Computational Optimization of Internal Combustion Engines

Computational Optimization of Internal Combustion Engines

Yu Shi Hai-Wen Ge Rolf D. Reitz •

•

Computational Optimization of Internal Combustion Engines

123

Dr. Yu Shi Department of Chemical Engineering Massachusetts Institute of Technology Bldg. 66-264 77 Massachusetts Avenue Cambridge, MA 02139 USA e-mail: [email protected]

Prof. Rolf D. Reitz Engine Research Center University of Wisconsin-Madison 1500 Engineering Dr. Madison, WI 53706 USA e-mail: [email protected]

Dr. Hai-Wen Ge Engine Research Center University of Wisconsin-Madison 1500 Engineering Dr. Madison, WI 53706 USA e-mail: [email protected]

ISBN 978-0-85729-618-4

e-ISBN 978-0-85729-619-1

DOI 10.1007/978-0-85729-619-1 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Ó Springer-Verlag London Limited 2011 CONVEREGE is a trademark of Deltatheta UK Limited, The Technocentre, Puma Way, Coventry, CV1 2TT, UK CONVERGE is a trademark of Convergent Science, Inc. (Details in http://www.convergecfd.com/) Forte is trademark of Reaction Design (Details in http://www.reactiondesign.com/) modeFRONTIER is a trademark of ES.TEC.O. s.r.l., AREA Science Park Padriciano, 99, Trieste, Italy, 34012 Oracle and Java are registered trademarks of Oracle and/or its affiliates. Other names may be trademarks of their respective owners. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Cover design: eStudio Calamar S.L. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Preface

Striking progress has been made in internal combustion engine design due to the development of computer models and optimization techniques. In this book we strive to document the state of the art in predictive IC engine modeling and optimization. The fact that this is an important topic for research and development is emphasized by society’s reliance on IC engines for transportation, commerce and power generation. Indeed, the world as we know it would be a quite different place were it not for the remarkable internal combustion engine! It drives all manner of utility devices (e.g., pumps, mowers, chain-saws, portable generators, etc.), as well as earth-moving equipment, tractors, propeller aircraft, ocean liners and ships, personal watercraft and motorcycles. However, its major application is powering the 600 million passenger cars and other vehicles on our roads today. 250 million vehicles (cars, buses, and trucks) were registered in 2008 in the United States alone. According to the International Organization of Motor Vehicle Manufacturers, about 50 million cars were made world-wide in 2009, compared to 40 million in 2000. Much of this dramatic increase comes from increased prosperity in China, which became the world’s second-largest car market in 2010. A third of all cars are produced in the European Union, and about 50% of those are powered by diesel engines. Thus, IC engine research spans both gasoline and diesel powerplants. The world’s economic expansion has been powered by cheap oil. It has been argued that the increase in population from 1.9 billion in the 1920s to today’s 6.6 billion has been made possible, in part, by fossil fuel combustion and by the Haber–Bosch process to make crop fertilizer. 80% of the roughly 80 billion barrels of crude oil consumed annually world-wide is used in IC engines for transportation. In the United States, 10 million barrels of oil are used per day in automobiles and light-duty trucks, and 4 million barrels per day are used in diesel engines, with total oil usage of about 2.5 gallons per day per person. Of this, 62% is imported oil, which at today’s $80/barrel, costs the US economy $1 billion/day. This cost is certain to increase as more-and-more economic development drives increased demand for automotive fuels world-wide.

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Preface

Associated with our massive oil use is the accompanying annual emission of 37 billion tons of CO2 (6 tons each for each person in the world) and other pollutant emissions, including nitric oxides (NOx) and particulates (soot). Pollutant emissions have serious environmental and health implications, and thus most governments have imposed stringent vehicle emissions regulations that are continually being tightened further. In addition, CO2 emissions contribute to Green House Gases (GHG), which some fear could lead to climate change with unpredictable consequences. Drastic reductions in fuel usage will be required to make appreciable changes in GHG trends. Today’s gasoline IC engine powered vehicle equipped with its 3-way catalyst for emission control converts only about 16% of the chemical energy in the fuel to useful work—the rest is lost to the environment. The modern automotive diesel engine is 20 to 40% more efficient than its gasoline counterpart. However, measures introduced to meet emissions mandates, such as the use of non-optimal fuel injection timings, large amounts of Exhaust Gas Recirculation (EGR) or ultra-high injection pressures reduce diesel engine fuel efficiencies, and also increase engine expense. Many diesel engine manufacturers have elected to use Selective Catalytic Reduction (SCR) exhaust after-treatment for NOx reduction. However, with SCR there is also a fuel penalty since a reducing agent such as urea (carbamide) must be sprayed into the exhaust stream at rates (and cost) of about 1% of the fuel flow rate for every 1 g/kWh of NOx reduction desired. Soot control is achieved using Diesel Particulate Filters (DPF), which generally require periodic regeneration. This is achieved by adjusting the fuel-air mixture strength so as to increase exhaust temperatures to burn off the accumulated soot, which imposes as much as a 3% additional fuel penalty. From these discussions it is clear that new technologies are urgently needed to improve the efficiency of both gasoline and diesel engines. For further improvements, engines need to be optimized to balance emissions, fuel cost, and market competitiveness. As described in this book, this task can be efficiently attacked using state-of-the-art computational models and optimization methods. This has been made possible, in part, by dramatic increases in computer speeds that have increased 10,000-fold in the past 15 years. Engine development is now greatly facilitated using multi-dimensional Computational Fluid Dynamic (CFD) tools and optimization algorithms, supported by significantly reduced requirements for experimental testing, which is extremely expensive. An additional enabling factor for engine CFD modeling has been the development of predictive models for the physical processes occurring in the combustion chamber. Many of these models are reviewed in this book, together with discussion of strategies to reduce computational cost and numerical inaccuracies. Example applications are presented for the optimization of 2-stroke spark-ignition gasoline and 4-stroke heavy- and light-duty diesel engines. The effects of design parameters including nozzle design, injection timing and pressure, swirl, EGR, engine size scaling, and piston bowl shape are considered, together with exploration of fuel effects for low temperature combustion strategies. It is also demonstrated how optimization results can be used in combination with regression

Preface

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analysis to explore and explain the complex interactions between engine design parameters. The present example applications also demonstrate that current multi-dimensional CFD tools are mature enough to guide the development of more efficient and cleaner internal combustion engines. New low temperature combustion concepts, such as Homogeneous Charge Compression Ignition (HCCI), Premixed Charge Compression Ignition (PCCI) and Reactivity Controlled Compression Ignition (RCCI) offer the promise of dramatically improved engine efficiencies. For example, optimized dual fuel RCCI operation (port injection of gasoline together with optimized in-cylinder multiple diesel fuel injections) was discovered with computer simulations using the models and tools described in this book (Kokjohn et al. 2009). The computer simulations predicted high-efficiency, lowemissions operation with excellent combustion phasing control at high and low engine loads without excessive rates of pressure rise. Subsequent engine experiments have confirmed the model predictions, and have demonstrated that US EPA 2010 NOx and soot emissions mandates can be met in-cylinder without aftertreatment, while achieving up to 57% gross indicated thermal efficiency (Kokjohn et al. 2011). The adoption of RCCI combustion engines could improve fuel efficiencies by up to 20% over standard diesel operation, while also providing dramatic cost reductions through the elimination of the need for exhaust after-treatment. RCCI is applicable with a wide range of fuels, including conventional gasoline and diesel, as well as biofuels such as ethanol and biodiesel and their blends. The implications of such improvements in fuel efficiency are very significant. For example, if RCCI were adopted to replace the relatively inefficient spark-ignition engine it is estimated that US transportation oil usage could be reduced by 34%, which equals 100% of the current US oil imports from Persian Gulf. If these efficiency improvements were combined with electric hybrid technologies in the vehicle, even greater reductions in oil usage would be possible. The ultimate goal of engine modeling is to guide designers to improve engine performance and to reduce pollutant emissions. The goal of this book is to provide an up-to-date reference to current developments and future directions in the field of engine modeling. We hope that you will think that we have achieved this goal.

Acknowledgments

This book expands on recent computational optimization studies of internal combustion engines performed at the Engine Research Center of the University of Wisconsin-Madison. The present work would not have been possible without the solid research foundation that our ERC colleagues have built over the past dec-ades. We would like to express our sincere gratitude to them. During the preparation of this book, we also received valuable suggestions from our colleagues, Dr. Shiyou Yang, Dr. Yuxin Zhang and Mr. Yue Wang, to whom we are indebted. The work included in this book was supported financially by several government and industry research projects. We are grateful to the US Department of Energy, Caterpillar Inc., Ford Motor Company, General Motors, and Detroit Diesel Company for their long term support. We also thank Dr. David Wickman of Wisconsin Engine Research Consultants for allowing use of the Kwickgrid software. ESTECO provided access to optimization software (modeFRONTIER), which facilitated some of the assessment studies in this book. We thank the Society of Automotive Engineers (SAE), American Society of Mechanical Engineers (ASME), American Chemical Society (ACS), SAGE Publications Ltd., Elsevier, and Taylor & Francis for allowing us to use figures and other materials from previously published articles. We also thank Springer for inviting us to write and helping us to prepare this book. Finally, we very much appreciate our families for their love, encouragement, support, and their understanding in our lives, in our research work, and in the preparation of this book. December 31, 2010

Yu Shi Hai-Wen Ge Rolf D. Reitz

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Contents

1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Roles of Internal Combustion Engines . . . . . . . . . . . . . . . . . 1.2 Modeling of Internal Combustion Engines . . . . . . . . . . . . . . 1.3 Computational Optimization of Internal Combustion Engines . 1.3.1 Engine Optimization with Parametric Studies . . . . . . . 1.3.2 Engine Optimization with Non-Evolutionary Methods . 1.3.3 Engine Optimization with Evolutionary Methods . . . .

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Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Optimization Algorithms . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Comparison of Different Optimization Algorithms 2.1.2 Multi-Objective Genetic Algorithms . . . . . . . . . . 2.1.3 Genetic Algorithm Source Code and Software . . . 2.2 Engine Modeling with Computational Fluid Dynamics. . . 2.2.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . 2.2.2 Physical Models . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . 2.2.4 CFD Codes and Software for Engine Simulations . 2.3 Regression Analysis Methods . . . . . . . . . . . . . . . . . . . .

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Acceleration of Multi-Dimensional Engine Simulation with Detailed Chemistry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Methods for Reducing Mesh- and Timestep-Dependency in Engine CFD Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Efficient Methods for Reaction Mechanism Reduction . . . . . . . 3.2.1 Overview of Reaction Mechanism Reduction . . . . . . . . 3.2.2 Automatic Mechanism Reduction of Hydrocarbon Fuels for HCCI Engines Based on DRGEP and PCA Methods with Error Control. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 An Adaptive Multi-Grid Chemistry (AMC) Model . . . . . . . . .

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3.3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Model Description. . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . An Extended Dynamic Adaptive Chemistry (EDAC) Scheme . 3.4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Model Description. . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Assessment of Optimization and Regression Methods for Engine Optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Assessment of Multi-Objective Genetic Algorithms . . . . . . 4.2 Assessment of NSGA II: Niching Technique, Convergence and Diversity Metrics. . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Design- and Objective-Space Niching of NSGA II . 4.2.2 Convergence and Diversity Metrics . . . . . . . . . . . . 4.2.3 Assessment of Niching Strategies . . . . . . . . . . . . . 4.3 Assessment of Regression Methods for Replacing CFD Evaluations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scaling Laws for Diesel Combustion Systems . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Scaling Laws . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Combustion Chamber Geometry . . . . . . . . 5.2.2 Power Output . . . . . . . . . . . . . . . . . . . . . 5.2.3 Spray Tip Penetration . . . . . . . . . . . . . . . 5.2.4 Flame Lift-Off Length . . . . . . . . . . . . . . . 5.2.5 Swirl Ratio. . . . . . . . . . . . . . . . . . . . . . . 5.2.6 Summary of Scaling Laws . . . . . . . . . . . . 5.3 Validation of Scaling Laws on a Light-Duty and a Heavy-Duty Diesel Engine . . . . . . . . . . . . . . . . . 5.3.1 Engine Specifications . . . . . . . . . . . . . . . 5.3.2 Numerical Models. . . . . . . . . . . . . . . . . . 5.3.3 Results and Discussion . . . . . . . . . . . . . . 5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Engine Optimization with Simple Combustion Models. . . . 6.1.1 Optimization of a 2-stroke Direct-Injection Spark-Ignited Engine . . . . . . . . . . . . . . . . . . . . . . 6.1.2 Optimization of a Caterpillar Heavy-Duty Diesel Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.3 Optimization of a DDC Heavy-Duty Diesel Engine.

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6.1.4

Optimization of a High-Speed Direct-Injection Diesel Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Engine Optimization with Advanced Combustion Models . . . 6.2.1 Optimization of a Heavy-Duty Compression-Ignition Engine Fueled with Diesel and Gasoline-Like Fuels . . Strategies for Simultaneous Optimization of Multiple Engine Operating Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 A Two-Step Method for Simultaneous Optimization of Multiple Operating Conditions . . . . . . . . . . . . . . . 6.3.2 A Consistent Method for Simultaneous Optimization of Multiple Operating Conditions . . . . . . . . . . . . . . . Coupling of Scaling Laws with Computational Optimization . 6.4.1 Downsizing of a HSDI Diesel Engine . . . . . . . . . . . . 6.4.2 Optimization of Downsized Engine . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6.2

6.3

6.4

6.5 7

Abbreviations, Nomenclature

Abbreviations AFR ALE AMC ARMOGA ATDC BFGS BML BTDC CA CFL CHA CI CDM CFD CFM CMC COSSO CSP CTC DAC DDB DDF DDM DFS DI DICI DISC DMZ DNS

Air-fuel ratio Arbitrary Lagrangian–Eulerian Adaptive multi-grid chemistry Adaptive range multi-objective genetic algorithm After top dead center Broyden–Fletcher–Goldfarb–Shanno Bray-Moss-Libby Before top dead center Crank angle Courant–Friedrichs–Lewy Chalmers Compression ignition Continuous droplet model Computational fluid dynamics Continuous formulation model Conditional moment closure Component selection and smoothing operator Computational singular perturbation Characteristic time combustion Dynamic adaptive chemistry Droplet deformation and breakup Droplet distribution function Discrete-droplet model Depth first search Direct injection Direct injection compression ignition Direct injection stratified charge Dynamic multi-zone Direct numerical simulation

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DOI DPF DPIK DRG DRGEP EDAC EGR EOI EPA EPFM EPO ERC EVO FTP GDI GISFC HCCI HSDI HTC HRR ILDM IMEP ISFC IVC KH KN KR LDEF LES LHF LISA LLNL MD MDDNPS MDEPF MDPF MMF MOC MOEA MOGA MOP NMHC NN NPR NPS

Abbreviations, Nomenclature

Duration of injection Diesel particulate filter Discrete particle ignition kernel Directed relation graph Directed relation graph with error propagation Extended dynamic adaptive chemistry Exhaust gas recirculation End of injection Environmental Protection Agency Eulerian particle flamelet model Exhaust port open Engine Research Center Exhaust valve opening Federal test procedure Gasoline direct injection Gross indicated specific fuel consumption Homogeneous charge compression ignition High speed direct injection High throughput computing Heat release rate Intrinsic low-dimensional manifolds Indicated mean effective pressure Indicated specific fuel consumption Intake valve closure Kelvin-Helmholtz K-nearest neighbors Kriging Lagrangian-Drop Eulerian-Fluid Large-eddy simulation Locally homogeneous flow Linearized instability sheet atomization Lawrence Livermore National Laboratory Methyl decanoate Mean deviation of the distance between neighbor Pareto solutions Mean distance between extreme Pareto solutions Mean distance to the Pareto front Maximum merit function Method of characteristics Multi-objective evolutionary algorithms Multi-objective genetic algorithm Multi-objective optimization problems Non-methane hydrocarbon Neural networks Non-parametric regression Number of Pareto solutions

Abbreviations, Nomenclature

NSGA NVO ODE PAH PCA PDF PFA PM PPC PPRR PRF PSO PSR QSOU QSS RANS RBF RBFS RIF RNG ROI RSM RT SCRE SF SGS SI SIMPLE SMD SMR SOC SOGA SOI SR SS-ANOVA TAB TDC UHC WHEAT WSR

Non-dominated sorting genetic algorithm Negative valve overlap Ordinary differential equation Polycyclic aromatic hydrocarbon Principal component analysis Probability density function Path flux analysis Particulate matter Partially premixed combustion Peak pressure rise rate Primary reference fuel Particle swarm optimization Perfectly stirred reactor Quasi-second-order upwind Quasi-steady-state Reynolds-averaged Navier-Stokes Radial basis functions R-value-based breadth-first search Representative interaction flamelet Renormalization group Radius-of-influence Reynolds stress model Rayleigh-Taylor Single-cylinder research engine Separated flow Subgrid-scale Spark ignition Semi-implicit method for pressure-linked equations Sauter mean diameter Sauter mean radius Start of combustion Single-objective genetic algorithm Start of injection Swirl ratio Smoothing spline analysis of variance Taylor analogy breakup Top dead center Unburnt hydrocarbon Wall heat transfer Well stirred reactor

Nomenclature A a

Pre-exponential constant in Arrhenius equation; area Speed of sound

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xviii

ad B 0, B 1 Bm bcr C Cl, Ce,1, Ce,2 C s , C3 Cd Cd, sphere Cs, CRT Cl Cp c cps D Dd d E e F F f f* fE g H H0 h I0 I1 J K K 0, K 1 Kf Kr Kc k L lF lt M m N

Abbreviations, Nomenclature

Drop acceleration Model constants in KH model Spalding mass transfer number Critical impact parameter Consumption rate of species in chemical reaction Model constants in k-e model Discharge coefficient Drag coefficient Drag coefficient of the spherical drop Model constants in RT model Liquid specific heat Constant pressure heat capacity Progress variable Model constant in dispersion model Diffusion coefficient; internal diameter of nozzle; distance between two drops Drag function Diameter; nozzle diameter Activation energy Specific internal energy Fitness value Force Drop distribution function; delay coefficient; friction factor; response function Discrete drop distribution function Fraction of energy dissipation Gravity force Thickness; lift-off length Enthalpy of formation Specific enthalpy Stretch factor; modified Bessel function of the first kind Modified Bessel function of the first kind Roughness of the response function; heat flux Heat conductivity coefficient; entrainment constant Modified Bessel function of the second kind Rate of forward reaction Rate of reverse reaction Equilibrium constant Turbulence kinetic energy; wave number; thermal conductivity Nozzle length; latent heat; length Laminar flame thickness Turbulence length scale Mass mass Number; engine speed

Abbreviations, Nomenclature

Nu n n P_ Pe Pr Pk p patm pv Q_ Qi Qd q qw R Rs Re r r32 S0 Sc Sh St s s0L T T t tc tcs tper tturb U u u* V V Vcell Vcol W _ W We w

Nusselt number Number density Unit normal vector Momentum source term in wall film model Peclet number Prandtl number Production term for turbulence kinetic energy Pressure; production rate of species in chemical reaction Atmosphere pressure Equilibrium fuel vapor pressure Source terms in energy equation rate of heat conduction Energy flux from inside the drop to the surface Energy flux at the drop surface Rate of progress of the elementary reaction Wall heat flux Universal gas constant; response function in gas-jet model Swirl ratio Reynolds number Radius; mass fraction ratio of products to reactants Sauter mean radius Entropy of formation Schmidt number Sherwood number Stokes number propagation flame speed; spray tip penetration Laminar flame speed Temperature Taylor number Time Time scale in CTC model Turbulence time scale in CTC model Turbulence persistence time Turbulence correlation time Velocity Fluctuating velocity Shear speed in heat transfer model Velocity on the sample space (particle velocity) Volume Volume of computational cell Collision volume Molecular weight Source term in turbulence kinetic energy equation Weber number Width

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xx

Abbreviations, Nomenclature

X x Y YY y Z Zst z0 a aT v Dt d de e / g j K k l v v0 v00 vl h q 0 ql R rw r r k, r e s sv X x

Molar fraction Spatial location Mass fraction Random number Distortion from sphericity Ohnesorge number Stoichiometric mixture fraction Proportion of fuel oxygen to fuel carbon Liquid surface tension coefficient Thermal conductivity Symbol of species Time step Tensorial Kronecker symbol Unsteady equilibrium thickness of thermal boundary layer Dissipation rate of turbulence kinetic energy Progress equivalence ratio Wave amplitude; compressibility factor for isentropic flow Model constant in heat transfer model Wavelength of the fastest growing wave Heat conductivity; wave length; smoothness parameter Viscosity Stoichiometric coefficient Forward molar stoichiometric coefficient Reverse molar stoichiometric coefficient Liquid kinematic viscosity Liquid volume fraction Density Liquid macroscopic denisty Flame surface density Wall stress tensor Surface tension Model constants in k-e model Viscous stress tensor Response time scale in gas-jet model Frequency of the fastest growing wave Chemical reaction rate; complex growth rate of disturbance; rate of progress of the reaction

Superscript . ~ + 0

Time rate of change Favre averaged Time averaged Non-dimensional parameters in heat transfer model Fluctuating term in time averaging

Abbreviations, Nomenclature 00

b n s

Fluctuating term in favre averaging Body force Time step Spray

Subscript 0 a acc air ax b bu c ch coll crit d eff eq exp f group h i imp inj KH k L l lp mp n noz p plasma prec RT r rel rst s sf

Standard condition Axial Acceleration Air Axial Burnt; backward; breakup Breakup Child; convection Chemistry Collision Critical Droplet; downstream Efficient Eqivalent Expansion Forward; film; friction Group in AMC model Thickness of liquid sheet Inertia Impingement Injection KH model Species Ligament Liquid; laminar Less populous More populous Normal direction to the surface Nozzle Pressure; piston; parcel Plasma Precursor RT model Reaction; reverse; piston ring Relative Rate-of-strain tensor Species; soot; surface; oil resistance Soot formation

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so sp spk T t tot u vap vena w s ?

Abbreviations, Nomenclature

Soot oxidation Spray Spark Turbulence Turbulence; tangent direction to the surface Total Unburned; upstream Vaporization Vena contracta Wall Turbulence Outer boundary

Chapter 1

Introduction

The internal combustion (IC) engine is one the greatest inventions since the industrial revolution. The computer marked the advent of the informational revolution. The use of computer models in IC engine design and optimization has significantly improved engine efficiency and reduced engine pollutant emissions over the past decades. In the foreseeable future, computer-aided engine optimization will continue to strengthen the vitality and the role of IC engines in modern transportation. The present chapter reviews the important role of IC engines and the challenges that IC engines are facing in terms of sustainability, and their impact on the environment is emphasized. We also briefly summarize the current status of engine modeling and review recent progress on computational optimization of IC engines in this chapter.

1.1 Roles of Internal Combustion Engines Internal combustion (IC) engines have dominated the transportation sector for a century. The high thermal efficiency and high power output-to-volume ratio are two major features that maintain the viability of IC engines as the primary power source in vehicles. But increasing fuel prices and depleting petroleum reserves have endangered this viability. Emerging technologies, such as the use of electromotors with high energy density batteries or fuel cells, are expected to play increasing roles in the transportation sector. Moreover, the US Environmental Protection Agency (EPA) ranks transportation as the second major greenhouse gas contributing sector after power generation (EPA 2010). And IC engines are blamed for contributing approximately one fourth of the total greenhouse gases that are emitted annually in the US. IC engines are also well-known contributors of nitric oxide and particulate matter emissions. However, the primary role of IC engines is not expected to be completely replaced by any of these technologies in the next few decades. In other words, means have to be sought to improve current IC

Y. Shi et al., Computational Optimization of Internal Combustion Engines, DOI: 10.1007/978-0-85729-619-1_1, Ó Springer-Verlag London Limited 2011

1

2

1 Introduction

engine designs in order to alleviate ever-increasing energy demands and to reduce harmful pollutant emissions. Traditionally, spark-ignition (SI) gasoline engines and compression-ignition (CI) diesel engines are employed for light-duty and heavy-duty applications, respectively. The design of an SI gasoline engine is usually lighter and more compact than that of a CI diesel engine and they also operate quieter, which is a demanding feature of passenger cars. In contrast, diesel engines are more powerful and consume less fuel per power output than that of gasoline engines, which is desirable for trucks and off-highway engineering applications. Recent progress in diesel engine downsizing has made diesel engines potential power plants for passenger cars with better fuel economy and lower pollutant emissions. Diesel engines now share more than 50% of the passenger car market in Europe, and this percentage is expected to further increase. Recently Gasoline Direct-Injection (GDI) engines have also shown much improved fuel economy and emissions compared to conventional intake charge SI gasoline engines. This drives the trend that more new passenger car models are being equipped with GDI engines in the US market. On the other hand, emerging engine combustion techniques, such as Homogeneous Charge Compression Ignition (HCCI) and Partially Premixed Combustion (PPC), enable more flexible choices of fuels in IC engines. For example, Kalghatgi et al. (2007) conducted an experimental study of a heavy-duty compression-ignition engine fueled with gasoline and diesel and operated at PPC mode. They showed that the gasoline CI engine has better fuel economy and lower emissions than the diesel CI engine. Due to the limited reserve of petroleum fuels, sustainable fuels, such as bio-fuels, are gradually becoming alternative energy sources for IC engines. Gasoline with 10% blended ethanol is now a standard pump fuel in many states of the US. It is anticipated that the amount of alternative fuel usage in transportation sector will keep increasing, which will require modifications of current engine designs. In the foreseeable future, new generation IC engines will directly benefit from better engine downsizing approaches, improved direct-injection systems, advanced in-cylinder combustion techniques, and alternative fuels. As a result, the future IC engine combustion system will become more complicated. Therefore, this book particularly focuses on describing engine combustion system optimization using state-of-the-art modeling tools with systematic optimization and regression methods.

1.2 Modeling of Internal Combustion Engines The advent of computers has created a new branch of scientific and engineering research, namely, numerical simulation. The gas exchange and combustion processes of IC engines are characterized by complex heat transfer, gas dynamics, multi-phase flows, and turbulence-chemistry interactions. IC engine combustion spans multiple regimes that include premixed flame propagation, mixing-controlled burning, and chemical-kinetics-controlled processes, which may occur

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simultaneously within a single device (Haworth 2005). The task of modeling IC engines is to completely or partly describe these physical and chemical processes using mathematical models with stable and accurate numerical schemes so that the output of the modeling can reveal desirable information about engine cycles. Early IC modeling studies can be traced back to 1950s when the computing capability of computers only allowed for efficient calculation of simple mathematical formulae. For example, the best known empirical engine model is the Wiebe function (Wiebe 1956, 1962), which is used to predict the burn fraction and burn rate. The Wiebe function and its derivatives, such as double Wiebe functions, have since been widely applied in zero-dimensional engine modeling tools. The historic aspects of the Wiebe function were recently reviewed by Ghojel (2010). Progress in engine heat transfer modeling was also made by Woschni (1967) who proposed the famous Woschni model for engine convective heat transfer calculation. The model formulae and constants were empirically based on many engine experiments and fundamental heat transfer physics. Such empirical heat transfer models were reviewed by Finol and Robinson (2006). Studies of that age showed that the combination of these empirically-based combustion and wall heat release models with well tuned model variables was able to match the pressure traces of engine experimental measurements satisfactorily. The infancy of Computational Fluid Dynamics (CFD) in-cylinder engine modeling started from the 1970s. However, until the 1980s, engine CFD modeling was not generally applied in engine development due to two facts: first, the computer capacity was still a limiting factor; second, general engine CFD code or software was not available. Instead, engine modeling with phenomenological models was the main stream in this period. For instance, coupling of phenomenological quasi-steady spray models (Hiroyasu et al. 1978) and soot and NO formation models (Heywood 1976; Hiroyasu and Kodota 1976) largely extended the capability of engine modeling tools compared to zero-dimensional simulations. Details of engine phenomenological models of different physical processes have been reviewed by Lakshminarayanan and Aghav (2010). In 1985, a group at the Los Alamos National Laboratory developed an opensource code called KIVA (Amsden et al. 1985) that integrated different components of engine CFD modeling, including moving meshes, compressible flows, spray and droplet evaporation, and fuel combustion chemistry. KIVA provides an open source CFD modeling tool for engine reactive flow simulations, which has significantly stimulated the development of engine physical and chemical models since then. Reitz and Rutland (1995) reviewed various advanced diesel engine submodels within the framework of KIVA 3 (Amsden 1993) and concluded that the CFD modeling tool was able to match experimental engine pressure traces and heat release well over investigated conditions and good quantitative agreements in NOx and soot emissions were also attainable. With the rapid increase of computational power of personal computers and demands for better simulating advanced engine combustion techniques, detailed fuel chemistry solvers have also become a standard part of many engine CFD tools since 2001 (Kong et al. 2001). Also, flexible mesh generation techniques are found in many commercial engine CFD

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1 Introduction

software nowadays, which significantly expedites the complex mesh generation process and thus speeds-up the overall engine simulation cycle. Despite the fact that even the state-of-the-art engine modeling tools normally have larger quantitative uncertainties than engine experiments, engine simulations have some significant advantages over experimental measurements in engine development and optimization. These advantages include low cost, the ability to study a wide range of parametric space, separated physical and chemical processes, and detailed in-cylinder information, which is normally not available or is inaccessible in experiments. Continuous efforts in the research fields of mesh generation techniques, numerical methods, heat transfer, turbulence, chemical kinetics, and multi-phase flows will further improve the predictability of IC engine modeling tools. Hence, the quantitative prediction capability of the next generation of IC modeling tools should be even better. Chapter 2 reviews current physical and chemical IC engine models in more detail.

1.3 Computational Optimization of Internal Combustion Engines Engine CFD simulations provide insights about the engine working cycle and pollutant formation. The ultimate goal of engine modeling is to directly guide designers to improve engine performance and to reduce pollutant emissions. Computational optimization of IC engines has become more accepted in assisting practical engine designs. The task of computational optimization of IC engines is to identify optimal combinations of design variables that can achieve minimum or maximum objective functions of interest. This section reviews recent progress in computational optimization of IC engines. Representative research from several relevant research areas are reviewed, and salient features of these studies are described in three categories as follows.

1.3.1 Engine Optimization with Parametric Studies Systematic optimization methods are not required for computational optimization of IC engines. Indeed, optimal solutions can be found through parametric studies that extend over the practical range of design variables using modeling tools. In parametric studies, the number of evaluations needed to achieve the optimal solutions significantly increases with the number of design variables, which limits their applications in complex design problems. The experience and intuition of engine designers are critically important to efficiently perform such parametric studies for engine optimization. The interaction of data analysis and experimental measurements can also expedite the exploration of the parametric space in order to locate optimal designs.

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In the study of Sher and Bar-Kohany (2002), a computer program MICE (Modeling Internal Combustion Engines), which featured a semi-empirical gas exchange model, was employed to study the effects of variable valve timings (VVT) on the torque and fuel consumption of a gasoline SI engine. Three design variables, including the exhaust valve opening, intake valve opening, and intake valve closing times, were parameterized. Because the evaluation of engine performance used a simple modeling tool which was fast, the parametric study was able to find the optimal combination of valve timings for different engine operating conditions. They concluded that the optimal timing of each valve depends linearly on the engine load and speed. Also, when the VVT strategy was applied, the maximum torque at any engine load was shifted towards a lower engine speed. CO and NOx phenomenological models were also used in this study, but the conclusion about the effect of VVT on the emissions was less reliable than the engine performance because the predictability of semi-empirical modeling tools for pollutant formation is normally poor, especially over a wide range of operating conditions. Ibrahim and Bari (2008) adopted a similar approach to optimize a natural gas SI engine using a two-zone combustion model. The EGR strategy in a high pressure inlet condition, the compression ratio, and the start of combustion timing were optimized in order to obtain the lowest fuel consumption, accompanied with high power and low NO emissions. They found that the use of 20–30% EGR effectively suppressed engine knock and allowed use of high inlet pressure for compression ratios up to 13 and the optimal EGR rate depended on engine speed. Parametric studies over a full range of three or more design variables normally create a large parametric space, which prohibits practical engine optimization using computationally expensive CFD modeling tools. In this case, the engine designers’ experience and reliable experimental data are very important to narrow down the parametric space so that parametric studies can still effectively and efficiently seek optimal solutions of interest. This interactive method that involves both computational and experimental efforts and human intelligence is usually used in production engine development and optimization. For example, in a series of optimization works, Lippert et al. (2004a, b) and Szekely et al. (2004) at General Motors and Suzuki Motor, demonstrated that parametric studies using CFD modeling and well-designed experiments significantly enhanced the understanding of charge stratification, combustion chamber shape, and spray impingement in a small displacement spark-ignition direct injection (SIDI) gasoline engine and thus expedited the overall engine development and optimization process. Through detailed CFD analysis for the SIDI gasoline engine, Lippert et al. (2004a) found that the reverse tumble that accompanies elevated swirl levels, is pivotal in lifting the mixture towards the spark gap; the piston depth strongly affected the engine performance and emissions; and an adequate bowl volume was key to sufficient mixing at higher loads in the part-load operation regime. Based on these findings, Szekely et al. (2004) further optimized the combustion chamber for this reverse-tumble, wall-controlled gasoline direct-injection engine. This was conducted by systematically optimizing each design element of the combustion

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system, including piston-bowl depth, piston-bowl opening width, piston-bowlvolume ratio, exhaust-side squish height, bowl-lip draft angle, distance between spark-plug electrode and piston-bowl lip, spark plug-electrode length, and injector spray-cone angle. They varied each design variable independently to investigate its sensitivity to combustion stability, fuel consumption, and emissions. Finally, a few optimal piston designs were recommended by interpreting the simulation results using human intelligence and data analysis tools. On the same engine, Lippert et al. (2004b) also identified several key factors that affect the high-load operating condition, which can be grouped as those pertaining to volumetric efficiency, to mixing and stratification, and to system issues. The corresponding design variables, such as the injection timings and strategy, the piston and port designs, and the intake flow structure and swirl level, were studied separately. Consequently, a significant improvement in fuel consumption and emissions was obtained relative to the initial baseline engine configuration, and the expected gains in torque and power over an equivalent port fuel injection (PFI) engine were also achieved. Similar parametric studies were also applied in CFD upfront optimization of the in-cylinder flow, spray pattern, and piston shape for a Ford 3.5L V6 EcoBoost GDI engine (Iyer and Yi 2009a, b; Xu et al. 2009). In the first phase, Iyer and Yi (2009a) assessed the effects of intake port design and spray injection timings on the tumble intensity using the MESIM 3D CFD code. By quantification and visualization of engine tumble flows they concluded that the effect of intake valve masking was beneficial for improving the air–fuel mixing, especially at part load. Delaying the start of injection timing allowed for the generation of higher tumble flow that, in turn, generated higher turbulence intensity at TDC. But a too late injection timing had a detrimental effect on air–fuel mixing. The study indicated that further optimization of the spray pattern and piston geometry was necessary. Thus, the companion study of Iyer and Yi (2009b) concentrated on optimization of the spray pattern. The main target of the second phase was to reduce soot emissions and to improve engine cold-start stability, which directly correlates with spray mixing and surface wetting. Three optimal spray patterns were selected from many parametric studies for further experimental assessment on a single-cylinder engine. Finally, a single optimal spray pattern with a wide spray angle was tested on a multi-cylinder engine with promising results. Xu et al. (2009) focused on the piston geometry of the same Ford GDI engine, particularly under engine cold-start conditions. In their study a multi-component spray model was found to be critical to the accuracy of the model prediction of the fuel air preparation process under cold start conditions. The CFD modeling methodology with the multi-component spray model was applied to optimize the piston top designs. It was found that robust fuel–air mixture formation was the key for stable combustion under the cold start condition. Effects of piston design parameters on fuel air mixture preparation were investigated and a wide bowl design was developed to generate improved mixture formation. In addition, they showed that smoothing the dome design of the wide bowl achieved further improvement of the turbulence intensity at the boosted condition while maintaining the same cold start performance.

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1.3.2 Engine Optimization with Non-Evolutionary Methods In computational engine optimization with parametric studies, the designers’ knowledge and experience are profoundly important in guiding the simulations to search for better design variables. This process is inefficient if a large number of design variables needs to be optimized; objective functions are contradicting; and global optimization is desirable. Systematic optimization methodologies can overcome these difficulties by replacing human intelligence with automatic searching methods. The section reviews a few computational optimization works with non-evolutionary methods. The performance of non-evolutionary methods relies heavily on spatial information, such as the gradient of response surfaces of objective functions to design variables. In real world optimization problems, such response surfaces can be very complicated and non-differentiable, which limits the use of non-evolutionary optimization methods. This explains why the application of non-evolutionary optimization methods is less popular than evolutionary methods in engine research community. But with some special algorithm treatments, a few studies have revealed that non-evolutionary methods can also be efficient and effective for some specific engine optimization problems. For example, Naik and Ramadan (2004) studied the effects of equivalence ratio (mass of injected fuel), injection timing, ignition timing, engine speed, spray cone angle, and velocity of fuel injection on GDI engine performance and HC emissions. Their optimization work only involved three parameters, i.e., fuel mass injected, ignition timing, and injection timing. Optimal combinations of these parameters were obtained in an automated optimization process by linking the engine CFD software KIVA and the optimization software VisualDOC with the Sequential Quadratic Programming (SQP) method. The entire optimization was done in two steps. The first step was to seek for optimal solutions of fuel mass injected and ignition timing for maximum work output. The subsequent step was to further optimize the injection timing of the optimal solutions obtained in the first step to minimize HC emissions. The two separated procedures ensure the effectiveness and efficiency of the SQP method in the engine design problem. Also, that fact that minimization of HC emissions is usually highly correlated with maximization of engine work, reduces the searching load of the optimization method for multi-objective functions, so that the use of SQP method was successful in this study. Tanner and Srinivasan (2005) explored the conjugate gradient optimization method for a non-road direct injection diesel engine optimization. In their conjugate gradient method, a line search is performed with a backtracking algorithm and the initial backtracking step employs an adaptive step size mechanism which depends on the steepness of the search direction (i.e., based on the gradient of the response surfaces). The optimization parameters included the start of injection, the injection duration and the number of nozzle orifices. The objective was to lower the engine soot and NOx emissions with simultaneously reduced fuel consumption. Because the conjugate gradient method is only capable of optimizing for a

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single objective function, a cost function that includes all objective functions had to be defined in their study. Consequently, three different optimizations were carried out using different weights and exponents in the cost function. They demonstrated that the final optimal solutions and the convergence of the optimization algorithm were sensitive to the choice of the cost function. In all tested cases, less than twenty-five engine simulations were required for an optimum to be reached. This is much more efficient than other engine optimization problems that have been reported in the open literature. But such high efficiency came with the facts that the investigated range of the design parameters was relatively narrow, the response surface of the engine performance to the injection parameters was not complicated and good initial values were guessed. In light of their successful optimization study with the conjugate gradient method, Tanner and Srinivasan (2009) pointed out that the development of an adaptive cost function strategy for the gradient-based method is necessary. The adaptive cost function is based on a penalty method such that the penalty term is stiffened after every line search. In this way, the cost function is adaptively correlated with the searching direction. The optimization method was used to investigate an asynchronous split injection scheme, in which the first and the second injection were carried out via two orifices that allow for independent parameter optimization, such as the orifice diameter and injection timing. They showed that this asynchronous split injection scheme outperformed the conventional split injection method in terms of engine performance and emissions. It was shown that only about 30 simulations were needed to achieve the optimal solutions. They concluded that the adaptive steepest decent method applied to engine optimization is a computationally very effective tool to explore new optimal injection strategies, but is only efficient when good enough initial values are available. Jeong et al. (2006) directly adopted a response surface method, i.e., the Kriging model to optimize the combustion chamber for a passenger car diesel engine. The Kriging estimator was used to predict the search direction during the optimization process. However, in order to obtain an unknown model variable for the estimator, they reformulated the problem into a sub-optimization process, in which a genetic algorithm was used. Technically, they developed a hybrid optimization method that involves both non-evolutionary and evolutionary methods. In the optimization, initial sample points were simulated using engine CFD modeling tools based on piston geometrical parameters that were generated through Latin Hypercube Sampling (LHS). Then the points which had a large probability of being optimum were estimated using the Kriging model, and used as additional sample points to update the Kriging model. The method successfully identified two optimal combustion chambers out of a total of 48 initial simulations and 43 additional samples. The CO, soot, and NOx emissions, as well as the engine thermal efficiency of the two optimal designs were improved compared to the baseline engine configuration. In terms of the total simulations, the method is more efficient than the previously employed evolutionary method, as claimed by the authors. But it should be emphasized that their method only found two optimal solutions, and the use of the

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k-means method to search for additional sample points most likely weakens its capability of reaching the global optimum. Aittokoski and Miettinen (2008) used a non-differentiable interactive multiobjective bundle-based optimization system (NIMBUS, Miettinen and Mäkelä 1995) to optimize the exhaust pipe dimensions for a two-stroke engine. Within the framework of NIMBUS, the optimality of the solutions is not directly evaluated based on objective functions. Instead, there is an interaction phase that requires the designers’ wishes to classify optimal solutions into five classes at each optimization iteration. Each class reflects the priority of the optimal solutions, the weight of the objective functions, and the target of the designers’ wishes. Any optimization method can fit in this framework, and particularly in the study of Aittokoski and Miettinen (2008), an extended Controlled Random Search (CRS, Price 1977; Ali and Storey 1994) method was employed. They found that the classificationbased interactive method is a convenient way to express designers’ wishes so that the designer can guide the solution process within a limited number of objective function evaluations. Therefore, interactive methods may be a good way to reduce the number of objective function evaluations required, and also enable control of the solution process.

1.3.3 Engine Optimization with Evolutionary Methods Compared to non-evolutionary methods, evolutionary methods, such as genetic algorithms (GA) and particle swarm optimization (PSO) methods, have been more widely used in computational engine optimization, because these methods are more generally applicable for optimizing complex non-linear real world problems. For example, Wickman et al. (2001) integrated a single-objective genetic algorithm with the engine CFD code KIVA to optimize nine design variables, including piston geometrical parameters, injection patterns, swirl ratio, and EGR rate, for a high-speed direct injection (HSDI) diesel engine and a heavy-duty diesel engine. Although each task took 2–4 weeks for 400 individual simulations, the optimization method was still deemed to be efficient considering the large search space and the complexity of the problem. They found that the small-bore and heavy-duty diesel engines both favored relatively large diameter shallow piston bowls, long injection durations at high pressure through small holes, and moderate swirl, at medium speed and high load. The optimal start of injection timing and EGR level were very sensitive to the NOx target value chosen. In addition, precise control over the global air/fuel ratio was very important for achieving simultaneous emissions and fuel consumption reductions. A similar approach was adopted by Shrivastava et al. (2002) to investigate the performance and emissions of a diesel engine using variable intake valve actuation with boost pressure, EGR and multiple injections. Again, the CFD code KIVA was extended to interface with a 1-D gas dynamic code in order to accurately predict the engine intake flow. In their study, a total of eight parameters, including SOI,

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injection duration, EGR, percentage of total fuel mass injected in first pulse of a split injection rate shape, dwell in between the pulses of the split injection, boost pressure, and the gas swirl and tumble ratios at Intake Valve Closing (IVC) were simultaneously optimized to locate solutions with reduced NOx, soot, and UHC emissions, as well as low fuel consumption for two engine speeds and loads. In all cases, the engine emissions and fuel consumption were considerably reduced for the optimal designs as compared to their baseline values. They also observed that the optimal boost pressure was considerably higher compared to the baseline value. The increase in boost pressure, in combination with the other variables such as the multiple injection parameters, led to a considerable reduction in soot formation. The high optimal EGR rate led to a drastic reduction in engine-out NOx. The effect of swirl and tumble ratios on emissions reduction was found to be most prominent at high speed and low load. Finally, longer intake valve open durations and a higher value of maximum valve lift led to better flow development at IVC. Chen et al. (2003) also used genetic algorithms to optimize an HCCI engine, specifically for a power generator. In their study, optimal sets of equivalence ratio, EGR rate, intake temperature, and pressure were sought to achieve maximum engine thermal efficiency and torque and minimum NO emissions. The GA optimization revealed that a mixture of high equivalence ratio with a large amount of EGR can be used to achieve high thermal efficiency and low NOx emission. GAsearched results also suggested that variable power demand can be conveniently met by only adjusting the intake pressure while keeping other conditions unchanged. Many studies have also shown that genetic algorithms are helpful in determining proper injection strategies for diesel engines under various operating conditions. For example, Kim et al. (2005) applied a micro-genetic algorithm to study the injection parameters and intake conditions for a heavy-duty diesel engine. They found that the GA optimization efficiently located optimal engine operating parameters that demonstrated low emissions and improved fuel consumption capabilities of a diesel engine. The predicted optimal injection timing was very advanced, which suggests that HCCI-like combustion is useful for low emissions diesel engines at the considered mid-load condition. The optimization showed that the resulting long ignition delay allowed enough time for mixing and reduced the extent of fuel rich regions. This indicates that high levels of EGR can be used to control NOx and prevent soot formation. Not surprisingly, the optimal combustion system recommended by the GA is exactly the premixed charge compression ignition (PCCI) engine strategy, which has been well accepted by the engine community recently. The powerful capability of GA is thus proven. Similarly, Bergin et al. (2005) identified a novel spin spray combustion approach for a heavy-duty diesel engine. The study demonstrated that 2006 nonroad emissions targets were met by optimizing the spray events with an injector that featured two rows of nozzle holes with asynchronous injection for each nozzle row. No other means of emission reduction were needed. The spin-spray combustion that is realized by injecting two neighbor sprays with different cone angles at different times creates large recirculation structures that greatly enhance mixing.

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The optimal configuration of spray cone angles, injection timing, and split injection amount leads to an optimal combustion event that favors soot oxidation, because the formation and decay of the spin spray combustion recirculation structure allows a more efficient transfer of energy from the injected liquid spray to the bulk fluid. In other words, this novel injection approach stores the kinetic energy within the flow field and leads to greater late cycle turbulence with significantly reduced soot emissions due to the resultant improved mixing. The enhanced mixing also results in more homogenous combustion, which directly benefits NOx reduction and thermal efficiency increase. It should be pointed out that all these studies were based on single objective genetic algorithms. For engine optimization with multiple objective functions, a single merit (cost) function has to be defined to include the multiple real objective functions. However, similar to the problem that was discussed by Tanner and Srinivasan (2005), the formula of such single merit function influences the final optimal solutions and algorithm convergence. Unfortunately, definition of an appropriate merit function is usually unclear to designers in the real world optimization process. This motivates interest in studies and application of multiobjective evolutionary methods (Deb 2001). These methods are becoming the predominant approach for computational engine optimization and design. For example, Tibaut and Marohni (2006), Kurniawan et al. (2007), and Genzale et al. (2007) are among the pioneers who coupled multi-objective genetic algorithms with engine CFD simulations for automatic engine design optimization. These studies used different optimization algorithms which were integrated in the commercial optimization software iSIGHT, modeFRONTIER, and from a multiobjective micro-genetic algorithm source code, respectively. None of these researchers compared the performance of the different multi-objective genetic algorithms, so information about which method suits computational engine optimization best was lacking. To address this problem, Shi and Reitz (2008a) assessed three widely used multi-objective genetic algorithms, namely, l-GA (Coello Coello and Pulido 2001), NSGA II (Deb et al. 2002), ARMOGA (Sasaki and Obayashi 2005). They applied the three methods to optimize the piston geometry, spray targeting, and swirl ratio for a heavy-duty diesel engine at high-load with CFD simulations. They also defined four quantities that quantify the performance of the optimization methods in terms of the optimality and diversity of the optimal solutions. NSGA II with a large population size was found to perform the best in their study. Chapter 4 describes this study in more detail. Jeong et al. (2008) developed a hybrid evolutionary method that includes a genetic algorithm and a particle swarm optimization method. The basic idea came from the fact that GAs maintain diverse solutions, while PSO shows fast convergence to the optimal solution in multi-objective optimization problems. They tested the hybrid algorithm using two sets of mathematical functions and showed that the hybrid algorithm had better performance than either a pure GA or a pure PSO. However, due to the high computational cost, the performance of the hybrid method was not compared with other methods for engine optimization problems.

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Shi and Reitz (2008b) extended their previous optimization work (Shi and Reitz 2008a) to low-load operating conditions of the same heavy-duty diesel engine using NSGA II and the engine CFD code KIVA 3v release 2 (KIVA3v2). By comparing the optimal solutions of the high-load condition to those of the lowload, they discovered that the high-load operating condition is more sensitive to the combustion chamber geometrical design compared with the low-load condition. By choosing an optimal combustion chamber design from the high-load optimization study and varying swirl ratio, and injection timing and pressure, excellently performing designs were also found using the high-load optimal chamber geometry for the low-load condition. Thus, they suggested that engine optimization studies for all operating loads should start with an optimization study of piston geometry and spray targeting for the high-load condition. Further optimization on the spray injection event and swirl ratio should then be conducted for the low-load condition. In practice, engine optimization over all operating conditions is of more interest, but it is also more challenging due to two facts. First, the optimal sets of design variables achieved from an optimization study of a specific operating condition are usually not applicable to other conditions. Second, many engine design variables are not adjustable under different operating conditions, such as the piston geometry. To tackle this difficulty, Ge et al. (2010a) proposed a methodology for engine development using multi-dimensional CFD and computer optimization. A multi-objective genetic algorithm NSGA II and the KIVA3v2 code were used to optimize a light-duty diesel engine. Design parameters of the diesel engine were divided into two categories: hardware design (piston geometry, number of nozzle orifices, injection angle) and controllable design (SOI, swirl ratio, boost pressure, and injection pressure). Hardware design parameters were optimized first under the full (high)-load condition, as suggested by Shi and Reitz (2008b). Then, the optimal hardware design was fixed for subsequent optimizations of the controllable parameters under different operating conditions. They illustrated that with fixed optimal hardware design and optimal sets of controllable parameters for each case, optimal designs which simultaneously reduce fuel consumption and pollutant emissions were obtained in all cases except for a very low load case. In addition, strong correlations among the controllable design parameters were not observed, which implies that these controllable parameters can be optimized separately. Different from single objective optimization methods, which always lead to a single global optimal objective function, multi-objective optimization methods normally produce many optimal solutions in engine design problems. It is a tedious work to analyze such large volume of data using human intelligence. Therefore, the use of regression methods in computational engine optimization is also desirable. The data-mining process is sometimes equally as important as the optimization process. In the studies of Shi and Reitz (2008a, b) and Ge et al. (2010a, b), a non-parametric regression analysis method, the COmponent Selection and Smoothing Operator (COSSO) method (Lin and Zhang 2006) was used to establish the response surfaces of design variables to objective functions. Jeong

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et al. (2008) used the Self-Organising Map (SOM), which is a data mining technique using an advanced variant of unsupervised neural networks and clustering analysis. Ge et al. (2009a) employed a K-nearest method to analyze a large amount of optimal solutions in an optimization study with a heavy-duty diesel engine. Shi and Reitz (2010a) assessed four regression methods, including K-nearest neighbors (KN), Kriging (KR), Neural Networks (NN), and Radial Basis Functions (RBF), for an engine optimization study. They trained these methods using results from engine CFD simulations and showed that by dynamically training the regression methods during the course of GA optimization, the predicted results from trained response surfaces agree well with the real CFD simulations. The performance of KN and KR methods was better than that of the NN and RBF methods in their comparative study. This study is also a subject of Chap. 4. Many studies have proven that engine CFD modeling tools with simplified ignition and combustion models, such as the Shell/CTC (Characteristic Time Combustion) model (Kong and Reitz 1993), can be reliable simulators for diesel engine optimization within conventional operating regimes where fuel/air mixing and diffusion flames dominate the combustion and pollutant formation processes (Bergin et al. 2005; Shi and Reitz 2008a, b). The individual simulation using such approaches only requires a few hours on the latest personal computers, so the whole optimization process can be completed within a week or two with multiobjective evolutionary methods, which is highly attractive for industrial optimization designs. But the advanced combustion techniques in modern diesel engines, such as HCCI, PCCI, and Modulated Kinetics (MK), are primarily controlled by fuel chemistry. In this case, accurate engine CFD simulations require a detailed description of the chemical kinetics of the fuels. It is not uncommon to find one to two orders of magnitude increase in the required computer time when solving detailed reaction mechanisms in engine CFD simulations compared to using simplified combustion models. Therefore, engine optimization using CFD simulation with detailed chemistry is generally not practically feasible, given the excessively long optimization cycle. Significant efforts have been made recently to accelerate engine CFD simulations with detailed chemistry, which can be categorized into four major approaches. First, the development of mesh-independent spray models (Munnannur 2007; Abani et al. 2008a; Abani and Reitz 2010) enables engine CFD simulations using coarser meshes without losing accuracy compared to those of fine meshes (Abani et al. 2008b). Second, multi-zone or multi-grid methods (Babajimopoulos et al. 2005; Shi et al. 2009a; Goldin et al. 2009; Liang et al. 2009a) divide computational domains into subdomains by grouping thermodynamically-similar cells, which largely reduces the calling frequency to the chemistry solver in engine CFD simulations. Third, efficient parallelization schemes (Shi et al. 2009b) take advantage of the multi-core architecture of latest central processing units. Finally, reaction mechanism reduction techniques (Lu and Law 2005; Pepiot-Desjardins and Pitsch 2008a; Sun et al. 2010) and the on-the-fly model reduction schemes (Liang et al. 2009b, c; Shi et al. 2010b) greatly decrease the reaction mechanism size needed to describe the chemical kinetics of fuel oxidation and combustion. These methods are described in Chap. 3 in detail.

14

1 Introduction

Cumulative benefits are attainable by combining these methods for enhancing combustion modeling efficiency, which makes possible computational engine optimization. It has been shown that by using one or more such chemistry solver acceleration techniques, the optimization cycle using engine CFD simulation with detailed chemistry can be reduced to approximately one month (Ge et al. 2010a, b; Shi and Reitz 2010c). Ge et al. (2010b) studied a HSDI diesel engine operated at a low-load condition in the MK combustion mode. They optimized the engine piston geometry, spray targeting, and swirl ratio with NSGA II and CFD simulations using the full chemistry solver and with the accelerated solver with the adaptive multi-grid chemistry (AMC) model (Shi et al. 2009a). Although for individual cases, the accelerated chemistry solver introduces approximation to the full chemistry solver, they found that the optimization using the AMC model produced consistent optimal solutions to those of the full chemistry model, but only cost half the computer time. In an extended study, Ge et al. (2010b) used the engine CFD simulations with the AMC model to optimize the same HSDI engine for a full range of operating conditions. Shi et al. (2010) integrated a on-the-fly mechanism reduction scheme with the AMC model into the engine CFD simulation software KIVA3v2, which further improved the computational efficiency for their optimization study of a heavy-duty compression-ignition engine fueled with diesel and gasoline-like fuels (Shi et al. 2010c). The entire optimization cycle for six tasks was completed within six weeks, which would be six months if the accelerated chemistry solver were not used. This engine optimization work showed that gasoline-like fuels exhibit great potential for cleaner combustion than with conventional diesel fuel. Different incylinder flow patterns were identified in the optimal engine designs with the different fuels. Due to the diffusion-type combustion, diesel fuel exhibits stagnation-point dominated flow fields in many optimal cases, while gasoline-like fuels show more volumetric-heat-release-driven flows due to their premixed-type combustion. The results of the optimization study also indicate that lower octane number gasoline-like fuels may be more helpful to improve the controllability of compression-ignition engines in the Partially Premixed Combustion (PPC) mode and to reduce engine noise. To conclude, high-fidelity CFD modeling tools with detailed fuel chemistry enable engine designers to obtain reliable simulation results. Efficient optimization methods and accelerated CFD solvers significantly shorten the computer time of optimization cycles, which makes the computational optimization approach more competitive than experiments. In the rest of the book, we will revisit several of the aforementioned optimization works in more detail to show that computational optimization of internal combustion engines is becoming an indispensable part of practical engine designs, and to provide an up-to-date reference to developments and future directions in the field of engine modeling.

Chapter 2

Fundamentals

2.1 Optimization Algorithms In Chap. 1, a survey was conducted of recent computational optimization studies of engine design using various methods. Most of these optimization algorithms can be categorized into two classes, i.e., gradient-based methods and gradient-free methods, or specifically, evolutionary methods. This section explores the advantages and limitations of these optimization algorithms with three mathematical problems. The commercial software modeFRONTIER (ESTECO 2008) was used to compare different optimization algorithms with model problems. The theoretical fundamentals of three multi-objective genetic algorithms (MOGA) are discussed in detail, while the assessment of these three MOGAs in computational engine optimization is the subject of Chap. 4.

2.1.1 Comparison of Different Optimization Algorithms For differentiable mathematical functions, their stationary points (where derivatives are equal to zero) correspond to local or global optimal solutions. Using gradient information, gradient-based methods seek such stationary points to locate optimal solutions. These methods are usually very efficient provided that the solution space is everywhere differentiable and the local optimum is also the global optimum. For example, the classical Broyden–Fletcher–Goldfarb–Shanno (BFGS) method (Broyden 1970), also known as the quasi-Newton method, requires the optimal function be twice continuously differentiable and the necessary condition for optimality is that the zero gradient point exists. Two mathematical optimization problems are used here to examine the performance of the BFGS method. The first problem seeks for the maximum value of the product of two sine functions, as

Y. Shi et al., Computational Optimization of Internal Combustion Engines, DOI: 10.1007/978-0-85729-619-1_2, Ó Springer-Verlag London Limited 2011

15

16

2 Fundamentals

Fig. 2.1 One-peak value problem

maxðf Þ;

where f ¼ f1  f2

f1 ¼ sinðp  x1 Þ; x1 2 ½0; 1 f2 ¼ sinðp  x2 Þ; x2 2 ½0; 1

ð2:1Þ

Obviously, the function f is everywhere differentiable within the parameter range [0, 1], as seen the solution space of function f in Fig. 2.1. The problem has only one local optimal solution, which is also the global optimum. The second problem is more complicated than the first one, which seeks the maximum value of the product of four individual functions with respect to two variables. maxðf Þ; where f ¼ f1  f2  f3  f4 f1;x1 ¼ ½sinð5:1p  x1 þ 0:5Þ6 ; x1 2 ½0; 1 " # ðx1  0:0667Þ2 f2;x1 ¼ exp 4 lnð2Þ 0:64

ð2:2Þ

6

f1;x2 ¼ ½sinð5:1p  x2 þ 0:5Þ ; x2 2 ½0; 1 " # ðx2  0:0667Þ2 f2;x2 ¼ exp 4 lnð2Þ 0:64 The function f in the second problem is also differentiable, but Fig. 2.2 illustrates that there are total 25 local optimal solutions distributed in the parametric domain. There exists a single set of the two variables x1 and x2 (near the origin) that reaches the global optimal solution of unity. The BFGS optimizer in modeFRONTIER 4 was employed to perform the optimization tasks for both problems. For the first problem, since it has only one local and global optimal solution, the BFGS method started with a single random set of the two input parameters. Figure 2.3 shows that the method found the

2.1 Optimization Algorithms

17

Fig. 2.2 Multiple peak values problem

Fig. 2.3 Function value of the one-peak problem using BFGS method

optimal solution of unity with only 31 evaluations, which is quite efficient, as expected. Technically, one can also start the BFGS method with a single set of input variables for the second problem. However, it is almost impossible to obtain the global optimal solution with such configuration as it is easy to see that the method has a very high chance of converging towards a local (non) optimal point. Therefore, in practice, one always randomly generates multiple initial sets of input variables for the BFGS method, and each initial set will eventually lead to either local or global optimum. Whether the final global optimal solution will be reached or not strongly depends on the initial guesses. We initialized the BFGS method for the second problem with 30 randomly generated datasets which are shown in Fig. 2.4(a). Unfortunately, none of these initial datasets led to the maximum function value of unity within 1,000 evaluations, as illustrated in Fig. 2.4(b). The maximum value that was found by the method is close to 0.7, but such finding

18

2 Fundamentals

Fig. 2.4 Results of the second problem (a) Initial datasets of the input variables (b) Function value of the multiple peaks problem using BFGS method

comes from one of the ‘‘lucky’’ initial datasets instead of optimization evaluation. It is anticipated from Fig. 2.2 that in order to reach the function value of unity, the initial guess point has to be very close to the final optimal solution. Otherwise, it is certain that gradient-based methods will follow the gradient information near other local optimal points and converge to those values. Increasing the number of initial datasets eventually leads to the BFGS method finding the global optimal solution, but such treatment is very inefficient. Real world engineering optimization problems, such as IC engine optimization, are normally much more complicated than these two problems. Furthermore, the problems are most likely not differentiable and the number of local optimal solutions can also be large, which renders the application of gradient-based methods inefficient or impractical for such engineering problems. Methods that do not rely on the gradient information of the optimization problems are needed. Evolutionary optimization methods, such as genetic algorithms and particle swarm methods, heuristically use the existing input parameters and present solutions to drive their search towards optimal solutions. These methods are distinguished by their heuristic methods that are used to determine the search directions. For example, genetic algorithms mimic the nature’s evolutionary principles, particularly, the ecosystem behavior that obeys the Darwinian idea of ‘‘survival of the fittest’’, and particle swarm methods specifically imitate swarm social behaviors. Strict mathematical proof of the algorithm convergence of these methods is normally hard or impossible to obtain. But, in engineering practice, these methods have been found to be widely applicable and efficient in optimization problems. The evolutionary methods, especially multi-objective genetic algorithms, are intensively used in this book to explore IC engine optimal designs. The concept of genetic algorithms (GAs) was first proposed by Holland (1975) and Goldberg (1989) was among the pioneers who suggested use of GAs in engineering problems. GAs are mathematical algorithms that simulate the evolutionary processes of ecosystems. Their broad applicability and ease of use and

2.1 Optimization Algorithms

19

global perspective are the primary reason that they have become increasingly popular in engineering optimization (Goldberg 1989). GA is a simple search technique that utilizes the ‘‘fittest’’ attributes of previously created designs to generate new designs with the aim of moving the evolution process towards better solutions. In this process, the design-space is coded in mathematical expressions (representing ‘‘genes’’), either with binary strings or real numbers, which are evaluated to provide the ‘‘fittest’’ information for the crossover of genes. Genetic algorithms are usually initialized with several randomly generated designs, and the number of the designs that are evaluated in each generation is called the population size. The crossover among evaluated designs gives higher possibility to those designs (genes) with better merit to survive to the next generation. Mimicking natural evolution, random changes of part of the coded design variables (gene mutation) are introduced to avoid local optimization and to maintain the diversity of solutions. Therefore, parameters that influence crossover and mutation are critical to the performance (optimality and diversity) of genetic algorithms. There are many methods for gene coding, crossover function, as well as mutation. The combination of these methods and additional ad-hoc treatments for special applications result in a variety of genetic algorithms. There also exist several useful textbooks on different aspects of genetic algorithms. Interested readers are encouraged to refer the studies of Holland (1975), Goldberg (1989), Gen and Cheng (1997), and Deb (2001). Intuitively, optimization problems with a single objective, such as the previous two problems, are just degenerate cases of multi-objective optimization problems. But in fact, there are fundamental differences in single-objective and multiobjective evolutionary optimization algorithms, because the heuristic method that is used to determine the optimality in the problems of these two classes is totally different, as well as the associated algorithm structure. For single-objective optimization problems, the definition of optimality is clear and obvious as there only exists a single best solution in any stage of the evolutionary process. But for multiobjective optimization problems, objective functions can contradict each other, which results in a pool of optimal solutions that needs to be tracked simultaneously by the optimization methods in the evolution. The notion of ‘‘optimum’’ in multi-objective optimization problems is normally referred as the Pareto optimum. The Pareto optimality of a solution indicates that there exist no other solutions that simultaneously out-perform the compared solution with all objective functions. Figure 2.5 gives a more visible illustration of the Pareto optimum. As it shows, Cases A-D are Pareto optimal cases because none of them are out-performed by other cases in this problem with the aim of minimizing both objectives. This also highlights another terminology, dominance, which is frequently used in descriptions of MOGAs. One design is said to be dominated because at least one of its objectives is worse than other cases. Obviously, designs A-D are not dominated by other cases. However, designs E-H are dominated cases. Based on the relationships between dominated and dominating, the cases that are not dominated by others can be grouped together, and the group in the objectivespace where all Pareto optimal solutions are located is called the Pareto front.

