:9)
where b was assumed to be a model constant. Although it was recognized early that the quadratic term is caused by the microscopic inertial force imposed on the fluid by the solid matrix obstructing the flow path, much more work had to be done to obtain a suitable correlation for this model constant b. It was not until 1964 that Ward [34] proposed to replace the form-drag parameter b by cF =K 1=2 , where the dimensionless parameter cF was initially believed to be a universal constant (0.55). However, it was later found that it does vary with the nature and structure of the porous medium [35,36]. In general, the three-dimensional expression of Forchheimer equation, expressed in terms of the volume-averaged notation, becomes r h pi ¼
m cF r hui pffiffiffiffi huihui K K
(27:10)
Many experimental studies have been made to determine the upper range of validity of Darcy’s law. The departure from the linear flow regime has been traditionally expressed by means of either the particle diameter-based Reynolds number (Rep ) or the permeability-based Reynolds number (ReK ): rhuiDp m pffiffiffiffi rhui K ReK ¼ m Rep ¼
(27:11)
(27:12)
Several studies suggest that at the breakdown of the Darcy equation, Rep range between 1 and 15 [37–40] and ReK range between 1 and 10 [34]. The importance of the Forchheimer–Darcy flow model has been demonstrated by several authors [41–43], but it was not until 1987 that Hassanizadeh and Gray [44] developed a rational and systematic framework that illustrates the theoretical basis of the Forchheimer equation. 27.2.3.2.3
Brinkman Equation (Macroscopic Viscous Stress Effect)
By considering that the force on a single particle in a creep flow is described by Stokes equation and the flow through a porous mass is described by the Darcy empirical equation, in 1947 Brinkman [45] reasoned that for a medium with sufficiently large porosity, the effect of the porous mass could be represented by adding the Laplacian term of Stokes equation to the Darcy equation. With this modification Brinkman obtained a new relationship that overcame the limitation of Darcy equation regarding the verification of the nonslip condition in wall-bounded porous media: rhpi ¼ m ~ r2 hui
m hui K
where m is the fluid dynamic viscosity and m ~ is an effective viscosity.
(27:13)
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Although Brinkman set m ~ equal to m, in general they are only approximately equal [46]. One of the main applications of Brinkman equation is its capability to model the flow behavior within the thin boundary layer developed in the porous media due to the presence of either an adjacent clear fluid region or a solid wall boundary [47]. In particular, the capability of Brinkman equation to deal with the channeling effect that arises in wall-bounded porous media due to the porosity increases close to the wall has a particular relevance to the flow modeling within agricultural packed produce. At this point it is important to recall some of the main limitations of Brinkman equation. It is valid only for creeping flows (i.e., negligible solid form effects) through a porous medium with porosity close to unity [48], and it requires a good prediction of the effective viscosity [49]. 27.2.3.2.4
Brinkman–Forchheimer-extended Darcy Equation (Generalized Model)
Several authors have added a Laplacian term to the Forchheimer equation to form what is known as the Forchheimer–Brinkman-extended Darcy equation or simply the general equation: rhpi ¼ m ~ r2 hui
m cF r «hui pffiffiffiffi huijhuij K K
(27:14)
The Brinkman–Forchheimer-extended Darcy formulation is the most commonly used equation to model the convective flow in a porous medium. This formulation accounts for the boundary layer development, microscopic viscous stresses and the microscopic inertial force. Vafai and Tien [50] presented the first formal derivation of the general equation by applying a volume-averaging technique to the fundamental flow equation for an incompressible, steady, two-dimensional laminar flow through an isotropic, rigid, and homogeneous porous media. The volume-averaging technique leads to a closure problem, and in order to obtain closure the forces acting on an REV due to solid matrix flow resistance were modeled using the well-established Forchheimer empirical equation. It is important to notice that Equation 27.14 has six physical properties: fluid density (r), fluid dynamic viscosity (m), porosity («), effective viscosity (m ~ ), permeability (K ), and form coefficient cF . Unlike r, m, and «, the physical properties m ~ , K, and cF depend on the specific shape and distribution of the particles within the porous media and they cannot be measured directly. In principle, these quantities can be obtained by matching the numerical results from solving Equation 27.14 with experimental data, but there are some other alternatives that are noteworthy. Beavers et al. [51] provided an empirical relationship between cF and the equivalent diameter of the packed bed and solid particles. Additionally, when dealing with a unidirectional flow through a bed of near spherical products, the Ergun empirical equation (Equation 27.15) is applicable. dP bm(1 w)2 u ar(1 «)u2 ¼ dx D2p «3 D p «3
(27:15)
where Dp is the mean particle diameter and a and b are shape factors that must be determined empirically. In 1952, Ergun [28] found no evidence of variation of the shape factors with the medium porosity and set a ¼ 1:75 and b ¼ 150. However, in 1985, Chau et al. [17] found that neither a nor b are constants, b is a function of porosity, and a is a function of the tortuosity of the medium and the Reynolds number. By equating the linear and quadratic terms in this equation with the linear and quadratic terms in the Forcheimer equation (Equation 27.10), it is possible to obtain analytical expression of K and cF.
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K¼
«3 D2p
657
(27:16)
b(1 «)2
cF a(1 «) pffiffiffiffi ¼ 3 « Dp K
(27:17)
One of the main advantages of this analytical–empirical approach is that in the case of wallbounded mediums, Equation 27.16 and Equation 27.17 can be combined with the sinusoidal damping decay of porosity close to the wall [52] to obtain the functional relation of K and cF with the wall distance.
27.2.4 FUNDAMENTAL THEORY OF TURBULENT FLUID FLOW
THROUGH
POROUS MEDIA
The majority of the porous materials considered in traditional engineering applications present very small pores, small permeabilities, and relatively small fluid velocity; conditions that in general lead to laminar flow regimes. However, the appearance of turbulent regimes within porous media at high-speed flows was confirmed by several experimental studies [40,53,54]. Numerous modern engineering processes (such as the combustion process within a porous inert media, pollution dispersion within urban regions, and food processing) can benefit from a better understanding of turbulence and its effects on the transport phenomena in a porous media. Recently new approaches have been developed for an adequate turbulent model for the flow field in porous media. Some of the key studies in this regard are reviewed in the following sections. 27.2.4.1
Transition to Turbulence
Early descriptions of high-velocity flows have incorrectly attributed the deviation from Darcy’s law to be caused by turbulence. In 1972, Bear [55] stated that most experiments indicate that turbulence occurs at Reynolds values at least one order of magnitude higher than the Reynolds numbers at which deviations from Darcy’s law is observed. In 1984, by conducting a flow visualization study, Dybbs and Edward [40] found that the onset of turbulence occurs at Rep higher than 300, while the deviation of Darcy’s occurs at Rep of order 10. Actually, one of the pioneering papers on turbulent flow through porous media [56] was strongly questioned because their model is based on the assumption that the Forchheimer flow resistance is caused mainly by turbulent mixing [57,58]. 27.2.4.2
Main Features of Turbulence in Porous Media
There are two fundamental characteristics that distinguish turbulence in porous media from turbulence in a flow system clear of solid porous obstructions. In turbulent flow through porous media, the representative dimension of the largest eddy is limited by the pore dimension, commonly much smaller than the macroscopic dimension of the system. The second main characteristic of turbulence in porous media is the distinction between microscopic and macroscopic turbulence. The only experimental evidence of turbulence in three-dimensional porous medium is of microscopic turbulence (turbulence detected by local probes placed within the pores of the medium), and although there has been no attempt to volume average the local signals within an REV to obtain the flow pattern of the macroscopic one, it was earlier predicted that macroscopic turbulence through a porous media is unlikely
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to persist. This early statement was based on the idea that by averaging the large number of strongly nonuniform microscopic turbulence signals along the tortuous and irregular paths within an REV, the microscopic turbulence will be smoothed out. Moreover, it was also believed that the presence of small bodies very close to each other will interrupt the energy cascade process, since the vortices generated by an upstream body will be obstructed by the neighboring bodies. Based on this, in 1991 Nield [59] stated that ‘‘ . . . true turbulence, in which there is a cascade of energy from large eddies to smaller eddies, does not occur on a macroscopic scale in a dense porous medium . . . .’’ 27.2.4.3
Theoretical Modeling of Macroscopic Turbulence in a Porous Media
It is noteworthy that to model turbulence within a porous media domain both a time-average operator and a volume-average operator need to be applied to the local Navier–Stokes equations, and the final form of the macroscopic turbulence model depends on the order in which these averaging are done [60]. Based on this, the turbulence models presented up to now follow two different approaches that lead to different governing equations: in the first one, the governing equations for the mean and turbulent fields are obtained by time-averaging the macroscopic equations, while in the second, a volume-average operator is applied to the local time-averaged equation. By following the first approach, in 1997 Antohe and Lage [58], derived a macroscopic k–« turbulence model for a Newtonian and incompressible fluid flow with constant thermophysical properties within a fluid saturated and rigid porous medium. The model was derived by time-averaging the general macroscopic transport equation for porous media, and it was closed by using the classical eddy diffusivity concept together with the development of the macroscopic transport equation for the turbulent kinetic energy and its dissipation. The authors noted that the developed model reduces to the well-known k–« model of clear turbulent flow when the permeability of the porous medium tends to infinity and they state some important characteristics of turbulence in porous media by performing a closer analysis of the turbulent kinetic energy transport equation. They found that in the case of porous media with a permeability small enough to minimize the form drag (Forchheimer term), the presence of the solid matrix dampens turbulence, while for a porous media with a large permeability, the effect of the solid matrix can be either increased or dampened turbulence. The authors also showed that in the case of a statistically steady, fully developed, unidirectional turbulent flow through a porous media, a macroscopic turbulent kinetic energy different from zero is unlikely to persist. This conclusion, born out of their turbulence model, confirms the predictions made by Nield [59]. The first attempt to obtain macroscopic turbulence quantities from microscopic quantities was made in 1999 by Nakayama and Kuwahara [61]. The authors, despite the predictions of Nield [59] and the model of Antohe and Lage [58], stated that the macroscopic turbulent kinetic energy in a forced flow through a porous media must stay at a certain level, as long as the presence of the porous matrix keeps on generating it. They also pointed out that since eddies larger than the scale of the porous structure are not likely to survive long enough to be detected, the small eddies should be modeled first. Based on these, they developed a macroscopic turbulence k–« model for a Newtonian and incompressible fluid flow with constant thermophysical properties, within a fluid-saturated and rigid-porous medium. This model was developed by spatially averaging the Reynolds-averaged transport equations along with the turbulent kinetic energy and the dissipation rate equations (i.e., by spatially averaging the standard k–« model used to model the microscopic turbulence within the porous media). The volume-averaged procedure leads to a closure problem on the momentum equation, which was overcome by using the empirical Forchheimer equation.
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The macroscopic transport equations for turbulent kinetic energy and energy dissipation were obtained by integrating over an REV the microscopic transport equations and neglecting all triple and high-order correlations. Again due to the volume-average procedure a closure model was required for some of the terms in the macroscopic equations. Unlike the model developed by Antohe and Lage [58], the final model developed by the authors showed that in the case of fully developed macroscopically unidirectional flow, with a zero mean shear through a porous media, the macroscopic value of the turbulent kinetic energy reaches a constant value distinct from zero. As a final remark it is important to note that the final form of any macroscopic turbulence model depends on which order the time and spatial averages are applied. This problem, caused by the unavoidable loss of information after each space- and time-averaging process that requires new closure models, remains controversial. By following the Antohe and Lage [58] approach, the model will inevitably lose the information of how local (in space) quantities contribute individually to the time-average quantities, while by following the Nakayama and Kuwahara [61] approach, the model will lose the information of how instantaneous values of the local quantities contribute individually to the space-average quantities.
27.2.5 HEAT TRANSFER
IN
POROUS MEDIA
Similar to the advances obtained in the study of the fluid flow in porous media, the modeling of heat transfer process through porous media has involved combination of empirical results and more rigorous theoretical models. The study of transport phenomena in porous media began in 1800s with the development of various macroscopic and empirical models of the heat transfer process in packed beds (such as the Schuman model). All these early models required the empirical determination of some particular model parameters; it should be noted that the majority of them customarily defined an interfacial convective heat transfer coefficient (hsf ) as a model parameter. Since the actual significance of this model parameter changed from one model to another, a rather incoherent literature on the reported value of hsf , even for a given porous media domain, was created. A careful description of these heuristics model was made in 1982 by Wakao and Kaguei [62]. By the early 1900s it was recognized that the pore level hydrodynamics have a significant impact on the macroscopic temperature field within the system due to the hydrodynamic dispersion and the molecular diffusion effects, and detailed studies at a microscopic level were made. By 1950s the relevance of hydrodynamic and mechanical dispersion together with the molecular diffusion in porous media was considered, and more rigorous approaches, based on the volume-average technique, were developed. 27.2.5.1
Volume-Averaged Models
At a microscopic or pore level, the general expression of the energy balance is still valid for each phase in the porous media domain. Therefore, the microscopic energy equations for the fluid and solid phases are
@Ts ¼ r ks rTs þ Qs s @t @Tf þ r uTf ¼ r ðkf rTf Þ rCp f @t rCp
(27:18)
(27:19)
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The boundary conditions at the fluid–solid interfacial area Afs are given by the continuity of temperature and heat flux: Tf ¼ Ts on Afs
(27:20)
nfs kf rTf ¼ nfs ks rTs þ V on Afs
(27:21)
where V represents a heterogeneous thermal source at the fluid–solid interface that could be coupled to a mass transfer process involving a chemical reaction, adsorption, or phase change. In Equation 27.18, Qs represents a homogeneous thermal source within the solid phase, which normally would be coupled to a diffusion and reaction process or to an electromagnetic heating process. Although the energy transfer at the microscopic level can be accurately modeled using the previous local balances, the complex and highly variable three-dimensional structure of porous medium makes it technically impossible to obtain a solution of these local balances to model the heat transfer process throughout the medium. To overcome this problem the local point energy equations are integrated over an REV to develop volume-averaged expressions, which upon closure provide a suitable macroscopic model for the heat transfer process through a porous media. As discussed previously, in order to apply this approach, it should be possible to assume the heterogeneous porous media as a continuum domain. The REV should be large enough to fully describe the porous medium structure and result in statistically meaningful local average temperatures but small enough to verify that over its linear dimension the variation of temperature (DTl ) is negligible compared to that across the overall system dimension (DTL ). Kaviany [27] states that DTL must be at least 10 times larger than DTl . Considering a rigid, impermeable, and uniform solid matrix, V and Qs as specified functions, and assuming the variation of the physical properties of the fluid and solid phases over the REV negligible, the final volume-averaged energy equation for the fluid and solid phase can be expressed by Equation 27.22 and Equation 27.23, respectively [63]: @hTf if f f « rCp f þ « rCp f hui rhTf i @t |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Accumulation Convection 2 0 0 0 f ¼ « rCp f r hu Tf i |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Dispersion
ð
13
ð
0 1 0 C7 nfs Tf dAA5 þ nfs kf r hTf if þ Tf dA V Afs Afs |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
1 6 B f þ r 4kf @«rhTf i þ V
Conduction
Interfacial flux
(27:22) @hTs is (1 «) rCp s @t |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Accumulation 2 0
ð
13
ð
0 1 0 C7 (1 «)hQs is nsf Ts dAA5 þ nsf ks r hTs is þ Ts dA |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl} V þ Homogeneous Afs Afs thermal source |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
1 6 B s ¼ r 4ks @(1 «)rhTs i þ V Conduction
Interfacial flux
(27:23)
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where prime quantities refer to the spatial deviation of the local quantity with respect to the intrinsic-averaged values defined at that particular location. Note that despite the use of intrinsic averages, the last two equations are superficial transport equations. Each of them represents some quantity per unit volume of the porous media and not per unit volume of either the fluid or the solid phase. The convective transport term in Equation 27.22 couple the energy transfer process with the fluid flow through the porous media, while the interfacial flux that appears in the macroscopic balances couple the heat transfer process within the different phases in the porous media. In the volume-averaged energy equations developed for each phase, the hydrodynamic dispersion, the conductive and the interfacial flux terms require closure. In an attempt to solve this complex system, the first studies assumed that the intrinsic average fluid temperature and the intrinsic average solid temperature at a given location were close enough to be considered equals. Under this assumption and adding Equation 27.22 and Equation 27.23, a oneequation model for the thermal energy process within a porous media can be obtained. However, this condition is not always verified. For very fast transient processes or when heat generation exists in the solid or fluid phase, the local thermal equilibrium cannot be assumed and a two-temperature treatment should be assumed. For modeling heat transfer in porous media the assumptions of local thermal equilibrium should be carefully considered. Further discussion on local thermal equilibrium and local nonthermal equilibrium models is given in Quintard and Whitaker [63] and Kaviany [64].
27.3 MODELING OF THE FORCED-AIR COOLING PROCESS USING THE POROUS MEDIA APPROACH In the following, a review of the most relevant numerical methods to predict the flow field and thermal behavior of horticultural products during the forced-air cooling process is presented.
27.3.1 REVIEW
OF
NUMERICAL MODELS
In 1988, Talbot [4] introduced the idea of using a mathematical model together with a commercial computer program to predict the cooling response of packed produce during the forced-air cooling process. The main objective of his work was to determine the possibility of using a finite element porous media analysis to predict the pressure and velocity fields of the airflow through a typical commercial container packed with 88, size 100, Valencia oranges. The three-dimensional velocity field was evaluated for six different package venting designs at two different flow rates, by using the Forchheimer–Darcy model (Equation 27.10) under the assumptions of a steady and laminar regime of an incompressible fluid flow. The permeability of the medium and the value of the form coefficients were obtained by using the experimental results of Chau et al. [17] together with Equation 27.16 and Equation 27.17. Due to the lack of a suitable method to experimentally measure the air velocity through the orange carton, the verification of the predicted flow field was performed using an indirect method of comparison. The output from the flow field analysis was used together with a modification of the heat transfer model developed in 1976 by Baird and Gaffney [65]. The temperature of the oranges during the process was then numerically calculated. By comparing this predicted cooling response with experimental temperature
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data, the author indirectly evaluated the feasibility of the porous media model to predict the airflow field pattern within produce containers during a forced-air cooling process. A poor comparison of experimental and predicted values was obtained. Talbot pointed out several experimental problems that may lead to this poor comparison (for instance, uncertainty in the temperature readings, problems to set a uniform initial temperature in the oranges, and the requirement of an improved specification of the convective heat transfer coefficient). He also stated some concerns about the application of porous media to predict the flow field in this type of finite-packaged structure. His first and main concern was that the effects of the carton’s walls on the flow field were not taken into account in the Forchheimer–Darcy model; and the second one involved the pressure drop produced by the air inlets and outlets of the packing containers, which cannot be modeled using a porous media approach. In 1999, Xu and Burfoot [18] developed a transient three-dimensional CFD model to predict not only the airflow behavior and the heat and moisture transfer within an unconfined bulk of spherical food products, but also the heat transfer and moisture diffusion within individual products. The entire bulk was divided into imaginary control volumes containing both air and solid. To predict the transport phenomena between control volumes, the packed structure was treated as a porous media. Additionally, in order to consider the temperature and moisture gradients that occur within each individual product in the bulk, inside each control volume, the heat and moisture transfer within a single spherical particle were evaluated. Using numerical simulation, the airflow field and the energy and moisture transfer between control volumes were calculated at a given time by using the CFD package CFDSCFX4 (AEA Technology, Harwell, Oxford, UK). These results were used to evaluate the convective heat and mass transfer coefficients at the surface of each spherical product within each control volume, and the flux of heat and moisture across each product surface. These fluxes were then used as boundary conditions to solve the heat and moisture transfer balances within the product, and to determine the temperature and moisture gradients within each of them. Finally by using these local balances, the heat and mass transfer rates were updated at the end of a given time step and used in the transport balances between different control volumes. In order to demonstrate the capability of the model to predict temperature and moisture changes within a bulk of large agricultural products, predicted and measured profiles of temperature and moisture loss across a bed of potatoes of 2.4 m height and 0.7 m in diameter during a forced-air cooling process from 15.58C to 68C were compared. The results showed similar spatial and temporal temperature variations with a maximum difference of 1.48C. The predicted weight loss of the bed also showed a good agreement with the experimental measurements; after 4 days of test period the predicted value was within 5% of the measured one. In 2001, Hoang et al. [19] developed a mathematical model to quantify the effect of different process parameters and package design on the cooling rate and moisture loss of fruits and vegetables stacked in pallets during the air cooling process. The model equations for the momentum, energy, and mass balance in this two-phase air–product matrix were developed by assuming the system as a continuous porous media domain. This model accounted for porosity variation in the space domain but did not consider deformations or shrinkage of the products with time. In order to model a laminar and transient flow field of a weakly compressible airflow, the momentum balance used was based on the Brinkman– Forchheimer-extended Darcy formulation, where the transient and Boussinesq–Oberbeck (buoyancy) terms were included, and the effective viscosity was assumed to be equal to the air viscosity. The heat transfer process within the pallet was modeled by using a two-equation model and by considering the heat generation not only due to the respiration process within the product but also due to the evaporation of water at the product–air interface. The moisture loss from the product phase was calculated based only on a convective mass transfer
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process, the moisture transport due to diffusion within the product was neglected (lumped method). The transfer of moisture through the air-phase of the system was assumed to occur due to convection and diffusion. It was also assumed that the water vapor in the air is in constant thermal equilibrium with the dry air (i.e., the water vapor has the same temperature as the air). By using a finite-volume code (CFX, AEA Technology, Harwell, Oxford, UK) the model equations were numerically solved and the airflow pattern within a pallet of chicory roots together with the temperature distribution and moisture loss of the product were analyzed and compared for two different pallet designs (open box vs. sealed box). The results showed a significant effect of the pallet design on the velocity field and flow distribution within the pallet, which in turn, strongly affected the cooling rate and moisture loss of the product. The higher the velocity field and flow distribution within the pallet, the more uniform the product temperature within the pallet but also the higher the weight loss. In both designs, the cooling rate was faster at the front and decreased towards the back of the pallet. In 2002, van der Sman [20] addressed two important observations that have raised doubts about the applicability of the Darcy–Forchheimer formulation to describe the airflow through vented boxes of large food products. The first doubt was the applicability of this model in the range of airflows commonly used by the industry. By using the kinematic viscosity of air and a typical product diameter of 5 cm, the author found that at the average porous velocities usually used by the industry (higher than 0.08 m=s) the particle-based Reynolds number becomes greater than 400. At this Reynolds number, the turbulent regime dominates the flow field within a porous media and the Darcy– Forchheimer formulation is questionable. By comparing predicted and experimental values of the pressure drop through a bulk of potatoes (L=d 15) and a bulk of oranges (L=d 7–9), where the Reynolds numbers ranges between 160 to 1600 and 300 to 400, respectively, van der Sman concluded that even at this high Reynolds number the pressure drop can be modeled by the Darcy–Forchheimer equation. The second doubt arose regarding the applicability of this model in the region of vented holes, where the standard length scales required for a porous media approach are not verified. To investigate this problem, a numerical solution of the Darcy–Forchheimer equation together with the continuity equation was obtained by using a finite element solver (FIDAP, Fluent Inc., Lebanon, NH) for a three-dimensional model of a vented box with horticultural produce. By comparing the pressure drops predicted by this model with the experimental pressure drop measured through a vented box of staggered packed produce (mandarins and tomatoes), the author concluded that the model can predict the pressure drop through vented boxes quite accurately. In 2002, Tanner et al. [21,22] developed and verified a generalized mathematical model capable of predicting heat and mass transfer process within refrigerated horticultural packages for a wide range of products and package designs. Their approach was based on dividing the physical domain into different zones that interact with each other and may or may not contain items of product, cooling fluid, and packing materials. Previously researchers who had incorporated a zoned approach neglected any possible interactions between model components other than through the fluid phase, but in this work the authors considered that all components within a zone or between different zones can freely interact with each other. For instance, apart from considering the energy flow due to the fluid flow through the package, they also considered heat convection from the product to the cooling fluid, heat convection between the packaging and the cooling fluid, and heat conduction within the product and packaging materials. The main challenge of this work was the development of a set of suitable submodels capable of describing all the possible heat and mass transfer mechanisms within the packed domain. They divided these submodels into three categories:
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the first one represents the conservation of energy and mass within each particular component of the system (product, fluid, and package), the second one represented transport phenomena within the same zone, and the last one represented interzone interactions. In order to reduce the number of transfer processes to be modeled in each type of submodel category, a series of assumptions were made, such as decoupling the heat and mass transfer processes, assuming a lumped parameter approach for the heat and mass transfer process within a product in a given zone. After the model reduction, the modeling equations required for each type of transport process were derived from conservation balances with respect to each type of component within the system and heuristics developed by the authors and based on an engineering judgment. The comparison between predicted and experimental data of the temperature history of air and products showed a good agreement. In 2003, Hoang et al. [23] presented and validated a transient three-dimensional model for cooling of a bulk of chicory roots in a wind tunnel. The equations presented to model the momentum, heat, and mass transfer in the cooling process of chicory roots can be derived from the general model previously presented by the authors [19] by neglecting the variations in the thermophysical properties of the air-phase with temperature. After a suitable determination of the different model parameters for the case of a bulk of chicory roots, a finitevolume code (CFX4.3) was used for the numerical implementation of the model. It should be noted that due to the variability in the packed structure and different sizes of the roots, the spatial variation of the porosity within the bulk product was not known and not considered in the model, except for the large deviation close to the wall that was estimated based on values obtained from literature. To test the performance of the model, numerical and experimental information regarding the cooling rate and moisture loss of chicory roots (0.15 m length and 0.05 m in diameter) packed in a small basket (0.49 0.39 0.5 m) and located inside a small wind tunnel were compared. Although the agreement between the experimental data and the simulation predictions was found to be rather good for the high air velocity at the inlet of the basket (0.28 m=s), large discrepancies among the air temperature, moisture content, and product weight loss were found when the inlet air velocity was decreased to 0.18 m=s. The authors suggested a series of possible reasons that may explain the discrepancy between the predicted and the experimental values. Based on the large size of the chicory roots compared to the size of basket, the suitability of the continuous porous media approach used to model the system was questioned. Another weakness in this study was the estimation of the convective heat and mass transfer coefficients that appear as model parameters in the heat and mass transfer equations. These parameters were estimated using the correlation equations proposed by Bird et al. [66], which in general lead to uncertainties of up to 50%. The uniform product temperature could not be justified, the forced-air experiments carried out in this study lead to Biot numbers between 0.3 and 0.4. Finally, the authors noticed that in the case under study the particle based Reynolds numbers ranges from 700 to 1000. Under the assumption of a porous media, this range of Reynolds number leads to turbulent regime that in turn invalidates the developed model. In 2003, Alvarez et al. [24] wrote a pioneering paper to model a turbulent flow regime through agricultural commodities stacked in small containers by assuming the system as a continuous porous media. By pursuing the approach of Nakayama and Kuwahara [61], the authors developed a one-equation model for a two-dimensional turbulent flow capable of providing a good approximation of the velocity and turbulent kinetic energy within packed objects. This information was then used to obtain an appropriate correlation to estimate the heat transfer coefficient through the stacked objects as a function of the flow characteristics (i.e., velocity and turbulence intensity values). Under the scope of this study the flow through the porous media was considered steady, incompressible, fully developed, and macroscopically uniform with zero mean shear. Also they considered the macroscopic convective term and
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the macroscopic viscous shear stress diffusion term (Brinkman term) to be negligible in the macroscopic momentum equation. In order to develop the one-equation model the dissipation rate was not estimated with a transport equation, instead it was explicitly given by an empirical correlation involving the turbulent kinetic energy and the macroscopic time average velocity. Finally, they proposed a three-equation model (mass, momentum and turbulent kinetic energy transport) involving four model parameters. To simulate the heat transfer process, a correlation that relates the Nusselt number at a given location with the thermophysical properties of the air-phase, structure parameters (such as porosity of the medium and equivalent diameter of the product), the superficial-averaged velocity and the turbulent kinetic energy at that location was developed. This correlation required the determination of three model parameters. To verify the capability of the developed model to predict the airflow distribution and the local heat transfer coefficients around different products within a packed structure, an experimental analysis of a two-dimensional system consisting of 75 mm diameter PVC spheres arranged in rectangular parallelepipeds within a rectangular air-blast tunnel was performed. After a suitable determination of the model parameters for the system under study, the authors found a good agreement between the simulated and experimental local Nusselt number for different spheres placed in the bed, the average relative variation was only 5.6%. In 2006, Zou et al. [25] presented a comprehensive CFD modeling system to simulate the airflow and heat transfer processes inside ventilated packages of horticultural produce. In this study no buoyancy effects were considered and the airflow transport process was assumed steady and decoupled from the transient heat process. The analysis of the transport processes and the modeling strategies applied in this study were divided based on the type of ventilated package under consideration (bulk and layered packages). In the case of bulk packages, the produce-air region was simply treated as an isotropic, rigid, saturated porous media with uniform spherical particles. The modeling of layered packages was more involved. Since the length scale of the packed structure (distance between two layer of products stacked onto each other) has the same order of magnitude as the size of produce items, a porous media approach cannot be strictly used. In order to solve this problem, the authors applied what they called a ‘‘pseudo-porous media’’ treatment. To simplify the treatment of the airflow modeling inside layered packages, they assumed that the only air movement between layers in the package involves a vertical airflow through the narrow gaps between the tray edges and the package walls. Similarly, the heat transfer process between layers was assumed to occur through these gaps and was modeled as a one-dimensional process perpendicular to the trays. In order to model the airflow within each layer of produce in the package, the product–air region between trays was treated as an isotropic, rigid, saturated porous media with uniform spherical particles. However, since the produce items in the layered packages are not in direct contact with each other, the modeling of the heat transfer process within a product layer did not make use of the porous media assumption, instead only the heat transfer through individual items was considered. In order to relate the vertical airflow between produce layers with the horizontal airflow within each layer in the package, the mass and momentum equation of these two regions were correlated. The velocity of the vertical airflow in the gap regions must satisfy the mass conservation equation of each product layer, and the pressure field for these two regions was forced to be the same. Zou et al. [26] used a CFD method, called ‘‘CoolSimu,’’ to numerically solve this mathematical model for both layered cartons and bulk packages of fruit undergoing forced-air cooling. A good agreement was found between the predicted and experimental data for product center temperatures. A lack of fit was found at certain locations inside the package and it was attributed to inaccurate temperature measurements and uncertainty in model input data.