20

2 Fundamentals

Fig. 2.5 Definition of Pareto optimum

Fig. 2.6 Function value of the one-peak problem using micro-GA

Discussion about the algorithm details is deferred to the next section where three popular multi-objective genetic algorithms are described. Here, we apply a single-objective optimization algorithm micro-GA (Senecal 2000) to redo the previous two problems, and the results are shown in Figs. 2.6 and 2.7, respectively. Compared to the gradient-based BFGS method for the first problem in Fig. 2.3, the single-objective genetic algorithm micro-GA is slightly less efficient as it approached the maximum function value at the 38th evaluation. But for the second problem in which the BGFG failed to find the optimal solution with 1,000 evaluations, micro-GA was able to locate the solution with only 331 evaluations. This indicates the superior feature of this evolutionary method for optimizing the proposed complex mathematical function. In principle, single-objective genetic algorithms can also be used to study multi-objective problems, because any number of objective functions can be grouped into a single merit function. However, the different expressions of the

2.1 Optimization Algorithms

21

Fig. 2.7 Function value of the multiple peaks problem using micro-GA

single merit function usually lead to different performance of SOGAs. Unfortunately, in most cases, such definition is unknown prior to completely solving the optimization problem. We again resort to a mathematical model to examine this, which forms the third problem with two objective functions (Deb 2001). f1 ¼ x1 g ¼ 2:0  Expððx2  0:2Þ=ð0:004Þ2 Þ  0:8Expðððx2  0:6Þ=0:4Þ2 Þ f2 ¼ g=x1

ð2:3Þ

x1 ; x2 2 ½0:1; 1 In this problem, the task of the optimization method is to seek the smallest possible f1 and f2 values. With the single-objective genetic algorithm (micro-GA), the present problem can be easily transformed to seek the maximum value of a merit function whose denominator includes both f1 and f2 . Two expressions, i.e., 1=ðf1 þ f2 Þ and 1=ð2f1 þ f2 Þ, were used by assigning different weights to f1 in the merit function. It is seen in Fig. 2.8 that by assigning more weight to the f1 in the merit function, the final optimal solutions are better than those of assigning equal weights to both f1 and f2 , although fewer Pareto solutions were found out of the total 2,000 evaluations. Therefore, the use of a single-objective genetic algorithm approach in multiobjective optimization problems is undesirable because the definition of the objective function can result in large uncertainties in the final optimal solutions. To illustrate this, we employed the multi-objective optimizer Non-dominated Sorting Genetic Algorithm (NSGA II) in modeFRONTIER to solve the third problem, and the optimal results are reported in Fig. 2.9. The figure shows that there exists only one Pareto front and also more Pareto solutions were found by NSGA II. IC engine optimization typically involves multiple objectives, such as emissions reduction and fuel consumption improvement. With this in mind, the rest of

22

2 Fundamentals

Fig. 2.8 Multi-objective optimization problem using single-objective micro-GA with two merit functions

Fig. 2.9 Multi-objective optimization problem using multi-objective NSGA II with two objective functions

the book focuses on multi-objective genetic algorithms. In the next section, three popularly used MOGAs are described with respect to their salient features and limitations.

2.1.2 Multi-Objective Genetic Algorithms A considerable number of MOGAs have been proposed in the past, among which the micro GA or l-GA (Coello Coello and Pulido 2001), Non-dominated Sorting Genetic Algorithm II (NSGA II) (Deb et al. 2002) and Adaptive Range Multiobjective Genetic Algorithm (ARMOGA) (Sasaki and Obayashi 2005) have been

2.1 Optimization Algorithms

23

applied to many engine optimization problems (Genzale et al. 2007; Shi et al. 2008a). The three MOGAs share a common feature that an elite-preserving operator is utilized i.e., the genetic algorithms allow the parents to compete with their offspring and elite designs have opportunity to be directly carried over to the next generation. It has been proven that GAs converge to the global optimal solution for some functions in the presence of elitism. Moreover, the presence of elites enhances the probability of creating better offspring (Deb 2001). We are particularly interested in the performance of these MOGAs in the computational optimization of IC engines. The discussion of the technical details of each algorithm and the associated complicated tests are beyond the scope of this book. Here, we only introduce the major features of these three genetic algorithms and their application in an engine geometry optimization will be assessed in Chap. 4. The major feature or advantage of the multi-objective l-GA proposed by Coello Coello and Pulido (2001) is that it only needs a very small population size. The smaller population size indicates that it requires fewer computers to complete a generation, which is suitable for the situation when computing resources are limiting. Normally, using small population size may lead to less diversified optimal solutions, but the l-GA employs a reinitialization process, combined with an external file to store non-dominated cases previously generated, as well as an additional efficient mechanism to keep diversity. Coello Coello and Pulido (2001) showed that a l-GA carefully designed is sufficiently able to produce the Pareto front of multi-objective optimization problems. Differing from other MOGAs, the population memory of the l-GA is divided into two parts: a replaceable and a non-replaceable portion. They are initially fed by randomly generated populations for the first optimization cycle, and the nonreplaceable portion will keep its initial populations during the entire run. Therefore this algorithm induces an additional variable, which is the percentage of each portion to be predefined for the optimization problem. l-GA employs conventional genetic operators for each cycle, such as tournament selection, two-point crossover, uniform mutation, and elitism. At the end of each cycle, two non-dominated populations (if there are two or more, otherwise, only one is selected) are compared with the external memory and the replaceable population memory, and if either of them or both dominate any population in the compared population memories, the dominated population will be replaced. In this way, both the external and the replaceable memory will tend to have more non-dominated cases. Some of the replaceable populations will be used as initial populations to start a new evolutionary cycle. There are three types of elitism involved in the l-GA which are described in detail by Coello Coello and Pulido (2001). The technique of selecting non-dominated populations discussed above is to make the evolution converge to the true Pareto front. In order to keep diverse solutions distributed on the Pareto front, an approach similar to the adaptive grid proposed by Knowles and Corne (2000) is also employed in l-GA. Briefly the selection of non-dominated solutions is based on their locations in the objective-space once the defined limit of the external memory has been reached, and the less crowded regions are given higher

24

2 Fundamentals

Fig. 2.10 Definitions of the Rank and the Crowding Distance

preference. This procedure also induces two extra parameters for the optimization problem, which are the expected size of the Pareto front and the number of positions that determines how to divide the objective-space for each objective defined by the user. In general, l-GA focuses on the utilization of elitism to converge the optimization process, and reducing the population size and keeping diverse solutions by preserving the initial randomicity and judging the locations of solutions. Motivated by the fact that elitism helps achieve better convergence in multiobjective evolutionary algorithms (MOEAs), Deb et al. (2002) proposed a new elitist non-dominated sorting GA, the Non-dominated Sorting Genetic Algorithm (NSGA II). NSGA II employs both the elite-preserving strategy, as well as an explicit diversity-preserving mechanism. The evolution process of NSGA II is that it first randomly generates a predefined size (N) population, which undergoes conventional selection, crossover, and mutation procedures to produce offspring for the next generation. From the second generation, the parent generation (size N) competes with its offspring generation (size N) to introduce elitism. In this procedure, the crowding tournament selection is used and two rules are applied to the selection operator: (1) Solutions with higher ranks are given preference to be selected; (2) If they have the same rank, the less crowding distances cases are assigned higher priority. Figure 2.10 illustrates the concepts of rank and crowding distance. As shown, solid circles dominate other cases. However, they do not dominate each other, and thus they form a non-dominated front defined as the first rank. The same procedure can be applied to the rest of the solutions to find the second rank and so on until every solution is assigned a rank. The crowding distance is defined by the average distance of a solution to its nearest neighbors. For example, the crowding distance of solution i in Fig. 2.10 is the average side-length of the rectangle (the dashed box). The mathematical definition of the crowding distance can be also applied to

2.1 Optimization Algorithms

25

higher dimensions, although it is only shown in a 2-D plot for a clear view. Therefore, N populations will be selected from 2N combined populations based on the aforementioned competition rules. These N populations will later undergo conventional selection, crossover, and mutation to complete an optimization cycle. It is the elitism that makes the GA converge to the optimal solutions and the assistance of the explicit crowding distance maintains the diversity of solution. In addition, the crowding distance concept needs no extra user defined niching parameter (such as dshare ) that is used by many other MOGAs, such as the ARMOGA discussed next. An adaptive range technique was proposed by Arakawa et al. (1998). Sasaki and Obayashi (2005) extended and improved the method with a MOGA that is similar to the one proposed by Fonseca and Fleming (1993) in order to reduce the number of evaluations. The idea is that instead of searching the predefined designspace, an adaptive range, based on the statistical study of the distribution of the preceding optimized solutions is utilized as the search range for the optimization cycle. The starting generation is determined by the user. ARMOGA focuses its search on a concentrated promising design-space where most of the potential optimal solutions are located, giving fast convergence to the Pareto front. Mathematical descriptions of the statistical method of determining the adaptive range are given by Sasaki and Obayashi (2005). It is apparent that the implementation of range adaptation for the design space contradicts the goal of achieving diverse optimal results to a certain degree. Therefore, techniques that aim to distribute optimal solutions uniformly need to be applied to ARMOGA. Similar to NSGA II, a rank is assigned to each individual. However, instead of using the rank and the explicit crowding distance directly, ARMOGA uses a fitness function with the assistance of the standard sharing approach to determine the preference of population of being selected for the next GA operation and thus for the next generation. The fitness value of each population is calculated from

Fi ¼ N 

R i 1 X

lðkÞ  0:5 ðlðRi Þ  1Þ;

ð2:4Þ

k¼1

where N is the number of solutions, and lðRi Þ is the number of solutions in rank Ri . The fitness value is then weighed divided by the niche count: Fi0 ¼ Fi=nci ;

ð2:5Þ

where the niche count is calculated from a sharing function nci ¼

N X j¼1

shðdij Þ;

ð2:6Þ

26

2 Fundamentals

0

  dij ashare 1  dij \dshare B dshare : shðdij Þ ¼ @ 0 others

ð2:7Þ

dij is the normalized distance summation between population i and j, which is as vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u M uX f i  f j k k dij ¼ t ; ð2:8Þ u  lk k¼1 k where uk and lk are the maximum and minimum k objective values in the present generation respectively, and M is the total number of objectives. Finally, the niching parameter dshare is defined in ð1 þ dshare ÞM  1 ¼ N  ðdshare ÞM ;

ð2:9Þ

and a similar sharing parameter ashare is user-defined. Thus, if the distance between two populations is lower than dshare , then the niche count increases to reduce the fitness of the solution, and thus the diversity is preserved. In addition to the niching technique, ARMOGA also improves the real-coding method detailed in the study of Sasaki and Obayashi (2005). Other than the above features, ARMOGA uses conventional GA operators. Engineering optimization problems are usually subject to many constraints, such as cost, mechanical stresses, and so on. These constraints should be handled during the course of the evolutionary optimization process. An easy and often used treatment is to mark designs that violate user-defined constraint(s) as infeasible designs, and their representative features are not allowed to participate in crossover and therefore thrown out from the current optimization generation. This method is effective in removing infeasible designs from the optimal solution pool. It is employed in all three MOGAs discussed above and in this book. However, the method can be too destructive under the circumstance that some infeasible designs actually can have many merits, especially those boundary designs that only slightly violate constraints but with optimal objective functions. In this case, a remedy is needed to recover those designs. Therefore, constraint handling methodologies are also an important subject of evolutionary optimization methods, and details are discussed in the textbook of Deb (2001).

2.1.3 Genetic Algorithm Source Code and Software Since Holland introduced the concept of genetic algorithm in 1975, various genetic algorithm methods have been proposed and many of them have been coded in popular programming languages. For example, the NSGA II C code that is intensively used throughout this book can be downloaded from the Kanpur Genetic

2.1 Optimization Algorithms

27

Algorithms Laboratory website (http://www.iitk.ac.in/kangal/codes.shtml). In addition, the Illinois Genetic Algorithms Laboratory also provides different genetic algorithm packages, which are available at http://www.illigal.uiuc.edu/web/. The genetic programming community is dedicated to developing evolutionary algorithm based tools for different optimization problems. The websites http://www. geneticprogramming.com/ and http://www.genetic-programming.com/ have collected useful information in this field. Usually, these genetic algorithm source packages can be used as black-boxes. The easiest way to interface between the optimization source code and users’ own program is to use file input/output operations and operating system scripts. This is because in most optimization problems, the evaluation of the problem itself is much more time consuming than the optimization methods and I/O operations. However, for real-time optimization problems, an interface in source code level is necessary. In the computational optimization of IC engines, the computation cost of the engine CFD simulations is much greater than the overhead due to genetic algorithms. So, in this book Linux shell scripts are employed to communicate the engine CFD results and the genetic algorithm via I/O operations. Other than source packages, there also exist many commercial software codes, and among them modeFRONTIER produced by ESTECO is widely used in both industry and academia. Commercial optimization tools provide integrated environments that facilitate the whole process of design optimization, such as Design of Experiments, optimal solution search, as well as statistical analysis. This book benefits from such software when different MOGAs are compared for engine optimization problems, which will be discussed in Chap. 4.

2.2 Engine Modeling with Computational Fluid Dynamics IC engine combustion is a complex process that involves several strongly coupled physical and chemical processes. The whole procedure is usually decomposed into a number of parts: liquid-phase spray dynamics, gas-phase fluid dynamics, and gas-phase chemical kinetics. Each part is described by corresponding mathematical formulations. After applying appropriate physical models, the governing equations are solved using numerical methods. In this section, the governing equations for the gas-phase and liquid-phase flows are presented. The corresponding physical models and numerical methods are also described. More details of the governing equations and spray models are given by Reitz (2006).

2.2.1 Governing Equations The motion of a gas-phase flow is described using the Navier-Stokes equations. The gas mixture consists of multiple species. The continuity equation for species k is

28

2 Fundamentals

  oðqYk Þ oðqYk Uj Þ o oYk þ x_ k þ q_ sk ; ¼ qD þ oxj ot oxj oxj

ð2:10Þ

where Yk is the mass fraction of species k, q the total mass density of the mixture, and U is the fluid velocity. D is the single diffusion coefficient with the assumption of Fick’s Law diffusion. x_ k and q_ si are source terms due to chemical reaction and spray evaporation/condensation, respectively. Summing Eq. 2.10 over all species yieds the continuity equation for the whole gas flow: oq oðqUj Þ ¼ q_ s : þ ot oxj

ð2:11Þ

The momentum equations for the gas-phase mixture is oðqUi Þ oðqUi Uj Þ op osij ¼ þ þ Fis þ Fib ; þ ot oxj oxi oxj

ð2:12Þ

where p is the pressure of the mixture. s is the viscous stress tensor:  sij ¼ l

 oUi oUj 2 oUk þ  dij ; oxj oxi 3 oxk

where d is the tensorial Kronecker symbol: ( 1:i¼j dij ¼ 0 : i 6¼ j

ð2:13Þ

ð2:14Þ

Fis is a spray induced source term. Fib is the body force, which is usually the gravitation force and equals to qg. The energy conservation equation can be expressed in terms of energy, enthalpy, sensible energy, or sensible enthalpy. In this book, we take sensible energy, which is the specific internal energy exclusive of chemical energy, as the primary physical quantity describing the energy of the gas phase. Its transport equation is oðqeÞ oðqeUj Þ oUj oJj _ s _ c þ ¼ p þ þQ þQ ; oxj oxj ot oxj

ð2:15Þ

where e is the sensible energy. The heat flux Jj is the sum of contributions due to heat conduction and enthalpy diffusion: Jj ¼ K

Ns X oT oYk  qD hk : oxj oxj k¼1

ð2:16Þ

Q_ s and Q_ c are the source terms due to spray and chemical reaction, respectively. Ns is the total number of species.

2.2 Engine Modeling with Computational Fluid Dynamics

29

Assuming an ideal gas, the state equation is used to relate pressure and density: p ¼ qRT

Ns X Yk ; W k k¼1

ð2:17Þ

where Wk is the molecular weight of the k-th species. To accurately simulate a chemical reaction system, elementary reactions should be taken into account. Consider the system consisting of Ns species and Nr elementary reactions. The elementary reactions are written in a general form as: Ns X

m0kj vk

k¼1

Ns X

m00kj vk ;

j ¼ 1; . . .; Nr ;

ð2:18Þ

k¼1

where vk is the symbol for the k-th species; m0kj and m00kj are forward and reverse molar stoichiometric coefficients, respectively. m0kj and m00kj are integer numbers for elementary reactions and may be non-integers for non-elementary reactions. Each reaction fulfills element and mass conservation. The mass reaction rate of the k-th species is the sum of the reaction rates of all reactions involving this species: x_ k ¼

Nr X

x_ kj ¼ Wk

j¼1

Nr X

ð2:19Þ

mkj qj ;

j¼1

where mkj ¼ m00kj  m0kj is the overall stoichiometric coefficient of the k-th species in j-th reaction. The rate of progress of the j-th reaction qj is written using the molar concentration ½Xk  ¼ qYk =Wk qj ¼ Kfj

Ns Y

0

½Xk mkj  Krj

k¼1

Ns Y

00

½Xk mkj ;

ð2:20Þ

k¼1

where Kfj and Krj are the forward and reverse rates of the j-th reaction, respectively. Kfj is usually computed using the empirical Arrhenius law:   Ej ð2:21Þ Kfj ¼ Afj T bj exp  RT The pre-exponential constant Afj , temperature exponent bj , and activation energy are given by the chemical kinetic scheme. The reverse rate is related to the forward rate through the equilibrium constant by Krj ¼ Kfj =Kcj : And the equilibrium constant Kcj is determined from ! p PNs mkj DS0j DHj0 atm k¼1  exp ; Kcj ¼ RT R RT

ð2:22Þ

ð2:23Þ

30

2 Fundamentals

where DS0j and DHj0 are the change of specific entropy and enthalpy of j-th reaction, respectively: DS0j ¼

Ns X

mkj S0k ;

ð2:24Þ

mkj Hk0 :

ð2:25Þ

k¼1

DHj0 ¼

Ns X k¼1

Theoretically, the liquid phase can also be described using the Navier-Stokes equations in a detailed way. However, its interactions with the gas-phase flow are extremely complicated due to the large differences in time scales and length scales. The first question to be answered in the two-phase flows is how to couple the carrier and dispersed phases. The simplest way is a one-way coupling which predicts the dispersion behavior of transported discrete particles within a given turbulent gas flow (carrier phase ? dispersed phase). The effects of dispersed particles on the carrier phase are neglected. However, such effects are not negligible in many cases. The turbulence modifies dispersed particles behavior, which, in turn, modifies turbulence, because micro turbulence is produced due to the presence of the particles. At the interface of the particles, gas phase boundary layers and wakes develop because of relative motion between the particle center and the carrier phase. If there is heat and mass transfer between the particles and carrier phase, which is common in spray flows, two-way coupling must be used (carrier phase $ dispersed phase). Furthermore, when the particle number density is sufficiently large and the effect of the particle–particle interaction cannot be neglected, four-way coupling must be used (carrier phase $ dispersed phase $ dispersed phase). For IC engine simulation, the effects of droplet interactions cannot be neglected and thus four-way coupling is usually considered. The locally homogeneous flow (LHF) model neglects the slip effect between the liquid phase and gas phase. The two phases are in dynamic and thermodynamic equilibrium. At each point in the flow field, they have the same velocity and temperature. LHF condition is the limiting case with infinitely small droplets. To take into account the effects of the finite rate transport between the two phases, the separated flow (SF) model has been proposed. In general, there are three different approaches in the SF model: the discrete-droplet model (DDM); the continuous droplet model (CDM); and the continuous formulation model (CFM). CDM is applicable only when a few phenomena must be considered. Otherwise, the computational cost will be very high. CFM treats the two phases as continuous phases and solves both of them with an Eulerian formulation. It is referred to as an ‘‘Eulerian approach’’ in mathematics, distinguishing it from the ‘‘Lagrangian approach’’. It takes the dispersed phase as a continuous fluid and introduces several continuous scalar fields to represent the dispersed phase. Quantities relevant to the dispersed phase are defined at nodes, which are generally coincident with those used for the continuous-phase grid, and the mean field equations are derived for

2.2 Engine Modeling with Computational Fluid Dynamics

31

both phases. Therefore, the dispersed phase is modeled at the macroscopic level with this approach. This method leads to significant difficulties in modeling complex phenomena such as droplet breakup, droplet interaction, and droplet evaporation, which are essential in IC engine applications. It is also very difficult to establish the representation of the turbulent stresses and transport in the liquid phase. DDM corresponds to another category: the ‘‘Lagrangian approach’’, which is performed at a mesoscopic level. In the DDM, the spray is represented by a finite number of droplet groups. The motion and transport of these droplet groups are tracked through the flow field using a Lagrangian formulation. The mean quantities of the liquid phase are computed through statistical methods. The effects of the liquid phase on the gas phase are considered by introducing appropriate spray source terms into the governing equations of the gas phase. It is convenient for the DDM to construct physical model and numerical algorithms. Thus the Lagrangian approach dominates current CFD simulations of two phase flows. All the simulations in the present book use the Lagrangian approach for the liquid phase (i.e., the ‘‘Eulerian-Langrangian’’ or ‘‘Lagrangian-Drop Eulerian-Fluid’’ approach for the two phase flow) and thus only this approach is discussed. This approach assumes that after primary breakup the formed droplets are small enough to be viewed as point sources. Thus, spray dynamics can be described by the spray equation (Williams 1958), in which the spray is represented by a droplet distribution function (DDF), f . All of the droplet properties are considered in the DDF: f ¼ f ðVd ; rd ; Td ; y; y_ ; x; tÞ;

ð2:26Þ

where x, Vd , rd , and Td are the spatial location, velocity, equilibrium radius (the radius that the droplet would have if it were spherical), and temperature of the droplet, respectively. y and y_ are distortion from sphericity and its time rate of change. This droplet distribution function is defined in such a way that fdVd drd dTd dyd y_ is the probable number of droplets per unit volume at position x and time t with velocity in the interval ðV; V þ dVÞ, radii in the interval ðrd ; rd þ drd Þ, temperature in the interval ðTd ; Td þ dTd Þ, and displacement parameters in the intervals ðy; y þ dyÞ and ð_y; y_ þ dy_ Þ. The first moment of f is the number density of the droplets: Z ð2:27Þ n ¼ fdVd drd dTd dyd y_ : The second moment about radius rd relates to the liquid volume fraction h and liquid macroscopic density q0l : Z 4 3 ð2:28Þ pr fdVd drd dTd dyd y_ ; h¼ 3 Z 4 3 q0l ¼ pr qd fdVd drd dTd dyd y_ : ð2:29Þ 3

32

2 Fundamentals

The time evolution of f is obtained by solving the spray equation: of o o _ ðf r_ d Þ þ ðf Td Þ þ rx  ðf Vd Þ þ rV  ðf FÞ þ ot ord oTd o o þ ðf y_ Þ þ ðf €yÞ ¼ f_coll þ f_bu ; oy o_y

ð2:30Þ

where F, r_d , T_ d , and €y are the time rates of changes of an individual drop’s velocity, radius, temperature, and oscillation velocity y_ .

2.2.2 Physical Models The equations presented in Sect. 2.2.1 cannot be solved directly due to their complexity. Physical models are required to simplify the equations or to facilitate their numerical solution. In this section, common physical models used in modern CFD simulations of internal combustion engine are summarized.

2.2.2.1 Turbulence Models Turbulence is the most challenging part of the fluid mechanics, and the only unsolved one of the six classical physics problems. A widely accepted concept about the turbulence is Kolmogorov’s turbulence law (Kolmogorov 1991). According to his theory, large scale turbulent fluctuations are generated by the mean flow through the Reynolds stresses. These large fluctuations give rise to smaller scales through the same inertial mechanism. When the scale becomes small enough, the turbulence kinetic energy is converted to heat by the viscous stresses. Thus the whole turbulence process covers a wide rage of length and time scales in physical space, and correspondingly a broad spectrum in wave number space. Both the smallest length and time scales, that are called the Kolmogorov scales, are proportional to Re3=4 . As the turbulence scale decreases, the turbulent motion becomes more independent of the large eddies and locally isotropic. The turbulence is then characterized by the kinetic energy dissipation rate. Theoretically, any turbulent flow can be accurately simulated using direct numerical simulation (DNS), which resolves the smallest time and length scales, i.e., Kolmogorov scales. Each simulation produces a single realization of the flow. The total grid number in 3D is therefore proportional to Re9=4 . The total time step is proportional to Re3=4 . Thus, the total computational cost is proportional to Re3 . Engineering flows usually have very large Reynolds number. Therefore, DNS of engineering flows is practically unacceptable. It may take several thousand years for a powerful parallel computer to simulate 1 second of flight of an airplane using DNS (Moin and Kim 1997). The computational cost of DNS will be significantly

2.2 Engine Modeling with Computational Fluid Dynamics

33

increased when chemical reaction and/or multiphase flow is involved. Therefore, DNS is currently and will be in the foreseeable future a tool only for fundamental research, rather than a tool for engineering application. Several strategies have been developed to avoid resolving the smallest time and/or length scales. The Reynolds averaged numerical simulation (RANS) method only describes time or ensemble averaged quantities of the flow field. The effects of the fluctuating variables are described through a turbulent viscosity model or Reynolds stress model. In the turbulent viscosity models, the turbulent viscosity is obtained from an algebraic relation or from turbulent quantities such as the turbulence kinetic energy and its dissipation rate, which is solved using a modeled transport equation. Among the turbulent viscosity models, the twoequation k-e model (Launder and Spalding 1972) is the most frequently used. In the Reynolds stress models, the modeled transport equations are solved for each component of the Reynolds stress and for the dissipation rate which provides a length or time scale of the turbulence (Pope 2000). Therefore, the turbulent viscosity hypothesis is not needed any longer. For compressible flows, the density cannot be taken as a constant. Therefore, we must consider the density in the same statistical fashion as the other fluid-mechanical quantities. If we directly apply the time-averaging on the Navier-Stokes equations, a wide variety of quantities involving density fluctuation occur in the averaged equations. Favre (mass) weighted averaging is used to solve this problem. In Favre averaging, all fluidmechanical quantities except the pressure are mass averaged. The correlations with the density fluctuation are eliminated. RANS methods are widely used in the simulation of engineering flows because of their computational simplicity. Due to its time averaging nature, the RANS methods cannot capture certain unsteady behaviors. An alternative is to use large eddy simulation (LES). LES explicitly computes the large structures of the flows, usually the ones larger than the grid size. The effects of the smaller ones are modeled using a subgrid-scale (SGS) model. The large structures in turbulent flows generally depend on the geometry of the system, while the small ones are more universal. Therefore, the models for LES may be more efficient and more global. LES is a powerful tool to predict unsteady phenomena in a turbulent flow, which are associated with combustion instability, turbulent mixing, and turbulence-chemistry interactions. LES has been applied to multiphase flows in last decade (Yeh and Liu 1991), and to the complex flows that occur in a variety of engineering applications (Haworth and Jansen 2000; Sankaran and Menon 2002; Apte et al. 2003; De Villiers et al. 2004; Bharadwa and Rutland 2009; Papoutsakis et al. 2009; Hu et al. 2010; Zhang et al. 2010; Corbinelli et al. 2010). LES of internal combustion engine is currently an active topic in academia (Naitoh et al. 1992; Haworth 1999; Lee et al. 2002; Kaario et al. 2003; Shethaji et al. 2005; Hu and Rutland 2006; Jhavar and Rutland 2006; Hori et al. 2007; Drake and Haworth 2007; Thobois et al. 2007; Richard et al. 2007; Joelsson et al. 2008; Li and Kong 2008; Banerjee et al. 2010), especially for unsteady phenomena prediction such as cyclic variation (Adomeit et al. 2007; Vermorel et al. 2007; Vermorel et al. 2009; Hasse et al. 2010). But it is not ready for engine optimization yet due to its high computational cost and immature

34

2 Fundamentals

physical models. A series of workshops on ‘‘LES for Internal Combustion Engine Flows’’ (LES4ICE) has been organized to advance LES applications for engine simulation. The Probability Density Function (PDF) method attacks the turbulence problem by capturing its stochastic nature. The turbulent flow is viewed as a random medium and described using a probabilistic mathematical model. The method computes the probability rather than exact values of certain quantities at certain positions and/or times. The whole turbulent flow is represented by a PDF which is similar to the distribution function in Eq. 2.26. The PDF can be either presumed or computed by solving its transport equation (Ge 2006). If a presumed PDF is used, the problem turns to determining the first several moments (usually the first and second moments) of the PDF from local conditions. In most contexts, the PDF method refers to the transported PDF approach where the PDF is computed by solving its transport equation, which can be deduced from the Navier-Stokes equations (Ge 2006). In the PDF transport equation, the terms of convection, mean pressure gradient, and chemical reaction source appear in a closed form (Pope 1985, 2000; Haworth 2010). Thus, it is a very attractive option for modeling turbulent combustion processes. The PDF transport equation is usually solved using Monte-Carlo/Langrangian particle methods, whose computational cost is proportional to the total dimension number, i.e., the total number of individual quantities considered in the PDF. According to statistics theory, the error of the particle method is proportional to N 1=2 , where N is the total particle number considered in the simulations. The PDF method has been applied to IC engine simulation (Haworth and El Tahry 1991; Taut et al. 2000; Zhang et al. 2005; Lee and Mastorakos 2007; Kung and Haworth 2008; Yamamoto et al. 2010). In spite of its advantages in dealing with detailed chemistry, the PDF method is prevented from most engine simulation and optimization application due to its expensive computational cost. Even when only 15 * 20 particles per cell are considered (Kung and Haworth 2008), its total computational cost is still not acceptable for industry application. RANS is still the dominant technique for current internal combustion engine simulation and optimization. Among them, the two-equation models are the most widely used because of their simplicity and effectiveness (Launder and Spalding 1972), while the Reynolds stress model (RSM, Hanjalic and Launder 1972) for engine simulation is rarely used. RSM has been mainly applied to simulate intake flows (Borgnakke and Xiao 1991; Luo and Bray 1992; Lebrère et al. 1996) and only a few studies on in-cylinder flows (Yang et al. 2000, 2005). In this book, all the example simulations were conducted using RANS with two-equation models and the models were developed in the framework of RANS. Some of these models in which turbulent scales are not involved may be directly applied to other turbulence models. RANS uses a time-averaging technique and the instantaneous quantities are decomposed into a time-averaged component and a fluctuating term:  þ U0 : U¼U

ð2:31Þ

2.2 Engine Modeling with Computational Fluid Dynamics

35

For compressible flows, Favre-averaging is usually used to eliminate the fluctuating term associated with density, which is defined as: ~ ¼ qU= U q:

ð2:32Þ

The corresponding fluctuating components are defined as: ~ U00 ¼ U  U:

ð2:33Þ

Applying time averaging to Eqs. 2.11 and 2.12 yields: ~ jÞ o q oð qU _s ; ¼q þ ot oxj ~ j Þ oð ~ i Þ oð ~ iU qu00i u00j Þ oð qU qU o p osij  s  b þ þ ¼ þ þ Fi þ Fi ; ot oxj oxi oxj oxj

ð2:34Þ

ð2:35Þ

u00i u00j is the Reynolds stress tensor that needs to be modeled. In the k  e models, q two additional quantities, the turbulence kinetic energy k ¼ 12 u00i u00i and its dissipation rate e; are added to close the equations. Their transport equations have been deduced and modeled. The length and time scales are determined by lt ¼

k3=2 ; e

k ts ¼ : e

ð2:36Þ ð2:37Þ

The standard k-e model assumes an isotropic turbulence. By introducing a kinematic eddy viscosity lt, the Reynolds stress tensor is modeled as  qu00i u00j

  ~ i oU ~ j 2 oU ~k oU 2 ~ kdij : ¼ lt þ  dij  q oxj oxi 3 oxk 3

ð2:38Þ

The turbulent viscosity lt is related to the Favre-averaged turbulence kinetic energy, ~k, and its dissipation rate, ~e, via: ~k2  ; lt ¼ C l q ~e

ð2:39Þ

where Cl is a model constant listed in Table 2.1. Substituting Eq. 2.38 into Eq. 2.35, the modeled momentum equation is obtained:

36

2 Fundamentals

Table 2.1 Model constants in the standard k-e model (Launder and Spalding 1974)

rk

re

Cl

Ce;1

Ce;2

Cs

1.0

1.3

0.09

1.44

1.92

-1.0

~ i Þ oð ~ iU ~ jÞ oð qU qU o p s b þ ¼ þF i þ Fi ot oxj oxi    ~ i oU ~ j 2 oU ~k o oU þ ðlt þ lÞ þ  dij : oxj oxi 3 oxk oxj ~ Transport equations for k and ~e are modeled as   ~ ~ jÞ oð q~kÞ oð q~kU o lt ok _ s; ~e þ W þ þ Pk  q ¼ þl ot oxj oxj rk oxj    ~ jÞ oð q~eÞ oð q~eU o lt o~e ¼ þl þ ot oxj oxj re oxj

~e _s ; ~e þ Cs W þ Ce;1 Pk  Ce;2 q ~k

ð2:40Þ

ð2:41Þ

ð2:42Þ

_ s is the spray source term. The production term for the turbulence kinetic where W energy Pk is given by     ~i ~ i oU ~ j 2 oU ~k ~i oU oU 2 ~ oU kdij qu00i u00j ¼ lt þ  dij  q : ð2:43Þ Pk ¼  oxj oxj oxi 3 oxk oxj 3 rk and re are the effective Prandtl numbers for k and e. The model constants Ce;1 , Ce;2 , and Cs are listed in Table 2.1. The first term on the right-hand side of Eq. 2.42 is the source term accounting for length scale changes due to velocity dilatation. Applying time averaging to Eqs. 2.10 and 2.15, we have   ~ jÞ oð qYk00 u00j Þ oð qY~k Þ oð qY~k U o oY~k _ k þ q _s ; D þx q ¼ þ ð2:44Þ þ k oxj ot oxj oxj oxj ~ jÞ ~ j oJj  s  c oð qe00 Uj00 Þ oð q~eÞ oð q~eU oU þ ¼  p þ þ Q_ þ Q_ : ot oxj oxj oxj oxj

ð2:45Þ

 Yk00 u00j and q e00 u00j are usually modeled The species and energy turbulent flux q using a gradient transport hypothesis1: l oY~k Yk00 u00j ¼  t q ; Sct;k oxj

1

ð2:46Þ

Note that this assumption may not be valid in certain circumstances where counter-gradient transport may occur.

2.2 Engine Modeling with Computational Fluid Dynamics Table 2.2 Model constants in the RNG k-e model (Han and Reitz 1995)

37

rk

re

Cl

Ce;1

Ce;2

Cs

g0

b

1.39

1.39

0.0845

1.42

1.68

-1.0

4.38

0.012

e00 u00j ¼  q

lt o~e ; Pr oxj

ð2:47Þ

where Sct;k is the turbulent Schmidt number of the k-th species; Pr is the turbulent Prandtl number for internal energy. The standard k-e model has been used in the original KIVA codes (Amsden et al. 1989; Amsden 1993) and widely used in engine simulation. It was later replaced by the Renormalization Group (RNG) k-e model (Han and Reitz 1995), which has been used in all simulations in this book. The RNG k-e model was originally derived by Yakhot and Orszag (1986) using Renormalization Group theory. Model constants in the RNG k-e model can be explicitly evaluated from the theory based on certain assumptions and mathematical development. The RNG k-e model was extended to compressible flows and two phase flows by Han and Reitz (1995). The resulting transport equation for turbulence kinetic energy has the same form as Eq. 2.42. The transport equation for its dissipation rate is different from the standard k-e model and is written as    ~ jÞ ~j oð q~eÞ oð q~eU oU o lt o~e ~e  R  C3 q ¼q þ þl þ oxj oxj re ot oxj oxj

~e _s : ~e þ Cs W ð2:48Þ þ Ce;1 Pk  Ce;2 q ~k R, is added to consider rapid distortion and Comparing to Eq. 2.42, one term, q anisotropic large-scale eddies. It can be modeled as rffiffiffi   oUj  2 R¼ Cl Cg g~e ; ð2:49Þ oxj 3 Cg ¼

gð1  g=g0 Þ ; 1 þ bg3

ð2:50Þ

where g is the ratio of turbulent to mean strain-time scale: g ¼ ts S ¼ ts ð2Sij Sij Þ1=2 ;

ð2:51Þ

and Sij is the mean strain: Sij ¼

  ~ j oU ~i 1 oU : þ 2 oxi oxj

ð2:52Þ

38

2 Fundamentals

The model parameter C3 is written as pffiffiffi 1 C3 ¼ ½1 þ 2C1  3mðn  1Þ þ ð1Þd 6Cl Cg g; 3

ð2:53Þ

where the temperature exponential factor involved molecular viscosity is m = 0.5; n is the exponent of a polytropic process. d is a Kronecker delta depending on the sign of velocity dilatation: ( 1 : r  U\0 : ð2:54Þ d¼ 0 : r  U[0 The model constants are listed in Table 2.2.

2.2.2.2 Turbulent Combustion Models Combustion processes in the gaseous phase involve many complex physical and chemical phenomena: reaction chemistry, turbulence transport, diffusion of heat and species, and thermodynamics. These processes are strongly coupled. The interaction between them cannot be neglected, especially the turbulence-chemistry interactions. The chemical reaction rates are strongly coupled to molecular diffusion at the smallest scales of turbulence. The heat release from the chemical reactions affects the turbulent flow, both from variations in the density field and from the effects of local dilatation. These processes are modeled using turbulent combustion models. The central problem for the turbulent combustion model is how to compute the _ k (or final composition) from the perfectly stirred reactor (PSR) mean reaction rate x reaction rate x_ k (or initial composition) and turbulent quantities. Because in either RANS or LES, the combustion occurs at the unresolved scales of the computations, the mean reaction rates must be approximated using combustion models. The simplest model is to assume that each computational cell is a PSR and turbulence _ k ¼ x_ k ðY~1 ; . . .Y~N ; T; ~ pÞ. Despite its evident flaws as a effects are neglected, i.e., x s turbulent combustion model, this approach actually gives very good predictions for conventional diesel combustion when coupled with detailed reaction mechanisms (Singh et al. 2007a). Coupled with the CHEMKIN package (Kee et al. 1990), this model has been widely used in multi-dimensional engine simulations and is usually referred as the ‘‘KIVA-CHEMKIN model’’. The examples in Chap. 6 use the KIVA-CHEMKIN model when detailed reaction mechanisms are considered. One simple approach is based on a turbulent mixing-controlled combustion concept, which assumes that the burning rate of the mixture is mainly determined by the turbulent mixing rate. Thus, the influence of the chemical kinetics or its interaction with the fluid mixing is neglected, and only the fast chemistry limit is taken into account. This class of models includes the eddy breakup model (Spalding 1971) and the eddy-dissipation model (Magnussen and Hjertager 1977), and the characteristic time combustion (CTC) model, etc. Because of their

2.2 Engine Modeling with Computational Fluid Dynamics

39

simplicity, these models are very popular in engineering simulations. For instance, the CTC model is widely used in IC engine simulations. The CTC model considers turbulence effects on combustion process by introducing a turbulent combustion characteristic time scale tc (Abraham et al. 1985). The time rate of change in mass fraction of the k-th species due to chemical reaction is written as dYk Yk  Yk ¼ ; dt tc

ð2:55Þ

where Yk is the local and instantaneous thermodynamic equilibrium value of the mass fraction; and tc indicates the characteristic time to achieve this equilibrium that is assumed to be the same for all species. tc is determined from the laminar time scale tl and the turbulent time scale tsc : tc ¼ tl þ ftsc ;

ð2:56Þ

where f is a delay coefficient determining the contribution of the turbulent effects. When a reaction mechanism is employed, the laminar time scale is set to the time step (Kong and Reitz 1993). When a simple reaction mechanism is employed, the laminar time scale is estimated from a correlated one-step reaction rate from a single droplet auto-ignition experiment (Kong et al. 1995): 0:75 1:5 tl ¼ A1 Xfuel XO2 expðE=RTÞ;

ð2:57Þ

where A ¼ 1:54  1010 and E = 77.3 kJ  mol-1 K-1. The turbulent time scale tsc is proportional to ts : ~k tsc ¼ C2 ts ¼ C2 : ð2:58Þ ~e The model constant C2 is set to 0.142 for the standard k-e model and 0.1 for the RNG k-e model. The delay coefficient is given by 1  er ; ð2:59Þ 0:632 where r is the mass fraction ratio of the amount of products to that of total reactive species (all except N2), which indicates the completeness of the combustion process and varies from 0 (no combustion yet) to 1 (complete combustion). Another category of turbulent combustion models is the flamelet model. Flamelet models view the turbulent flame as an ensemble of stretched laminar flamelets attached to the instantaneous position of the flame surface. The underlying concept is that the flame reaction zones are very thin. For the turbulent diffusion flame, the flamelet model assumes that the terms involving transients and gradients parallel to the instantaneous surface of the constant mixture fraction to be small. By assuming equal diffusivity of all species, the species conservation equations can locally and instantaneously be transformed into a stationary laminar flamelet equation (Peters 1984). The only two control parameters are the mixture fraction and its dissipation rate v. The mixture fraction f ¼

40

2 Fundamentals

indicates the progress of the chemical reaction, while its dissipation rate indicates strain effects. For a given state of the turbulent flow with certain value of mixture fraction and its dissipation rate, the flamelet models assume that the local balance between diffusion and reaction is similar to the one in a prototype laminar flame with the same mixture fraction and its dissipation rate. The balance equations of species are then replaced with the conservation equation of the mean and variance of the mixture fraction. The flamelet structure is pre-calculated by solving the onedimensional flamelet equations. Usually the counter-flow structure is used to build the flamelet library. The results are stored in a structured table. The composition state space can be determined by looking up the table according to the mixture fraction and its dissipation rate. The mean values of the compositions are obtained usually through a presumed PDF approach, which models turbulence effects. In this way, the calculation of the turbulent flow and mixture fields is separated from the calculation of the chemistry. Detailed chemical reaction mechanisms and molecular diffusion processes are then implemented into CFD with acceptable computational costs. The Representative Interactive Flamelet (RIF, Pitsch et al. 1996) model was developed for diesel combustion simulation, in which only the cylinder-averaged dissipation rate is considered. A multiple flamelet model, the Eulerian particle flamelet model (EPFM), was developed for DI diesel engine simulation (Hasse et al. 2000). Hu and Rutland (2006) developed a steady-state flamelet model for LES of diesel combustion. For the turbulent premixed flame, a unity Lewis number and an infinitely thin flame structure are assumed and the species transport equation is transformed into a single balance equation for progress variable (Veynante and Vervisch 2002) or a G-equation (Peters 1999). The reaction rate is computed from the laminar burning velocity, a correction factor representing turbulence stretch, and flame surface density. The Bray-Moss-Libby (BML) model (Bray and Libby 1994) computes the flame surface density from a mean progress variable and a crossing length scale using an algebraic formulation. The other approaches compute the flame surface density by solving a transport equation, for instance, the flame surface density model (Boudier et al. 1992; Trouve and Poinsot 1994; Lee et al. 2008), and the coherent flame model (Dillies et al. 1993; Musculus and Rutland 1995; Vermorel et al. 2007). The G-equation model tracks the propagating flame using a level-set method. Turbulent effects are taken into account by the G-equation model, which has been extensively used for IC engine simulation (Tan and Reitz 2003; Singh et al. 2007b; Liang et al. 2007; Pauls et al. 2007; Yang and Reitz 2009a; Toninel et al. 2009). The turbulent partially premixed flame is the most common flame type in DI engines. It is usually assumed that the partially premixed flame is a combination of a diffusion flame and a premixed flame, and it thus is modeled using a hybrid model (Hu et al. 2007). The fourth category of turbulent combustion models are the PDF models. The convection and chemical reaction source terms are treated exactly in the PDF models, which is very attractive for turbulent combustion modeling (Haworth 2010). Turbulence-chemistry interaction is also well described. Its challenge is still the expensive computational cost.

2.2 Engine Modeling with Computational Fluid Dynamics

41

The conditional moment closure (CMC) model focuses on certain states between the fresh mixture and fully burnt products in the premixed flame, or between fuel and oxidizer in the diffusion flame (Klimenko and Bilger 1999). The average composition is determined from the conditional moments, hqYk jc ¼ c i, where c is a progress variable for premixed flames, or the mixture fraction for diffusion flames. The CMC model may be viewed as a multi-surface description of turbulent flames. Any conditional quantities correspond to their conditional average values along the iso-surface of c ¼ c . CMC modeling of IC engine combustion has been reported (Barroso et al. 2005; Seo et al. 2008; Wright et al. 2009).

2.2.2.3 Ignition Models In an SI engine, the combustion is initiated by a spark. The ignition process consists of three stages: breakdown, arc, and glow. When the voltage between the anode and cathode reaches the breakdown voltage, an arc will form. If the energy flux rate that dissipates into the charge is large enough and the local mixture fulfills an ignitibility condition, the mixture will be ignited and a flame kernel will form. Undergoing the influence of flame propagation, spark energy, and flow transport, the flame kernel grows into a self-sustaining propagating flame. A simple approach to model the spark ignition process is to add an energy source to the charge at the spark plug position (Amsden et al. 1989; Yorita et al. 2007). Most of the models employ empirical models for the breakdown and arc phases and a 1D model for the flame kernel, i.e., only the radius and position of the flame kernel is considered (Sher et al. 1992; Yossefi et al. 1993; Shen et al. 1994; Song and Sunwoo 2000; Duclos and Colin 2001; Falfari and Bianchi 2007; Dahms et al. 2009). Duclos and Colin (2001) integrated an electrical circuit model, an arc model, and a flame kernel model into a multi-dimensional CFD code. The flame kernel model is also a 1D model, with multiple particles representing the kernels in a statistical sense. Fan and Reitz (2000) developed a discrete particle ignition (DPIK) model, in which a set of Lagrangian particles are used to represent the flame surface. The model was improved by Tan and Reitz (2003). By neglecting the effects of convection, the i-th particle’s distance to the spark plug, rk;i , is computed as: drk;i qu ¼ ðsplasma þ sT Þ; dt qb

ð2:60Þ

where qu and qb are the density of unburned and burnt gas mixture, respectively. sT is the turbulent flame speed computed from laminar flame speed s0L and local turbulent intensity. splasma is plasma induced propagation flame speed and it is computed based on energy balance of the ignition kernel: _

splasma ¼

geff Qspk 2 q ðe  h 4prk;i u u b

þ p=qb Þ

;

ð2:61Þ

42

2 Fundamentals

where Q_ spk is the electrical energy discharge rate. geff is the coefficient that takes into account the heat loss to the spark plug. The value of geff is about 30% (Heywood 1988). eb and hu are the internal energy of the burnt mixture and the specific enthalpy of the unburned mixture, respectively. Turbulent strain and curvature effects on the kernel flame are taken into account by multiplying the laminar flame speed by a stretch factor I0 (Herweg and Maly 1992):  1=2  0 1=2 lF u lF qu 2 ; ð2:62Þ I0 ¼ 1  15lt rk;i qb s0L where lF ¼ Cp qk s0 is the laminar flame thickness, lt is the turbulent integral length u L

scale, and u0 is the turbulence intensity. Details of the integration of the DPIK ignition model with the G-equation flame propagation model for modeling SI engine combustion are given by Tan and Reitz (2006). For a CI engine, the combustion is initiated by auto-ignition, which depends on the local chemical kinetic, thermodynamic, and fluid dynamic properties of the incylinder mixture. A detailed reaction mechanism, such as the ERC (Engine Research Center, University of Wisconsin-Madison) reduced n-heptane mechanism, is able to accurately predict the auto-ignition events. For computational efficiency considerations, a single-step Arrhenius kinetics model has been widely used in CI engine combustion simulations. The Shell ignition model (Halstead et al. 1977) offers an option that improves accuracy and efficiency, which consists of five species and eight generic reactions based on the degenerate branching characteristics of hydrocarbon auto-ignition. The model was originally developed to predict knock in gasoline engines. The generic species and reactions involved in the model are as follows: RH þ O2 ! 2R

Kq

ðR1Þ

R ! R þ P + Heat

Kp

ðR2Þ

R ! R þ B

f1 Kp

ðR3Þ

R  ! R þ Q

f 4 Kp

ðR4Þ

R þ Q ! R þ B

f2 Kp

ðR5Þ

Kb

ðR6Þ

f3 Kp

ðR7Þ

Kt

ðR8Þ

B ! 2R R ! termination 2R ! termination

where RH is the hydrocarbon fuel (CnH2m); R* is the radical formed from the fuel; B is the branching agent; P is oxidized products consisting of CO, CO2, and H2O with specific proportions; Q is a labile intermediate species. Reaction R1 is the

2.2 Engine Modeling with Computational Fluid Dynamics

43

initiation reaction, followed by chain-propagation cycle (reactions R2–R6). Reactions R7 and R8 are two termination reactions. 2.2.2.4 NOx Emission Model The NOx formation process can be modeled by including related elementary reactions into the detailed reaction mechanism. A successful practice of this approach is the ERC reduced n-heptane mechanism with 34 species and 74 reactions, which adapted the NOx formation mechanism from the GRI methane/air combustion reactions (Smith et al. 2009): N þ NO N2 þ O N þ O2 NO þ O N2 O þ O 2NO N2 O þ OH N2 þ HO2 N2 O þ M N2 þ O þ M NO þ HO2 NO2 þ OH NO þ O þ M NO2 þ M NO2 þ O NO þ O2 NO2 þ H NO þ OH: This model has proven to be a very reliable model and has been extensively used in IC engine simulation and optimization. It is also used in the examples in Chap. 6 when the detailed chemistry mechanism is used. However, when a simple reaction mechanism is used, minor species such as OH and HO2 are absent and the abovementioned model cannot be implemented. A simpler model, the extended Zel’dovich mechanism (Heywood 1976), is then used to predict NOx emission. The extended Zel’dovich mechanism consists of the following reactions: N2 þ O NO þ N;

ðR9Þ

N þ O2 NO þ O;

ðR10Þ

N þ OH NO þ H:

ðR11Þ

The mechanism assumes partial equilibrium of the reaction O þ OH O2 þ H; and steady state of species N:

44

2 Fundamentals

d½N ¼ 0: dt The final rate equation for NO is then derived: d½NO 1  ½NO=ðK12 ½O2 ½N2 Þ : ¼ 2K1f ½O½N2  dt 1 þ K1b ½NO=ðK2f ½O2  þ K3f ½OHÞ

ð2:63Þ

The subscripts 1, 2, and 3 refer to reactions R9, R10, and R11, respectively. Subscripts ‘‘f’’ and ‘‘b’’ indicate the forward and backward reactions. The rate constants as recommended by Bowman (1975) are: K1f ¼ 7:6  1013 expð38000=TÞ K1b ¼ 1:6  1013 ; K2f ¼ 6:4  109 expð3150=TÞ K2b ¼ 1:5  109 expð19500=TÞ; K3f ¼ 1:0  1014 K3b ¼ 2:0  1014 expð23650=TÞ; K12 ¼

K1f K2f : K1b K2b

ð2:64Þ

ð2:65Þ

ð2:66Þ

ð2:67Þ

In order to obtain quantitative comparisons with experiments, a calibration factor b is introduced: d½NO d½NO ¼b : ð2:68Þ dt dt The additional factor of b = 1.533 is also used to convert NO to NOx according to the EPA standard. This model is employed in the examples in Chap. 6 when the simplified reaction mechanism is used.

2.2.2.5 Soot Model Soot modeling remains one of the biggest challenges in IC engine simulation due to the complex structure, composition, and formation/oxidation mechanisms of soot. Quantitative soot prediction is still not feasible, especially for IC engine optimization purposes. Hiroyasu’s two-step soot model (Hiroyasu and Kodota 1976) is the most widely used soot model in engine simulation. The two-step soot model only considers soot formation from a soot precursor and soot oxidation by oxygen. Two empirical expressions for soot formation and soot oxidation are used. The net soot production rate is determined from

2.2 Engine Modeling with Computational Fluid Dynamics

45

dMs dMsf dMso ¼  ; dt dt dt

ð2:69Þ

where the soot formation rate is given by   dMsf Esf n ; ¼ Asf qprec p exp  dt RT

ð2:70Þ

where qprec is the partial density of the soot precursor; p is the pressure; T is the temperature; Esf ¼ 12500 cal/mol is the activation energy; Asf is the Arrhenius pre-exponential factor normally set to 40; and the exponential factor for pressure, n is set to 0.5. The soot oxidation rate is determined using the Nagle and Strickland-Constable model (Nagle and Strickland-Constable 1962), and is calculated as dMso 6Wc ¼ Ms Rox  Aso Ms ; dt qs Ds

ð2:71Þ

where Ms is the soot mass; qs is the soot density; Ds is the soot particle diameter; Wc is the molecular weight of carbon. Rox is given by   KA pO2 Rox ¼ x þ KB pO2 ð1  xÞ; ð2:72Þ 1 þ KZ pO2 with x¼

PO2 : PO2 þ KT =KB

PO2 is the partial pressure of oxygen. The model parameters are:   30000:0 KA ¼ 20:0 exp  ; RT   15200:0 ; KB ¼ 4:46  103 exp  RT   97000:0 ; KT ¼ 1:51  105 exp  RT   4100:0 KZ ¼ 21:3 exp  ; RT where R ¼ 1:98 kcal  mol1 K1 . Assuming that the transient changes in the oxygen and precursor concentrations are negligible, the change of soot mass during one time step in a computational cell can thus be estimated as   _ sf M DMs ¼  Ms ½1  expðAso  DtÞ: ð2:73Þ Aso

46

2 Fundamentals

When a simple reaction mechanism is employed, the soot precursor is usually set as the fuel vapor. Other species such as acetylene or benzene may be taken as soot precursors as long as they have been included in the reaction mechanism. For instance, Kong et al. (2007) coupled the two-step soot model with the ERC reduced n-heptane mechanism, which includes acetylene. Acetylene is then taken as the soot precursor in the soot model. In the examples in Chap. 6, if acetylene is included in the reaction mechanism, acetylene is taken as soot precursor; otherwise, fuel vapor is taken as soot precursor. More advanced soot models have been developed for IC engine simulation. Tao et al. (2006) developed a multi-step phenomenological soot model, which considers surface growth, soot inception and coagulation, soot oxidation by oxygen and OH, soot precursor oxidation by oxygen. Vishwanathan and Reitz (2009) developed a new reduced n-heptane reaction mechanism which included polycyclic aromatic hydrocarbons (PAH), and PAH is taken as the soot precursor. In the present book, only the two-step soot model is used for simplicity.

2.2.2.6 Nozzle Flow Model Sprays are produced when the relative velocity between the liquid and the surrounding air or gas is high enough. Pressure atomizers and rotary atomizers eject the liquid at high velocity, while twin-fluid, air-assist, and air-blast atomizers expose a low-speed liquid to a high-velocity air flow (Lefebvre 1989). Among them, pressure atomizers dominate the IC engine application, and most of the injectors in IC engines feature a simple circular orifice. The injector nozzle geometry affects the fuel atomization and consequently influences the engine combustion and exhaust emissions significantly. However, it is very difficult for a numerical simulation to describe the relevant physics, due to the very small length and time scales of nozzle flows. Comprehensive numerical simulations (Gorokhovski and Herrmann 2008; Ning et al. 2009) and experiments (Liu et al. 2010; Balewski et al. 2010) have been conducted and have provided useful insights about the physics of the nozzle flow. Nevertheless, such expensive simulations are not acceptable for industry. Only phenomenological models can be applied for IC engine simulation and optimization. The ERC nozzle flow model (Sarre et al. 1999) has been extensively used in IC engine simulations. The nozzle flow model provides initial conditions about the initial spray droplets for the following breakup processes. The input parameters of the nozzle flow model include the liquid flow rate, injection pressure, cylinder pressure, physical properties of the liquid, nozzle hole diameter, ratios L=D and r=d, as shown in Fig. 2.11. The output parameters of the nozzle flow model are the instantaneous discharge coefficient, spray angle, effective injection velocity, and effective flow exit area, which relates to the initial droplet size or initial liquid blob size. The discharge coefficient Cd quantifies the difference between the exact flow rate and the one predicted using the ideal Bernoulli equation and is defined as

2.2 Engine Modeling with Computational Fluid Dynamics

47

Fig. 2.11 schematic of orifice geometry r d D L

Cd ¼ Umean =

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ðpin  pout Þ=ql ;

ð2:74Þ

where Umean is the mean liquid velocity at the exit; and pin and pout are the pressure at the inlet and outlet, respectively. Cd is modeled as Cd ¼ ðKinlet þ f  L=D þ 1Þ1=2 ;

ð2:75Þ

f ¼ maxð0:316Re0:25 ; 64 Re1 Þ;

ð2:76Þ

with

and the inlet loss coefficient Kinlet is determined from tabulated data (Benedict 1980). Based on this discharge coefficient, a first estimation of the inlet pressure is:   q Umean 2 pin ¼ pout þ l : ð2:77Þ 2 Cd Assuming a flat velocity profile and using Nurick’s expression (Nurick 1976) for the size of the contraction, the velocity at the smallest flow area (vena contracta) yields: Uvena ¼ Umean =Cc ;

ð2:78Þ

2

1=2 Cc ¼ Cc0  11:4r=d ;

ð2:79Þ

with the contraction coefficient

where Cc0 is the contraction coefficient when r=d ¼ 0. The pressure at the smallest flow area is then given as pvena ¼ pin 

ql 2 U : 2 vena

ð2:80Þ

If pvena is lower than the vapor pressure pvapor , it is assumed that the flow is fully cavitating. The inlet pressure and discharge coefficient are then given as pin ¼ pvapor þ

ql 2 U ; 2 vena

ð2:81Þ

48

2 Fundamentals

 C d ¼ Cc

pin  pvapor pin  pout

1=2 :

ð2:82Þ

The pressure at the vena contracta can also be estimated from the outlet pressure:

q 2 1  Cc2 þ Kexp þ f  L=D ; ð2:83Þ pvena;r ¼ pout þ l Umean 2 where Kexp is the expansion loss coefficient for the flow downstream of the cavitation region and determined from tabulated data (Benedict 1980). If pvena in Eq. 2.83 is already lower than pvapor , but pvena in Eq. 2.80 still predicts a turbulent flow, a cavitating reattaching flow is assumed, which is treated like a turbulent flow. In the cases of turbulent or cavitating reattaching flows, the exit velocity of the droplets is set to the mean velocity Umean , and the initial droplet size is set to the nozzle diameter. When the nozzle flow is fully cavitating, the exit velocity and initial droplet size are set to Ueff ¼ Uvena 

Deff

pout  pvapor ; ql Umean

 1=2 Umean ¼D : Ueff

ð2:84Þ

ð2:85Þ

2.2.2.7 Primary Breakup Models The primary breakup process is where the bulk liquid disintegrates into filaments and drops due to interaction with the surrounding gas. Instabilities on the interface are the major driving forces for the breakup process. Although the primary breakup process is essential for the following spray dynamics and combustion events, and significant progress has been made in the numerical simulation of primary breakup process recently (Gorokhovski and Herrmann 2008), such accurate simulations are not acceptable for IC engine simulation due to their extremely expensive computational cost. Alternatively, the primary breakup process can be simply modeled using a presumed droplet size distribution (Babinsky and Sojka 2002). Among them, the simplest distribution is a mono-disperse distribution (uniform distribution), i.e., the initial droplet radius is set equal to an input parameter SMR, or r32 . The KIVA-II code offers the v-squared distribution as another option (Amsden et al. 1989): f ðrÞ ¼ r 1 er=r ;

ð2:86Þ

where r ¼ r32 =3 is the number—averaged droplet radius and r32 is defined as: P 3 R 3 r f ðrÞdr r r32 ¼ P 2 ¼ R 2 : ð2:87Þ r r f ðrÞdr

2.2 Engine Modeling with Computational Fluid Dynamics

49

A Rosin-Rammler distribution (‘‘two-parameter Weibull distribution’’ in the mathematics literature) is frequently used to model droplet size distributions (Rosin and Rammler 1933; Han et al. 1997): a

f ðrÞ ¼ ara r a1 eðr=rÞ :

ð2:88Þ

The Nukiyama-Tanasawa distribution (Nukiyama and Tanasawa 1939) has also been used to model droplet size distributions. It has a more general form as: q

f ðrÞ ¼ ar p ebr ;

ð2:89Þ

where b, p, and q are adjustable parameters. The Maxwell, Rayleigh, v-squared, and Rosin-Rammler distributions are several special forms of the Nukiyama-Tanasawa distribution (Ge 2006). Since it has three input parameters, its application in IC engine simulations is rare. Other presumed distributions, and other methods to determine the initial droplet size distribution (e.g., maximum entropy method and discrete probability function approach) are explained in detail in Babinsky and Sojka (2002). For the pressure-swirl atomizer, the transition from internal injector flow to a fully developed hollow-cone spray can be modeled using a linearized instability sheet atomization (LISA) model (Schmidt et al. 1999) The LISA model considers two stages: film formation and sheet breakup. In the first stage, a liquid film surrounding an air core is formed due to centrifugal motion of the liquid within the injector. The thickness of the film, df , is related to the liquid mass _ by flow rate, m,

m_ ¼ pql Ua df d0  df ; ð2:90Þ where d0 the injector hole diameter; Ua ¼ Uinj cosðhÞ is the axial component of the total injection velocity at the injector exit and h is the cone half-angle. The total injection velocity Uinj is computed from the pressure drop across the injector exit: sffiffiffiffiffiffiffiffiffi 2Dp Uinj ¼ Cd;lisa ; ð2:91Þ ql where Cd;lisa is the effective discharge coefficient that is computed from a given discharge coefficient or the discharge coefficient determined from a nozzle flow model (c.f., Sect. 2.2.2.6):  rffiffiffiffiffiffiffiffiffi 4m_ ql : ð2:92Þ Cd;lisa ¼ max Cd ; 2 pd0 ql cosðhÞ 2Dp The second argument in the MAX function is used to guarantee that the size of the air core is non-negative. The sheet breakup process is modeled based on wave stability theory. The model assumes that a two-dimensional, viscous, incompressible liquid sheet of

50

2 Fundamentals

thickness, 2h, moves with velocity, U, through a quiescent, invisid, incompressible gas medium. A spectrum of infinitesimal disturbances, g ¼ g0 expðikx þ xtÞ;

ð2:93Þ

is imposed on the initially steady motion and produces fluctuating velocities and pressures for both the liquid and the gas, where g0 is the initial wave amplitude, k ¼ 2p=k is the wave number, and x ¼ xr þ ixi is the complex growth rate of the surface disturbances. A simplified form of the dispersion relation for pressureswirl atomizers (Senecal et al. 1999) is written as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q 2 2 rk3 ; ð2:94Þ xr ¼ 2ml k2 þ 4m2l k4 þ Uinj k  ql ql where ml is the liquid kinematic viscosity; X is the most unstable disturbance with the largest value of xr , and is assumed to be responsible for sheet breakup. Once the unstable waves on the sheet surface grow to a critical amplitude, ligaments are formed due to the sheet breakup. The breakup time sb;lisa for this process can be formulated based on an analogy with the breakup length of cylindrical liquid jets:   1 g sb;lisa ¼ ln b ; ð2:95Þ g0 X where gb is the critical amplitude at breakup. The corresponding breakup length lb;lisa can be estimated by   Uinj g lb;lisa ¼ sb;lisa Uinj ¼ ð2:96Þ ln b ; X g0 where the quantity lnðgb =g0 Þ is given a constant value 12. Based on mass balance, the resulting ligament diameter at the point of breakup can be derived as rffiffiffiffiffiffiffiffi 16h dL ¼ ; ð2:97Þ Ks where Ks is the wave number corresponding to the maximum growth rate X. Based on the assumption that the sheet is in the form of a cone with its vertex at a point behind the injector orifice, the sheet half-thickness h at the breakup position lb;lisa is estimated as

h0 d0  sb;lisa ð2:98Þ h¼ 2lb;lisa sinðhÞ þ d0  sb;lisa with h0  ðdf =2ÞcosðhÞ. If it is assumed that breakup occurs when the amplitude of the most unstable wave is equal to the radius of the ligament dL , a mass balance gives the drop size dD : dD3 ¼

3pdL2 ; KL

ð2:99Þ

2.2 Engine Modeling with Computational Fluid Dynamics

where the most unstable wavelength KL is given by " #1=2 1 1 3ll þ KL ¼ dL 2 2ðql rdL Þ1=2

51

ð2:100Þ

that is based on an analogy to Weber’s result for growing waves on cylindrical, viscous liquid columns.