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27.3.2 LIMITATIONS
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OF THE
POROUS MEDIA APPROACH
A detailed review of the published literature shows that despite the extensive efforts made to model the fluid flow and heat transfer during the forced-air cooling process of agricultural products using a porous media approach, no consensus solution is found. The first drawback that the porous media approach faces, when modeling the cooling process of packed structures of produce, is the breakup of the continuous medium assumption when the container to particle diameter is under 10. Furthermore, when modeling the heat transfer process within packages using a porous media approach, the nonlocal thermal equilibrium present between the solid and fluid phases leads to a complex two-equation model involving a series of model parameters whose determination has seriously limited the accuracy of the model. The numerical calculation of these parameters for complex structures has not been attained yet, and despite over 50 years of modeling and experimental research to estimate them from experimental data and correlated against fluid flow rates, fluid and solid properties, and bed structure, no agreement is found between the correlations proposed by different researchers. Another approach to study the thermal behavior of layers of agricultural products in trays appeared in 1994 when Alvarez et al. [67] showed that the thermal heterogeneity of the forced-air cooling process is not only generated by the increase in the air temperature, as it flows through the system, but also due to the heterogeneity in the airflow pattern inside the bins, which leads to significant variations in the local heat transfer coefficient between the air and product interface. This approach consists of studying the thermal behavior of individual products within the bin by determining the local surface heat transfer coefficient on each of them. It is targeted at obtaining a more fundamental understanding of how the local behavior of the fluid flow affects the heat transfer process within the products. Because this approach deals with local quantities, it is not constrained to any containerto-particle diameter ratio and it does not require any additional model parameters. However, it has been extremely difficult to apply, and so far, there have been only few studies that attempt to experimentally link the local fluid flow behavior within the bed to the heat transfer process. One of the most relevant studies in this regard was made by Alvarez and Flick [7], where the airflow within a packed bin of spherical food models was studied using a hot-wire anemometer. The results showed considerable heterogeneity of the airflow inside the bin (presence of preferential airflow pathways and back-mixing zones) and high levels of turbulence intensity (20% to 50%) especially in stagnant zones, such as, behind the nonperforated region of the inlet wall or behind spheres. In order to show the significant impact of this complex flow behavior on the heterogeneity of the heat transfer process, Alvarez and Flick [8] performed an experimental study to determine the heterogeneity in the local heat transfer coefficient around individual products within the package. Based on their experimental configuration, no significant differences were found in the heat transfer coefficients of spheres along the height of the package, but significant differences were found along the main direction of the flow (up to 40% between the first and the fourth row) and the width of the package (heat transfer coefficient near the wall was 10% lower than far away from it). In addition to this, by considering the velocity profiles measured in the previous part [7], the authors developed a suitable correlation to predict the heat transfer coefficient for individual spheres as a function of the airflow parameters (Reynolds number and turbulent intensity) at the front of each of them. The main drawback that has limited the application of this approach is the difficulty in measuring the flow field through complex packed structures. Even in the case of identical products, uniformly distributed within the package, the measurement of the fluid flow inside
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the bed without disturbing the packaging arrangement becomes impossible by means of conventional measurement methods. One of the main limitations of the Alvarez and Flick [7] work was caused by the use of a hot-wire anemometer to measure the airflow behavior. Since this technique requires the removal of some products from the package that may impact the flow field to some extent, the authors were able to perform the measurements only in some locations inside the bin. Recently nonintrusive image-based techniques have been identified as possible techniques to successfully trace the three-dimensional flow field that develops inside complex structures, such as individual packages of horticultural products. The experimental information provided by these novel techniques can be used to perform an analytical analysis of the heat transfer process within each object in the package. Although this method can in turn be used to analyze the impact of different design parameters on the efficiency of the forced-air cooling process, the large number of parameters to be considered (airflow rate, size, number, and arrangement of vent openings) makes this approach impractical. An ideal approach would be to utilize the experimental flow field information to develop and validate a mathematical model, capable of accurately predicting the airflow field and the heat transfer process within individual packages of horticultural products, without requiring the use of effective or lumped parameters. Until some years ago, the solution of the full Navier–Stokes equations to obtain the flow field around packed objects had been considered impossible due to computational limitations and geometrical complexities. But, nowadays, the use of modern CFD codes provides a powerful technique to obtain a detailed resolution of the flow field and heat transfer process in complex packed structures.
27.4 USE OF CFD AS A DESIGN TOOL FOR INDIVIDUAL HORTICULTURAL PACKAGES—A CASE OF STUDY The integration of modern CFD codes and new experimental flow field measurements offer a promising approach to improve the understanding of the flow field and heat transfer process within packages of fresh produce in forced-air coolers. However, before applying this novel approach as a design tool to develop improved packaging systems that help promote a rapid and uniform cooling of the packed produce, several aspects need to be addressed. The first problem to solve is the use of a nonintrusive technique to accurately measure the airflow inside a complex packaged structure. Although experimental techniques, such as laser Doppler velocimetry (LDV), nuclear magnetic resonance (NMR), and particle image velocimetry (PIV) have improved in recent years and show a strong potential, each is constrained by important limitations. Once this problem is overcome, the experimental information of the flow field can be used together with a CFD software to validate a mathematical model capable of modeling the flow field. Upon validation, this CFD model can be used to model the heat transfer process of packed horticultural produce and provide design guidelines that improve the efficiency of the cooling process.
27.4.1 USE
OF
PIV
TO
STUDY THE AIRFLOW
IN
PACKED STRUCTURES
Particle image velocimetry is a novel nonintrusive image-based technique capable of determining instantaneous flow fields over two- or three-dimensional domains [68]. The flow field is optically determined by measuring the motion of small markers seeded in
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the flow. A pulsed sheet of laser light illuminates the flow domain at different instants of time and the locations of the markers at the time of each pulse are recorded by the light scattered by them onto a camera lens. By dividing the illuminated plane into a large number of image subregions and performing a statistical correlation between two consecutive images of each of them, the local velocity field within the illuminated plane in the physical domain is determined. Although PIV is being extensively used in aerodynamics and biomechanics studies [69,70], its requirement of optical access to the flow has limited its application in complex flow passages, such as those commonly found in food systems. 27.4.1.1
Transparent Model for PIV Applications
To measure the flow field inside packed structures, it is necessary to develop a transparent model of the solid particles. This model must allow optical access to the flow field, and it must exhibit a perfect refractive index match between the transparent matrix and the working fluid (in order to eliminate not only the refraction of the laser sheet as it passes through the system, but also the distortion of light scattered from the seeded particles [71,72]). Since gases have refraction indexes of different order of magnitude than solids, air cannot be used as the working fluid, and an appropriate transparent liquid=solid model compatible with PIV measurements must be developed. Ferrua and Singh [73,74] investigated various combinations of transparent solids and liquids that ensure a perfect refractive index matching, good chemical compatibility, no toxicity, and low fluid viscosity. They used an optimal combination of fused silica as the transparent solid material (refractive index of 1.4609 at 532 nm and 208C) and a 1:0.3 mass mixture of baby oil (Johnson & Johnson, Skillman, NJ) and a mineral oil Drakesol 260 (Penreco, Dickinson, TX). The matching of refractive index achieved is illustrated in Figure 27.1 by the nondistortion of a grid of lines placed behind a packed structure of fused silica spheres semi-immersed in the oil mixture. 27.4.1.2
Fabrication of a Transparent Fixed Bed of Packaged Products
An experimental setup for using PIV for a transparent system is shown in Figure 27.2. The design of the packed test section was based on the geometrical proportions and packed structure of a typical package use for berries. Considering the spherical shape of most berries, the fruits were modeled using spheres whose volume represents the average volume of the fruit. Apart from the fact that it has been customary to represent horticultural produce such as strawberries, potatoes, and oranges by spheres, to perform experimental and numerical studies [2,7,8,20], the use of spheres as the product model simplifies the CFD analysis by facilitating the creation of a computational model to accurately reproduce the geometry of the experimental system [73]. The packed test section used in these trials reflected the packing structure and the smaller cross-sectional dimensions of a typical 0.5 kg strawberry package, after scaling it to 1=2. It consisted of 22 fused silica spheres of 1.6 cm diameter arranged in a cubic centered distribution within a small section of the 5.3 cm wide 4.3 cm high rectangular duct. The test section was constrained by a pair of vented walls that reproduce the shape, size, and distribution of the standard vents in the smaller wall of a 0.5 kg strawberry package. Figure 27.3a shows a schematic diagram of the experimental test section and perforated walls. Figure 27.3b shows a top view of the actual experimental setup.
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FIGURE 27.1 Effect of the refractive index matching as observed by the nondistortion of a grid of line placed behind a packed structure of fused silica spheres, semi-immersed in a mixture of Johnson & Johnson baby oil and Drakesol 260 oil (1:0.3 volume). (a) No oil. (b) Oil.
The oil mixture was pumped, at room temperature (228C), through the system at a flow rate of 2.4 L=min. The density and dynamic viscosity of the oil mixture are 829 kg=m3 and 0.01325 Pa s respectively. 27.4.1.3
Results
Figure 27.4 shows the results obtained within a horizontal plane through the middle layer of spheres within the packed test section. Figure 27.4a illustrates the geometrical location of the plane in the packed structure, Figure 27.4b shows the local vector field obtained after
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Packed test section
1.5 m
0.04 m
Vented walls Reservoir Pump
FIGURE 27.2 Schematic diagram of the experimental setup.
5.3 cm
4.3 cm
(a)
5.3 cm
FIGURE 27.3 (a) Schematic diagram of the packed test section. (b) Top view of the transparent packed test section.
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correlating a single pair of images, and Figure 27.4c shows the final averaged velocity field obtained for that particular plane within the system.
27.4.2 NUMERICAL MODELING OF
THE
EXPERIMENTAL FLOW FIELD
The initial step in developing a mathematical model capable of predicting the experimental flow field within a packed structure is to elucidate the governing flow regime. For the test apparatus presented in the preceding section, the flow regime in the rectangular duct was found to be undoubtedly laminar, the Reynolds number calculated based on the mass flow rate pumped through the system and the duct’s hydraulic diameter was 52, significantly lower than the transitional value of 2100. However, due to the lack of information regarding the airflow behavior through packed structures where the container-to-particle diameter is
FIGURE 27.4 (a) Location of the horizontal plane where the velocity field was measured (1.76 cm height). (b) Vector field. (continued )
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60
Vel Mag 0.0666378
0.0555315
50
0.0444252
Y mm
0.0333189
0.0222126
40 0.0111063
0
30
20
(c)
20
30
40
50
60
X mm
FIGURE 27.4 (continued) (c) Velocity field.
under 10, there is no suitable definition of Reynolds number that allows the determination of the governing flow regime within the experimental test section. To determine the flow regime within the packed structure, the experimental information provided by PIV was used to calculate local values of turbulence intensity within different planes inside the domain. The small values of turbulent intensity indicated a laminar flow regime within the packed structure. Based on the previous discussion, the flow regime within the experimental system was modeled by the steady-state Navier–Stokes equations for an incompressible Newtonian fluid with constant viscosity: @ui ¼0 @xi uj
@ui 1 @p @ 2 ui ¼ þn þ gi r @xi @xj @xj @xj
(27:24)
(27:25)
The next step to be accomplished was the validation of this mathematical model. Recent developments in CFD packages make it possible to numerically solve the Navier–Stokes equations within complex packed structures. By comparing the numerical simulation of the flow field with the experimental information provided by PIV, the capability of the model to predict the flow behavior within packed structures can be analyzed. 27.4.2.1
Computational Model
The first step in any CFD simulation is the creation of a computational model that accurately reproduces the experimental domain under study. A three-dimensional CFD model of the packed test section is shown in Figure 27.5. Figure 27.5a is a side view of the test section model along the main direction of the flow
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(x-axis) and shows the three horizontal layers of spheres within the package (H1 to H3). Figure 27.5b is a top view of the model; it shows the five vertical layers of spheres aligned with the main flow direction. For symmetry, only three layers are explicitly identified as VF1 to VF3. Figure 27.5b also shows the five vertical cross-sectional layers within the package as VC1 to VC5. Figure 27.5c shows a three-dimensional projection that provides a global view of the computational model developed. The mesh generation within this computational model is one of the most challenging aspects of the CFD analysis. The computational mesh plays a significant role on the accuracy and stability of the numerical simulation. It must be properly distributed within the system to obtain good resolution in regions where critical features of the flow occurs, but without unnecessarily increasing the computational time. Also, it should not present rapid changes in the cell volume between adjacent cell, and it must verify a set of quality parameters, such as skewness values lower than 0.97. Due to the different length scales present in the model, the
Flow direction
H3 layer
H2 layer
H1 layer Gy
(a)
Gz
Gx
VC1 layer
VC3 layer
VC2 layer Gy
VC5 layer
VC4 layer
Gx
G
Flow direction VF1 layer VF2 layer VF3 layer (b)
FIGURE 27.5 (a) Side view along the main direction of the flow (x-axis) of a CFD model of the packed test section. (b) Top view along the main direction of the flow (x-axis) of a CFD model of the packed test section. (continued )
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FIGURE 27.5 (continued) (c) Three-dimensional projection of a CFD model of the packed test section.
complexity of the physical domain within the test section, and the different behavior of the flow along the system, an unstructured hybrid mesh was required. The first zone to be meshed was the fluid region within the packed test section. The main problem to overcome in this region was the presence of highly skewed elements in areas around contact points between spheres and between spheres and walls. In order to overcome this issue a small gap was created between them by using model spheres with a diameter equal to 99% of the real ones, as suggested by Nijemeisland and Dixon [75]. To create a fine mesh in the constricted flow zones close to the sphere–sphere or sphere–wall contact regions, without compromising the density of the fluid mesh in the entire package, a thin region surrounding each sphere was created. These thin regions were united to create a unique volume, which was meshed using an unstructured hybrid TGrid scheme (Fluent) with an interval size of 0.1 (Figure 27.6). The remaining fluid zone within the packed structure was also meshed using an unstructured hybrid TGrid scheme, but with an interval size of 0.15 (Figure 27.7). The spheres were meshed using an unstructured hybrid TGrid scheme (Figure 27.8). The openings in the vented walls were meshed using a structured Cooper scheme (Fluent) consisting of hexahedral and wedge elements. The upstream and downstream rectangular ducts were meshed using a structured Cooper scheme, with coarser hexahedral and wedge elements close to the inlet and outlet regions, respectively, and finer ones as the duct approach the test section. The total computational mesh created in this manner contained about 1,360,000 elements, with 51% of them inside the packed test section (368,436 within the spheres and 334,221 within the fluid). No elements failed the check for skewed or inverted elements. The element
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Y Z
X
FIGURE 27.6 Detailed view of the mesh scheme in flow passages close to sphere–sphere proximity points.
with the worst skew was located within the packed test fluid region with a value of 0.95 (lower than the critical value of 0.97). 27.4.2.2
Numerical Solution
Due to the elliptic nature in the space domain of the Navier–Stokes equations (Equation 27.24 and Equation 27.25) boundary conditions must be prescribed all around the domain surface.
Y Z
X
FIGURE 27.7 Mesh of the fluid region within a vertical plane along the main flow direction (x-axis) through the center of the spheres in the VF1 layer.
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Y Z
X
FIGURE 27.8 Unstructurated hybrid mesh created within a sphere model.
An appropriate set of boundary conditions is another critical requirement of any simulation. To replicate the experimental conditions, a mass flow rate equal to the one pumped through the experimental system was specified along the x-direction at the inlet of the computational domain. Although this prescription erroneously implies a uniformly distributed velocity field through the inlet, the upstream duct is long enough to allow a good development of the numerical simulation along it to finally obtain a good prediction of the flow field at the entrance of the packed test section. At the outlet, the boundary information depends strongly on where the boundary is prescribed. The definition of the computational model outlet at the end of the downstream duct, where a fully developed flow can be assumed, justified the prescription of an outflow boundary there. A segregated implicit solver formulation was used in order to perform the numerical solution of the steady, incompressible laminar regime. The pressure–velocity coupling was solved using the SIMPLE algorithm. The STANDARD scheme was used to perform pressure interpolations and the discretization of the convective term of the momentum equation was achieved by using a first-order upwind algorithm. The numerical solution of the mathematical model proposed required approximately 35 min of CPU time on an AMD Athlon 64 3200. Convergence was obtained after 220 iterations. 27.4.2.3
CFD Results
In order to display and characterize the flow field inside the packed test section, the velocity vectors within different planes of the computational packed structure were plotted. The locations of these planes are indicated in Figure 27.9. Each horizontal plane goes through the center of all the spheres within the same horizontal layer (i.e., H1, H2, and H3 layers), while the vertical one goes through the center of all the spheres located in the vertical layer aligned with the main flow direction at the middle width of the package (i.e., VF1 layer). Figure 27.10 shows the velocity field in the vertical plane VF1. A significant uneven distribution of the flow is observed within this vertical plane, 64% of the total mass flow rate
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VF1 plane
H3 plane
H2 plane Y
Y Z
X
H1 plane
Z
X
FIGURE 27.9 Location of horizontal and vertical planes within the packed structure where the velocity fields were plotted.
forced through the packed structure is bypassed through the headspace at the top of it, and the mass-weighted average of the velocity field through the head space (7.78 cm=s) is almost twice the averaged value within the spheres (4.39 cm=s). The location of the horizontal vent adjacent to the top layer of spheres (H3) may actually increase the channeling effect through the head space of the package. It is also important to notice the large z-component of the velocity at the level of the horizontal vent in either of the vented walls. Figure 27.11 shows a detailed plot of the velocity field near a contraction of the flow path due to the proximity of two spheres. The flow is accelerated as its pathway is narrowed and it significantly slows down as it goes through the narrow space between the spheres (recall the three-dimensional behavior of the flow domain). Figure 27.12 shows the velocity field in the horizontal plane H1. Except for the regions near the inlet and outlet bottom vents of the walls, a slower flow within this section of the packed bed is observed (the mass-weighted average velocity is only 2.1 cm=s). Although a vertical component of the velocity is observed within this plane near the location of the wall’s
1.88e+01 1.79e+01 1.70e+01 1.60e+01 1.51e+01 1.41e+01 1.32e+01 1.22e+01 1.13e+01 1.04e+01 9.42e+00 8.48e+00 7.54e+00 6.60e+00 5.65e+00 4.71e+00 3.77e+00 2.83e+00 1.88e+00 9.42e−01 0.00e+00
Y Z
X
Velocity vectors colored velocity magnitude (cm/s)
Jul 26, 2006 FLUENT 6.2 (3d, segregated, lam)
FIGURE 27.10 Velocity vector field in the vertical plane along the x-direction VF1.
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3.30e+00 3.14e+00 2.97e+00 2.81e+00 2.64e+00 2.48e+00 2.31e+00 2.15e+00 1.98e+00 1.82e+00 1.65e+00 1.49e+00 1.32e+00 1.16e+00 9.90e−01 8.25e−01 6.60e−01 4.95e−01 3.30e−01 1.65e−01 0.00e+00
Y Z
X
Velocity vectors colored by velocity magnitude (cm/s)
Jul 26, 2006 FLUENT 6.2 (3d, segregated, lam)
FIGURE 27.11 Detailed view of the velocity field in a contracted fluid pathway due to the proximity of two spheres.
vents, the main component of the average velocity is in the x-direction, being 70 times larger than the y-component and more than 400 times larger than the z-component. Figure 27.13 shows the velocity field in the horizontal plane H2. Unlike the previous one, this horizontal plane does not correspond exactly with the location of any vent. Analogous to
9.96e+00 9.47e+00 8.97e+00 8.47e+00 7.97e+00 7.47e+00 6.97e+00 6.48e+00 5.98e+00 5.48e+00 4.98e+00 4.48e+00 3.99e+00 3.49e+00 2.99e+00 2.49e+00 1.99e+00 1.49e+00 9.96e+01 4.98e+01 0.00e+00
Y
X
Z Velocity vectors colored by velocity magnitude (cm/s)
FIGURE 27.12 Velocity vector field in the horizontal plane H1.