2.2.2.8 Secondary Breakup Models The secondary breakup process is often modeled using the hybrid Kelvin-Helmholtz wave model and Rayleigh-Taylor model (Beale and Reitz 1999). The Kelvin-Helmholtz (KH) model is based on liquid jet stability analysis (Reitz and Bracco 1986). The analysis examines the stability of the surface of a cylindrical liquid jet to perturbations using a first order theory. The viscous liquid jet with velocity Ul is injected into a stagnant incompressible inviscid gas. An infinitesimal axisymmetric surface displacement is imposed to the initially steady surface: g ¼ <½g0 expðikz þ xtÞ:

ð2:101Þ

A dispersion equation, that includes the physical and dynamical parameters of the liquid jet and surrounding gas, relates the growth rate x to its wavelength k ¼ 2p=k and is derived from the linearized hydrodynamical equations. Velocity potential and stream functions are written in the form of wave solutions as functions of the cylindrical coordinates (r; z) and time t: U1 ¼ C1 I0 ðkrÞ expðikz þ xtÞ;

ð2:102Þ

W1 ¼ C2 I1 ðLrÞ expðikz þ xtÞ:

ð2:103Þ

C1 and C2 are integration constants. I0 and I1 are modified Bessel functions of the first kind. L2 ¼ k2 þ x=ml with ml the liquid kinematic viscosity. The gas pressure at the interface r ¼ r0 is given as  x2 K0 ðkr0 Þ : kg p ¼ q Urel  i k K1 ðkr0 Þ

ð2:104Þ

K0 and K1 are modified Bessel functions of the second kind. With the assumption of g r0 , the kinematic, tangential stress, and normal stress equations at the interface are written as Ul;r ¼

og ; ot

oUl;z oUl;r ¼ ; or oz

ð2:105Þ ð2:106Þ

52

2 Fundamentals

 2  oUl;r r 2o g  2 g þ r0 2 þ p; pl ¼ 2ll or oz r0

ð2:107Þ

which forms boundary conditions for Eqs. 2.102–2.104. Ul;r and Ul;z are the radial and axial liquid velocity components. Equations 2.105 and 2.106 are used to determine the integration constants C1 and C2 . Substituting Eqs. 2.102–2.104 into Eq. 2.107, the dispersion equation is obtained as: 0  I ðkr0 Þ 2kL I1 ðkr0 ÞI10 ðLr0 Þ x2 þ2Ul;r k2 x 1  2 I0 ðkr0 Þ k þ L2 I0 ðkr0 ÞI1 ðLr0 Þ   L2  r02 I1 ðkr0 Þ rk q 2 K0 ðkr0 Þ 2 2 ð1  k r Þ þ ðU k  ixÞ : ð2:108Þ ¼ 2 rel 0 ql K1 ðkr0 Þ L þ r02 I0 ðkr0 Þ ql r02 K0 and K1 are modified Bessel functions of the second kind. Equation 2.108 is solved numerically and it is found that there is a single maximum in the wave growth rate curve. Curve fits of the numerical solutions have been generated for the maximum growth rate and the corresponding wavelength, which results in KKH ¼

9:02rd ð1 þ 0:45Z0:5 Þð1 þ 0:4T0:7 Þ

XKH ¼

0:6 ð1 þ 0:865We1:67 air Þ

rffiffiffiffiffiffiffiffi 0:34 þ 0:38We1:5 r air : 0:6 ð1 þ ZÞð1 þ 1:4T Þ ql rd3

;

ð2:109Þ

ð2:110Þ

The gas Weber number is defined as 2 rd =r; Weair ¼ qUrel

ð2:111Þ

and the Ohnesorge number 1=2

Z ¼ Wed Re1 l :

ð2:112Þ

Urel is the relative velocity between the gas and the droplet, and r is the surface tension. The droplet Weber number is defined as 2 rd =r; Wed ¼ ql Urel

ð2:113Þ

and liquid Reynolds number is defined as Rel ¼ ql jUrel j2 rd =ll :

ð2:114Þ

T is the Taylor number: 1=2

T ¼ Weair Z:

ð2:115Þ

The KH model is implemented by postulating that a parent parcel with radius rd , breaks up to form new droplets with radius rd;c , which is determined by:

2.2 Engine Modeling with Computational Fluid Dynamics

rd;c ¼ B0 KKH ;

53

ð2:116Þ

where B0 is a model constant. The rate of change in the radius of the parent droplet parcel is described by drd rd  rd;c ¼ ; dt sKH

ð2:117Þ

where the breakup time scale sKH is defined as sKH ¼

3:726B1 rd : XKH KKH

ð2:118Þ

B1 is a model constant. Rayleigh-Taylor (RT) instability is believed to be responsible for additional droplet breakup. Thus the RT model is usually used in conjunction with the KH model to predict instabilities on the surface of the drop that grow until a certain characteristic breakup time when the drop finally breaks-up. The RT model is also based on wave instability theory. The unstable RT waves are thought to occur due to the rapid deceleration of the drops. Neglecting both the gas and liquid viscosity, the frequency of its fastest growing wave and corresponding wavelength are given by

XRT

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ½ad ðql  qÞ1:5 pffiffiffiffiffiffi ¼ ; ql þ q 3 3r

KRT

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3r : ¼ 2pXRT ad ðql  qÞ

ð2:119Þ

ð2:120Þ

ad is the droplet acceleration in the direction of travel. When the wavelength is smaller than the droplet diameter, the RT waves are assumed to be growing on the surface of the droplet. The wave growth time is then tracked. When it reaches its RT breakup time scale, which is defined as sRT ¼ Cs =XRT ;

ð2:121Þ

the drop is assumed to breakup. The radii of the new droplets is computed using rd;c ¼ 2CRT KRT ;

ð2:122Þ

where Cs and CRT are model constants. A liquid breakup length can be introduced, which is based on the theory that breakup process occurs at a different rate within and beyond the length of the liquid core (Xin et al. 1998). The RT model is then only applied to the decelerating drops beyond this liquid breakup length. However, the drops that are adjacent to the liquid core and within the breakup length are decelerated by drag with the ambient gas, too. These drops should also be

54

2 Fundamentals

influenced by the RT model. Thus, activity of the RT model is not determined by the liquid breakup length, but by the instability condition in Eq. 2.121.

2.2.2.9 Turbulent Dispersion Models A droplet moves according to its velocity: dxd ¼ Vd : dt

ð2:123Þ

If only the drag force and body force are considered, the acceleration of a droplet is written as: dVd Fd ¼ ¼ Dd ðU  Vd Þ þ g; dt md

ð2:124Þ

with drag function Dd : Dd ¼

3 qjU  Vd j Cd ðRed Þ; 8 qd rd

ð2:125Þ

drag coefficient Cd : ( Cd ¼

2=3

24Re1 d ð1 þ Red =6Þ; 0:424;

Red \1000 Red 1000

;

ð2:126Þ

droplet Reynolds number Red : Red ¼

2qrd jU  Vd j ; ^ lair ðTÞ

T^ ¼ ðT þ 2Td Þ=3;

ð2:127Þ ð2:128Þ

and gas instantaneous velocity U (gas velocity seen by the droplet): ~ þ u00 : U¼U d

ð2:129Þ

Turbulence effects on a droplet’s movement are modeled by the turbulent dispersion model, which provides a closure form for the gas turbulent velocity u00d . Each component of u00d is randomly chosen from a Gaussian distribution with pffiffiffiffiffiffiffiffiffiffi standard deviation r ¼ 2k=3. u00d is chosen once every turbulence correlation time tturb , which is the minimum of an eddy breakup time and a time for the droplet to penetrate an eddy:   k k3=2 1 ; ð2:130Þ tturb ¼ min ; cps e e jU  Vd j

2.2 Engine Modeling with Computational Fluid Dynamics

55

where the empirical constant cps ¼ 0:16432. When the cumulative time step Dtc [ tturb , the droplet velocity and position are updated using (Amsden et al. 1989): DVd ¼ Dt½Dd ðU  Vd Þ þ g þ du0 ;

ð2:131Þ

Dxd ¼ Vd Dt þ dx0 ;

ð2:132Þ

dx0 ¼ tper du0 þ dx0b :

ð2:133Þ

with

du0 and dx0b are sampled from Gaussian distributions with variances r2u0 and 2 r2x0  tper r2u0 , with r2u0 ¼ r2x0

1  eDd tturb 1  e2Dd Dt r2 ; D t 1 þ e d turb



2tturb r2u0 2Dd Dt þ 2 2 r2 ; ¼ ts Dt  1e Dd Dd r

ð2:134Þ



ð2:135Þ

and turbulent persistence time tper : tper ¼

r2 1 tturb ð1  eDd Dt Þ  : Dd r2u0

ð2:136Þ

2.2.2.10 Droplet Deformation Model The drops are assumed to be spherical, which in reality is only true for very small drops. Especially when the relative velocity between the drop and the surrounding gas is high, the drop deforms, which will change its drag coefficient. Its deformation depends on the drop’s Reynolds number and oscillation amplitude. In this case, the liquid drop drag coefficient has been related empirically to the magnitude of the drop deformation using Cd ¼ Cd;sphere ð1 þ 2:632yÞ;

ð2:137Þ

where Cd;sphere is the drag coefficient of the spherical drop; y is a dimensionless parameter describing drop distortion in Eq. 2.26 and is proportional to the displacement of the drop’s surface from its equilibrium position divided by the drop radius. y ¼ 0 represents the lower limit of a sphere, and y ¼ 1 the upper limit of a flat disk. y can be computed using the Taylor analogy breakup model (O’ Rourke and Amsden 1987) or the droplet deformation and breakup (DDB) model (Ibrahim et al. 1993). The TAB breakup model considers a liquid drop to be analogous to a spring-mass system (Taylor’s analogy), and the drop breakup is due to an increase

56

2 Fundamentals

in the amplitude of the drop oscillation. The acceleration of the drop distortion parameter is given as €y ¼ 5

2 ll y_ 8ry 2 q Urel  þ : ql rd2 ql rd3 3 ql rd2

ð2:138Þ

The DDB model is formulated based on energy and volume conservation of the distorting drop and is written as "   # 2 ll y_ 27 p2 r 4 6 3 q Urel €y ¼ 4 2 2  þ 1  2 : ð2:139Þ ql rd y 16 ql rd3 3py 8 ql rd2 The DDB model takes into account the increased frontal area of the distorted drop and thus is more accurate (Tennison et al. 1998).

2.2.2.11 Droplet Collision Model The original collision model in the KIVA-II code, the O’Rourke model (O’ Rourke 1981) only considers collisions between particles that are located in the same computational cell. The collision frequency of a certain pair of particles is m¼

Nmp pðrlp þ rmp Þ2 jVlp  Vmp j: Vcell

ð2:140Þ

The subscripts mp and lp denote the more populous and less populous droplet parcels, respectively. Vcell is the volume of the local cell containing the drops. The probability that the larger particle undergoes n collisions with the smaller particle follows a Poisson distribution, and thus the probability of no collision is P0 ¼ emDt ;

ð2:141Þ

where Dt is the computational time step. A random process is utilized to determine whether the collision event will occur or not. Another independent random number YY from the interval (0,1) is used to calculate the collision impact parameter b: b ¼ YY 1=2 ðrlp þ rmp Þ;

ð2:142Þ

which determines the collision outcome by comparing with the critical impact parameter bcr : bcr ¼ ðrlp þ rmp Þfmin½1; 2:4ðc3  2:4c2 þ 2:7cÞ=Welp g1=2

ð2:143Þ

with c ¼ rS =rL , and Weber number of the larger drop Welp ¼ qd jVlp  Vmp jrlp =aðTd Þ:

ð2:144Þ

2.2 Engine Modeling with Computational Fluid Dynamics

57

The mean temperature Td is: Td ¼

3 3 rmp Td;lp þ rmp Td;mp 3 3 rlp þ rmp

;

ð2:145Þ

and a is the liquid surface tension coefficient: aðTd Þ ¼

Td  Tcr a0 : T0  Tcr

ð2:146Þ

When b\bcr , coalescence occurs. Otherwise, each collision is assumed to be a grazing collision. In the case of a coalescence collision, the droplet number of the new parcel is mDt and the properties of the new parcel are determined from the conservation laws of mass and momentum. If it is a grazing collision, momentum conservation and a certain fraction of loss in kinetic energy and angular momentum is taken into account. The new velocities of the droplet parcels are given as: mlp Ulp þ mmp Ump þ mmp ðUlp  Ump Þpffiffiffiffiffiffiffiffiffiffiffiffi 1  fE ; ð2:147Þ mlp þ mmp   Nlp Nlp mlp Ulp þ mmp Ump þ mlp ðUmp  Ulp Þpffiffiffiffiffiffiffiffiffiffiffiffi ¼ 1 1  fE ; Ump þ Nmp Nmp mlp þ mmp Unew mp ¼

Unew mp

ð2:148Þ where m is the mass of droplet parcel. The fraction of energy dissipation during the collision fE is given as fE ¼

ðb  bcr Þ2 ðrlp þ rmp  bcr Þ2

 1:

ð2:149Þ

Since the O’Rourke model only considers collision events between groups of identical droplets (parcel) that are located in the same computational cell, the outcome of the model depends on mesh size. To remove mesh dependency, Munnannur and Reitz (2009) proposed a Radius-of-Influence (ROI) collision model. The ROI model considers potential collision between every pair of droplet parcels whose distance Dlp;mp is smaller than the maximum of their influence radii, Rlp and Rmp : Dlp;mp  maxðRlp ; Rmp Þ:

ð2:150Þ

The collision frequency is then computed as: m¼

Nmp pðrlp þ rmp Þ2 jVlp  Vmp j: Vcol

ð2:151Þ

58

2 Fundamentals

The collision volume Vcol is based on the radii of influence: 4 Vcol ¼ pðRlp þ Rmp Þ3 : 3

ð2:152Þ

Thus, the influence of mesh topology is removed and the collision events only depend on the droplet parcel distribution in space. The other elements of the ROI model are the same as the O’Rourke model.

2.2.2.12 Evaporation Model Assuming a single composition and homogeneous distribution of temperature inside the droplet, the rate of droplet radius due to evaporation is given by the Frossling correlation (Faeth 1977): r_ d ¼

drd qD Bm Shd ; ¼ dt 2qd rd

ð2:153Þ

where Shd is the Sherwood number for mass transfer: 1=2 1=3 lnð1 þ Bm Þ ; Shd ¼ ð2:0 þ 0:6Red Scd Þ Bm

ð2:154Þ

^

with Schmidt number Scd ¼ lairqDðTÞ. qD is the fuel vapor diffusivity in air and it is calculated from the estimated temperature T^ in Eq. 2.128 and: qDðTÞ ¼ D1 T D2 ; Y

ð2:155Þ

Y

F;1 where D1 and D2 are model constants. Bm ¼ F;s 1YF;s is the Spalding mass transfer number, with YF;s and YF;1 the fuel vapor mass fraction at the droplet’s surface and at the outer boundary of the film surrounding the droplet. The surface mass fraction YF;s is computed from the Clausius-Clapeyron equation:

YF;s ðTd Þ ¼

1þ

h

1

p Wair WF pv ðTd Þ

1

i;

ð2:156Þ

where WF is the molecular weight of fuel vapor; Wair is the local average molecular weight of all species except fuel vapor. pv is the equilibrium fuel vapor pressure. The rate of droplet temperature change is determined from the energy balance equation: 4 q pr 3 Cl T_ d  4qd prd2 r_ d LðTd Þ ¼ 4prd2 Q_ d ; 3 d d

ð2:157Þ

2.2 Engine Modeling with Computational Fluid Dynamics

59

where Cl is the liquid specific heat; LðTd Þ is the latent heat of vaporization; Q_ d is the rate of heat conduction to the droplet surface per unit area and is computed using the Ranz-Marshall correlation (Faeth 1977): kair ðTÞðT  Td Þ Q_ d ¼ Nud ; 2rd

ð2:158Þ

where the Nusselt number Nud :   1=2 1=3 lnð1 þ Bm Þ Nud ¼ 2:0 þ 0:6Red Prd ; Bm

ð2:159Þ

lair ðTÞCp ðTÞ , local specific heat at constant pressure kair ðTÞ Cp , and thermal conductivity coefficient of air kair : with Prandtl number Prd ¼

kair ðTÞ ¼

K1 T 3=2 ; T þ K2

ð2:160Þ

where K1 and K2 are model constants. Ra and Reitz (2009) developed a more accurate model that considers transient heat transfer inside the droplet. Instead of setting a uniform droplet temperature, the droplet surface temperature Td;s is computed from a heat and mass transfer balance at the interface between the droplet and surrounded gas when the droplet size is larger than a preset critical value. The energy balance at the interface is written as 4qd prd2 r_ d LðTd;s Þ ¼ 4prd2 ðQi þ Qd Þ;

ð2:161Þ

where Qi is the energy flux from inside the droplet to the surface. It is modeled as a convective heat transfer process with internal circulation taken into account and written as Qi ¼

kl ðTd  Td;s Þ; de

ð2:162Þ

where kl is the liquid thermal conductivity. de is the unsteady equivalent thickness of the thermal boundary layer and calculated from the effective thermal diffusivity: de ¼

pffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffi paeff t ¼ pval t;

ð2:163Þ

with v ¼ 1:86 þ 0:86 tanh½2:225 log10 ðPel =30Þ; and Pel is the Peclet number of the droplet. Qd is also computed from the droplet surface temperature Td;s . Equation (2.158) is then turned into

60

2 Fundamentals

Qd ¼

kair ðTÞðT  Td;s Þ Nud : 2rd

ð2:164Þ

Since the effective heat transfer coefficient for the outer heat flux is coupled with the vaporization rate, the surface temperature of the droplet is determined by solving two balance equations iteratively, and assuming a quasi-steady heat transfer process. Other evaporation models consider multi-component fuel effects. Continuous multi-component models (Lippert and Reitz 1997; Zuo et al. 2000; Zhu and Reitz 2002; Ra and Reitz 2003, 2004; Yang and Reitz 2009b, 2010), discrete multicomponent models (Ra and Reitz 2009), and discrete/continuous multi-component models (Yang et al. 2010) have been developed and applied to IC engine simulation. However, in the examples of this book, multi-component effects are not considered.

2.2.2.13 Spray Wall Impingement Model Spray wall impingement is very important for both PFI and DI engines. Fuel wall films in the intake ports can cause an undesirable fuel delivery delay and an associated fuel metering error in PFI engines. In some DISI engines, the fuel is directly injected into a specially designed piston bowl and the spray wall impingement is used to generate an optimal stratified mixture. While in DI diesel engines, the spray wall impingement may lead to unacceptable UHC and/or soot emission, as well as low fuel efficiency. Therefore, an accurate spray/wall interaction model also plays important role in engine simulations. The outcome of the wall impingement event depends on the properties of the drop, wall surface, and gas boundary layer in the near-wall region. If the wall temperature Tw is less than the liquid boiling temperature TB , a collision of a drop on the solid surface may result in sticking, bouncing, spreading, or splashing. The stick regime occurs when the impact energy is low and the wall temperature is below the pure adhesion temperature Tpa . The impinging drop adheres to the solid surface or coalesces with a liquid film existing on the surface. As the Weber number is increased, drop rebound occurs from the wall or liquid film due to the effect of an air layer that is trapped between the drop and the wall or liquid film. The velocity and direction of the rebounding drop is often determined from experimental and analytical correlations. The spreading regime occurs at higher incident drop Weber numbers. Here the drop spreads on the wall surface for a dry wall, or merges with the liquid wall film upon impact for a wet wall. When a train of drops impacts the wall surface, the time between multi-drop impacts, or the impact frequency, must be considered. The splash regime occurs at high incident Weber numbers. The splash-back of liquid corresponds to the development of the crown instability, which leads to secondary atomization of the impinging drop and/or wall film. Following O’Rourke and Amsden’s approach (2000), the criterion for splash is

2.2 Engine Modeling with Computational Fluid Dynamics 2 Esplash ¼

We 1=2

minðHf =dd ; 1Þ þ Red

61 2 [ Esplash;crit ;

ð2:165Þ

where Hf is the thickness of the liquid film. The drop Reynolds number here is 2 ¼ 3330:0 is used in this about the drop velocity normal to the surface. Esplash;crit book (O’Rourke and Amsden 2000). Splashed drop radii are assumed to have a Nukiyama-Tanasawa distribution: "  2 # 4 rd2 rd exp  Pðrd Þ ¼ pffiffiffi 3 ; ð2:166Þ rd;max p rd;max where rd;max relates to the incident drop radius rd;0 as rd;max

! 2 Esplash;crit 6:4 ; 0:06 : ¼ rd;0 max ; 2 We Esplash

ð2:167Þ

The normal component of the splashed droplet velocity Un is also assumed to have a Nukiyama-Tanasawa distribution: "   # 4 Un2 Un 2 exp  PðUn Þ ¼ pffiffiffi 3 ð2:168Þ Un;max p Un;max with Un;max ¼ 0:2Un;0 and Un;0 is the normal component of the incident drop velocity. The fluctuating component of the secondary droplet tangential velocity un 2 is assumed to follow a Gaussian distribution with variance of 0:01Un;0 . The final velocity of the secondary droplet is written as Ud ¼ Un n þ ð0:12Un;0 þ un Þðet cos W þ ep sin WÞ þ 0:8Ut;0 et ;

ð2:169Þ

where Ut;0 is the tangential component of the incident drop velocity. n is the unit vector normal to the surface. et is the unit vector tangent to the surface and in the plane of n and the incident drop velocity. ep ¼ n  et . W is the angle of tangential velocity with the vector et in the plane of the wall that lies in the interval of ðp; pÞ. Its value is chosen from the following distribution (Naber and Reitz 1988): 8 1 > > b¼0 < ; 2p     ; ð2:170Þ PðWÞ ¼ b jWj > > exp b 1  ; b [ 0 : 2pðeb  1Þ p where b is a parameter related to the impact angle a: sin a ¼

e b þ 1 b2 : eb  1 b2 þ p2

ð2:171Þ

62

2 Fundamentals

The liquid film is modeled using a thin film assumption and integrating cross the film thickness. Continuity, momentum, and energy equations are reduced to a 2D film. The continuity equation is transformed into   oHf _ imp  M _ vap ; ql Awall þ ðUf  Uw Þ  rS Hf ¼ M ð2:172Þ ot where Awall is the wall area; Uw is the wall velocity; rS is the gradient operator on _ vap is the rate of fuel vaporization. M _ imp is the mass source terms due the surface. M to impingement: Z _ imp ¼  4 prd3 qd Vd  nf ðVd ; rd ; Td ; y; y_ ; xs ; tÞdVd drd dTd dyd€y: ð2:173Þ M 3 The wall film momentum equation is   oðHf Uf Þ þ ðUf  Uw Þ  rS ðHf Uf Þ þ Hf rS pf ¼ sw et ql ot Uf  Uw _ þ Pimp  ðP_ imp  nÞn  ll ðTf Þ Hf =2 _ imp ½ðUw  nÞn  Uf  þ dpf n þ ql Hf g; þM

ð2:174Þ

where sw is the stress tensor on the gas-side of the film; et is the unit vector tangent to the surface in the direction of Uf  Uw ; Tf is the mean film temperature; P_ imp is the momentum source terms due to impingement: P_ imp ¼ 

Z

4 3 pr q Vd Vd  nf ðVd ; rd ; Td ; y; y_ ; xs ; tÞdVd drd dTd dyd€y; 3 d d

ð2:175Þ

with xs is the coordinates of the wall. pf is the film pressure that is assumed to arise entirely from the impingement: _ imp Uw  P_ imp Þ  n: p f ¼ ðM

ð2:176Þ

dpf is the pressure difference across the film; g is the acceleration due to gravity. The mean film temperature Tf is assumed to be a piecewise linear profile (Stanton and Rutland 1998). The profile varies from the wall temperature Tw to an interface temperature Ts . The energy equation of the film is written as (Stanton and Rutland 1998):    oðTf Hf Þ Ts  Tw ql Cv;l Awall þ Hf ðUf  Uw Þ  rS Tf þ 6 ot   Ts  Tf Tf  Tw þ Q_ imp  Q_ splash ;  ð2:177Þ ¼ kl Awall Hf =4 Hf =4

2.2 Engine Modeling with Computational Fluid Dynamics

63

where Cv;l and kl are specific heat and thermal conductivity of the liquid, respectively; Q_ imp and Q_ splash are the energy source terms due to impingement and splash, respectively. Energy conservation at the interface with the gas flow is written as kl

Ts  ½2Tf  ðTw þ Ts Þ=2 _ vap L ¼ hl ðT1  Ts Þ; þM Hf =2

ð2:178Þ

with L the latent heat, hl the heat transfer coefficient of the film, and T1 the gas temperature.

2.2.2.14 Liquid Phase Source Terms Effects of the liquid phase on the gas phase flow are modeled by introducing appropriate source terms in the conservation equations of the gas flow (c.f., Eqs. 2.10–2.12, 2.15, and 2.41. The averaged source terms are given as q_ s ¼ 

Z

4prd2 r_ d qd fdVd drd dTd dyd€y;

 Z  4 3 0 2 pr F þ 4prd r_ d Vd qd fdVd drd dTd dyd€y; F ¼ 3 d Z 

4 3 ~  u0 Þ prd Cp;l T_ d þ F0  ðVd  U Q_ s ¼  3   1 ~ 2 qd fdVd drd dTd dyd€y; þ4prd2 r_ d el ðTd Þ þ ðVd  UÞ 2 Z _ s ¼  4 prd3 F0  u0 qd fdVd drd dTd dyd€y: W 3 s

ð2:179Þ ð2:180Þ

ð2:181Þ ð2:182Þ

where F0 ¼ F  g.

2.2.2.15 Crevice Flow Model Crevice flow processes are the major sources of unburned hydrocarbons in SI engines (Reitz and Kuo 1989). Accurate modeling of the crevice flow is still a challenge for multi-dimensional engine simulation (Lee and Reitz 2010). Sometimes, when the crevice volume is not resolved in the computational mesh, a phenomenological crevice flow model is required. The crevice flow model used in the present book solves coupled ordinary differential equations that describe the piston ring dynamics and the flows through

64

2 Fundamentals

Fig. 2.12 schematic of piston-cylinder-ring crevices with 5 different regions and gas flow path

Head Combustion Chamber

Linear

Ring-side clearance h 1 2

3

4 5 Piston

Oil Ring

the ring-side clearances and ring gaps (Reitz and Kuo 1989). The solution provides a boundary condition to the multi-dimensional engine simulation. Figure 2.12 shows a schematic of a piston with two compression rings and an oil ring, which separate the whole crevice volume into five regions. Any two regions are connected through the ring end-gap as shown in Fig. 2.12. Neighboring regions may be connected by the ring-side clearance depending on the position of the ring in the groove. The crevice flow model assumes that: (1) each crevice region has uniform pressure, and the pressure in the top crevice region is the same as the pressure in the combustion chamber; (2) the crevice volume has a large surface-to-volume ratio so that the flow in the crevice is isothermal and at the wall temperature; (3) the gas composition in all regions is the same; (4) the flow through the ring crevice is laminar; (5) the cylinder bore is round with the piston always centered in the bore. The model crevice volume is then viewed as a reservoir. This reservoir exchanges mass with the cells along the periphery, acting as a source or sink for cylinder mass. Mass exchange between connected regions is based mass conservation, e.g., for region i, Vi

dqi ¼ m_ i1;i  m_ i;iþ1 ; dt

ð2:183Þ

where Vi and qi are the volume and density of region i, respectively. m_ i1;i is the flow through the ring-side clearances and is computed from isothermal compressible flow equations for the flow in a narrow channel of height h and ring width w:  2 p2  p2d m_ hu  i; ð2:184Þ ¼ pu A 2RT fw h þ ln pd

2.2 Engine Modeling with Computational Fluid Dynamics

65

where pu and pd are the pressure upstream and downstream, respectively; A is the area normal to the flow direction; T is wall temperature; and f ¼ 24=Rec is the friction factor. Here the Reynolds number is defined as: Rec ¼

m_ 2h : A l

ð2:185Þ

The flow through the ring end-gaps represents additional source terms for regions 1, 3, and 5. The flow rate m_ is calculated using the isentropic orifice-flow equation: m_ ¼ Cd;c Ag qag;

ð2:186Þ

where Cd;c ¼ 0:86 is the discharge coefficient; Ag is the area of ring end-gap; a is the speed of sound; and g is the compressibility factor for isentropic flow: 8( " #)12 2c  cþ1 > c > 2 p p piþ1 iþ1 iþ1 > >  ; [ 0:52 > < c1 pi pi pi g¼ > : ð2:187Þ   cþ1 > > 2ðc1Þ > 2 piþ1 > : ;  0:52 pi cþ1

The motion equation of the piston ring is written as: mr

dh ¼ Fp þ Ff þ Fi þ Fs ; dt

ð2:188Þ

where mr is the ring mass and h is the ring top-side clearance. The pressure force on the top ring is calculated as: Fp ¼ ðp1  p3 ÞAr =2;

ð2:189Þ

where Ar is the ring-side surface area. The friction force Ff is calculated as Ff ¼ f pdr hr pbr ;

ð2:190Þ

where dr is the outside diameter of the ring; hr is the thickness of the ring; pbr is the pressure behind the ring. The friction coefficient f is given as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Up f ¼ 4:8 loil ; ð2:191Þ pbr hr where loil is the oil viscosity; and Up is the instantaneous piston velocity. The inertia force is given as Fi ¼ mr ap ;

ð2:192Þ

66

2 Fundamentals

where ap is the acceleration of the piston. The oil resistance force is calculated as   dh w 3 ; ð2:193Þ Fs ¼ 0:1loil Lr dt hs where Lr is the ring length in the circumferential direction and hs is the distance between the piston groove and the ring in the direction of the ring motion.

2.2.2.16 Boundary Conditions Accurately imposed boundary conditions are essential for IC engine simulation. For instance, heat loss on the solid wall, which is important for engine efficiency, exhaust emissions, and component thermal stresses, is very sensitive to the corresponding boundary conditions used in the simulation. Four types of boundary conditions are considered in the present book: inflow boundary; outflow boundary; rigid wall boundary; periodic boundary. For the inflow boundary, the Dirichlet (or first-type) boundary condition is usually used, i.e., the quantities are set to known values. For the outflow boundary, a Neumann (or second-type) boundary condition is usually used, i.e., the normal components of the gradients of the quantities are set to zero. Several options are available for the rigid wall boundary. The velocity boundary conditions on rigid walls can be free slip, no slip, or turbulent law-of-the-wall. Temperature boundary conditions on the rigid walls can be adiabatic, isotherm, or turbulent law-of-the-wall. The turbulent law-of-the-wall boundary conditions for both velocity and temperature have been proven to be more accurate options (Han and Reitz 1997). In the near wall region, it is assumed that: (1) the normal components of the gradients are much larger than tangential components; (2) gas velocity is parallel to the wall; (3) pressure gradients are neglected; (4) viscous dissipation, and Dufour and enthalpy diffusion effects on the energy flux are neglected. The normal components of the gas velocity are set to the normal wall velocity: U  n ¼ Uwall  n:

ð2:194Þ

The tangential components of the velocity are determined by matching to a logarithmic profile (Amdsen et al. 1989): 8   < j1 ln Clw 17=8 þ Blw ; 1 [ Relw v ; ð2:195Þ ¼ u : 11=2 ; 1  Relw where 1 ¼ qyv=lair ðTÞ is the Reynolds number based on the gas velocity relative to the wall v¼jU  Uwall j, which is evaluated a distance y from the wall; y is small enough to be in the logarithmic region or the laminar sub-layer region of the turbulent boundary layer. The Reynolds number Relw defines the boundary

2.2 Engine Modeling with Computational Fluid Dynamics

67

between these two regions; u is the shear speed which is related to the tangential components of the wall stress by: rw  ðrw  nÞ  n ¼ qu2

v v

ð2:196Þ

with v ¼ U  Uwall . Other constants are related to the model constants in the k-e model: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1=2 j ¼ Cl ðCe;2  Ce;1 Þre ; ð2:197Þ   1=2 7=8 Blw ¼ Relw  j1 ln Clw Relw :

ð2:198Þ

For commonly accepted values of the k-e model, constants Blw ¼ 5:5 and Clw ¼ 0:15. Friction heating is taken into account by introducing a source to the internal energy: fw ¼ rw  v ¼ qu2 v:

ð2:199Þ

The temperature wall function is given as (Han and Reitz 1997): T þ ¼ 2:1 ln yþ þ 2:1Gþ yþ þ 33:4Gþ þ 2:5;

ð2:200Þ



y with yþ ¼ l u ðTÞ and Gþ ¼ QcqlwairuðTÞ. Qc is the chemical heat release. The correair sponding wall heat flux qw is written as:

qw ¼

qCp u lnðT=Tw Þ  ð2:1yþ þ 33:4ÞGlair ðTÞ=u : 2:1 ln yþ þ 2:5

ð2:201Þ

Neglecting the source term G, Eq. 2.201 is simplified as qw ¼

qCp u lnðT=Tw Þ : 2:1 ln yþ þ 2:5

ð2:202Þ

Boundary conditions for the turbulence kinetic energy and its dissipation rate on the rigid walls are given as (Amdsen et al. 1989): rk  n ¼ 0;

ð2:203Þ

k3=2 : y

ð2:204Þ

ew ¼ j

Periodic boundaries are used only when the flow field is assumed to have an Nfold periodicity about the axis, i.e., a sector mesh is used. If the whole physical domain is viewed in a cylindrical coordinate system, the periodic boundaries are those for which h ¼ 0 and h ¼ 2p=N. For a scalar quantity q and a vector v, the boundary condition states

68

2 Fundamentals

qðr; h; zÞ ¼ qðr; h þ 2p=N; zÞ;

ð2:205Þ

vðr; h; zÞ ¼ R  vðr; h þ 2p=N; zÞ;

ð2:206Þ

where R is the rotation matrix corresponding to the angle 2p=N. Swirl flow that is common in the IC engine affects turbulent mixing and the consequent combustion process. Initialization of the swirl flow is required for an engine simulation without a full intake flow simulation. Assumption of a wheel flow profile is usually not accurate enough because the turbulent boundary layer near the wall forces the swirl velocity to decrease in the wall region. A Bessel function profile represents the flow more accurately (Amsden et al. 1989). A dimensionless constant that lies between zero (the wheel flow limit) and 3.83 (zero velocity at the wall) is used to define the azimuthal velocity profile. For IC engine application, a value of 3.11 is usually used (Wahiduzzaman and Ferguson 1988). Combustion chamber wall temperatures are usually estimated based on limited experimental data. However, conjugate heat transfer analysis have been performed that allow wall temperatures to be predicted accurately (Wiedenhoefer and Reitz 2003a, b; Yoshikawa and Reitz 2009). In the examples considered in this book estimated wall temperatures are applied.

2.2.3 Numerical Methods The CFD code used in the present book, KIVA3v2, employs a finite volume method with a structured staggered mesh consisting of arbitrary hexahedrons. Convective fluxes are computed using a quasi-second-order upwind (QSOU) scheme (Amsden et al. 1989). A SIMPLE (Semi-Implicit Method for PressureLinked Equations) algorithm (Patankar and Spalding 1972) is used to compute pressure. An explicit scheme is used for temporal differencing. The spatial differencing is based on the Arbitrary Lagrangian–Eulerian (ALE) computing method (Hirt et al. 1997). Except for the velocity, all gas flow quantities are stored in the cells. The gas velocities are stored in momentum cells which are centered about the vertices. Thus, the velocities are located at the vertices while other quantities are located at the cell centers. A ghost fluid technique is used to deactivate cells as the piston moves. The spray equation, Eq. 2.30, is solved using a Monte-Carlo/particle method. The spray is represented by a set of drop parcels. Each parcel p is composed of a number of droplets Np with equal locations xp , velocities Vd;p , sizes rd;p , temperatures Td;p , and oscillation parameters yp and y_ p . The continuous distribution f is approximated by the discrete distribution f  : f ¼

NP X

Np dðx  xp ÞdðVd  Vd;p Þdðrd  rd;p Þ

p¼1

 dðTd  Td;p Þdðy  yp Þdð_y  y_ p Þ:

ð2:207Þ

2.2 Engine Modeling with Computational Fluid Dynamics

69

The particles evolve following the corresponding equations described in Sects. 2.2.2.8–2.2.2.13. Time steps Dt are determined in a dynamic way to fulfill accuracy and stability requirements with good computational efficiency, and the global time step is set to the smallest time step. The Courant–Friedrichs–Lewy (CFL) condition is used to determine the convection time step Dtc :   Vi nþ1 n Dtc ¼ fc Dtc min ; ð2:208Þ dVflux;i where subscript i is the cell index and superscript n is the time step index. dVflux is the flux volume. A factor fc ¼ 0:2 is typically used for confidence in stability and accuracy. The acceleration time step is determined as nþ1 Dtacc

 ¼ fa min

 Dxi ; jUni  Un1 j i

ð2:209Þ

where fa is a positive real number of order unity with default value of 0.5. Dx is the characteristic cell size. The rate-of-strain tensor time step is given as Dtrst ¼ fr min jki j1 ;

ð2:210Þ

where k is the eigenvalue of the rate-of-strain tensor (Asmden et al. 1989). The chemistry time step is based on the change rate of the energy:  _ c;n  Q nþ1 ¼ fch min ni n : Dtch ð2:211Þ qi e i The spray time step is determined in a similar way: nþ1 Dtsp

! qni qni eni ¼ fsp min s;n ; s;n ; q_ i Q_ i

ð2:212Þ

which limits the change rate of mass and energy due to spray evaporation. A time nþ1 is considered to limit the rate that the time step can grow: step Dtgr nþ1 Dtgr ¼ fgr Dtn :

ð2:213Þ

fgr is greater than unity and is usually set to 1.02. The final time step is given by nþ1 nþ1 nþ1 nþ1 nþ1 ; Dtrst ; Dtch ; Dtsp ; Dtgr ; Dtmx ; Dtmxca Þ: Dtnþ1 ¼ minðDtcnþ1 ; Dtacc

ð2:214Þ

Dtmx and Dtmxca are the input maximum time step and maximum time step based on input maximum crank angle, respectively.

70

2 Fundamentals

2.2.4 CFD Codes and Software for Engine Simulations The KIVA family of codes from the Los Alamos National Laboratory dominated the multi-dimensional IC engine simulation open source codes for more than three decades. The first of the family was RICE (Rivard et al. 1975), which was a 2D Eulerian code that used rectangular computational zones as its mesh. The effect of piston motion was added in the REC code (Gupta and Syed 1979). Although it was developed specifically for IC engine simulation, the KIVA codes are also applicable to various other multi-dimensional problems in fluid dynamics. The APACHE code (Ramshaw and Dukowicz 1979) followed RICE and added the generality of arbitrarily shaped computational cells. A general Eulerian– Lagrangian formulation and a subgrid scale turbulence model were added to the CONCHAS code (Butler et al. 1979) that followed the APACHE code. The CONCHAS-SPRAY code (Cloutman et al. 1982) included a statistical spray model, wall functions for solid wall boundaries, and a generalized chemistry solver. The KIVA code (Amsden et al. 1985) followed the CONCHAS-SPRAY code and featured extended spray models and the ability for both 2D and 3D simulations. Improvements of the KIVA-II code (Amsden et al. 1989) over KIVA included improved computational efficiency and accuracy, the k-e turbulence model, improved spray models, and improved boundary conditions, etc. The KIVA-3 (Amsden 1993) utilized a block-structured mesh to improve computational efficiency in dealing with complex engine geometries, such as intake ports and valves. KIVA-3 V (Amsden 1997) retained all the features of the KIVA-3 code and added an effective model for intake and exhaust valves (Hessel 1993). Other improvements that were mainly driven by the Engine Research Center at the University of Wisconsin-Madison included advanced physical models (RNG k-e model, LES model, nozzle flow model, KH-RT breakup model, ROI collision model, KIVA-CHEMIKIN model, G-equation model, evaporation model, LISA model, wall function model, soot model, combustion model, as discussed above), code parallelization, and applications for automated engine optimization. All of the codes of the KIVA family use structured meshes, except for the latest member of the KIVA family, the KIVA-4 code (Torres and Trujillo 2006), which uses unstructured meshes that can be composed of a variety of elements including hexahedra, prisms, pyramids, and tetrahedra. Modules are used to exchange the data between subroutines and versions of the KIVA-4 code are parallelized. OpenFOAM is a free, open source CFD software package produced by a commercial company, OpenCFD Ltd (OpenFOAM). It consists of a flexible set of C ++ modules for different engineering applications including IC engine simulation. A 3D unstructured mesh of polyhedrals is used in Open FOAM. Commercial software that is capable of IC engine simulation include Star-CD (Star-CD 2001), FLUENT (2006), FIRE (2006), VECTIS (2006), CONVERGETM (Senecal et al. 2002, 2007), and FORTÉTM (Liang et al. 2010; Naik et al. 2010; Puduppakkam et al. 2010). Star-CD and VECTIS are multi-purpose CFD software codes with advanced automatic meshing techniques. FLUENT are FIRE are also a

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71

multi-purpose CFD software with dynamic unstructured mesh technique. CONVERGETM uses an orthogonal structured mesh with adaptive mesh refinement and mesh embedding, which simplifies mesh generation. FORTÉTM is mainly based on the KIVA3v Release 2 code and has implemented the most advanced chemistry solvers and pioneers detailed chemistry applications in IC engine simulation. The integration of detailed chemistry in engine modeling is discussed in Chap. 3.

2.3 Regression Analysis Methods A great amount of data can be generated in an engine optimization study using CFD tools. It is necessary to apply data-mining to the results in order to select designs of interest and also to explicitly illustrate the influences of design parameters on engine performance and emissions. Once the relationship (response surface) is established between the design parameters and the objectives of interest, information about this relationship can be used to further improve engine designs. Therefore, regression analysis is a very important procedure in computational engine optimization. Liu et al. (2006) used a non-parametric regression (NPR) method, namely the component selection and smoothing operator (COSSO), to study a high-speed direct injection (HSDI) diesel engine optimization problem and analyzed the complex correlations between NOx and soot emissions, and fuel consumption responses and control factors. They validated that the interactions between design parameters and their influence on responses could be quantitatively assessed. COSSO is based on a smoothing spline analysis of variance (SS-ANOVA) model and it was originally proposed by Lin and Zhang (2006). Within this framework, the response function can be expressed as following: f ðxÞ ¼ b þ

d X j¼1

fj ðxðjÞ Þ þ

X

fjk ðxðjÞ ; xðkÞ Þ þ   

ð2:215Þ

j\k

where b is a constant for fitting, fj are the main effects of each inputs, fjk are twoway interactions for each pair of input parameters, and the sequence can be continued for higher order interactions, but it is usually truncated to enhance interpretability. Usually only main effects or two-way interactions are considered. The response function f is determined by minimizing: n 1X ½yi  f ðxi Þ2 þ kJðf Þ; n i¼1

ð2:216Þ

where yi is the i-th measured data point and f ðxi Þ is the corresponding predicted value with the form of Eq. 2.215. Therefore, the first term of Eq. 2.216 ensures a least-square fit of the data. The role of the second term is to penalize the roughness of the response function to avoid an excessively noisy fit, and Jðf Þ quantifies the

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2 Fundamentals

roughness of the response function f . The smoothness parameter k works as a weight to control the trade-off between fitting data and removing noise. COSSO determines the penalty function J from the sum of component norms and the smoothness parameter k, from a cross validation technique. An iterative technique to optimize the number of components to be included in Eq. 2.215 is also employed in COSSO to determine the response function based on the framework of the SS-ANOVA. It is also worth noting that with the COSSO method a design needs to be selected as the reference point (center id) for the non-parametric study, and in this sense, the study can be regarded as sensitivity analysis of all parameters about the reference design of interest. So, care has to be taken when interpreting the response surfaces constructed using such regression methods, such as COSSO, because the shape of the response surfaces can be sensitive to the selection of the reference design. It is suggested to perform such regression analysis based on several optimal solutions that represent the most important design features. This analysis methodology is employed throughout this book. In non-parametric regression methods, no assumption is made about the distribution of the data. This is particularly useful for engine optimization problems due to the complexity of the response surfaces between design parameters and objectives. There are other regression or data-mining methods that can also be used for data analysis. For example, in the optimization study of a heavy-duty diesel engine, Ge et al. (2009a) analyzed a large amount of data from engine simulations over a wide range of operating conditions using a K-nearest neighbor method. Accordingly, four methods, including K-nearest neighbors (KN), Kriging (KR), Neural Networks (NN), and Radial Basis Functions (RBF) methods, are briefly introduced here. They will be used to explore their capacity of data-mining for engine optimization in Chap. 4. The K-nearest neighbors method is a very simple regression method, which estimates the value of the objective functions of the evaluated design based on its nearest K neighbor designs. The distance between the evaluated design and its neighbors can be used to weight the neighbors’ contribution, so that the nearer neighbors contribute more to the average than the more distant ones. The method is not computationally intensive, so it is suitable for very large databases, i.e., greater than 1,000. But it is poorly informative and highly localized on small datasets, and thus its prediction ability is limited, especially for data extrapolation. In addition, the regression results can be sensitive to the number of nearest neighbors (parameter K). Kriging belongs to the family of linear least-squares estimation algorithms and was originally the main tool for applications in geostatistics (named after D. A. Krige (1951)). Its behavior is controlled by a covariance function, called a variogram (e.g., Gaussian), which rules the correlation between the values of the function at different points. Essentially Kriging is a spatial interpolation technique that fits a random function to sampled known points to calculate unknowns. Similar to many other regression methods, the interpolates are weighted averages of the known points, and the weights are calculated based on minimization of the

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73

Kriging variance of the estimate. A function can be rougher or smoother, can exhibit large or small ranges of variation, can be affected by a certain amount of noise, and all these features are embodied in the Kriging variogram model. In this regard, the Kriging method is particularly applicable for highly non-linear responses, but it is relatively computationally expensive compared to other methods, e.g., the K-nearest neighbors method. The neural network methods have also been widely and successfully applied to many engineering problems. They are also normally called artificial neural networks, which process data information by mimicking the structure and functional aspects of biological neural networks. The most important aspect of any neural network method is learning, i.e., to find a solution to unknowns based on the known observations in some optimal sense. So, intuitively the learning process on the existing observations can be conducted using optimization methods to minimize the cost criterion and to approximate real solutions. The neural network package available in the commercial software modeFRONTIER that is used in this book is based on classical feed-forward neural networks, with one hidden layer, and with an efficient Levenberg–Marquardt back propagation training algorithm. The initialization of the network’s parameters is based on the proper initialization approach by Nguyen and Widrow (1990). It is noted that the computational cost of using neural networks can be high, especially with large data samples. Also, it usually requires a large diversity of trained data in order to achieve good performance of neural network methods. Radial Basis Functions (RBF) are powerful tools for multivariate scattered data interpolation. The values of those radial basis functions only depend on the distance from a specified reference origin. The typical presumed representative RBFs are Gaussian, Multiquadric, Polyharmonic spline, and Thin plate spline functions. They can be used to build an approximation function that is represented as a sum of N radial basis functions, each associated with a different center and weight. The weights can usually be estimated based on linear least-squares. So, the performance of RBF methods largely relies on the choice of the function type. The computational cost of RBF methods is slightly less than or similar to neural network methods, but it is more expensive than the K-nearest neighbor method and Kriging families. The assessment of different regression methods is a subject of Chap. 4, specifically to explore the feasibility of using regression analysis to partially replace CFD evaluations. Chap. 6 intensively uses the COSSO method and proves its reliability in engine optimization problems.

Chapter 3

Acceleration of Multi-Dimensional Engine Simulation with Detailed Chemistry

Detailed chemistry is necessary for kinetics-controlled combustion processes, such as HCCI and low-temperature combustion. However, the use of detailed chemistry can lead to significantly increased computational costs. This chapter summarizes several different strategies available to reduce computational costs when detailed chemistry is solved in the simulations.

3.1 Methods for Reducing Mesh- and Timestep-Dependency in Engine CFD Modeling Numerical models that have less mesh- and timestep-dependency are essential for consistency in simulations, which is very important for engine combustion chamber optimizations in which the mesh topology and structure vary. For computational optimization purposes, if a CFD model gives close numerical results when coarse meshes or fine meshes are used, the coarse meshes should be considered for higher efficiency in optimization. In the single phase flow CFD simulation, grid convergence analysis is usually conducted at first to determine an appropriate mesh resolution that can balance accuracy and efficiency. For two phase flows that are simulated using the Lagrangian-Drop Eulerian-Fluid (LDEF) approach, issues of mesh- and timestep-dependency become more severe. As pointed out by Mckinley and Primus (1990), when mesh resolution is inadequate, the LDEF approach does not accurately capture strong gradients of velocity, temperature and fuel vapor concentration in the gas phase. This deficiency can be explained by considering the two-way coupling procedure of the LDEF approach. Figure 3.1 illustrates four-way coupling in the LDEF approaches with different mesh resolutions in the 2D case. Liquid drops (or parcels of drops) are represented as circles. Take an example that one property of the gas phase (e.g., density, temperature) is stored at cell centers denoted by small green circles in the plots. If this quantity is used in the spray equation, it needs to be interpolated from the cell

Y. Shi et al., Computational Optimization of Internal Combustion Engines, DOI: 10.1007/978-0-85729-619-1_3, Ó Springer-Verlag London Limited 2011

75

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3 Acceleration of Multi-Dimensional Engine

Fig. 3.1 LDEF Approach on (left) coarse mesh and (right) fine mesh (Wang et al. 2010)

centers to the droplet’s position in a zero-order (assumption of homogeneous properties in one cell) or first-order (linear interpolation) way. In the case of zeroorder interpolation, the gas properties seen by the droplets in Fig. 3.1 are the same in the coarse mesh, while they are not for the fine mesh. The droplet properties need to be assigned back to the Navier-Stokes equations as spray source terms. As depicted in Fig. 3.1, because of the different cell volumes, the resulting spray source terms may be very different. As an extreme example, the spray source terms in the left two cells in the finer mesh are zero, while in the coarser mesh they are non-zero at that position. In another words, the spray source terms that are better resolved in a fine mesh are averaged on a coarse mesh. Thus, many spray-induced gradients are smoothed out in the coarse mesh. Another source of mesh-dependency arises from the droplet interaction (collision). The original collision model used in the KIVA code only considers collision events between droplet parcels located in the same computational cell. For instance, the collision event in the coarse mesh that is indicated by the dashed line is not considered in the fine mesh (c.f., Fig. 3.1). Apparently, a sufficiently refined mesh will give more accurate results. However, the resulting prohibitive computational cost is not acceptable for current engineering simulations, especially for optimization studies. Additionally, too fine a mesh may violate the assumption that the liquid volume fraction is negligible in the LDEF approach. There are a number of efforts in the literature on the development of meshindependent spray models. One strategy is to use a fixed mesh resolution in the near nozzle region, so that at least the numerical results of spray simulations are consistent. Schmidt and Rutland (2000) introduced a collision mesh method. A mesh that is independent of the mesh used for the CFD calculation of the gas flow is used for the collision calculations. Adaptive mesh techniques (Lippert et al. 2005; Senecal et al. 2007; Xue and Kong 2009) have been developed in which the mesh resolution is automatically refined based on gradients of certain quantities such as velocity. The local mesh resolution of the near nozzle region then depends on the spray-induced high velocity gradient, which will also reduce mesh dependency. However, this adds computational cost. Béard et al. (2000) and Abani and Reitz (2010) developed subgrid gas particle models to improve liquid-to-gas phase coupling. The vaporization-induced subgrid gradient in vapor concentration is modeled in a more accurate way. Abraham and Magi (1999) proposed a ‘‘Virtual Liquid Source’’ approach to avoid the two-way coupling between liquid and gas where the near-nozzle liquid drops are replaced

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77

with a liquid core. Liquid was assumed to move with the injection speed within the core, and spray source terms were added in the cells adjacent to the core surface. A similar approach was adopted by Versaevel et al. (2000). Wan and Peters (1997) used a one-dimensional model for the liquid spray and coupled it with a threedimensional Eulerian gas simulation. Since the spray was modeled, instead of twoway coupled with the gas phase cell, the mesh-dependency of the spray source terms could be removed. Mesh-dependency in the droplet collision model is resolved by using the ROI model (c.f., Sect. 2.2.2.11), in which the volume of the local cell is removed from the model formulation. Mesh dependency in coupling from the gas to liquid phases is mainly from the gas velocity in the droplet momentum equation, Eq. 2.124 (Béard et al. 2000; Yang et al. 2000; Abani et al. 2008a, b). To improve this issue, a gas-jet model has been developed based on unsteady turbulent round jet theory (Yang et al. 2000; Abani and Reitz 2007). The gas velocity in Eq. 2.124 is estimated from the gas-jet model instead of interpolating from the CFD solution. The unsteady gas jet theory states that the jet tip develops with: dx 3 Uinj;eff ðx; tÞdeq ; ¼ x dt K

x  x0 :

ð3:1Þ

where x is the jet tip penetration; K is an entrainment constant; Uinj,eff is the effective injection velocity; deq is the equivalent diameter, which is related to the nozzle diameter dnoz and liquid-gas density ratio by: rffiffiffiffi ql : ð3:2Þ deq ¼ dnoz q The downstream spray-axial location x0 is computed as: x0 ¼

3deq : K

ð3:3Þ

The unsteady gas jet theory assumes the effective injection velocity to be an integral of the responses to any change of the injection speed from the start of injection t0 to the current time t: Uinj;eff ðx; tÞ ¼ Uinj ðt0 Þ þ

Zt

 Rðx; t  sÞ

dUinj ðsÞ ds

t0

 ds;

ð3:4Þ

s

in which the response function R yields:   ts ; Rðx; t  sÞ ¼ 1  exp  sv ðx; sÞ

ð3:5Þ

where sv is a response time scale that is related to a local flow time scale sf by a Stokes number St:

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3 Acceleration of Multi-Dimensional Engine

sv ðx; sÞ ¼ St  sf ðx; sÞ ¼ St 

x : Uinj ðsÞ

ð3:6Þ

Considering the fact that downstream particles respond to any change from the nozzle injection more slowly than near-nozzle particles, Eqs. 3.4 to 3.6 are modified by replacing the spray tip penetration x with the local spray-axial location of the particle y (Wang et al. 2010): Uinj;eff ðy; tÞ ¼ Uinj ðt0 Þ þ

Zt



dUinj ðsÞ Rðy; t  sÞ ds

t0

 ds;

ð3:7Þ

s

  ts Rðy; t  sÞ ¼ 1  exp  ; sv ðy; sÞ

ð3:8Þ

y : Uinj ðsÞ

ð3:9Þ

sv ðy; sÞ ¼ St  sf ðy; sÞ ¼ St 

The local gas jet speed at the spray axis is correspondingly calculated as: Ujet;ax ðy; tÞ ¼

3 Uinj;eff ðy; tÞdeq ; y K

y  x0 :

ð3:10Þ

Assuming axi-symmetry, the gas jet speed at any radial location r can be calculated as: Ujet ðy; r; tÞ ¼

3Uinj;eff ðy; tÞdeq  ; 2 Ky 1 þ K12r 2 y2

y  x0 :

ð3:11Þ

The mean gas velocities in the droplet momentum equation as well as the breakup models are then replaced with this gas velocity. Unlike mesh-dependency, investigation of the timestep-dependency of spray models is rarely reported in the literature. Multiple physical processes in engines have different time scales that vary according to the change of engine conditions. A globally-imposed CFD timestep with stability criterion could keep the code running robustly, but would not always accurately capture the time scale of each physical process. On one hand, if the timestep is larger than the time scale but does not violate numerical stability criteria, the physical process is predicted in an under-resolved way; on the other hand, if the timestep is smaller than the time scale, the computation will not run efficiently. In terms of spray models, Munnannur (2007) reported a ‘‘Mean Collision Time’’ approach, in which a collision time scale is estimated and included into the global CFD timestep determination, Eq. 2.213. Since this collision time scale is much smaller during the early stage of spray development, the computational cost is increased significantly. Wang et al. (2010) proposed a sub-cycle method that uses a different timestep for the spray breakup and collision calculation from the CFD timestep, and thus the computational cost is reduced to an acceptable level. Timestep-dependency in

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79

the RT breakup model is reduced by describing the evolution of drop radii using an equation similar to Eq. 2.116 in the KH model and the equation is solved analytically. The models have been applied to simulate direct injection engine combustion (Shi et al. 2010d). In the present book, the gas-jet model and the ROI collision model are used in some examples to reduce mesh-dependency.