Jul 26, 2006 FLUENT 6.2 (3d, segregated, lam)
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4.49e+00 4.27e+00 4.04e+00 3.82e+00 3.59e+00 3.37e+00 3.14e+00 2.92e+00 2.70e+00 2.47e+00 2.25e+00 2.02e+00 1.80e+00 1.57e+00 1.35e+00 1.12e+00 8.98e−01 6.74e−01 4.49e−01 2.25e−01 0.00e+00
Y
X
Z
Velocity vectors colored by velocity magnitude (cm/s)
Jul 26, 2006 FLUENT 6.2 (3d, segregated, lam)
FIGURE 27.13 Velocity vector field in the horizontal plane H2.
the plane through the bottom layer of spheres, the mass-weighted average velocity is 2.1 cm=s and the main flow direction is along the x-direction. Although still negligible, a more significant out-of-plane velocity component (y-direction) is observed within this plane. The x-component of the mass-weighted average velocity (1.69 cm=s) is now 70 times larger than both the y- and the z-components. Figure 27.14 shows the velocity field in the horizontal plane H3. This section does not correspond exactly with the location of any vents in the walls, but they are very close to the horizontal ones. The mass-weighted average velocity within this section of the packed structure is higher than in the previous planes (3.7 cm=s). The x-component of this average velocity is 2.1 cm=s, 140 times higher than the z-component but only 5 times higher than the y-component. The proximity of the horizontal vent of the inlet and exit walls of the packed structure leads to higher velocities. Furthermore, there are significant out-of-plane velocity components at the inlet and outlet of the package due to the proximity of the top layer of spheres (Figure 27.14b) to the horizontal vents. In all the planes previously analyzed the fluid circulation in small gaps between spheres, transversal to the main flow direction, is very low. The mass flow distribution through the inlet vents of the packed structure is not proportional to the open area for each of them. The majority of the fluid enters the system by the horizontal vent, but while the percentage of open area of this vent is 54% of the total open area, the mass flow rate through it is 66%. These results show the complex behavior of the local flow field within packed structures where the container-to-particle diameter is lower than 10 and support the approach pursued by Alvarez and Flick [7] to study its effects on the value of local heat transfer coefficients within packed structures. 27.4.2.4
Validation
To validate the flow field model, the simulated flow field using CFD was compared against experimental information provided by PIV trials at different locations within the packed structure.
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Computational Fluid Dynamics in Food Processing 1.04e+01 9.90e+00 9.37e+00 8.85e+00 8.33e+00 7.81e+00 7.29e+00 6.77e+00 6.25e+00 5.73e+00 5.21e+00 4.69e+00 4.17e+00 3.65e+00 3.12e+00 2.60e+00 2.08e+00 1.56e+00 1.04e+00 5.21e+01 0.00e+00
Y
X
Z
Velocity vectors colored by velocity magnitude (cm/s)
Jul 26, 2006 FLUENT 6.2 (3d, segregated, lam)
(a)
1.04e+01 9.90e+00 9.37e+00 8.85e+00 8.33e+00 7.81e+00 7.29e+00 6.77e+00 6.25e+00 5.73e+00 5.21e+00 4.69e+00 4.17e+00 3.65e+00 3.12e+00 2.60e+00 2.08e+00 1.56e+00 1.04e+00 5.21e+01 0.00e+00
Y Z
X
Velocity vectors colored by velocity magnitude (cm/s)
Aug 22, 2006 FLUENT 6.2 (3d, segregated, lam)
(b)
FIGURE 27.14 Velocity vector field in the horizontal plane H3. (a) Top view. (b) Side view.
Figure 27.15 shows the comparison obtained on a line along the main direction of the flow in a horizontal plane that goes through the bottom layer of spheres (y ¼ 0.54 cm). The line within this plane corresponds to the intersection of this plane with the plane VF2 as shown in Figure 27.15a.
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Y Z
(a)
X
0.06
Velocity Vxz (m s−1)
0.05 0.04 Fluent
0.03
PIV
0.02 0.01 0 0
(b)
0.01
0.02
0.03
0.04
0.05
0.06
Distance x (m)
FIGURE 27.15 Comparison of the experimental velocity data and CFD results along a horizontal line in the main flow direction within a horizontal plane through the bottom layer of spheres (H1 layer). (a) Location of the line (y ¼ 0.54 cm, z ¼ 3.61 cm). (b) Plot of the planar velocity profile along the line.
Figure 27.16 and Figure 27.17 show analogous information to the one presented in Figure 27.15 but for horizontal lines along the main direction of the flow at different horizontal planes within the packed structure. The comparison showed an excellent agreement between experimental and predicted values except in regions close to the inlet and outlet walls at the middle and top layer of spheres. This discrepancy can be justified due to the presence of a strong vertical component (y-direction) of the velocity field (Figure 27.18). This vertical component of the velocity introduced significant errors in the two-dimensional measurements taken with PIV in the horizontal planes (x–z plane). This experimental limitation may be overcome by imaging vertical planes within this domain.
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Y Z
(a)
X
0.03
Velocity Vxz (m s−1)
0.025 0.02 Fluent
0.015
PIV
0.01 0.005 0 0
0.01
0.02
(b)
0.03 0.04 Distance x (m)
0.05
0.06
FIGURE 27.16 Comparison of the experimental velocity data and CFD results along a horizontal line in the main flow direction within a horizontal plane through both the bottom and middle layer of spheres (H1 and H2 layers). (a) Location of the line (y ¼ 1.10 cm, z ¼ 3.61 cm). (b) Plot of the planar velocity profile along the line.
27.4.3 USE OF FLOW FIELD MODEL IN PACKED OBJECTS
TO
PREDICT HEAT TRANSFER PROCESS
By using the validated flow field model, a CFD simulation was performed in order to elucidate the impact of the local flow field on the heat transfer process within the packed test section.
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Y Z
(a)
X
0.06
Velocity Vxz (m s−1)
0.05 0.04 Fluent
0.03
PIV
0.02 0.01 0 0
(b)
0.01
0.02
0.03
0.04
0.05
0.06
Distance x (m)
FIGURE 27.17 Comparison of the experimental velocity data and CFD results along a horizontal line in the main flow direction within a horizontal plane through the top layer of spheres (H3 layer). (a) Location of the line (y ¼ 2.69 cm, z ¼ 3.61 cm). (b) Plot of the planar velocity profile along the line.
In this numerical analysis, air at 08C was conveyed inside the rectangular duct at a flow rate that reproduces the flow field conditions previously analyzed and modeled. The required mass flow rate of air was calculated based on a Reynolds number matching analysis. The spheres within the computational model were assumed to represent strawberries with an initial temperature of 218C. Under the scope of this study, uncoupled heat and momentum transfer process was assumed (i.e., negligible buoyancy effects) and no energy sources due to product respiration or moisture evaporation were considered.
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9.90e+00 9.43e+00 8.97e+00 8.51e+00 8.05e+00 7.58e+00 7.12e+00 6.66e+00 6.20e+00 5.73e+00 5.27e+00 4.81e+00 4.35e+00 3.88e+00 3.42e+00 2.96e+00 2.50e+00 2.03e+00 Y 1.57e+00 1.11e+00 6.47e−01 Z
X
Velocity vectors colored by velocity magnitude (cm/s)
Aug 22, 2006 FLUENT 6.2 (3d, segregated, Iam)
FIGURE 27.18 Strong out-of-plane flow field developed at the inlet and outlet regions of the comparison line along the top layer of spheres (y ¼ 2.69 cm, z ¼ 3.61 cm).
The steady-state laminar airflow field was simulated based on the flow model previously validated (Equation 27.24 and Equation 27.25). Analogous to the CFD simulation of the oil mixture flow field, a mass flow inlet condition and an outflow boundary were prescribed along with the nonslip condition in all solid walls within the model. Based on the preceding assumptions, the energy equations for the fluid and solid regions within the computational domain become
@Tf rCp f þ r uTf ¼ r ðkf rTf Þ @t
rCp
@Ts ¼ r ks rTs s @t
(27:26) (27:27)
The boundary conditions at the fluid–solid interfacial area Afs are given by the continuity of temperature and heat flux: Tf ¼ Ts on Afs
(27:28)
nfs kf rTf ¼ nfs ks rTs on Afs
(27:29)
No heat flux was assumed to occur through the walls of the rectangular duct. 27.4.3.1
Numerical Solution
The numerical scheme used to simulate the steady, incompressible laminar airflow regime was identical to the one discussed in Section 27.4.2.2. The transient heat transfer process was
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simulated by using a first-order implicit time discretization scheme and a first-order upwind scheme to discretize the convective term of the energy equation. The numerical solution of the transient heat transfer process required approximately 30 min of CPU time on an AMD Athlon 64 3200 to simulate 1 h of real process. An adaptative time stepping scheme was used and no more than 10 iterations were required to achieve convergence within each time step. 27.4.3.2
Results
A qualitative analysis of the heat transfer simulation showed significant differences not only in the temperature evolution of individual spheres within the packed structure but also in the individual temperature profile within each of them. Figure 27.19 illustrates the heterogeneous temperature evolution of the surface temperature of the spheres after 20 min of cooling. During the first 10 min of process only the temperature of spheres near the inlet wall and at the top of the packed structure is significantly affected. This can be explained due to the higher airflow velocities within these regions of the packed structure. By considering the temperature of the spheres within the first vertical layer perpendicular to the flow direction (VC1 layer), a significant effect of the location of the spheres with respect to the inlet wall’s vents was observed; spheres closer to the horizontal vent (through which 66% of the air is entering into the packed structure) cool faster than those located at the bottom of the package (Figure 27.20). Also, the effect of the vent locations on the local flow field significantly affects the temperature profile within each individual sphere at the top of the package, probably due to the effect on the value of local heat transfer coefficients (Figure 27.21).
2.95e+02 2.94e+02 2.93e+02 2.92e+02 2.91e+02 2.90e+02 2.88e+02 2.87e+02 2.86e+02 2.85e+02 2.84e+02 2.83e+02 2.82e+02 2.81e+02 2.80e+02 2.79e+02 2.77e+02 2.76e+02 Y 2.75e+02 2.74e+02 2.73e+02 Z
X
Contours of static temperature (K) (Time = 1.324e + 03)
Jul 27, 2006 FLUENT 6.2 (3d, segregated, Iam, unsteady)
FIGURE 27.19 Temperature profile of individual spheres within the packed structure at approximately 20 min of cooling.
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Top sphere
Horizontal vent (inlet wall)
Y Z
Bottom sphere X
Volume-averaged temperature (C)
22.0 Bottom sphere
21.0
Top sphere
20.0 19.0 18.0 17.0 16.0 15.0 14.0 13.0 12.0 0.0
2.0
4.0
6.0
8.0
10.0
Time (min)
FIGURE 27.20 Effect of the location of the sphere, in the first vertical layer near the entrance wall (VC1 layer), with respect to the horizontal wall’s vent on its volume-average temperature history during the first 10 min of process.
After 20 min of process, the cooling of spheres in the middle layer of within the packed structure (i.e., H2 layer) is noticeable. In this layer, while the cooling front of the spheres closer to the inlet wall moved along the main flow direction (x-direction), the cooling front of the other spheres moves from top to bottom (Figure 27.22). There was a profound effect of the significant flow bypassing the system through the head space of the package on the heat transfer process within the entire package. The spheres near the exit wall and close to the top of the package were at a lower temperature than spheres closer to the entrance but at the bottom (Figure 27.23). This observation clearly supports the idea proposed by Alvarez and Flick [8] that the thermal heterogeneity of the forced-air cooling process is not only generated
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687
Outlet wall Inlet wall
Top layer of spheres (H3)
Y X Z
Contours of surface heat transfer coefficient (W m−2 K−1) (Time = 5.5000e+01) Aug 23, 2006 FLUENT 6.2 (3d, segregated, Iam, unsteady)
FIGURE 27.21 Effect of vent locations and head space bypass on local values of the heat transfer coefficient within individual spheres located at the top layer of the package (H3) after 10 min of cooling.
by the increase in the air temperature, as it flows through the system, but also due to the heterogeneity in the airflow pattern inside the packed structure. After 40 min of cooling the temperature profile within the package did not follow the direction of the main flow. As expected, the spheres located at the top horizontal layer and next to the horizontal inlet vent exhibit the lowest temperatures, while the ones located in the bottom horizontal layer and close to the exit wall exhibit the highest temperature within the package (Figure 27.24).
Vertical cross-section (VF2)
Middle layer (H2)
Bottom layer (H1) Y
Y Z
X
Z
X
FIGURE 27.22 Temperature profile after 20 min of cooling of a vertical cross-section along the main flow direction (VF2) of two of the spheres in the horizontal middle layer of the packed structure (H2 layer). (continued )
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Inlet wall⬘s vents
Outlet wall⬘s vents
Y Z
X
Contours of static temperature (K) (Time = 2.700e + 03)
Aug 23, 2006 FLUENT 6.2 (3d, segregated, Iam, unsteady)
FIGURE 27.22 (continued)
The previous analysis shows the heterogeneity of the heat transfer process within the packed structure as a consequence of the nonuniformity of the airflow field distribution within the system. Figure 27.25a shows the center temperature history of three different spheres within the vertical layer along the main flow direction through the middle width of the package structure (VF1 layer). As expected for two spheres located at the bottom of the package, the lowest temperature was reached for the one near the entrance wall. However, it is noteworthy that significant difference that occurs between the two spheres located next to the exit wall but one on the bottom and the other on the top of the package. The history of center temperature of the sphere located at the top was not only significantly lower than the one from the bottom sphere, but also exhibited a different temperature profile (similar to the profile exhibited by the sphere close to the entrance wall). These differences in the temperature history may be explained by the influence of the location of the vents in the confined walls, and the void space at the top of the package, on the behavior of the airflow rate around the sphere. The significant difference in the time-averaged values of the surface heat transfer coefficients of each of these spheres supports the preceding observations (Figure 27.25b).
27.5 CONCLUSIONS The porous media approach has been used by several researchers in modeling flow field and heat transfer in air cooling of packaged products. The key limitations of this approach as presented in this chapter must be carefully evaluated when considering it for such applications. The use of nonintrusive optical techniques (such as PIV) to trace the flow field within packed structure provides a valuable understanding and quantitative description of the complex local behavior of fluid flow within a packed domain. Results presented in this chapter show that the information provided by this novel flow measurements techniques can be successfully used to develop and validate a mathematical model capable of accurately
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Vertical cross-section (VF1)
Y X
Z
Grid
Aug 23, 2006 FLUENT 6.2 (3d, segregated, Iam)
2.93e+02 2.92e+02 2.91e+02 2.90e+02 2.89e+02 2.88e+02 2.87e+02 2.86e+02 2.85e+02 2.84e+02 2.83e+02 2.82e+02 2.81e+02 2.80e+02 2.79e+02 2.78e+02 2.77e+02 2.76e+02 2.75e+02 2.74e+02 2.73e+02
Inlet wall⬘s vents
Outlet wall⬘s vents
Y Z
X
Contours of static temperature (K) (Time = 1.2700e+03)
Aug 22, 2006 FLUENT 6.2 (3d, segregated, Iam, unsteady)
FIGURE 27.23 Temperature profile after 20 min of cooling of a vertical cross-section through the center of the spheres located in a vertical layer along the main flow direction at the middle width of the package (i.e., VF1 layer).
predicting the airflow field within complex packaged structures. This approach is of significant relevance in cases where the container to particle diameter is lower than 10, in which case the porous media approach commonly used to simulate the airflow field within produce packages is not verified.
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Computational Fluid Dynamics in Food Processing Vertical cross-section (VF1)
Y Z
2.90e+02 2.89e+02 2.89e+02 2.88e+02 2.87e+02 2.86e+02 2.85e+02 2.84e+02 2.83e+02 2.83e+02 2.82e+02 2.81e+02 2.80e+02 2.79e+02 2.78e+02 2.77e+02 2.77e+02 2.76e+02 2.75e+02 2.74e+02 2.73e+02
Vertical cross-section (VF2)
X
Inlet wall⬘s vents
Outlet wall⬘s vents
Y Z
X
Contours of static temperature (K) (Time = 2.7400e+03)
Aug 22, 2006 FLUENT 6.2 (3d, segregated, Iam, unsteady)
FIGURE 27.24 Temperature profile after 40 min of cooling of a vertical middle cross-section of the spheres located in the vertical layers along the main flow direction VF1 and VF2.
The availability of modern CFD packages facilitates the numerical simulation of the flow field within a complex structure and the analysis of its impact on the heat transfer process. The capability of the CFD analysis to provide a significant amount of detailed information in a relatively short time makes it an ideal design tool to address the critical needs of improving the efficiency of the forced-air cooling process.
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Temperature at the center of the spheres (C)
Modeling Airflow through Vented Packages Containing Horticultural Products
Bottom sphere close to entrance wall Bottom sphere close to exit wall Top sphere close to exit wall
22.0 20.0 18.0 16.0 14.0 12.0 10.0 8.0 6.0 0.0
(a)
10.0
20.0
30.0
40.0
50.0
60.0
70.0
Time (min)
Top sphere close to exit wall (h = 14.2 W m−2 K−1)
Bottom sphere close to exit wall (h = 9.0 W m−2 K−1) (b)
Bottom sphere close to entrance wall (h = 22.8 W m−2 K−1)
FIGURE 27.25 (a) Temperature history at the center of three different spheres within the vertical layer along the main flow direction through the middle width of the packed structure (VF1 layer). (b) Time average value of the area-averaged heat transfer coefficient.
NOMENCLATURE Afs b cF Cp Dp
fluid–solid interfacial area (m2 ) model constant (Equation 27.9) form coefficient (Equation 27.10) constant pressure heat capacity (J kg1 K1 ) mean particle diameter (m)
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K ka nfs nsf p Rep ReK Ta 0 Ta
specific permeability (m2 ) thermal conductivity (J m1 s1 K1 ) unit normal vector directed from the fluid phase towards the solid phase unit normal vector directed from the solid phase towards the fluid phase pressure (N m2 ) particle diameter based Reynolds number permeability based Reynolds number temperature of phase a (K) spatial deviation of a local temperature with respect to the intrinsic averaged value at that particular location (K) velocity vector (m s1 ) spatial deviation of a local velocity with respect to the intrinsic averaged value at that particular location (m s1 ) Darcy or filtration velocity (m s1 ) averaging volume (m3 ) volume of phase a in the averaging volume (m3 ) porosity volume fraction of phase b density (kg m3 ) superficial average of a given function c within phase b (Equation 27.2) intrinsic average of a given function c within phase b (Equation 27.3) dynamic viscosity (N s m2 ) effective viscosity, Equation 27.13 (N s m2 ) heterogeneous thermal source (J m2 s1 ) homogeneous thermal source within the solid phase (J m3 s1 )
u 0 u uD V Va « «b r hcb i hcb ib m m ~ V Qs
REFERENCES 1. A.A. Kader. Postharvest biology and technology: An overview. In: A.A. Kader (ed.), Postharvest Technology of Horticultural Crops, 2nd edn., Publication 3311. Davis, CA: University of California, 1992, pp. 15–20. ´ mond, F. Mercier, S.O. Sadfa, M. Bourre´, and A. Gakwaya. Study of parameters affecting 2. J.P. E cooling rate and temperature distribution in forced-air precooling of strawberry. American Society of Agricultural Engineers 39 (6): 2185–2191, 1996. 3. A.G. Fikiin, K.A. Fikiin, and T.N. Bojkov. Thermal behavior of layers of fruits and vegetables in industrial packages and transport units during quick precooling. In: New developments in refrigeration for food safety and quality, IIR Proceedings Series Refrigeration Science and Technology, Paris: International Institute of Refrigeration & Lexington: ASAE Press, Vol. 6, 1996, pp. 254–266. 4. M.T. Talbot. An approach to better design of pressure-cooled produce containers. Proceedings of the Florida State Horticultural Society 101: 165–175, 1988. 5. J.F. Thompson, F.G. Mitchell, T.R. Rumsey, R.F. Kasmire, and C.H. Chrisosto. Commercial cooling of fruits, vegetables and flowers. University of California Division of Agriculture and Natural Resources Publication 21567, 1998, pp. 1–61. 6. G. Alvarez and G. Trystam. Design of a new strategy for the control of the refrigeration process: fruit and vegetables conditioned in a pallet. Food Control 6 (6): 345–347, 1995. 7. G. Alvarez and D. Flick. Analysis of heterogeneous cooling of agricultural products inside bins. Part I: aerodynamic study. Journal of Food Engineering 39: 227–237, 1999. 8. G. Alvarez and D. Flick. Analysis of heterogeneous cooling of agricultural products inside bins. Part II: thermal study. Journal of Food Engineering 39: 239–245, 1999. 9. C. Vigneault and B. Goyette. Design of plastic container opening to optimize forced-air precooling of fruit and vegetables. Applied Engineering in Agriculture 18 (1): 73–76, 2002.
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10. B.A. Anderson, A. Sarkar, J.F. Thompson, and R.P. Singh. Commercial scale forced air cooling of strawberries. Transactions of the ASAE 47 (1): 183–190, 2004. 11. L.R. Castro, C. Vigneault, and L.A.B. Cortez. Effect of container opening area on air distribution during precooling of horticultural produce. Transactions of the ASAE 47 (6): 2033–2038, 2004. 12. J.K. Wang and K. Tunpun. Forced-air precooling of tomatoes in cartons. Transactions of the ASAE 12 (6): 804–806, 1969. 13. J.J. Gaffney and C.D. Baird. Forced air cooling of bell peppers in bulk. Transactions of the ASAE 20 (5): 1174–1179, 1977. 14. M.A. Neale and H.J.M. Messer. Resistance of root and bulb vegetables to air flow. Journal of Agricultural Research 21: 221–231, 1976. 15. L.R. Wilhelm, D.W. Jones, and C.A. Mullins. Air flow resistance of snap beans. ASAE Paper 78-3058, 1978. 16. L.R. Wilhelm, F.D. Tompkins, and C.A. Mullins. Air flow resistance of bean and pea pods. Transactions of the ASAE 26 (3): 946–949, 1981. 17. K.V. Chau, J.J. Gaffney, C.D. Baird, and G.A. Church. Resistance to air flow of oranges in bulk and in cartons. Transactions of the ASAE 28 (6): 2083–2088, 1985. 18. Y. Xu and D. Burfoot. Simulating the bulk storage of foodstuffs. Journal of Food Engineering 39: 23–29, 1999. 19. M.L. Hoang, P. Verboven, M. Baelmans, and B.M. Nicolaı¨. Effect of process, box and product properties on heat and mass transfer during cooling of horticultural products in pallet boxes. In: ASAE Annual International Meeting. Sacramento, CA, 2001, Paper Number 013014. 20. R.G.M. van der Sman. Prediction of airflow through a vented box by the Darcy–Forchheimer Equation. Journal of Food Engineering 55: 49–57, 2002. 21. D.J. Tanner, A.C. Cleland, L.U. Opara, and T.R. Robertson. A generalised mathematical modelling methodology for design of horticultural food packages exposed to refrigerated conditions: part 1, formulation. International Journal of Refrigeration 25: 33–42, 2002. 22. D.J. Tanner, A.C. Cleland, L.U. Opara, and T.R. Robertson. A generalised mathematical modelling methodology for design of horticultural food packages exposed to refrigerated conditions: part 2, heat transfer modeling and testing. International Journal of Refrigeration 25: 43– 53, 2002. 23. M.L. Hoang, P. Verboven, M. Baelmans, and B.M. Nicolaı¨. A continuum model for airflow, heat and mass transfer in bulk of chicory roots. Transactions of the ASAE 46 (6): 1603–1611, 2003. 24. G. Alvarez, P.E. Bournet, and D. Flick. Two-dimensional simulation of turbulent flow and transfer through stacked spheres. International Journal of Heat and Mass Transfer 46: 2459–2469, 2003. 25. Q. Zou, U.O. Linus, and R.A. McKibbin. CFD modeling system for airflow and heat transfer in ventilated packaging for fresh foods: I. Initial analysis and development of mathematical models. Journal of Food Engineering 77 (4): 1037–1047, 2006. 26. Q. Zou, U.O. Linus, and R.A. McKibbin. CFD modeling system for airflow and heat transfer in ventilated packaging for fresh foods: II. Computational solution, software development, and model testing. Journal of Food Engineering 77 (4): 1048–1058, 2006. 27. M. Kaviany. Principles of Heat Transfer in Porous Media. 2nd edn. New York: Springer-Verlag, 1995, pp. 1–13. 28. S. Ergun. Fluid flow through packed columns. Chemical Engineering Progress 48 (2): 89–94, 1952. 29. F.A. Howes and S. Whitaker. The spatial averaging theorem revisited. Chemical Engineering Science 40: 1387–1392, 1985. 30. H.P.G. Darcy. Les Fontaines Publiques de la Ville de Dijon. Paris: Victor Dalmont, 1856. 31. M. Kaviany. Principles of Heat Transfer in Porous Media. 2nd edn. New York: Springer-Verlag, 1995, pp. 33 and 67. 32. S. Whitaker. Advances in theory of fluid motion in porous media. Industrial and Engineering Chemistry 61 (12): 14–28, 1969. 33. P. Forchheimer. Wasserbewegung durch Boden. Zeitschrift des Vereines Deutscher Ingenieure 45: 1736–1741 and 1781–1788, 1901. 34. J.C. Ward. Turbulent flow in porous media. Journal of Hydraulic Division, ASCE 90 (HY 5): 1–12, 1964.
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35. O. Coulaud, P. Morel, and J.P. Caltagirone. Numerical modeling of nonlinear effects in laminar flow through a porous medium. Journal of Fluid Mechanics 190: 393–407, 1988. 36. G.S. Beavers, E.M. Sparrow, and D.E. Rodenz. Influence of bed size on the flow characteristics and porosity of randomly packed beds of spheres. Journal of Applied Mechanics 40: 655–660, 1973. 37. M.R. Tek. Development of a generalized Darcy equation. Transactions of AIME 210: 376–377, 1957. 38. D.E. Wright. Nonlinear flow through granular media. Journal of Hydraulic Division, ASCE 94 (HY 4): 851–872, 1968. 39. J. de Vries. Prediction of non-Darcy flow in porous media. Journal of the Irrigation and Drainage Division, ASCE IR2: 147–162, 1979. 40. A. Dybbs and R.V. Edward. A new look at porous media fluid mechanics—Darcy to turbulent. In: J. Bear and V. Carapcioglu (eds.), Fundamentals of Transport Phenomena in Porous Media. Dordrecht: Martinus Nijhoff, 1984, pp. 199–256. 41. G.S. Beavers and E.M. Sparrow. Non-Darcy flow through fibrous porous media. Journal of Applied Mechanics, ASME 36: 711–714, 1969. 42. A. Bejan and D. Poulikakos. The non-Darcy regime for vertical boundary layer natural convection in a porous medium. International Journal of Heat and Mass Transfer 27: 717–722, 1984. 43. V. Prasad and A. Tuntomo. Inertial effects on natural convection in a vertical porous cavity. Numerical Heat Transfer 11: 295–320, 1987. 44. S.M. Hassanizadeh and W.G. Gray. High velocity flow in porous media. Transport in Porous Media 2: 521–531, 1987. 45. H.C. Brinkman. A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Applied Science Research A1: 27–34, 1947. 46. T.S. Lundgren. Slow flow through stationary random beds and suspensions of spheres. Journal of Fluid Mechanics 51 (2): 273–299, 1972. 47. G. Neale and W. Nader. Practical significance of Brinkman’s extension of Darcy’s law. The Canadian Journal of Chemical Engineering 52: 475–478, 1974. 48. C.K.W. Tam. The drag on a cloud of spherical particles in low Reynolds number flow. Journal of Fluid Mechanics 38 (3): 537–546, 1969. 49. R.C. Givler and S.A. Altobelli. A determination of the effective viscosity for the Brinkman– Forchheimer flow model. Journal of Fluid Mechanics 258: 355–370, 1994. 50. K. Vafai and C.L. Tien. Boundary and inertia effects on flow and heat transfer in porous media. International Journal of Heat and Mass Transfer 24: 195–203, 1981. 51. G.S. Beavers, E.M. Sparrow, and D.E. Rodenz. Influence of bed size on the flow characteristics and porosity of randomly packed beds of spheres. Journal of Applied Mechanics 40: 655–660, 1973. 52. D. Vortmeyer and J. Schuster. Evaluation of steady flow profiles in rectangular and circular packed beds by a variational method. Chemical Engineering Science 38 (10): 1691–1699, 1983. 53. H.S. Mickley, K.A. Smith, and E.I. Korchak. Fluid flow in packed beds. Chemical Engineering Science 20: 237–246, 1965. 54. I.F. Macdonald, M.S. El-Sayed, K. Mow, and F.A.L. Dullien. Flow through porous media: the Ergun equation revisited. Industrial Engineering and Chemical Fundamentals 18: 199–208, 1979. 55. J. Bear. Dynamics of Fluids in Porous Media. New York: Elsevier, 1972, pp. 181–182. 56. T. Masuoka and Y. Takatsu. Turbulence model for flow through porous media. International Journal of Heat and Mass Transfer 39 (13): 2803–2809, 1996. 57. D.A. Nield. Comments on ‘‘Turbulence Model for Flow through Porous Media.’’ International Journal of Heat and Mass Transfer 40 (10): 2449, 1997. 58. B.V. Antohe and J.L. Lage. A general two-equation macroscopic turbulence model for incompressible flow in porous media. International Journal of Heat and Mass Transfer 40 (13): 3013–3024, 1997. 59. D.A. Nield. The limitations of the Brinkman–Forchheimer equation in modeling flow in a saturated porous medium and at an interface. International Journal of Heat Fluid Flow 12: 269–272, 1991. 60. M.H.J. Pedras and M.J.S. de Lemos. On the definition of turbulent kinetic energy for flow in porous media. International Comunications in Heat and Mass Transfer 27 (2): 211–220, 2000. 61. A. Nakayama and F. Kuwahara. A macroscopic turbulence model for flow in a porous medium. Journal of Fluids Engineering, ASME 121: 427–433, 1999.
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62. N. Wakao and S. Kaguei. Heat and Mass Transfer in Packed Beds. New York: Gordon Breach Science, 1982. 63. M. Quintard and S. Whitaker. Theoretical analysis of transport in porous media. In: K. Vafai (ed.), Handbook of Porous Media. New York: Marcel Dekker, 2000, pp. 1–52. 64. M. Kaviany. Principles of Heat Transfer in Porous Media. 2nd edn. New York: Springer-Verlag, 1995, pp. 119–126, 157–191, and 391–404. 65. C.D. Baird and J.J. Gaffney. A numerical procedure for calculating heat transfer in bulk loads of fruits and vegetables. ASHRAE Transactions 82 (2): 525–540, 1976. 66. R.B. Bird, W.E. Stewart, and E.N. Lightfoot. Transport Phenomena. 1st edn. New York: John Wiley & Sons, 1960. 67. G. Alvarez, G. Letang, and F. Billiard. Modellisation du transfert de chaleur et de matie`re au cours de la re´frige´ration des fruits et le´gumes conditionne´s en palette. In: Refrigeration and the quality of fresh vegetables, IIR Proceedings Series Refrigeration Science and Technology. International Institute of Refrigeration, Paris, 1994, 5: 111–115. 68. R. Adrian. Particle-imaging techniques for experimental fluid mechanics. Annual Review of Fluid Mechanics 23: 261–304, 1991. 69. W.L. Lim, Y.T. Chew, T.C. Chew, and H.T. Low. Pulsatile flow studies of a porcine bioprosthetic aortic valve in vitro: PIV measurements and sheare-induced blood damage. Journal of Biomechanics 34: 1417–1427, 2001. 70. B.B. Lieber, V. Livescu, L.N. Hopkins, and A.K. Wakhloo. Particle image velocimetry for wholefield measurement of ice velocities. Cold Regions Science and Technology 26: 97–112, 2002. 71. L.M. Hopkins, J.T. Kelly, A.S. Wexler, and A.K. Prasad. Particle image velocimetry measurements in complex geometries. Experiments in Fluids 29: 91–95, 2000. 72. J.T. Kelly, A.D. Prasad, and A.S. Wexler. Detailed flow patterns in the nasal cavity. Journal of Applied Physiology 89: 323–327, 2000. 73. M.J. Ferrua and R.P. Singh. Designing a model of strawberry package for particle image velocimetry. Paper presented at the 2004 IFT Annual Meeting, Las Vegas, NV, July 12–16, 2004. No. 99B-10. 74. M.J. Ferrua and R.P. Singh. Measurement of fluid flow around solid objects using particle image velocimetry. In: Proceedings of FOOMA—International Food Machinery and Technology Exhibition, Tokyo, Japan, 2006, pp. 241–244. 75. M. Nijemeisland and A.G. Dixon. Comparison of CFD simulations to experiment for convective heat transfer in a gas–solid fixed bed. Chemical Engineering Journal 82: 231–246, 2001.
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CFD Modeling of Indoor Atmosphere and Water Exchanges during the Cheese Ripening Process Pierre-Sylvain Mirade
CONTENTS 28.1 28.2 28.3
Introduction ............................................................................................................. 697 Operation of Cheese Ripening Rooms..................................................................... 699 Airflow Patterns in Cheese Ripening Rooms........................................................... 700 28.3.1 Description of the CFD Models Constructed............................................. 700 28.3.2 Heterogeneity in Airflow Patterns .............................................................. 702 28.3.2.1 Air Velocity Fields Calculated .................................................... 703 28.3.2.2 Validation of the Numerical Results........................................... 704 28.3.3 Effect of Design of Blowing Duct on Ventilation Homogeneity ................ 708 28.3.3.1 CFD Results ............................................................................... 708 28.3.3.2 Validation of the CFD Results ................................................... 709 28.4 Indoor Atmosphere in Cheese Ripening Rooms...................................................... 709 28.4.1 Air Temperature and Relative Humidity Fields ......................................... 709 28.4.2 Mean Age of Air......................................................................................... 711 28.4.3 Gas Circulation........................................................................................... 712 28.4.3.1 CFD Modeling of Gas Transport ............................................... 713 28.4.3.2 Comparison of the Two Methods of Gas Injection .................... 713 28.5 Consequences on Water Exchanges of Cheeses ....................................................... 715 28.5.1 Heat and Water Transfer Coefficients ........................................................ 716 28.5.2 Water Losses of Real Cheeses..................................................................... 718 28.5.3 Simulation of the Coupling between Airflow and Water Losses ................ 719 28.6 Conclusion ............................................................................................................... 723 Acknowledgments .............................................................................................................. 723 Nomenclature ..................................................................................................................... 724 References .......................................................................................................................... 724
28.1 INTRODUCTION Approximately a third of the world’s milk production is used in cheese manufacture, which is a way of preserving milk as it is highly perishable. Cheese is a highly nutritious food that offers a diversity of flavors and textures [1]. In the 25 countries of the European Union, total 697
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cheese production in 2004 exceeded 8,200,000 tonnes, almost 60% of which was in Germany, France, and Italy. Indeed, France is considered the quintessential ‘‘cheese country,’’ with over 400 different varieties of ripened cheese and a consumption per capita reaching 25 kg a year, i.e., one of the highest consumption levels of ripened cheese in the world. In the successive operations involved in cheese manufacture—standardization of milk, enzymatic or acid coagulation, draining and ripening—the ripening process is crucial, since this is the step where texture, aroma, and flavor (i.e., cheese quality) develop. Cheese ripening is an outcome of several biochemical and metabolic processes including proteolysis, which is the most complex, glycolysis and lipolysis. It is therefore crucial to control both airflow, i.e., air velocity, air change rate, and renewal in new air, and climatic conditions (air temperature and relative humidity, gas concentration) inside the cheese ripening rooms, since this will determine both the efficiency and the homogeneity of cheese ripening and the water losses of the cheeses. However, it is difficult to achieve homogeneity in the distribution of climatic conditions at every single point of a ripening chamber. Consequently, industrial plants experience significant differences in the distribution of indoor atmospheric conditions, which causes damage to the cheeses being ripened, as has often been underlined in the few studies published on this topic. For example, the problem of damage to crust formation observed inside an Emmenthal ripening room was attributed, by the author, to differences of over 10% in the relative humidity field [2]. Air velocities ranging from less than 0.05 to 0:40 m s1 were measured inside the stacks of 10 cm diameter cheese models filling an 84 m3 ripening room, thus leading to a threefold increase in the heat and water transfer coefficients [3]. Significant heterogeneity in air velocity distribution, with marked differences in the cooling of the cheeses due to air velocities ranging from 0.1 to over 2:5 m s1 , was also highlighted in two cheese-cooling stores [4]. The heterogeneity in climatic conditions that exists in ripening chambers means that cheese-makers have to regularly move the cheeses to achieve even water losses and a uniform appearance of the cheese surface. Nevertheless, only a few studies on this very real problem can be found in the literature because they are performed directly by industrial manufacturers or else by scientists or engineers in close collaboration with them, and therefore they remain confidential. Even books dealing with cheese ripening processes do not provide accurate information on the interrelationship between ventilation, indoor atmosphere, and cheese quality, in which the authors only recommend a homogeneous atmosphere with low air circulation around the cheeses (air velocity not exceeding 0:1 m s1 ), while maintaining a ‘‘high enough’’ air change rate per hour in the plant [5,6]. In fact, the role played by ventilation at whole-room level is complex and remains poorly quantified. Air circulation on the one hand allows the evacuation of the heat and moisture produced by the cheeses inside the stacks and, on the other hand, determines both water losses and gas concentrations in the atmosphere closely surrounding the cheeses, which itself influences the cheese ripening process. For example, during the manufacturing of the Camembert cheese, the presence of ammonia and oxygen in the atmosphere of the ripening room makes it easier to reduce acidity on the cheese surface [7] and for the Penicillia to grow [8]. Furthermore, the presence of carbon dioxide in the indoor atmosphere is reported to increase the opening of the curd of hard cheeses by stimulating propionic fermentation [6]. Cheese ripening was originally performed in caves or in vaulted cellars often underground, where natural ventilation with low air velocity allowed a perfect control of the indoor atmospheric conditions throughout the ripening time, which can last from a few days to several months depending on the cheese-making technology. AOC Roquefort cheese is still produced under these conditions inside underground cellars fitted out under an immense mass of fallen rocks in which humid and fresh air naturally penetrates through long faults. As a result of the industrialization of the manufacture of cheese that has occurred over the last
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50 years, modern ripening rooms are now being fitted with mechanical ventilation in combination with air temperature and relative humidity conditioning. Air distribution inside the ripening chambers is increasingly realized through blowing ducts made of textile materials in order to ensure low air velocities and therefore a correct treatment of the products. There are various types of textile blowing ducts: some are partially or fully porous, while others are fitted with holes or slits. Although their design obviously impacts on airflow patterns inside industrial plants, very few blowing duct design studies can be found in the literature, especially in relation to the cheese ripening process [9]. The only closely related studies published deal with the effect of the location of blowing areas on the effectiveness of ventilation in relation to comfort in the buildings [10] or on the efficiency of contaminant removal in clean rooms [11]. Other interesting studies concern the assessment of airflow within large rooms [12–14] or the internal climate in greenhouses [15,16]. The authors mostly combined experimental investigation with CFD modeling to assess airflow and indoor atmosphere patterns in all these studies. This chapter presents recent studies dealing with cheese ripening chambers ventilated through blowing ducts made of textile materials as a review of the modeling of airflow and indoor atmosphere (air temperature and relative humidity fields, gas concentrations) patterns, while evaluating the consequences on water exchanges of cheeses bathing in this atmosphere.
28.2 OPERATION OF CHEESE RIPENING ROOMS The geometry and operation of modern cheese ripening rooms are relatively simple. The airflow conditioned in temperature and relative humidity is generally supplied continuously through one or several circular blower ducts made of textile materials and depending on the width of the plant, located level with the ceiling. The type and design of the blower ducts change according to cheese variety and sometimes in relation to the ripening phase, such as at the end of ripening just before the packaging step. After being introduced through the blower ducts, the air circulates continuously around the cheeses placed into stacks whose height is generally about half the height of the ripening room, thereby exchanging heat and, above all, moisture. The air is then extracted in the lower part of the room level with the floor via the air conditioning system. This is located either at one end of the plant or, more rarely, in the middle. Figure 28.1 provides an illustration of the typical geometry of a modern cheese ripening room, representing a pilot ripening room built in our laboratory whose operation is truly representative of current standards in industry. All the results presented in this paper were obtained in this plant, and therefore a full description of its geometry and operation has been given. This pilot ripening room was 5.8 m long, 4.95 m wide, and 2.95 m high, which give an overall volume of about 84 m3 . As this pilot room was to be used for the assessment of airflow patterns and not the heat and water transport stemming from the interaction between the cheeses and their surroundings, real cheeses were replaced by empty cans 10 cm in diameter and 4.4 cm high, i.e., inert objects presenting the same resistance against air circulation. Six rows (visually three, since they were placed two by two) of seven stacks of 16 racks of 21 cans (i.e., a total of 14,112 cans) were then installed inside this room to obtain a filling pattern that was representative of current industrial practice. Free space, i.e., the height between two consecutive racks, was 10 cm. An air conditioning system composed of two fans and two batteries was installed in a space located above the ceiling of the pilot ripening room. This controlled the temperature and flow rate of the air blown into the room. Inside the pilot ripening room, the ventilation system was designed to mimic a common industrial configuration, i.e., an air conditioning system placed at the end of the room, extracting air in its lower part and blowing the conditioned air through a duct in its upper part. This system was
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composed of a 340 mm blowing duct made of textile material and a 315 mm suction duct. In its standard configuration, the blowing duct running along the ceiling at half-width in the room was fitted on each side with three rows of several hundred holes 6 mm in diameter. Blowing ducts fitted with eight rows of more than one thousand holes 3 mm in diameter or with one row of several tens of holes 20 mm in diameter were also used to ventilate the pilot room. After being blown into the room, the air was extracted at 35 cm from the ground by means of a suction duct placed against a vertical wall at half-width in the room. The suction duct was connected to the space located above the ceiling of the pilot ripening room where the fans were installed. The full airflow rate blown into the room was 1600 m3 h1 , i.e., an air change rate of 19 volumes per hour, which corresponds to normal industrial practice. The air velocity magnitudes were 11 m s1 at the output of the holes, regardless of the blowing duct considered.
28.3 AIRFLOW PATTERNS IN CHEESE RIPENING ROOMS Few experimental and numerical studies of the overall operation of modern cheese ripening rooms are available in the literature because most of them are confidential as a result of being performed directly by industrial manufacturers or jointly with scientists. Nevertheless, this section presents CFD results validated by experimental measurements and performed at the laboratory, highlighting heterogeneity in air velocity distribution inside the pilot ripening room whose geometry is depicted in Figure 28.1 [3,9,17].
28.3.1 DESCRIPTION OF
THE
CFD MODELS CONSTRUCTED
Based on the geometrical configuration of the pilot ripening room, the Fluent 6.0.20 code [18] was used to construct numerical models based on an unstructured 3D mesh of about 1.2 million hexahedral and tetrahedral cells. The inside of the blowing and extraction ducts was considered as being outside the computational domain, thus air inflow corresponded to the Rows of stacks of cheese models
Blowing duct fitted with holes
System for automatically moving the sensors
Airflow rate: 1600 m3 h−1
Data logger
Stacks of racks of cheese models
Blowing duct Extraction duct
Extraction duct
(a)
(b)
FIGURE 28.1 Illustration of the geometry of the pilot ripening room constructed in the laboratory: (a) an inside view and (b) a top view.
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output from the holes of the blowing duct and air outflow to the bottom of the extraction duct. About 5000 hexahedral cells were used for meshing each of the rows of the stacked racks of cheese models. Each hole of the blowing duct was meshed with at least eight triangular cells, while the outlet area was meshed with 328 triangular cells. To make it possible to link the fine mesh of the holes to the coarser mesh built into the other parts of the blowing duct, hexahedral ‘‘boundary layer’’-type cells were placed in the vicinity of the holes. In the inlet area corresponding to the holes, an air velocity of 11 m s1 determined from in situ measurements performed with a hot-film anemometer (Model 8465, TSI, Minnesota) and a turbulence rate arbitrarily valued at 10% were specified. A classical outflow-type boundary condition was applied at the bottom of the extraction duct. This kind of boundary condition is conventionally used to model flow exits where details of the flow velocity and pressure are unknown prior to solution of the flow problem. During the numerical calculations, airflow was considered as steady, incompressible, isothermal, and turbulent. To assess the sensitivity of the calculations to turbulence modeling, main flow turbulence was taken into account using the very popular standard k« model [19], the renormalization group (RNG) k« model [20], or the kv model [21] far from the walls, which were assumed to be smooth and where the standard wall function was applied. The SIMPLE algorithm [22] was chosen for coupling pressure and velocity and introducing pressure into the continuity equation. The first-order or second-order upwind differencing scheme was also chosen in the computational models as a discretization scheme for the convection terms of each governing equation. Although first-order schemes are known to increase numerical discretization error and therefore to give less accurate results, especially when the flow is not aligned with the mesh, better convergence of calculation is obtained when using first-order versus second-order schemes [23]. Calculations were performed on an Athlon 1900XP þ PC with 1.5 GB of RAM and computation time was about 25 to 28 h depending on the model being solved. In all the models, the material filling the pilot ripening room was taken into account as a porous medium. Porous media are modeled by adding a momentum source term to the standard fluid flow equations. The source term is composed of two parts: a viscous loss term (the first term on the right-hand side of Equation 28.1) and an inertial loss term (the second term on the right-hand side of Equation 28.1). In the case of a simple homogeneous porous medium, source term Si is formulated in the CFD code following the equation: Si ¼
m 1 vi þ C2 rjvi jvi a 2
(28:1)
where i x, y, z. To model turbulent flows through packed beds, Ergun [24] established a semiempirical correlation applicable over a wide range of Reynolds numbers. Comparing the Ergun equation with Equation 28.1, the permeability a and inertial loss coefficient C2 can be identified as a¼
D2p «3 150 (1 «)2
(28:2)
3:5 (1 «) Dp «3
(28:3)
C2 ¼
where « is defined as the ratio of the volume of voids divided by the volume of the packed bed region.
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Although a stack of cheeses is not exactly like a packed bed owing to distances between cheeses varying greatly, unlike the elements filling a packed bed, and although the cheeses could not be considered as spherical particles, the Ergun formulation was nevertheless applied to the stack. However, the Dp and « values were assumed to be variables according to the three spatial directions due to the anisotropy of the porous medium. Thus, in the purely empirical approach developed, Dp was redefined as being a characteristic length of the elements filling the volume considered as a porous medium, and « remained a void fraction but defined as the surface of voids divided by the total surface of the face of the porous volume perpendicular to the flow direction under study. In the stack of cheese models, the parameter Dp corresponded to the diameter of one can in the vertical direction and to its height in both transverse and longitudinal directions. The void fraction « could be easily calculated in relation to the vertical direction from the geometry of the stack. Hence, a value of 40% was determined [9]. On the other hand, for the transverse and longitudinal directions, the « values were identified by visually comparing the measured fields to the air velocity fields calculated from many CFD calculations taking into account the filling of the ripening room as a porous medium with void fractions equal to 40% in the vertical direction and to 60%, 70%, 80%, 85%, 90%, or 95% in the other two directions. Indeed, the calculation of the void fraction from the actual geometry of one stack proved impossible in these directions due to serious difficulties in accurately determining the total surface of cans that was perpendicular to the air circulation and consequently blocked it. Hence, a value of 90% was determined further to the visual comparison of the calculated and measured air velocity fields, meaning a very poor resistance of the cheese models against the air circulation in the transverse and longitudinal directions [9]. This poor resistance resulted from the large free spaces between the cans, particularly between the top of the cans of one rack and the bottom of next rack located above. From a scientific point of view, this method of adjusting the coefficients in the porous medium is far from satisfactory. A methodology based on an anisotropic megaporous medium coupled with the Darcy–Forchheimer model is still in progress in the laboratory; in this approach, viscous resistance, inertial resistance, and porosity factors had to be adjusted according to the three spatial directions. The first results obtained showed that in a food industry setting such as a stack of cheeses, the viscous resistance factor was equal to zero whatever the spatial direction considered [25]. This amounts to neglecting the Darcy term in comparison with the Forchheimer term in the expression of the momentum source added to the standard fluid flow equations. In other words, it means that the mean static pressure gradient is linear with the squared velocity within the porous medium, and not proportional to the velocity as expressed by the Darcy formulation. This assumption is often made in bioclimatology when assessing interactions between airflows and plants in greenhouses or wind circulation in forests [26].
28.3.2 HETEROGENEITY IN AIRFLOW PATTERNS The air velocity fields calculated and measured within the pilot ripening room were represented as colored velocity intensity maps ranging from ‘‘white’’ color areas in which air velocities were lower than 0:1 m s1 to ‘‘black’’ color areas where air velocities exceeded 0:4 m s1 . To make the flow pattern easier to assess inside the stacks where air velocities were very low, all magnitudes higher than 0:4 m s1 were plotted in black, including all those that reached 1 m s1 in the vicinity of the outlet holes of the blowing duct. Given the symmetry in the distribution of air velocity according to a vertical plane crossing the blowing duct, only the half-width of the room is plotted in Figure 28.2 through Figure 28.5.
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249 209 169 129 Air velocity (m s−1)
89
>0.4 0.3−0.4
Height in the pilot ripening room (cm)
289
49
0.2−0.3 0.1−0.2 0−0.1
9 262
224
186
148
110
72
34
Width in the pilot ripening room (cm)
FIGURE 28.2 Vertical section located at half-length of the pilot ripening room showing the calculated air velocity field around and through the stacks for a blower duct made of textile materials and using holes 6 mm in diameter. The bold rectangles represent the silhouette of the stacks of cheese models, the circle indicates the location of the blowing duct, and the coordinates given are in relation to the location of the walls. In the upper left-hand corner, a top view shows where the section crosses the room. Given the symmetry of the room, only a half-width is depicted.