3.2 Efficient Methods for Reaction Mechanism Reduction 3.2.1 Overview of Reaction Mechanism Reduction The development of reaction mechanisms for surrogate fuels has significantly impacted engine design using CFD. For example, the comprehensive n-heptane (Curran et al. 1998a), iso-octane (Curran et al. 2002), and methyl decanoate (MD) (Herbinet et al. 2008) mechanisms, which are used as surrogates for diesel, gasoline, and bio-diesel, respectively, have been used to investigate HCCI engines in a few studies (Hwang et al. 2008; Hoffman and Abraham 2009). Although the increasing capacity of computers enables the use of large chemical mechanisms in engine simulations, it is also noted that the size of reaction mechanisms is increasing rapidly. The increased mechanism size is a consequence of the higher carbon number of the surrogate fuel species and the larger number of fuel components considered. For instance, the use of n-heptane (C7, 561 species) as a conventional diesel surrogate is being supplemented with the use of n-octane (C8) to n-cetane (C16, 2116 species) (Westbrook et al. 2009). Iso-octane (C8, 857 species) as a gasoline surrogate is being replaced by the combined n-heptane and iso-octane Primary Reference Fuel (PRF) mechanism (1,034 species (Curran et al. 1998b)) to better reflect the fuel reactivity of gasoline. The bio-diesel surrogate Methyl Butanoate (C5, 264 species) (Fisher et al. 2000) is being replaced by MD (C11, 2,878 species) to better represent the long molecular chain of real bio-diesel fuels. In practice, a large number of simulations are required to optimize engine design. This further renders the use of comprehensive chemical mechanisms prohibitive for practical engine CFD simulations. To overcome this difficulty, large detailed reaction mechanisms are usually reduced to mechanisms with smaller sizes, i.e., with less species and reaction numbers. It is required that the reduced mechanisms are able to maintain the major features and predictive capacity of the detailed ones. A variety of methodologies that employ different mathematical approaches and emphasize different physical and chemical aspects have been proposed for mechanism reduction. These methods include but are not limited to, sensitivity analysis and reaction rate analysis (such as Principal Component Analysis (PCA)) (Turanyi et al. 1989; Turanyi 1990a), chemical lumping (Huang et al. 2005; Pepiot-Desjardins and Pitsch 2008b), intrinsic low-dimensional manifolds (ILDM) (Maas and Pope 1992), computational

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singular perturbation (CSP) (Lam and Goussis 1994), directed relation graph (DRG) (Lu and Law 2005) and its derivative version directed relation graph with error propagation (DRGEP) (Pepiot-Desjardins and Pitsch 2008a) and a similar graph-based method path flux analysis (PFA) (Sun et al. 2010), and optimizationbased methods (Bhattacharjee et al. 2003; Mitsos et al. 2008). Sensitivity analysis on chemical mechanisms investigates the effects of parameter perturbations on the local or overall performance of chemical kinetic models. In the context of mechanism reduction, the presence of a species or a reaction is parameterized and the redundancy of a species or a reaction to chemical mechanisms can be identified by a brute force method that investigates the sensitivity of each species or reaction in the chemical mechanisms. It is evident that this is a very time consuming process, especially for reducing large mechanisms. Turanyi et al. (1989) pointed out that kinetic information about chemical mechanisms can be derived from a matrix whose elements are rate sensitivity coefficients calculated in reaction rate analysis. The matrix directly provides information about overall rate sensitivities of reactions, and thus unimportant reactions can be identified. However, the study of Vajda et al. (1985) showed that the overall rate sensitivity analysis resulted in over-elimination of important reactions under some circumstances. In their study, eigenvalues and eigenvectors of the transpose product of the rate sensitivity matrix were used to identify the principal component vectors of the rate sensitivity matrix in order to extract important reactions, and a better reduced formaldehyde oxidation mechanism was obtained in that study. This method is called Principal Component Analysis (PCA), which has been used to assist mechanism reduction in several studies (Turanyi 1990b; Nagy and Turanyi 2009). Chemical lumping methods group species with similar composition, functionalities, or evolutionary history into representative lumped species or pseudospecies, so that the overall number of species is reduced. The key issues in chemical lumping methods are identification of lumped species and estimation of kinetic parameters of the lumped groups. Lumped groups may (Pepiot-Desjardins and Pitsch 2008b) or may not (Huang et al. 2005) have chemical meanings depending on the lumping method used. Timescale analysis methods, ILDM and CSP, are similarly based on the Jacobian analysis of Ordinary Differential Equations (ODEs) of species concentrations. The analysis decomposes the Jacobian matrix into fast and slow sub-spaces. Consequently, quasi-steady-state (QSS) species and fast elementary reactions are identified and simple algebraic expressions of the QSS species concentrations and global reaction rates are obtained. The software package developed by Lu et al. (2001) reduces mechanisms using the CSP method and provides automatically generated Chemkin-II compatible subroutines for application purposes. However, the Jacobian analysis is computationally expensive for large chemical mechanisms. In addition, the global reaction rates can no longer be expressed in Arrhenius form and this renders the direct use of reduced mechanisms in standard chemistry packages difficult. For the purpose of this book efficient methods for mechanism reduction are of particular interest. The term efficient here has no strict definition, but in general it indicates that the computational overhead of the method is negligible compared to

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81

the gain due to the reduced mechanism size. In addition, the computational cost of the method should scale less than quadratically with the size (i.e., species number) of the mechanism. Otherwise, the mechanism reduction method is not suitable for an on-the-fly mechanism reduction scheme, as will be discussed in Sect. 3.4. The directed relation graph (DRG) (Lu and Law 2005), the directed relation graph with error propagation (DRGEP) (Pepiot-Desjardins and Pitsch 2008a) and the path flux analysis (PFA) (Sun et al. 2010) methods fall into this category because they are efficient and effective for mechanism reduction. Essentially, all three methods are based on graph theory, which measures the connectivity among species. Species that are not closely (with user-specified tolerance) connected to pre-selected important species are deemed to be redundant and thus are removed from the detailed mechanisms. In the original DRG approach (Lu and Law 2005), a graph is constructed using the method that each species represents a vertex in the graph and each directed edge represents the immediate dependence of one species on another. The dependence is quantified by the normalized contribution of species B to A as: P i¼1;I jtAi xi dBi j rAB ¼ P ; ð3:12Þ i¼1;I jtAi xi j with  dBi ¼

1 0

if reaction i involves B ; otherwise

where i is the reaction index for the total I reactions, vAi is the stoichiometric coefficient of species A in the ith reaction, and xi is the progress variable (rate) of the reaction i. Therefore, rAB is a measure of the error introduced to the production rate of A due to elimination of all the reactions that contain B. Once the searchinitiating species are determined, a depth first search (DFS) is applied to the graph constructed by Eq. 3.12 for all species to identify the dependent set recursively. If the connectivity quantified by Eq. 3.12 is less than the user-specified tolerance, the searched species can be safely removed from the active species list without introducing a large error to the reduced mechanism. Lu and Law (2006a) also proved that the computational cost of the DRG method scales linearly with the mechanism size. However, as pointed out by Pepiot-Desjardins and Pitsch (2008a) and Liang et al. (2009b), the DRG method assumes equal importance of all species selected to be kept in the mechanism, which is not necessarily the case. Furthermore, considerable information about contribution strengths, as captured by the rAB values, is lost due to the binary truncation. In order to overcome these shortcomings and to produce smaller mechanisms, an error propagation technique was introduced to measure the dependency of a search-initiating species to other species. Thus, the mechanism reduction procedure is equivalent to identifying species (vertex in the graph) for which there exist ‘‘strong’’ paths connecting them

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3 Acceleration of Multi-Dimensional Engine

to a species in the initial set. In this DRGEP method, the connection strength between the initiating species and the species being visited diminishes as the path extends (geometrically damped error). To quantify the decreasing dependence, an ‘‘R-value’’ is defined at each vertex V with reference to the initial vertex V0, i.e., RV0 ðVÞ ¼ maxfPrij g; X

ð3:13Þ

where X is the set of all possible paths leading from V0 to V, and Prij is the chain product of the weights of the edges along the given path and rij is given by Eq. 3.12. Based on this definition, vertex V will be marked as ‘‘reachable’’ if RV0(V) is larger than a user-specified threshold value e. Thus, all vertices reachable from initial vertices V01 to V0i (including V01 to V0i themselves) comprise the species of the reduced mechanism. Consequently, unreachable species and their corresponding reactions are removed from the detailed mechanism. It is noted that the measure of dependence between two species, as defined in Eq. 3.12 was initially used in the DRGEP method proposed by Pepiot-Desjardins and Pitsch (2005). However, Lu and Law (2006b) argued that this might be risky in the case that two species are only connected by long-chain series reactions that involve intermediate QSS species. Later, Pepiot-Desjardins and Pitsch (2008a) adopted an improved expression to measure the dependence of one species to another as, P     i¼1;I tAi xi dBi  ; ð3:14Þ rAB ¼ maxðPA ; CA Þ with PA ¼ CA ¼

X i¼1;I

X i¼1;I

maxð0; tAi xi Þ;

maxð0; tAi xi Þ;

where PA and CA indicate the production and consumption rate of species A, respectively. It has been demonstrated by Pepiot-Desjardins and Pitsch (2008a) that the use of Eq. 3.14 for the geometrically damped error calculated in Eq. 3.13 is able to resolve the issue mentioned above. In addition, the graph search can be conducted using an efficient R-value-based breadth-first search (RBFS) algorithm, such as the one proposed by Liang et al. (2009b). The path flux analysis (PFA) method proposed by Sun et al. (2010) shares a similar idea with the DRG and DRGEP methods, namely, measuring the contribution of candidate species to the pre-selected important species based on their connectivity. However, instead of measuring such connectivity directly or indirectly using Eqs. 3.12 to 3.14, the PFA method adopts different formulae to calculate the reaction path fluxes among species. The direct interactions (normalized fluxes) for production and consumption of species A and B are defined as:

3.2 Efficient Methods for Reaction Mechanism Reduction

83

pro1st rAB ¼

PAB ; maxðPA ; CA Þ

ð3:15Þ

con1st ¼ rAB

CAB : maxðPA ; CA Þ

ð3:16Þ

The direct fluxes between species A and species B are defined by PAB and CAB as: PAB ¼

X

maxðmA;i xi dBi ; 0Þ;

ð3:17Þ

maxðmA;i xi dBi ; 0Þ:

ð3:18Þ

i¼1;l

CAB ¼

X i¼1;l

In addition to the direct interaction, the indirect interactions between A and B via a third species (Mi) are also defined for production and consumption as: pro2nd ¼ rAB

X 

 pro1st pro1st ; rAM r Mi B i

ð3:19Þ

 con1st con1st : rAM r Mi B i

ð3:20Þ

Mi 6¼A;B con2nd rAB ¼

X  Mi 6¼A;B

The overall lumped normalized flux between species A and B is the summary of all direct and indirect fluxed defined in Eqs. 3.14, 3.19 and 3.20: pro1st pro2nd con1st con2nd rAB ¼ rAB þ rAB þ rAB þ rAB :

ð3:21Þ

Once this flux is below the user-specified tolerance, the connectivity between species A and B is deemed to be low. Similar to the DRG methods, a recursive method is employed in the PFA method to detect the importance of each species to the pre-selected major species in order to screen out redundant ones. The study of Sun et al. (2010) showed that the PFA method was able to recover more reaction fluxes among species in the generated reduced mechanism as compared to the DRG and DRGEP methods. They also demonstrated that the reduced mechanism generated using the PFA method is slightly smaller and better than that of the DRG method. Nevertheless, it should be noted that the computational cost of the PFA method is higher than the DRG and DRGEP methods because of the calculation of the indirect reaction fluxes among species. It is of interest to compare the performance and efficiency of the three mechanism reduction methods, particularly for engine applications. Therefore, we explored the three methods to reduce detailed n-heptane (561 species and 2,539 reactions, Curran et al. 1998), iso-octane (857 species and 3,606 reactions, Curran et al. 2002), and methyl decanoate (MD) (2,878 species and 8,555 reactions,

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Table 3.1 Comparison of three efficient mechanism reduction methods for HCCI engine simulation Method Red. No. No. CA50 Peak pres. Max HR Simulation Reduction Mech. SP RXN (°) (%) (%) time (s) time (s) DRG

n-hep. i-oct. MD DRGEP n-hep. i-oct. MD PFA n-hep. i-oct. MD

130 165 625 126 161 513 129 155 562

445 651 2,370 459 693 1719 501 613 1,931

1.30 0.78 0.89 0.84 0.96 0.67 0.81 0.99 1.46

0.34 0.59 1.1 1.9 1.5 2.26 0.06 0.76 0.42

0.04 0.41 2.2 3.0 1.9 2.7 0.17 0.63 1.6

28.0 66.0 1470.0 28.0 66.0 1470.0 28.0 66.0 1470.0

0.03 0.07 0.51 0.04 0.08 0.53 0.25 0.55 3.98

Herbinet et al. 2008) mechanisms for HCCI engine simulations. The results are listed in Table 3.1. The user-specified tolerance of each mechanism reduction method was gradually increased in order to generate smaller reduced mechanisms until the differences in the simulation results between the detailed mechanism and the reduced mechanism exceeded allowed values. In this comparison, the differences in CA50 (engine combustion phasing), peak pressure, and maximum heat release were limited to 1.5 °CA, 3%, and 3% between the detailed and reduced mechanisms. The discussion on the detailed methodology of mechanism reduction is deferred to the next section. It is seen in the table that the DRGEP method produces the smallest mechanisms within the allowed small error tolerances, which is followed by the PFA and DRG methods. In general, the three mechanism reduction methods are very efficient as the time spent on mechanism reduction is negligible compared to the simulation time using the detailed mechanisms, but the PFA method costs more time than the other two. The small computational cost makes the three methods suitable for the on-the-fly mechanism reduction scheme discussed in Sect. 3.4. One of the common shortcomings of the three methods is that the accuracy of the generated reduced mechanism heavily relies on the user-specified tolerance which is determined empirically and lacks a physical meaning. Although gradually increasing the user-specified tolerance will normally produce smaller mechanisms with worthy performance, the relation between the performances of the generated reduced mechanisms and the user-specified accuracy tolerance is typically not a function of the user-specified algorithm tolerance. In the present comparison, the authors have found that for the DRG and PFA methods there exist critical tolerances above which the generated reduced mechanisms show drastically poor performance, while for the DRGEP method, this performance drop is smaller. This comparison has strengthened the authors’ confidence in using the DRGEP method for both automatic and on-the-fly mechanism reductions in the following sections.

3.2 Efficient Methods for Reaction Mechanism Reduction

85

3.2.2 Automatic Mechanism Reduction of Hydrocarbon Fuels for HCCI Engines Based on DRGEP and PCA Methods with Error Control With the systematic mechanism reduction methods discussed above, the process of reducing the size of detailed reaction mechanisms becomes more convenient and efficient than using intuition- and experience-based methods. However, such a process can be still tedious given the fact that mechanism reduction is usually conducted over a wide range of thermodynamic conditions in order to achieve better performance of the generated reduced mechanisms. To facilitate this process, an automatic methodology is proposed in this section. Practical examples are demonstrated for reducing three large hydrocarbon surrogate fuel mechanisms for HCCI engine simulations. The DRGEP and PCA methods are employed for species and reaction elimination, respectively. The detailed theory of the DRGEP method can be found in the previous section and also in the study of PepiotDesjardins and Pitsch (2008b). The PCA method has wide application in different research areas, and interested readers are encouraged to read the papers published by Vajda et al. (1985) and Turanyi (1990b) for its particular use in reaction mechanism reduction. The SENKIN program (Lutz et al. 1988) integrated with engine physical models was used to conduct closed-cycle, single-zone HCCI engine simulations. The program requires engine specifications, operating conditions, and a fuel reaction mechanism as inputs. Parameters of interest, such as CA50 (crank angle where 50% accumulated heat is released), peak in-cylinder pressure, and maximum total heat release, are output to an ASCII file. Concurrently, pressure, temperature, as well as the mass fraction of each species in the mechanism are stored in a binary file for each time-step of the simulation. The binary file serves as an input for the DRGEP method or the PCA method. Mechanism reduction is then performed on user-specified sampling points during the engine cycle. Six sampling points, namely, in-cylinder temperatures of 600, 800, 1,000, 1,200, 1,500, and 2,000 K, were found sufficient to generate the reduced mechanism. At each sampling point, a set of important species and reactions is identified based on the thermal conditions and species mass fractions at that point using the mechanism reduction methods. The overall set of important species and reactions are the union of the individual subsets, which are flagged and stored in two binary (0 or 1) arrays. The authors have developed a Chemkin-II-library-based FORTRAN subroutine that transforms the information in the binary arrays to a reduced mechanism in ASCII format, thereby automating the reduced mechanism generation process. Based on the theory of the DRGEP and PCA methods, smaller tolerances result in reduced mechanisms of larger size. However, the complex non-linear nature of comprehensive reaction mechanisms does not necessarily ensure that reduced mechanisms of larger size perform better than those of smaller size when comparing parameters such as the combustion phasing, peak pressure, and maximum

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heat release in HCCI engine simulations. Also, reduced mechanisms may be generated from detailed mechanisms of different sizes and require different tolerances to achieve a good compromise between accuracy and efficiency. Therefore, an approach is needed to find an appropriate set of tolerances when applying the DRGEP and PCA methods in an automatic mechanism reduction scheme that ensures the reduced mechanisms satisfy user-specified accuracy requirements. In this context, a trial-and-error method is proposed. Namely, the mechanism reduction process begins with a set of small error tolerances and the performance of each generated reduced mechanism is compared with the detailed mechanism for parameters of interest. The algorithm error tolerances are monotonically increased until the user-specified tolerances of accuracy are violated. In this way, the desired accuracy of the reduced mechanism is always satisfied and the reduced mechanism achieves a minimum size. It is noted that consecutive reductions are not performed using engine simulations with the comprehensive mechanism. Instead they are conducted on the simulation results from the preceding generation, as explained next. A two-stage mechanism reduction was employed by performing the DRGEP method and the PCA method sequentially. The primary goal of mechanism reduction is to eliminate as many unimportant species as possible, and the DRGEP method is a very effective approach for this purpose. Once the unimportant species are removed, additional reduction is possible by considering the reactions using the PCA method. As seen in the theory of the PCA method, eigenvalue-eigenvector analysis on an n  n matrix is required, where n is the number of reactions. The computational time dependency of this manipulation is scaled by the power of 3 to 4 of n, while the DRGEP method scales linearly with n. Consequently, the computational time for mechanism reduction can be significantly reduced by applying the PCA method to the mechanism generated by the first-stage DRGEP reduction. Finally, the mechanism reduction process is automated using a script program. The program flow chart is illustrated in Fig. 3.2. In general, an HCCI engine simulation and subsequent DRGEP reduction are first performed using the comprehensive chemical mechanism and user inputs that include engine specifications and operating conditions, initial algorithm tolerances, as well as errors allowed for the absolute differences of CA50, peak pressure, and maximum heat release between the detailed mechanism and generated reduced mechanisms. If the results of the present HCCI simulation using the mechanism of the preceding generation do not violate the user-specified tolerances, a reduced mechanism is generated for the next generation HCCI simulation. For each consecutive generation the DRGEP tolerance is linearly increased in a log-scale, e.g., 0.0002–0.0003 or 0.002–0.003. The loop is repeated until the user-specified tolerances are exceeded. Instead of immediately applying the second stage PCA reduction, the DRGEP reduction is conducted to the last valid HCCI simulation with a reduced tolerance (restore the tolerance from the last valid HCCI simulation), so that a smaller reduced mechanism may be obtained. This loop, which usually involves 0 to 3 generations, is repeated with the DRGEP tolerance fixed until either the user-

3.2 Efficient Methods for Reaction Mechanism Reduction

87

Fig. 3.2 Flow chart of automatic mechanism reduction

specified tolerances are violated or the reduced mechanism does not change. The second-stage reduction with the PCA method is conducted to the reduced mechanism of the last valid HCCI simulation from the DRGEP stage. The process follows the same procedure used in the DRGEP reduction, except that two algorithm error tolerances (identical in the present study) are altered in each generation for the PCA method. The final reduced mechanism is generated from the last HCCI simulation that satisfies all user-specified tolerances. Errors introduced by this automatic reduction process are well bounded within the user-specified ranges. To test the proposed approach, the three comprehensive hydrocarbon fuel mechanisms described above including the n-heptane (Curran et al. 1998), isooctane (Curran et al. 2002), and methyl decanoate (MD) (Herbinet et al. 2008) mechanisms were selected. They are widely used as surrogate fuels for diesel,

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Table 3.2 Engine specifications

Engine

Caterpillar DI diesel

Combustion chamber Bore 9 Stroke (mm) Bowl width (mm) Displacement (L) Connection rod length (mm) Geometric compression ratio IVC timing (°CA ATDC) EVO timing (°CA ATDC)

Quiescent 137.16 9 165.1 97.8 2.44 261.6 16.1:1 -143 130

Table 3.3 Operating conditions of test cases Test k IVC temperature (K) IVC pressure (bar) 1 2 3 4 5 6

0.2 0.6 1.0 0.6 1.0 1.4

n-hep.

iso-oct.

MD

n-hep.

iso-oct.

MD

350 370 390 350 370 390

390 410 440 430 450 470

350 370 390 350 370 390

1.888 0.670 0.427 1.374 0.878 0.666

2.096 0.739 0.480 1.630 1.061 0.798

1.906 0.675 0.429 1.384 0.882 0.668

IMEP (bar)

speed (rev/min)

5 5 5 11 11 11

821 821 821 1,737 1,737 1,737

gasoline, and biodiesel in engine simulations. HCCI simulations were conducted on a Caterpillar 3401E engine whose specifications are summarized in Table 3.2. Six cases that cover practical operating conditions of the HCCI engine were selected. The low load (Cases 1 to 3) and medium load (Cases 4 to 6) conditions correspond to Mode 2 and Mode 5 of the federal test procedure (FTP) tests for the CAT engine. It is noted that in order to obtain reasonable intake valve closure (IVC) conditions and ignition timings, the IVC temperatures were adjusted based on the fuel reactivity and operating conditions. IVC pressures were calculated based on temperature, amount of fuel, as well as global equivalence ratio. Similar to the DRGEP studies of Liang et al. (2009b, 2009c) and Shi et al. (2010b), fuel, CO, and HO2 were chosen as the initial species, because each of the initial species plays a primary role in the three major combustion processes of hydrocarbon fuels, namely, fuel decomposition, CO oxidation, as well as H2-O2 reactions. For the first-stage DRGEP reduction, 1 9 10-4 was used as the initial tolerance for the three comprehensive mechanisms. For the second stage PCA reduction, 1 9 10-2 was used as the two initial tolerances for the MD mechanism and 1 9 10-3 was used for the smaller n-heptane and iso-octane mechanisms. The performance of the reduced mechanisms in HCCI engine simulations was evaluated by comparing the predicted CA50, peak pressure, and maximum heat release with those of the detailed mechanism. Here, allowed differences in CA50, peak pressure, and maximum heat release are limited to 1.5°CA, 3%, and 3% between the detailed mechanisms and reduced mechanisms.

3.2 Efficient Methods for Reaction Mechanism Reduction

89

Fig. 3.3 Methyl Decanoate (MD) mechanism reduction. a Test 1, b Test 2, c Test 3, d Test 4, e Test 5, f Test 6

The mechanism reduction approach was first applied to the detailed MD mechanism. For the six tests listed in Table 3.3, six reduced mechanisms were obtained, each with different final algorithm tolerances and different final sizes. Figure 3.3 shows the evolutionary process of the mechanism reduction for each test. In the figure, each generation number represents a set of algorithm error tolerances and the values of the tolerances increase with the generation number. The two numbers at the right bottom corner of Fig. 3.3 indicate the final size of

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each reduced mechanism, which correspond to the number of species (solid square) and the number of reactions (solid circle). The vertical dashed line in each sub-figure of Fig. 3.3 distinguishes the first-stage DRGEP reduction and the second-stage PCA reduction. As expected, it is seen that the DRGEP method effectively removed redundant species as the process evolved and the PCA method primarily reduced unimportant reactions after the DRGEP method was applied. The performance of the reduced mechanism at each generation was monitored by comparing the three parameters, i.e., CA50, peak pressure, and maximum heat release, with those of the detailed mechanism, as illustrated by the open symbols in Fig. 3.3 (relative errors are expressed in percentage). An important observation is that the errors between the detailed mechanism and the reduced one do not necessarily monotonically increase as the algorithm error tolerances increase. For example, in Fig. 3.3(a), for test 1, the reduced mechanism obtained at generation 13 is better than those of generations 11 and 12. This again indicates that the present trial-and-error method is necessary and effective for mechanism reduction using the DRGEP and PCA method. This approach can be also applied to any other mechanism reduction methods without rigorous error control. The reduced mechanism generated from each test is assured to satisfy the userspecified error tolerances for that test. In practice, it is desired to have a final reduced mechanism that is able to be applied to all cases within the investigated operating conditions. A common and conservative way is to combine all the reduced mechanisms obtained from each test, and the overall reduced mechanism should be able to cover the investigated range. However, by further testing the performance of each reduced mechanism, it can be seen that this is not necessary for the present problem. In Fig. 3.4, each sub-figure indicates the performance of using the reduced mechanism of an individual test for all other test cases. It is seen that the largest reduced mechanism from Test 1, Fig. 3.4(a), maintains very good results compared to the detailed MD mechanism for all cases studied. In addition, it is observed that the reduced mechanism from the mid-load and stoichiometric case of Test 5, Fig. 3.4(e), is also representative for all cases. The Test 5 reduced mechanism well reproduced the results of detailed mechanism within the userspecified error tolerances yet has far fewer species compared to the Test 1 mechanism. As seen in Fig. 3.4(c) and (f), the two smallest reduced mechanisms from the rich mixture cases failed to predict satisfactory results for all conditions tested. Figure 3.5 further illustrates the performance of the reduced mechanisms of Test 1 and Test 5, respectively, by comparing the pressure traces for each test condition to those predicted by the detailed mechanism. As an example, the algorithm error tolerances as a function of generation number are illustrated in Fig. 3.6 for the mechanism reduction process of Test 5. As described earlier, the present approach applies error tolerances to the reduced mechanism of the preceding generation by gradually increasing their values. It is seen that for Test 5 the DRGEP reduction terminated with the tolerance of 0.02, and the PCA reduction terminated with tolerances of 0.09. An attempt was made to directly apply a tolerance of 0.02 to the detailed mechanism simulation using a single run of the DRGEP method. However, it was found that the simulation

3.2 Efficient Methods for Reaction Mechanism Reduction

91

Fig. 3.4 Performance of the reduced MD mechanisms. a Reduced mechanism of Test 1 (657 species, 1,637 reactions). b Reduced mechanism of Test 2 (414 species, 1,160 reactions). c Reduced mechanism of Test 3 (381 species, 823 reactions). d Reduced mechanism of Test 4 (534 species, 1,033 reactions). e Reduced mechanism of Test 5 (435 species, 1,098 reactions). f Reduced mechanism of Test 6 (327 species, 683 reactions)

results largely exceeded the user-specified error tolerances. Thus, the DRGEP tolerance was lowered to 0.01 and PCA tolerances of 0.09 were sequentially applied to the detailed mechanism simulation for the Test 5 conditions. The generated reduced mechanism contained 502 species and 1,265 reactions, which is larger than that of the present approach. This may be due to the fact that a large DRGEP tolerance can be applied to a mechanism of small size, as also found by Shi et al. (2010b). It can be concluded that the present proposed step-wise approach not only saves computational time for mechanism reduction (since the reduction methodologies are only applied to evaluate the results using reduced mechanisms), but also is able to produce smaller reduced mechanisms.

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Fig. 3.5 Comparison of pressure trace between the detailed MD mechanism and the reduced mechanisms of Test 1 and Test 5. a Reduced mechanism of Test 1. b Reduced mechanism of Test 5

Following the same procedure as the MD mechanism reduction, the detailed iso-octane and n-heptane mechanisms were automatically reduced for the investigated cases. Figures 3.7 and 3.8 indicate the evolutionary processes and the performance of the reduced mechanisms of iso-octane and n-heptane, respectively. Only Test 2 and Test 5 are shown since the former one generated reduced mechanisms of the largest size for both iso-octane and n-heptane, and the latter one was found to be representative in the previous MD mechanism reduction. As seen in Fig. 3.7(b), the largest reduced mechanism of iso-octane predicts satisfactory results for all cases investigated. Figure 3.7(d) shows that except for the peak pressure of Test 2, the reduced mechanism of Test 5 is also able to well reproduce the detailed mechanism of other cases. For n-heptane, Fig. 3.8(b) illustrates that the reduced mechanism of Test 2 reproduced the detailed mechanism reasonably well. Using the reduced mechanism of Test 5, the very lean combustion case was not well matched in terms of the combustion phasing. However, for all other cases, the errors are well bounded within the user-specified tolerances.

Fig. 3.6 Algorithm error tolerances for Test 5 of MD mechanism reduction

3.2 Efficient Methods for Reaction Mechanism Reduction

93

Fig. 3.7 iso-octane mechanism reduction. a Reduction process of Test 2. b Performance of the reduced mechanism of Test 2 (195 species and 647 reactions). c Reduction process of Test 5. d Performance of the reduced mechanism of Test 5 (167 species and 640 reactions)

It is seen that the automatic mechanism reduction approach is able to achieve reduced mechanisms with minimum user intuition and input. The approach includes a two-stage mechanism reduction procedure. In the first stage, the directed relation graph with error propagation (DRGEP) method is used to efficiently and effectively remove redundant species and reactions. In the second stage, a more time-consuming method, the Principal Component Analysis (PCA) method is applied to the reduced mechanism of the first stage to further remove unimportant reactions and species. During the mechanism reduction process, the overall performance of reduced mechanisms is monitored by comparing parameters of interest with the corresponding detailed mechanisms to ensure that userspecified error tolerances are satisfied. Nevertheless, it should be pointed out that each reduced mechanism has only a narrow applicable range as they are generated based on a set of particular state variables. This suggests that reduced mechanisms that are generated with local and instantaneous thermal conditions may be better suitable for those conditions. So, an on-the-fly mechanism reduction scheme may perform better in terms of accuracy and efficiency, which is the subject of Sect. 3.4.

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Fig. 3.8 n-heptane mechanism reduction. a Reduction process of Test 2. b Performance of the reduced mechanism of Test 2 (140 species and 491 reactions). c Reduction process of Test 5. d Performance of the reduced mechanism of Test 5 (120 species and 431 reactions)

3.3 An Adaptive Multi-Grid Chemistry (AMC) Model 3.3.1 Background An approach called multi-zone modeling was developed by Aceves et al. (2000, 2001) in order to accelerate the calculation of HCCI engine combustion with detailed reaction mechanisms. The multi-zone model assumes a decoupling of the turbulent mixing process and chemistry prior to and during the main heat release. It has been demonstrated to be able to predict overall engine performance, but has difficulty of predicting quantitative emission levels. This is because the model neglects the details of the fluid flow and mixing process after starting to apply the multi-zone approach. Flowers et al. (2003) improved this model by introducing a coupled CFD/multi-zone model and obtained better predictions of emissions. But this multi-zone model has been shown by Aceves et al.’s further work (2005) to be sensitive to the transition temperature above which the model is applied. Babajimopoulos et al. (2005) further extended the multi-zone model by considering equivalence ratio zones in addition to temperature zones, and applied the model to study stratified charge HCCI cases. The approach of determining zones in their

3.3 An Adaptive Multi-Grid Chemistry (AMC) Model

95

work is relatively complicated, but the gradient-preserving remapping method that was used to distribute zone information back onto individual cells is very effective. A factor of eight timing reduction was reported in their study, in which the GRIMech 3.0 (53 species, 325 reactions) (Smith et al. 2009) was employed. Here, an adaptive neighbor search method called the Adaptive Multi-grid Chemistry model is presented, which groups thermodynamically-similar cells in the simulation of complex combustion systems, such as DI engines. The method is systematically compared with generic search methods in order to study its applicability under different circumstances. These methods have been coupled with the improved ERC KIVA3v2 code, such that the AMC model can be used in an engine CFD code for simulation of HCCI and DI engine combustion with comprehensive chemistry.

3.3.2 Model Description Most reactive flow CFD codes, such as KIVA3v2, use a splitting-operator scheme that separately evaluates the chemistry source term and transport terms on staggered time steps. This requires solving the change of species composition and heat release due to chemical reactions for each cell at every staggered time step. The Chemkin II library with the VODE ODE solver (Brown et al. 1989) has been coupled into the KIVA code to satisfy this requirement, which solves for the mass density of species in the continuity equation and the energy equation. Compared to solving for the turbulence and spray development, this process is very computationally expensive, even with relatively simple chemical kinetics mechanisms. This indicates that efforts of reducing computing time need to be placed on reducing the calling frequency to the Chemkin solver. This can be achieved by grouping cells on multiple grids with similar gas properties. Two key steps are involved: 1) map (group) eligible cells together and solve the grouped cells together with the chemistry solver; 2) redistribute the group information back onto the individual cells so that the gradients can be preserved, as discussed next. The key of mapping appropriate cells into a group is to find proper measures of similarity, as well as establishing the grouping criteria. In a Well Stirred Reactor (WSR), the temperature, pressure, and species factions describe the composition space that determines the reaction progress. Due to the temperature sensitivity of chemical reactions, it is obvious that temperature should be used as one of the grouping criteria. In the low Mach number flows in DI and HCCI engines, pressure gradients are small, and thus the pressure is not needed as a grouping criterion. Strictly, grouping cells with similar composition requires search and comparison for every individual species, but this is inapplicable because of two concerns. First, the search expense would be too large and thus would reduce the computational efficiency of the multi-grid model. Second, it is difficult to define an appropriate criterion of similarity for each species and thus to efficiently group as many cells as possible. Hence, it is necessary to define an indicator that can represent both

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composition information and combustion progress. The so called progress equivalence ratio (Babajimopoulos et al. 2005) was used here, which is defined by /¼

# 0 # 2C# CO2 þ HH2 O =2  z CCO2 0 # O# CO2 H2 O  z CCO2

:

ð3:22Þ

In this equation, the superscript # denotes the number of atoms of each species. The equivalence ratio is defined based on complete combustion, but the products CO2 and H2O are excluded as indicated by the subscripts in /. Z0 defines the proportion of fuel oxygen to fuel carbon, and for hydrocarbon fuels without oxygen, Z0 is zero. In the multi-zone model of Babajimopoulos et al. (2005), all cells in the cylinder were sorted in ascending order with temperature to form a specified number of zones based on prescribed fraction of mass within each temperature bin. In each temperature zone the cells were again sorted in ascending order using the progress equivalence ratio. The cells of each temperature zone were divided into as many zones as needed to reach the criterion that the maximum / range in each zone is D/max ¼ 0:02. This mapping procedure is similar to a method in which all cells are sorted in temperature ascending order, and then using each sorted cell as a reference, all other cells are grouped with cells that have similar equivalence ratio as the reference cell. This grouping procedure is simpler and more straightforward than the previous multi-zone approach, and it is referred as the global mapping method here. The global mapping method is appropriate for HCCI engines, because cells with similar equivalence ratio are most likely to also have close species compositions. However, for DI engines, because significant gradients of mass fraction of species can exist, there is no guarantee that cells with similar equivalence ratio contain similar mass fractions of each species, especially for those cells that are distributed in very different physical locations. The global mapping method will be compared with the present alternatively adaptive neighbor mapping method to be described next. Based on the above discussion, it is necessary to limit the searching area in order to better group cells that have similar species composition. However, due to convection and diffusion, neighbor cells can have similar thermodynamic conditions, as well as species composition. In the early stages of combustion when large gradients, such as temperature gradients exist, the similarity may merely exist among closely adjacent cells and therefore the grouping process needs to be limited in a narrow region. However, as time progresses energy and species are transported and mixed such that there is a trend toward local uniformity. Correspondingly, the grouping process can be extended to larger and larger regions. This means the grouping region should be determined adaptively. Accordingly, a temperature inhomogeneity measure was used as an indicator for assessing the grouping region adaptively, where sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n 1 X ðTi  TÞ2 : ð3:23Þ rT ¼ n  1 i¼1

3.3 An Adaptive Multi-Grid Chemistry (AMC) Model

97

Fig. 3.9 Adaptive multi-grid grouping

In Eq. (3.23), T denotes the average in-cylinder temperature and Ti is the individual temperature of each of the n cells. The concept of adaptive neighbor search is further illustrated in Fig. 3.9 using a 2-D schematic mesh. It can be seen that the first level search just covers four adjacent cells (six if 3-D mesh) of the reference cell. If the in-cylinder temperature inhomogeneity is below pre-specified values, the search can then be expanded to the second level or higher. In this study, the maximum search level was limited to four, where a maximum of 129 cells can be reached using the fourth level search in 3-D block structural mesh. It should be noted that a similar treatment can also be applied to unstructured meshes. In this case, a convenient approach would be to pre-define a representative search radius and to define the search level as a multiplier used to adjust the search area accordingly. In general, the present adaptive multi-grid mapping method can be summarized as follows. Calculation of temperature inhomogeneity is performed first in order to determine the search level. All cells are then sorted in temperature ascending order to form a temporary array. From the first sorted cell, a neighbor search is conducted based on the computed level, and the neighbor cells are recorded in another temporary array. Within the recorded cells, a cell is selected as the reference cell, and the remaining cells are compared with the reference cell individually. If the absolute difference of their temperature is within a prescribed tolerance D (K) and the relative difference of their progress equivalence ratio is within D/ (%), the cells are grouped. This procedure is repeated using each cell as the reference cell, and the group that contains the most cells is selected and the corresponding cells are flagged to prevent them from being grouped again in later operations on the array of sorted cells. The temperature of the cells in the group is mass-averaged to form a representative average of the group, and the group’s pressure is volumeaveraged. The concentration of species is integrated over the grouped cells to conserve the mass of the group. The grouping procedure is then repeated for other ungrouped and sorted cells until all cells are assigned to a group. In this procedure, it is likely that some groups just contain one cell, and the likelihood is higher for cells at high temperatures since they may be spatially isolated during the grouping procedure. After the mapping process, because the number of groups is less than

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the number of cells, the computational time spent on the chemistry solver can be reduced dramatically. After the cells are mapped into a group and the group is allowed to react using the averaged conditions, it is not possible to exactly remap the mass fractions of each species back onto the original cells, because that requires solving the chemistry for each cell. Thus, an algorithm is needed to redistribute the species back to the cells, such that the gas properties of each cell remapped from the group would be comparable with those if the chemistry of each cell were to be solved individually. A straightforward way of remapping the information of groups back onto their cells is to assign the mean value of the group’s characteristics to each included cell. This means that all the cells in a group would have the same gas properties. It is obvious that this procedure contributes an artificial diffusion to the species continuity equations if composition gradients are present among the grouped cells. This relatively inaccurate method is referred to as the averaged remapping method. An improved method adopted from Babajimopoulos et al. (2005) was also used here, which attempts to preserve gradients of temperature and species composition. The method is described as follows. First, before the mapping procedure, a new quantity ch is defined using the number of C and H atoms of all participating species except the combustion products, CO2 and H2O, where ch ¼ 2C# CO2 þ

H# H2 O : 2

ð3:24Þ

The ch number of a group is the sum of the ch number of all cells in that group. After the chemistry calculation, all species, except CO2, H2O, O2, and N2 are assigned back to the group’s cells based on ch. In this case, the mass of species k in an individual cell is obtained from the ratio mk;cell ¼ mk;group

chcell chgroup

ð3:25Þ

In this way the mass of each species in the group is also conserved. Evidently, some cells can have more or fewer C or H atoms than before the mapping process, and thus the rest of the cells in the group need to be adjusted to maintain the total number of C and H atoms in that group. The number of C atoms in a cell is then balanced from the remaining CO2 species from X mk;cell k

Wk

ck þ

mCO2 ;cell # ¼ Ccell ; WCO2

ð3:26Þ

where Wk is the molecular weight of species k and ck is the number of carbon atoms in species k, and Eq. (3.26) is solved for mCO2 ;cell . Similarly cells that are short of H atoms are balanced using the remaining H atoms from H2O species. Finally, O2 is distributed to maintain the total number of O atoms in each cell and adjustment of N2 is used to conserve the mass of each cell. Since after the

3.3 An Adaptive Multi-Grid Chemistry (AMC) Model Table 3.4 Comparison of different multi-zone models Models Mapping method Remapping method

99

Case study examples

Speedup factor *9

Multi-zone (Babajimopoulos et al. 2005) AMC model (Shi et al. 2009a)

/-T mapping

Mass and element conservation

HCCI engine combustion

/-T mapping with grid spatial information

Mass and element conservation

Cell agglomeration (Goldin et al. 2009)

Selected species and Species gradient of temperature in grouped cells. hash table Ad-hoc treatment for mass conservation Dynamic Species density partitioning gradient mass scheme using conservation is data-mining guaranteed methods based on /-T map

HCCI, diesel DI, 3–10 and gasoline DI engines (Ge et al. 2010c) 1D and 2D 2–20 premixed and diffusion flames. Partially premixed IC engine HCCI and DI 8–20 engines

DMZ (Liang et al. 2009a)

remapping process the mass fraction of each species in each cell is known, the change of the specific internal energy of each cell can be obtained from the difference between the internal energy of formation of the species present in the cell before the grouping process and that after the remapping process. The cell temperature can be computed from the updated specific internal energy and the mass faction of species. The method is called the gradient-preserving remapping method in this study. It is shown in by Shi et al. (2009a) that both global and neighbor grouping methods are satisfactory to predict HCCI engine combustion, but the simpler global grouping method leads to inaccuracies in the predicted emissions for DI cases. The global mapping saves more computer time for HCCI engine simulations, as compared to using the neighbor mapping. An averaged remapping method is explored but not suggested in the AMC model due to increased numerical diffusion. Instead, a gradient-preserving method is found to be applicable for both HCCI and DI cases. In addition, the AMC model predictions are shown to be fairly insensitive to convergence tolerance parameters in parametric studies. A transition temperature of 1,000 K is used to study DI engine cases in the next section. It should be pointed out that there exist several similar multi-zone or multi-grid techniques that modify existing CFD codes in order to accelerate the chemistry calculation. No general conclusion can be drawn with regard to which model performs the best because the demonstrated combustion problems are different in different studies. Table 3.4 surveys the major features of four multi-zone approaches (including the AMC model) that were developed in recent years.

100 Table 3.5 Specifications of the Honda engine

3 Acceleration of Multi-Dimensional Engine Engine

Honda

Bore (mm) Stroke (mm) CR IVC (ATDC) EVO(ATDC)

86 86 8.9 -158 153

Readers are encouraged to refer to the corresponding citations for more details about those models. In the rest of the book, the present AMC model is applied to accelerate the chemistry solver.

3.3.3 Results and Discussion In order to test the efficiency of the AMC model, all simulations in this section were conducted on computers with the same hardware configurations (3.00 GHz Intel P4 CPU and 2G bytes memory), and the wall clock time was recorded for the comparisons. Kranendonk et al. (2007) used swept-wavelength H2O absorption thermometry to directly measure in-cylinder temperature and H2O mole fraction for a Honda gasoline engine fueled with n-heptane and operated under HCCI conditions. The specifications of the engine are listed in Table 3.5. The position of the line-of-sight laser beam and the numerical mesh are illustrated in Fig. 3.10. The measured data represent the averaged value of the spatial locations that are traversed by the laser beam. The engine operating conditions are given in Table 3.6 for two different Fig. 3.10 Position of laser beam path for in-cylinder temperature and H2O mole fraction measurements of the Honda engine

3.3 An Adaptive Multi-Grid Chemistry (AMC) Model Table 3.6 HCCI operating conditions of the Honda engine

101

Operating conditions

Low-speed

High-Speed

Speed (rev/min) IMEP (bar) EGR (%) A/F IVC temperature (K)

600 2.503 0 36.7 459

1,500 2.597 0 42.7 512

speeds. The measured temperature and H2O concentration provide validation data for chemical kinetics mechanisms, such as the ERC PRF mechanism (Ra and Reitz 2008) used in this study. Table 3.7 summaries the sub-models of the KIVA3v2 code used in both HCCI and DI engine studies. The present AMC model reduced the computer time by an order of magnitude with results consistent with those predicted using the full chemistry model. Using the AMC model, for the low speed case (600 rev/min) the computer time was reduced from 48.27 to 3.99 h, and for the high speed case (1,500 rev/min) the computer time was reduced from 48.23 to 4.06 h. Figures 3.11 and 3.12 compare the calculated results using the AMC model with the full chemistry and the measured data for the two different speeds. The simulations correctly predict the onset of cool flame and main heat release for both cases, which also validates the PRF chemistry mechanism regarding to its ability to describe ignition and combustion characteristics. Two simulated temperatures are compared with the experimental data in Figs. 3.11(b) and 3.12(b). They are the average in-cylinder temperature in the entire computational domain and the average temperature of only those cells that are traversed by the laser beam in the pent-roof region, as shown in Fig. 3.10. It can be seen that the average cell temperature for the lower speed case agrees very well with the measured data. However, the calculated temperature of the higher speed case is slightly lower than the experimentally measured value. Note that both the average in-cylinder temperatures are significantly lower than the measured temperatures. This indicates that even for this HCCI case a significant temperature

Table 3.7 KIVA3v2 sub-models Functions Models Turbulence Modified RNG k-e (Han and Reitz 1995) Spray development KH-RT Model (Beale and Reitz 1999), Gas-jet and ROI collision models (Abani et al. 2008a) Spray Standard KIVA model (O’ Rourke and Amsden 2000) impingement Ignition and ERC PRF mechanism (Ra and Reitz 2008) (n-heptane part, 39 species and combustion 141 reactions including NOx chemistry) Soot Two-step model with C2H2 as precursor (Kong et al. 2007) NOx Twelve-step kinetics model (extracted from GRI 3.0 mechanism (Smith et al. 2009) embedded in the fuel mechanism

102

3 Acceleration of Multi-Dimensional Engine

Fig. 3.11 Honda engine at 600 rev/min. a Comparison of pressure trace. b Comparison of temperature. c Comparison of H2O mole fraction

gradient exists in the combustion chamber. This is also observed in Fig. 3.13 which demonstrates the stratified temperature distribution of the lower speed case. The stratification is due to the effects of wall heat transfer. Figures 3.11(c) and 3.12(c) show that simulations slightly under-predicted H2O mole fractions during the cool flame and main heat release stages. A GM-Fiat engine was experimentally and numerically investigated by Opat et al. (2007) under PCCI conditions with ultra-high EGR rates. The study successfully explained experimental CO and unburned hydrocarbons (UHC) emission trends as a function of SOI. It was found that advancing the injection timing increased the proportion of the fuel that was targeted above the piston bowl, leading to high CO emissions. Retarding the injection timing reduced the spray mixing time and targeted the fuel into the piston bowl where the lack of available oxygen also resulted in high CO emissions. Therefore, there exists an optimal injection timing that produces minimum CO emissions, which was called the ‘‘sweet spot’’. The AMC model was applied to those cases to assess its performance in predicting emission trends. The engine specifications and operating conditions are given in Tables 3.8 and 3.9, respectively. The mesh had 7,419 cells at BDC with a 51.4° closed-valve sector (seven hole nozzle).

3.3 An Adaptive Multi-Grid Chemistry (AMC) Model

103

Fig. 3.12 Honda engine at 1,500 rev/min. a Comparison of pressure trace. b Comparison of temperature. c Comparison of H2O mole fraction

Fig. 3.13 Temperature distribution of the Honda engine at 600 rev/min. a CA = -10 ATDC, b CA = -5 ATDC Table 3.8 Specifications of the GM-Fiat engine

Engine

GM-fiat

Bore (mm) Stroke (mm) CR IVC (ATDC) EVO (ATDC) Inj. Pre. (bar) Nozzle Hole Spray angle °

82 90.4 16.6 -132 112 860 7 155

104 Table 3.9 PCCI operating conditions of the GM-Fiat engine

3 Acceleration of Multi-Dimensional Engine Operating conditions

GM-fiat

Speed (rev/min) IMEP (bar) EGR (%) Boost pressure (bar) Equivalence ratio SOI (ATDC)

2,000 5.5 65 1.9 0.95 -39 to -21

In the experimental tests, a large amount of EGR, including unburned fuel, was recycled and mixed with the intake gases. Therefore, a reactive mixture was present initially even before the injection event. This increases the computational burden for the full chemistry model. Thus, the global mapping method was adopted before the injection due to the assumed homogeneous initial composition. As seen in Fig. 3.14, the average computer time of all cases using the AMC model was about 5 h compared to about 16 h using the original code with full chemistry. The timing reduction is close to a factor of three. The results are also quantitatively consistent with those of the full chemistry simulations, as can been seen in Fig. 3.15. The AMC model successfully predicts the emission trends over the entire SOI sweep for the soot, NOx, and CO emissions. The UHC emissions are over-predicted as the SOI is retarded, but the emissions trend is correctly captured. To summarize, with the present reduced chemistry mechanism, the AMC model is able to reduce computing time by more than factors of ten for HCCI cases and three for DI cases without losing prediction accuracy compared to the original code. If a larger and more comprehensive chemical kinetics mechanism is used, the computer time reduction would be expected to be further increased.

Fig. 3.14 Comparison of computer time of the full chemistry model and the AMC model.

3.3 An Adaptive Multi-Grid Chemistry (AMC) Model

105

Fig. 3.15 Comparison of experimental and simulated results for the GM engine operated under PCCI conditions. a Soot emissions. b NOx emissions. c UHC emissions. d CO emissions

3.4 An Extended Dynamic Adaptive Chemistry (EDAC) Scheme 3.4.1 Background In the preceding section the use of the multi-grid technique where thermodynamically-similar computational cells are grouped and solved together was seen to save a great amount of computer time. The efficiency of the multi-grid technique is based on reducing the calling frequency to the chemistry solver. Therefore, in order to further accelerate the chemistry solver, the computer time of each call to the chemistry solver (either for a cell or a group if the multi-grid technique is applied) needs to be reduced. Reduced mechanism combustion and emissions predictions aim to reproduce corresponding detailed mechanisms over a wide range of thermodynamic conditions. Further mechanism reduction should be determined adaptively and automatically based on the local and instantaneous thermodynamic conditions. Liang et al. (2009b) developed a dynamic adaptive chemistry (DAC) scheme based on the DRGEP method. In their study, single zone adiabatic HCCI engine simulations were conducted using a detailed n-heptane mechanism (578 species) and multicomponent fuel cases (Liang et al. 2009c), and it was found that the on-the-fly

106

3 Acceleration of Multi-Dimensional Engine

mechanism reduction scheme not only resulted in negligible computational overhead but also achieved as much as 30-fold time reduction. The present work assesses the use of the DAC scheme for HCCI and DI engine multi-dimensional simulations using relatively small mechanisms, and issues associated with its implementation are discussed.

3.4.2 Model Description The goal of mechanism reduction is to eliminate as many unimportant species and reactions as possible, while maintaining the prediction accuracy of the reduced mechanism to be comparable to the detailed mechanism under the conditions of interest. In the aforementioned DRG, DRGEP, and PFA methods, unimportant species are identified based on their connectivity to pre-selected initial species, such as fuel, CO, and HO2. Once a species is removed from the detailed mechanism, its associated reactions are also removed. In this way, the methods attempt to directly reduce the number of species with which the computer time of the chemistry solver scales quadratically. We have also shown in Sect. 3.2 that the DRGEP methods performed better than the other two in mechanism reduction for HCCI engine simulations, and therefore the present adaptive chemistry scheme emphasizes this method. The DRGEP method extracts a set of active species including the initial species and their strongly connected species based on the local and instantaneous thermodynamic conditions. Consequently, a reaction is active (thus is included) in the reduced mechanism only if all participating species are in the set of active species. Species not in the active set are treated as inactive, with their mass fractions are kept fixed. The principle of the DRGEP method gives surety that, were they to be included, the small changes in the mass fraction of these inactive species would have negligible effect on heat release rate and the evolution of key species. However, though the inactive species are not chemically active in the adaptively reduced mechanism, they do play an important role in three-body reactions and pressure-dependent reactions, and thus their mass fractions have to be considered. Liang et al. (2009b) proposed a formulation of the kinetics equations that minimizes the size of the ODE system while still accounting for third body effects. The ODE equations can be expressed as 8 a y_ 1 ¼ f1 ðXðT; p; ya1 ; . . .; yam ; yi1 ; . . .; yin ÞÞ > > > > < .. . > > y_ am ¼ fm ðXðT; p; ya1 ; . . .; yam ; yi1 ; . . .; yin ÞÞ > > : T_ ¼ fmþ1 ðXðT; p; ya1 ; . . .; yam ; yi1 ; . . .; yin ÞÞ: ð3:27Þ In Eq. 3.27, the reaction system involves m active and n inactive species: X ðT; p; ya1 ; . . .; yam ; yi1 ; . . .; yin Þ, where the superscripts ‘‘a’’ and ‘‘i’’ denote active

3.4 An Extended Dynamic Adaptive Chemistry (EDAC) Scheme

107

and inactive species, respectively. The ODEs are formulated with respect to only active species, eliminating redundant equations due to inactive species and thus leading to a compact Jacobian matrix. All species are considered when the rate functions are evaluated, which eliminates the need to explicitly include the third body species in the reduced mechanisms. Note that the species mass fractions in Eq. 3.27 refer to the total mixture, and therefore their summation is unity. Also note that since only the reaction rate of the active reactions is evaluated in the right-hand-side terms of Eq. 3.27, the set of active reactions must be distinguished from the inactive set. This is done by using a binary flag array to mark the active reactions. The DAC scheme has been successfully employed to study HCCI engine combustion (Liang et al. 2009b, c). However, the application of the method in DI engine simulations is not straightforward and its good performance and efficiency are not obvious. This is because the single-zone HCCI model neglects convection and diffusion effects that can superimpose perturbations on the DAC scheme whose mechanism reduction considers reaction fluxes only. In HCCI engines, the convection and diffusion processes exist mainly in boundary layers, but in DI engines they are more significant due to the non-premixed combustion. In the study of Liang et al. (2009b), the search-initiating species were fixed as fuel, CO, and HO2, but these three species are not all necessarily important throughout the simulated engine cycle (Liang et al. 2009c). This is also true for DI engine simulations. Thus, the search-initiating species should be determined spatially and temporally based on information obtained from the combustion process. The study of Liang et al. (2009c) concluded that NO and its effect on hydrocarbon ignition can be well predicted and captured without adding NO to the search-initiating species. However, it was found that this conclusion depends on the specific NOx sub-mechanism that is coupled with the hydrocarbon oxidation mechanism, as well as the simulation conditions, and does not always hold for all cases. Therefore, a remedy is needed to ensure that NO is accurately predicted when the DAC scheme is applied to DI engine simulations. Furthermore, the error tolerance of the DAC scheme that is suitable for the single-zone model and a particular chemical mechanism does not necessarily globally meet the requirement of multi-dimensional simulations and mechanisms with different sizes. The causes of the above issues and proposed solutions are discussed in the present study. To simplify the analysis, HCCI simulations using a single-zone model combined with a posteriori studies using the DAC scheme are employed. The performance of the DRGEP method depends on a proper set of searchinitiating species from which the connected species can form the most representative reduced mechanism based on the local and instantaneous thermal conditions. In the original DAC scheme (Liang et al. 2009b), fuel, CO, and HO2 were selected to initiate the DRGEP method search for important species. Each of the initial species should play a primary role in the three major combustion processes of hydrocarbon fuels, namely, fuel decomposition, CO oxidation, as well as H2-O2 reactions. However, the inclusion of the original DAC species for all combustion processes could overestimate the importance of a certain initial species for a

108

3 Acceleration of Multi-Dimensional Engine

Fig. 3.16 Profiles of temperature and equivalence ratio with different initial equivalence ratio. a Initial equivalence ratio = 0.5. b Initial equivalence ratio = 1.5

particular combustion stage. For example, during the post-ignition stage at high temperature almost all fuel molecules and large hydrocarbons have been decomposed to small molecules, and thus only CO oxidation and H2-O2 reactions dominate the combustion processes. Since each initial species can lead to a subsidiary set of connected species in the reduced mechanism, the exclusion of unnecessary initial species would increase the efficiency of the DAC scheme. In addition, once a system undergoes complete combustion (or reaches equilibrium), none of the three DAC species should be considered as proper initial species as the chemical system has shifted to produce CO2 and H2O. Therefore, due to the nature of heterogeneous combustion in DI engine simulations, it is necessary to dynamically select the search-initializing species for each cell based on its combustion status. In order to select a proper set of the search-initializing species, the combustion state of each cell has to be known prior to applying the DRGEP method for mechanism reduction for that cell. Thus, to quantify the combustion state, the cell temperature and progress equivalence ratio were monitored. These two quantities have been extensively used in multi-grid approaches (Babajimopoulos et al. 2005, Shi et al. 2009a) to group cells with similar combustion characteristics. The so-called progress equivalence ratio was defined in Eq. (3.12). However, the progress equivalence ratio merely indicates the completeness of the combustion, and thus no information is provided about the degree of fuel decomposition. Following Eq. (3.12), we define the equivalence ratio as. /l ¼

2Cl# þ Hl# =2 O# lþO2

:

ð3:28Þ

Here, the subscript l represents all large hydrocarbons (more than 3 carbon atoms), and O2 is the only oxidizer considered. / and /l are shown in Fig. 3.16 for two HCCI simulations using a single-zone model. It is seen in Fig. 3.16 (a) that for lean mixture combustion, both the progress equivalence ratio (/) and the equivalence ratio of large hydrocarbons (/l) drop rapidly to zero as the temperature increases, which indicate the completeness of fuel decomposition and combustion,

3.4 An Extended Dynamic Adaptive Chemistry (EDAC) Scheme

109

respectively. However, for rich mixtures, Fig. 3.16(b) shows that the progress equivalence ratio increases after the combustion occurs due to the incomplete oxidation of CO and therefore the inclusion of CO in the search-initializing species is necessary for the DRGEP method. Regardless of the mixture initial conditions, the large hydrocarbons equivalence ratio continuously decreases to zero as the combustion proceeds, which means the fuel species can be excluded from the set of the initial species once /l is below a critical value. In order to choose a proper critical value for a wide range of thermal conditions, the contribution matrices of the heat formation rate due to a single reaction to the entire combustion system are listed in Table 3.10(a) and (b) for the two studied HCCI cases, as suggested by Ando et al. (2009). The contribution of a single reaction is quantified based on the percentage of its heat formation rate (- heat release, ? heat absorption) to the overall heat release or absorption rate of the system at a particular temperature. Reactions which contribute more than 10 percent to the heat formation rate for any of the temperatures from 700 to 2,300 K at an interval of 100 K are listed in the tables for lean and rich mixture HCCI simulations. It is observed that for both lean and rich combustion, when /l is below 0.001, reactions involving large hydrocarbons contribute no or negligible heat formation to the combustion system, and the combustion chemistry shifts from fuel decomposition to small hydrocarbons and H2–CO combustion. Consequently, fuel should be excluded from the set of initial species to avoid unnecessary large hydrocarbons being included into the active species set. It is also found that the inclusion of CO as the initial species enables the connection to small hydrocarbons when they are deemed important by the DRGEP method. Therefore, using CO and HO2 as the initial species when /l is below 0.001 produces suitable reduced mechanisms to describe the post-ignition stage of hydrocarbon combustion. In addition, when both / and /l are below 0.001 the combustion process is deemed to be complete. As a result, the combustion products CO2 and H2O are used as the initial species when this condition is satisfied. Species that comprise the NO sub-mechanism are not necessarily closely connected to any of the search-initializing species under the conditions that the DRGEP method is performed. HCCI engine simulations using a single-zone model were investigated with two different n-heptane mechanisms, including a NO submechanism (Patel et al. 2004, Golovitchev 2006), and the results showed that species that are included in the NO sub-mechanism were only reachable (thus were included in the reduced mechanism) from the search initializing species (n-heptane, CO, HO2) when the temperature was above 2,300 K and the equivalence ratio was below stoichiometric. Obviously, this could introduce a large error when the DAC scheme is applied to study DI engines. Therefore, in order to ensure the generality of the DAC scheme in engine simulations, a special treatment is needed. Since NO is the primary NOx species in engines, a straightforward method is to include NO into the set of search-initializing species. The DRGEP method’s predictive accuracy as compared to the full chemistry should scale with the error tolerance. However, the involvement of NO into the

-0.1

0

0

0

1.500

1.500

-20.3

88.6

-37.2

-42.4

8.2

1

/ of large hydrocarbons

/ (progress equivalence ratio)

nc7h16 ? oh \=[ c7h15-2 ? h2o

nc7h16 ? o2 \=[ c7h15-2 ? ho2

c7h15-2 ? o2 \=[ c7h15o2

c7h15o2 ? o2 \=[ c7ket12 ? oh

c7ket12 \=[ c5h11co ? ch2o ? oh

c5h11co \=[ c2h4 ? c3h7 ? co

(b) Initial equivalence ratio = 1.5

oh ? ho2 \=[ h2o ? o2

-2.1

0

ch3 ? ch3o \=[ ch4 ? ch2o

27.7

51.2

-38.2

-31.9

-0.1

-20.3

1.500

1.495

0

-1.7

-1.4

0

hco ? M \=[ h ? co ? M

0

0

0

h ? o2 ? M \=[ ho2 ? M

h2o2 ? M \=[ 2oh ? M

0

0

0

2oh \=[ o ? h2o

0

ch2o ? oh \=[ hco ? h2o

0

o ? oh \=[ o2 ? h

0

0

-0.6

15.8

1.5

26.6

55.4

-0.1

-20.4

hco ? o2 \=[ ho2 ? co

0

0

ch3 ? ho2 \=[ ch3o ? oh

0

0.4

c3h7 \=[ c2h4 ? ch3

ch3o ? co \=[ ch3 ? co2

0.1

c7h152 \=[ c2h5 ? c2h4 ? c3h6

co ? oh \=[ co2 ? h

1.2

c5h11co \=[ c2h4 ? c3h7 ? co

-40.1

-43.5

11.4

86

-35.7

nc7h16 ? o2 \=[ c7h15-2 ? ho2

c7h15-2 ? o2 \=[ c7h15o2

c7h15o2 ? o2 \=[ c7ket12 ? oh

-20.8

nc7h16 ? oh \=[ c7h15-2 ? h2o

c7ket12 \=[ c5h11co ? ch2o ? oh

-32.2

0.5

0.498

0.5

0.496

800

/ progress equivalence (ratio)

700

/ of large hydrocarbons

(a) Initial equivalence ratio = 0.5

Temperature (K)

29.4

40.5

-17.1

-11.8

-2.3

-10.2

1.516

1.389

-0.2

-24.8

0

-18

-14.4

0

-0.9

0

0

0

-0.6

-7.5

22

1.2

32.2

43.1

-10.6

-7.5

-0.4

-5.1

0.490

0.400

900

29

37.2

-1.7

-0.7

-1

-3.5

1.533

0.982

0

-4.6

0.1

-38.6

-15.3

50.4

-0.5

0

0

0

-8.4

-6.8

5.6

8.7

9.2

12.5

-2.2

-1.7

0.5

-1.4

0.479

0.166

1000

0.8

1.1

-0.3

-0.2

0.5

-3.9

1.551

0.818

-0.1

-9.5

1

-28

-16.8

67.4

-0.9

0

0.1

-0.1

-9.8

-9.2

1.6

18.1

2.9

4

-0.8

-0.6

0.2

-2

0.470

0.136

1100

0.1

0.2

0

0

0.3

-3.9

1.573

0.679

-0.2

-12

7.7

-21.8

-17.6

70.1

-5

0.1

0.6

-0.1

-9.4

-9.7

0.6

17.7

0.5

0.6

-0.1

-0.1

0.1

-1.8

0.455

0.091

1200

0

0

0

0

0.2

-3.1

1.597

0.516

-0.3

-13.9

25.1

-11.2

-18.6

56

-15.6

0.4

2.5

-0.3

-8.2

-9.4

2.1

12.3

0.1

0.1

0

0

0.1

-1.3

0.439

0.045

1300

0

0

0

0

0.2

-2

1.624

0.323

-0.6

-15.8

39.2

-3.4

-19.5

42.7

-23

1.2

5.2

-0.5

-6.8

-9

3.8

6.6

0

0

0

0

0

-0.7

0.423

0.014

1400

0

0

0

0

0.2

-1.1

1.650

0.186

-1.3

-17.6

45.5

-0.7

-18

35.4

-24.3

2.6

8.7

-1.8

-6.8

-9.5

4.5

1.6

0

0

0

0

0

-0.2

0.403

0.001

1500

0

0

0

0

0.4

-0.5

1.678

0.090

-1

-13.3

50.4

-0.2

-12.5

9.7

-23.1

7.9

19

-5.4

-10.4

-10.6

5.6

0

0

0

0

0

0

0

0.378

0.000

1600

0

0

0

0

0.2

-0.2

1.708

0.036

-1.6

-13.7

45.3

-0.1

-11.6

6.4

-24.3

14

24.8

-7.9

-8.8

-9.7

3.7

0

0

0

0

0

0

0

0.349

0.000

1700

0

0

0

0

0.1

-0.1

1.738

0.011

-3.4

-13.3

37.3

0

-10

5.6

-25.4

21.2

29.5

-11.5

-6.9

-8.4

2.5

0

0

0

0

0

0

0

0.315

0.000

1800

0

0

0

0

0

0

1.774

0.002

-8.4

-8

26.2

0

-7.1

6.3

-27.4

28.8

34

-17.7

-5

-5.6

1.7

0

0

0

0

0

0

0

0.270

0.000

1900

Table 3.10 Heat contribution matrix of individual reactions to the system (percentage, - heat release, ? heat absorption)

0

0

0

0

0

0

1.815

0.000

-15.7

-2

15.5

0

-3.7

8.2

-29.8

35.1

37

-24.6

-2.8

-2.4

1.2

0

0

0

0

0

0

0

0.214

0.000

2000

0

0

0

0

0

0

1.861

0.000

-22.7

-0.1

6.9

0

-1.4

8

-31.2

41.2

40.8

-29.1

-0.6

-0.4

0.4

0

0

0

0

0

0

0

0.145

0.000

2100

0

0

0

0

0

0

0

0

0

0

0

0

2.024

0.000

27.1

0

0

0

0

-0.4

19.5

-0.2

8.7

4

0

0

0

0

0

0

0

0

0

0

0.006

0.000

2300

(continued)

1.931

0.000

-30.4

0

2.3

0

-0.4

5.8

-31.7

49.2

42.3

-27.9

0

0

0

0

0

0

0

0

0

0

0.035

0.000

2200

110 3 Acceleration of Multi-Dimensional Engine

0

0

0

0

0

0

h ? o2 ? M\=[ho2 ? M

h2o2 ? M\=[2oh ? M

ch2o ? oh \=[hco ? h2o

hco ? o2 \=[ho2 ? co

hco ? M\=[h ? co ? M

ch3 ? ch3o \=[ ch4 ? ch2o

0

0

ch3o ? co \=[ ch3 ? co2

2oh \=[o ? h2o

0

ch2 ? o2 \=[ ch2o ? o

0

0

ch3 ? ho2 \=[ ch3o ? oh

0

0.4

c3h7 \=[ c2h4 ? ch3

co ? oh \=[ co2 ? h

0.2

c7h152 \=[ c2h5 ? c2h4 ? c3h6

o ? oh \=[o2 ? h

700

Temperature (K)

Table 3.10 (continued)

-3.4

0

-1.9

-1.5

0

-0.1

0

0

0

0

0

-1

17.1

3.2

800

-20.7

0

-12.8

-10.3

0

-0.6

0

0

0

-0.3

0

-6.2

19.5

9.3

900

-31

0

-19.5

-14.4

0

-0.9

0

0

0

-2.1

0

-10.2

20.6

11.1

1000

-9.1

0.9

-28.5

-13.8

54.6

-0.7

0

0.1

0

-10.2

0

-9.3

0.3

35

1100

-13.9

6.5

-19.7

-14.7

54.6

-3

0.1

0.5

-0.1

-9.4

0

-10.1

1.9

32.8

1200

-18.5

18.5

-9.5

-16.6

42.5

-8

0.3

1.8

-0.1

-7

0

-9.9

7

27.8

1300

-21.4

27.1

-2.7

-18.6

-21.7

33.8

-0.6

-19.8

27.4

-13.5

-11.8 34.4

1.4

6

-0.2

-4

-0.2

-8.8

12.8

14.7

1500

0.7

3.5

-0.1

-4.6

-0.1

-9.1

11.2

20.9

1400

-20.2

42.9

-0.2

-20

10.6

-14

2.8

10.3

-0.2

-5.6

-0.4

-9.5

12.2

10.6

1600

-17.8

47.8

-0.1

-22.6

4

-15.4

4.5

14.5

-0.3

-4.9

-1

-8.3

8.2

5.1

1700

-17

51

0

-25

1.7

-15.5

6.6

17.7

-0.4

-3.4

-1.9

-7.1

4.9

1.6

1800

-16

51.5

0

-26.2

0.8

-14.8

8.4

19.3

-0.7

-2.6

-2.7

-6.3

3.7

0.4

1900

-14.7

49.9

0

-26.2

0.4

-13.7

10.9

20.7

-1.4

-2

-4.2

-5.5

3.7

0.1

2000

-13.1

46

0

-22.8

0.1

-12.9

16.6

24.6

-3.8

-1.6

-7.4

-4.8

4.8

0

2100

-10.9

36.3

0

-16.7

0.1

-12.7

25

29.9

-7.9

-1.3

-11.4

-4

4.4

0

2200

-8

31

0

-14.1

0

-12.6

30.8

32.8

-11.3

-1

-12.5

-2.9

2.6

0

2300

3.4 An Extended Dynamic Adaptive Chemistry (EDAC) Scheme 111

112

3 Acceleration of Multi-Dimensional Engine

Fig. 3.17 Illustration of reaction pathways of different mechanisms using DRGEP method

search-initializing species adds more species to the set of active species and therefore decreases the efficiency of the DAC scheme. To achieve a compromise between the prediction accuracy and computational efficiency, NO was only added to the search-initializing species when the cell temperature was above a prespecified critical temperature in the present DAC scheme. In this research, the critical temperature was chosen as 1,800 K. The critical temperature was determined based on many previous studies that have shown this is a temperature below which negligible NO formation is found in engine combustion processes (Park and Reitz 2007, Akihama et al. 2001). It should be noted that if NO is present in EGR gases, the DAC scheme is able to account for the effect of NO on the ignition process without including it in the initiating-species pool (Liang et al. 2009c). As seen in Fig. 3.17, the error propagates along the reaction pathway from the search-initializing species to a target species in the DRGEP method. Therefore, the error depends on both the dependence between the intermediate species and the length of the pathway. This indicates that the connectivity between the same two species in different mechanisms could be different, and a proper error tolerance has to be determined based on the chemical mechanism used in simulations. It is also intuitive that since the dependence between two directly connected species is less than or equal to one, so the propagated error between species could be smaller in a mechanism of larger size, which has longer pathways. Rigorously, an error control mechanism is needed to determine the error tolerance based on a real-time comparison between the predicted results of the reduced mechanism and those of the full mechanism. Nagy and Turanyi (2009) proposed a method to produce reduced mechanisms from very large reaction mechanisms based on simulation error minimization. However, it is not practical for the present on-the-fly mechanism reduction because of the large computational overhead of the method, which suggests that a

3.4 An Extended Dynamic Adaptive Chemistry (EDAC) Scheme

113

Fig. 3.18 Flow chart of EDAC scheme

priori comparison would be more appropriate to determine the error tolerance for the application of the DAC scheme in multi-dimensional engine simulations. In the present study, a 2-D HCCI simulation was employed to determine the error tolerance values for different mechanisms. As a further simplification, once a cell has completed combustion, i.e., its progress equivalence ratio and temperature are below the pre-specified critical values, the error tolerance of that cell can be increased, so that more species can be removed to further reduce the size of mechanism while maintaining the accuracy. DI engine simulations involve spray development and droplet evaporation processes. Consequently, the vapor distribution in the cylinder is critical to combustion. The DAC scheme introduces numerical error in computing chemical heat release that can affect the evaporation process. Thus, the present method decouples the DAC scheme from the evaporation process by not applying the scheme to cells that contain liquid fuel droplets. This does not sacrifice computational efficiency significantly because the number of cells that contain liquid fuel droplets and are undergoing chemical reaction is usually small compared to the number of CFD cells. The present improved DAC scheme is termed the extended dynamic adaptive chemistry (EDAC) scheme. To highlight the details of the EDAC scheme, a flow chart is depicted in Fig. 3.18. Symbols with solid lines represent the main flow of the EDAC scheme, and the dashed lines indicate the selection of the searchinitializing species. The dotted lines indicate the parameters that that determine the error tolerance. The error tolerance is e and ec is the pre-selected tolerance based on 2-D HCCI simulations.