28.3.2.1
Air Velocity Fields Calculated
Figure 28.2 shows the air velocity patterns simulated around and into the stacks according to a vertical section located at half-length in the pilot ripening room and obtained from a CFD model accounting for turbulence using the standard k« model and the first-order differencing scheme for the blowing duct with holes 6 mm in diameter [17]. This figure shows that the air blown through the holes flows along the ceiling and the lateral wall at a velocity higher than 0:4 m s1 (the values even reached 1 m s1 in proximity to the blowing duct), before being separated into two bodies when reaching the top of the side stacks. From here, the first body of air continues to flow down along the wall before entering the stacks, while the second body of the airflow appears to travel towards the blowing duct, giving rise to a swirl above the side stacks with air velocities equal to 0:2 m s1 . The swirl leads to the formation of a poorly ventilated area above the stack located at half-width in the room and underneath the blowing duct, and in which air velocities do not exceed 0:1 m s1 . In the passages between the rows of stacks, the numerical model calculated air velocities ranging from 0.1 to 0:2 m s1 , with a slight increase in velocity when approaching the ground. Inside the side stacks of the cheese models, a marked gradient in relation to height appears as the air velocities peak at 0:3 m s1 in the lower part of the stack while the upper part is clearly poorly ventilated, except in the last rack at the top of the stack owing to the swirl located above. Furthermore, ventilation within the stack located in the middle of the room was clearly poor whatever the height considered (Figure 28.2). Thorough analysis of the air velocities calculated at that site revealed that more than half these values were below
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289
209
169
129
Air velocity (m s−1)
89
>0.4 0.3−0.4
49
0.2−0.3
Height in the pilot ripening room (cm)
249
0.1−0.2 9
0−0.1 262
224 186 148 110 72 Width in the pilot ripening room (cm)
34
FIGURE 28.3 Vertical section located at half-length of the pilot ripening room showing the measured air velocity field around and through the stacks for a blower duct made of textile materials and using holes 6 mm in diameter. The bold rectangles represent the silhouette of the stacks of cheese models, the circle indicates the location of the blowing duct, and the coordinates given are in relation to the location of the walls. In the upper left-hand corner, a top view shows where the section crosses the room. Given the symmetry of the room, only a half-width is depicted. Each intersection line corresponds to a measurement point.
0:05 m s1 . The heterogeneity in air distribution highlighted by these calculations certainly has a strong impact on cheese ripening factors such as heat and water exchanges. The other calculated values confirm the airflow pattern depicted in Figure 28.2, i.e., poor ventilation in the stacks located in the middle of the chamber and a marked gradient in the side stacks, but with a slight variation in magnitude as a result of a 3D effect due to the presence of the suction duct at one end of the pilot ripening room. 28.3.2.2
Validation of the Numerical Results
To rapidly measure the air velocities above the stacks of cheese models and between the rows of the stacked racks, a fast method set up at the laboratory [27] was applied using a specially built system (Figure 28.1) to support and automatically move a measurement system at a slow and constant velocity of 1:5 cm s1 . The measurement system comprised a multidirectional hot-film anemometer (Model 8465, TSI, St. Paul, MN) connected to a data logger (Model DT600, DataTaker, Rowville, Australia). Inside the stacks where automatic and constant movement of the probes was impossible, recordings of air velocity had to be averaged over at least 40 s at each measurement point to obtain a constant value for mean velocity. The sensors (Model 8475, TSI) were moved into the free space of 50 mm between two stacked racks and positioned at the exact measurement point via a telescopic antenna. To easily connect the measurements performed with the two methods, a regular experimental mesh was set up in the three spatial directions, with one measurement point each 19 cm in width, 21 cm in length, and 20 cm in height.
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249 209 169 Air velocity (m s−1) >0.4
129
0.3−0.4
89
0.2−0.3 0.1−0.2
Height in the pilot ripening room (cm)
289
49
0−0.1 262 (a)
224
186
148
110
72
9 34
Width in the pilot ripening room (cm)
249
209
169 Air velocity (m s−1)
129
>0.4
89
0.3−0.4 0.2−0.3
49
Height in the pilot ripening room (cm)
289
0.1−0.2 0−0.1
9 262
(b)
224
186
148
110
72
34
Width in the pilot ripening room (cm)
FIGURE 28.4 Vertical section located at half-length of the pilot ripening room showing the calculated air velocity field and through the stacks for a blower duct made of textile materials and using holes (a) 3 mm in diameter and (b) 20 mm in diameter. The bold rectangles represent the silhouette of the stacks of cheese models, the circle indicates the location of the blowing duct, and the coordinates given are in relation to the location of the walls. In the upper left-hand corner, a top view shows where the section crosses the room. Given the symmetry of the room, only a half-width is depicted.
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249
209
169
129
Air velocity (m s−1)
89
>0.4 0.3−0.4 0.2−0.3
Height in the pilot ripening room (cm)
289
49
0.1−0.2 0−0.1
9 262
(a)
224 186 148 110 72 Width in the pilot ripening room (cm)
34
289
209
169
129
Air velocity (m s−1) >0.4
89
0.3−0.4 0.2−0.3
Height in the pilot ripening room (cm)
249
49
0.1−0.2 0−0.1
9 262
(b)
224 186 148 110 72 Width in the pilot ripening room (cm)
34
FIGURE 28.5 Vertical section located at half-length of the pilot ripening room showing the measured air velocity field around and through the stacks for a blower duct made of textile materials and using holes (a) 3 mm in diameter and (b) 20 mm in diameter. The bold rectangles represent the silhouette of the stacks of cheese models, the circle indicates the location of the blowing duct, and the coordinates given are in relation to the location of the walls. In the upper left-hand corner, a top view shows where the section crosses the room. Given the symmetry of the room, only a half-width is depicted. Each intersection line corresponds to a measurement point.
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From a qualitative point of view, Figure 28.3 that shows the air velocities measured at half-length of the room confirms the results of the CFD model, i.e., higher air velocities along the ceiling and the side wall, the presence of a large swirl above the stacks, a marked gradient in air velocity distribution according to height in the side stacks and poor ventilation in the stacks located in the middle. Comparison between Figure 28.3 and Figure 28.2 shows that the CFD model quite correctly simulates the airflow patterns inside the room and the stacks of cheese models, but with some discrepancies in the prediction of airflow magnitudes. Indeed, the numerical model underestimates the air ventilation level in areas with strong gradients, such as in the swirl or at the side stacks. Three possible explanations for this limited accuracy may be put forward: (i) the integration into the model of the standard k« model and of the first-order upwind differencing scheme, (ii) the use of porous media, which only roughly describe the preferential paths for airflow over the cheese models on the racks, or (iii) the potential impossibility of obtaining truly independent results due to an insufficiently fine mesh despite the 1.2 million cells used in the simulations [28]. Dependence on mesh size was impossible to quantify because no additional cells could be added to the model due to the limited amount of memory size on the computer used. From a quantitative point of view, when considering the 6 mm blowing duct, Table 28.1 indicates that the discrepancy between simulation and measurement calculated from 4200 points of comparison came to about 0:12 m s1 in the half-volume of the room, 0:07 m s1 in the right-hand-side stacks, and 0:03 m s1 in the stacks located in the middle, when using the standard k« model for modeling turbulence and the first-order upwind differencing method as discretization scheme for the convection terms in the equations. As can be seen in TABLE 28.1 Mean Discrepancies in Air Velocity Calculated as the Absolute Value of the Difference between the Calculated and Measured Magnitudes Divided by the Number of Points of Comparison, According to Model Used for Solving the Problem and Blowing Duct Tested Blowing Duct Tested Hole Diameter (mm) 6 6 6 6 6 20 20 3 3 a
Models Used for Solving Turbulence Modeling=Discretization Schemea k–«=first order k–v=first order RNG k–«=first order k–«=second order k–v=second order k–«=first order k–v=first order k–«=first order k–v=first order
Convergence Reached
Mean Discrepancy between Measured and Calculated Air Velocity (m s1 )
Yes=No
Right-Hand-Side Stacks
Stacks Located in the Middle
Half-Volume of the Ripening Room
Yes Yes No No No Yes Yes Yes Yes
0.07 0.06 0.05b 0.05b 0.06b 0.08 0.07 0.07 0.06
0.03 0.03 0.02b 0.03b 0.03b 0.06 0.05 0.03 0.03
0.12 0.12 0.13b 0.12b 0.13b 0.15 0.15 0.12 0.11
The discretization scheme used in the numerical calculations was either a first-order or second-order upwind differencing scheme. b Since convergence was not reached and divergence did not occur (the residuals remained stable around a value significantly lower than the value at the first iteration but slightly higher than the convergence criterion), discrepancy between calculation and measurement was evaluated when the residuals were minimal during solving.
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Table 28.1, changing the turbulence model and working with second-order schemes do not improve the accuracy of the prediction of air velocity in the room or in the stacks, possibly due to the mesh created which did not have enough cells to give more accurate results. Regardless of the models chosen, the discrepancy between calculation and measurement still ranged from 0.12 to 0:13 m s1 in the half-volume of the room due to the poor performance of modeling in the swirl area, from 0.05 to 0:07 m s1 in the side stacks and around 0:03 m s1 in the other stacks. On the other hand, computation time increased dramatically and convergence=divergence of computation did not occur when using a second-order discretization scheme or the RNG k« turbulence model; the residuals remained high and stable around a value lower than the value at the first iteration, but slightly higher than the convergence criterion. Hence, the standard k–« model and the first-order upwind differencing scheme proved to be robust, time-saving and, given the mesh built, as accurate as the other models and schemes tested. The mean discrepancy in the air velocity prediction was 0:12 m s1 in the half-volume of the room and 0:05 m s1 inside the stacks.
28.3.3 EFFECT
OF
DESIGN
OF
BLOWING DUCT ON VENTILATION HOMOGENEITY
In the same pilot ripening room, the influence of the design of the blowing ducts made from textile materials on both ventilation homogeneity and ventilation level was experimentally and numerically tested through three blowing ducts with holes of different diameters: 3, 6, and 20 mm, at constant total air inflow rate and velocity magnitudes at the output from the holes [9]. 28.3.3.1
CFD Results
Figure 28.4 shows the air velocity field calculated around and into the stacks of cheese models according to a vertical section located at half-length in the pilot ripening room, for the blowing ducts with holes 3 mm in diameter (Figure 28.4a) and 20 mm in diameter (Figure 28.4b), respectively. CFD results concerning the 6 mm blowing duct are depicted in Figure 28.2. Although the airflow rate blown into the room and the velocity magnitudes at the output from the holes were the same in all three configurations, analysis of Figure 28.4 and Figure 28.2 reveals different ventilation levels and ranging heterogeneity around the cheese models. However, regardless of the design of the blowing duct, qualitatively speaking, air circulates in the same way once blown through the holes, giving rise to velocities higher than 0:4 m s1 along the ceiling and the lateral wall, a poor ventilation underneath the blowing duct and in the stack located in the middle of the plant, a large swirl above the stacks, and a marked gradient in air velocity distribution with height in the side stacks. On the other hand, the gradient of air velocities varies with the diameter of the blowing duct holes: smaller holes gave lower air velocities and lower heterogeneity around the cheese models. At a duct hole diameter of 3 mm, the air velocities ranged from less than 0.1 to 0:3 m s1 (Figure 28.4a), whereas with a hole diameter of 6 mm they ranged from less than 0:1 m s1 to nearly 0:4 m s1 (Figure 28.2), and with a hole diameter of 20 mm, peak air velocity even reached 0:6 m s1 (Figure 28.4b). This variation probably results from the different number of holes between the three configurations. Indeed, reducing the hole diameter implies a strong increase in the number of holes in order to maintain the same airflow rate blown into the chamber, since there was no variation in air velocity magnitudes at the hole outlets. Consequently, the number of the air jets around the blowing duct increases, therefore increasing friction between them, causing a loss of energy in the airflow that reaches the top of the side stacks and penetrates inside them with a velocity that decreases further as the hole diameter tends towards 3 mm. Increasing the hole diameter contributes to an increase in the inlet jet momentum, thus allowing the jet to remain stable for longer and enabling high velocities to predominate until the airflow reaches the top of the side stacks.
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28.3.3.2
709
Validation of the CFD Results
Figure 28.5a, Figure 28.3, and Figure 28.5b show the air velocity values measured at halflength of the pilot ripening room when ventilated with the 3 mm blowing duct, the 6 mm blowing duct, and the 20 mm blowing duct, respectively. Comparison between numerical and experimental air velocity values reveals a quite correct qualitative prediction of the airflow patterns inside the room and the stacks of cheese models, but with an underestimation of the air ventilation level in areas with strong gradients, such as in the vicinity of the blowing duct where the friction phenomena between the different jets take place and in the swirl located above the stacks or in the lower part of the side stack. In addition, Figure 28.5a and Figure 28.5b confirm the numerical results indicating that an increase in blowing duct hole diameter from 3 to 20 mm leads to an increase in ventilation level and air velocity gradient in the side stack. Table 28.1, which also details absolute values for the mean discrepancy between calculation and measurement for the 3 and 20 mm diameter blowing ducts, again underlines that coupling the k« turbulence model and the first-order upwind differencing scheme constitutes a good compromise solution for saving time while yielding accurate prediction of air velocities. Although the parameters of the porous medium modeling the filling of the pilot ripening room were previously adjusted based on the results obtained with the 6 mm blowing duct, the accuracy of the numerical models for the other two blowing ducts was absolutely satisfactory. The greatest discrepancy observed between prediction and measurement, which was 0:15 m s1 , corresponded to the 20 mm blowing duct, i.e., the hole diameter leading to the strongest gradient in air velocities within the side stack and in the swirl area visible above the same stack. Using the k« or kv model and especially the first-order differencing scheme to predict velocity magnitudes in this configuration performed poorly compared to the two other cases in which velocity gradients were lower, thereby increasing mean discrepancy with the measured values. Better accuracy would almost certainly have been achieved by working with the RNG k« model or=and second-order discretization schemes, provided that convergence of calculations had been fully satisfied, but this condition was never fulfilled (Table 28.1). Although no variation occurred in the total airflow rate blown in the ripening room nor in the velocity magnitudes at the output from the holes, both experimental and numerical results revealed that changing the hole diameter led to differences in ventilation levels in the chamber and around the cheeses, almost certainly due to a variation in the friction phenomena occurring between the different air jets in the vicinity of the blowing duct. Hence, careful attention should be paid to the choice and use of textile blowing ducts for ventilating cheese ripening rooms and, more generally, industrial food plants.
28.4 INDOOR ATMOSPHERE IN CHEESE RIPENING ROOMS Besides air velocity patterns, indoor atmosphere variables including temperature, relative humidity, and gas (CO2 , O2 , NH3 ) concentrations in ripening rooms are also crucial parameters during the cheese ripening process. Therefore, CFD models initially constructed to calculate air velocities in the pilot ripening room were then adapted to predict air temperature and relative humidity fields as well as CO2 concentrations [17,29].
28.4.1 AIR TEMPERATURE
AND
RELATIVE HUMIDITY FIELDS
Once the air velocity field in the pilot ripening room was determined, the numerical model was modified to solve the energy conservation and species transport equations in order to calculate air temperature and relative humidity fields [29]. An air temperature of 286 K and a relative humidity of 86% were specified in the outlet from the blowing holes. Constant heat
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Blowing boundary conditions: 11 m s−1, 138C, 86%
249 209 169 1 129
13.8−14.0
13.2−13.4 13.0−13.2
49
3
5
4
13.6−13.8 13.4−13.6
89
2
Air temperature (8C)
471
414
357
300
243
186
129
6 72
Height in the pilot ripening room (cm)
289
9 15
Width in the pilot ripening room (cm)
FIGURE 28.6 Vertical section located at half-length of the pilot ripening room showing the calculated air temperature field around and through the stacks for the 6 mm blower duct. The bold rectangles represent the silhouette of the stacks of cheese models, the circle indicates the location of the blowing duct, and the coordinates given are in relation to the location of the walls. In the upper left-hand corner, a top view shows where the section crosses the room. Inside the bold rectangles, digits 1 to 6 indicate the location of the cheeses for which calculated water losses are reported in Table 28.2.
and water vapor source terms were directly introduced into the porous media to account for the interaction between air and cheeses. Their values were determined from industrial data, i.e., a heat flux of 10 W m3 and a water vapor flux of 3 kg s1 m3 corresponding to a daily water loss of 1% for a cheese weighing 400 g. The temperature field calculated at half-length of the pilot ripening room is shown in Figure 28.6 covering the full width of the plant. Figure 28.6 indicates that apart from one relatively large area located underneath the blowing duct in which air temperature exceeded 13.48C, air temperature everywhere else underwent low variations of only 0.28C, even including the inside of the side stacks in which a strong gradient in air velocity distribution was highlighted (Figure 28.2 and Figure 28.3). Figure 28.6 also illustrates that any effect of this gradient was noticeable in the air temperature patterns. On the other hand, the area with high air temperature, located approximately at half-width of the room and in the upper part of the middle stack, could be unambiguously correlated to the poorly ventilated area visible in Figure 28.2 and Figure 28.3 at that site. It therefore appears that in this part of the middle stack and just underneath the blowing duct, the ventilation was not efficient enough to evacuate the heat generated inside the stack by the cheeses, giving rise to an accumulation of heat and thus an increase in air temperature. Figure 28.7 depicting the relative air humidity field calculated at half-length of the pilot ripening room reveals that air moisture equal to 86% immediately at the output of the blower duct holes rapidly reaches 90%–92% near the walls of the plant following a mixing of different air streams. As in the case of air temperature, the poor ventilation in the upper part of the middle stack and underneath the blower duct almost certainly caused the increase in relative air humidity that locally peaked at 97%. This increase revealed a strong accumulation of
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Blowing boundary conditions: 11 m s−1, 13⬚C, 86%
249 209 169 1 129 Relative air humidity (%) 96−98 94−96 92−94 90−92 <90
89
2
49
3 4 471
5 414
357
300
243
186
129
6 72
Height in the pilot ripening room (cm)
289
9 15
Width in the pilot ripening room (cm)
FIGURE 28.7 Vertical section located at half-length of the pilot ripening room showing the calculated relative air humidity field around and through the stacks for the 6 mm blower duct. The bold rectangles represent the silhouette of the stacks of cheese models, the circle indicates the location of the blowing duct, and the coordinates given are in relation to the location of the walls. In the upper left-hand corner, a top view shows where the section crosses the room. Inside the bold rectangles, digits 1 to 6 indicate the location of the cheeses for which calculated water losses are reported in Table 28.2.
water vapor in air that was further increased by the fact that air temperature also increased. Indeed, in the range of high humidity, a 18C increase in air temperature reduces the relative air humidity by 5%–6%, obviously provided that the water mass in the air does not vary in the meantime. Calculations indicated a combined increase in air temperature and moisture, which means that the water mass in air increased in reality by 1 g kg1 of dry air (i.e., by about 12%) as a result of low air velocities at that location. Figure 28.7 also highlights a slight dissymmetry in the relative humidity field according to a plane crossing the blowing duct, almost certainly due to a slight dissymmetry in the air velocity field, although this dissymmetry was far from obvious when examining the air velocity patterns in the full width of the room. In reality, the rows of stacked racks of cheese models were not accurately distributed in relation to the blowing duct; the median plane of the filling of the ripening chamber was out of line with the median plane of the blowing duct by about 15 cm.
28.4.2 MEAN AGE OF AIR As previously described in Section 8.4, the notion of mean age of air (MAA) can be used to assess ventilation effectiveness in industrial food plants where air is used to treat products. MAA distribution can easily be determined through the resolution of an additional userdefined scalar transport equation in a CFD model. Inside a room, local MAA values provide information on the average time it takes for air to travel from the inlet area to any point of the room, and thus on the ‘‘freshness’’ of the air [11,30,31]. By solving the specific scalar transport equation allowing MAA to be computed by means of a user-defined function incorporated into the Fluent code, Chanteloup [32] calculated MAA distribution in three dimensions in the pilot ripening room and compared the results
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267 241 215
o
189 163 Mean age of air (s)
137 111
210−230 190−210 170−190 150−170
85 59
Height in the pilot ripening room (cm)
293
33
<150
7 484
432
380
328
276
224
172
120
68
16
Width in the pilot ripening room (cm)
FIGURE 28.8 Vertical section located at half-length of the pilot ripening room showing the distribution of the calculated mean age of air around and through the stacks for the 6 mm blower duct. The bold rectangles represent the silhouette of the stacks of cheese models, the circle indicates the location of the blowing duct, and the coordinates given are in relation to the location of the walls. In the upper left-hand corner, a top view shows where the section crosses the room.
obtained with the air temperature and relative humidity fields previously established [29]. Figure 28.8 shows a strong heterogeneity in MAA distributions calculated at half-length of the pilot ripening room since MAA values ranged from less than 150 s near the ceiling and the lateral walls of the room to approximately 220 s at half-width and half-height of the room. The lower MAA values obviously corresponded to the most ventilated areas while the higher values were concentrated in a location where air velocities were clearly lower than 0:1 m s1 . Comparing Figure 28.8 with Figure 28.6 and Figure 28.7 again proved that MAA appeared to be a better and more sensitive parameter than air velocity in detecting insufficiently ventilated areas leading to a combined accumulation of heat and moisture that is potentially harmful to the cheese ripening process. The MAA criterion was so pertinent that the dissymmetry in airflow patterns due to a dissymmetry in the filling of the room in relation to the blowing duct was clearly highlighted.
28.4.3 GAS CIRCULATION In order to model how a gas added to air (namely CO2 ) circulated in the volume of the pilot ripening chamber, the CFD model was adapted with the aim of determining the optimal injection point for introducing an exogenous gas to accelerate the ripening process [17]. Two possible configurations were investigated: first, using the blowing duct to inject the additional gas via the holes, which is in theory the simpler solution, and second, directly injecting the gas into the core of the stacks of cheese models by means of injection points represented in the numerical model by nine small cubes of 20 cm3 . Each of the faces of these nine cubes injected CO2 at a velocity of 11 m s1 to maintain the same quantity of gas introduced into the ripening chamber atmosphere when compared to the first method where injection was performed through the blowing duct holes. The nine injection volumes
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of cubic shape were located at half-width, half-height, and at quarter, half and three-quarters of the length of the three rows of stacks. 28.4.3.1
CFD Modeling of Gas Transport
In order to calculate CO2 transport into the chamber, the following additional convection– diffusion equation needs to be solved: @ ( rYCO2 ) þ r ( r~ vYCO2 ) ¼ r ~ JCO2 þ RCO2 þ SCO2 @t
(28:4)
where YCO2 is the local mass fraction of the CO2 species predicted by the Fluent code [18] through the solution of Equation 28.4, RCO2 is the net rate of production by chemical reaction and was zero in this configuration since no chemical reaction took place, SCO2 is the rate of creation by addition from the disperse phase plus any user-defined sources, and ~ JCO2 is the diffusion flux of CO2 species arising from the concentration gradients. In turbulent flows, the Fluent code [18] computes the diffusion flux in the following form: m ~ JCO2 ¼ rDCO2 ,m þ t r YCO2 Sct
(28:5)
where DCO2 ,m is the diffusion coefficient for CO2 species and Sct is the turbulent Schmidt number with a default setting of 0.7. In practice, the computation of Equation 28.4 and Equation 28.5 is performed after total convergence in computation of the continuity and momentum equations has occurred, i.e., once the velocity field has been determined. Many assumptions were made in the numerical model built, i.e., no interaction occurred between the CO2 species and the cheeses, natural convection was not taken into account given that the energy equation was not solved, and the gas extracted by the suction duct was not recycled back into the chamber through the blowing duct. Computation time reached 60 h on an Athlon 1900 XP þ PC with 1.5 GB of RAM, when the additional transport equation for modeling gas circulation that required an unsteady computing was solved. 28.4.3.2
Comparison of the Two Methods of Gas Injection
CFD modeling aimed to dynamically determine where and how an exogenous gas has to be introduced into the pilot ripening room so that a homogeneous distribution is reached as quickly as possible. Figure 28.9a displays the kinetics of the mean concentration in CO2 calculated for each of the three rows of stacks following an injection of 1% of CO2 performed through the holes of the blowing duct. This figure illustrates how the concentration remains the same, whatever the row of stacks, with a slight difference in the first 4 min of injection between the stacks located in the middle compared with the other stacks which was almost certainly due to poor ventilation in that area. Besides the rapid achievement of homogeneity between the different rows, Figure 28.9a also shows that the mean concentration exactly matches that of the injection points after only 15 min of operation. Figure 28.9b, which gives the kinetics of the mean concentrations in CO2 calculated according to three vertical sections in the ripening room, i.e., located near the extraction duct (at 177 cm distance), at half-length of the room and far from the extraction duct (at 492 cm distance), confirms the findings derived from Figure 28.9a, namely homogeneity in CO2 distribution reached sufficiently rapidly together with concentration values after 15 min
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Mean concentration of CO2 (%)
1
0.8
0.6
0.4 Right-hand-side row of stacks Row of stacks in the middle Left-hand-side row of stacks
0.2
0 0
3
6
(a)
9
12
15
Time (min)
Mean concentration of CO2 (%)
1
0.8
0.6
0.4 Vertical section at 177 cm distance from the extraction duct
0.2
Vertical section at half-length Vertical section at 492 cm distance from the extraction duct
0 0 (b)
3
6
9
12
15
Time (min)
FIGURE 28.9 Variation over time of the calculated mean concentrations of CO2 previously injected into the pilot ripening room through holes 6 mm in diameter for (a) the right-hand-side, middle and lefthand-side rows of cheese model stacks and (b) three vertical sections located at 177 cm from the extraction duct, at half-length of the room, and at 492 cm far from the extraction duct, respectively.
equal to 1%, i.e., the percentage at the inlet area. On account of a 3D effect due to the extraction of the air at just one end of the room, slight differences between the three sections appear on Figure 28.9b, especially for the section farthest from the extraction duct during the first 9 min of injection. However, using the blowing duct to add an exogenous gas appeared to be an efficient solution for evening out gas distribution throughout the whole volume of the ripening room. As regards the second method consisting in injecting the gas by means of nine cubic volumes directly placed inside the stacks, Figure 28.10, which is a top view giving the CO2 concentration calculated in a horizontal plane crossing the nine injection cubic volumes, clearly shows that this method was inefficient in evening out gas distribution inside the room. After 15 min of injection, calculations indicated that CO2 concentration was far from
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555 505
405 355 305 Mean concentration of CO2 (%)
255 205
0.8−1.0
155
0.6−0.8 0.4−0.6
105
0.2−0.4
55
0.0−0.2
Length in the pilot ripening room (cm)
455
5 490 440 390 340 290 240 190 140 90
40
Width in the pilot ripening room (cm)
FIGURE 28.10 Distribution of the calculated mean concentrations of CO2 15 min after an injection performed directly into the stacks of cheese models by means of nine injection volumes of 20 cm3 , according to a top view spanning these volumes. The three rectangles represent the silhouette of the rows of stacks of cheese models, the circle indicates the location of the extraction duct, and the coordinates given are in relation to the location of the walls.
homogenous since it ranged from nearly 0% to 1% just around the injection volumes. Immediately outside these volumes, CO2 concentrations inexorably dropped as the gas was carried away by the airflow patterns before being extracted by the exit duct. Hence, mean gas concentration values were higher in the stacks located in the middle that were poorly ventilated than in the side stacks. The calculations also revealed that even after 1 h of injection (data not shown), CO2 concentrations had not varied since the first 10 min, regardless of the location in the room, and thus remained heterogeneous. Unlike the first method, adding gas by means of injection volumes placed at different locations in the stacks led to a heterogeneous distribution in the unit, as determined by the numerical results obtained. More homogeneous values would almost certainly have been obtained if the number of injection volumes within the stacks had been increased, but this option remains inconceivable from an industrial point of view. Indeed, each injection point would require a duct connected to a gas generator, thereby hampering cheese-makers who regularly move the cheese stacks.
28.5 CONSEQUENCES ON WATER EXCHANGES OF CHEESES Both calculations and measurements showed differences in air velocities in the side stacks of cheese models inside the pilot ripening room, with magnitudes ranging from less than 0:05 m s1 to only 0.3, 0.45, or more than 0:5 m s1 according to the hole diameter of the blowing ducts tested. It therefore appeared relevant and useful to assess the effect of this heterogeneity on the water losses of real cheeses that would have been placed at a few specific points inside the pilot ripening room. The location of these points is indicated in Figure 28.6 and Figure 28.7 by the digits 1 to 6.
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28.5.1 HEAT AND WATER TRANSFER COEFFICIENTS In order to calculate heat and water exchanges between airflow and cheeses, the convective heat and water transfer coefficients, h and k, first have to be determined. These coefficients are related to both the geometrical characteristics (shapes and dimensions) of the object considered and the airflow characteristics (mean air velocity and turbulence intensity), but not to the composition of the object. A few years ago, the laboratory adapted a psychrometric method based on wind tunnel experiments in order to accurately measure the heat and water transfer coefficients for different shapes and dimensions of objects found in the food industry in relation to mean air velocity and turbulence intensity [33]. In an airflow where air velocity and turbulence intensity were controlled, the psychrometric method consisted in regularly recording water losses due to evaporation of a fully wetted plaster cast of the object, together with its surface temperature and the air temperature. The mean values of h and k are then calculated independently according to the two following equations: 4 4 Fm Lvap «s s Tair T s h¼ Tair T s Tair T s k¼
Fm Pvap (Tdew ) aws Pvap (T s )
(28:6)
(28:7)
In these equations, the mean water flux (Fm ) was determined from the measured water loss from the plaster cast. The air temperature (Tair ) was measured by means of a K-type thermocouple placed at 5 mm from the surface of the object. The mean surface temperature of the plaster cast (Ts ) was measured by means of three K-type thermocouples placed just under the surface. Their number and location were judiciously chosen based on the results obtained during a previous study [34]. The water activity at the surface of the object (aws ) was equal to 1 owing to the saturation of the plaster cast. Figure 28.11 and Figure 28.12 show the experimental values of the mean convective heat transfer coefficient (Figure 28.11) and the mean water transfer coefficient (Figure 28.12), both determined by psychrometry in the laboratory wind tunnel on plaster casts of cylinders 100 mm in diameter and 40 mm high, in an air velocity range lower than 0:5 m s1 [3]. During the experiments, turbulence intensity was set at 12%, i.e., a value corresponding to the mean value measured in different types of industrial food plants [35]. Although h and k were measured independently, their values obeyed the Lewis relation [36] and were proportional even for these low air velocities. Moreover, the experimental values of h and k were smoothed by an exponential law, which is the most appropriate mathematical function for representing the mixed convection that occurs at this low velocity range. Indeed, power laws that are widespread in heat transfer problems are normally valid only for forced convection, i.e., at higher air velocities [37]. In addition, an exponential law gives coefficient values that have a real physical meaning when the air velocity tends towards zero, i.e., when natural convection predominates. Figure 28.11 and Figure 28.12 indicate a threefold increase of the measured heat and water transfer coefficients when the air velocity around the plaster cast increases from less than 0.1 to 0:5 m s1 . This proves that the location of the cheeses in the ripening room is an important factor in explaining variation in the water losses. Figure 28.13 confirms that location has an influence on heat and water exchanges as it shows the measured water losses of 18 plaster casts 100 mm in diameter and 40 mm high, fully saturated with water and placed at different locations within the stacks filling the ripening room. The location of the plaster casts was chosen following the airflow study [3].
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Convective heat transfer coefficient h (W m−2 K−1)
Indoor Atmosphere and Water Exchanges during the Cheese Ripening Process 14 h = 3.95 e 2.23 v with R 2 = 0.96 12 10 8 Experimental data 6 4 2 0 0
0.1
0.2
0.3
0.4
0.5
0.6
Air velocity v (m s−1)
Water transfer coefficient k ⫻108 (kg m−2 Pa−1 s−1)
FIGURE 28.11 Influence of air velocity on the mean convective heat transfer coefficient values measured by psychrometry in a wind tunnel at the surface of a plaster cast of a cylinder 100 mm in diameter and 40 mm high.
12 k ⫻10 8 = 2.92 e 2.42 v with R 2 = 0.99 10
8 Experimental data 6
4
2
0 0
0.1
0.2
0.3
0.4
0.5
0.6
Air velocity v (m s−1)
FIGURE 28.12 Influence of air velocity on the mean water transfer coefficient values measured by psychrometry in a wind tunnel at the surface of a plaster cast of a cylinder 100 mm in diameter and 40 mm high.
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8
6
4
2
0 0
0.1
0.2
0.3
0.4
0.5
Air velocity (m s−1)
FIGURE 28.13 Influence of air velocity on the measured weight loss of plaster casts of cylinders 100 mm in diameter and 40 mm high; the cylinders were fully saturated with water and placed at different locations within the stacks of cheese models filling the pilot ripening room.
28.5.2 WATER LOSSES
OF
REAL CHEESES
Water losses of cheeses can also be calculated from the following two equations: Pdm ¼ k S aws Pvap(Teq ) Pvap(Tdew ) 3600 1000 24 4 4 Tair h Teq Tair þ s«s Teq þ kLvap aws Pvap(Teq ) Pvap(Tdew ) ¼ 0
(28:8) (28:9)
A program was created using Matlab software (The MathWorks, Natick, MA) to calculate water loss from cheese, i.e., Pdm , from Equation 28.8. In this equation, the value of the water transfer coefficient k is determined from the exponential law of Figure 28.12, given the mean air velocity around the cheese calculated by the CFD model. Other variables are imposed, including total surface S of the cheese (equal to 0:03 m2 ), water activity at the cheese surface (0.98 or 1), air temperature Tair (148C), and relative air humidity RH (95% or 98%), which go to define dew temperature (Tdew ). The last variable of Equation 28.8 to be evaluated, i.e., the mean temperature of the cheese surface (Teq ), results from equilibrium between heat transfers occurring by convection, radiation, and evaporation; Teq is determined numerically by solving Equation 28.9, in which the convective heat transfer coefficient h takes a value based on the experimental law of Figure 28.11, given the mean air velocity calculated by the CFD model. Concerning the radiation exchange formulation in Equation 28.9, the temperature of all the surfaces surrounding the cheese placed in the stack was assumed to be equal to the air temperature, thus artificially increasing heat transfer by radiation and therefore causing an overestimation of the mean surface temperature. In fact, calculations showed that the radiation term, although overestimated, had little effect on the water losses from the cheese, since the change in the mean surface temperature ranged from 0.038C to 0.298C at the very most. Based on a room air temperature of 148C, Figure 28.14 gives values of water losses from cheeses initially weighing 400 g as a function of water activity at the cheese surface, relative air
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Calculated water losses of cheese (g 24 h−1)
12
11.2
Relative air humidity of 98% / water activity at the cheese surface of 1 Relative air humidity of 95% / water activity at the cheese surface of 1 Relative air humidity of 95% / water activity at the cheese surface of 0.98
8.2 8 6.8 6.1 5.0 4.1
3.7
4
3.7 2.5
2.2
4.5
3.3
2.4
1.6
1.5
0 0.05
0.3(a)
0.1
0.45(b)
0.6(c)
Air velocity (m s−1) (a):
Peak air velocity around cheeses in the pilot ripening room when using the 3 mm blowing duct Peak air velocity around cheeses in the pilot ripening room when using the 6 mm blowing duct (c): Peak air velocity around cheeses in the pilot ripening room when using the 20 mm blowing duct (b):
FIGURE 28.14 Influence of air velocity, relative air humidity, and water activity at the cheese surface on the calculated water loss for cheeses 100 mm in diameter and initially weighing 400 g.
humidity, and mean air velocity magnitudes, in a range corresponding to the heterogeneity highlighted in the three configurations of the pilot ripening room investigated [9]. Regardless of the relative air humidity and water activity at the cheese surface, water losses logically increase as mean air velocity increases around the cheese, owing to the variation of the water and heat transfer coefficients with air velocity indicated in Figure 28.11 and Figure 28.12. Figure 28.14 illustrates how modifying the diameter of the holes of the blowing duct can strongly affect the disparity in water losses according to the location of the cheeses in the ripening chamber. For example, replacing the blowing duct with 20 mm diameter holes by the one with 3 mm diameter holes can double the water losses from cheeses placed in the lower part of the side stacks near to the ground, although no variation occurred in the full airflow rate. Table 28.2 presents the daily water losses of six cheeses initially weighing 400 g located as indicated by digits 1 to 6 in Figure 28.6 and Figure 28.7, and calculated from Equation 28.8 considering the air velocity, relative humidity, and temperature fields simulated. The water activity at the surface of the cheeses was assumed to be either equal to 1 as in the beginning of the ripening process, or 0.97 as occurs during the ripening process. Analysis of Table 28.2 reveals that cheese water loss could increase by 500% to 600% depending on whether it is located in the upper part of the middle stack (location 1) where there is very low air velocity and high relative air humidity and temperature, or in the lower part of the side stacks (locations 4 and 6) where air velocity reached 0:4 m s1 and where air temperature and relative humidity were lower.
28.5.3 SIMULATION
OF THE
COUPLING
BETWEEN
AIRFLOW
AND
WATER LOSSES
The previous results allow the water losses of cheeses and air temperature and relative humidity fields to be determined without numerically solving the coupling that exists between the airflow and the food products bathing in this air, which can cause differences, for example, in the fluxes of water evaporation between different points of the same stack of
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TABLE 28.2 Calculated Water Losses of Six Cheeses Initially Weighing 400 g versus Airflow Characteristics (Air Velocity, Temperature, and Relative Humidity) Determined by the CFD Model, and versus Two Water Activities (1 and 0.97) at the Cheese Surface
Cheese 1 Cheese 2 Cheese 3 Cheese 4 Cheese 5 Cheese 6
Air Velocity (m s21)
Air Temperature (8C)
Relative Air Humidity (%)
Water Activity at the Cheese Surface
Water Losses (g 24 h21)
Water Losses (% Initial Weight 24 h21)
0.05 0.05 0.05 0.38a 0.25a 0.38a
13.7 13.5 13.3 13.3 13.3 13.3
97 95 93 91 93 92
1=0.97 1=0.97 1=0.97 1=0.97 1=0.97 1=0.97
2.3=0 3.8=1.6 5.3=3.1 12.8=8.7 7.7=4.5 11.5=7.3
0.6=0 1.0=0.4 1.3=0.8 3.2=2.2 1.9=1.1 2.9=1.8
Note: The location of the six cheeses inside the pilot ripening room is indicated in Figure 28.6 and Figure 28.7. a
Air velocity values corresponding to measured values since the calculated values were almost certainly underestimated by the CFD model at that site.
products. In the broad approach previously presented, heat and water fluxes were assumed as constant in the calculations of relative air humidity and temperature patterns in the pilot ripening room. However, in reality, during air treatment operations heat and moisture fluxes vary with time, and their time-point values depend on air and product surface characteristics. Indeed, heat and moisture fluxes are proportional to the difference in temperature and in water vapor pressure, respectively, between the air and the food product surface. Moreover, both fluxes are affected by airflow characteristics and product shape as a result of the influence of these parameters on heat and water transfer coefficients. As general purpose CFD codes such as Fluent, Star-CD or CFX were designed for solving turbulent fluid flow problems coupled with heat and mass transfers, it is theoretically possible to calculate the spatial distribution of the air characteristics (velocity, temperature, relative humidity) and time variations of product temperature and weight. Nevertheless, there are several major factors that limit the capacities of these codes and the accuracy of the results obtained, including: (i) the lack of efficient modeling procedures to describe water diffusion inside solids and (ii) the use of the wall function approach in modeling turbulent boundary layers near product surfaces, which leads to large errors in transfer coefficient predictions or which leads to very fine meshes and therefore to a cell number requiring an immense memory size well in excess of the computers currently used. In order to accurately predict the air velocity, air temperature, and relative humidity as well as the water loss of stacked food products, a specific user-defined function which can be compiled in the CFD code ‘‘Fluent 6.1.22’’ was recently developed in the laboratory [38]. Validation of the function implemented was achieved by comparing the results obtained for a few hot and moist cylinders placed in a cold and dry airflow with those obtained from the solving of analytical solutions using a program written in Matlab programming language, giving the kinetics for temperature and water concentration at any point of a cylinder radius. Figure 28.15a and Figure 28.15b show the relative air humidity calculated after 37 h (Figure 28.15a) and 45 days (Figure 28.15b) using the specific function developed around six cheeses 100 mm in diameter and 45 mm high, arranged in a row and placed in an airflow
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98.0 Relative air humidity (%) 97.5
97.0 96.5
1
2
4
3
5
6
96.0 Airflow
95.5
Inlet boundary conditions: 0.01 m s−1, 12°C, 95.4%
95.0 (a)
98.0 Relative air humidity (%) 97.5
97.0 96.5
1
2
3
4
5
6
96.0
95.5 95.0
Airflow Inlet boundary conditions: 0.01 m s−1, 12°C, 95.4%
(b)
FIGURE 28.15 Distribution of predicted relative air humidity for a row of six cheeses using a specific user-defined function built and incorporated into a CFD code in order to accurately simulate the interrelationships at play between airflow and the water transfers of unwrapped food products bathing in air, after (a) about 37 h of ripening process and (b) 45 days of ripening process.
whose characteristics at the inlet area were a velocity of 0:01 m s1 , a temperature of 128C, and a relative humidity of 95.4%. The 3D computational model developed used symmetry conditions for all the external faces except for the inlet and outlet areas, and thus simulated water exchanges as they occurred in the core of a stack of cheeses. Airflow was considered as turbulent—with modeling using the standard k« model—nonisothermal and unsteady since heat and water transfer phenomena vary naturally with time. Salt transfers occurring inside the cheeses and which interfere with water transfers and water activity were neglected. A total of 350,000 cells were used for meshing the computational model, and the full convergence of all the discretized equations was reached after about 3.2 h on a Pentium Xeon 3.2 GHz PC with 4 GB of RAM. Figure 28.15a and Figure 28.15b show relative air humidity fields calculated after about 37 process hours (Figure 28.15a) and 45 process days (Figure 28.15b), which vary both
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CFD-calculated water losses of cheese (g)
10
8
6
4 Cheese 1
Cheese 3
Cheese 6
2
0 0
10
20
30
40
50
Time (days)
FIGURE 28.16 Evolution over time of the water losses from three cheeses (cheeses 1, 3, and 6) placed in a row of six cheeses and calculated using a specific user-defined function built and incorporated into a CFD code in order to accurately simulate the interrelationships at play between airflow and the water transfers of unwrapped food products bathing in air.
spatially and over time. As the air circulates around the cheeses as it moves from the inlet to the outlet, its relative humidity increases due to the accumulation of the moisture evaporating from the wet surface of the cheeses, thus generating the higher values around the cheeses located farthest from the air inlet. Around an individual cheese, relative air humidity peaks locally in the wake generated by the circulation of air around the cylinder, which is known to be a low velocity region. Comparison between Figure 28.15a and Figure 28.15b reveals that the user-defined function implemented in the CFD code correctly simulated the variations in the water transfer phenomenon over time, i.e., a decrease in the water evaporation on account of a decrease of the water content inside the cheeses and in water activity at the cheese surface. Figure 28.16 presents the water loss kinetics of three cheeses (cheeses 1, 3, and 6 of the previous row) predicted by the user-defined function. The numerical model logically reported differences in water losses according to the location of the cheeses, with the higher water loss for the first cheese in contact with ‘‘dry’’ air and the lower water loss for the cheese located near the outlet of the computational domain where the air is moistest. These differences decrease over time and tend towards equilibrium, since water content and activity at the surface of the first cheese decrease more rapidly compared with the others due to its higher water loss. The user-defined function developed and incorporated in the CFD code Fluent then makes it possible to compute temperature and water concentration fields and determine the water loss kinetics of the cheeses together with the temperature and relative humidity fields of the air flowing through the stacked food products. The laboratory is currently extending the approach developed to accurately calculate airflow and the water exchanges within a 3D stack filled with 100 cheeses. A full quantitative experimental validation will be performed afterwards.
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28.6 CONCLUSION Based on various recent studies performed in a pilot ripening room constructed in the laboratory, this chapter has clearly demonstrated that CFD techniques can be very useful tools for assessing the operation and indoor atmosphere of industrial cheese ripening rooms, even though the representation of the filled plant using cheese models was significantly simplified in the numerical models. In general, the calculated predictions of airflow patterns within the pilot cheese ripening chamber were in fairly close agreement with actual measurements. However, in some regions, i.e., in the side stacks or in the swirl located above these stacks, the measurements indicated stronger velocity gradients than predicted by the model. Moreover, careful attention must be paid to the choice of the blowing ducts in cheese ripening chambers, since blowing duct design has a very real influence on airflow patterns, and therefore on water losses from cheeses. Indeed, the model clearly highlighted differences in ventilation levels around cheese models following a simple change in the diameter of the holes of the blowing duct. Further calculations were performed to identify a solution for introducing an exogenous gas into the ripening room in a homogenous way. To achieve this, the calculations indicated that it was far more efficient to use the blowing duct than to introduce the gas directly into the stacks. However, in light of the results presented in this chapter, it is very difficult to give quantitative recommendations on ventilation and indoor atmosphere in ripening chambers, and equally difficult to evaluate the impact of the calculated gas distributions on the cheese ripening process. Further data are required in order to fully understand and quantify the interaction between the indoor climate of ripening rooms—air velocity, temperature and relative humidity, gas concentrations, renewal in fresh air, etc.—and the cheeses being ripened (weight losses, gas consumption and production at the cheese surface by microbial flora, microbial growth, etc.). Studies are in progress in the laboratory, together with research aimed at determining appropriate coefficients to represent the rows of cheese stacks in the CFD model through porous media coupled with the general Darcy–Forchheimer formulation. The development of a system based on high-performance sensors coupled with information on airflow patterns would give ripening room operators greater flexibility in looking to improve the consistency and quality of the cheese-making process. To achieve this, research will need to focus on controlling cheese ripening by monitoring indoor atmosphere and on obtaining evenly distributed ripening conditions around the cheeses. Further progress can be expected in the years to come due to the increasing calculation power of computers and the increasingly flexible CFD codes available. Thus, it will likely be possible to fully simulate how a ripening room operates by implementing unsteady numerical models capable of accurately predicting heat, mass, and gas exchanges between indoor atmosphere and several hundred cheeses being ripened.
ACKNOWLEDGMENTS The author sincerely thanks A. Kondjoyan, J.D. Daudin, A. Lasteyras, J.M. Auberger, S. Portanguen, L. Lasteyras, T. Rougier, D. Peyne, A. Carles, T. Laboue, R. Lardy, V. Chanteloup, and C. Chevarin for their active participation and efficient contribution to the discussions, experiments, and numerical calculations that formed much of the results on which this chapter is based. The author is also grateful to the French Ministry of Research and ‘Arilait Recherches’ for their financial support to a major part of the studies presented.