114

3 Acceleration of Multi-Dimensional Engine

Fig. 3.19 HCCI simulations. a Pressure trace using ERC mech. b NOx and Soot using ERC mech. c Pressure trace using CHA mech. d NOx and Soot using CHA mech.e Pressure trace using LLNL mech. f NOx and Soot using LLNL mech

3.4.3 Results and Discussion The 2-D HCCI tests were used to select an appropriate error tolerance for DI simulations (c.f., Table 3.5). The 2-D mesh had 136 cells at bottom dead center (BDC). Three error tolerances 1e-4, 1e-3, and 1e-2 were tested for the original DAC scheme with four initial species including n-heptane, CO, HO2 and NO. The test n-heptane mechanisms including the NOx chemistry were the ERC reduced

3.4 An Extended Dynamic Adaptive Chemistry (EDAC) Scheme

115

Fig. 3.20 Honda engine at 600 rev/min. a Comparison of pressure trace. b Comparison of temperature. c Comparison of H2O mole fraction

mechanism (34 species and 77 reactions, Patel et al. 2004), the Chalmers reduced mechanism (61 species and 262 reactions, Golovitchev 2006), and the LLNL detailed mechanism (543 species and 2,538 reactions, Curran et al. 1998). Except as otherwise mentioned, all the tests in this section were calculated on PCs with the 3.00 GHz Intel P4 CPU and 2G bytes of memory. Figure 3.19 shows pressure traces and NOx and soot emissions using the different mechanisms and error tolerances. The computational times are included in the legends of the figures. It is seen that for the smallest ERC mechanism, the pressure calculated by the full chemistry solver is well matched using the DAC scheme with all selected error tolerances. However, inaccurate emission results are seen in Fig. 3.19(b) with error tolerance of 1e-2. For the Chalmers mechanism, it is seen in Fig. 3.19(c) that peak pressure was over-predicted using error tolerance of 1e-2. Error tolerance of 1e-3 calculated had good agreement with the full chemistry pressure while under-predicting the soot emissions. Neither 1e-3 nor 1e-2 gave good results with the LLNL mechanism (Fig. 3.19(e) and (f)). The results indicate that the error tolerance of the DAC scheme should decrease as the size of mechanism increases. The DAC scheme reduced the computer time by a factor of 9 for the HCCI simulation with the LLNL mechanism (e = 1e-4). Even though the reduction is

116

3 Acceleration of Multi-Dimensional Engine

Fig. 3.21 Honda engine at 1,500 rev/min. a Comparison of pressure trace. b Comparison of temperature. c Comparison of H2O mole fraction

significant, its efficiency is less than the factor of 30 of Liang et al. (2009b) in a similar single-zone adiabatic HCCI simulation. To examine the performance of the combination of the AMC model and the EDAC scheme in 3–D HCCI engine simulations, the simulations of the Honda HCCI engine that were conducted with the AMC model in the preceding section were repeated while also activating the EDAC scheme (with error tolerance of 1e3 as the small ERC PRF mechanism was used). The computer times were 2.88 and 2.95 h for the low speed and high speed cases, as compared to 3.99 and 4.06 h with the AMC model only, and 48.27 and 48.23 h, respectively, with the full chemistry solver. Figures 3.20 and 3.21 prove that using both the AMC model and the EDAC scheme predict very consistent results with the full chemistry solver, in good agreement with the experiments. The detailed LLNL mechanism alone was not used for the DI simulations because of its unacceptably long computer times. Instead, the present schemes were tested against the full chemistry solver for the ERC n-heptane mechanism and Chalmers n-heptane mechanism. The 3-D sector mesh has 7,419 cells at BDC, which is the same with that of Sect. 3.3.3 with engine specifications of Table 3.5. In order to assess the performance of the EDAC scheme over a wide range of operating conditions, for each mechanism three operating conditions including

3.4 An Extended Dynamic Adaptive Chemistry (EDAC) Scheme

117

Table 3.11 Engine operating conditions for tests of the EDAC scheme Operating conditions FTP1 FTP4 FTP5

FTP5D

Speed (rev/min) Inj. Pres. (bar) IMEP (bar) EGR (%) Equivalence ratio IVC temperature (K) IVC pressure (bar) Pilot SOI (°ATDC) Pilot fuel amount (g/cycle) Pilot injection duration (CA) Main SOI (°ATDC) Main fuel amount (g/cycle) Main injection duration (CA)

2,500 860 8.8 20 0.75 350.0 1.5 -25.0 0.00768 5.4 -5.0 0.01792 12.6

1,500 860 2.1 0 0.2 350.0 1.09 N/A N/A N/A -10.0 0.0064 2.7

2,000 860 5.5 65 0.95 350.0 1.9 N/A N/A N/A -20.0 0.016 9.0

2,500 860 8.8 20 0.75 350.0 1.5 N/A N/A N/A -5.0 0.0256 18.0

FTP1, FTP4, FTP5 were studied as listed in Table 3.11. It is noted that for the high-load FTP5 case, a dual-injection strategy was also investigated, as indicated by case FTP5D. The simulation results are summarized in Tables 3.12 and 3.13 for the ERC n-heptane mechanism and the Chalmers mechanism. The parentheses indicate the percentage time saving or computational error in emissions compared to the baseline cases. It is seen that for the ERC mechanism, as much as 30% timing reduction was achieved, while for the larger CHA mechanism, this increased to almost 50%. For the ERC mechanism, the error tolerance of 1e-3 from the 2-D HCCI simulation is satisfactory under all operating conditions, as seen in Table 3.12. However, the same tolerance introduced discrepancies in the emission results for non-premixed combustion cases (FTP 5 cases in Table 3.13(c) and (d)) with the CHA mechanism, which indicates that 1e-4 is a better option. For the ERC mechanism, no apparent differences are observed by avoiding spray containing cells. This is attributed to the fact that the connection between the species in a small mechanism is very strong and thus the influence of the DAC scheme on the evaporation is not pronounced. For the CHA mechanism, decoupling of the evaporation process from the DAC schemes considerably improved the emission results for non-premixed combustion cases. When a proper error tolerance was selected, the differences of the emissions predicted using the DAC schemes to those of the full chemistry solver are below 5%, except at some extremely low emission levels. It is also noted that an additional 8–10% time saving can be obtained without losing accuracy using the present DAC scheme. The top-left plot in Fig. 3.22 shows the temperature distribution in a cut plane on the spray axis and the locations of liquid droplets using the full chemistry solver at 15° ATDC. The other plots illustrate how many species were solved in each cell

(a) FTP1 Case Tot. time (h) 11.60 Chem. time (h) 10.79 DAC overhead (h) N/A Soot (g/kg fuel) 0.00015 NOx (g/kg fuel) 38.23 UHC (g/kg fuel) 20.90 CO (g/kg fuel) 76.10 (b) FTP4 Case Tot. time (h) 9.78 Chem. time (h) 9.15 DAC overhead (hr) N/A Soot (g/kg fuel) 0.38 NOx (g/kg fuel) 0.0032 UHC (g/kg fuel) 69.20 CO (g/kg fuel) 365.00 (c) FTP5 Single injection case Tot. time (h) 16.37 Chem. time (h) 15.45 DAC overhead (h) N/A Soot (g/kg fuel) 1.15 NOx (g/kg fuel) 7.22 UHC (g/kg fuel) 14.20 CO (g/kg fuel) 216.00 9.14 (21) 7.80 (28) 0.51 0.00014(6.7) 40.32 (5.5) 20.50 (1.9) 75.50 (0.79) 8.39 (14) 7.28 (20) 0.47 0.37 (2.6) 0.0036 (13) 66.90 (3.3) 359.00 (1.6) 14.22 (13) 12.81 (17) 0.49 1.16 (0.87) 7.26 (0.55) 14.50 (2.1) 220.00 (1.9)

10.28 (11) 8.85 (18) 0.56 0.00014(6.7) 38.85 (1.6) 21.20 (1.4) 77.40 (1.7)

8.97 (8.3) 7.81 (15) 0.51 0.37 (2.6) 0.0034 (6.3) 67.30 (2.7) 357.00 (2.2)

15.24 (6.9) 13.80 (11) 0.54 1.15 (0) 6.94 (3.9) 14.90 (4.9) 218.00(0.93)

15.55 (5) 14.10 (6.8) 0.53 1.15 (0) 7.03 (2.6) 15.00 (5.6) 218.00(0.93)

8.94 (8.6) 7.80 (15) 0.50 0.37 (2.6) 0.0035 (9.4) 67.00 (3.2) 358.00 (1.9)

10.19 (12) 8.83 (18) 0.55 0.00015 (0) 39.09 (2.2) 20.90 (0) 77.50 (1.8)

14.32 (13) 12.92 (1.6) 0.48 1.13 (1.7) 7.32 (1.4) 14.00 (1.4) 220.00 (1.9)

8.51 (13) 7.39 (19) 0.47 0.37 (2.6) 0.0035 (9.4) 67.30 (2.7) 360.00 (1.4)

9.21 (21) 7.90 (27) 0.51 0.00017(13) 41.18 (7.7) 20.30 (2.9) 76.40 (0.39)

14.26 (13) 12.88 (17) 0.46 1.13 (1.7) 7.01 (2.9) 14.20 (0) 210.00 (2.8)

8.06 (18) 6.98 (24) 0.43 0.37 (2.6) 0.0035 (9.4) 66.50 (3.9) 354.00 (3.0)

9.12 (21) 7.87 (27) 0.45 0.00014(6.7) 38.97 (1.9) 21.10 (0.96) 78.30 (2.9)

Table 3.12 DI engine simulations using the ERC n-heptane mechanism (34 species, 77 reactions) Apply DAC to all cells Apply DAC to cells that contain no liquid fuel Full chem. DAC 1e-4 DAC 1e-3 DAC 1e-4 DAC 1e-3 EDAC 1e-4

(continued)

13.32 (19) 11.96 (23) 0.43 1.14 (0.85) 7.54 (4.4) 14.60 (2.8) 229.00 (6.0)

7.52 (23) 6.47 (29) 0.41 0.37 (2.6) 0.0035 (9.4) 67.30 (2.7) 361.00 (1.1)

7.96 (31) 6.73 (38) 0.43 0.00017(13) 40.81 (6.7) 20.70 (0.96) 77.80 (2.2)

EDAC 1e-3

118 3 Acceleration of Multi-Dimensional Engine

(d) FTP5 Dual injection Tot. time (h) Chem. time (h) DAC overhead (h) Soot (g/kg fuel) NOx (g/kg fuel) UHC (g/kg fuel) CO (g/kg fuel)

Table 3.12 (continued)

case 18.30 16.80 N/A 1.04 16.08 9.84 117.00

Full chem. 16.64 (9.1) 14.63 (13) 0.51 1.01 (2.9) 15.93 (0.93) 9.26 (5.9) 113.00 (3.4)

15.49 (15) 13.58 (19) 0.44 1.04 (0) 16.21 (0.81) 10.40 (5.7) 119.00 (1.7)

Apply DAC to all cells DAC 1e-4 DAC 1e-3 16.87 (7.8) 14.89 (11) 0.49 1.01 (2.9) 16.00 (0.50) 9.25 (6.0) 113.00 (3.4)

15.73 (14) 13.79 (18) 0.43 1.01 (2.9) 16.31 (1.4) 9.27 (5.8) 114.00 (2.6)

15.58 (15) 13.71 (18) 0.41 1.02 (1.9) 16.12 (0.25) 9.58 (2.6) 113.00 (3.4)

Apply DAC to cells that contain no liquid fuel DAC 1e-4 DAC 1e-3 EDAC 1e-4

14.28 (22) 12.42 (26) 0.38 1.05 (0.96) 16.56 (3.0) 10.50 (6.7) 122.00 (4.3)

EDAC 1e-3

3.4 An Extended Dynamic Adaptive Chemistry (EDAC) Scheme 119

(a) FTP1 Case Tot. time (h) 44.87 Chem. time (h) 43.97 DAC overhead (h) N/A Soot (g/kg fuel) 0.00018 NOx (g/kg fuel) 24.05 UHC (g/kg fuel) 47.10 CO (g/kg fuel) 113.00 (b) FTP4 Case Tot. time (h) 39.85 Chem. time (h) 39.06 DAC overhead (h) N/A Soot (g/kg fuel) 0.14 NOx (g/kg fuel) 0.020 UHC (g/kg fuel) 62.00 CO (g/kg fuel) 288.00 (c) FTP5 Single injection case Tot. time (h) 59.47 Chem. time (h) 58.28 DAC overhead (h) N/A Soot (g/kg fuel) 0.83 NOx (g/kg fuel) 3.71 UHC (g/kg fuel) 12.70 CO (g/kg fuel) 257.00

Full chem. 24.05 (46) 21.83 (50) 1.35 0.00012(33) 25.63 (6.6) 46.00 (2.3) 110.00 (2.7) 23.04 (42) 20.99 (46) 1.26 0.14 (0) 0.021 (5) 57.80 (6.8) 278.00 (3.5) 44.53 (25) 41.86 (28) 1.39 1.01 (22) 3.54 (4.6) 13.60 (7.1) 359.00 (40)

26.12 (34) 24.00 (39) 1.35 0.14 (0) 0.021 (5) 58.60 (5.5) 279.00 (3.1)

47.70 (20) 44.97 (23) 1.51 1.00 (20) 3.12 (16) 14.30 (13) 308.00 (20)

DAC 1e-3

27.50 (39) 24.18 (45) 1.44 0.00018 (0) 24.49 (1.8) 47.30 (0.42) 112.00 (1.3)

DAC 1e-4

46.66 (22) 43.99 (25) 1.44 0.86 (3.6) 3.47 (6.5) 12.70 (0) 277.00 (7.8)

26.52 (33) 24.38 (38) 1.34 0.14 (0) 0.02 (0) 58.60 (5.5) 279.00 (3.1)

27.87 (38) 25.51 (42) 1.43 0.00018 (0) 24.06 (0.04) 46.50 (1.3) 111.00 (1.8)

DAC 1e-4

42.71 (28) 40.14 (31) 1.34 0.93 (12) 3.80 (2.4) 14.10 (11) 311.00 (21)

23.41 (41) 21.37 (45) 1.24 0.13 (7.1) 0.021(5) 58.40 (5.8) 281.00 (2.4)

24.36 (46) 22.11 (50) 1.33 0.00014(22) 25.88 (7.6) 45.70 (3.0) 111.00 (2.7)

DAC 1e-3

42.04 (29) 39.52 (32) 1.30 0.87 (4.8) 3.52 (5.1) 13.30 (4.7) 278.00 (8.2)

22.92 (42) 20.93 (46) 1.20 0.13 (7.1) 0.02 (0) 58.90 (5) 281.00 (2.4)

24.72 (45) 22.59 (49) 1.25 0.00018 (0) 24.73 (2.8) 46.30 (1.7) 111.00 (1.8)

EDAC 1e-4

Table 3.13 DI engine simulations using the Chalmers n-heptane mechanism (61 species, 262 reactions) Apply DAC to all cells Apply DAC to cells that contain no liquid fuel

(continued)

37.93 (36) 35.50 (39) 1.22 0.94 (13) 4.34 (17) 14.70 (16) 311.00 (21)

20.98 (47) 19.04 (51) 1.15 0.14 (0) 0.007 (65) 58.80 (5.2) 283.00 (1.7)

22.38 (50) 20.25 (54) 1.20 0.00017(5.6) 26.99 (12) 45.00 (4.5) 110.00 (2.7)

EDAC 1e-3

120 3 Acceleration of Multi-Dimensional Engine

Full chem.

(d) FTP5 Dual injection case Tot. time (h) 58.49 Chem. time (h) 56.76 DAC overhead (h) N/A Soot (g/kg fuel) 0.76 NOx (g/kg fuel) 7.65 UHC (g/kg fuel) 5.91 CO (g/kg fuel) 115.00

Table 3.13 (continued)

48.12 (18) 45.01 (21) 1.40 0.84 (11) 5.48 (28) 4.15 (30) 180.00 (57)

44.04 (25) 40.98 (28) 1.27 1.20 (58) 5.37 (30) 9.00 (52) 330.0 (187)

Apply DAC to all cells DAC 1e-4 DAC 1e-3 46.83 (20) 43.73 (23) 1.34 0.78 (2.6) 6.85 (10) 5.14 (13) 130.00 (13)

43.15 (26) 40.22 (29) 1.20 0.89 (17) 6.38 (17) 6.45 (9.1) 179.00 (56)

42.08 (28) 39.16 (31) 1.18 0.76 (0) 7.09 (7.3) 5.70 (3.6) 117.00 (1.7)

Apply DAC to cells that contain no liquid fuel DAC 1e-4 DAC 1e-3 EDAC 1e-4

38.49 (34) 35.61 (37) 1.12 0.86 (13) 7.25 (5.2) 6.57 (11) 177.00 (54)

EDAC 1e-3

3.4 An Extended Dynamic Adaptive Chemistry (EDAC) Scheme 121

122

3 Acceleration of Multi-Dimensional Engine

Fig. 3.22 Comparison of number of species using different DAC schemes (FTP5D, dual-injection, Chalmers mechanism)

Fig. 3.23 Comparison of computer times of different solvers (Open symbols: time reduction; Closed symbols: computer time)

on that cut plane when the various DAC schemes were applied. The top-right plot shows the original DAC scheme when decoupling the spray is not considered, and the bottom-left one excludes the spray containing cells in the scheme. The bottomright is the EDAC scheme without spray cells. It is seen if the spray containing cells are excluded, the number of species is increased, especially near nozzle region where the liquid droplets cluster. The present EDAC scheme is able to reduce computational times, and its efficiency increases with the size of the mechanism. It was also combined with the adaptive multi-grid chemistry (AMC) model and applied to simulate the GM-Fiat engine that was investigated previously using the AMC model alone. In addition, the detailed LLNL n-heptane mechanism was used show that it is now practical to use mechanisms of such large size for DI engine simulations. Figure 3.23 shows that the computational time is reduced by a factor of 3 using the AMC alone. By combining with the EDAC scheme, the new chemistry solver reduces the computer time by a factor of more than 4. As seen Fig. 3.24(a–d), the predicted emissions of the efficient methods are highly consistent with those of the full chemistry solver.

3.4 An Extended Dynamic Adaptive Chemistry (EDAC) Scheme

123

Fig. 3.24 Comparison of chemistry solvers and experimental data. a Soot emission. b NOx emission. c UHC emission. d CO emission

An additional simulation with SOI timing of -21 °ATDC from the SOI sweep was performed with the detailed LLNL mechanism. In this case dynamic loadbalancing parallel scheme (Shi et al. 2009b) was also used to parallelize the computation of the efficient chemistry solver. The simulation took 116.0 h wall time and 426.0 h CPU time using four individual Pentium IV 3.0 G PCs, as compared to an estimated 4 months or 13 months if the full chemistry solver were used on four processors or a single processor, respectively. The simulated pressure trace matches the experimental data well, as shown in Fig. 3.25. Considering the capability of current multi-core processors, the parallel computation was also repeated on a PC with an Intel Core2 2.4 G Quad-CPU, and it took 64.6 h to complete and the total CPU time was 241.8 h.

3.5 Summary In order to accelerate the chemistry solver of the improved ERC KIVA3v2 engine CFD code, an adaptive multi-grid chemistry (AMC) model and an extended dynamic adaptive chemistry (EDAC) scheme have been developed. The methods

124

3 Acceleration of Multi-Dimensional Engine

Fig. 3.25 Comparison of experimental pressure trace with simulated results using full LLNL mechanism (543 species)

have been systematically studied with respect to their sensitivity to the model constants, and their accuracy and efficiency for HCCI and DI engine simulations. It was found that by combining both methods and with the use of the present ERC reduced n-heptane mechanism the new chemistry solver accelerated the calculation more than ten fold for HCCI engine simulations and by as much as four-fold for DI simulations, without losing prediction accuracy as compared to the full chemistry solver. A successful example of applying the very detailed LLNL nheptane mechanism (543 species) to a DI engine simulation was also demonstrated in this chapter. To the authors’ knowledge, this is the first attempt to use chemical mechanisms of this large size in DI engine simulations. The efficiency of the new chemistry solver is essential for engine optimization using CFD tools with detailed chemistry, as will be further examined in Chap. 6.

Chapter 4

Assessment of Optimization and Regression Methods for Engine Optimization

Engine optimization problems by nature are multi-objective problems, which involve simultaneously optimizing multiple design parameters. Based on the review of optimization methods in Chap. 2, it was determined that multi-objective genetic algorithms (MOGA) are an appropriate optimization method. This chapter assesses the performance of different MOGAs for engine optimization problems. The assessment was conducted using three popular MOGAs [l-GA (Coello Coello and Pulido 2001), NSGA II (Deb et al. 2002), ARMOGA (Sasaki and Obayashi 2005)] applied to a heavy-duty diesel engine operated at a high-load condition. In addition to this assessment, the niching technique of NSGA II was also evaluated. Convergence and diversity metrics of MOGAs were defined to complete the assessment of different niching techniques. Regression analysis was then conducted on the design datasets that were obtained from the optimizations with two niching strategies. Four regression methods, including K-nearest neighbors (KN), Kriging (KR), Neural Networks (NN), and Radial Basis Functions (RBF), were compared. The purpose of the comparison was to evaluate whether it is appropriate to use a regression tool to partially replace the actual CFD evaluation tool in engine optimization design using genetic algorithms. As a result, a dynamic learning strategy was proposed.

4.1 Assessment of Multi-Objective Genetic Algorithms The assessment was conducted by comparing the performance of the three MOGAs for optimization of a heavy-duty diesel engine under high-load. The effects of the piston geometry, spray-relevant parameters, as well as initial swirl ratio on emissions and fuel economy were of particular interest. Reductions of NOx and soot emissions were two main objectives. In addition, Gross Indicated Specific Fuel Consumption (GISFC) was also investigated. Tables 4.1 and 4.2 list the engine specifications and operating conditions, respectively.

Y. Shi et al., Computational Optimization of Internal Combustion Engines, DOI: 10.1007/978-0-85729-619-1_4, Ó Springer-Verlag London Limited 2011

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Table 4.1 Engine and injector specifications

Engine

Caterpillar DI diesel

Combustion chamber Swirl ratio Bore 9 Stroke (mm) Bowl width (mm) Displacement (L) Connection rod length (mm) Geometric compression ratio Fuel injector nozzles Spray pattern included angle Rail pressure (bar) Nozzle orifice diameter (mm)

Quiescent, direct injection 0.7 137.16 9 165.1 97.8 2.44 261.6 16.1:1 8 holes, equally spaced 154° 2,000 0.217

Table 4.2 Baseline operating condition

Speed (rev/min)

1672

IVC temperature (K) IVC pressure (kPa) SOI (°BTDC) Injection quantity (mg/cyc) Injection duration (°CA) EGR level (%) Global equivalence ratio O2 Concentration (vol.%)

385 310 13 229 19 25 0.6 17.65

The piston geometry was parameterized and automatically meshed using an automated grid generator, Kwickgrid (Wickman 2003), which simplifies the grid generation process by decoupling the geometry from the mesh structure. The piston shape is described using a reduced set of dimensionless input parameters, allowing more flexibility than the standard KIVA grid generation code (Amsden 1993). The input parameters include outline parameters that define the overall piston bowl shape, and Bezier curvature parameters that describe the curves between the outline points. For example, two outline parameters, Ax and Bx, and three Bezier curvature parameters, Xa0, X0a, Xab, were used for defining the combustion chamber geometry in the optimization study of Chap. 6, and they are also illustrated in Fig. 4.1. As shown in the figure, points A and B determine the major geometrical dimensions of the chamber, and curves 1–3, corresponding to Xa0, X0a, and Xab control the shapes. Bx is defined as the ratio of the bowl diameter and the cylinder diameter. Ax is defined as the ratio of the bottom bowl and outer bowl diameters. If the position of one outline point varies in the z-direction, the height is normalized by bowl depth, e.g., Az and Cz in Fig. 6.35. After the outline parameters are determined, the Bezier parameters can vary to cover a wide range of different piston shapes. Quadratic Bezier curves are considered, such that: given two fixed points A and B, and Bezier point 3 (c.f., Fig. 4.1), the Bezier curve can be written as: BðtÞ ¼ ð1  tÞ2 PA þ 2ð1  tÞtP3 þ t2 PB ;

t 2 ½0; 1;

ð4:1Þ

4.1 Assessment of Multi-Objective Genetic Algorithms Fig. 4.1 Parameters of bowl geometry

127

cylinder axis

B

A - bottom bowl diam. B - bowl diam. 1-3 - points

1

2

A

3

cylinder wall

Fig. 4.2 Examples of Bezier curvature parameters

where PA, PB, and P3, are the coordinates of the points A, B, and 3, respectively. The related Bezier curvature parameters are given by Xab ¼

x3  xA ; xB  xA

ð4:2Þ

Yab ¼

y3  y A : yB  y A

ð4:3Þ

Examples of the Bezier curves are given in Fig. 4.2, in which Yab = 0. When Xab = 0, the point 3 is identical to point A, and the resulting curve is a straight line between points A and B. If Xab is greater than unity, a reentry bowl shape is reproduced. To keep bowl volume constant, the depth of the bowl is usually varied. An approximating and iterative methodology is used to generate meshes with the defined geometry and to maintain the compression ratio and user-selected mesh size (usually about 2 mm or smaller) until a convergence criterion is satisfied. Table 4.3 lists the investigated ranges of these five geometrical variables, as well as the spray injection angle and swirl ratio. This technique enables a wide search of different piston designs, including re-entrant shapes and open-type bowls. The ERC improved KIVA3v2 code was employed for the CFD evaluation of the engine design. It is also noted that the Shell/CTC combustion model was used to save computational time. The sub-models of the KIVA code are summarized in Table 4.4.

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Table 4.3 List of optimization parameters and their ranges Parameter

Range

A- diam. of bowl bottom B- bowl diameter 1 – Bezier curve control point (from 1 to 2) 2 – Bezier curve control point (from 2 to 1) 3 – Bezier curve control point (from A to B) Injector spray half-angle Swirl ratio

74–80% bowl diameter 71–84% cylinder diameter 0.1–0.7 0.3–0.9 0.8–1.5 60–85° 0.5–2.0

Table 4.4 KIVA3v2 sub-models Functions Models Turbulence Spray development Spray Impingement Ignition and Combustion Soot NOx

Modified RNG k-e (Han and Reitz 1995) KH-RT Model (Beale and Reitz 1999), Standard KIVA model (O’ Rourke and Amsden 2000) Shell/CTC (Kong et al. 1995) Two-step model (Nishida and Hiroyasu 1989, Patterson et al. 1994) Extended Zel’dovich (Heywood 1988)

Table 4.5 Parameter configurations for the assessment of MOGAs Group 1 2 3 MOGAs Coding Crossover possibility Mutation possibility Start gen. of adaptation Pops. Gens. Total Evals.

l-GA Binary 0.7 0.1 N/A 4 320 1,280

NSGA II Binary 0.9 0.143 N/A 4 320 1,280

ARMOGA Real 0.9 0.143 20 4 320 1,280

4

5

NSGA II Binary 0.9 0.143 N/A 32 40 1,280

ARMOGA Real 0.9 0.143 15 32 40 1,280

Based on the discussion in Chap. 2, the performance of MOGAs is defined by optimality and diversity, namely the goals for multi-objective optimization problems are: 1. To find a set of solutions as close as possible to the Pareto-optimal front. 2. To find a set of solutions that are as diverse as possible. Correspondingly, the five groups of numerical experiments listed in Table 4.5 were evaluated for the design optimization of the engine specified in Table 4.1. Both an in-house code (for l-GA) and commercial optimization software, modeFRONTIER (for NSGA II and ARMOGA) were used. Because the goals of MOGAs are to find a set of solutions as close as possible to the true Pareto front and also to make the solutions as diverse as possible, the corresponding features need to be quantified with the information given by the Pareto solutions. Four quantities were defined for assessing MOGAs as follows: the Number of Pareto

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Solutions (NPS), the Mean Distance to the Pareto Front (MDPF), the Mean Distance between Extreme Pareto Solutions (MDEPS), and the Mean Deviation of the Distance between Neighbor Pareto Solutions (MDDNPS). It is obvious that NPS can be observed from the Pareto front directly, and it represents how many optimal designs are available to the decision maker. The other three quantities are defined the next. The optimization goal is to minimize fuel consumption and emissions represented by the three objectives that are GISFC, NOx, and soot. However, the three objectives have different orders of magnitude. Therefore, it is necessary to normalize the objectives with the corresponding maximum and minimum values of the investigated group of solutions. By doing so all objectives are given the same weight in assessing MOGAs. The MDPF indicates how close the Pareto solutions of a MOGA are to the true Pareto front. Since the location of the true Pareto front for the engine design problem is unknown, the global maximum and minimum values of each objective of Pareto solutions were used and the objectives of every Pareto solution were normalized with the global values. The normalized values were then averaged to yield MDPF, which is expressed mathematically as M N Objj  Objglobal min 1X 1X MDPF ¼ M i¼1 N i¼1 Objglobal max  Objglobal

! ;

ð4:4Þ

min

where M is the NPS for a MOGA, and N is the number of objectives. It is obvious that smaller MDPF is preferred for approaching the true Pareto front. It is of interest to investigate the boundaries of the objective-space defined by the Pareto solutions of each MOGA, because it represents how large the space is covered by optimal solutions. Similar to the MDPF, MDEPS is also normalized with the global maximum and minimum values of each objective. The extreme Pareto solutions are searched for each MOGA on its Pareto front, which have either maximum or minimum objective values. These are referred to as the group maximum and minimum values. Therefore the MDEPS is defined as: MDEPS ¼

N Objgroup 1X N i¼1 Objglobal

 Objgroup max  Objglobal max

min

;

ð4:5Þ

min

where N again is the number of objectives. Larger MDEPS implies that the Pareto solutions for the MOGA are distributed in a larger optimal objective-space. A large optimal objective-space is a desirable feature of MOGAs. However, it is also preferred that the optimal solutions are distributed in the optimal space uniformly. The MDDNPS is used to evaluate how evenly the optimal solutions are spread. Different from the previously defined two quantities, the normalization of MDDNPS is based on the group maximum and minimum objective values. The neighbor solution is defined as a solution on the Pareto front, which has the smallest Euclidean distance to another Pareto solution, and the Euclidean distance between solutions i and j is given by:

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Fig. 4.3 Assessment of performance of MOGAs. a NPS. b MDPF. c MDEPS. d MDDNPS

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !2 u N u1 X Obji;k  Objj;k t : Dij ¼ N i¼1 Objgroup max;k  Objgroup min;k

ð4:6Þ

After all neighbor solutions are determined, their mean value can be obtained, and then the standard deviation is given by vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u M  u 1 X 2 ð4:7Þ MDDNPS ¼ t Di;neighbor  Dmean ; M  1 i¼1 where M is the NPS. Thus, a smaller MDDNPS indicates a more even spread of the Pareto solutions in the objective-space. The performance of the various MOGAs was assessed by Shi and Reitz (2008a), and the results of an engine study are presented in Fig. 4.3. As observed in Fig. 4.3(a), NSGA II with a population number of 32 produces the most Pareto solutions. It is also observed that MOGAs with large populations generate more Pareto solutions than those with small populations. Like the proverb ‘‘A good beginning is half done’’, a large initial population enlarges the search

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131

parametric space and thus increases the possibility that initial designs contain needed characteristics to generate optimal designs with respect to all objectives of interest. Therefore, the increased randomicity introduced by the large initial populations is very important for highly non-linear multi-objective optimization problems (MOPs), such as engine optimal design. However, simply increasing the initial population does not help increase the number of Pareto solutions for MOGAs, such as for l-GA. Because the merits of the initial designs need to be preserved in the subsequent evolutionary processes, and the populations are required to be of the same order of magnitude as the initial populations. A large population in each generation allows for tournament selection and crossover to be conducted in a large space that diversifies objectives, and thus produces more trade-offs that lead to more Pareto solutions. The greater the number of generations, the closer the MOGAs approach the true Pareto front, and this is illustrated in Fig. 4.3(b), which also shows that l-GA and ARMOGA with population 4 give smaller values of MDPF compared to NSGA II and ARMOGA with population 32. The exception is NSGA II with population 4 gives the worst results of MDPF, which indicates that NSGA II does not perform well when its population size is too small. The MDEPS shown in Fig. 4.3(c) represents the ability of a MOGA to extend the boundaries of its objective-space. As indicated in this figure, NSGA II performs better than the other MOGAs in general. MOGAs with large populations generally outperform the ones with small populations, and this again is due to the effect of the initial randomicity discussed before. It is also interesting to observe that ARMOGA with a population of 4 has the best MDEPS after the number of evaluations reach 1,000, which is due to the adaptive range searching technique applied in the algorithm. The start of adaptation for this case begins at the 20th out of the total of 320 generations, and there is increasing possibility that the search range will focus on a parametric space that produces solutions that are distributed on the boundaries of the objective-space with increasing generations. Although ARMOGA with a population size of 32 started its initial adaptation at the 15th generation, compared to its total 40 generations, the chance of searching boundaries was less. Unfortunately in the current study it seems that this case focused its search range far from the boundaries during the last generations, which resulted in the decreased MDEPS. This finding suggests that the adaptive range technique is a very promising method to extend the optimal objective-space, but it requires a sufficient number of generations, so an early application of the adaptation is recommended. Figure 4.3(d) shows MDDNPS that represents how evenly the optimal solutions are spread along the Pareto front. NSGA II again shows better performance, especially when it is run with large populations. It is understandable since NSGA II employs an explicit and parameter-independent methodology to avoid a potential optimal solution being selected in an optimization cycle that is surrounded by crowded existing solutions. The niching technique of ARMOGA differs from NSGA II in that it relies on the setup of two niching parameters, which are also problem-dependent. Because of the adaptation of the search space, the capacity of evenly distributing optimal solutions using ARMOGA is limited.

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Fig. 4.4 Pareto solutions distributed in the objective-space. a Pareto solutions from 640 evaluations. b Pareto solutions from 1,280 evaluations

Although l-GA also applies the concept of a crowding distance into its evolutionary processes, the diversity-preservation of the l-GA depends on its external memory and non-repeatable initial populations, which results in the largest value (worst performance) of MDDNPS. Figure 4.4(a) and (b) further illustrates the Pareto solutions that are distributed in the objective-space and are collected from 640 to 1,280 evaluations, respectively. Although more Pareto solutions are produced as the optimization process proceeds, it is seen in Fig. 4.4(a) and (b) that the location of the Pareto front does not move significantly from 640 evaluations to 1,280 evaluations. This indicates that the optimization process can be ceased at 640 evaluations or even earlier. Together with Fig. 4.3(a), it is observed in Fig. 4.4 that the number of Pareto solutions using NSGA II or ARMOGA is much larger than that of l-GA which was employed in the engine optimization study of Genzale et al. (2007). When using a large population size, the Pareto solutions produced by NSGA II and ARMOGA sufficiently and uniformly cover the Pareto front as depicted in Fig. 4.4.

4.2 Assessment of NSGA II: Niching Technique, Convergence and Diversity Metrics 4.2.1 Design- and Objective-Space Niching of NSGA II In engineering optimization problems, it is usually required to achieve diversified solutions. This requirement can be further explained by an example of engine optimization. For instance, in-cylinder clean combustion techniques are usually combined with aftertreatment methods for the reduction of emissions. In this case, optimal solutions of in-cylinder combustion can guide the selection of aftertreatment devices. This requires that the optimization process provides solutions with

4.2 Assessment of NSGA II

133

Fig. 4.5 Illustrations of Pareto solutions, ranking and crowding distance

diversified objective functions, such as emission results. However, under other circumstances, more diversified parameters of the solutions indicate that it is more likely to obtain a design that can minimize the changes to the current baseline design in order to save redesigning costs, such as the piston geometry of engines. The diversity of optimal designs may focus on different aspects (either on the objective-space or design-space) based on the requirements of customers and designers. This can be achieved by performing different niching strategies with MOGA, as shown next. Although it is applied with different methodologies in different MOGAs, the niching strategy is a method that can detect whether optimal designs are forming a crowded cluster, and if so, to guide the MOGA to produce more diversified designs based on the existing information. Figure 4.5 illustrates the concepts of rank and crowding distance. As shown, the solid circles are the Pareto cases that dominate (out-perform) other cases. However, they do not dominate each other, and thus they form a non-dominated front defined as the first rank. The same procedure can be applied to the rest of the solutions to find a second rank, and so on until every solution is assigned a rank. The crowding distance is defined by the average distance of a solution to its nearest neighbors. For example, the crowding distance of solution i in Fig. 4.5 is the average side-length of the rectangle (the dashed box). The mathematical definition of the crowding distance can obviously be applied to higher dimensions, although it is only shown in a 2-D plot here for a clear view. Therefore, N populations will be selected from 2 N combined populations based on the competition rules of NSGA II. In this way, a crowded cluster of solutions can be prevented from evolving into the next generation, and the optimal solutions can be distributed on the Pareto front more uniformly. In the original NSGA II source code, such niching strategy is applied to the objective-space which ensures that diversified objective functions are produced during the optimization process. The NSGA II source code was modified to integrate the niching strategy to the design-space so that more diverse design parameters can be expected. It was thought that performing both niching strategies concurrently to the

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4 Assessment of Optimization and Regression Methods for Engine Optimization

objective- and design-spaces would reduce the optimization efficiency, and thus either the objective niching or the design niching was performed for each of the case studies.

4.2.2 Convergence and Diversity Metrics Observation on the movement of the Pareto front as the optimization proceeds indicates if the optimization process moves towards convergence. However, if the number of objectives exceeds three, visualization of the Pareto front becomes impossible. Therefore, a convergence metric of the optimization process using MOGA has to be defined in order to better monitor the optimization process. Defining a convergence metric can be regarded as reducing the dimensionality of the Pareto front to one-dimension. The method proposed by Deb and Jain (2002) was adopted and modified here for engine optimization studies and it is described in the following steps. 1. Identify the Pareto (non-dominated) solutions of each generation that has been done, and those n solutions form a solution pool P; 2. From the second generation, the Pareto solutions of the current generation can be compared with solutions in the pool P that is formed by the previous generation(s) in Step 1. For each Pareto solution of the current generation, calculate the smallest normalized Euclidean distance to the n solutions of the pool P using vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u M  uX fk;i  fk;j 2 ; j ¼ 1; . . .; n; ð4:8Þ di ¼ min t fkmax  fkmin k¼1 where M is the total number of objectives, and fkmax and fkmin are the maximum and minimum values of the k-th objective from all n solutions in the pool P; 3. A convergence metric is determined by averaging the normalized distance for all nn Pareto solutions of the current generation: CN ¼

1 Xnn d; i¼1 i nn

ð4:9Þ

4. In order to keep the value of the convergence metric within [0,1], it is normalized by its maximum value after all N generations are assigned a convergent value from Step 3:  j ¼ C j = maxðCi ; i ¼ 1; . . .; NÞ; C

j ¼ 1; . . .; N:

ð4:10Þ

Usually, the maximum value is from the beginning generations, e.g., the second generation.

4.2 Assessment of NSGA II

135

Fig. 4.6 Illustration of diversity metric

In order to assess the diversity of the Pareto solutions in either the objectivespace or design-space, a corresponding metric is needed. Although more complicated methods were employed in the studies of Deb and Jain (2002) and Farhang-Mehr and Azarm (2002), this work introduces a simplified method for measuring the diversity, which is proper for the present engine optimization and similar engineering problems as well. Taking the objective-space for example, the method divides the space into many sub-grids based on the user-specified spans and if more sub-grids contain sole or few Pareto solutions, the results are deemed to be more diverse. As further illustrated by Fig. 4.6, the set of the Pareto solutions in the left figure is better than the right one in terms of the diversity of the two objectives. The method can also be extended to study more objectives. However, since the number of Pareto solutions is usually of the order of 100 in typical engine optimization problems, it is suggested that the number of studied objectives should not exceed 3 and the number of spans of each objective should not exceed 10 in order to keep the total sub-grids of the order of 1,000. Obviously, the same method can be applied to investigate the design-space as well. To further quantify the diversity metric, different weights are assigned to the subgrids that contain different numbers of Pareto solutions, and these sub-grids containing fewer solutions are given higher weights (1/n, n is the number of Pareto solutions that are located in that grid). Therefore, the averaged weighting summation for all sub-grids that include the Pareto solutions represents a quantified diversity metric, and a larger value indicates more diversified solutions (maximum value is 1).

4.2.3 Assessment of Niching Strategies Optimization results from using KIVA3v2 and NSGA II with two niching strategies are compared in terms of their convergence and diversity metrics and performance. The same optimization case of high-load condition evaluated in Sect. 4.1 (Shi and Reitz 2008a) was repeated with the two niching techniques.

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Fig. 4.7 Comparison of convergence metric. a Convergence metric. b Pareto front from the optimization using the objective niching. c Pareto front from the optimization using the design niching

Figure 4.7(a) shows normalized convergence metrics using objective niching and design niching. The fluctuations that appear in both curves imply that the later generations in the optimization process do not necessarily produce solutions better than the previous ones. However, in general, the value of the convergence metric becomes smaller as the optimization proceeds. It is seen that both optimization processes converge very fast (in the first ten generations), and after about 20 generations, the curves become relatively flat, which indicates that the Pareto front does not move significantly from generation 20 to the end of the optimization. To further illustrate this, Pareto fronts in the objective-space of generations 20 and 51 for the two niching strategies are depicted in Fig. 4.7(b) and (c), respectively. It is observed that the Pareto fronts of generation 20 and 51 overlap in many places and their relative locations with respect to the origin are very close as well. The consistency between Fig. 4.7(a–c) also proves the fidelity of the present method of calculating the convergence metric for MOGA. This figure also concludes that the objective niching and the design niching perform similarly in terms of their convergent rates. The results discussed here reveal the significance of dynamically generating the convergence metric in optimization, because the designer can have sufficient confidence to terminate the optimization process if it is seen that further evaluations are redundant.

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Fig. 4.8 Comparison of performance (MDPF)

Since the study of convergence metrics of the two niching methods merely represents their historic performance (comparison between the later generations and previous generations), it is important to also compare the two methods directly in terms of the optimality of their Pareto solutions. The same method (Shi and Reitz 2008a) described in Sect. 4.1 was used to assess their performance by comparing two quantities. The comparison is given in Fig. 4.8 which shows that the two niching methods perform closely with respect to these two quantities, although it is seen that the design niching method generated slightly better results since its MDPF values are a little smaller than those with objective niching. The diversity metric was analyzed based on the values of the objectives and design parameters of the Pareto solutions of the optimizations using the two niching methods. For the objectives, the investigated ranges were determined automatically by the maximum and minimum values of that objective over all Pareto solutions up to the current generation, and the ranges were discretized with 10 spans (this corresponds to 1,000 grids in the three-dimensional objectivespace). For the design parameters, the investigated boundaries were pre-specified prior to the optimization, and in this work, only three parameters, the SOI, swirl ratio, and spray angle, were analyzed. Because the investigated range of the start of injection was limited to -12 to -15 ATDC (Shi and Reitz 2008a), it was discretized by 3 spans and 10 spans were used for the other two parameters, which are in ranges of 0.5–2.0 and 60.0–85.0 for swirl ratio and spray angle, respectively. Figure 4.9(a) shows that the diversity metrics in the objective-space for the two niching methods are close, which further indicates that using both niching strategies can produce similar sets of Pareto solutions with respect to the diversified objectives, i.e., emissions and fuel consumption. But, by simply altering the objective niching to design niching, the optimization process produced more diversified designs as seen in Fig. 4.9(b). At the end of the optimization for objective niching, there was no grid in the design-space containing just one Pareto solutions, and there was one grid containing two Pareto solutions, and the undesirable result was that 27 Pareto solutions were clustered in one grid. For the

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Fig. 4.9 Comparison of diversity metric. a Diversity metric in the objective space. b Diversity metric in the design space

design niching, there were 6 grids containing only one Pareto solution, and a maximum 14 Pareto solutions were found in one grid. The results prove the superiority of design niching when implemented into the NSGA II code for engine optimization.

4.3 Assessment of Regression Methods for Replacing CFD Evaluations Regression analysis over existing CFD evaluation results reveals the relationship (response surface) between design parameters and objective functions. With sufficient existing datasets and regression methods of high fidelity, design parameters can be mapped to objective functions through algebraic expressions, and thus this can be used to partially or entirely substitute real CFD evaluations in practical optimization problems to save computational expense. This section investigates the four regression methods (including K-nearest neighbors (KN), Kriging (KR), Neural Networks (NN), and Radial Basis Functions (RBF)) that are described in Chap. 2 in order to assess their performance in engine optimization problems. Datasets calculated from KIVA were used to train those regression methods to generate corresponding response surfaces that reflect the relationships between the design parameters and the objectives. Predictions of an entire GA generation (24 cases with the present population size) based on the response surfaces (virtual design) were compared with the results calculated by the KIVA code (real design), and the relative errors between the objectives of the virtual and real designs were used to quantify the performance of each regression method. To gain more statistical information, the mean, maximum, median, and minimum values of the error are reported as well as the standard deviation of the error.

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139

As a preliminary test, a Design of Experiment (DoE) method, the Optimum Latin Hypercube method, was used to produce a set of design parameters. A total of 120 cases were created based on the investigated range (Shi and Reitz 2008a) of the design parameters and the KIVA code was first run to obtain the objectives of these cases. This process created a data pool (more uniformly distributed than the GA generated data pool) to train the regression methods. Since KIVA results are available from the previous optimization studies, several generations were selected to test the performance of the regression methods, and without losing generality, only generations from the group using objective niching are considered here. According to Brahma et al. (2008) and the authors’ experience, a logarithmic transformation (similar to the concept of Box-Cox transformation (Draper and Smith 1981)) was applied to the objectives, i.e., the objectives (GISFC, NOx, and soot) of the trained dataset were transformed by a logarithm function and correspondingly the predicted results based on this dataset need to undergo a power of 10 transformation before comparing with the KIVA results. It is noted that the values of soot emissions ranged from 10-3 to 101 g/kg fuel in the present study, and if a logarithmic transformation was directly applied, the resulting values could be negative and positive. In the authors’ experience, this deteriorates the prediction accuracy of the virtual designs, and thus the logarithm transformation for soot emissions was given by: sootlog ¼ 1  logðsootÞ

ð4:11Þ

to ensure positive soot values after logarithmic transformation. Another advantage of using this formula is that it prevents unrealistic negative soot values from being produced for the virtual designs. The generated response surfaces using the four regression methods were used to predict the objectives for the cases from five generations (11, 21, 31, 41, and 51) of the group using the objective niching, and only the mean errors are reported here. It is seen in Fig. 4.10 that the mean error of the GISFC is the smallest, which implies that the relationship between the GISFC (i.e., engine power since the amount of injected fuel was fixed) and the design parameters is less complicated than that of emissions and thus can be well captured by the regression methods. The complicated influences of the design parameters on the soot emissions cause unsatisfactory prediction accuracy, as shown in Fig. 4.10(c). In general, the mean errors of all regression methods for each objective are of the same order of magnitude, and the RBF method performs slightly better than the others on the emissions, which could be due to its suitability for scattered data (generated by DoE here) interpolations. Further observation shows that the implementation of the logarithm transformation improves the prediction accuracy for most of cases, especially for soot emissions, although this is not true for the RBF method, which could be due to the use of Gaussian function (the exponential transformation is already applied intrinsically) in the RBF. As stated before, the ultimate goal is to explore the feasibility of using a regression method to partly replace actual computationally-expensive CFD

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Fig. 4.10 Comparison of regression methods trained with a dataset generated with a DoE method. a Mean percentage error for GISFC. b Mean percentage error for NOx. c Mean percentage error for soot. d Legend

simulations. The next comparisons aim at this purpose, and the methodology is described as follows. As can be seen in Fig. 4.10, the prediction accuracy of the emissions is not satisfactory for replacing a part of the real CFD simulations. This can be understood, because it is somewhat unreasonable to expect 120 DoE-generated designs with nine parameters over such wide ranges to reveal all the complicated relationships between the design- and objective-spaces for the current engine design problem. However, the inherent characteristics of the genetic algorithms provide a method for possible improvement of utilizing regression methods. Since each of the cases in a GA generation inherits design features from the previous generations, it is expected that this could benefit the learning process of regression methods if all previous generations were trained to form the response surfaces, which are then used to predict the next generation. It is also of interest to compare results trained on these two niching groups to investigate how the niching method influences the training process by producing different data pools for the regression methods. The logarithmic transformation helped to improve the prediction accuracy for the KN, KR and NN methods and

4.3 Assessment of Regression Methods for Replacing CFD Evaluations

141

Fig. 4.11 Comparison of regression methods trained with datasets from the optimization process using different niching strategies: percentage errors of GISFC. a Mean percentage error. b Maximum percentage error. c Median percentage error. d Minimum percentage error. e Standard deviation of the percentage error. f Legend

thus it was adopted for them, but for the RBF method no transformation was applied. Statistical studies of the relative errors between virtual designs predicted by the regression methods and the real designs from KIVA simulations are reported in

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4 Assessment of Optimization and Regression Methods for Engine Optimization

Fig. 4.12 Comparison of regression methods trained with datasets from the optimization process using different niching strategies: percentage errors of NOx. a Mean percentage error. b Maximum percentage error. c Median percentage error. d Minimum percentage error. e Standard deviation of the percentage error. f Legend

Figs. 4.11, 4.12, and 4.13 for GISFC, NOx, and soot, respectively. Five generations (11, 21, 31, 41, and 51) were analyzed for each group. For each analyzed generation, all of its previous generations were used as the training dataset. The solid lines with solid symbols represent the error of the regression methods trained

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143

Fig. 4.13 Comparison of regression methods trained with datasets from the optimization process using different niching strategies: percentage errors of soot. a Mean percentage error. b Maximum percentage error. c Median percentage error. d Minimum percentage error. e Standard deviation of the percentage error. f Legend

with the dataset from the optimization process using objective niching, and the dashed lines with open symbols represent design niching. Compared to results of Fig. 4.10 the regression methods trained with datasets from the optimization processes show a similar trend that the mean error of GISFC is the smallest and is followed by NOx and soot. But the absolute values of the

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4 Assessment of Optimization and Regression Methods for Engine Optimization

mean errors are much smaller, which indicates that it is important to dynamically learn from previous datasets in order to better predict the next. Results predicted using regression methods trained with the dataset from the optimization process using objective niching are much better than those with design niching. This is most likely due to the proximity of designs in the dataset using objective niching since it is also seen in the figures that the K-nearest neighbors method (indicated by the black squares) performs the best in most of the cases, followed by the Kriging method. It is conjectured that the performance of interpolation of the regression method is more important than that of extrapolation if it is trained with datasets from the MOGA optimization processes. Figures 4.11, 4.12, and 4.13 also show that the errors increase with the size of the trained dataset, especially for the NN and RBF methods. A possible cause is bad-fitting or over-fitting data which could be more likely produced as the size of the trained dataset increases. This indicates that the training process does not necessarily need to be conducted over all previous existing results. Furthermore, different from training with a scattered dataset in Fig. 4.10, the RBF method did not predict satisfactory results. The neural network method behaved unexpectedly poorly in the prediction of soot emissions. Another important finding is that for all objectives, the median errors are less than the mean errors. The median errors of the K-nearest neighbors and Kriging methods are below 1, 5, 15% for GISFC, NOx, and soot if they are trained with the datasets from the optimization using objective niching, as shown in Figs. 4.11(c), 4.12, and 4.13(c), respectively. This indicates that half of the real KIVA simulations could be possibly replaced by virtual designs predicted using a reliable regression method, which promises savings in computational resources. Remaining questions are (1) does the computational expense of using a regression method exceed that of the KIVA CFD evaluations because the number of trained cases increases as the optimization proceeds? (2) prior to each generation, how to determine which cases are calculated from the regression methods and which should use KIVA in order to minimize the errors? As far as concerns about computational time, it was observed that by using the Response Surface Methods (RSM) package of modeFRONTIERTM 4.0 the learning time of the K-nearest neighbors method and the Kriging method increases approximately linearly with the number of trained data, and it is about quadratic for the RBF method and cubic for the neural network method. However, even with over a thousand cases, none of the learning times exceeded the running time of a KIVA case. This means that just one processor is needed to complete learning and evaluation of N virtual designs, and thus N-1 processors can be saved for every generation. Regarding the second concern, error control should be based on the proximity of the cases in the current generation to the trained previous cases. It is unnecessary to fix the number of virtual designs in each generation. Instead it can be determined adaptively based on the proximity.

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145

4.4 Summary The assessment of multi-objective genetic algorithms indicates that the NSGA II algorithm performs well with a large population size. As will be seen in Chap. 6, the KIVA code coupled with NSGA II enabled a variety of engine optimization studies, including studies of piston geometry, injection parameters, and others. Convergence and diversity metrics for engineering optimization problems with MOGAs are defined and quantified to dynamically monitor the optimization process. It has been shown that with dynamic learning, regression methods, especially the K-nearest neighbors and Kriging methods, predicted results in good agreement with the KIVA CFD evaluations for the next generation. A logarithm transformation in the objective-space improved the prediction accuracy for the KN, KR, and NN methods, but not for the RBF method. These findings promise a proposed methodology, where a part of the real evaluations can be replaced by virtual designs through learning from previously existing data.

Chapter 5

Scaling Laws for Diesel Combustion Systems

Scaling laws are developed to guide the transfer of combustion system designs between diesel engines of different sizes using simple formulations. In this chapter, the concepts and formulation of scaling laws are presented. A practical example is provided to study a light-duty and a heavy-duty production diesel engines using the established scaling laws.