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NOMENCLATURE aws C2 Dp h, h k, k Lvap Pdm Pvap RH S Tair Tdew T s , Teq vi x, y, z
water activity at the surface of the plaster cast or the cheese inertial resistance factor (m1 ) mean particle diameter (m) 1 mean convective heat transfer coefficient (W m2 K ) 2 1 1 mean water transfer coefficient (kg m Pa s ) latent heat of water vaporization (J Kg1 ) water loss from cheese (g 24 h1 ) saturating vapor pressure at the considered temperature (Pa) relative air humidity (%) surface of the cheese (m2 ) air temperature around the plaster cast or the cheese (K) dew temperature calculated from air temperature and relative humidity (K) mean surface temperature of the plaster cast or the cheese (K) air velocity according to the direction i (m s1 ) three spatial directions
GREEK SYMBOLS a « «s Fm m r s
permeability (m2 ) void fraction emissivity of the object (0.91 for plaster) mean water flux (kg m2 s1 ) dynamic viscosity of the fluid (kg m1 s1 ) fluid density (kg m3 ) Stefan–Boltzmann constant (5:67 108 ) (W m2 K4 )
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Index A Activation energy, 387, 592 Adiabatic compression, 546, 548, 551 Adiabatic heating, 538, 549 Agglomeration, 250–251, 267; see also Coalescence and agglomeration model, for spray drying Air blast and jet impingement, CFD applications in, 25 Air curtains CFD design of, 131–136 in chilled multideck retail display cabinet, 105–107, 118–119 in display cabinets, 92–93 3D simulation of, 93 for open refrigerated display cases, 130 Airflow in cheese ripening, 698 effects in microwave heating, 318–322 modeling in retail cabinets, 92–93 patterns heterogeneity, 702–703 Air humidity influence, in retail cabinets, 94 Air velocity patterns, in meat dryers CFD modeling mean age of air and, 241–245 steady-state numerical models, 227–232 unsteady numerical models, 232–240 features of, 233–234 ventilation cycle amplitude, 234–236 dissymmetry, 238–240 form, 237–238 Ambient air movement, in retail cabinets, 94–95 ANDINA-F CFD codes, 19 Antibody–antigen interactions, 636 Ascorbic acid enzymatic reaction heat of, 637 enzyme mediated oxidation of, 640 quantification, by microcalorimetric biosensor, 637
B Bacillus sp. sporothermodurans, 404
stearothermophilus, 404, 610 subtilis, 539 Bacteria deactivation, in thermal sterilization, 339–343 Bacterial spores, 539 Baked bread, quality measurement, 295–296, 303 Baking index, 306–308 Baking ovens, 288–289 CFD model applications gelatinization process, 306–308 operation under increased oven load, 304–305 optimum temperature profile condition, 308–309 monitoring system, 295–296 oven geometry, 296–297 traveling-tray, 294–296, 300 Baking process airflow velocity profile, 289, 300, 302–303 CFD modeling applications, 304–309 dough thermal properties, 298 duct temperatures, 299 flow sources, 298 heat sources, 299 three-dimensional flow system, 297–298 transient state, 298 traveling-tray baking oven, 294–296, 300 turbulent air flow, 298 validation, 300–303 color and flavor development, 293–294 gelatinization in, 292, 305–308 heat transfer mechanism, 290–291, 299 kinetic reactions, 290 mass transfer mechanism, 291 ovens, see Baking ovens solidification, 292 stages, 288–289 temperature profiles, 288–289, 300–301, 303–304 volume expansion, 292 Baldwin–Lomax turbulent stress model, 407 Beef carcass, CFD modeling heat load profiles, 209 heat transfer coefficient around carcass leg, 211–212 727
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728 initial and boundary conditions, 208–209 surface temperatures, 210–212 surface water activity profiles, 211, 213 validation, 209–213 Beef chilling, CFD-conduction model, 214–217; see also Beef carcass; Beef leg Beef leg, CFD modeling analysis and results, 204–205 boundary conditions, 200 chemical potential, 201–202 thermal equilibrium, 201 water activity equilibrium, 201–202 mathematical model boundary layer treatment, 202 continuity equation, 198 energy transport equation, 199 initial conditions, 202 momentum equation, 198 transport equations, 198–200 turbulent dissipation rate equation, 199–200 water transport equation, 199 numerical solution, 202–204 representation as ellipse, 197–198 surface temperature profile, 204–206 water concentration profiles, 204–205 Bingham model, 13 Biochemical reactions, 590 Biochip, 643–644 Biosensors, 631 calibration characteristics of, 632 fluid flow in, 634–636 mass transfer in, 636 mathematical models of, 633–637 microcalorimetric, 637 miniaturization of, 632 oxygen limited performance of, 639–641 principle of, 632 Bird–Carreau viscous fluid model for HDPE, 520 Black leaf tea manufacture, 590 Blowing duct, design of, 702 Boundary layer thickness, 627 Boussinesq approximation, 8, 174, 176, 318, 492 Bread-baking oven, 294 Breadmaking, 288 Brinkman equation (Macroscopic viscous stress effect), 655–656 Brinkman–Forchheimer-extended Darcy equation, 656–657 Brown-Tamm models, 173 Buoyancy force, 548
Computational Fluid Dynamics in Food Processing Butterfly valve CFD model of, 623 cleaning characteristics of, 623–625 simulation set-up of, 624 wall shear stress, 624
C Caramelization, 293 Carbon dioxide (CO2 ), use to measure infiltration, 188–190 Carbopol solution, shear thinning, 573–575 Carrot–orange soup, thermal sterilization of, 343–344 k-Casein, 382, 418 Catechin depletion, 592–594 oxidation, 591 Central differencing scheme (CDS), 339 Ceramic membranes, 434 CFD, see Computational fluid dynamics CFX CFD code, 19–20, 179 Charge-coupled device (CCD) array, 125 Cheese production, 697–698 ripening rooms airflow patterns in, 700–709 geometry and operation of, 699–700 indoor atmosphere in, 709 CHEMKIN system, 543–544 Cherry juice, reaction processes kinetic, 341 Chilled multideck retail display cabinet; see also Retail cabinets air curtain in, 105–107 CFD model boundary conditions, 113–116 buoyancy, 112–113 convergence and mesh independence, 116–117 experimental investigation, 109 humidity, 113 impact on performance, 118–125 mesh size, 111 postprocessing, 117–118 steady state=transient, 113 turbulence model, 111–112 two or three dimensional model for, 109, 111 defrost in, 107 description of, 105–107 simulations results air curtain, 118–119 cold feet effect, 121–124
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Index modeling of duct, 119–120 shelving, 120–121 verification, 124–125 standard testing, 108 Cleanability, 605 of butterfly valve, 623–625 CFD prediction of, 609 fluctuations, 608 fluid exchange for, 619 fluid parameters on, 608 process parameters mechanical force, 606 temperature and detergent, 605 time, 606 in RFC, 611–612 in spherical-shaped valve house, 609 CMC, see Sodium carboxymethyl cellulose Coalescence and agglomeration model, for spray drying agglomerate porosity, 277–278 collision partners, 275–276 mass conservation, 278 Coanda effect, 44, 47–48 Cold feet effect, 92, 94, 104 in aisle, 123–124 in whole store, 121–122 Cold storage facilities, CFD applications in, 25–26 Compression-type refrigerating system, 86 Computational fluid dynamics aided retail cabinets design, 84–99 analysis CMC-filled egg, 362–368 with commercial software, 21–23 egg pasteurization processes, 368–378 intact egg, 364–371 applications in air blast and jet impingement, 25 in cold storage facilities, 25–26 in combined flow and heat transfer, 28 to display cabinets, 90–95 in drying, 30 in egg-processing sector, 347–348 in flows and combined mass transfer, 27 in food industry, 2–4, 23–30, 334 in household and industrial refrigeration, 26 in isothermal flows, 29 publications on, 3–4, 6–7 in refrigerated display cases, 26 in sterilization, 26–28 in stirred tanks, 28–30 benefits for consumer, 33–34 challenges confronting model simplification, 32
729 nonhomogenous fluid domain, 30–31 time-step selection, 33 turbulence modeling, 31 uneven meshing, 32–33 y+criterion, 31–32 chilled multideck retail display cabinet by, 108–113 codes, 18–21, 436 conduction model, for beef chilling, 214–217 design of air curtain, 129–140 of food processing, 539 grid system in, 541 high-temperature short-time approximation and, 34 for horticultural packages, 667 industrial processes by, 2–3 methods for modeling accuracy convection schemes, 14–16 multiple frames of reference, 17–18 sliding mesh, 16–17 spatial convergence techniques, 18 unstructured mesh, 16 modeling applications to food industry, 2–4, 33–34 baking process, 294–308 of beef carcass, 197–213 construction of, 700 governing equations of, 5–8 heat and mass transfer, see Beef carcass; Beef leg membrane separations systems, 434–462 non-Newtonian fluid, 12–14 numerical analysis, 14 in plate heat exchangers, 407–413, 418–423 porous media and multiphase modeling, 11–12 turbulence modeling, 8–11, 14 processing system design, 34 product quality, 34 software pricing, 33–34 Concentration polarization, 434–435, 453–456 Conservation of energy, law of, 5 Convective heat transfer in eggs, CFD modeling, 360–361 Coriolis forces, 556 Couchman–Karasz equation, 269 Courant number, 620 Crush–tear–curl (CTC) process, 597 Crystal growth rates, 566 Crystallization processes, CFD simulation of, 565–567 Crystal size distribution (CSD), 565 Cylindrical mixing tank, rotating reference frame simulation of, 556
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730
D Dairy industry, 404–405; see also Milk fouling model Darcy equation (Microscopic viscous stress effect), 654 Darcy–Forchheimer model, 11, 701 Darcy’s law, 11 Debye length, 635 Deformation tensor, 565 Detached eddy simulation (DES), 10–11 Differential viscoelastic Oldroyd-B model, 568–569 Diffusion based particle drying model heat transport in, 259–260 Lagrangian particle tracking in, 256 moisture transport, 257–259 shrinking of particles, 260–261 Diffusion coefficient model, for spray drying, 263–265 Digital particle image velocimetry (DPIV), 26, 187–188 Direct heat exchanger systems, 405 Direct numerical simulation (DNS), 10–11 Discharge air grille (DAG), 129, 131–139 Discrete transfer radiation model (DTRM), 145 Dispersive mixing, 562 Display cabinets, CFD applications, 90–95; see also Retail cabinets airflow modeling air curtains, 92–93 evaporator and rear ducts, 93 shelves, 93 air humidity influence, 94 ambient air movement, 94–95 condensing units, 86 glass doors fogging and defogging, 95 mist cooling-humidification, 95 product temperature distribution, 91–92 radiation, 94 Display cabinet zone air circulation rate, 151–152 air supply temperature, 151–153 cooling load and aisle temperature for, 157, 158 and product temperature, 153–154 diffuser positions in, 154 evaporator coil air off temperature, 152 extract and supply system, 157–165 measuring points in, 145 meshing scheme in, 145 modeling, 146–151 rows of, 146–147 with hot air heating system, 152–154
Computational Fluid Dynamics in Food Processing with underfloor heating system, 154–155 without accessory heating system, modeling of, 147–151 Distributive mixing, 560–561, 571 Dittus–Boetler correlation, 392–393, 395, 397 Double impingement, 498, 501 Dough materials CFD simulation of, 568 viscoelastic rheological behavior of, 568 Dough mixers cluster distribution index, 572 3D FEM numerical simulations of, 572 flow patterns in, 571 processes CFD analysis of, 568 Newtonian fluid models, 571 Down-channel velocity profile, 514–515 Dry crust (dry rim), 224 DRY–DRY collision, 277–278 Drying CFD applications in, 30 process, 223–224 Dry sausages manufacture, 223–224; see also Meat dryers
E Eddy viscosity models, 9 Eggs; see also Sodium carboxymethyl cellulose-filled egg CFD of thermal processing conditions, 353–360 conductive and convective heat transfer, 360–368 grid generation, 352–353 surface heat transfer coefficient, 353–354, 356–360 thermal property values used for, 355 eggshell thickness, 352 geometry analysis, 349–352 pasteurization processes CFD analysis, 368–378 SE inactivation, 371–372 shape, 349–351 yolk size and location, 351–352 Electrical potential difference, membrane separations by, 442–443 Electric double layer (EDL), 634–635 Electrodialysis (ED), 440, 442–443 Electrodialysis reversal (EDR), 442–443 Electrokinetic biochip, for taste analysis, 641 Electrokinetic flow, 634 Electromagnetics-heat transfer coupling, 317 Electroosmotic flow (EOF), 634, 643
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Index Electrophoretic mobility, 636 Elongational flow, 562 Energy, conservation of, 475 EN Standard 23953, 87, 89 Enzymatic oxidation, 590 activation energy for, 592 reaction rate constants for, 592 Enzymatic reaction, 636–637 Enzymatic taste biosensor (ETB), 641 Epicatechin (EC), 590 Epicatechin-gallate (ECG), 590 Epigallocatechin (EGC), 590 Epigallocatechingallate (EGCG), 590 Ergun equation, 11 Escherichia coli, 539 Euler–Lagrange approach, for stationary flows, 272 European Hygienic Engineering and Design Group (EHEDG), 608 Evaporator and rear ducts cabinets, 93 Extra viscous stress splitting (EVSS), 510 Extrusion, definition, 505–506 of food, 511 numerical simulation of, 506–510 scaling, 528, 530
F Fanning friction factors, 383, 386, 390–393, 398 Farinograph, 572, 581 Fermentation, tea, see Tea fermentation Fictitious domain method, 519 FIDAP modeling, 19–21 Film theory model, of membrane separations, 454 Finite element method (FEM), 507 FLIR systems, 125 Flow and combined mass transfer, CFD applications, 27 mechanisms, 634 modeling, 671–672 through heat exchanger, 13 through ventilated packaging, 13 Flow behaviors of novel membrane and module, 461–462 spacers effect on, 456–461 Fluctuations, in flow, 608 Fluent code, 19–21, 44–45, 179, 623, 713 Fluid compression rate, 550 conductive measurement method, 626 exchange predictions by CFD simulation, 619–620
mesh description for, 620 in MPV, 621 simulation set-up for, 620 in sphere-shaped valve, 621 in upstand, 622 and wall shear stress, 622 flow, in biochip, 643–644 pressure variation in, 545 and soil mechanics, 627 temperature profile of, 546, 550–552 velocity profile of, 546, 550–551 Food CFD application in, 2–4, 23–30, 334 high-pressure processing (HPP) of, 537 nonthermal treatment of, 539 preservation, 538 processing equipment cleaning process of, 605 flow conditions, 607 hygiene prediction in, 606–607 for liquid processing, 609 products heat treatment of, 265 quality measurements on, 631 spray drying, see Spray drying thermal sterilization, see Thermal sterilization Forchheimer–Brinkman model, 591 Forchheimer equation (Microscopic form effect), 654–655 FORTRAN subroutines, 544 Fouling in dairy industry, 404–405 pattern of dryer equipment, 271 Fourier’s law, 385 Free jets, 471–472 Fritzsche and Lilienblum’s equation, 170
G Galerkin’s method, 509 Gambit, 572, 623 GAMBIT modeling, 20 Gas flow, in spray dryer, 252 Gasket materials, 625 Gelatinization, in baking process, 292, 305–308 Gel-polarization model, of membrane separations, 454 Glass doors fogging and defogging, in retail cabinets, 95 Glass transition temperature for food products, 270 of lactose, 269
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732 specific heat and, 268 sticky-point temperature and, 271 Glucose, enzymatic assay of, 646 Gosney and Olama model, 172–173 Grash of number, 26, 335, 341 Guggenheim-Anderson-de-Boer (GAB) equation, 202
H Hagen–Poiseuille equation, 387 Halocarbon refrigerants, 86 Hardy–Cross method, 232 Heat and mass transfer CFD modeling; see also Beef carcass; Beef leg on 3D model of beef carcass, 205–213 on 2D model of beef leg, 197–205 Heat exchangers with CFD modeling, 13 fouling and cleaning, 404–405 hydrodynamics modeling, 405–407 system for milk treatment, 406 Heat transfer, 682 coupling with microwaves, 317–318 model, 540 during tea fermentation, 591 Heat treatment equipments, 404, see also Heat exchangers Helical ribbon mixers, CFD analysis of, 564 Henry’s law, 455 Herschel-Bulkley model, 13, 383, 385 High-performance liquid chromatography (HPLC), 642 High-pressure food processing applications, 538 batch process of, 539 compression steps of, 543 computational fluid dynamics (CFD) models of, 539 features of, 538 heat transfer model for, 540 limitation of, 538 research work of, 540 solid–liquid mixture in, numerical approximations of, 540 High-pressure vessel, geometry of, 541, 549 High-temperature short-time (HTST) approximation and CFD, 34 Hollow fiber membrane, 448 Horizontal display cabinet, 86 Horizontal plane, velocity vector field, 679–680 Horticultural packages, CFD design tool, 667–688 Hot-wire anemometry, 125, 186
Computational Fluid Dynamics in Food Processing Household and industrial refrigeration, CFD applications in, 26 HYBRID convection scheme, 15 Hybrid-differencing scheme (HDS), 339 Hydrodynamic parameter, 608, 617 Hydrostatic pressure, 441–442, 538 Hygienic design CFD for, 604 of food processing equipment, 604–605, 607, 609
I Impinging jets, 471–472, 487 Indirect-type refrigerating system, 86 Infiltration measurement, 188–189 Infusion kinetics, of loose tea leaves, 594–595 Insoluble material formation, 266–267 Interparticle collision, in spray drying, 273–275 Isothermal flows, CFD applications in, 29 Isothermal wall-jet, 15
J Jet impingement heat transfer CFD applications, 496–500 characteristics, 490–491, 494–496 effect on food quality, 498–500 flow patterns, 489–490, 492–494 governing equations, 491–492 industrial equipment, 497–498 parameters effect, 496–497 principles, 488–489 turbulence models, 492–496 wall treatment for, 496 microwave heating, 324–328 ovens baking times and air temperatures for, 470 CFD applications, 471, 475–481 conventional ovens and, 470, 488, 499 flow field characterization, 471–473 fluid flow and heat transfer for, 476–481 heat transfer characterization, 473–475 shear-stress transport model, 476 turbulence models, 475 Jets, classification of, 471
K Kameleon, commercial CFD code, 46 k–e model, 701, 703
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Index k–v model, 492, 496, 500 k–e turbulence model, 9, 44, 46–47, 175–176, 178, 180, 252, 476, 480, 492, 496, 500
L Lab-on-a-chip design, 642 for glucose measurement, 645 simulation of, 644 a–Lactalbumin, 382 b–Lactoglobulin (b–LG), 382, 405, 418–420 Lactobacillus delbrueckii, 381 Lactose crystallization mixed-suspension, mixed-product-removal (MSMPR) model of, 567 numerical simulation of, 566 volume fraction of, 567 Laminar fluid flow, theories of continuity equation for, 653 momentum equation for, 653–654 Laminar jets, 471 Large eddy simulation (LES), 10–11 Laser Doppler anemometry (LDA), 186–187, 473 Laser Doppler velocimetry (LDV) technique, 45, 133–135, 137 Leveque’s correlation, 445 Lewicki equation, 201 Liquid food boundary conditions for, 542 compression of, 545, 546 convection currents of, 548 in nonadiabatic high-pressure processing, 548 numerical approximations of, 548 partial differential equations for, 542 temperature distribution of, 548 thermal sterilization bacterial deactivation and vitamins destruction in, 339–343 in top insulated can, 337–339 in vertical can, 333–337 Lumped capacitance technique, 475 Lyapunov exponent, 561
M Macerated dhool moisture content of, 592 packed bed of, 591 thermal physical properties of, 592–593 Macroscopic turbulence in porous media, theoretical modeling of, 658–659 Maillard reactions, 293 Manas-Zloczower mixing index, 562–563
733 Mass and heat transport, in drying of skim-milk droplet, 254–255 Mass (continuity), law of conservation, 5, 475 Mass transfer, in biosensors, 636 Matlab software, 718 Maxwell equations, for electromagnetics of microwave heating, 315–316 Mean age of air (MAA), 241–245, 711–712 Mean convective heat transfer coefficient, 716 Mean water flux, 716 Meat dryers airflow patterns in, 224–226 air relative humidity in, 226 CFD analysis mean age of air and, 241–245 steady-state numerical models, 227–232 unsteady numerical models, 232–20 height, 241–245 operation of, 224–227 ventilation cycle influence, 225–227, 234–240 Membrane and module, mass transfer of, 461–462 Membrane distillation (MD), 440, 445–446 Membrane emulsification (ME), 440, 461 Membrane filtration, 441–442 Membrane fouling, 434 Membrane processes, in food industry, 439–441 Membrane reactor (MR), 440 Membrane separations systems advantages and disadvantages, 439–440 CFD applications fluid behavior predictions, 451–453 fluid flow and mass transfer problems, 450 modeling, 435–439 turbulent conditions, 453 CFD codes, 436 concentration polarization in, 453–456 by electrical potential difference, 442–443 gel-polarization model, 454 by hydrostatic pressure difference, 441–442 under laminar conditions, 452–453 membrane modules hollow fiber, 448 plate-and-frame configuration, 448 spiral wound, 446–447 tubular membranes, 448 mesh schemes for, 437–438 by partial vapour pressure gradient membrane distillation, 445–446 pervaporation, 443–445 spacers effect on flow behaviors, 456–461 under turbulent conditions, 453 Menter-Langtry g u model, 19 Mesh structure in MPV, 616 Mesh superposition technique (MST), 519, 558
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734 Metal microfilters, 434 Michae¨lis–Menten model, 590–591, 636, 638 Microcalorimeter well, 638 Microcalorimetric biosensor, for ascorbic acid quantification, 637 Microfiltration, 440 Microfluidic channel fluid flow in, 633 injection process in, 645 Microorganisms inactivation, 538–539 Microplate calorimeter biosensor, 641 Microplate differential microcalorimetry, 637–638 Microwave heating and airflow heating in oven, 324–328 airflow modeling, 318–320 electromagnetics of, 315–318 power loss in, 317 Microwave oven airflow in, 320–322 heat transfer coefficient and flow pattern, 322–325 jet impingement-microwave heating, 324–328 mesh in, 321–322, 325–326 model of, 320–321 natural and forced convection heating, 322–323 MiDiCalyy, 638 Milk fouling model, 418 milk protein deposition profiles, 426 in PHE system, 422–429 principle of, 421 temperature profiles, 424, 428 validation of, 422–423 velocity profiles, 423–424 Milk powder, sorption isotherms of, 262–263 Mist cooling-humidification, in retail cabinets, 95 Mixed-suspension, mixed-product-removal (MSMPR) model, 567 Mixers, moving parts in multiple reference frame (MRF) technique, 556–557 time-dependent sliding mesh technique, 557 Mixing elements motion of, 556 Mixing flows, 558, 568 CFD simulation of, 556, 559–564 efficiency of, 562 measures, 560 processes, CFD analysis of, 564 time-averaged efficiency of, 562 Mixograph, 577 Mixproof valve (MPV) CFD analysis for, 615 cleanability prediction in, 617 flow modeling using Star-CD, 614
Computational Fluid Dynamics in Food Processing flow patterns in, 618–619 mesh configuration of, 615–617 MOFOR modeling, 20 Momentum, law of conservation, 5, 475 Motionless mixers, CFD analysis of, 564, see also Mixers Moving-mesh technique, 558 Multifluid model (MFM), 20 Multiphase flow technique, 13 Multiple reference frame (MRF) technique, 17, 557 Multiple shared space modeling (MUSES), 20
N Nanofiltration (NF), 440, 441, 444, 454 Natural convection, of fluid, 332, 360, 542 Navier–Stokes equations, 2, 5, 8, 12, 14, 130, 336, 475, 491, 543, 672 Near-wall treatment, 614, 626 Newtonian corn syrup mixing index for, 574–575 rheological fluid models for, 572 Newtonian fluids, 562 hydraulic performance of PHEs with, 383, 385–392 laminar mixing of, 564 Navier-Stokes equation of, 596 Newtonian model, 13 Newton–Raphson’s technique, 508 Newton’s second law of motion, 5 Nicotinamide adenine dinucleotide phosphate (NADPH), 645 Nonadiabatic compression, 549 Non-Newtonian fluid modeling of CFD, 12–14, 383 Numerical analysis of CFD, 14 Nusselt number (Nu), 260, 392–395, 397, 479, 496–497
O Open refrigerated display cases CFD design of air curtain for, 129–140 DAG geometries, 138 features of, 129–130 model description for, 131–139 boundary conditions for, 132, 134–135, 137 inside domain, 136–139 outside domain, 134–136 turbulence intensity at DAG, 134, 139 vertical velocity, 133
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Index contours and streamlines by PIV and CFD, 136 contours and vectors at DAG, 137 Oven, see Baking ovens; Microwave oven
P Packaged products airflow with PIV, 667–668 computational model for, 672–675 fabrication of transparent fixed bed, 668–669 flow field model for heat transfer process, 682–684 local heat transfer coefficients of, 679 location of horizontal and vertical planes, 677 three-dimensional projection of CFD model, 674 validation of, 679–681 PARSOL modeling, 20 Partial vapour pressure gradient, membrane separations by membrane distillation, 445–446 pervaporation, 443–445 Particle image velocimetry (PIV) technique, 45, 125, 133–137, 473, 492–493, 667–668 Particle population balance theory, 565 Pasteurization, eggs CFD for, 368–378 SE inactivation, 371–373 Peclet number (Pe), 339 Peleg equation, 202 Pervaporation (PV), 434, 440, 443–445, 454–456 Phan–Thien–Tanner (PTT) models, 514, 517, 568–569 PHOENICS, CFD codes, 16, 19–20, 178–179, 332–333, 541–544 Physicochemical transducer, 632 Pilot ripening room, geometry, 700–702 Plate-and-frame configuration membrane modules, 448 Plate heat exchangers (PHEs) CFD modeling, 406–411 fouling model, 418–421 temperature profile, 410–411 validation, 411–413, 422–423 fouling analysis, 418–429 geometrical properties, 383–385 hydraulic performance, 385–392 hydrodynamics of, 403–414 milk fouling process in, 423–429 operating conditions for, 422 thermal performance, 392–399, 418–429
use in food and dairy industries, 382–383 yoghurt processing in, 385–399 Poisson–Boltzmann equation, 635 Polyflow, 564, 572 POLYFLOW model, 20–21 Polymer extrusion, scale-up theories, 528–533 Porous media forced air cooling process, 661–665 heat transfer, 659–661 limitations, 666 and multiphase modeling for CFD, 11–12 transport phenomena, 652–659 and turbulence features of, 657 modeling of, 658 Power-law model, 13, 511–512 Prandtl numbers (Pr), 175, 392–395, 408, 491–492 Pressure-implicit with splitting of operators (PISO) technique, 22, 202 Pressure-transmitting fluids, 548 Protein denaturation, in baking process, 292–293 Pseudoboehmite, 566 Psychrotrophic microorganisms inactivation, 404
Q QUICK convection scheme, 15, 18
R Radial–angular plane temperature profile, of carrot–orange soup, 343–344 Radial flow cells, 609, 610 cleaning tests for, 611–612 turbulent flow in, 611 wall shear stress in, CFD prediction of, 611–613 Reaction kinetics, in biosensors, 636 Reaction rate constants, 592 Refrigerated display cases, CFD applications in, 26 Refrigerated rooms, air movement in analytical and empirical models, 172–174 applications, 175–185 CFD models, 174–180 cold stores, 170–171, 176–178 door protection air curtains, 172, 178–185 flexible fast-opening doors, 172 loading docks and vestibules, 172 strip curtain, 171–172 frozen stores, 170–171 infiltration, 171, 188–189 natural convention, 168–170 optimization of, 168–190
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C029 Final Proof page 736 9.4.2007 5:07pm Compositor Name: WOMAT
736 problems to operators, 168 validation of CFD models flow rate measurement, 188 gas decay measurement, 188–189 temperature measurement, 185–186 velocity measurement, 186–188 Refrigerated truck, CFD of airflow in air duct influence, 63–65 airspace thickness between wall and pallets, 61–63 empty truck case, 58–60, 66–67 experimental device, 48–49 flow-field, 55–58 with impermeable pallets, 60–65 loaded configuration with slotted pallets airflow characteristics, 70–71 air path lines inside load, 72 impermeable pallets truck case and, 67–70 jet characteristics, 65–66 ventilation efficiency, 73–74 modeling approach boundary conditions, 50–51 governing equations, 50 numerical resolution, 51–54 pallets’ interstices, 51–52 slotted wall, 52 ventilation efficiency analysis, 53–54, 73–74 numerical modeling, 45–46 and temperature distributions, 45 turbulence modeling, 57, 74–78 empty truck, 74–75 flow above pallets, 75–77 flow inside load, 77–78 slotted pallets, 75–78 turbulence models, 46–47 and velocity characteristics, 60–61 Refrigerated vehicles, see Refrigerated truck Relative air humidity of cheese, distribution of, 721 Renormalization group (RNG) k-e model, 9, 145, 476, 481, 701, 708 Reomixer, 576 flow pattern effects on, 578 geometry reset cycle, 579 material points in, 578, 580 mean time-averaged efficiency of, 581 velocity profile, 578 Residence time distribution (RTD), 511 Retail cabinets; see also Chilled multideck retail display cabinet; Display cabinets air curtains, 89–90 CFD aided design, 84–99 CFD applications air curtains and airflow modeling, 92–93
Computational Fluid Dynamics in Food Processing air humidity, 94 evaporator and rear ducts, 93 glass doors fogging and defogging, 95 mist cooling-humidification, 95 product temperature distribution, 91–92 radiation, 94 shelves, 93 CFD codes mass transfer, 97–98 methodology, 95–97 turbulence models, 97 validation, 98–99 classification air circulation, 87 energy consumption, 87 geometry, 85–86 refrigeration equipment, 86 storage temperature, 84–85 features of, 84 standardized temperature tests, 87–89 Retail food stores environment using CFD, 143–166 modeling display cabinet zone in, 146 Return air grille (RAG), 129–133, 135 Reverse osmosis (RO), 434–435, 440–442, 444–445, 454 Reynolds-averaged equations, 491 Reynolds-averaged Navier-Stokes (RANS) equations, 8, 11, 559 Reynolds fluxes, 174 Reynolds number (Re), 26, 132, 394–395, 397–398, 408, 495–497, 500, 543, 559, 612, 633, 671–672 Reynolds-number standard k e model, 9 Reynolds stresses, 8, 174, 491–492, 559 Reynolds stress model (RSM), 9, 11, 44–45, 492, 500 RFC, see Radial flow cells Rheological fluid models, 572 Richardson number, 26 Rotating planetary pin mixograph type mixer, 577
S Salmonella enteritidis (SE), 348 inactivation during pasteurization, 371–372 spatial distribution of, 373 thermal death time (TDT) approach, 371 Shear flows, 562 Shear stress fluid, 568 transport model, 476, 480–481, 492–496, 500
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C029 Final Proof page 737 9.4.2007 5:07pm Compositor Name: WOMAT
737
Index Shear thinning Carreau models, 568–569 power law fluids, CFD analysis of, 565 Shrink factor (Sf ), in drying process, 260–261 Silicon microsieves, 434 Single-paddle mixer rheology effects, 570 versus twin-paddle mixer, mixing ability of, 572–573 Single-screw extruder modeling, 511 Skewness values, 510 Skim-milk droplet diffusion coefficient of, 265 mass and heat transport in drying of, 254–255 Sliding mesh for modeling accuracy in CFD, 16–17 stirred tank application, 17 Slowest heating zone (SHZ), 332–333 Sodium carboxymethyl cellulose bacteria deactivation and vitamins destruction, 342–343 flow pattern of, 335–338 properties of, 334–335 shear thinning, 574–575 temperature profile, 335–338 thermal sterilization, see also Thermal sterilization in top insulated can, 337–339 in vertical can, 333–337 velocity vector of, 335–338 Sodium carboxymethyl cellulose-filled egg CFD analysis, 362–368 properties, 361–362 for validation of CFD model, 361 Software packages, in food industry, 539 Solid-liquid food mixture compression pressures of, 543, 545–547 high-pressure compression of, 540 simulation of, 540 temperature distribution, 546, 547 Sorption isotherms determination of, 262–263 GAB equation for, 261–262 Spacers, effects on flow behaviors, 456–461 Spatial convergence techniques, for modeling accuracy in CFD, 18 Specific mechanical energy (SME), 511, 518 Sphere-shaped valve, flow pattern in, 621 Spiegler–Kedem model, of membrane separations, 454 Spiral wound membrane modules, 446–447 Spray dryer CFD model for, 278–283 drying process and, 250–252
flow field profiles, 252 particle tracking, 252–254 simulation airflow pattern, 280 conditions of, 279 droplet feed and powder particles, 279, 282 parcels colliding with spray dryer wall, 279, 282 particle trajectories, 279, 281 temperature and moisture content of air, 279–281 transient and steady-state simulations for, 252 turbulence in, 252 Spray drying CFD model, 278–283 coalescence and agglomeration model, 275–278 diffusion based model approach, 256–265 fouling pattern of dryer equipment, 271 interparticle collision models, 272–275 mass and heat transport phenomena, 254–256 sorption isotherms approach, 261–264 stickiness submodels, 267–271 thermal reactions submodels, 265–267 Standardized temperature test for retail cabinets, 87–89 warmest and coldest temperature during, 91 Static mixer, see Motionless mixers Sterilization, CFD applications in, 26–28 Stickiness spray drying submodels glass transition and sticky-point temperature for, 268–271 Stirred tanks, CFD applications in, 28–30 Stirred yoghurt, see Yoghurt Stokes–Einstein equation, 339 Streamline upwinding=Petrov–Galerkin (SUPG), 509 Streptococcus salivarius, 381 Submerged jets, 471 Sulfur hexafluoride (SF6 ), use to measure infiltration, 188, 190 Superficial airflow velocities, 592
T Tamm’s model, 170, 173 Taste analysis electrokinetic biochip for, 641 lab-on-a-chip design, 642–643 Tea bag brewing method, 594 design, with in-use brewing, 596–599 infusion CFD simulation of, 594, 597
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C029 Final Proof page 738 9.4.2007 5:07pm Compositor Name: WOMAT
738 integrating product design, 594 multiphysical process of, 595 round computer-simulated infusion of, 600 dynamic infusion of, 599 static infusion of, 598 Tea fermentation airflow impacts on, 591 biochemical reactions of, 590 CFD simulation of, 590 heat generation, 591 integrated product–process design, 592 Tea leaf macerated dhool, 591 packed bed of, 597–598 Tea polyphenols, 590 Tea solid concentration computer-simulated contours of, 598–599 with UV absorbance, 597 dissolved, mass transfer of, 596 Theaflavins, 590 accumulation of, 593–594 temperature effects on, 593 Thearubigins, 590 Thermal load, in drying process, 251 Thermal reactions, model for spray drying, 265–267 Thermal sterilization bacteria deactivation and vitamins destruction, 339–343 conditions and equations for, 340 convection discretization scheme, 339 kinetics, 340–341 in horizontal can, 343–344 in top insulated can temperature profile, 338–339 velocity vector profile, 337–338 in vertical can flow pattern of, 336–337 governing equations and boundary conditions, 336 grid mesh used in, 333–334 properties of, 334–335 temperature profile, 336–337 velocity vector of, 336–337 Thermodynamics, first law of, 5 Three-tip kneading blocks, disk surface, 524 Threshold value, for EHEDG test soil, 611 Threshold wall shear stress, for hygiene prediction, 607 Time-dependent sliding mesh technique, 557 Track etched membranes, 434
Computational Fluid Dynamics in Food Processing Transparent liquid-solid model, for PIV applications, 668 Transport phenomena, theoretical analysis of, 652 Transport properties system, 544 Traveling-tray baking oven, 294–296 Tubular heat exchangers, 404–405; see also Heat exchangers Tubular membranes, 448 Turbulence intensity, 608 Turbulence model of CFD, 8–11, 14, 46–47, 74–78 for chilled multideck retail display cabinet, 111–112 for flow modeling, 614 Turbulent flows at high Reynolds numbers, 559 in RFC, 611 techniques to handle, 559 through porous media, 657–658 Turbulent jets, 471 Turbulent kinetic energy, 614 Twin-screw extruder, 517, 519
U Ultrafiltration (UF), 434–435, 440–442 Unstructured mesh, for improving modeling accuracy in CFD, 16 UPWIND convection scheme, 15, 18 Upwind differencing scheme (UDS), 339
V Valve house, spherical-shaped cleaning procedure of, 609 mixproof valve (MPV), 610 Vane anemometry, 186 VD–VD=DRY collision, 276–278 Ventilation homogeneity, 45, 237, 708 Vertical multideck display cabinet, 85, 144–145 Virtual reality modeling language (VRML) output, 117 Viscoelastic constitutive model, 517 Viscoelastic flow models, 556 Viscosity fluid, mixing of, 559 Viscous dissipation, 562 Viscous Newtonian fluid model, 568–569 Vitamins destruction, in thermal sterilization, 339–343 Volume-averaging technique, 652–653
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C029 Final Proof page 739 9.4.2007 5:07pm Compositor Name: WOMAT
739
Index
W Wall distance turbulence model, 20 Wall shear stress cleanability prediction of, 617–619, 626 in complex equipment, 613–617 magnitude of, 622 measurement, by electrochemical sensors, 608 threshold value of, 611 in turbulent flow, 609 Water exchanges of cheeses, 715 airflow and water losses of, 718–722 heat and water transfer coefficients, 716–718 losses of cheeses, 718 physical properties of, 543
Water=glycerine solution, particle image velocimetry (PIV) experiments on, 565 Water transfer coefficients, 716
Y Yasuda–Carreau equation, 518 Yeast fermentation, in baking process, 292 Yoghurt manufacturing defects of, 391 processing in PHEs hydraulic performance, 385–392 thermal performance, 392–399 rheology of, 381–383
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C029 Final Proof page 740 9.4.2007 5:07pm Compositor Name: WOMAT
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_ColorInsert_A
Airflow
Airflow
Final Proof page 1 25.4.2007 7:43pm Compositor Name: BMani
273.8 K 275.8 K 277.8 K 279.9 K 281.9 K 283.9 K 285.9 K 288.0 K 290.0 K 292.0 K
Porous media
Airflow
Bottom layer (XY plane, Z = 1)
Lower middle layer (XY plane, Z = 2)
Upper middle layer (XY plane, Z = 3)
Top layer (XY plane, Z = 4)
Airflow
Solid region (tray)
FIGURE 1.4 The modeling of flow through ventilated packaging using a multiphase flow technique. (From Zou, Q., Opara, L.U., and McKibbin, R., J. Food Eng., 77, 1037, 2006; Zou, Q., Opara, L.U., and McKibbin, R., J. Food Eng., 77, 1048, 2006.)
Rear duct
Turning vane
Evaporator
(a1)
(a2)
Dead space Velocity Side of duct 0.8
Rest of duct not modeled
Velocity 1.1 0.8
0.5 0.5 0.3
110 mm
0.3
0.0
Evaporator moved forward
50 mm
0.0
[m s−1]
[m s−1]
(b1)
(b2) Temperature
15 mm
−0.0
Angle 60 mm
Temperature −0.0
−0.8
−0.8
−1.5
Product −2.3
Product
−3.0
(c1)
−3.0
(c2)
FIGURE 1.11 Visualizations of air curtain used to modify cabinet design. (From Foster, A.M., Madge, M., and Evans, J.A., Int. J. Refrig., 28, 698, 2005.)
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_ColorInsert_A
Ceiling
Y
W (m s−1)
Inlet
Top of pallets
X
−2.5 −1.1 Numerical results
Final Proof page 2 25.4.2007 7:43pm Compositor Name: BMani
2.8
1
Y
W (m s−1) −0.5
4.9
3.8
−0.3
X
0
Numerical results
−0.2 - 0
0.2
0.3
−0.4 - −0.2 m s−1
2 – 4 m s−1 0 – 2 m s−1
0.1
m s−1
−2 – 0 m s−1 0 - 0.2 m s-1
−4 – −2 ms−1
0.2 - 0.4 m s-1 Experimental results
Experimental results
(a)
(b)
Y
W (m s−1) −0.02
−0.01
X 0
0.01
0.02
Numerical results
−0.2 - 0.1 m s-1 -0.1 - 0
m s-1
0 - 0.1 m s-1 0.1 - 0.2 m s-1 Experimental results
(c)
FIGURE 2.13 Velocity field above the loading at (a) L=4, (b) L=2, and (c) 3L=4: comparisons between numerical and experimental data.
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_ColorInsert_A
w2 (m 2 s −2)
0
0.1
Final Proof page 3 25.4.2007 7:43pm Compositor Name: BMani
1
2
3
4
(a) 3 − 4 m2 s−2 1 − 2 m2 s−2
2 − 3 m2 s−2
0 − 1 m2 s−2
(b)
FIGURE 2.14 Contours of the mean-square of the turbulent velocity in the z direction (w2 ) above the loading at L=4. (a) Numerical values and (b) experimental values.
0
0.2
0.4
0.6
0.8
1
(a)
−10 −12 −13 −15 −16 −18 −19 −20 −22 −24 −25 −26 −28
(b)
FIGURE 2.15 Numerical contours of velocity and temperature in the most sensitive planes of the truck: (a) velocity contours: W=W0, (b) contours of temperature (8C); T0 ¼ 288C; Te ¼ þ308C.
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_ColorInsert_A
T (⬚C)
−28
−26
−24
−22
Final Proof page 4 25.4.2007 7:43pm Compositor Name: BMani
−20
−18
−16
(a)
(b)
FIGURE 2.19 Numerical results concerning contours of iso-temperatures in the most sensitive plane of the truck located between lateral wall and pallets with and without air ducts. (a) Without air duct and (b) with air duct.
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_ColorInsert_A
Temperature
Final Proof page 5 25.4.2007 7:43pm Compositor Name: BMani
15 mm
−0.0
−0.8
−1.5
−2.3
Product
−3.0 [°C] Y Z
X
CFX
FIGURE 4.4 Velocity vectors predicted by CFD in a vertical plane at the top of the cabinet. The length of the vector is proportional to the air velocity, the color represents the temperature (air curtain 1.5 m s1 and 15 mm).
Turning vane
Z Y
X
CFX
FIGURE 4.7 Streamlines predicted by CFD from the exit of the evaporator for the modified cabinet.
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_ColorInsert_A
Final Proof page 6 25.4.2007 7:43pm Compositor Name: BMani
FIGURE 4.8 2D model of a multideck display cabinet showing velocity vectors and temperature contours. The air curtain is bent in toward the cabinet where shelves have been removed.
19.1
21.7
19.6
22.1
21.9
21.5
21.8
22.1
22.0
18.0
22.0
18.1 16.7
> 2.9000E + 02 2.8773E + 02 2.8462E + 02 2.8150E + 02 2.7838E + 02 2.7527E + 02 < 2.7300E + 02
22.4
18.2
> 2.9800E + 02 2.9720E + 02 2.9610E + 02 2.9500E + 02 2.9390E + 02 2.9280E + 02 < 2.9200E + 02
13.3
13.3 14.3 12.6
0.25 m above floor
21.8
21.6
21.1
21.7 22.2 22.4 22.4
16.5
23.3
2 m above floor
FIGURE 4.9 Plan view of store at a height of 0.25 m and 2.0 m. Colors show predicted temperatures (K) and values of measured temperature (8C) are superimposed.
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_ColorInsert_A
Final Proof page 7 25.4.2007 7:43pm Compositor Name: BMani
CFX 80 Velocity (vector 1) 6
Temperature (contour 1) (10) 20 (9) 16 (8) 12
5
3
2
8
(6)
4
(5) −0 (4) −4
7 6 5 4
(3) −8 (2) −12
3
(1) −16
0 [m
(7)
s−1] 2
1
FIGURE 7.7 CFD predicted velocity vectors and temperature contours for a vertical section through the entrance with a jet velocity of 6 m s1.
CFX 80 Temperature (contour 1) (10) 20
Velocity (vector 1) 10
(9) 16 (8) 11
8
5
(7)
7
(6)
3
(5) −1 (4) −6
3
(3) −10 (2) −14 (1) −18
0 [m s−1] 1
2345
FIGURE 7.8 CFD predicted velocity vectors and temperature contours for a vertical section through the entrance with a jet velocity of 10.4 m s1.
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_ColorInsert_A
Final Proof page 8 25.4.2007 7:43pm Compositor Name: BMani
CFX 80 Velocity (vector 1) 18
2
1 Temperature (contour 1) (10) 20 (9) 17
14
(8) 14 (7) 11 (6) 8
9 (5) 5 (4) 2 5
(3) −1 (2) −4
0 [m s−1]
(1) −7 Y z
X
FIGURE 7.9 CFD predicted velocity vectors and temperature contours for a vertical section through the entrance with a jet velocity of 18 m s1 .
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_ColorInsert_B Final Proof page 1 9.4.2007 12:59pm Compositor Name: BMani
STAR
pro-STAR 3.2 21-July-06 Velocity magnitude m s−1 ITER = 1700 Local MX = 18.18 Local MN = 0.1470
Z Y
18.18 16.89 15.60 14.31 13.03 11.74 10.45 9.163 7.875 6.587 5.299 4.011 2.723 1.435 0.1470
X
FIGURE 10.13 Airflow pattern.
STAR
pro−STAR 3.2 12−July−06 Temperature (°C) ITER = 1700 Local MX = 185.0 Local MN = 75.36 185.0 177.2 169.3 161.5 153.7 145.8 138.0 130.2 122.3 114.5 106.7 98.86 91.02 83.19 75.36
Z Y
FIGURE 10.14 Contour of air temperature.
X
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_ColorInsert_B Final Proof page 2 9.4.2007 12:59pm Compositor Name: BMani
STAR
pro-STAR 3.2 21−July−06 ITER = 1700 Local MX = 45.91 Local MN = 10.00 Moisture in dry air (g/kg) 45.91 43.35 40.78 38.22 35.65 33.09 30.52 27.96 25.39 22.83 20.26 17.70 15.13 12.57 10.00
Z Y
X
FIGURE 10.15 Contour of moisture content of air.
STAR
pro-STAR 3.2 21-July-06
Z Y
FIGURE 10.16 Particle trajectories.
X
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_ColorInsert_B Final Proof page 3 9.4.2007 12:59pm Compositor Name: BMani
84 87 90 92 95 97 100 103 105 108 111 113 116 118 121
(a)
0.0e+0 3.1e+5 6.2e−5 9.3e−5 1.2e−4 1.5e−4 1.9e−4 2.2e−4 2.5e−4 2.8e−4 3.1e−4 3.4e−4 3.7e−4 4.0e−4 4.3e−4
(b)
(c)
FIGURE 13.2 (a) Temperature profile, (b) velocity vector, and (c) flow pattern of CMC in a vertical can heated by condensing steam after 1157 s. The right-hand side of each figure is centerline. (From Abdul Ghani, A.G., Farid, M.M., Chen, X.D., and Richards, P.J., J. Food Eng., 41, 55, 1999.)
40 46 52 57 63 69 75 81 86 92 98 104 110 115 121
(a)
40 46 52 57 63 69 75 81 86 92 98 104 110 115 121
(b)
108 109 110 111 112 113 114 115 116 116 117 118 119 120 121
83 86 88 91 94 96 99 102 105 107 110 113 116 118 121
(c)
(d)
FIGURE 13.4 Temperature profiles in a can filled with CMC and heated by condensing steam (top insulated) after periods of (a) 54 s, (b) 180 s, (c) 1157 s, and (d) 2574 s. The right-hand side of each figure is centerline. (From Abdul Ghani, A.G., Farid, M.M., Chen, X.D., and Richards, P.J., J. Food Eng., 41, 55, 1999.) 0 7 14 22 29 36 43 50 57 64 72 79 86 93 100
(a)
0 6 12 17
0.0e+0
23 29 35 40 46 52
3.5e−4 4.4e−4
57 63 69 75
8.8e−4
8.8e−5 1.8e−4 2.6e−4
5.3e−4 6.2e−4 7.0e−4 7.9e−4 9.7e−4 1.1e−3 1.1e−3 1.2e−3
80
(b)
(c)
FIGURE 13.5 Deactivation of bacteria in a can filled with CMC and heated by condensing steam after (a) 180 s, (b) 1157 s, and (c) 2574 s, respectively. The right-hand side of each figure is centerline. (From Abdul Ghani, A.G., Farid, M.M., Chen, X.D., and Richards, P.J., J. Food Eng., 42, 207, 1999.)
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_ColorInsert_B Final Proof page 4 9.4.2007 12:59pm Compositor Name: BMani
Residual vitamin C (%)
Residual vitamin B1 (%)
Residual vitamin B2 (%)
FIGURE 13.6 Vitamins C, B1, and B2 destruction in a can filled with concentrated cherry juice and heated by condensing steam after 1640 s. The right-hand side of each figure is centerline. (From Abdul Ghani, A.G., Farid, M.M., Chen, X.D., and Richards, P.J., 10th World Congress of Science and Technology, 1999.)
(a)
(b)
FIGURE 13.7 Radial–angular plane temperature profile of carrot–orange soup in a 3D cylindrical can lying horizontally and heated by condensing steam after 600 s at two different planes in the direction of (a) radial–angular plane and (b) radial–vertical plane. (From Abdul Ghani, A.G., Farid, M.M., and Chen, X.D., J. Food Eng., 51, 77, 2002.)
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_ColorInsert_B Final Proof page 5 9.4.2007 12:59pm Compositor Name: BMani
2.68e-01 2.51e-01 2.34e-01 2.18e-01 2.01e-01 1.84e-01 1.67e-01 1.51e-01 1.34e-01 1.17e-01 1.00e-01 8.37e-02 6.70e-02 5.02e-02 3.35e-02 1.67e-02
2.88e-04 2.70e-04 2.52e-04 2.34e-04 2.16e-04 1.98e-04 1.80e-04 1.62e-04 1.44e-04 1.26e-04 1.08e-04 9.00e-05 7.20e-05 5.40e-05 3.60e-05 1.80e-05 0.00e+00
FIGURE 18.4 Velocity and concentration profile of membrane flow channel with a baffle. (From Liu, S.X., Peng, M., and Vane, L.M., J. Membr. Sci., 265, 124, 2005.)
FIGURE 18.10 Concentration contour and flux distribution for baffle distance of 5.7 mm. (From Liu, S.X., Peng, M., and Vane, L.M., J. Membr. Sci., 265, 124, 2005.)
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_ColorInsert_B Final Proof page 6 9.4.2007 12:59pm Compositor Name: BMani
Temperature
Temperature
Temperature
3.032e+01
5.610e+01 5.470e+01 5.330e+01 5.190e+01 5.050e+01 4.910e+01 4.770e+01 4.630e+01 4.490e+01 4.350e+01 4.211e+01 4.071e+01 3.931e+01 3.791e+01 3.651e+01 3.511e+01
6.150e+01 5.995e+01 5.841e+01 5.686e+01 5.532e+01 5.377e+01 5.223e+01 5.068e+01 4.914e+01 4.759e+01 4.605e+01 4.450e+01 4.296e+01 4.141e+01 3.987e+01 3.032e+01
Solid−liquid at 200 MPa after 12 s
Solid−liquid at 400 MPa after 24 s
4.000e+01 3.935e+01 3.871e+01 3.806e+01 3.742e+01 3.677e+01 3.613e+01 3.548e+01 3.484e+01 3.419e+01 3.355e+01 3.290e+01 3.226e+01 3.161e+01 3.097e+01
Solid−liquid at 500 MPa after 30 s
FIGURE 22.5 Radial–vertical temperature profile of the solid–liquid food mixture (beef fat and water) at compression rates of 200, 400, and 500 MPa, respectively. The red arrow shown in the figure is just for a point in the computation process. (From Abdul Ghani, A.G. and Farid, M.M., Journal of Food Engineering, in press.)
Velocity
Temperature
1.858e−03
3.589e+01
1.734e−03
3.484e+01
1.610e−03
3.379e+01
1.486e−03
3.274e+01
1.362e−03
3.169e+01
1.238e−03
3.064e+01
1.115e−03
2.959e+01
9.908e−04
2.853e+01
8.669e−04
2.748e+01
7.431e−04
2.643e+01
6.192e−04
2.538e+01
4.954e−04
2.433e+01
3.715e−04
2.328e+01
2.477e−04
2.223e+01
1.238e−04
2.118e+01
3.629e−12
2.013e+01
FIGURE 22.10 Temperature and velocity profiles of the fluid at the early stage (t ¼ 30 s) of compression rate of 500 MPa. (From Abdul Ghani, A.G. and Farid, M.M., Journal of Food Engineering, in press.)
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_ColorInsert_B Final Proof page 7 9.4.2007 12:59pm Compositor Name: BMani
(b)
0.222 0.222 0.221 0.221 0.22 0.22 0.219 0.219 0.218 0.218 0.217 0.217 0.216 0.216 0.215 0.215 0.214 0.214 Z 0.213 0.213 X Y 0.212
FIGURE 23.4 (b) Volume fraction of lactose crystals on a horizontal plane. (Note that the two shaded boxes in flow domain are the inlet and outlet positions. The lowest volume fraction of crystals is located near the inlet.) Absorbance 3.0
0.0
t = 20 s
40 s
60 s
120 s
t = 20 s
40 s
60 s
120 s
FIGURE 24.5 Computer-simulated contours of tea solid concentration (above, expressed in absorbance) and velocity fields (below) during the static infusion of a round tea bag.
Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_ColorInsert_B Final Proof page 8 9.4.2007 12:59pm Compositor Name: BMani
Absorbance 3.0
0.0
t = 20 s
40 s
60 s
120 s
FIGURE 24.6 Computer-simulated contours of tea solid concentration (above, expressed in absorbance) and velocity fields (below) during the dynamic infusion of a round tea bag. The velocity fields are presented for a cycle of dunking.
h/D = 1
t w (Pa)
FIGURE 25.2 Wall shear stress (left) and fluid exchange in computational cell closets to boundary (right) predicted using Star-CD. For the fluid exchange on the right, blue colors represent the old fluid and red colors the new fluid.