5.1 Introduction Engine design is a time consuming and expensive process in which many costly experimental tests are usually conducted. Even with efficient and reliable CFD tools, engine optimization could take a very long time to complete. Engine design work is often repeated for different engines that share similar features. This motivates a study of scaling laws, which describe scaling relationships between engines with different sizes, such as large off-road heavy-duty diesel engines and small high-speed auto engines. CFD simulation again offers an efficient and informative option for this task. The intent of the scaling laws is to maintain geometric similarity of key parameters influencing diesel combustion, such as incylinder spray tip penetration and flame lift-off length. Based on relatively simple formulations, one well-established engine can be down-scaled or up-scaled to another engine, which has similar features as the original engine. In this way, the amount of engine design work is significantly reduced in both time and cost. Initial work was proposed by Bergin and Reitz (2005) who proved that similar combustion behavior in two different size engines can be obtained by scaling a few basic engine geometry parameters, engine speed, and the injected fuel mass. Stager and Reitz (2007) developed an extended model by adding a law to scale the flame lift-off length. The scaling laws were applied to two ideally-scaled engines where the small engine was obtained by halving the dimensions of the larger engine. Numerical results of multidimensional simulations showed that the scaling laws worked well over a range of injection timings for engines with low temperature Y. Shi et al., Computational Optimization of Internal Combustion Engines, DOI: 10.1007/978-0-85729-619-1_5,  Springer-Verlag London Limited 2011

147

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combustion, and the results also suggested that three regions could be defined in this range where turbulence and chemical kinetics timescales played different roles in influencing combustion and emissions. Shi and Reitz (2008c) conducted a CFD-based scaling study of two production diesel engines (one 0.5 L light-duty GM-Fiat engine and one 2.5 L heavy-duty Caterpillar engine). It was found that the in-cylinder pressure trace and heat release rate results could be well predicted based on the scaling laws. Emission results were well captured in combustion regions controlled by turbulent time scales. Some processes (such as soot and NOx formation) are determined by chemical reaction time scales and thus previous scaling laws had difficulty to reproduce them. The same two engines were also investigated experimentally (Staples et al. 2009), and the scaling laws in Bergin and Reitz (2005) and Stager and Reitz (2007) were validated where the Caterpillar engine was modified before testing in order to be consistent with the scaling laws. Experimental results showed that overall engine performance including IMEP and ISFC were in good agreement for two scaled engines. Extended scaling laws accurately predicted the SOC, CA10, and CA90. NOx and PM emissions matched trend-wise and in approximate magnitude. NOx emissions showed dependence on chemical timescale differences that are caused by engine speed and temperature. Higher PM emissions in the small engine were thought to be due to reduced time and increased heat transfer. Lee et al. (2010) investigated the impact of design constraints/limitations on the applications of scaling laws and identified key physical parameters that need to be respected within engine design constraints. Ge et al. (2011) applied the scaling laws for downsizing a light-duty HSDI diesel engine from 450 to 400 cc. They found that the scaling laws work well at least for engine downsizing with small size variations.

5.2 Scaling Laws Scaling laws are desired to produce identical performance and emission levels in engines of different sizes. However, it is very difficult to achieve this aim in reality. Establishment of any scaling arguments for diesel engines should at least target the following goals: (1) geometric similarity should be maximized, so that the two scaled engines have similar boundary conditions. This includes scaling of the bore, stroke, squish height, and piston bowl shape, and the resulting compression ratio should be the same in the two engines. By setting the same boost pressure and temperature, the same wall temperatures, and the same initial flow conditions, such as the swirl ratio, similar initial thermodynamic and fluid dynamic conditions prior to spray injection can be achieved in the combustion chamber; (2) similarity in spray dynamics should also be considered. Spray development has a primary effect on engine performance and pollutant emissions as it determines the mixing of the fuel and air. The aim is to have similar fuel distributions before the combustion event. It is usually quantified in terms of spray tip penetration, which is the essential parameter determining the fuel distribution; (3) similarity in the combustion

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characteristics in the scaled engines should be maintained in order to provide similar engine performance and emissions.

5.2.1 Combustion Chamber Geometry Volume-related quantities are scaled by V, such as the displacement volume and the volumes at TDC and BDC, while length is scaled by L, such as the bore, stroke, squish height and bowl diameter. The resulting compression ratios should be the same. Valve opening and closing timings, swirl, wall temperatures, boost pressures and temperatures are also kept the same. All of these scaling laws ensure that the thermodynamic and fluid dynamic conditions before spray injection are similar between two engines. As an internal flow, the diesel combustion process is strongly influenced by the piston bowl geometry. The in-cylinder flow after spray injection is dominated by the spray-induced flow because the injected droplets have much higher speeds. The surrounding gas flow is dragged by droplets and interacts with the piston bowl movement. This can form a tumble flow, which has a significant impact on the consequent processes of mixing, combustion, and pollutant formation. Optimization of piston bowl shape is thus an important part of the whole process of engine design. In engine scaling, the piston bowl shape is also kept the same so that the resulting spray targeting, and the interaction of the spray induced tumble flow and geometry are the same for the two engines.

5.2.2 Power Output The power outputs of the two engines should scale with their displacement volumes. Assuming that the down-scaled engine has the same combustion and thermal efficiencies, its power output should be scaled by the injected fuel mass m. Thus, the injected fuel mass m scales with V. The injected fuel mass is related to the fuel injector nozzle hole diameter d0 , injection velocity Uinj , and injection duration Dt by: p m ¼ ql d02 Uinj Dt: 4

ð5:1Þ

5.2.3 Spray Tip Penetration In direct injection engines spray tip penetration, which is defined as the distance between the spray plume tip and nozzle tip, is a primary parameter that characterizes the following fuel distribution and mixing. Additionally, if the spray tip penetration is too long, spray wall impingement may occur, which will lead to poor emission

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results. To maintain similarity in the fuel distributions, the spray tip penetrations should be scaled by the length scale of the cylinder, which is L. Parameters that affect spray tip penetration include the injector orifice diameter, ambient gas conditions, and fuel characteristics (Siebers 1999). Hiroyasu et al. (1978) experimentally investigated the effects of nozzle orifice size, injection pressure, fuel density, and ambient density on transient spray tip penetration. They found that spray tip penetration is directly proportional to time in the early stages of injection, but becomes proportional to the square root of time as the injection progresses according Eq. 5.2. The time duration of the first stage is defined as breakup time tbreak. Modest changes in ambient temperature had little to no effect on spray tip penetration. Even in experiments where the temperature varied from room temperature to 320C, the change in spray tip penetration was minimal. The jet disintegration theory of Levich (1962) gives consistent results and the spray tip penetration s were described using the following empirical explicit equations: 8  12 > > < 0:39t 2Dp ; t\tbreak ql ; s¼ 1   > 1 > : 2:95 Dp 4 ðd0 tÞ2 ; t  tbreak ð5:2Þ q with the breakup time scale tbreak ¼ 28:65ql d0 ðqDpÞ1=2 . ql and q are density of the liquid fuel and air, respectively. Dp is the pressure drop across the injector, which is related to the injection velocity Uinj, through Bernoulli’s principle: 1 2 : Dp ¼ ql Uinj 2

ð5:3Þ

Generally, only the second stage (t  tbreak ) is considered except for very short injections. Substituting Eq. 5.1 into Eq. 5.2 gives s2 / Uinj d0 t:

ð5:4Þ

5.2.4 Flame Lift-Off Length The combustion process of diesel combustion can be well characterized by the flame lift-off length, which is defined as the length away from the injector tip that the combusting flame stabilizes once the initial auto-ignition phase is over. Dec (1997) developed a conceptual model of DI diesel combustion based on laser sheet imaging. His study indicated that a rich reaction zone exists just downstream of the lift-off length in the central region of the fuel jet. Significant local heat release and fuel-rich product gases are generated in this region. Furthermore, it has also been hypothesized that soot formation begins in the product gas in this region under typical diesel conditions, and then the soot concentration and particle size grow as the product gas is transported further downstream.

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151

Siebers et al. (2002) investigated the effects of oxygen concentration on flame lift-off on DI diesel fuel jets, and concluded that lift-off length is inversely proportional to the ambient gas oxygen concentration. They also confirmed previously observed trends in lift-off length with respect to other parameters, such as the injector hole size, ambient gas temperature, and injection pressure. Pickett et al. (2005) extended Siebers’ study on lift-off length and studied the relationships between ignition processes and the lift-off length. A power-law relationship of the lift-off length to various parameters was summarized in their paper (Pickett et al. 2005) based on an extensive database obtained using #2 diesel fuel. The expression is: H / T 3:74 q0:85 d00:34 Uinj Zst1 :

ð5:5Þ

T is the ambient temperature. Zst is the stoichiometric mixture fraction. This correlation was also compared with a scaling law for lift-off length proposed by Peters (2000), which is based on a flame stabilization concept and given as H / Uinj Zst aT S2 L ðZst Þ;

ð5:6Þ

where aT is thermal diffusivity, and SL as a function of Zst is laminar flame speed. Equation 5.6 was found to be in reasonable agreement with Eq. 5.5 regarding to the scaling of ambient temperature and density, and injection velocity. However, it was shown that the experimental lift-off length trends for orifice diameter and ambient oxygen concentration were not in agreement with Eq. 5.6. Both injector geometry and injection conditions are of much interest to the present scaling study. Therefore, Eq. 5.5 was selected as one of the scaling arguments (Stager and Reitz 2007; Shi and Reitz 2008c; Staples et al. 2009).

5.2.5 Swirl Ratio Swirl is usually defined as organized rotation of the charge about the cylinder axis (Heywood 1988) and is generated by the confined, annular jet flow through the valve, which gives rise to strong recirculation regions and high turbulence levels (Arcoumanis et al. 1984). Due to friction swirl decays during the engine cycle but it persists through the compression, combustion and expansion processes. When swirl is discussed in an operating engine, a mathematical term swirl ratio is normally used to define the swirl, which is (Arcoumanis et al. 1984): Rs ¼

xs ; 2pN

ð5:7Þ

where xs is the angular velocity of a rigid-body rotating flow, and N represents the engine speed. In diesel engines swirl is used to improve mixing of the injected fuel and surrounding air charge. Ogawa et al. (1996) numerically investigated the

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effects of swirl ratio on NOx and soot emissions of DI diesel engines. Kook et al. (2006) focused their research on the effects of swirl motion on CO emissions and fuel consumption of low-temperature combustion engines by means of numerical studies and experiments. Optimization studies (Genzale et al. 2007; Shi and Reitz 2008a; Ge et al. 2009a, b) also found significant influence of swirl on engine-out emissions and fuel economy on heavy-duty and light-duty diesel engines. These previous studies indicated that swirl motion is influential during the postcombustion process besides its direct influence on the fuel mixing process prior to combustion. Hiroyasu et al. (1978) proposed two factors to supplement the empirical equations of spray tip penetration and angle in quiescent air in order to consider the fact that the spray is bent by air swirl. These two dimensionless correlation factors are defined as:   pRs Ns 1 Cs ¼ 1 þ ; ð5:8Þ 30Uinj Ch ¼ Cs2 ¼

 1þ

pRs Ns 30Uinj

2 ;

ð5:9Þ

where Cs and Ch are proportional to the reduction in axial penetration and the azimuthal deflection of the spray axis, respectively; s is the spray tip penetration.

5.2.6 Summary of Scaling Laws All of the time scales (Dt and t) are scaled by the same factor. When Eq. 5.1 is divided by Eq. 5.4, we get: d0 /

m L3 / ¼ L: s 2 L2

ð5:10Þ

Thus, the nozzle diameter d0 should be scaled by the factor L. The flame lift-off length H should be scaled by the geometry length L, and since the scaled engines should have the same ambient conditions and fuel properties, it can be directly deduced from Eq. 5.5 and Eq. 5.10 that Uinj / Hd00:34 / L  L0:34  L2=3 :

ð5:11Þ

Therefore, the injection velocity Uinj should be scaled by L2=3 . Consequently, the injection pressure should be scaled by L4=3 with the help of Eq. 5.3. And scaling relation for time scales can be deduced from Eq. 5.4: 1 1 t / s2 Uinj d0 / L2  L2=3  L1 ¼ L1=3 :

ð5:12Þ

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153

Table 5.1 Scaling relations

Parameter

Scaling factor: length

Scaling factor: volume

m s H d0 Uinj Dp Dt, t N Rs

L3 L L L L2/3 L4/3 L1/3 L-1/3 =

V V1/3 V1/3 V1/3 V2/9 V4/9 V1/9 V-1/9 =

In order to achieve the same injection duration on a crank angle basis such that the in-cylinder pressure as a function of a crank angle and the specific indicated work are independent of scales, N / t1 / L1=3 :

ð5:13Þ

Thus, the engine speed is scaled with L1=3 . To keep similarity in the swirl flow, the non-dimensional parameters Cs and Ch should be kept the same, which implies Rs / Uinj N 1 s1 / L2=3  L1=3  L1 ¼ 1:

ð5:14Þ

Thus, swirl ratio should be kept the same for scaled engines. The final scaling relations are listed in Table 5.1.

5.3 Validation of Scaling Laws on a Light-Duty and a Heavy-Duty Diesel Engine 5.3.1 Engine Specifications The scaling laws described in the previous section were validated in a light-duty GM-Fiat engine and a heavy-duty Caterpillar engine, which are single-cylinder experimental engines corresponding to respective production models. The specifications of these two engines are described in Table 5.2. As indicated in Table 5.2 and examined by the scaling relations in Table 5.1, the two engines differ in many geometrical parameters and injection related variables. Figure 5.1 shows a comparison of the piston profiles of the two engines, which shows that the engines also feature different bowl curves. The GM-Fiat engine has a deep bowl design with vertical side wall, but the bowl shape of the Caterpillar engine is shallow and the curved chamber wall is relatively closer to the cylinder wall.

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Table 5.2 Engine specifications Engine type

GM-fiat

Caterpillar

Bore (cm) Stroke (cm) Bowl diameter (cm) Connecting rod length (cm) Squish height (cm) Displacement (L) Compression ratio Swirl ratio IVC EVO Injector type Manufacturer Injection pressure (bar) Number of holes Nozzle holes diameter (lm)

8.2 9.04 4.99 14.5 0.067 0.477 16.53 2.2 * 5.6 142 BTDC 142 ATDC High-pressure solid-cone Bosch 1,600 8 133

13.716 16.51 9.8 26.16 0.157 2.439 16.1 0.5 143 BTDC 130 ATDC High-pressure solid-cone HEUI 1,500 6 158

To eliminate the differences in bowl geometrical similarity the baseline piston bowl profile of the GM-Fiat engine was up-scaled to produce the bowl profile for a modified Caterpillar engine. Correspondingly, other parameters, such as the injection related parameters and operating conditions were scaled based on the scaling arguments listed in Table 5.1. More detailed discussion is given in the following sections.

5.3.2 Numerical Models An improved version of the KIVA3v2 code was used to simulate the closed-valve portion of the engine cycle. The ignition and combustion processes were solved by a direct chemistry solver (Chemkin II) coupled in the KIVA code and a reduced n-heptane reaction mechanism (Patel et al. 2004) was used to simulate diesel fuel chemistry. A reduced NO mechanism (Kong et al. 2007) that contains only four species (N, NO, NO2, N2O) and nine reactions extracted from the GRI NO mechanism was used to calculate the sum of NO and NO2 to give the engine-out NOx emissions. Soot emissions were predicted with a two-step model acetylene (C2H2) as the soot precursor (Kong et al. 2007). The simulated results of the present KIVA-Chemkin code were compared with the experimental study conducted on the GM-Fiat engine by Lee and Reitz (2006). Figure 5.2 represents one of the comparisons. The engine was operated at low-load with IMEP around 5 bar, and SOI equal to 10 BTDC. The EGR rate was 51% in order to suppress the ignition and realize low-temperature combustion. As can be seen in Fig. 5.2, the numerical pressure trace matches the experimental result well, although it gives slightly higher peak pressure and earlier ignition. The predicted engine-out NOx is in very good agreement with the experimental value. However,

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155

Fig. 5.1 Original piston bowl profiles

Fig. 5.2 Comparisons of experimental and numerical results (SOI = 10 BTDC)

higher soot emissions are produced. Possible reasons include discrepancies of the initial mixture composition at the intake valve closing time between the simulation and experiment (which were found to have a significant influence on soot). Based on the present and many previous validation studies (Patel et al. 2004; Sun and Reitz 2006; Opat et al. 2007), the model was deemed adequate.

5.3.3 Results and Discussion Before exploring the scaling relationships between the investigated engines, the issue of the mesh size dependency needed to be addressed for the CFD scaling

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study. In addition to the numerical issues, other practical concerns are also highlighted and discussed in this section, such as the effect of injection rate shape, engine heat transfer, and initial flow motion at IVC. Next, a numerical study was conducted on the two engines based on the displacement scaling factor of Table 5.1. The investigation was done for the two engines operated at low-and mid-load. Inspired by the results obtained from the displacement scaling, a new scaling factor based on the TDC volume was suggested, and improved matching results were obtained for the engines at low-load. This work was also extended to engines at low and high speed with TDC scaling.

5.3.3.1 Mesh Size Dependency It is known that current CFD engine simulation tools show grid dependency to a certain degree due to their spray, turbulence, and combustion models. However, the models are usually calibrated for a certain mesh size. For diesel applications, the grid dependency of the spray model is important and it is necessary to minimize the interference of grid-dependent models from the present CFD engine scaling study in order to obtain comparable results on both the small and large engines. For the same resolution, the same computational mesh size in the small and large engine is required. However, this would increase the computational burden of simulating the large engine, since the computational time increases proportionally with L3, where L is the ratio of bore sizes of the large and small engines, 1.672 for the present study. Note that the spray targeting in the present study targets the piston bowl, and thus the grid size in the axial direction in the squish region is less important than that of the radial and azimuthal directions in the bowl region. So focus was placed on a study of mesh sizes in the bowl region. A sector of the large Caterpillar engine was created with the same mesh size as in the small GM-Fiat engine in the bowl, and the simulation results were compared with a coarse mesh sector of the Caterpillar engine, which are shown in Fig. 5.3. As can be seen in Fig. 5.3b, the thermal characteristics predicted with the two meshes are almost identical. Although there is some discrepancy in the soot emissions using the different mesh sizes as shown in Fig. 5.3c, considering the similar in-cylinder details shown in Fig. 5.3d, the coarse mesh of the Caterpillar engine was used in this scaling work to make the computational time affordable.

5.3.3.2 Injection Rate Shape According to the scaling relations listed in Table 5.1, the smaller engine has a lower injection pressure, thus smaller injection velocity, which is proportional to the 4/3 power of the scaling factor. This suggests that care must be taken in the large engine if the maximum injection pressure is limited. The current investigated Caterpillar engine has a maximum injection pressure 1500 bar, as listed in Table 5.2, and

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157

Fig. 5.3 Comparison of results using coarse and fine meshes. a Mesh density at TDC. b Pressure trace and heat release. c Emissions. d In-cylinder details-soot distribution (side view)

based on the scaling relations and the ratio of the sizes of the two engines, the maximum injection pressure of the GM-Fiat engine would be around 750 bar. The injection rate shape defines how much fuel is injected into the cylinder in each crank angle during the injection event, and this influences the combustion phasing. In order to match the combustion phasing of the small engine and the scaled large engine, the injection rate shape has to be scaled to supply a proportionally injected fuel amount. In this study, the experimental injection rate shape

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Fig. 5.4 Comparison of scaled injection rate shapes of the small and large engines

obtained with injection pressure of 700 bar from the GM-Fiat engine was selected and scaled for use in the large engine, which is described in Fig. 5.4.

5.3.3.3 Engine Heat Transfer Based on the specifications given in Table 5.2, the ratios of the surface area to the displacement volume are 0.71 and 0.41 for the GM-Fiat and the Caterpillar engines, respectively. The convection heat loss component through the cylinder walls of the small engine is larger than that of the large engine. If it is assumed that the heat release of the two engines is proportional to the injected fuel amount (which is required in the current study), the thermal efficiency of the small engine will be lower than that of large engine. Therefore a treatment is needed to consider the effect of heat transfer for an engine scaling study. To compensate for the relatively greater heat loss of the small engine, the intake temperature was increased. The increment of the intake temperature of the small engine was determined such that the motoring pressure trace of the small engine matched that of the scaled large engine under the same compression ratio. An increase of 10 K intake temperature was found to be required from this procedure. Although it might be argued that for a fired engine more heat loss is produced than that of the motoring case, the important consideration is that the combustion process starts at the same thermal conditions in the two engines. It was also found that a large difference of intake temperature between the engines affects the initial thermal condition significantly, and therefore can influence the controlling roles of chemistry and turbulence scales between the scaled engines. For example, the ignition timing would be advanced in the small engine due to an increase of the intake temperature. However, the increase of 10 K will be further justified in the subsequent discussion, and was found to be an appropriate value in this study.

5.3 Validation of Scaling Laws on a Light-Duty and a Heavy-Duty Diesel Engine

159

Fig. 5.5 Comparison of swirl ratio during compression stroke

5.3.3.4 Intake Flow and Initial Flow Field at IVC As described above, the swirl ratios of the investigated engines have to be equal to produce similar initial flow fields at IVC with comparable influences on the spray tip penetration. However, the intake systems of the two real engines have different capabilities of generating initial swirl. Referring to Table 5.2, it is seen that the small GM-Fiat engine generates variable swirl ratios from 2.2 to 5.6 (steady benchmarking results) using butterfly valves, but the Caterpillar engine has a fixed swirl ratio of about 0.5. It is of interest to numerically investigate how to produce the same swirl level for the two engines, and thus to provide guidelines for practical engine design. As a preliminary work, the mesh of the Caterpillar engine with the intake system was scaled down to the GM-Fiat engine based on the ratio of the bore sizes. Other parameters, such as the valve-lifts and engine speeds were also scaled based on the scaling relations in Table 5.1. A motoring simulation was conducted to compare the intake flow and initial flow fields at IVC of the two engines. Figures 5.5 and 5.6 show swirl ratio and tumble flow profiles during the compression stroke. It can be seen that the swirl and tumble ratios in the radial and azimulthal directions (averaged momentum values) are almost identical in both engines. Further examination of Fig. 5.7 reveals that the velocity distribution in the small engine also resembles that of the large engine at BDC. The large engine has higher values of velocity, which was also found to roughly scale with the mean piston speed with the scaling factor L2/3. These findings confirm that the geometry of the intake system and the lift profiles of the valves determine the intake flow and flow field in the cylinder. As long as they are geometrically scaled and the engine speed is also scaled, similar flow fields result. Furthermore, the results of Figs. 5.5 and 5.6 verify the current scaling factor with respect to the engine speed, since the swirl ratio and tumble flow are the normalized results with respect to the engine speed, and they show matching trends. Note that the self-consistency of the results

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Fig. 5.6 Comparison of tumble flow during compression stroke. Left: tumble in radial direction; right: Tumble in azimuthal direction

Fig. 5.7 Velocity distribution at the BDC. Top: side view; bottom: top view

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161

Table 5.3 Scaled parameters of the displacement volume scaling engines Engine type GM-fiat Caterpillar (Scaled)

Scaled?

Bore (cm) Stroke (cm) Bowl diameter (cm) Connecting rod length (cm) Squish height (cm) Displacement (L) TDC volume (L) Compression ratio Swirl ratio IVC EVO Injection pressure (bar) Number of holes Nozzle holes diameter (lm) Spray angle

N/A N/A Yes N/A No Yes Yes Yes Yes No No Yes Yes Yes Yes

8.2 9.04 4.99 14.5 0.163 0.477 0.0329 15.5 1.8 142 BTDC 142 ATDC 726 8 133 130

13.716 16.51 8.59 26.16 0.223 2.439 0.1682 15.5 1.8 143 BTDC 130 ATDC 1,500 8 229 130

also confirms that numerical grid size effects are unimportant for modeling the intake process. For the next study to simplify the problem, sector meshes were used, but the flow field at IVC was initialized using a swirl ratio, which was set to be equal for the two engines. 5.3.3.5 Displacement Volume Scaling It is well known that the thermal efficiency of a diesel engine is correlated with its compression ratio. In order to match the thermal efficiency of the scaled engines, it is necessary to keep the same compression ratio. This presents two options, which are either to use the relation of the displacement volume to scale the TDC volume, or to use the TDC volume to scale the IVC volume. The use of displacement volume scaling is discussed in this section, and inspired by the results, an investigation based on TDC volume scaling was further explored. Following the scaling relations listed in Table 5.1, the scaled parameters of the Caterpillar engine based on the displacement scaling factor V = 2.439/0.477 are compared with the corresponding parameters of the GM-Fiat engine in Table 5.3. As indicated in the fourth column of Table 5.3, it is not possible to simultaneously scale some primary geometrical parameters of the Caterpillar engine, such as bore size, stroke, and connecting rod length. The bowl profile of the Caterpillar engine was scaled from the bowl profile of the GM-Fiat engine, which gives the scaled bowl volume. However, the squish height at TDC was not scaled due to the presence of valve cut-out volumes at TDC of the practical engine. The geometrical compression ratio for the two engines was adjusted to be 15.5, and since they have similar IVC timings, their effective compression ratios are also close. The simulation was

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Table 5.4 Operating conditions for the displacement volume scaled engines. A: low-load; B: mid-load Engine type GM-fiat Caterpillar Scaled? (Scaled) Speed (rpm)

Gross IMEP (bar) Equivalence ratio EGR rate (%) Oxygen (volume%) IVC Temperature(K) IVC Pressure (bar) Injected fuel (mg/cyc.) Injection duration (CA)

A

B A B A B A B A B A B A B A B A B

1,000 2,000 3,000 2,000 5.0 7.5 0.25 0.75 0 55 20.91 11.97 380 380 1.791 1.791 12.8 22.2 N/A 13.2

834 1,668 2,502 1,668 5.0 7.5 0.25 0.75 0 55 20.91 11.97 370 370 1.736 1.736 65.5 114 N/A 13.2

Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes N/A Yes

conducted under low-load (for HCCI, Case A) and mid-load (for SOI sweep, Case B) operating conditions, which are shown in Table 5.4. Stager and Reitz (2007) found that for early injection timings the scaling of engine combustion and emissions were dependent on mixing and charge preparation processes that are controlled by turbulent timescales. For late injection timings, however the scaling was found to be controlled by kinetic (chemistry) timescales and hot gas residence times. Scaling of mid-range injection timings were controlled by a combination of both the turbulence and kinetic timescales. It is of interest to further investigate the scaling relations between the engines of different sizes over a broad range of injection timings. Therefore, Start of Injection (SOI) sweeps from 35 BTDC to 5 BTDC were conducted on the two engines. In addition, the two engines were also explored under a Homogeneous Charge Compression Ignition (HCCI) condition in order to remove the influence of spray mixing and charge preparation from the scaling study and to gain a more direct sense of the influences of chemistry timescales in engine scaling. 5.3.3.6 HCCI Engines The HCCI simulation was run at low-load (Case A in Table 5.4), which makes it relevant to practical engines. The research was also extended to low and high speed cases in order to study the influence of residence times on engine scaling.

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Fig. 5.8 Pressure trace and heat release rate for HCCI conditions (Case A, Table 5.4)

In Fig. 5.8, the pressure trace and heat release rates of the scaled engines are compared. Two stage heat release is seen in the HCCI engines. The cool flame stage occurs slightly later in the large engine than in the small engine, which is due to the higher intake temperature of the small engine in order to compensate for its greater heat loss, as discussed previously. But the main heat release (scaled) of the large engine matches that of the small engine, and they have matched pressure traces. This indicates that the simple strategy of treating the unscaled heat loss is valid in the present study. The early ignition of the small engine is also reflected in the start of combustion timings (defined as the crank angle when 10% of accumulated heat is reached) with different engine speeds shown in Fig. 5.9. It can be seen that the start of combustion timing is linearly retarded with the linearly increasing engine speeds. This confirms that the ignition delay on a real time basis is the same for both engines operating under different speeds, which is understandable since the HCCI combustion is chemistry-controlled. In addition, the chemistry ignition delay between the two engines can be estimated from the linear relation in Fig. 5.9 to be about 0.375 ms in all cases. The later combustion phasing of the large engine is the reason that it produces slightly less NOx than the small engine, which is shown in Fig. 5.10 (left). The matched soot emissions in Fig. 5.10 (right) further confirm the chemistry processes in the two engines are equally scaled. To summarize, the scaling laws of Table 5.1 work very well for scaling engines at HCCI conditions, which means that the influence of the chemistry timescales on the combustion and emissions are considered and scaled. The discrepancy of ignition timing that leads to different NOx emissions is essentially caused by the unscaled heat loss due to the different surface-to-volume characteristics of the two engines. However, the proposed method of treating this problem by increasing the intake temperature is effective.

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Fig. 5.9 Comparison of start of combustion timing (10% burn) of the HCCI engine under different speeds

Fig. 5.10 Comparison of NOx (left) and soot (right) emissions of the HCCI engine under different speeds

5.3.3.7 SOI Sweep Simulations were conducted over a SOI sweep to investigate the scaling relations due to turbulence and chemistry timescales, and their interactions. Figures 5.11, 5.12, 5.13 illustrate the comparison for the engines at mid-load (Case B in Table 5.4). As indicated in Fig. 5.11, the pressure traces of the scaled Caterpillar engine are close to those of the GM-Fiat engine over the broad range of injection timings, as well as its heat release rates (scaled by the displacement volume). This indicates that the current scaling argument regarding the engine power output works fairly well. The small inset plots in Fig. 5.11 are included to show that the scaled liquid spray tip penetrations in the Caterpillar engine also agree with those in the GMFiat engine, which further supports the scaling argument for spray tip penetration. However, the combustion phasing of the large engine is earlier than that of the small engine, which is also represented by the shorter ignition delay (the time from injection timing to the crank angle when 10% of accumulated total heat release is reached) as shown in Fig. 5.12. Based on the scaling relations the large engine has lower speed, and thus the mixture preparation during the spray development is longer in real time for the

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Fig. 5.11 Comparison of the displacement volume scaled engines at mid-load: pressure trace and heat release rate with different SOI.a SOI = -35, b SOI = -20, c SOI = -5

large engine. Therefore, a more flammable mixture is formed compared to the small engine, which results in the earlier ignition timing on a crank angle basis. This result differs from the HCCI engine comparison, since the ignition is primarily determined by how much flammable fuel-air mixture has been prepared. The timescale of spray mixing and interaction with turbulence is much larger than the chemistry timescale. More support for this conclusion is also revealed in Fig. 5.12 that illustrates the difference in the ignition delay increases with retarded SOI timing where less time is available for mixing. The NOx and soot emissions show opposite trends over the SOI sweep in Fig. 5.13. With retarded injection timing, the difference in NOx emissions between the two engines decreases, and in the traditional diesel combustion region (SOI [ -15), the results are close. Inversely, the soot emissions are close at early injection timings, and then the difference increases with retarded injection timing. The comparison of the temperature distributions shown in Fig. 5.14 explains why the large engine produces more NOx emissions at early injection timings. It has a larger high temperature area where the NOx formation is active. The difference is caused by the different injection pressures since for the large engine, the higher injection pressure benefits the mixing process and produces a more flammable mixture close to the piston symmetry axis, which is later ignited. Although the spray tip penetration is found to be scaled with the current scaling

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Fig. 5.12 Comparison of the displacement volume scaled engines at mid-load: ignition delay

Fig. 5.13 Comparison of the displacement volume scaled engines at mid-load: NOx (left) and soot (right) emissions

law, the spray mixing process appears to be weakly scaled due to the different injection pressures. The soot formation region is located at the bottom of the bowl, as shown in Fig. 5.15, due to the similar temperature distribution in that region seen in Fig. 5.14. Examination of the turbulence quantities and local equivalence ratios also revealed local similarity (not shown). Considering that the ignition delay for this early injection case is about twice the injection duration, it can be concluded that the effects of local turbulence levels and bulk flow on the mixing process after the end of injection are scaled or are not important. For the late injection case, a difference in the temperatures is also seen in Fig. 5.16 for the same reasons as discussed before. However, it is noticed that the high temperature area around the piston axis in the large engine is around 1,900 K, at which temperature NOx formation is not prominent. This explains why with the retarded SOI timing, the difference in NOx emissions reduces. Compared to the

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Fig. 5.14 Comparison of SOI = 35 BTDC cases: Temperature distribution (side view, in the plane of the spray)

Fig. 5.15 Comparison of SOI = 35 BTDC cases: Distribution of soot mass fraction (side view, in the plane of the spray)

Fig. 5.16 Comparison of SOI = 5 BTDC cases: Temperature distribution (side view, in the plane of the spray)

early injection case, the combustion temperature of the late injection case is lower, and thus the chemistry timescales of reactions relevant to NOx formation are also larger. Therefore, the difference of NOx formation in the two scaled engines is relatively insensitive to the difference of real time (due to the difference of speed). As can be seen in Fig. 5.17, more soot is formed in the squish region of the large engine. In addition, the concentration of soot is also larger in the large engine. For the late injection case the ignition delay is comparable to (or less than) the injection duration, which results in more interaction between the spray development and the turbulent flow. Furthermore, the preparation of the flammable mixture is faster for the late injection case due to higher ambient temperature (consequently faster vaporization) and stronger squish flow, and the chemistry timescale also becomes smaller under more thermally active ambient conditions. This leads to stronger interaction between the mixing process and the chemistry.

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Fig. 5.17 Comparison of SOI = 5 BTDC cases: Distribution of soot mass fraction (side view, in the plane of the spray)

Table 5.5 Scaled parameters for the TDC volume scaled engines Engine type GM-Fiat (Scaled) Caterpillar (Scaled)

Scaled?

Bore (cm) Stroke (cm) Bowl diameter (cm) Connecting rod length (cm) Squish height (cm) Displacement (L) TDC volume (L) Geometrical compression ratio Effective compression ratio Swirl ratio IVC EVO Injection pressure (bar) Number of holes Nozzle holes diameter (lm) Spray angle

N/A N/A Yes N/A Yes No Yes No Yes Yes Yes No Yes Yes Yes Yes

8.2 9.04 5.13 14.5 0.133 0.477 0.0359 14.3 13.3 1.8 142 BTDC 142 ATDC 755 8 137 130

13.716 16.51 8.59 26.16 0.223 2.439 0.1682 15.5 13.3 1.8 126 BTDC 130 ATDC 1,500 8 229 130

5.3.3.8 TDC Volume Scaling The results from the displacement volume scaling above imply that the flow and thermal conditions at TDC are very important to combustion and emissions. This motivated consideration of an alternative scaling strategy referred as TDC volume scaling. The idea is that instead of matching the displacement volume, the ratio of the bore sizes of the two engines is used to scale the piston bowl geometry, squish height, and crevice volume at TDC. This gives the same in-cylinder geometry at TDC based on the scaling arguments. In this section, the piston geometry of the Caterpillar engine used in the previous section of the displacement volume scaling was maintained and the GM-Fiat piston geometry was scaled from the Caterpillar piston with the scaling factor L = 8.2/13.716. Table 5.5 lists the scaled parameters for the TDC volume scaling study. Note that the strokes of the two engines are not scaled linearly with the bore size, with the result that the displacement volume cannot be scaled with the current scaling factor. Therefore the geometrical compression ratio defined with the

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Table 5.6 Operating conditions of the TDC volume scaled engines: A, B, and C are low-, mid-, and high-load, respectively Engine type GM-Fiat Caterpillar Scaled? (Scaled) (Scaled) Speed (rpm) Gross IMEP (bar)

Equivalence ratio

EGR rate (%)

Oxygen (volume%)

IVC Temperature(K)

IVC Pressure (bar)

Injected fuel (mg/cyc.)

Injection duration (CA)

A B C A B C A B C A B C A B C A B C A B C A B C

2,000 4.5 7.0 1.0 0.25 0.75 0.75 55 55 25 17.93 11.97 17.65 380 380 380 1.790 1.791 1.791 11 22.2 32.5 6.2 12.4 18

1,685 4.5 7.0 1.0 0.25 0.75 0.75 55 55 25 17.93 11.97 17.65 370 370 370 1.736 1.732 1.732 51.5 104 151 6.2 12.4 18

Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

displacement volume is no longer the same for the two engines. In order to obtain the same effective compression ratio, the IVC timing of the Caterpillar engine has to be retarded to 126 BTDC. The simulation was extended to consider more operating conditions from low-load to high-load, which are given in Table 5.6. Cases A, B, and C represent low-, mid-, and high-load respectively. Similar to the study of displacement volume scaling, simulations were conducted with SOI sweeps on the engines operated at low- and mid-load. With the TDC volume scaling, the pressure, heat release rate, and the scaled spray tip penetration for both engines at low-load match very well over the SOI sweep, which are shown in Fig. 5.18. However, because the IVC timing of the large engine needs to be altered to match the effective compression ratio, its compression processes differ slightly from those of the small engine, but no noticeable influence of this discrepancy was seen on the combustion and emissions. Compared to Fig. 5.13, more similarities of the emission trends are seen in Fig. 5.19 using the TDC volume scaling. This indicates that TDC conditions are

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Fig. 5.18 Comparison of the TDC volume scaled engines at low-load: pressure trace and heat release rate with different SOI. a SOI = -35, b SOI = -20, c SOI = -5

Fig. 5.19 Comparison of the TDC volume scaled engines at low-load: NOx (left) and soot (right) emissions

significant to diesel combustion and emissions due to the interactions between the squish flows and the fuel mixing and post-combustion processes. The injection duration of the low-load case (6.2CA) is about half that of the mid-load case (see Tables 5.4 and 5.6). The short injection duration reduces the

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Fig. 5.20 Comparison of the TDC volume scaled engines at low-load: ignition delay

Fig. 5.21 Comparison of engines at low speed and lowload (1,000 and 843 rev/min for the small and large engine, respectively): ignition delay

time of spray jet flow interaction with the ambient turbulent flow. This leaves more time for the transport of evaporated fuel by turbulence and bulk flow. Figure 5.20 reveals that the ignition delay is larger than the injection duration for all SOI timings, which allows time for mixing before combustion. As in the HCCI engine study with similar fuel distribution, the combustion should be expected to scale if the chemistry timescale is more influential. Therefore, the explanation of better matching of the combustion characteristics and emission trends in the two engines at low-load can be understood. Simulation of the two engines at low-load was repeated at 1,000 and 843 rev/min for the small and large engine, respectively. The balance of bulk flow and chemistry timescales is changed due to the longer injection duration in real time.

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Fig. 5.22 Comparison of engines at low speed and low-load (1,000 and 843 rev/min for the small and large engine, respectively): NOx (left) and soot (right) emissions

Fig. 5.23 Comparison of the TDC volume scaling engines at mid-load: pressure trace and heat release rate with different SOI. a SOI = -35, b SOI = -20, c SOI = -5

This results in less scaled results in Fig. 5.21 and 5.22, especially for the NOx emissions. However, close soot trends were found, as seen in Fig. 5.22 (right), which is due to the increased time for soot oxidation during the expansion process, since both engines have the same low global equivalence ratio. In spite of the fact that the ignition delays are similar, the NOx is higher in the larger engine which

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Fig. 5.24 Comparison of the TDC volume scaling engines at mid-load: ignition delay

Fig. 5.25 Comparison of the TDC volume scaling engines at mid-load: NOx (left) and soot (right) emissions

has more time for NOx formation. This again demonstrates the significant role of chemistry on emissions in engine scaling. Compared to the results obtained with displacement volume scaling in Figs. 5.11, 5.12, 5.13, the results of the TDC volume scaling at mid-load do not show noticeable improvement with respect to the differences of the emissions trends, which are shown in Figs. 5.23, 5.24, 5.25. In general, the large engine produces more NOx and soot emissions. The discrepancy of soot emissions increases as the SOI timing is retarded, but the difference in NOx emissions decreases. As discussed before, the longer injection duration at mid-load, and thus the longer time of interaction of the jet flow with the bulk flow and weaker effect of the chemistry on the combustion is one of the reasons that the emissions are less scaled. Together with the previous discussion on scaling engines at low speed and

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Fig. 5.26 Distributions of C2H2 and soot mass fraction (SOI = 5 BTDC). Top and middle: C2H2. Bottom: soot

low-load, the scaling results of the engines at higher speed and mid-load suggests that scaled operation at low speed and mid- or high-load is more challenging. In the current study, acetylene (C2H2) is taken as the precursor of soot formation, and higher concentration areas of C2H2 correspond to more soot production propensity. Before acetylene was formed, the distributions and quantities of the local temperature, evaporated fuel, as well as oxygen concentration were found to be very similar in the two engines. However, a comparison between Fig. 5.26 (top) and (middle) regarding the C2H2 mass fraction reveals that in the same two CA span, more C2H2 is generated in the large engine (note that the large engine is shown at one CA ahead of the small engine because of its earlier ignition). This directly results in more soot emissions in the large engine shown in Fig. 5.26 (bottom). The large engine has lower speed based on the current scaling laws, and therefore longer real time in one CA. The C2H2 formation reactions are fast under conditions of high temperature and low oxygen concentration, which means that the chemistry timescale is much smaller than the time period of one

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Fig. 5.27 Comparison of soot emissions of engines at high speed (engine speed 3,000 and 2,502 rev/min for the small and large engines, respectively)

CA. Therefore, a longer reaction time results in more C2H2 being formed. For early injection cases, the chemistry timescale of reactions of C2H2 is relative large due to the higher local oxygen concentration (better mixing), which makes the soot formation less sensitive to the timing difference in one CA span between two engines. It should be pointed out that the better scaled soot emissions trend for the low-load case was primarily due to the effect of the soot oxidation process, whose chemistry timescale is much larger than soot formation (or C2H2 formation). Based on this discussion, it is expected that scaled engines operated at a higher speed would produce smaller differences in soot emissions. This is proved in Fig. 5.27 that shows less discrepancy of soot emissions between the two engines when operated at high speed. The small and large engines were run under the consideration of Case C listed in Table 5.6 with engine speeds of 3,000 and 2,502 rev/ min, respectively.

5.4 Summary Engine size-scaling arguments based on power output, spray tip penetration, and flame lift-off were explained. Several important issues for a study of engine sizescaling were addressed prior to investigation of the scaling relations between two production engines. These include numerical mesh dependency and turbulence and heat transfer effects. Different scaling behaviors related to turbulence and chemistry timescales and their effects on combustion and emissions in engines of different size were considered. The following conclusions can be drawn: • The present scaling arguments are useful for analysis of engine size-scaling. Global performance results, such as the pressure trace and heat release rates are well scaled based on the scaling laws.

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• Soot emissions for the large engine operated at mid- or high-load conditions did not scale as well as at light load. This is due to the fact that the soot formation process, which is controlled by chemistry timescales, at mid- or high-load is more significant compared to that at light-load, in which the soot oxidation, which is controlled by turbulence mixing timescales, dominates. Therefore, at different engine speeds (or different real time) the different timescales that control the net soot emissions contribute to the more poorly-scaled soot emissions for engines operated at mid- or high-load. For the low-load operating condition, better scaling of soot emissions was seen because sufficient time is available for oxidation. • The large engine has longer time available for reactions compared to high speed small engines. Therefore, more NOx is produced, especially in cases with early injection timings. Hence, higher EGR ratios may be needed to suppress the NOx formation. • Unscaled heat losses and NOx can be compensated for by slightly increasing the intake temperature of the small size engine. Thermal management of the cooling system can be used to scale the heat losses for engines of different sizes. • Engines operated under HCCI conditions that are chemistry-controlled exhibit well-scaled thermal and emissions results since the power output is scaled with the fuel amount and global equivalence ratio. • In order to generate the same level of swirl, the geometry of the intake system must be scaled. The swirl ratio was found to affect the engine heat transfer. Therefore, for HCCI engines, the swirl level influences the ignition timing, and can be used to control the ignition timing for different size engines operated at different speeds. • Conditions with reduced interaction time between the injection-generated jet flow and the bulk flow, or with increased time available for chemistry had better scaled combustion characteristics and emissions. This is because the current scaling laws consider lifted flames and lifted flames are more likely under these conditions.

Chapter 6

Applications

This chapter presents several examples of engine optimization using multidimensional CFD and genetic algorithms. The examples in the first part use simple combustion models to benefit efficiency. The ones in the second part use detailed chemistry for better accuracy, especially for the cases in which the simple combustion models fail. The third part discusses strategies for simultaneous optimization of multiple operating conditions. The fourth part presents a methodology that combines scaling laws and computational optimization for engine development.

6.1 Engine Optimization with Simple Combustion Models Under certain conditions, such as in the conventional diesel combustion regimes, engine simulations using simple combustion models, such as the Characteristic Time Combustion (CTC) model, are able to predict satisfactory results if the model constants are fine tuned against experimental data. Such models enable efficient evaluation of engine performance and emissions. For example, an individual closed-cycle engine simulation using the CTC model with the KIVA3v2 CFD code and with around 50,000 computational grids only costs several hours on a regular personal computer. Given sufficient computational resources, computational engine optimization can be completed within a week, which considerably expedites engine development. This section provides four examples to demonstrate the use of relatively simple combustion models, particularly the CTC model in engine computational optimization problems. The first case study seeks the optimal designs of a gasoline spark-ignition engine. The next two examples investigate the optimal combinations of combustion chamber geometry and injection parameters of heavy-duty diesel engines. Optimization of a high-speed passenger-car diesel engine is the subject of the last example.

Y. Shi et al., Computational Optimization of Internal Combustion Engines, DOI: 10.1007/978-0-85729-619-1_6,  Springer-Verlag London Limited 2011

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6.1.1 Optimization of a 2-Stroke Direct-Injection Spark-Ignited Engine 6.1.1.1 Research Background and Objectives Direct-injection (DI) technology has made many appearances throughout the history of internal combustion engines. In the 1950s, direct-injection was adopted in aircraft engines using existing diesel injection techniques. In 1954, directinjection was applied to the Mercedes Benz 300SL in an attempt to overcome carburetor limitations (Iwamoto et al. 1997). The return to direct-injection today has been motivated chiefly by the desire to improve fuel economy. Direct-injection techniques that employ charge stratification at light load have tremendous potential for reducing fuel consumption. At part load, combustion occurs at extremely lean conditions (overall lean) and thermal efficiency is increased. Some manufacturers of DI technology have claimed thermal efficiencies that are comparable to that of diesel engines. Reductions in fuel consumption have been reported to be as high as 30% (Iwamoto et al. 1997). Another benefit of DI technology is that the engine is run in unthrottled mode. This eliminates the irreversibility associated with the throttling process, resulting in a reduction in the overall pumping loss of the cycle. At full load, fuel is injected early in the cycle and results in a homogeneous mixture similar to that found in port fuel injected or carbureted engines. A further benefit at full load is an improvement in volumetric efficiency. This is accomplished through charge cooling that occurs as the fuel droplets being sprayed into the cylinder evaporate. This lowers the kinetic energy (and hence the back pressure) of the gas in the cylinder, allowing more air to be inducted. One of the critical necessities of a successful DI system is the ability to establish a stratified, fuel-rich mixture in the region of the spark plug. Several different approaches to this have been made. Among these approaches include controlling the shape and penetration of the fuel spray, the creation of a cavity in the piston, and manipulation of engine bulk gas motion (i.e., swirl and tumble). Direct-injection engines suffer from high unburned hydrocarbon and nitrogen oxide emissions. Spray impingement on piston and wall surfaces is the cause of high unburned hydrocarbon emissions. High local temperatures are responsible for the elevated production of oxides of nitrogen. The promise of substantial reductions in fuel consumption and in some cases improvements in power and performance, make DI technology extremely attractive. The many intricate details of the mixture formation and the challenges associated with emissions make direct injection a complex, multifaceted problem. Following this, it is therefore desirable to develop a technique to first model, and then optimize the many variables involved in a DI system. In this example, an optimization study combining multidimensional CFD modeling and a genetic algorithm has been carried out on a 2-stroke, sparkignited, direct-injection, single-cylinder research engine. The goal of the study was to optimize the part load operating parameters of the engine in order to achieve the lowest possible emissions, improved fuel economy, and reduced

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Table 6.1 Initial Conditions for Simulations Intake ports

Exhaust ports

Cylinder

Initial pressure (kPa) Initial temperature (K)

98.1 490

270 1,220

101.3 320

wall heat transfer. Parameters subject to permutation in this study were the startof-injection timing, injection duration, spark timing, fuel injection angle, dwell between injections, and the percentage of fuel mass in the first injection pulse. A part load, intermediate-speed condition representing a transition operating regime between stratified charge and homogeneous charge operation was studied. Two candidate optimal designs emerged from this optimization study, each offering distinct advantages and benefits over the baseline operating case. These benefits included reduced emissions of nitrogen oxide and unburned hydrocarbons, and improved fuel efficiency. Injection angle was found to have an insignificant effect on engine performance at this operating condition. Some candidate optimal designs were obtainable with both single and split-fuelinjection strategies, while others were unique to the latter. Split-fuel-injection was found to be a versatile, and useful technique for enhancement of engine performance. Soot production was not taken into account in the present study, and could have brought about a different optimization direction, should it have been considered.

6.1.1.2 Numerical Models Pressure boundary conditions used in the present study were obtained from a 1-dimensional gas dynamics code developed at the University of WisconsinMadison Engine Research Center (ERC) (Zhu and Reitz 1999). The code utilizes the Method of Characteristics (MOC) to model the unsteady gas exchange process of the internal combustion engine. The MOC technique is different from other finite-difference or finite-volume based methods, in that it provides insight about wave propagation, and effective time-varying boundary conditions. The ERC 1-D code not only solves for the intake and exhaust flow, but also includes calculation of in-cylinder mixing, and tracking of species. The code is used to provide realistic pressure boundary conditions at the intake and exhaust ports. These boundary conditions are fed into the KIVA code for the multidimensional simulation. The KIVA simulation of the two-stroke DISC engine in the present study is conducted from exhaust port open (EPO) all the way through the time before the next EPO event (i.e., one complete cycle is simulated). The full gas exchange process is modeled three-dimensionally with KIVA. Pressure boundary conditions are from the 1-D simulation, and exhaust gas composition in the cylinder is specified in the main KIVA input file. Initial temperatures and pressures are also set for the various intake ports (1 boost port, and two transfer ports), the exhaust

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port, and the cylinder. Table 6.1 gives these initial conditions that were based on experimental data of Hudak (1998). Head and liner temperatures are set as 400 K, while the piston is given a temperature of 450 K (Stiesch et al. 2001). Swirl is initialized to zero. A strong clockwise tumble is set up in the cylinder as the intake charge scavenges the cylinder. The spray, ignition, and combustion calculations proceed directly from the scavenging, being affected by the flow field set up by this gas exchange process. The Linearized Instability Sheet Atomization (LISA) model (Schmidt et al. 1999) is used to represent the breakup process whereby fuel in the injector is discharged as a thin, film-like conical sheet. The TAB (Taylor Analogy Breakup) breakup model (O’Rourke and Amsden 1987) is used to estimate the secondary breakup of droplets. After breakup, a Rosin-Rammler function is applied to provide the droplet size distribution (Han et al. 1997). The ignition process and early stages of combustion were modeled using the Discrete Particle Ignition Kernel (DPIK) model (Fan and Reitz 2000). A one step reaction is used to represent the chemistry in the early spark kernel growth stage of combustion, with: C8 H18 þ12:5O2 ! 8CO2 + 8H2 O;

ð6:1Þ

where gasoline fuel is modeled using the properties of iso-octane, and with the assumption of stoichiometric combustion. The change in the density of species, i, is given by:   qf qO2 dqi  SL  Zst  Wi  R; ¼ CW  min ; ð6:2Þ dt Wf 12:5WO2 where CW = 80.0 is a model constant that compensates for flame wrinkling and assures complete combustion within the flame kernel; Zst is the stoichiometric coefficient of the species in Eq. 6.1. MWi is the molecular weight of i-th species, and R is the flame surface density in any given computational cell of volume Vcell: R¼

Np;cell pdk2 ; Np;tot Vcell

ð6:3Þ

where Np,cell and Np,tot are the number of ignition kernel particles in the cell and the total number of particles, respectively. Energy is supplied to the ignition initiation cell at a constant rate of 0.001 J/s for approximately 0.75 ms. This represents the actual spark energy and is in addition to the energy release that results from the chemical reaction of Eq. 6.1. Once the ignition kernel achieves a certain critical diameter, the Characteristic Time Combustion model is invoked and this model replaces the ignition model. The critical diameter, dk, is given by a constant multiplied by the integral turbulent length scale, lt: dk  Cm1 lt ¼ Cm1  0:16k1:5 =e;

ð6:4Þ

6.1 Engine Optimization with Simple Combustion Models

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where Cm1 is set to 2.1. Further details of the combustion model are given by Subramanian et al. (2003). 6.1.1.3 Optimization Methodology A micro-genetic algorithm (a single objective GA) was used in this study. Once the current population has converged, the best individual is maintained, while the other four individuals are randomly generated (Carrol 1996). This creates a population that has opportunities for completely new characteristics (the four random ones), while at the same time maintaining the best individual from the past evolutionary process. The genetic algorithm does not determine when an optimum is found. It is up to the user to determine that a particular solution is indeed the optimum. This is generally indicated by a prolonged period where no improvement in the merit function value is seen (Senecal 2000). The genetic algorithm checks for convergence to determine whether it should restart the population with the best individual thus far and four other randomly generated designs. In the present code, a particular gene is considered to have converged if 95% of the individuals in the population have the same value for that particular gene (Senecal 2000). The population in turn, is regarded as converged when every gene in the population has converged. It is important to note that convergence of a micro-population does not mean that an optimum has been found. The present genetic algorithm code can be configured to run in either series or parallel mode. Series execution conducts each individual evaluation one after the other, on a single processor. This type of execution requires the least amount of hardware and can be effective for simpler problems that involve seconds or minutes of computer time per function evaluation. For complex calculations like the present multidimensional engine simulation problem, parallel execution is the most effective method. This method involves the use of four different machines, each performing one individual evaluation. A UNIX shell script automates the file transfer and job submission processes.

6.1.1.4 Optimization Parameters and Ranges The optimization study was comprised of six parameters that were subject to permutation. These were SOI timing, injection duration, spark timing, injection cone angle, time between injections, and the percentage of mass in the first injection pulse. The ranges and resolution of these parameters is given in Table 6.2. The form of the merit function utilized in the present study was inspired by the work of Senecal and Reitz (2000) in their operating parameter optimization of a heavy-duty, direct injection diesel engine. The form was originally proposed by Montgomery (2000). The function was modified to account for the specific performance and emissions characteristics of interest in the present study, and has the form:

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Table 6.2 Optimization study parameters and ranges

Parameter

Range

Resolution

Start-of-injection (CA ) Injection duration (CA ) Spark timing (CA ) Injection cone angle () Time between injections (CA ) Mass in first pulse (%)

260–340 6–24 300–370 0–180 10–30 10–100

64 32 32 64 32 32

Merit ¼ 

NOx þHC NOx;m þHCm

2

1000 ISFC þ WHEAT þ ISFC WHEAT0 0

;

ð6:5Þ

where NOx and HC are the compounded nitrogen oxide and hydrocarbon emissions in units of g/kW h. The subscript m denotes ‘‘mandated’’ values for emissions, which were based on the EPA mandated value (years 2008 and later) for outboard and personal watercraft engines under 4.3 kW in power (81 g/kW h). ISFC is the brake specific fuel consumption in units of g/kW h. WHEAT is the total cylinder wall heat transfer in units of ergs. ISFC0 and WHEAT0 are the fuel consumption, and wall heat transfer values obtained in the KIVA simulation of the baseline operating case (261.95 g/kW h and 5.21 9 108 ergs respectively). Wall heat transfer is calculated according to the work of Han and Reitz (1996).

6.1.1.5 Engine and Computational Mesh The engine modeled in this study was a 2-stroke, direct injection, single-cylinder research engine (SCRE). It is a single-cylinder version of the 2.4 L V-6 outboard engine, designed and manufactured by Mercury Marine. The engine is loopscavenged, and has a displacement of 389 cm3. It has a rated power of 20 kW at an engine speed of 5,000 rev/min. The engine features a pump driven liquid cooling system. Intake of fresh air into the crankcase is accomplished by reed valves. Lubrication is sprayed into the incoming air upstream of the reed valves. The fuel-to-oil ratio in experiments was 100:1 and was accomplished by controlling oil pump speed (Hudak 1998). Air induction into the cylinder is accomplished by a boost port, and two transfer ports. The boost port sets up a tumbling flow in the cylinder that aids the scavenging of exhaust products, and subsequent mixture preparation. Blow-down and displacement of exhaust gas occurs through a single exhaust port. The engine is equipped with a flat-surface piston. There is no piston cavity, and the combustion chamber is formed by a hemispherical dome in the engine head. Fuel injection is accomplished with a pressure-swirl injector manufactured by Chrysler (Hudak 1998). Engine specifications are given in Table 6.3. The computational mesh employed in this study is a Cartesian-type mesh containing 11,000 computational cells. The mesh is shown in Fig. 6.1.

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Fig. 6.1 2-stroke engine computational mesh (Subramanian et al. 2003)

Table 6.3 Engine specifications

Bore Stroke Connecting rod length Combustion chamber volume Geometric compression ratio Actual compression ratio Exhaust port timing Intake transfer port timing Intake boost port timing

85.8 mm 67.3 mm 139.7 mm 32.3 cm3 11.2 7.4 95 ATDC 117 ATDC 117 ATDC

6.1.1.6 Results and Discussion The full six parameters of interest, SOI timing, injection duration, injection cone angle, spark timing, percentage of mass in the first pulse, and time between consecutive injection pulses (split-injection) (see Table 6.2), were varied. The merit function was as defined in Eq. 6.5, and its variation as a function of generation number is shown in Fig. 6.2. The vertical axis gives the maximum merit function value achieved in the micro-population of the current generation. The generation number is indicated on the horizontal axis. The initial best design (best individual in Generation 1) and the Optimum (best individual in the final generation) are indicated on the plot with their accompanying merit function value. The baseline design had a merit function value of 467 and is indicated across all generations with a horizontal line. In order to demonstrate convergence, the optimization was run through 85 generations. This means that 85 different micropopulations were created one after the other, based on the best genetic material of the previous generation. The optimization was terminated at Generation 85, but the optimum was essentially found in Generation 14. After Generation 14, the basic design stayed the same, with only mild fine-tuning of individual parameters, which occurred in

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Fig. 6.2 Maximum merit function (MMF) history

Table 6.4 Characteristics of successful designs Baseline case Best of generation #12 (A-2)

Optimum (A-1)

SOI (CA ) Duration (CA ) Spark timing (CA ) Spray angle () Dwell (CA ) Mass in 1st pulse (%) Merit function value

323.5 7.7 324.8 137.1 18.4 71.0 482

280 12.4 334.0 54 0 100.0 467

263.8 19.9 324.8 31.4 15.1 18.7 479

Generation 60 and 66 respectively. These changes yielded very small increases in MMF. Interestingly, the MMF value at Generation 12 was already close to that of the optimum (MMF at Generation 12 was 479 while the optimum had MMF of 482). What is of interest between these two relatively comparable designs in terms of MMF, is that they in fact embodied completely different characteristics from each other. Table 6.4 lists the characteristics of these two individuals, along with those of the baseline operating case, for reference. It can be seen that the two designs indeed represent radically different operating strategies. The best of Generation 12 (referred to as individual A-2) involved a substantially advanced SOI timing compared to the baseline case. It featured a longer injection duration of 19.9 compared to 12.4 in the baseline case. The spark timing was also advanced in relation to the baseline case. A smaller spray cone angle than that of the baseline case was selected. A-2 also features a small pilot injection of about 19% of the fuel, followed by a 15 crank angle degree (1.25 ms) pause. The remaining 81% of the fuel is then injected. The Optimum design (A-1) on the other hand selected a retarded SOI timing that even overlaps with the ignition event. A much shorter injection duration is selected, giving an extremely high injection velocity (the baseline case has an injection velocity of approximately 84 m/s, while A-1

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Fig. 6.3 In-cylinder images for Design A-2. Left: CA = 282 ATDC; right: CA = 334 ATDC

Table 6.5 Improvements achieved by designs A-1 and A-2

WHEAT NOx HC ISFC

A-2 (%)

A-1 (%)

9: 16.6; 37.7; 6.9;

3.5: 2.9; 53.8; 0.9;

features an injection velocity of about 260 m/s). The first injection contains over 70% of the fuel, and 18 crank angle degrees (1.5 ms) elapse before the second, smaller injection occurs. The fuel is sprayed out an extremely wide angle of 137. Figure 6.3 shows the fuel injection and spray development of individual A-2 during the second injection (282 ATDC). The left image shows the second injection pulse occurring with the first pulse, already dispersing and evaporating. The in-cylinder temperature distribution is indicated in color with the scale included below the image. The right image shows the air-fuel ratio in the cylinder prior to ignition. The scale is included below the image. From both images, it can be seen that the strong clockwise tumble created by the boost port persists beyond the scavenging period. This tumbling flow mixes the fuel and carries a substantial number of fuel particles over to the right-hand-side (exhaust port-side) spark plug. At the time just prior to ignition (Fig. 6.3 (right)) a near-stoichiometric charge exists in the vicinity of this spark plug. Figure 6.4 shows the fuel injection event for the optimum, or individual A-1. It can be seen that the actual spreading angle of the fuel spray is much smaller than the injector-supplied angle of 137. The spray collapses into a slug-like jet that penetrates into the cylinder. It is thought that this collapse is due to the very high injection pressure that, in turn, results in highly atomized fuel particles. These particles transition rapidly to the vapor phase, except for a small portion of them that remain in liquid form, deep within the spray near the axis of the cylinder. It is these particles (at the cylinder axis) that form the slug-like jet. The droplet Sauter mean diameter (SMD) during the injection event for design A-1 was found to be approximately 4 microns. In the baseline case, the droplets had an average diameter of about 27 microns. Table 6.5 shows the improvements in emissions, heat transfer, and fuel consumption achieved with both designs A-1 and A-2.

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Fig. 6.4 In-cylinder images for Design A-1

Fig. 6.5 Pressure and temperature comparison between baseline case and designs A-2 and A-1

These performance parameters are indicated as improvements over the baseline case, as a percentage. The direction of the arrows indicates either an increase (upward pointing arrow) or a decrease (downward pointing arrow) over the baseline case. It can be seen that both designs experience higher wall heat transfer, with A-2 having the highest increase. A-2 achieves a sizeable reduction in both NOx and HC emissions, while reducing fuel consumption by about 7%. Design A-1 is able to reduce engine-out hydrocarbon emissions by a staggering 54%. It achieves about 20% of the NOx reduction of A-2, and manages a marginal reduction in indicated specific fuel consumption. To explain these performance characteristics, cylinder pressure and temperature traces for designs A-1 and A-2 are contrasted against those of the baseline case in Fig. 6.5. From the upper graph it can be seen that design A-2 provides a substantially higher peak pressure and temperature than the baseline case. This gives better power, which translates into lower fuel consumption, as indicated in Table 6.5. The fuel utilization is better, and this is probably what gives the reduction in hydrocarbon emissions. Uniform combustion and flame travel, result

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in fewer hot spots, that, in turn, help abate the formation of NOx. These good combustion and fuel utilization characteristics, naturally result in higher heat transfer, which is what is observed. From the lower graph it can be seen that design A-1 has only slightly higher peak temperatures and pressures than the baseline case. Power is improved marginally and, hence, so is the fuel consumption. The simultaneous injection and ignition, probably results in richer combustion, converting the fuel into incompletely burned components like CO and possibly even soot-but this was not modeled. The extremely good reduction in unburned hydrocarbons is probably due to the fact that the fuel is burned as soon as it gets to the spark plugs, and has less opportunity to wet the piston or to collect elsewhere in the chamber and remain unburned. Also, the high atomization and vaporization seen, reduces the possibility of impingement greatly. The combustion rate on the other hand is slower and gives a lower pressure and temperature rise, as compared to design A-2. This is why power improvement, is minimal. NOx reduction was relatively small, indicating that there are probably more high temperature regions in design A-1 compared to design A-2. These hot regions are likely to be in the vicinity of the spark plugs, where the rich combustion is occurring. Figure 6.6 shows a scatter plot of HC versus NOx emissions for many of the individuals from the Case A evolution (85 generations in all). Some individuals have been omitted because their values of HC were extremely high and would mask the details of the other individuals with more reasonable HC values. These outliers are caused by extremely poor or unsuccessful combustion designs. Hence most of the fuel remains as unburned HC and power is extremely low which gives a very large value for HC in g/kW h. The optimum (A-1) and individual A-2 are indicated on the plot, along with the baseline operating case for reference. It can be seen that a wide range of possible emissions characteristics are possible with the different designs. It is also clear that the optimization strategy was able to successfully find candidate optimal designs, in terms of the performance characteristics studied. Figure 6.7 shows a similar scatter plot, displaying the indicated specific fuel consumption (ISFC) versus total wall heat transfer (WHEAT). The plot verifies the fact that both designs A-1 and A-2 act to increase wall heat transfer. A-2 is able to achieve a sizeable reduction in fuel consumption (around 7%), while A-1 gives a marginal reduction over the baseline case.

6.1.1.7 Summary Optimization of the part load operating parameters for reduction of emissions, fuel consumption, and heat transfer in a 2-stoke, direct-injected engine has been successfully conducted. Two candidate optimal designs have been revealed, each offering distinct characteristics, and advantages over the baseline operating strategy. The results demonstrate the successful application of single merit function, evolutionary search techniques with multidimensional engine modeling for engine performance enhancement. Additionally, the results are insightful and

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Fig. 6.6 Scatter plot displaying HC versus NOx

Fig. 6.7 Scatter plot displaying ISFC versus WHEAT

cost-effective, while allowing considerable flexibility in the variety, and diversity of parameters investigated. This study has shown that it is possible to obtain similar performance characteristics using substantially different operating strategies in the engine studied. Additionally, the computational evidence suggests that the fuel injection angle plays a relatively unimportant role in the performance characteristics of this engine, at the operating condition studied. This is likely due to the effective spray atomization which produces drops that are so small that their dispersion is controlled by the injector jet momentum. At the operating condition of the study, comparable performance was seen to be achievable with both single and split-fuelinjection strategies. It should however be noted that a unique good performing operating strategy did emerge from the investigation of split-injections that was

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not replicated in the single injection designs (i.e., design A-2). This demonstrates the ability of split injections to produce varied engine responses, some that are not possible with a single-fuel injection strategy. Finally, it should further be mentioned that in the present optimization study, emissions such as carbon monoxide and soot were not considered in the determination of the engine performance merit function. Should they have been considered, the outcome of the study could potentially be quite different. Also, designs A-1 featured some form of rich, diffusion-flame-like combustion near the spark plug locations that may very well have given rise to soot formation. The version of the CFD code used did not feature a gasoline soot model. This and the fact that soot is not a regulated emission for spark-ignited engines at that time, are reasons why it was not considered in merit function calculations. The use of the multiobjective methodology is discussed in the next sections.

6.1.2 Optimization of a Caterpillar Heavy-Duty Diesel Engine 6.1.2.1 Research Background and Objectives Due to its superior durability, drivability and fuel efficiency, the diesel engine has found broad application in both heavy-duty vehicles and off-highway engineering vehicles and equipment. Concerns about the effects of global warming have stimulated increased interest in diesel engines since fuel consumption based on the power output of the diesel engine is lower than that of the gasoline engine. However, the traditional diesel engine suffers from relatively high nitrogen oxide (NOx) and soot emissions, and strategies to reduce either the NOx or soot usually result in increased emission of the other. With more-andmore stringent emission standards, the diesel is facing the challenge of meeting these more environmentally-friendly emissions regulations while maintaining fuel economy. For any combustion process, boundary and initial conditions are two influential aspects, and particularly the preparation of the fuel-air mixture also critically influences compression ignition diesel combustion. For a diesel engine operated at different loads, the in-cylinder thermal conditions vary considerably, which results in different spray behaviors, combustion characteristics, and pollutant formation. It can be anticipated that different injection strategies and matching of the piston geometry and spray plume are needed for engines under different operating conditions in order to reduce emissions and fuel consumption. This example presents an optimization study of a heavy-duty diesel engine operated at both high-load and low-load for better understanding of the effects of bowl geometry, spray targeting, and swirl ratio on engine operation. KIVA3v2 code with the Characteristic Time Combustion (CTC) model was integrated with NSGA II code (http://www.iitk.ac. in/kangal/codes.shtml) to perform the optimization. The non-parametric regression analysis tool (Lin and Zhang 2006; Liu et al. 2006), COSSO, is also used to

190 Table 6.6 Engine and injector specification

6 Applications Baseline engine

Caterpillar DI Diesel

Combustion chamber Swirl ratio Bore 9 Stroke (mm) Bowl width (mm) Displacement (L) Connection rod length (mm) Geometric compression ratio Fuel injector nozzles Spray pattern included angle Injection pressure (bar) Nozzle orifice diameter (mm)

Quiescent, direct injection 0.5 137.16 9 165.1 97.8 2.44 261.6 16.1:1 8 holes, equally spaced 154 1,600 0.217

post-process the optimized results to provide more visible relations between design parameters and objectives. Three primary objectives of the present study are summarized as follows: 1. To search for optimal combinations of piston bowl geometry, spray targeting, and swirl ratio to enhance the mixing and post-combustion oxidation processes in order to simultaneously reduce both NOx and soot emissions and to improve fuel economy for a heavy-duty diesel engine at high-load and low-load. 2. To identify dominant design parameters that influence combustion and pollutant formation for this type of engine at the specific operating conditions of interest. 3. To reveal the relationships between design parameters and objectives both qualitatively and quantitatively by an advanced regression technique and with in-cylinder visualization.

6.1.2.2 Engine Description and Operating Condition The modeled engine is a single-cylinder, direct-injection, 4-stroke diesel research engine, based on a Caterpillar production engine. The geometric specifications and fuel injector parameters are summarized in Table 6.6. The investigated operating conditions were determined based on Mode 4 and Mode 6 investigated by Montgomery and Reitz (1996) which correspond to 95% and 20% load at high speed, respectively. However, slight changes were made for the modeling work, as indicated below. The global equivalence ratio and EGR rate play different roles on emissions reduction. For high-load operation, they are usually limited by current turbo chargers. For the low-load case, the EGR rate cannot be increased to a high level due to the low available exhaust pressure that determines the mass flow rate of the recirculated exhaust gases. In this situation, the global equivalence ratio and EGR levels need to be balanced by considering the engine operating conditions, the intake charge conditions, and emissions

6.1 Engine Optimization with Simple Combustion Models Table 6.7 Baseline operating conditions

191

Conditions

High-load

Low-load

Speed (rev/min) IVC temperature (K) IVC pressure (kPa) Load (%) Injection quantity (mg/cyc) EGR level (%) Global equivalence ratio O2 Concentration (vol%)

1,672 385 310 95 229 25 0.60 17.65

1,672 370 153 20 70.9 20 0.33 19.52

trade-off relations. Based on the assumption of complete combustion, Shi and Reitz (2008a) used a simple analysis code to estimate the initial conditions, which is also adopted here. The engine speed of Mode 6 was adjusted to be the same as Mode 4 in order to isolate the effect of speed on the results. Table 6.7 lists the operating conditions considered.

6.1.2.3 Optimization Parameters and Objectives The primary goal of this study is to find optimal combustion boundary conditions, i.e., combustion chamber (bowl) shapes, for a heavy-duty engine at high-load and low-load. In addition, optimal combinations of spray targeting and swirl ratio levels as a function of combustion chamber shape were searched simultaneously in order to further understand the effects of the initial flow conditions and the spray development on combustion, with the objectives of reducing both NOx and soot emissions and improving fuel economy. Shi and Reitz (2008a) found that the SOI and the bowl pip height also influence the spray targeting and development significantly. These two parameters were therefore included to supplement their previously considered seven design variables. For the low-load case, Montgomery and Reitz (1996) pointed out that high injection pressure does not necessarily benefit emissions reduction and decrease fuel consumption due to over-mixing of the mixture and the possibility of large amounts of spray impingement. This motivates the interest of investigating the effects of injection pressure at the low-load operating condition. To summarize, a total of nine parameters, including the injector spray angle, swirl ratio, SOI, and six different parameters that define the bowl geometry were studied for the high-load case. An additional parameter of injection pressure was applied to the low-load case. The compression ratio was kept fixed as 16.1 and the six bowl geometric parameters enable a search of a wide range of bowl shapes, and also allow for the consideration of reentrant-type bowls. The number of geometry parameters used gives a reasonable search space using the Kwickgrid methodology (Wickman 2003) that is described in Sect. 4.1, although more parameters are available in the grid generator to define the bowl shapes. Figure 6.8 illustrates the six bowl geometry parameters optimized.

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Fig. 6.8 Parameters of bowl geometry

Table 6.8 List of optimization parameters and their ranges

Parameters A—(% bowl depth) B—(% bowl diameter) C—(% cylinder diameter) 1—Bezier curve control point 2—Bezier curve control point 3—Bezier curve control point Injector spray half-angle Swirl ratio SOI (ATDC) Injection pressure (bar)

Range High-load

Low-load

65 to 75 74 to 80 71 to 84 0.1 to 0.7 0.3 to 0.9 0.8 to 1.5 60 to 85 0.5 to 2.0 -15 to -13 2,000

65 to 75 74 to 80 71 to 84 0.1 to 0.7 0.3 to 0.9 0.8 to 1.5 60 to 85 0.5 to 2.0 -10 to +10 850 to 2,000

Table 6.8 provides the ranges of the parameters, which were determined so as to avoid infeasible bowl designs but still to maintain diversity. Examples of different bowl shapes (axisymmetric) within the parametric space given by Table 6.8 are shown in Fig. 6.9. The spray angles target a wide region of the piston curvature, from the bowl floor up to the bowl lip. Considering the ability of the intake system of the experimental engine (Montgomery and Reitz 1996), the range of swirl ratio was restricted to a relative narrow range. The SOI range for the highload operation was determined based on maximum power-output of the baseline design of the engine, and for the low-load case a broader range was considered to explore more emissions trade-offs. The injection pressure for the high-load case was fixed at 2,000 bar in order to reduce the injection duration. NOx and soot emissions are two of the most important concerns for diesel engine designs, and the existence of a trade-off relation is well known to engine researchers. Therefore reductions of these two emissions were two main objectives. Gross indicated specific fuel consumption (GISFC1) was also included as the third objective. 1 GISFC refers to the work delivered to the piston over compression and expansion strokes, i.e., from BDC to TDC to BDC. In the present work, ‘‘GISFC’’ is defined as the output work from IVC to EVO for convenience. Apparently, there is a difference between these two ‘‘GISFC’’. This difference is a constant for the same engine and same operating conditions. Therefore it will not affect the results and conclusions.

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Fig. 6.9 Illustration of representative bowl geometries generated by Kwickgrid (one half geometry shown due to symmetry)

Fig. 6.10 Pareto front and optimal solutions relative to the baseline shown at upper right for the high-load condition

6.1.2.4 Results and Discussion The most important and interesting optimal solutions are located on the Pareto front. In the present optimization study of the high-load engine with the nine design parameters, a total of 65 optimal designs were found on the Pareto front, which is shown in Fig. 6.10. These optimal designs were found to be able to reduce NOx and soot emissions and to improve fuel economy simultaneously, compared to the baseline engine under the same operating conditions. Since the

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Fig. 6.11 Pareto front and optimal solutions relative to the baseline shown at upper right for the low-load condition

goal of the current work is to minimize three objectives, it might be expected that Pareto solutions would form a surface in a three-dimensional objective-space. However, examination of Fig. 6.10 reveals that the shape is more line-like. This implies that two of the objectives are somewhat correlated. Further observation of the figure indicates that GISFC and soot have very similar trends in that designs that feature low GISFC also have low soot, and vice versa. The general information collected from the Pareto solutions shows that a design with a small and deep bowl has higher GISFC, but favors low NOx emissions. For a shallow and wide bowl design, soot is reduced dramatically, and so is GISFC. However, a penalty has to be paid in NOx emission, which demonstrates the well-known soot and NOx trade-off in diesel engines. It is also found that all Pareto solutions featured a flat spray included angle and medium level swirl ratios. The fact that advancing SOI timing increases the portion of premixed combustion and thus produces more NOx emissions can also be concluded based on the analysis of the Pareto solutions. The low-load optimization results are shown in Fig. 6.11. Differing from Fig. 6.10, the solutions cover more of the objective-space, and the Pareto cases are also more diversified. This is mainly due to the fact that broader ranges of injection parameters were optimized, including SOI and injection pressure. The injection process also found some extreme Pareto cases, which have very high values for some of the objectives (up and down arrows indicate change compared to baseline also shown in the figure), but show promise for the other two objectives, such as Cases 1 and 5. Compromise results, such as Cases 2 to 4, are of more interest.

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Case 3 simultaneously reduces emissions and fuel consumption compared to the baseline case. Compared to the high-load optimization, the GISFC is less correlated with soot, which makes the line-like Pareto front appear as a surface (not shown with current view angle). Further examination of the low-load optimal designs indicates that the Pareto solutions feature different aspects from the high-load optimal solutions. Firstly, the spray included angles are no longer restricted to high values, although most of the optimal solutions still have flat spray targeting. Secondly, the effect of bowl size become less important compared to that of the high-load optimal designs. No small bowl design was found on the Pareto front, and all optimal designs feature mid range or large bowl diameters and also have a relatively large bowl floor. Thirdly, the Pareto solutions seek high swirl ratios, and most of them are larger than 1.5. Fourthly, high injection pressure does not certainly benefit emissions and fuel economy, and most of optimal solutions have a moderate injection pressure in the range of 1,400–1,700 bar. All these observations imply that spray target and its matching with the bowl geometry and initial flows behave differently under high- and low-load conditions. Therefore more details were explored with non-parametric and parametric studies as follows. In order to explore the relationships between the design-space and objectivespace, as well as to identify influential design parameters on emissions and fuel consumption, a non-parametric regression method, COSSO, was employed in this study. This method allows all of the GA results to be unified into response surfaces for visualization of trends. As shown in Fig. 6.10, Design 1 has a small and deep bowl, and Designs 2 and 3 feature with wide and shallow bowls. The first and second designs were selected as reference designs for the non-parametric studies, which are referred to as the small bowl and large bowl designs. They were systematically chosen such that their SOIs, swirl ratios, and spray targeting, as well as their general bowl curvatures were similar. It is of more interest to know the interacting effects of spray targeting and swirl motion on emissions and fuel consumption, and thus the response surfaces constructed on the related design parameters are given in Figs. 6.12 and 6.13, respectively. The trends of soot and GISFC on the objective-space were similar, and their response surfaces also resemble each other. Therefore, the response surfaces of GISFC are not listed in Figs. 6.12 and 6.13. Comparison between Figs. 6.12 and 6.13 shows that the response surfaces of NOx and soot for the small and large bowl designs are similar in general. For NOx emissions, the spray included angle is the most influential parameter, and the peak NOx emissions were found at medium values of the spray angle as illustrated in Figs. 6.12a, b and 6.13a, b, respectively. In Figs. 6.12b and 6.13b, reduced NOx emissions are favored by a low swirl condition, however, changes with swirl ratio are less than those associated with spray angle changes, so that the swirl ratio was the secondary effect on NOx emissions. SOI has less effect on NOx emissions for the small bowl design in Fig. 6.12a, but a slightly larger variation with SOI can be observed in Fig. 6.13a for the large bowl design.

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Fig. 6.12 Response surfaces for the small bowl design (Design 1 in Fig. 6.10) under the high-load condition. a Interaction of SOI and spray angle on NOx. b Interaction of spray angle and swirl on NOx. c Interaction of SOI and spray angle on soot. d Interaction of spray angle and swirl on soot

The order of parameters and how significantly they influence soot are the same as that obtained from the response surfaces of NOx, and the spray angle is still the dominant parameter. Similar to its effect on NOx, medium values of the spray angle contribute more soot. For both small and large bowls, the soot emissions reduce slightly as the swirl ratio increases, as shown in Figs. 6.12d and 6.13d. Note that NOx scale in Fig. 6.13 is larger than in Fig. 6.12. This means that NOx emissions are more sensitive to changes of spray angle, swirl ratio, as well as SOI in large bowl pistons. However, the soot emissions are affected more by the changes of those parameters in small bowl designs. Since it was shown previously that low-load operation was relatively insensitive to the bowl size compared to the high-load condition, the focus of the present nonparametric study and the subsequent parametric analysis were placed on spray injection parameters. The compromise Design 3 in Fig. 6.11 was selected as the reference design for COSSO. As indicated in Fig. 6.11, the results of GISFC are

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Fig. 6.13 Response surfaces for the large bowl design (Design 2 in Fig. 6.10) under the high-load condition. a Interaction of SOI and spray angle on NOx. b Interaction of spray angle and swirl on NOx. c Interaction of SOI and spray angle on soot. d Interaction of spray angle and swirl on soot

less correlated with soot emissions at low-load, and thus it is necessary to visualize the response surface for GISFC as well. The response surfaces of NOx with respect to SOI, spray angle, swirl ratio, and injection pressure and their interacting effects are given in Fig. 6.14. It is observed that retarding SOI has the primary influence of reducing NOx emissions, which is consistent with experimental observations, since the combustion temperature reduces as the SOI is retarded. But note that after 5 ATDC, the effect of SOI becomes weaker since the surface along with spray angle becomes flat. NOx emissions peak at about 77 spray angle, and this finding is similar to that obtained from the study on the high-load cases. Decreasing injection pressure helps reduce NOx emission as shown in Fig. 6.14c. Compared to the other parameters, the swirl ratio has the least effect on NOx emissions, though it can be seen that a high swirl ratio slightly promotes NOx production in Fig. 6.14b and c.

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Fig. 6.14 NOx response surfaces for the selected design (Design 3 in Fig. 6.11) under low-load condition. a Interaction of SOI and spray angle on NOx. b Interaction of spray angle and swirl on NOx. c Interaction of swirl and injection pressure on NOx

Fig. 6.15 Soot response surfaces for the selected design (Design 3 in Fig. 6.11) under low-load condition. a Interaction of SOI and spray angle on soot. b Interaction of spray angle and swirl on soot. c Interaction of swirl and injection pressure on soot

For the soot emissions, the SOI is still an important parameter, but the effects of other parameters become more important than they were on NOx. As seen in Fig. 6.15a, soot emissions are minimized at about 77 spray angle, opposite to the observation on NOx. However, retarding SOI also helps to reduce soot emissions, and this is believed to be the reason that most of the Pareto designs for low-load condition feature very late injection timings. Increasing swirl ratio or injection pressure benefits soot emissions as seen in Fig. 6.15b and c, which also indicates the difficulty of engine design due to the trade-off between NOx and soot. Comparison of Figs. 6.15 and 6.16 demonstrates that GISFC responds differently to the investigated parameters, which is a further challenge to engine design for low-load operation. For example, it was found above that retarding SOI helps reduce both NOx and soot emissions, However, Fig. 6.16a frustrates this finding in that the late injection timing deteriorates fuel economy significantly. However, it is also seen that if a large spray angle is employed, the effect of SOI on GISFC weakens. Therefore, in order to obtain both emissions reduction and fuel economy, a combination of large spray angle and late injection is needed. Figure 6.16c illustrates that GISFC decreases as the injection pressure increases. Furthermore, the effect of swirl ratio is again seen to be the least.

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Fig. 6.16 GISFC response surfaces for the selected design (Design 3 in Fig. 6.11) under low-load condition. a Interaction of SOI and spray angle on GISFC. b Interaction of spray angle and swirl on GISFC. c Interaction of swirl and injection pressure on GISFC

Table 6.9 Parametric study on the small bowl design for the high-load condition

Parameters

SOI (ATDC)

Swirl

Spray ()

Baseline Case 1 Case 2 Case 3 Case 4

-11.09 -15.00 -11.09 -11.09 -11.09

0.62 0.62 2.0 0.62 0.62

84.59 84.59 84.59 60.00 77.00

The above non-parametric analysis offers a pictorial view of the relationships between the design parameters and the objectives in the form of response surfaces. It is also of interest to explore the in-cylinder flow details in order to better understand how the emissions and fuel consumption are influenced by the spray targeting, as well as its matching with particular optimal combinations of the swirl and bowl geometry. Therefore, some representative designs were further studied parametrically and visualized. The parametric study also provides a validation of conclusions drawn from the non-parametric analysis. Two piston designs representing the small and large bowls were selected to perform the parametric analysis. The SOI, initial swirl ratio, and spray included angle were varied independently in different numerical experiments for each design as listed in Tables 6.9 and 6.10. Figure 6.17a and b illustrate the spray targeting with the different spray included angles for the two bowls. The simulations were conducted with the same KIVA-code with the CTC model used for the optimization study, and simulation results are listed in Tables 6.11 and 6.12 for the two designs, respectively. Compared to the baseline cases, advancing SOI (Case 1) increases NOx emissions slightly, but its effect on soot and GISFC are smaller. However, for the large bowl (Case 2 in Table 6.12) both emissions and fuel economy are deteriorated. High swirl ratio case leads to insignificant improvements for the small bowl design on soot and GISFC (Case 2 in Table 6.11). For the large bowl design, a lower value of spray angle of 60 reduces the NOx emission (Case 3 in Table 6.12), but soot and GISFC are increased. For the other cases, in Tables 6.11 or 6.12, small spray angles of 60 and 77 predict increased emissions and higher

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Table 6.10 Parametric study on the large bowl design for the high-load condition

Parameters

SOI (ATDC)

Swirl

Spray ()

Baseline Case 1 Case 2 Case 3 Case 4

-11.09 -15.00 -11.09 -11.09 -11.09

0.80 0.80 2.0 0.80 0.80

84.53 84.53 84.53 60.00 77.00

Table 6.11 Results of parametric study for the small bowl design for the high-load condition

Objectives

NOx (g/kg fuel)

Soot (g/kg fuel)

GISFC (g/kW h)

Baseline Case 1 Case 2 Case 3 Case 4

20.12 26.27 27.56 23.71 34.05

0.34 0.35 0.30 0.58 0.81

213.44 214.93 212.20 220.49 228.78

NOx (g/kg fuel)

Soot (g/kg fuel)

GISFC (g/kW h)

31.66 34.14 46.74 29.98 38.02

0.18 0.18 0.42 0.51 0.66

200.14 201.14 203.45 216.24 225.83

Table 6.12 Results of Objectives parametric study for the large bowl design for the high-load Baseline condition Case 1 Case 2 Case 3 Case 4

Fig. 6.17 Spray targeting and piston profiles (high-load). a Spray targeting of the small bowl design. b Spray targeting of the large bowl design

fuel consumption, compared to the baseline cases. It is apparent that the results obtained from the parametric study are consistent with the response surfaces given by the non-parametric analysis in Figs. 6.12 and 6.13, and the reliability of the method is thus further verified.

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Fig. 6.18 Thermal conditions and emissions history for the small bowl design at the high-load condition. a Pressure traces and heat release rate (HRR). b NOx and soot emissions

Fig. 6.19 Thermal conditions and emissions history for the large bowl design at the high-load condition. a Pressure traces and heat release rate (HRR). b NOx and soot emissions

Since the results are relatively insensitive to the change of SOI, these cases are not analyzed further. Figure 6.18 shows a comparison of pressure traces, heat release rates and emissions between the baseline case and Cases 2 to 4 for the small bowl design, and the comparison for the large bowl design is given in Fig. 6.19. As can be seen in Fig. 6.18a, although the baseline case has the lowest peak pressure, its HRR trace implies that significant late cycle-combustion occurs starting around 20CA, which contributes more expansion work, and this explains why the baseline case has the best fuel economy. Because of its lower peak pressure (corresponding to a lower mean temperature), the baseline case also has the lowest NOx emission, as indicated in Fig. 6.18b. In Fig. 6.18b, except for Case 4, the soot production rates are roughly the same for all cases. But the oxidation rates are lower for Cases 3 and 4, in which the spray angles are smaller compared to the baseline case and Case 2. The high soot oxidation rates for the

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Fig. 6.20 Temperature distribution for the small bowl design at the high-load condition (side view)

baseline case and Case 2 are due to their relatively high temperatures during the expansion process. This phenomenon points out the importance of the late cyclecombustion process on soot reduction. Case 2 has higher swirl ratio than that of the baseline case, which probably strengthens the soot oxidation process and thus produces less engine-out soot emissions. For the large bowl design, as indicated in Fig. 6.19a, the late cycle-combustion of the baseline case is still the reason that it has the lowest fuel consumption, but the peak pressure of Case 3, in which spray targeted directly to the bowl crown (Fig. 6.17b), has the lowest value. It is therefore not surprising to find that Case 3 has the lowest NOx emissions in Fig. 6.19b. For the large bowl design, the high swirl ratio does not result in a high soot oxidation rate for Case 2, and thus the baseline case has the lowest soot emissions. The above discussions are further examined with the help of visualization of in-cylinder temperature distributions and flow motions, as illustrated in Figs. 6.20 and 6.21. The crank angle when the temperature distribution is plotted in Figs. 6.20 and 6.21 is 25 ATDC during late cycle-combustion. For the small and large bowls, cases with flat spray angles that target the piston top-land have slower burning rate at TDC compared to other cases. This is due to the fact that the small space around the piston top-land limits the spray mixing process. For Cases 4 in Figs. 6.20 and 6.21, the 77 spray included angle causes the spray jet to be injected towards the bowl edge, where sufficient ambient air can be entrained during the mixing and combustion process, and thus the burning rate is accelerated. Due to the high combustion temperature, NOx formation is favored and the soot production rate also increases.

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Fig. 6.21 Temperature distribution for the large bowl design at the high-load condition (side view)

As the piston descends, during the reverse squish process, the soot is transported to the area close to the piston top (not shown here) by the in-cylinder bulk flow, for which the direction is indicated by the velocity vectors in the figures. However, during this stage, the relatively low temperature (due to less late cyclecombustion) does not benefit soot oxidation and thus eventually the highest engine-out soot emissions result. For the cases with the smallest spray angle 60, the spray jet is targeted at the bowl floor, where a fuel film is formed because of the large spray impingement. The evaporation rate of the fuel film is much slower than for atomized spray droplets, which leads to a slower combustion rate and thus a lower temperature. This is the reason that Cases 3 for the small and large bowl design produce less NOx, but the fuel film contributes to increase the soot emissions. The piston profile of the large bowl has a smaller distance between the piston top and the bowl floor than that of the small bowl. Stronger squish flow is therefore formed during the spray development and this enhances the spray mixing. On the other hand, considering that the spray penetration is almost the same for each piston design (because they have the same injection conditions), the jet in a large and shallow bowl entrains less air along its trajectory than a jet in the small and deep bowl does, which results in higher local equivalence ratios, and thus higher combustion temperatures. The higher NOx emissions and combustion efficiency in large bowl designs can thus be explained. It was shown in the non-parametric study section that both emissions and fuel consumption are subject to the interaction effects of the SOI, spray angle, swirl ratio, as well as the injection pressure for low-load. A parametric study was also conducted on the reference design, Design 3 in Fig. 6.11, in order to further reveal and understand the behavior of the optimal designs. For each parameter, two

204 Table 6.13 Parametric study for low-load condition

6 Applications Parameters

SOI (ATDC)

Spray ()

Swirl

Inj. Pre.

Baseline Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8

9.81 5 0 9.81 9.81 9.81 9.81 9.81 9.81

83.87 83.87 83.87 77.00 60.00 83.87 83.87 83.87 83.87

1.87 1.87 1.87 1.87 1.87 3.00 0.50 1.87 1.87

1,683 1,683 1,683 1,683 1,683 1,683 1,683 2,000 1,200

Fig. 6.22 Spray targeting for the reference design (low-load)

values were studied independently, and thus a total of eight cases were examined, as listed in Table 6.13 and in Fig. 6.22. Note that the swirl ratio of Case 5 was selected to be 3.00, which is beyond the upper boundary of the previous search range. The results of the parametric study are listed in Table 6.14, which also agree with the results from the response surfaces predicted by the non-parametric study. Figures 6.23, 6.24, 6.25, and 6.26 show the in-cylinder pressure, heat release rate, and emissions as functions of crank angle for Cases 1 to 8 compared with the baseline case. As shown in Fig. 6.23, the late injection event of the baseline case prevents high temperature combustion and increases the piston work during the late expansion stroke. This is the reason that the baseline design produced low NOx and improved fuel consumption due to lower heat losses. Similarly, the low combustion temperature also suppresses soot formation, but does not negatively affect the soot oxidation. This can be observed from the fact that the slopes of the soot histories for the three cases are close in Fig. 6.23b, which implies that they

6.1 Engine Optimization with Simple Combustion Models Table 6.14 Results of parametric study for low-load condition

205

Objectives

NOx (g/kg fuel)

Soot (g/kg fuel)

GISFC (g/kW h)

Baseline Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8

21.81 20.44 34.53 34.00 11.99 27.93 18.90 25.19 15.80

0.044 0.127 0.120 0.060 0.100 0.030 0.069 0.034 0.069

193.14 195.53 191.51 191.37 238.64 189.49 203.26 190.99 200.32

Fig. 6.23 Thermal conditions and emissions history for low-load (Cases 1 and 2—effect of SOI). a Pressure traces and heat release rate (HRR). b NOx and soot emissions

have similar soot oxidation rates. This is understandable considering that at the present low-load condition the global equivalence ratio is very low, and the excess in-cylinder air oxidizes soot very fast after the combustion starts. The oxidation time determined by SOI then becomes a secondary effect on soot oxidation. However, the approach of retarding SOI to reduce emissions and fuel consumption cannot be applied to the high-load case, because the large amount of fuel injected also reduces in-cylinder temperatures, which causes difficulty with ignition. Moreover, the high local equivalence ratio decreases the soot oxidation rate, and the available time for the soot oxidation process becomes more important. It is apparent that the highest fuel consumption of Case 4 is due to its large spray impingement, as indicated in Fig. 6.22. The formed fuel film contributes most to soot production for this case, and because less fuel is burned, the combustion temperature of Case 4 is lower than that of the other cases, which benefits NOx reduction. According to the spray targeting with a spray angle of 77 pictured in Fig. 6.22, the utilization of the surrounding air during combustion for this case is the best, and thus more NOx emissions are produced and fuel consumption is

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Fig. 6.24 Thermal conditions and emissions history for low-load (Cases 3 and 4—effect of spray angle). a Pressure traces and heat release rate (HRR). b NOx and soot emissions

Fig. 6.25 Thermal conditions and emissions history for low-load (Cases 5 and 6—effect of swirl ratio). a Pressure traces and heat release rate (HRR). b NOx and soot emissions

reduced. But the baseline case provides more oxygen after the main combustion stage, which reduces engine-out soot emissions through an enhanced oxidation process. The above discussions are illustrated by the corresponding curves in Fig. 6.24. The change of swirl ratio in Cases 5 and 6 influences emissions and fuel consumption as depicted in Fig. 6.25. It is worthy of note that the effect of swirl ratio directly reveals the trade-offs among NOx, soot and GISFC. The increase of swirl ratio helps promote fuel-air mixing and thus improves the premixed combustion, which favors reduction of soot emissions and fuel economy, but results in more NOx emissions. A decrease of swirl ratio leads to reverse trends of emissions and fuel consumption. Therefore simply altering the swirl level is unable to reduce both NOx and soot emissions, while simultaneously obtaining fuel economy. Optimal spray targeting with corresponding bowl designs are both crucial in terms of reducing emissions and fuel consumption.

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Fig. 6.26 Thermal conditions and emissions history for low-load (Cases 7 and 8—effect of injection pressure). a Pressure traces and heat release rate (HRR). b NOx and soot emissions

Similar to the effect of swirl ratio, the present study on the effect of injection pressure also shows the existence of trade-offs among NOx, soot and GISFC. This can be explained since increasing the injection pressure increases the liquid phase momentum that helps the fuel/air mixing, similar to the effect of increasing the momentum of the gas phase, for example, by increasing the swirl level. The effect of injection pressure becomes more complicated when spray impingement has to be considered. In the present study, Case 7 has the highest injection pressure, and its heat release rate is also the largest, as shown in Fig. 6.26, which is the source of high NOx emissions, but this drives fast soot oxidation and improves fuel consumption. Cases 3, 5, and 7 were also visualized to show how the combination of spray targeting, swirl motion, as well as injection pressure influences the emissions and combustion efficiency. As depicted in Fig. 6.22, the spray targeting of Case 3 favors utilization of the surrounding air along the jet trajectory. Therefore, better mixing and combustion can be expected, which contributes to the largest high temperature region in the cylinder, as shown in Fig. 6.27a. The high temperature region is where NOx mainly forms. Because the spray jet of Case 3 targets the bowl edge close to the bowl floor, it is difficult to further oxidize burnt residual gases that are trapped by the swirl centrifugal effect (Liu et al. 2006). This results in a relatively high soot concentration area in Fig. 6.27b for Case 3. The swirl ratio was increased to 3.0 for Case 5, and this apparently improved fuel-air mixing, which can be confirmed by the reduced combustion area in the mid range of the bowl close to piston top, as shown in Fig. 6.27b. The stronger centrifugal effect of the higher swirl ratio traps soot near the bowl edge, where the oxidation rate is relatively low. Case 7 has a very similar temperature distribution to that of the baseline case, but its high temperature area is larger than that of the baseline case, which is attributed to its increased spray penetration. No significant fuel film is found due to the higher injection pressure, because the spray jet is targeted at the bowl lip and also the fuel evaporates fast under the thermal conditions prevailing at this

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Fig. 6.27 In-cylinder details of representative designs. a Temperature distribution (side view). b Soot distribution (side view)

injection timing. Because of the low boost pressure and intake temperature, the spray penetration for the low-load case is longer than that for the high-load case. This is why the optimal solutions for low-load are relatively insensitive to the bowl size, since mid-size or large-bowls are needed to avoid spray impingement. According the present study, the curvature of the bowl top edge becomes more important if the combined effect of swirl ratio and spray targeting are taken into consideration. For the low-load condition more focus on piston bowl design details may be needed, and for the high-load condition, the global geometry is more important. Hence, it is suggested to start the search for an optimal piston bowl

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209

Table 6.15 Parametric study for the low-load condition using the second high-load piston design in Fig. 6.10

Parameters

SOI (ATDC)

Spray ()

Swirl

Inj. Pre.

Case 1 Case 2 Case 3

9.81 9.81 9.81

84.53 84.53 84.53

1.87 0.8 0.8

1,683 1,683 1,200

Table 6.16 Results of parametric study for the low-load condition using the second high-load piston design in Fig. 6.10

Objectives

NOx (g/kg fuel)

Soot (g/kg fuel)

GISFC (g/kW h)

Case 1 Case 2 Case 3

20.34 17.32 13.12

0.049 0.047 0.078

196.21 201.00 211.93

geometry design with the high-load case, and then to improve the details under a low-load condition. For a practical engine, the combustion chamber geometry and the spray included angle cannot be varied easily. Thus it is of interest to seek a compromise optimal design for both conditions. It is desired to achieve emissions reduction and improved fuel consumption at both high-load and low-load by optimizing other flexible design parameters, such as the swirl ratio and the injection timing and pressure. It was shown in Fig. 6.10 that high-load Design 2 reduced emissions and fuel consumption simultaneously, compared to the baseline design. In addition, it is also observed that its combustion chamber shape shares similar features with Design 3 in Fig. 6.11 for the low-load optimization. Therefore, Design 2 and its corresponding spray angle (84.53) were selected to conduct a study under the low-load condition. The three cases listed in Table 6.15 were studied, and the results are given in Table 6.16. Compared to the results from the original optimized bowl design, Cases 1 and 2 are seen in Table 6.16 to reduce both NOx and soot emissions, without sacrificing fuel economy significantly. This indicates that optimal piston designs exist for both high-load and low-load conditions, but it would be necessary to provide different swirl ratios through intake system design and to employ different injection pressures and timings, for example by using a common-rail injection system to accommodate the different loads in order to achieve clean and highly efficient combustion.

6.1.2.5 Summary This example demonstrates the use of multi-dimensional CFD simulations code with a relatively simple combustion model and with a multi-objective genetic algorithm, NSGA II, to optimize the piston bowl geometry, spray targeting, spray injection event, and swirl ratio for a heavy duty diesel engine at high- and lowload. Optimal solutions were obtained that simultaneously reduced emissions and

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improved fuel consumption for both low- and high-load operating conditions. A non-parametric regression analysis tool (COSSO) enabled a quantitative study of the influences of each parameter and their interactions on the optimal objectives. The results from the non-parametric study were then verified by a detailed parametric study that further explored several of the most influential design parameters. In-cylinder visualization was used to enhance the understanding of the flow interactions. The following conclusions can be drawn from the present study: • The use of MOGA enables an efficient search of global optimal solutions with conflicting objectives. The use of non-parametric regression analysis together with the GA optimizations helps to quantify the influences of design parameters on the optimal objectives, which were also consistent with the results obtained from a stand-alone parametric study. This study confirmed that the trends revealed by the NPR method are reliable. • The optimization showed that the high-load operating condition is more sensitive to the combustion chamber geometrical design compared to the low-load condition. This was revealed by examining the optimal solutions for the highload optimization, in which the Pareto cases feature a broad range of bowl sizes and geometries. • By choosing an optimal combustion chamber design from the high-load optimization study and varying swirl ratio, injection timing and pressure, excellent performing designs were also found using the high-load optimal chamber geometry for the low-load condition. This, taken with the second conclusion suggests that engine optimization studies for all operating loads should start with an optimization study of piston geometry, spray targeting for the high-load condition. Then further optimization on the spray injection event and swirl ratio should be conducted for the low-load condition.

6.1.3 Optimization of a DDC Heavy-Duty Diesel Engine In this example, a heavy-duty diesel engine produced by Detroit Diesel Company (DDC) was investigated. Similar to the example in Sect. 6.1.2, a multi-objective genetic algorithm methodology was coupled with the KIVA3v2 code and automated mesh generator. Three different operating conditions, which represent lowload, mid-load, and full-load conditions, were considered. The input parameter ranges were determined using a design of experiments methodology. The NSGA II was used for the optimization and the KIVA3v2 code with improved ERC submodels was used. The characteristic time combustion model and Shell ignition model were employed to improve computational efficiency. Three individual optimizations were performed. SOI, spray angle, hole size, and the number of holes were optimized. The optimizations are subject to design constraints including peak cylinder pressure and the temperature at exhaust valve opening. The sensitivity of engine performance to the design parameters of interest was

6.1 Engine Optimization with Simple Combustion Models Table 6.17 Baseline engine specifications

Table 6.18 Operating conditions of Mode A25, B50, and A100

211

Combustion chamber

Direct injection

Swirl ratio Bore 9 Stroke (mm) Displacement (L) Connection rod length (mm) Geometric compression ratio Fuel injector nozzles Spray pattern included angle Nozzle orifice diameter (mm)

0.5 133 9 168 2.334 269.3 16.1:1 6 holes, equally spaced 146 0.2304

Boost pressure (bar) Boost temperature (K) Fuel injected (mg) DOI () RPM EGR (%)

A25

B50

A100

1.59 402.7 68.62 5.5 1,265 40.5

2.45 398.45 131.34 15 1,558 29.5

3.45 350.86 246.07 27 1,266 25.54

evaluated using a K-nearest neighbor regression method (c.f., Sect. 2.3) and a response surface analysis method. The KIVA3v2 code was integrated with commercial optimization software, modeFRONTIERTM (ESTECO). As a compromise between the run time and the model requirements, the mesh cell size was specified at 2 mm.

6.1.3.1 Engine Description and Operating Conditions The base engine has an open bowl piston design. The basic features of the engine are listed in Table 6.17. Three different modes A25, B50, and A100, were optimized in the present work. They represent low-load, mid-load, and full-load conditions, respectively. The operating conditions are listed in Table 6.18.

6.1.3.2 Results and Discussion Numerical simulation was first validated by comparing with available experimental data (Ge et al. 2009a). Figure 6.28 shows the measured pressure and heat release rate (indicated by symbols) and the corresponding numerical results (indicated by lines). The numerical results are in reasonable agreement with the experimental data. Figure 6.29 shows the comparison of measured and simulated NOx and soot emissions. The NOx emissions were well predicted using the present models. The predicted soot emissions were in reasonable agreement with the measurements.

212 Table 6.19 Search space of nozzle optimization

6 Applications Parameter

Min.

Max.

Resolution

Spray angle #holes Flow rate (L/min) SOI (A25) (ATDC) SOI (B50) SOI (A100)

140 5 1.65 -10 -10 -10

160 12 2.05 8 8 6

11 8 5 10 10 9

The trend of predicted soot emission with SOI for Mode A25 matches the trend of the measurement very well. The optimization search space is detailed in Table 6.19. The resolution is the total number of discrete steps in the search space for each parameter. The optimizations are subject to physical constraints including peak in-cylinder pressure (\22 MPa) and exhaust temperature (\1,180 K). Figure 6.30 shows all of the citizens including Pareto citizens, and the baseline design for all three operating conditions A25, B50, and A100. Normal citizens, Pareto citizens, and the baseline design are indicated by red circles, black triangles, and blue squares, respectively. Also shown on the A25 and B50 plots are alternative designs (green inverted triangle), which have superior performance compared to the baseline design. Note that the Pareto citizens are determined from the perspective of three objectives. Therefore, some Pareto solutions are not optimal in 2D plots (c.f., right column of Fig. 6.30). At A25 the alternative design has a 19% NOx reduction, 32% soot reduction, and 2.7% GISFC reduction compared to the baseline design. At B50 the alternative design has a 14.5% NOx reduction, 46% soot reduction, and a 1% GISFC increase compared to the baseline design. The baseline design is on the Pareto front for A100. For Mode A100, the pollutant emissions of the baseline engine are nearly optimal. Figure 6.31 shows the response surfaces of GISFC, soot, and NOx emissions for SOI versus nozzle flow rate, number of holes, and the spray angle for mode A25. Also shown is the baseline design (black circle). The base design has a SOI of -7.25 ATDC, spray angle of 73 (half angle), 6 nozzle holes, and a 1.75 L/min. nozzle flow rate. The alternate nozzle design has a SOI of 4 ATDC, spray angle of 77, 11 nozzle holes, and a 1.9 L/min. nozzle flow rate. The retarded injection timing is the most influential parameter in achieving the reduced NOx emissions. The increased spray angle and the increased number of holes led to the reduced soot and GISFC. Figure 6.32 shows the response surfaces of GISFC, soot, and NOx emissions for SOI versus nozzle flow rate, number of holes, and the spray angle for mode B50. Also shown is the baseline design (black circle). The base design has a SOI of -3.0 ATDC, spray angle of 73 (half angle), 6 nozzle holes, and a 1.75 L/min. nozzle flow rate. The alternate nozzle design has a SOI of 0 ATDC, spray angle of 76, 7 nozzle holes, and a 1.45 L/min. nozzle flow rate. The retarded injection timing is the most influential parameter in achieving the reduced NOx emissions. The increased spray angle led to the reduced soot emissions.

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Fig. 6.28 Pressure and heat release rate of: a Mode A25; b B50; and c A100

Fig. 6.29 Engine-out NOx and soot emissions. Experimental soot data of the A25 case (lines) is from laser diagnostic measurement (right axis). The remaining experimental data is from smoke meter and shown on the left axis

Figure 6.33 shows the response surfaces of GISFC, soot, and NOx emissions for SOI vs. nozzle flow rate, number of holes, and the spray angle for mode A100. Also shown is the baseline design (black circle). The base design is nearly optimal at A100.

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Fig. 6.30 All citizens and Pareto citizens from optimization, and baseline design of nozzle optimization. Top row: Mode A25; middle row: Mode B50; bottom row: Mode A100

Overall, the number of nozzle holes is the most important parameter for fuel economy and pollutant emissions. A number of nozzle holes within the range between 5 and 9 gives better fuel economy and pollutant reduction for full load case. For mid-load and low-load cases, the number of nozzle holes is equally as important as the SOI. More nozzle holes result in better fuel consumption. For the low load case, more nozzle holes result in lower soot emissions, too. More nozzle holes and lower flow rate implies smaller nozzle hole area and smaller initial drop size. Smaller drops have higher evaporation rates and this leads to a shorter spray

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215

Fig. 6.31 Response surfaces of SOI and flow rate, SOI and nozzle hole number, SOI and spray angle for mode A25. Left column: GISFC; middle column: soot; right column: NOx. Black circle: baseline engine

penetration distance. For the full load case, the in-cylinder temperature and pressure is higher. Thus, the droplets evaporate much faster than the lower load cases. In fact, the larger droplets generated by the larger nozzle hole have longer penetration without wall impingement, which will benefit the mixing of the fuel vapor and oxygen. The same size of nozzle hole may result in significant wall impingement in the mid- or low-load cases. Therefore, a smaller nozzle hole is preferred in these cases. The effects of the flow rate are not as significant as the number of nozzle holes, because its relative change is smaller than the number of nozzle holes: the ratio of maximum and minimum is 1.25 and 2.4 for flow rate and hole number, respectively. For NOx emissions, SOI is the first or second most important parameter. NOx formation is relatively slower than many other elementary reactions and the total NOx emission is proportional to the total lifetime of the high temperature mixtures. Early injection usually has earlier ignition, which provides longer time for NOx formation. Thus, an early injection usually has higher NOx emissions than a late injection. For fuel economy and soot, the spray angle is slightly more important. A medial spray angle is not favored. A wide spray angle leads to better fuel economy, while NOx reduction requires a narrow one. In general, a

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Fig. 6.32 Response surfaces of SOI and flow rate, SOI and nozzle hole number, SOI and spray angle for mode B50. Left column: GISFC; middle column: soot; right column: NOx. Black circle: baseline engine

wide spray angle gives better soot reduction. Under certain conditions, a narrow one also gives lower soot emission, especially for the full load case. The combustion efficiency strongly depends on the mixing of fuel and oxygen. Most of the oxygen is located in the squish region, especially during the expansion stroke. If the spray is led to the squish region (with wide spray angle), better mixing can be expected. That is why a wide spray angle usually has better fuel economy and lower soot. With a medial spray angle, the risk of spray wall impingement is higher. Therefore, a medial spray angle is not favored for all cases, especially for mid- and low-load cases. For the full load case, spray wall impingement is not severe. Due to the long injection duration, the effects on fuel economy and soot emissions are relatively small. Assuming equal weighting of the different operating conditions, mode-averaged response surfaces can be generated (c.f., Fig. 6.34). Comparing with Figs. 6.31, 6.32, and 6.33, the mode-averaged response surfaces are closer to the full load case (Mode A100, c.f., Fig. 6.33) than to the others. Therefore, the full load case is the most representative case for nozzle design optimization. Shi and Reitz (2008b) drew a similar conclusion from their work.

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Fig. 6.33 Response surfaces of SOI and flow rate, SOI and nozzle hole number, SOI and spray angle for mode A100. Left column: GISFC; middle column: soot; right column: NOx. Black circle: baseline engine

6.1.3.3 Summary In the present section, a multi-dimensional CFD code was integrated with a commercial optimization software—mode FRONTIER. Using the multi-objective genetic algorithm (NSGA-II), the nozzle design parameters of a heavy duty diesel engine were optimized. The following conclusions can be drawn from the work: • MOGA is an efficient and feasible tool for engine optimization. Response surfaces of the MOGA results clearly quantify the influences of the design parameters on the optimal objectives. • At low load a higher number of nozzle holes and a wider spray angle were favored for reducing the soot emissions and fuel consumption. • The mode-averaged response surfaces have closer pattern with the ones of high load. Therefore, the high load case is the most representative case for engine optimization.

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Fig. 6.34 Mode-averaged response surfaces of SOI and flow rate, SOI and nozzle hole number, SOI and spray angle with the same weight for Mode A25, B50, and A100. Left column: GISFC; middle column: soot; right column: NOx

6.1.4 Optimization of a High-Speed Direct-Injection Diesel Engine 6.1.4.1 Research Background and Objectives Growing concern over environmental issues has prompted regulatory authorities to increase already stringent emission standards for the automobile industry. Meanwhile, the international crude oil price is increasing, and Green House Gases (GHG) are becoming more concerned. Thus, fuel economy is becoming more and more important from both a customer’s and a regulator’s perspective. The diesel engine is a promising option for passenger cars due to its high fuel conversion efficiency, which can be 40% more than that of modern SI engines (Cowland et al. 2004). In this example, a high-speed direct-injection (HSDI) diesel engine sized for passenger cars was optimized using the MOGA and KIVA3v2 code discussed above. Spray targeting, swirl, and 11 parameters describing the piston bowl geometry were simultaneously optimized for a full-load case. The results were analyzed using the COSSO non-parametric regression analysis method. Sensitivities of the design

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parameters on the fuel economy and pollutant emissions are illustrated in response surfaces. Some of the optimal designs were further analyzed for more insights. Physical mechanisms that explain correlations between design parameters under certain operating conditions are explained based on the regression analysis results.

6.1.4.2 Mathematical Models and Numerical Methods The improved version of the KIVA3v2 code discussed in earlier chapters was used for the multi-dimensional CFD modeling of the engine combustion processes. The closed-valve period of the engine cycle was considered. The gas jet model (Abani and Reitz 2007) and radius-of-influence collision model (Munnannur and Reitz 2009) were employed to reduce mesh dependency. All the optimization tasks were conducted using a high-throughput computing (HTC) technique. The HTC software CONDOR (Thain et al. 2005) was designed to fully utilize distributively owned, heterogeneous computing resources, which are available in university campus or other research communities. For instance, the condor pool at the University of Wisconsin-Madison consists of more than 4,000 computers. Like other full-featured batch systems, CONDOR provides a job queuing mechanism, scheduling policy, priority scheme, resource monitoring, and resource management. CONDOR is configured to only use idle desktop machines. When the machine is no longer available, CONDOR transparently produces a checkpoint and migrates the running job to another idle machine. A shared file system is not necessary for CONDOR. Based on these features, CONDOR and similar HCT systems are ideal for massive computer optimization.

6.1.4.3 Engine Description and Operating Conditions The engine investigated in the present work is a production diesel engine for passenger cars. Table 6.20 lists the specifications and the operating conditions considered. The present case represents a full-load condition.

6.1.4.4 Optimization Parameters and Objectives Engine operated under the three modes was optimized separately. However, except for the SOI timing, the optimizations of the three modes had the same search space, as shown in Table 6.21. In the current study, the bowl shape was characterized using eleven parameters, including five outline parameters (the height of the central pedestal of the piston, Az; position of the bowl bottom, Bx; radius of bowl, Cx and Dx; height of point C, Cz), and 6 other parameters for Bezier curves that connect the control points (Xab, Xba, Xbc, Xcb, Ycb, Ycd). The other features of the piston geometry were kept as the same as a baseline engine design. When

220 Table 6.20 Engine specification and operating conditions

Table 6.21 Optimization search space

6 Applications Bore 9 Stroke (mm) Connection rod length (mm) Effective compression ratio Fuel injector nozzles Spray pattern included angle Nozzle orifice diameter (mm) IVC (ATDC) EVO (ATDC) Swirl ratio IMEP (bar) Fuel injected (mg) RPM SOI (ATDC) DOI () EGR (%)

Spray angle () Nozzle hole number Swirl ratio Az Bx Cx Cz Dx Xab Xba Xbc Xcb Ycb Ycd SOI (ATDC)

81.0 9 88.0 160.0 12.75:1 8 holes, equally spaced 153 0.121 -129.5 120.0 2.0 18.0 55.6 4,000 -16 42.4 0.16

Minimum

Maximum

140 5 0.5 0.5 0.8 0.45 0.60 0.45 0.1 0.3 0.5 0.5 0.3 0.3 -20

160 12 2.5 0.8 1.0 0.65 0.85 0.70 0.7 0.9 3.5 3.5 0.9 0.9 -5

the piston bowl geometry is optimized, the computational mesh should be generated automatically for efficiency using Kwickgrid methodology (Wickman 2003) that is described in Sect. 4.1. Figure 6.35 gives an example of grids generated by Kwickgrid. The numbers 1- 6 indicate the Bezier curve control points, which correspond to the parameters Xab, Xba, Xbc, Xcb, Ycb, and Ycd, respectively. As a compromise between computation efficiency and the model accuracy, the cell size was specified as 1 mm in this work (note the engine is smaller than previously investigated heavy-duty engines). This resolution has been shown to give adequately mesh independent results by Abani et al. (2008a, b). The KIVA3v2 code and Kwickgrid were integrated with the NSGA-II code. All of the parameters were set as real variables except for the number of nozzle holes, which had to be an integer. The integer (binary) variable was limited to a finite

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Fig. 6.35 Example of grids generated by Kwickgrid

Fig. 6.36 Fired and motored in-cylinder pressure of baseline case

number of choices. In the present optimization, the total number of possibilities in nozzle hole number is 8 (5–12 holes), however, the number of nozzle holes varies, the amount of injected fuel, injection velocity and injection duration was kept the same as the baseline engine. Thus, the total flow area of the nozzle holes is kept the same as the original value. With fewer nozzle holes, the size of nozzle hole is larger and so is the initial droplet size. To fully understand the influence of the design parameters, extensive search spaces were employed in the present work. Since plenty of computer nodes were available on Condor pool, many jobs were run simultaneously. A large population size for the genetic algorithm was then preferred. In the present work, the population size was set to 32, which showed good performance in the study of Shi and Reitz (2008a). Typical computer times were about 6–12 h to complete one generation.

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Fig. 6.37 NOx (left) and soot (right) emissions computed using the CTC and KIVA-CHEMKIN (CK) models

6.1.4.5 Results and Discussion The baseline case was simulated using both the CTC and KIVA-CHEMKIN models. The pressure traces are plotted in Fig. 6.36, which includes the motored case. Both the CTC and KIVA-CHEMKIN models match experimental data very well. NOx and soot emissions predicted by the CTC and KIVA-CHEMKIN models, which are shown in Fig. 6.37, are also close. This implies that the results of the CTC model are reliable for the present engine full-load operating condition of interest. Since the computational cost of the CTC model is much less than the KIVA-CHEMKIN model, and many cases need to be computed to cover the design space, the CTC model was used in optimization. The optimization was terminated at the 72nd generation, which results in about 2,300 designs. The convergence metric of this optimization was then calculated using Eqs. 4.8 to 4.10. Figure 6.38 shows the history of the normalized convergence. As can be seen, convergence was reached by the 30th generation. But GA generations were allowed to continue after the 30th generation to fill more diversified solutions to the Pareto front. All the citizens together with highlighted Pareto solutions and the baseline case, are plotted in Fig. 6.39. Normal citizens, Pareto citizens, and the baseline design are indicated by black hollow squares, blue triangles, and the red circle, respectively. The baseline engine performance is seen to be improved upon significantly in terms of all the objectives. Figures 6.40, 6.41, and 6.42 summarize the response functions of all the design parameters, as evaluated using the COSSO method. Their effects on the GISFC, soot and NOx are illustrated in Figs. 6.40, 6.41, and 6.42, respectively. The absolute error values of these response functions are about 10 g/kW h, 0.7 g/kgf, and 1.2 g/kgf for GISFC, soot, and NOx, respectively. In general, the number of nozzle holes, which ranges from 5 to 12, has the most significant impact on the GISFC and soot emission. A nozzle with 6–8 holes benefits combustion efficiency

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Fig. 6.38 Normalized convergence history of the optimization

Fig. 6.39 All citizens and Pareto solutions from optimization, and the baseline

and soot reduction. A nozzle with fewer holes gives lower NOx emissions. The AFR (air to fuel ratio) of the full-load case is about 20 (corresponding global equivalence ratio of 0.75). Therefore, it is essential to deliver the fuel to each corner of the combustion chamber to achieve good combustion efficiency. Plus, the pressure and temperature in this case are very high, so the droplets evaporate very fast. If the initial droplet size is too small, the spray penetration will be too short for the fuel to reach the near wall squish region (which has more oxygen than the cylinder center). A nozzle with more holes produces smaller droplets, which have shorter spray penetrations. In this case, it becomes very difficult for the fuel to mix with the oxygen near the wall and results in poor combustion efficiency. On the other hand, if the initial droplet size is too large, it presents the risk of spray wall impingement, which will lead to poor combustion efficiency and high

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Fig. 6.40 Response functions of individual design parameters on GISFC (g/kW h)

soot and UHC emissions. Thus, the key issue for combustion efficiency of the fullload case lies in keeping spray penetration as long as possible while avoiding spray wall impingement. These effects of nozzle hole number (hole size) on the GISFC and pollutant emissions are clearly reflected in the response functions. SOI is the most critical parameter for NOx emissions. The NOx formation reactions are relatively slow as compared to many other elementary reactions involved in the heat release. Therefore, the total NOx emission is proportional to the total lifetime of the high temperature mixtures. Early injection usually has earlier ignition, which provides more time for NOx formation. Thus, a late injection consistently gives lower NOx emissions. SOI also has a strong impact on the combustion efficiency. With different SOI, different percentages of fuel are injected into the bowl or squish regions. If too

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Fig. 6.41 Response functions of individual design parameters on soot emission (g/kgf)

much fuel is injected into one region, it is very difficult to transport the abundant fuel into the other region. In this sense, the effects of SOI and spray angle on the GISFC are the same: to deliver the appropriate amount of fuel to the squish and bowl regions. A SOI around -15 ATDC is seen to gives the best GISFC. This implies that, with this SOI, the ratio of the fuel delivered into the squish region and the bowl region is the same as the ratio of the amount of available oxygen in these two regions. The response functions of spray angle show that a wider spray angle simultaneously reduces fuel consumption and pollutant emissions. A wider spray delivers more fuel into the squish region where there is more oxygen. Swirl adds a tangential velocity to the flow. Therefore, it enhances the mixing in the tangential direction and this enhances the evaporation of droplets. Consequently, it further reduces the spray penetration. Thus, for the same reason as the effects of nozzle

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Fig. 6.42 Response functions of individual design parameters on NOx emission (g/kgf)

hole number, strong swirl reduces GISFC. Too weak a swirl leads to poor mixing between fuel and oxygen in the tangential direction, and eventually to deteriorate combustion efficiency. The best fuel consumption is achieved when the swirl ratio is around 1.8. Note that strong swirl always benefits the soot reduction. However, a clear tradeoff between fuel consumption and NOx formation is observed in terms of the effects of the swirl flow. The design parameters of the piston bowl can be separated into two categories: (1) outline parameters; and (2) Bezier curvature parameters. Among the five outline parameters (Az, Bx, Cx, Cz, and Dx), Cx is the most important one in terms of its impact on GISFC and pollutant emissions. Cx is the primary parameter defining the radius of the piston bowl. It can be seen that Cx & 0.6 gives the best

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Fig. 6.43 Selected response surfaces of GISFC

GISFC and soot emissions, while keeping NOx emissions at an acceptable level. Since the position of point C is very important at full-load, the bowl curvature about point C becomes very important as well. One of its curvature parameters, Xbc, is seen to be the most important Bezier curvature parameter for GISFC and pollutant emissions. The curvature parameters have strong effects on the flow pattern in the piston bowl, especially the tumble flows. Therefore, their impacts on soot emission are more evident than on the fuel economy and NOx. In general, the influences of these curvature parameters are proportional to the areas they cover. According to Fig. 6.35, the curvature parameters Xbc, Xcb, and Ycb cover the largest surface of the piston bowl. They are also the most influential curvature parameters under the most operating conditions. The other outline parameters play relatively less important roles in terms of the combustion efficiency and pollutant emissions. Some parameters almost have no influence on GISFC or pollutant emissions, for instance, Xab for soot, Xba for NOx and soot, Ycd for GISFC and NOx. Thus, it is concluded that the effects of some parameters on GISFC or pollutant emissions can be neglected, for instance, Az, Cz, Xab, Ycb. The response curves in Figs. 6.40, 6.41, and 6.42 provide information about the relative importance of each design parameter. In addition, the response surfaces, as

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Fig. 6.44 Selected response surfaces of soot emission

shown in Figs. 6.43 and 6.44, illustrate the joint effects of two design parameters on the objectives. The correlation between two design parameters can also be easily observed from the response surfaces. If one parameter is more important than another and these two are strongly correlated, the important one should be determined first, and then the less important one can be optimized based on their response surfaces. Figures 6.43 and 6.44 show some selected response surfaces of GISFC and soot emission, respectively. Only the response surfaces of strongly correlated parameters are presented. Because SOI has a dominant influence on NOx emission, response surfaces of NOx emission are not presented. It can be seen from

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Fig. 6.43a that the effects of SOI and spray angle on GISFC are strongly correlated. A wide spray prefers an early injection, while a narrow spray prefers an injection a bit later. As mentioned above, the function of SOI is to inject adequate amount of fuel into piston bowl and squish regions. With the same SOI, if the spray angle gets narrow, more fuel will be injected into the piston bowl. Since the injection occurs mainly before TDC, a delay in the injection reduces the amount of fuel heading to the piston bowl and this retains lower GISFC. As observed from Fig. 6.40, the number of nozzle holes has a more important influence on GISFC than the spray angle and swirl ratio. However, their response surfaces (c.f., Fig. 6.43b, c) show that these two parameters are correlated with the number of nozzle holes. With high swirl ratio, a nozzle with fewer holes (i.e., larger initial droplet sizes) is preferred. This is consistent with the discussion about Figs. 6.40, 6.41, and 6.42. A long spray penetration without wall impingement helps the fuel to mix with the available oxygen. Strong swirl reduces spray penetration, while a large initial droplet size increases the spray penetration. Therefore, a nozzle with fewer holes coupled with a strong swirl provides very good fuel economy. In addition, the distance between spray plumes is also larger with fewer holes, and thus the higher swirl would not cause significant plume interaction to deteriorate fuel economy. The spray angle is also clearly correlated with the number of nozzle holes. When the spray angle is small, the spray is targeted at the piston bowl. Therefore, the risk of spray wall impingement is high. A short spray penetration is preferred. When the spray angle is large, the spray is targeted at the squish region. Spray wall impingement is then not a problem any longer. A long spray penetration will benefit the mixing of fuel and oxygen. Thus, as seen in Fig. 6.43, a narrow spray with a 7-hole nozzle, or a wide spray with a 5-hole nozzle, has the best fuel economy. Some design parameters of the piston bowl are also strongly correlated, for instance, Xab and Xba for GISFC, as shown in Fig. 6.43d. Their response surface shows a saddle-like shape. For soot emissions, a correlation between the number of nozzle holes and swirl ratio can be seen from Fig. 6.44a. This response surface shows a very similar shape to their response surface of GISFC (c.f., Fig. 6.43b). The art of tuning the number of nozzle holes and swirl ratio is to avoid spray wall impingement while keeping long spray penetration. Soot emission is very sensitive to spray wall impingement and the local mixing conditions. As with fuel economy, a weaker swirl works well with a medial hole size, while stronger swirl prefers a larger hole size (fewer holes). Overall, it is seen that strong swirl always enhances the mixing of fuel and oxygen and reduces soot emissions. The geometry of the piston bowl has a significant effect on the soot emissions. It can be seen from Fig. 6.44b–d that the geometric parameters are strongly correlated with the spray parameters and swirl. As the most important parameter for piston bowl design, Cx shows distinct interactions with SOI, spray angle, and swirl ratio. For an early injection, the effects of Cx can be neglected, because more of the fuel goes to the squish region and the combustion in the piston bowl is relatively less important. Retarding SOI, more fuel enters piston bowl. The shape of the piston bowl then plays a very important role for soot formation and oxidation.

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Table 6.22 Comparison of the performance of baseline engine and three optimal engines Design Baseline 1 2 3 GISFC (g/kW h) Soot (g/kgf) NOx (g/kgf)

249.8 2.68 29.23

229.7 (8%;) 1.22 (54%;) 19.46 (33%;)

236.2 (5%;) 0.66 (75%;) 13.93 (52%;)

241.2 (3%;) 1.08 (60%;) 8.71 (70%;)

An appropriate design of piston bowl coupled with an appropriate injection event can generate a strong tumble flow component, which can significantly reduce soot emissions. The response surface of Cx and spray angle, as well as the one of Cx and swirl ratio, shows that a moderate bowl throat radius works well with a narrow spray angle and a weak swirl, and a big bowl throat radius with a wide spray angle and a strong swirl. The interactions of geometric parameters are also evident in terms of soot emissions, for instance, Cx and Cz (Fig. 6.44e), Xbc and Cx (Fig. 6.44f). Three interesting designs were selected from the optimization results for further analysis. Table 6.22 lists the performance of these designs compared with the baseline engine at full-load. According to the numerical results, these designs simultaneously and significantly improve the baseline engine performance in terms of GISFC and pollutant emissions. Figure 6.45 shows the comparison of in-cylinder pressure, heat release rate, and pollutant emissions between the baseline engine and these three selected designs. During the expansion stroke, the three designs have higher combustion efficiencies than the baseline engine, which is indicated by the higher heat release rates in this period. The baseline engine has a higher peak pressure than the optimal engines. The in-cylinder averaged temperature of the baseline engine is therefore higher. Additionally, because the injection of the baseline engine is earlier, the final NOx emission of the baseline engine is much higher than the optimal engines. Figures 6.46, 6.47, 6.48, and 6.49 show contour plots on a cut-plane along the spray axis. Figure 6.46 shows the fuel vapor distribution as well as a vector plot of the gas velocity of the baseline engine and the optimal designs at CA = 30 ATDC. It can be seen that the baseline engine fails to deliver enough fuel into the squish region, while for all the optimal designs more fuel enters the squish region and mixes well with the oxygen. Geometry-generated tumble flows in the bowl regions of the optimal designs are stronger than that of the baseline engine, which enhances the mixing in the piston bowl and benefits soot oxidation. Design 2 has the strongest tumble flow, which makes this design the best one for soot reduction. Figure 6.47 shows the fuel vapor distribution and gas velocity field of the baseline engine and optimal designs at CA = 100 ATDC, which is close to EVO. For the baseline engine, there is still a lot of fuel left in the piston bowl region, and this confirms that too much fuel is directed into the piston bowl and cannot mix with the leftover oxygen in the squish region. Much less fuel is left in the optimal engines, i.e., the combustion in these optimal engines is more complete. The distribution of oxygen also supports this fact. Figure 6.48 shows the oxygen distribution of the baseline engine and optimal designs at CA = 100 ATDC. It can

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Fig. 6.45 In-cylinder pressure and heat release rate (top), and pollutant emissions (bottom) of the baseline engine and three selected designs (see Table 6.22)

Fig. 6.46 Fuel vapor distribution and velocity field of the baseline engine and optimal designs at CA = 30 ATDC

be seen that there is a lot of oxygen left near the cylinder wall in the baseline engine. Considering that the mass of flow in the cylinder increases linearly with the radius (Dm ¼ 2prqDrDh, r is the radius and h is the depth), oxygen near the cylinder wall occupies a much larger region than oxygen near the axis. The gradient of the oxygen concentration is also very large. The left-over oxygen in the combustion chamber at EVO of baseline engine and optimal engines are about 0.0769, 0.0662, 0.0654, 0.0657 g, respectively. Combining with the observations from Fig. 6.47 we can conclude that the poor fuel economy of the baseline engine is due to the fact that the fuel in the piston bowl fails to mix and react with the oxygen near the cylinder wall. The optimal engines have a much more homogeneous distribution of oxygen in the cylinder. Especially, the oxygen near the cylinder wall is well utilized. Comparing to designs 2 and 3, the peak pressure of design 1 is higher (c.f., Fig. 6.45) being due to its earlier ignition. Therefore, the design 1 has higher GISFC, even though its left-over oxygen is more than the other optimal designs. Figure 6.49 shows the soot distribution of the baseline engine and optimal designs at CA = 100 ATDC. The baseline engine has much higher soot emissions than the optimal engines. The main reason is the inappropriate amount of fuel delivered into the piston bowl. Geometry-generated tumble flow is also a plus.

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Fig. 6.47 Fuel vapor distribution and velocity field of the baseline engine and optimal designs at CA = 100 ATDC

Fig. 6.48 Oxygen distribution of the baseline engine and optimal designs at CA = 100 ATDC

Thanks to the good mixing of fuel and oxygen and strong tumble flow, design 2 has the lowest soot emissions. There is some soot left near the cylinder head and crevice region in both designs 1 and 3.

6.1.4.6 Summary In this example, a HSDI diesel engine for passenger cars was optimized using the multi-dimensional CFD code and multi-objective genetic algorithm

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Fig. 6.49 Soot distribution of the baseline engine and optimal designs at CA = 100 ATDC

methodology. Bowl geometry, spray targeting, and swirl ratio were optimized simultaneously. The following conclusions can be drawn from the present work: • The full-load case should be optimized to deliver the fuel into each corner of the combustion chamber and to mix with the available oxygen. It is crucial to distribute the appropriate amount of fuel into the squish and bowl regions to achieve good fuel economy and pollutant reduction. Optimizations of the nozzle hole layout, bowl radius, and swirl ratio should be focused on. • SOI is always the key parameter for NOx reduction. • When one bowl shape outline parameter becomes more important, the influences of the Bezier curvature parameters about this point increases as well. The correlation between them usually cannot be ignored. • In general, the influence of a Bezier curvature parameter is proportional to the total area of the surface that it covers.

6.2 Engine Optimization with Advanced Combustion Models This section provides several examples of engine optimizations that use detailed fuel chemistry for better accuracy, especially for engine premixed combustion modes. To accelerate the simulations, an efficient chemistry solver with the AMC model and the DAC scheme (c.f., Chap. 3) was employed.

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6.2.1 Optimization of a Heavy-Duty Compression-Ignition Engine Fueled with Diesel and Gasoline-Like Fuels 6.2.1.1 Research Background and Objectives Homogeneous Charge Compression-Ignition (HCCI) engines have received much attention in recent decades due to their clean and efficient combustion. However, in practical engines, it is difficult to achieve a fully premixed air-fuel charge using an in-cylinder direct injection system, and the fully premixed air-fuel charge also usually results in unacceptable engine noise that accompanies the very fast pressure rise rate under mid- to high-load operating conditions. There is also no incycle control over combustion phasing in HCCI engines so that engine control becomes very difficult. The concept of Partially Premixed Combustion (PPC) in compression-ignition engines promises to avoid these difficulties faced by HCCI engines while attaining clean combustion. Due to the low volatility of diesel fuel, it is required to significantly advance the injection timing to obtain a partially premixed charge prior to the auto-ignition of the fuel. However, such early injection can result in combustion chamber wallwetting due to spray impingement with the walls. The resulting fuel film can be a source of high UHC emissions and low fuel economy. Also, injecting diesel fuel early will cause heat release to occur during the compression stroke which is also undesirable. An alternative method to achieve a premixed charge is to suppress fuel auto-ignition and thus to increase the time allowed for air-fuel mixing. One such application is the modulated kinetics (MK) combustion engine (Kimura et al. 1999, 2001). MK combustion features a late injection timing in order to shorten the spray penetration (due to the high gas density) and also uses ultra-high EGR levels to suppress ignition. The studies of Kimura et al. (1999, 2001) indicated that MK combustion significantly reduces NOx and soot emissions without sacrificing fuel economy. But due to the late injection, the operating range of MK combustion is limited to low- to mid-load conditions. Clearly fuels with high volatility and low ignitability are desirable to achieve a more premixed air-fuel charge, and conventional gasoline is a good candidate fuel. However, until recently, gasoline has only been used in spark ignition engines, mainly due to the limitation of available control mechanisms of the injection system in CI engines. Kalghatgi et al. (2006, 2007) are among the pioneers who investigated the combustion processes of compression-ignition engines fueled with gasoline. Their studies pointed out that the gasoline CI engine effectively reduced NOx and soot emissions with acceptable heat release rates, as compared to diesel fuel under the same operating condition. The principle reason is that the longer auto-ignition time of gasoline separates the injection event and main heat release and thus minimizes the heat release in the diffusion flame regime. They also found that a dual-injection strategy is an effective way to achieve partially premixed charge and to reduce the maximum heat release rate and cyclic variations in a CI engine fueled with gasoline. However, as indicated by Shi et al. (2010 d), in

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Table 6.23 Operating conditions of the Caterpillar DICI engine Mid-load

High-Load

Speed (rev/min) Fuel amount (g/cycle) IMEP (bar) EGR (%) Global equivalence ratio IVC temperature (K) Boost pressure (bar) IVC (ATDC) EVO (ATDC)

1,300 0.270 (0.282 for E10) 21 30 0.8 435 3.0 -85 130

1,300 0.135 (0.141 for E10) 11 30 0.6 435 2.0 -85 130

general CI engines fueled with gasoline-like fuels have higher in-cylinder gas pressure rise rate (thus engine noise) and unburned hydrocarbons (UHC) emissions than those of conventional diesel engines. An injection system that is calibrated or optimized for a CI engine fueled with diesel requires modifications for gasolinelike fuels due to their distinct spray characteristics and fuel reactivity. Therefore, it is of much interest to compare optimal injection parameters of a CI engine fueled with diesel and gasoline-like fuels, to provide guidance for engine design. The objective of this work is to seek for optimal combinations of injection parameters for a heavy-duty compression ignition engine fueled with diesel and gasoline-like fuels (gasoline and 10% ethanol blended gasoline E10) and operated under midand high-load conditions. The results are then discussed for both non-parametric and parametric studies in order to reveal guidelines for optimal engine design with the different fuels. In modern engines, the vast number of variables that control the combustion process results in a large number of iterations to achieve optimal designs. Obviously, the use of simple combustion models is not applicable in the present research, because the focus of this study is to compare the influence of different fuels on engine optimal designs. This necessitates the use of more computationally expensive engine CFD tools with detailed fuel chemistry. Since with detailed chemistry over 90% of the computational time is spent on the chemistry solver, acceleration of the solver is critically important. The efficiency, feasibility, and reliability of the AMC model for engine optimization was validated by Ge et al. (2010b). As discussed in Chap. 3 in detail, the Adaptive Multi-grid Chemistry (AMC) model Shi et al. (2009a) and the Extended Dynamic Adaptive Chemistry (EDAC) scheme (Shi et al. 2010b) were both employed to achieve more efficient calculations with detailed fuel chemistry for the present optimization problem.

6.2.1.2 Engine Description and Operating Condition The studied engine is the same Caterpillar heavy-duty engine as described in Sect. 6.1.2. The main engine specifications are listed in Table 6.6. The engine operating conditions are listed in Table 6.23.

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6.2.1.3 Model Validation The present work adopted a modified version of the KIVA3v2 code with an efficient chemistry to evaluate the performance of a CI heavy-duty engine fueled with diesel, gasoline and E10 under mid- and high-load conditions. The CFD tool with detailed fuel chemistry (the reduced Primary Reference Fuel (PRF) mechanism by Ra and Reitz (2008) and reduced ethanol mechanism from the LLNL detailed mechanism by Marinov (1999)) was validated against the experimental data by Hanson et al. (2009) on the same engine. Figure 6.50 compares the pressure traces and emissions for a SOI sweep from -8 to -2 ATDC. Figure 6.51 shows the comparison for an EGR sweep study. It is seen that the CFD simulations agree with the experimental trends fairly well, especially the major emission trends are captured. This strengthens the confidence of using both the AMC and EDAC models in the present optimization study.

6.2.1.4 Results and Discussion The optimization studies were conducted using a multi-objective genetic algorithm, NSGA II. The NSGA II related parameters were set according to Shi and Reitz (2008a, b) and a population size of 32 was used. Six tasks (two operating conditions and three fuels) were conducted, which used 192 computer nodes running in parallel on the University of Wisconsin Condor system (Thain et al. 2005). The entire optimization was completed in approximately six weeks (estimated time would be more than six months with the original chemistry solver). The optimization focused on selecting injection system parameters with the different fuels. In-cylinder air motion due to swirl was also considered due to its large impact on the air-fuel mixing process. Therefore, eight parameters were optimized, which are summarized in Table 6.24 together with their lower and upper bounds. Six objective functions were selected: soot, NOx, UHC, and CO emissions, fuel consumption (indicated by GISFC), as well as an engine noise indicator, the Peak Pressure Rise Rate (PPRR). In addition, three feasibility constraints were defined: maximum cylinder pressure and PPRR of 20 MPa and 30 bar/CA, respectively, and lowest maximum average temperature of 1,200 K, below which the engine would misfire. If one or more of the constraints were violated, a penalty was assigned to its objectives, and thus the design was given the lowest priority for selection in the evolution. This simple penalty mechanism proved to be very effective to remove infeasible designs. The optimization was terminated at the 25th generation (i.e., 32 (population) 9 25 (generation) = 800 individual evaluations for each fuel) based on the convergence metric (as discussed in Chap. 4) shown in Fig. 6.52a. The figure shows that further GA evolutions only produce more cases to fill the existing Pareto front (optimal solution set). Since it is impossible to visualize Pareto solutions with 6 objectives in a single plot, the values of the six objectives of the

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Fig. 6.50 Comparison of simulation and experiment (Hanson et al. 2009) (gasoline main SOI sweep (70% injected fuel) with 0% EGR and 30% pilot injection at -137CA). a Pressure traces. b Soot. c NOx. d UHC. e CO

Pareto solutions are mapped onto three plots, as shown in Fig. 6.52b–d for soot and NOx, UHC and CO, as well as GISFC and PPRR, respectively. Figure 6.52b shows the trade-off relation of soot and NOx emissions for diesel (squares), while for gasoline (circles) and E10 (triangles), most of the Pareto solutions have extremely low soot emissions, as well as NOx. As seen in Fig. 6.52c, the optimal diesel solutions tend to produce more CO emissions while

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Fig. 6.51 Comparison of simulation and experiment (Hanson et al. 2009) (EGR sweep). a Experimental pressure traces. b Simulated pressure traces. c Soot. d NOx. e UHC. f CO

gasoline and E10 generate more UHC emissions. CO indicates the combustion completeness with diesel, but UHC is the indicator for gasoline and E10 under the present operating condition. The optimal diesel fuel designs have lower PPRRs than those of gasoline and E10 and the fuel consumption of the optimal designs with the three fuels is distributed widely in Fig. 6.52d. In general, designs with higher PPRR have better fuel economy, and for gasoline and E10 it is more difficult to obtain a good compromise between fuel economy and PPRR.

6.2 Engine Optimization with Advanced Combustion Models Table 6.24 Optimization parameters and their ranges

239

Parameter

Range

Pilot SOI (ATDC) Injection pressure of pilot injection (bar) Amount of pilot injection (%) Main SOI (ATDC) Injection pressure of main injection (bar) Spray included angle () Swirl ratio Number of holes

-85.0 to -55.0 300 to 2,000 0 to 50 -35.0 to 10.0 500 to 2,000 60.0 to 85.0 0.0 to 2.0 6 to 12

Fig. 6.52 Convergence metric and Pareto solutions for mid-load. a Convergence metric. b Pareto solutions (Soot and NOx). c Pareto solutions (UHC and CO). d Pareto solutions (GISFC and PPRR)

The EPA on-highway HD 2010 emissions regulations mandate dramatically low engine exhaust PM, NOx, and non-methane HC (NMHC) levels, which are 0.0136, 0.27, 0.19 g/kW h, respectively (http://www.dieselnet.com/standards/). Searching all Pareto solutions reveals that relatively few optimal diesel fuel designs satisfy the NOx regulation, and none meets the PM and NMHC standards. For gasoline and E10, 95% of the optimal designs are below the soot limit, and a few designs with both soot and NOx emissions lower than the standards are also

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found. However, none of the optimal gasoline and E10 designs meets the NMHC limit, which indicates that further oxidation of the exhaust gases is needed. A similar conclusion was reached by Manente et al. (2009) whose experiments suggested that a conventional oxidation catalyst should be used to oxidize UHC and CO emissions when a CI engine is fueled with gasoline-like fuels. Benchmark designs (i.e., Case 1 in all parametric studies) for further regression analysis were set to be designs with central values of the investigated ranges of the design parameters listed in Table 6.25, except that the main SOI was advanced to -25 ATDC instead of its central value -12.5 ATDC (since the E10 engine was found to misfire). The results of the benchmark designs for the three fuels are indicated by stars in Fig. 6.52b–d. Due to the early injection timing, the peak pressure rise rate of E10 for the benchmark design is very high. The effects of each individual parameter on the objectives are summarized in Table 6.26. In the table each symbol designates the predicted change of an objective as a function of a design parameter. Vertical arrows indicate primary influences and the tilted arrows represent secondary effects. An upward directed arrow indicates that the value of the objective increases with the design parameter, and downward arrows indicate a monotonic decrease. Horizontal arrows represent negligible influences, while arc signs indicate that there is either a minimum value (downward) or a maximum value (upward) of objectives in the range of the design variables. A combination of downward and upward arcs means that both a local minimum and a maximum value were found. Filled arcs are for primary effects as opposed to hollow arcs for the secondary effects. The numbers represent the mean values of the design parameters and objectives of all the Pareto solutions, which provide the general performance for each fuel. The tabulated results are consistent with the observations of Fig. 6.52b–d. Gasoline and E10 fuels significantly favor the reduction of soot and NOx, while producing more UHC emissions than diesel, but with slightly lower CO emissions. It is also seen that the PPRR level increases with the fuel octane number as the optimal designs with E10 fuel have the highest PPRR, followed by gasoline and diesel fuel. Interestingly but not surprisingly, the primary design parameter with diesel fuel is the amount of fuel in the first injection pulse, as four objectives show a strong dependency on this parameter, followed by the second injection timing. This is different from the engine with gasoline and E10, where the second injection timing predominantly affects engine performance and emissions, followed by the second injection pressure and spray included angle. The principle reason is that the combustion phasing with diesel fuel is controlled by both the pilot injection and the main injection due to the high reactivity of diesel. However, as in the study of Shi et al. (2010d), a rich mixture and a high ambient pressure are both important to ignite gasoline and E10 within a reasonable time scale to avoid engine misfire. Under the mid-load condition of this study, the amount of the first injection gasoline and E10 is not able to form locally a rich enough mixture. Therefore, it is the second injection that triggers the combustion and affects the subsequent emission formation. It is also found that E10 needs a very early main injection timing as

(a) Design parameters -70.0 SOI1 (ATDC) Pressure1 (bar) 1,150 First pulse (%) 25.0 -25.0 SOI2 (ATDC) Pressure2 (bar) 1,250 Spray angle () 72.5 Swirl ratio 1.0 Hole number 9 (b) Simulation results Soot (g/kW h) 0.055 NOx (g/kW h) 8.491 UHC (g/kW h) 7.581 CO (g/kW h) 11.60 GISFC (g/kW h) 226.1 PPRR (bar/CA) 30.14 -66.8 EOI1 (CA) EOI2 (CA) -15.7 CA50 (ATDC) -13.0

Case 1

-84.6 578 5.0 -10.7 965 76.3 1.6 7

0.049 1.961 1.146 4.360 187.5 10.42 -78.9 2.8 2.8

0.124 0.368 3.876 9.947 223.6 4.982 -72.8 16.6 19.5

Case 3

-78.0 699 31.0 6.8 954 60.4 0.4 10

Case 2

0.046 2.260 1.151 2.836 181.7 8.179 -63.4 6.8 5.0

-64.2 1,352 6.6 -9.3 648 76.6 1.8 8

Case 4

0.006 3.583 1.532 4.516 180.6 69.04 -66.3 -14.4 3.3

-70.0 1,150 25.0 -25.0 1,250 72.5 1.0 9

Case 1

Table 6.25 Representative optimal designs for the mid-load condition Diesel Gasoline

0.003 0.515 12.33 12.59 218.5 4.189 -49.5 -1.2 18.3

-55.2 1,926 49.9 -8.4 1,238 66.0 0.7 6

Case 2

0.003 0.810 2.339 3.539 183.2 12.49 -50.6 0.9 12.5

-56.1 1,798 46.9 -7.7 974 66.0 0.5 10

Case 3

0.000 2.321 4.437 4.422 183.2 29.42 -59.3 -5.0 10.7

-79.3 1,873 0.17 -17.5 1,113 73.7 1.7 11

Case 4

0.000 2.432 9.100 4.038 189.7 30.39 -66.1 -13.9 10.4

-70.0 1,150 25.0 -25.0 1,250 72.5 1.0 9

Case 1

E10

0.004 0.169 7.630 7.616 206.6 3.136 -79.0 -20.8 19.4

-80.0 648 0.5 -33.6 1,670 79.7 1.5 8

Case 2

0.004 0.144 4.703 4.061 200.8 4.208 -63.5 -24.3 18.4

-67.0 883 24.0 -33.8 1,783 73.9 0.7 7

Case 3

0.006 0.163 6.978 9.051 211.6 2.099 -75.3 -16.8 23.1

-78.0 1,658 20.9 -28.9 1,166 81.0 0.0 8

Case 4

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Table 6.26 Effect of individual design parameters on objectives for mid-load

Soot

NOx

0.116

1.582

UHC

CO

GISFC

PPRR

10.22

206

8.58

215.0

9.94

(a) Diesel SOI1

–68.0

Pressure1

1070

First pulse

0.102

SOI2

–2.66

Pressure2

982

Spray angle

73.0

Swirl ratio

1.39

Hole number

8.61

(b) Gasoline SOI1

–69.1

Pressure1

1260

First pulse

0.319

SOI2

–12.3

Pressure2

1280

Spray angle

70.6

Swirl ratio

1.47

Hole number

8.80

(c) E10 SOI1

–68.6

Pressure1

1120

First pulse

0.301

SOI2

–29.9

Pressure2

1520

Spray angle

77.2

Swirl ratio

0.83

Hole number

9.27

0.00335

0.882

0.00578

0.6909

2.716

14.35

11.06

8.61

6.363

205.0

11.0

compared to gasoline due to its lower reactivity under the mid-load condition. This is also indicated by the averaged values in Table 6.26. Since the amount of fuel in the first injection is critically important, its timing also plays a role in diesel fuel performance. Retarding the first injection timing with diesel reduces UHC and CO emissions, as well as GISFC and PPRR. For gasoline and E10, a higher injection pressure of the main injection shortens the injection duration with promoted premixed combustion, which is found to benefit

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243

Fig. 6.53 In-cylinder images of representative diesel cases for mid-load. a Case 1. b Case 2. c Case 3. d Case 4. e Color bars

the reduction of soot, UHC, CO and GISFC. Spray included angle, swirl ratio, and the number of nozzle holes have only a moderate influence on the objectives for the different fuels. The regression analysis reveals that there are complex relationships between the design parameters and engine performance and emissions. To gain insightful understandings about the causes of the influences, in-cylinder image processing and parametric studies are used to further verify and investigate the optimal designs. Accordingly, in addition to the benchmark design, Case 1, three optimal designs from the Pareto solutions were reevaluated. They were chosen to further discuss the effects of primary design parameters on engine objective functions with each fuel. The design parameters and simulation results of the selected optimal designs are shown in Table 6.25(a) and (b), respectively. In addition to the value of the 6 objectives, Table 6.25(b) also lists the end-of-injection timings for the first and second injections, as well as the location of 50% accumulated heat release, CA50. Results are visualized at four different representative timings during the engine cycle of each case in Fig. 6.53, 6.54, and 6.55 for the three fuels. The first image of

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each case illustrates the contours of fuel mass fraction from 0 to 1% in a vertical cut-plane through the spray axis at the end of the first injection (EOI1). The second image shows the fuel distribution (0–1%) at the time when 10% of the total energy is released (CA10). The third image visualizes temperature contours (1,000–2,500 K) on the cut-plane at CA50. The last image demonstrates the distribution of CO mass fraction (0–1%) on the plane at CA90. The colored spheres in the images represent spray droplets and their colors indicate the size distribution of the droplets from 0 to 100 lm diameter. In these images, blue (light) represents the lower boundary while red (dark) indicates the upper boundary. The superimposed arrows on the CA50 and CA90 images represent the directions of the bulk flow. The regression analysis indicates that diesel combustion was most sensitive to the amount of fuel injected in the first pulse. The reason is revealed by comparing Case 1 and Case 2 with Case 3 and Case 4 in Fig. 6.53. It is seen that a large portion of the diesel fuel injected at early timings enters the crevice region in Cases 1 and 2. The fuel resides in the crevice region and is released during the expansion stroke. If the main combustion occurs before TDC (with higher likelihood for diesel), the escaped fuel contributes to high UHC emissions and poor fuel economy. But if the combustion occurs late in the cycle, such as in Case 2 with CA50 of 19.5 ATDC, the escaped fuel can be oxidized further, as illustrated in the temperature distribution of Case 2 at CA50. This also explains why for gasoline and E10, a larger amount of fuel in the first injection does not necessarily lead to higher UHC emissions since they usually burn after TDC. If the first injection forms a combustible air-fuel mixture, the combustion phasing will be largely determined by its associated parameters, such as injection timing and pressure. For example, for cases with only a small amount of pilot fuel that is not able to trigger the ignition, the combustion characteristics are mainly determined by the second injection, as for Cases 3 and 4 in Fig. 6.53. Within a proper window of injection timings, a spray with included angle of around 75 results in a stagnation-point flow field in the combustion chamber, as indicated by the flow direction for Cases 1, 2, and 4 at CA50 for diesel in Fig. 6.53. This benefits air-fuel mixing as the air in both squish and bowl regions are better utilized, which is also consistent with the regression analysis. So, the location of CO formation and soot formation (not shown here) for these cases is close to the stagnation point. The centrifugal effect of the swirling flow further confines the stagnation flow. With a higher swirl ratio as for Case 4, the location of CO and soot formation is closer to the piston bowl outer wall. For small spray included angles, the air motion due to the spray jet is guided by the combustion chamber walls, as shown in Case 2 at CA50, which results in more CO and soot being directed into the squish region as it is not co-located with the high temperature region of the bowl. Most of the optimal solutions of the gasoline and E10 cases had a relatively large amount of fuel in the first injection. The reason is that a locally rich mixture is needed in order to ignite those two fuels. This is confirmed by observing that most cases start combustion in the region at the piston bowl edge and the squish region where the first injection fuel and the second injection fuel overlap, as seen

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Fig. 6.54 In-cylinder images of representative gasoline cases for mid-load. a Case 1. b Case 2. c Case 3. d Case 4. e Color bars

in Figs. 6.54 and 6.55. Therefore, together with the regression analysis, the second injection timing is found to be the most influential parameter for gasoline-like fuels under the mid-load condition. According to the fuel distribution at CA10, most of the fuel is prepared (mixed) prior to combustion for gasoline and E10, and the mixing level increases as the fuel reactivity decreases. Retarding the second injection timing results in higher UHC and CO emissions, as well as fuel consumption, but on the contrary, this benefits NOx reduction and also lowers PPRR. As a result of the premixed combustion, no stagnation-point flow field is found in the studied cases at CA50. It is seen that the flow directions are primarily determined by the location of the highest volumetric heat release during the combustion. At CA90, CO is distributed more widely for the gasoline and E10 cases as compared to diesel. This favors CO oxidation with the ambient oxygen. The higher UHC emissions of gasoline and E10 are mainly attributed to their later combustion phasing. Overall, by filtering the optimal solutions with criteria, practical engine optimal designs are summarized in Table 6.27 for each fuel at mid-load in order to provide design guidance. The diesel engine requires both late first (*-55 ATDC) and

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Fig. 6.55 In-cylinder images of representative E10 cases for mid-load. a Case 1. b Case 2. c Case 3. d Case 4. e Color bars

second injection (*9 ATDC) timings. In addition, the amount of fuel injected in the first pulse should be limited below 10%. The preferred nozzle numbers are from 8 to 10 with narrow injection angles from 60 to 70. For gasoline and E10, up to 50% first injected fuel is seen in the practical cases. The first injection timings of gasoline-like fuels are about 10 earlier (*-65 ATDC) than those of diesel, and the second injection timings are about 20 (*-10 ATDC) to 30 (*-20 ATDC) degree earlier. The number of holes for gasoline-like fuels spreads widely in the studied range, i.e., from 6 to 12, and the injection angles are from 65 to 75. Injection pressures and swirl ratios for these cases depend on the combinations of the other design variables, which are distributed widely for all three fuels. An optimization study at high-load was also conducted following the same procedure as that used for the mid-load condition described previously. The simulations were again terminated at the 25th generation, based on the convergence metric shown in Fig. 6.56a.

PPRR

SOI1

Pre1

Inj%

SOI2

(a) Diesel (Soot < 0.068 g/kW h, NOx < 1.35 g/kW h, PPRR < 10 bar/CA) 1 0.05 0.85 7.60 31.77 250.19 4.30 -55.02 738.57 6 8.92 2 0.04 0.61 6.89 13.35 252.76 2.35 -65.83 1,598.2 3 8.96 3 0.02 0.68 12.00 22.93 275.47 2.36 -55.17 738.57 6 8.92 4 0.04 1.03 8.90 22.62 234.14 5.96 -55.03 738.57 6 8.92 5 0.05 0.93 5.31 25.41 233.45 10.11 -55.17 1,525.6 6 8.45 (b) Gasoline (Soot < 0.0136 g/kW h, NOx < 1.35 g/kW h, GISFC < 210 g/kW h, PPRR < 10 bar/CA) 1 0.04 0.30 13.77 13.33 197.39 4.90 -64.75 351.78 49 -11.55 2 0.00 0.95 26.34 11.17 205.26 9.20 -84.54 825.18 46 -15.69 3 0.00 1.02 24.68 11.44 206.84 9.29 -71.07 1,395.4 49 -6.75 4 0.00 1.06 19.92 13.48 208.24 6.73 -70.17 1,720.4 43 -7.44 5 0.01 0.95 4.14 6.57 185.02 9.22 -56.51 1,933.1 47 -7.70 6 0.00 0.93 4.32 6.74 185.70 7.51 -56.51 1,933.1 47 -7.62 7 0.01 0.95 7.94 7.79 207.72 2.34 -84.78 1,949.1 13 -16.29 (c) E10 (Soot < 0.0136 g/kW h, NOx < 0.27 g/kW h, GISFC < 210 g/kW h, PPRR < 10 bar/CA) 1 0.01 0.20 12.03 7.98 204.38 3.71 -68.30 865.03 45 -34.57 2 0.01 0.19 10.88 10.37 200.99 5.00 -68.24 1,173.0 49 -34.20 3 0.00 0.20 7.76 7.80 199.77 4.62 -57.69 1,180.2 50 -17.04 4 0.01 0.25 7.54 5.03 189.70 8.38 -57.29 854.16 34 -34.97

Table 6.27 Practical optimal designs at mid-load No. Soot NOx UHC CO GISFC 68.21 60.08 68.43 68.43 68.42 72.66 74.61 76.21 64.71 66.24 66.41 66.38 73.30 77.57 71.90 71.50

1,431.8 1,650.6 776.94 1,660.6 756.31 767.37 805.68 1,712.8 1,409.5 1,752.1 1,752.1

Angle

1,415.0 1,165.1 1,415.0 1,415.0 1,415.7

Pre2

0.72 0.06 1.61 1.60

1.66 1.50 1.00 1.51 0.52 0.52 0.53

0.01 1.97 0.00 1.76 0.00

Swirl

8 10 11 8

12 10 11 6 10 10 7

10 10 8 10 9

Hole

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Fig. 6.56 Convergence metric and Pareto solutions for high-load. a Convergence metric. b Pareto solutions (Soot and NOx). c Pareto solutions (UHC and CO). d Pareto solutions (GISFC and PPRR)

Similar to the mid-load case, it is seen in Fig. 6.56b that the optimal designs with diesel fuel show a trade-off between the soot and NOx emissions. Different from the mid-load condition, some of the optimal designs for gasoline and E10 produce high soot emissions that are comparable to the diesel fuel case. However, designs with simultaneously reduced soot and NOx are still found in Fig. 6.56b for gasoline and E10. As illustrated in Fig. 6.56c, the combustion completeness is represented by the higher CO emissions compared to the UHC for all three fuels different from the mid-load condition discussed previously. The high octane gasoline and E10 fuels have good fuel economy at high-load, as seen in Fig. 6.56c by the lower CO emissions and in Fig. 6.56d by the lower GISFC. However, the trade-off between GISFC and PPRR becomes more problematic for the high-load engine with gasoline and E10. None of the optimal diesel fuel designs was found to have soot and NMHC emissions lower than the EPA 2010 regulations. About 35% of the optimal designs had NOx levels below the limit, but they were also accompanied with very high GISFC. For gasoline, only a few designs had both soot and NOx emissions lower than the regulated values. For E10, several optimal designs with soot emissions slightly higher than the regulated limit were seen and

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249

about 30% optimal designs had NOx emissions below the regulation. It should be noted that for gasoline and E10, low NOx does not necessarily indicate high GISFC, as in the case of diesel. However, the low NMHC emission regulation is still not reachable with gasoline and E10 under the high-load condition. Following the same convention as for the mid-load case, the influence of the design parameters on engine performance and emissions are listed in Table 6.28. The average values of CO and GISFC of all Pareto solutions confirm that the engine operating under high-load has better fuel economy with gasoline and E10 than diesel although the engine noise level indicated by the PPRR is higher. This is primarily due to the better mixing characteristics of the gasoline and E10 sprays because the air-fuel mixing process becomes more important as the engine load increases. However, for gasoline and E10, air-fuel mixing related parameters are not as important as they are for diesel. For diesel, the fuel amount in the first injection is no longer the sole dominant parameter. As seen in Table 6.28(a), more parameters, including the second injection timing, pressure, swirl ratio, and the number of holes that influence the air-fuel mixing process play more important roles. This again confirms that focus needs to be placed on improving spray mixing at high-load. The second injection timing is found to be still critically significant for gasoline and E10. In addition, the second injection pressure becomes more important at high-load with gasoline, while E10 is more sensitive to the spray included angle. Again, four individual cases, including the benchmark case were selected for each fuel and the design parameters and the corresponding results are given in Table 6.29(a) and (b), respectively. The regression analysis showed different effects of each design parameter on engine performance and emissions, compared to at midload. The same as the mid-load cases, cases at four representative timings during the engine cycle were chosen to visualize the in-cylinder flow fields (the fuel mass fraction range was increased to 2% and that of CO was changed to 3%). Early injection of the diesel fuel pilot spray results in wall fuel films which eventually enter the crevice region and are directly correlated with the UHC emissions. This was also previously found in the mid-load cases. Retarded main injection is needed to prevent the engine from violating the peak pressure and PPRR constraints (20 MPa and 30 bar/CA, respectively). However, this deteriorates fuel economy as the time allowed for air-fuel mixing shortens. Therefore, enhanced mixing is needed at high-load, as also pointed out in the regression analysis. Case 2 in Fig. 6.57 has 10 nozzle holes with the smallest hole area of the four cases studied. Since the spray penetration scales linearly with the hole area (Shi and Reitz 2008c), Case 2 has the shortest spray penetration, although it also has the highest injection pressure (tip penetration scales as the  power). The smaller hole size produces smaller droplets downstream of the nozzle, as seen in Fig. 6.57b at CA10, and consequently the fuel spray evaporates faster. Hence, decreasing nozzle size (increasing the number of holes) reduces soot, UHC, CO emissions with improved fuel economy, as shown in Table 6.28(a). Compared with the mid-load results, a significant amount of CO is formed under the highload condition, and the CO is distributed along the combustion chamber walls and

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Table 6.28 Effect of individual design parameters on objectives for high-load

Soot

NOx

UHC

CO

GISFC

PPRR

0.4473

0.4697

8.96

33.6

255

4.21

0.1876

0.5201

5.81

16.24

(a) Diesel SOI1

–72.9

Pressure1

898

First pulse

0.14

SOI2

2.15

Pressure2

932

Spray angle

76.9

Swirl ratio

1.27

Hole number

8.06

(b) Gasoline SOI1

–69.4

Pressure1

862

First pulse

0.264

SOI2

–1.03

Pressure2

1450

Spray angle

69.8

Swirl ratio

1.13

Hole number

8.53

223

9.77

(c) E10 0.217 SOI1

–64.0

Pressure1

1039

First pulse

0.344

SOI2

2.58

Pressure2

1194

Spray angle

69.0

Swirl ratio

1.16

Hole number

8.46

0.4312

6.93

20.398

230.73

8.12

in the squish region. This highlights the importance of swirl for this operating condition. As in the mid-load cases, the flow patterns at CA50 again are found to be driven by the spray injection in the CI engine with diesel fuel.

(a) Design parameters SOI1 (ATDC) -70.0 1,150 Pressure1 (bar) First pulse (%) 25.0 -25.0 SOI2 (ATDC) Pressure2 (bar) 1,250 Spray angle () 72.5 Swirl ratio 1.0 Hole number 9 (b) Simulation results Soot (g/kW h) 0.104 NOx (g/kW h) 3.506 UHC (g/kW h) 12.17 CO (g/kW h) 17.96 GISFC (g/kW h) 227.5 PPRR (bar/CA) 27.38 -63.5 EOI1 (CA) EOI2 (CA) -6.4 CA50 (ATDC) -10.1

Case 1

-75.4 1,866 23.0 -8.8 1,301 78.5 1.9 8

0.120 1.773 5.051 8.190 201.2 10.11 -70.8 9.9 6.2

0.183 0.375 4.265 24.39 227.8 4.454 -61.8 19.2 18.2

Case 3

-65.1 1,189 13.2 1.5 1,850 61.1 1.7 10

Case 2

0.277 0.264 9.394 20.11 246.8 3.706 -69.9 26.5 24.1

-74.2 1,523 19.1 5.3 1,119 82.6 1.6 6

Case 4

0.006 3.369 0.109 1.185 190.3 174.4 -62.6 -3.7 -0.7

-70.0 1,150 25.0 -25.0 1,250 72.5 1.0 9

Case 1

Table 6.29 Representative optimal designs for the high-load condition Diesel Gasoline

0.034 0.988 1.771 27.09 206.9 29.0 -59.5 13.3 18.9

-62.4 888 8.5 -9.7 1,588 70.7 1.6 11

Case 2

0.032 0.648 4.309 7.042 212.2 11.1 -66.7 10.7 18.9

-71.3 1,088 15.3 -8.8 1,891 60.0 0.6 6

Case 3

0.063 0.830 4.092 8.295 205.9 27.0 -58.0 14.3 15.1

-70.8 345 23.6 -3.4 1,883 79.2 1.5 7

Case 4

0.013 2.769 0.321 3.611 191.0 159.0 -62.3 -2.7 3.3

-70.0 1,150 25.0 -25.0 1,250 72.5 1.0 9

Case 1

E10

0.060 0.411 3.296 7.007 215.3 8.060 -54.1 21.2 22.8

-66.3 744 31.6 -1.5 997 67.5 1.2 9

Case 2

0.060 0.523 6.081 6.181 215.2 17.22 -46.7 17.7 16.7

-58.1 1,170 37.1 1.2 1,616 73.0 1.3 6

Case 3

0.107 0.735 3.096 12.32 200.9 8.333 -57.6 19.1 13.5

-67.1 1,697 37.0 3.3 1,748 68.5 0.9 11

Case 4

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Fig. 6.57 In-cylinder images of representative diesel cases for high-load. a Case 1. b Case 2. c Case 3. d Case 4. e Color bars

For the high-load condition with high in-cylinder pressure and global equivalence ratio, auto-ignition is no longer a problem for both gasoline and E10. This is reflected by the location of the high temperature region at CA50 in Figs. 6.58 and 6.59, which is not necessary to be the overlapping region of the first and second spray plumes. Examination of all optimal solutions of the gasoline and E10 cases reveals that the second injection timing is around TDC for most cases, which is very different from the mid-load cases. This is most likely driven by the requirement of meeting the peak pressure constraint of 20 MPa in the optimization process. The larger area over which fuel is distributed at CA10 for gasoline and E10 signify the larger proportion of premixed combustion as compared to the diesel fuel case. But the difference at high-load is less than that for the mid-load case, as seen in Figs. 6.53, 6.54, and 6.55. This is obviously due to the late main injection timing under this operating condition and also the longer injection duration. However, optimal designs with low soot emissions are still found for gasoline and E10. Different from the diesel cases, the sensitivity of the gasoline and E10 cases to the main injection pressure is primarily through the injection

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Fig. 6.58 In-cylinder images of representative gasoline cases for high-load. a Case 1. b Case 2. c Case 3. d Case 4. e Color bars

parameters. In the optimization study, the total nozzle area was fixed, and thus increasing injection pressure is equivalent to decreasing the injection duration, which increases the time for air-fuel mixing. Distinguished from the mid-load cases where E10 required much earlier main injection timing than gasoline, the main SOI of E10 for the high-load condition is slightly later than gasoline in general, as also shown by the averaged values in Table 6.28. Since auto-ignition of both E10 and gasoline is not an issue for the high-load condition, the main consideration in the GA evolutionary process of the optimization study is meeting the constraints. Too-well-premixed air-fuel charge (CA50-EOI2 [ 5 CA) and too early combustion phasing (CA50 \ 15 ATDC) results in unacceptably high pressure rise rates. This trend can also be observed from Cases 1, 2, and 4 of gasoline and Cases 1 and 3 of E10 in Table 6.29 (b). Under the high-load condition the reactivity of E10 is slightly lower than gasoline, which allows for more time for the mixing processes. Therefore, it is necessary to retard the combustion phasing later than for gasoline in order to achieve similar PPRR levels. This also explains why, in general, E10 has lower fuel efficiency than gasoline.

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Fig. 6.59 In-cylinder images of representative E10 cases for high-load a Case 1. b Case 2. c Case 3. d Case 4. e Color bars

Both spray-driven stagnation-point flow patterns and volumetric-heat-releasedriven flow patterns are seen in Figs. 6.58 and 6.59. Due to the late CA50 of E10, the spray included angle and swirl ratio play more important roles than for gasoline. As can be seen in Fig. 6.59, larger spray included angles ensure better utilization of ambient air in both the piston bowl and squish regions and thus enhance combustion. However, smaller spray included angles help to slow down the combustion and to lower PPRR levels, even though this sacrifices oxidation of soot, UHC and CO, as illustrated in Table 6.28(c). Spray targeting and the flow patterns during the combustion profoundly influence the distribution of CO and soot during the late engine cycle, as represented by the CO mass fractions in Fig. 6.57, 6.58, and 6.59. Again, practical engine optimal designs are summarized in Table 6.30 for each fuel at high-load in order to facilitate engine design. For the diesel fuel, the first injection amount should be limited below 20%. The first injection timings are from *-65 ATDC to *-85 ATDC, and the main injections range from *-10 ATDC to *0 ATDC. High swirl level is required, which is seen to

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be above 1.5 for many cases. Nozzle hole numbers range from 6 to 10 with wide injection angles from *70 to *80. For gasoline-like fuels, the first injection amounts are between 30 and 40%, and the first injections are located between *-65 ATDC and *-80 ATDC. The swirl ratio is close to 1 for most cases. Nozzle hole numbers are from 8 to 11 with large injection angles from *70 to *80. Similar to the mid-load cases, the injection pressure varies over a large range for all three fuels, depending on other design variables. The above optimization results indicate that it is possible to run a CI heavy-duty engine with gasoline-like fuels and to achieve cleaner and more efficient combustion than with diesel-like fuels under mid- and high-load conditions. In addition, it is noted that compared to GDI engines CI engines fueled with gasoline-like fuels have higher compression ratio, thus better thermal efficiency. The combustion mode of gasoline-like fuels under the mid-load condition is Partially Premixed Combustion (PPC), which is advantageous over either HCCI or conventional diffusion combustion modes with diesel-like fuels. For the pure HCCI mode, control of the onset of auto-ignition is problematic. As seen in the optimization study, the second injection timing with gasoline-like fuels at the midload condition provides a mechanism to control engine combustion. The high volatility and low ignitability of gasoline-like fuels promote air-fuel mixing and allows a longer mixing time and late but still reasonable combustion phasing, which is essential for low soot and NOx emissions and high efficiency. However, this is hardly achievable for diesel-like fuels. The premixed combustion mode with diesel fuel results in high UHC and CO emissions due to the fact that the early injection leads to wall-wetting while the late injection has poor air-fuel mixing and combustion efficiency, such as seen in PCCI combustion (Opat et al. 2007) and MK-type combustion (Kimura et al. 1999, 2001), respectively. In addition, conventional diesel diffusion combustion exhibits the well-known trade-off relationship between soot and NOx emissions, as also shown in the previous optimization studies of this chapter. For the mid-load case, it was also found that both the fuel physical (e.g., volatility) and chemical (e.g., ignitability) properties are important. But the chemical properties are more influential, as seen in the comparison of gasoline and E10 cases. E10 has different preferred optimal injection variables than gasoline, especially the second injection timing. Furthermore, the higher octane number E10 more likely features unacceptably high pressure rise rates than gasoline and diesel. This suggests that lower octane number gasoline-like fuels (e.g., PRF80) may be better, or more injection pulses may be needed. Nevertheless, the high volatility of gasolinelike fuels is very beneficial to achieve clean and efficient CI engine combustion, which indicates that the volatility requirement of fuels will most likely increase in future, as discussed by Kalghatgi et al. (2007). Although, the optimal octane number of gasoline-like fuels in CI engines should be emphasized in future. Compared to the mid-load condition, the high-load condition was found to be less sensitive to fuel reactivity. The second injection timings of optimal solutions were all close to TDC with the different fuels. However, mixing-related parameters, such as injection pressure and swirl strength were found to be more important

PPRR

SOI1 Pre1

Inj%

SOI2

(a) Diesel (Soot < 0.272 g/kW h, NOx < 1.35 g/kW h, GISFC < 220 g/kW h, PPRR < 10 bar/CA) 1 0.24 0.83 3.34 26.87 218.86 5.89 -75.43 1,890.8 1 -7.36 2 0.22 1.33 2.89 19.67 202.31 5.43 -63.06 930.53 8 -8.41 3 0.26 1.09 3.61 24.76 208.08 3.76 -83.27 1,594.5 7 -7.35 4 0.26 0.78 3.10 28.07 217.60 7.51 -68.12 364.73 1 0.96 5 0.20 1.03 4.51 10.33 207.70 3.89 -55.81 305.47 20 -3.27 6 0.21 1.21 1.95 19.15 204.61 4.28 -83.09 1,625.6 5 -6.60 7 0.27 0.88 3.92 22.61 210.43 3.35 -68.29 520.23 8 -5.14 8 0.27 0.63 4.54 23.69 219.94 3.64 -82.27 1,505.5 10 4.11 9 0.23 0.90 2.51 24.92 213.28 9.53 -59.15 333.63 5 2.13 10 0.24 1.11 9.57 15.59 212.05 3.60 -80.35 1,328.6 25 -3.75 11 0.24 0.89 2.18 16.74 210.96 3.61 -71.12 834.36 1 -5.06 (b) Gasoline (Soot < 0.272 g/kW h, NOx < 1.35 g/kW h, GISFC < 210 g/kW h, PPRR < 10 bar/CA) 1 0.22 0.92 12.81 17.50 209.12 5.06 -76.19 1,004.3 34 3.23 2 0.25 0.72 6.98 17.64 207.87 7.88 -78.39 1,176.2 34 6.51 3 0.26 1.16 5.38 23.48 200.50 5.61 -81.86 1,175.2 34 0.54 4 0.21 0.72 5.25 22.35 202.42 6.85 -75.59 819.02 34 -0.68 5 0.16 1.07 5.29 14.55 202.55 8.88 -76.43 318.46 34 5.30 6 0.23 0.88 4.51 16.75 201.46 5.76 -71.35 997.99 35 2.07 7 0.24 0.74 5.05 19.26 202.75 9.80 -72.54 1,365.7 34 4.93 8 0.16 1.08 4.28 13.75 200.42 8.39 -75.60 302.94 36 5.30 9 0.20 0.94 5.13 16.16 205.41 7.43 -70.77 531.85 31 5.18 (c) E10 (Soot < 0.272 g/kW h, NOx < 1.35 g/kW h, GISFC < 210 g/kW h, PPRR < 10 bar/CA) 1 0.19 1.23 4.11 23.38 201.36 9.11 -57.93 1,171.4 34 3.23 2 0.23 1.17 5.22 27.15 203.50 7.24 -66.19 1,601.6 34 3.30 3 0.22 0.69 8.05 28.28 209.33 9.78 -69.01 1,337.4 40 3.08

Table 6.30 Practical optimal designs at high-load No. Soot NOx UHC CO GISFC 73.64 79.14 82.43 80.89 79.99 81.31 82.66 82.06 79.41 82.61 82.39 76.34 76.27 78.39 60.06 73.63 73.62 78.39 73.37 74.50 72.61 72.52 63.03

1,543.4 1,543.4 1,543.2 1,396.1 1,904.9 1,860.2 1,395.7 1,904.8 1,896.8 1,543.4 1,615.8 1,550.0

Angle

1,306.2 936.47 876.15 1,794.6 924.59 1,013.7 926.46 1,563.0 1,983.8 978.76 1,085.7

Pre2

11 11 10

8 11 10 9 11 8 11 11 9

6 6 7 10 7 7 8 9 10 7 8

Hole

(continued)

0.81 0.80 0.86

1.75 0.96 0.96 1.02 1.26 0.73 0.96 1.26 1.57

0.68 1.59 1.19 1.77 1.60 1.84 1.18 1.22 1.92 1.57 1.45

Swirl

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4 5 6 7

0.15 0.15 0.19 0.12

0.62 1.15 1.02 1.29

Table 6.30 (continued) No. Soot NOx

5.13 5.01 3.17 4.20

UHC

17.72 11.90 17.64 14.92

CO 209.50 202.92 202.78 198.53

GISFC 9.72 8.42 7.39 9.61

PPRR -55.28 -64.86 -55.38 -62.82

SOI1 1,202.3 842.69 1,134.0 1,103.2

Pre1 35 37 34 39

Inj% 6.25 3.51 3.19 3.06

SOI2 1,623.3 1,622.2 1,416.9 1,610.7

Pre2 62.96 78.24 79.29 69.99

Angle 0.89 1.03 0.87 0.38

Swirl 9 11 11 11

Hole

6.2 Engine Optimization with Advanced Combustion Models 257

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for the high-load cases. It is noted that due to the long injection duration, diffusion combustion was not avoidable for all three fuels investigated at highload. Also, considering the maximum pressure and peak pressure rise rate constraints, the degree of premixed combustion should be limited. At high-load, the size of the nozzle holes and the injection pressure were found more influential than for the mid-load case. The total area of the nozzle holes was fixed in the present study, so the injection duration was only a function of injection pressure. But the optimization study suggests that increasing the total nozzle hole area may be helpful for gasoline-like fuels since reduced injection duration was found to be beneficial. Although optimization of a low-load condition was not conducted, general guidance is offered from the results of the present study. Igniting gasoline-like fuels at low-load is difficult considering the low ignitability of lean mixtures. Therefore, the use of HCCI with advanced engine thermal management system (such as fuel reformation in the Negative Valve Overlap (NVO) period (Hiraya et al. 2002; Cao et al. 2008)) may be necessary to extend the operating limit to low-load for a CI engine fueled with gasoline-like fuels. Also, the use of dual-fuel as proposed by Kokjohn et al. (2009) could extend the operating limit of gasoline CI engines. Finally, it should be pointed out that the high volatility of gasoline-like fuels is helpful for an HCCI engine in order to better prepare a fully premixed charge.

6.2.1.5 Summary This example presents a comprehensive optimization study of a heavy-duty CI engine operated under mid- and high-load conditions and fueled with diesel, gasoline, and E10. The focus was optimization of injection system parameters, including pilot and main injection timings, pressures, and amounts. Concluding remarks are as follows. • Due to the large amount of individual engine CFD evaluations that are required for optimization with detailed fuel chemistry, an efficient chemistry solver was necessary and was successfully applied in the research. • Gasoline-like fuels exhibit great potential for cleaner combustion than with conventional diesel fuel. For the mid-load condition, the ignitability of gasolinelike fuels significantly influences the specification of the injection-related design parameters for engine performance and emissions. As a result, the engine performance with gasoline-like fuels is greatly affected by the second injection timing, while for the diesel fuel the first injection amount was found to be critical. For the high-load condition, mixing-related parameters dominate the family of optimal designs as the ignitability is no longer a major factor, and injection pressure, swirl, and nozzle designs are more influential. Consequently, higher injection pressure, swirl ratio and smaller nozzle holes that promote air-fuel mixing are desirable but they are also subject to requirements of meeting the constraints.

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• Different in-cylinder flow patterns were identified in the optimal engine designs with the different fuels. For example, due to the diffusion combustion, the diesel fuel exhibits stagnation-point flow fields in many optimal cases, while gasolinelike fuels show more volumetric-heat-release-driven flows due to the premixed combustion. The results of the optimization study also indicate that lower octane number gasoline-like fuels may be more helpful to improve the controllability of CI engines in PPC mode and reduce engine noise.

6.3 Strategies for Simultaneous Optimization of Multiple Engine Operating Conditions It was found that different engine loads favor different nozzle design and piston bowl shapes. For instance, high load favors an injector with less nozzle holes, while low load favors an injector with more nozzle holes (Ge et al. 2009a, b). Clearly, only one uniform set of designs for the nozzle and piston bowl shape can be delivered to a production department. Thus, it raises a question: how can we use the state-of-the-art CFD tools to directly suggest an optimal design for engine production? This section discusses methodologies of simultaneous optimization for multiple operating conditions. Two methods, which are proposed by the authors, will be discussed. Both of them classify the design parameters into two categories: hardware design parameters and controllable design parameters. The controllable parameters indicate parameters that can be changed during run-time, while hardware parameters cannot.

6.3.1 A Two-Step Method for Simultaneous Optimization of Multiple Operating Conditions The first method is based on optimization of full-load cases. The whole optimization procedure is then divided into two steps: 1. determine the optimal design for the hardware parameters; 2. determine the controllable parameters for each considered operating condition with the optimal hardware design from Step 1. The idea is illustrated in Fig. 6.60. Optimizations at different loads will give different sets of optimal hardware parameters. The first problem that needs to be addressed is to indicate at which engine load the hardware parameters should be optimized. Single case optimizations showed that full load is the most representative case (Shi and Reitz 2008b; Ge et al. 2009b). Therefore, the hardware parameters were optimized at full-load operating conditions. The controllable parameters were then optimized with the optimal set of hardware parameters for each considered operating condition. In the present work, the hardware parameters include nozzle design and piston bowl shape, and the controllable parameters include SOI, swirl, boost pressure, and injection pressure. Due to the large number of design parameters and optimization iterations in

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Fig. 6.60 Flowchart of multi-mode optimization

Step 1, simplified combustion models—CTC model and shell model–were used. The more accurate chemistry solver with the AMC model was used in Step 2. As with the optimization in Sect. 6.1.4, the bowl shape was characterized using eleven parameters. Computational meshes were automatically generated using the Kwickgrid methodology. The present method was practiced on the same engine as the one in Sect. 6.1.4. The engine specifications are listed in Table 6.20. Two full-load operating conditions were considered in Step 1. Four other operating conditions, including two mid-load cases and two low-load cases, were taken into account in the second stage optimization. 6.3.1.1 Optimization of Hardware Parameters Under Full-Load Operating Conditions Hardware parameters, including spray angle, number of nozzle holes, and piston bowl design, were optimized together with swirl ratio and SOI under full-load operating conditions. Two full-load cases, Case A and Case B, were considered. The specific operating conditions are listed in Table 6.31. Engine operation under these two modes was optimized separately and Table 6.32 lists the search space of the present optimization. Since 15 design parameters were considered in these two optimizations, many generations are needed for the optimization to achieve convergence. Thus, simplified combustion models are preferred at this stage. The CTC model and the Shell model have been proven to be reliable for conventional diesel combustion under full-load conditions (Ge et al. 2009b). The same methodologies as used by

6.3 Strategies for Simultaneous Optimization of Multiple Engine Operating Conditions Table 6.31 Full-load operating conditions

Speed (rev/min) IMEP (bar) Fuel injected (kg/h) SOI (ATDC) DOI ()

261

Case A

Case B

4,000 18.0 6.7 -16.04 42.4

2,000 22.7 3.8 -7 28.5

Table 6.32 Optimization search space Parameter Min.

Max.

Parameter

Min.

Max.

Spray angle () Nozzle hole number Swirl ratio SOI (ATDC), Case A SOI (ATDC), Case B Az Bx Cx

160 12 2.5 -5 10 0.8 1.0 0.65

Cz Dx Xab Xba Xbc Xcb Ycb Ycd

0.60 0.45 0.1 0.3 0.5 0.5 0.3 0.3

0.5 0.70 0.7 0.9 3.5 3.5 0.9 0.9

140 5 0.5 -20 -25 0.5 0.8 0.45

Ge et al. (2009b) were used in this section. The optimizations were stopped at the 72nd generation, which resulted in about 2,300 valid designs for each case. Figure 6.61 shows all citizens from the optimization of Cases A and B, as well as the baseline designs. Pareto designs are indicated by blue triangles. Six designs, which are indicated by arrows in Fig. 6.61, were selected from these Pareto designs and validated using the KIVA-CHEMKIN model. The piston shapes of these optimal designs were illustrated in Fig. 6.62. SOI sweeps of these six designs as well as the baseline design were made for both Case A and B. GISFC and engine-out emissions results are shown in Fig. 6.63. It can be seen that Designs II and IV show good performance in both fuel consumption and engine-out emissions. Especially, Design IV simultaneously reduces fuel consumption and pollutant emissions for both full-load cases. Comparison of the performance of the baseline engine and Design IV is shown in Table 6.33. Significant improvements over the baseline engine were achieved for the two full-load cases, with about 10% reduction in NOx emission, about 50% reduction in soot emission, and 1 * 5% improvement in fuel consumption. Thus, the hardware designs of Design IV was selected as the optimal hardware design and used for further optimization. Note that the results computed using the KIVA-CHEMKIN model are slightly different from the ones computed using the CTC model. Therefore, the results in Fig. 6.61 are a little different from the data in Fig. 6.63 and Table 6.33.

6.3.1.2 Optimization of Controllable Parameters for All Operating Conditions The above optimization of the two full-load cases eventually suggested an optimal hardware design, including the nozzle design and piston bowl shape. In this section, controllable parameters, including SOI, swirl ratio, boost pressure, and

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Fig. 6.61 All citizens and Pareto solutions from the optimization, and the baseline design for Case A (top) and B (bottom). Arrows indicated are the selected optimal designs

Fig. 6.62 Piston bowl shapes of Designs I-VI: from left to right, from top to bottom

injection pressure, were optimized for each considered case. Since only 4 parameters were considered in these optimizations, advanced combustion models could be used for more accurate prediction. Especially, the part-load cases are more kineticscontrolled and therefore use of a detailed reaction mechanism greatly improves the

6.3 Strategies for Simultaneous Optimization of Multiple Engine Operating Conditions

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Fig. 6.63 SOI sweeps of the baseline design and selected optimal designs for Case A (left) and B (right)

accuracy of the predictions (Ge et al. 2010a). Thus, instead of the CTC and Shell models, the AMC model (Shi et al. 2009b) with the ERC n-heptane mechanism (Patel et al. 2004) was used in the optimizations in this section. Other models are the same as the ones in the previous section. The AMC model for optimization has been validated in detail for the same baseline engine in a previous study (Ge et al. 2010b).

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Table 6.33 Comparison of the performance of baseline engine and Design IV NOx (g/kgf) Soot (g/kgf) GISFC (g/kW h) Case A Case B

Baseline Design IV Baseline Design IV

50.1 45.4 (9.5%;) 32.8 28.4 (14%;)

1.92 0.74 (65%;) 1.29 0.80 (38%;)

249.4 237.3 (5%;) 216.6 213.8 (1.3%;)

SOI -16. -15.1 -7 -7.1

Table 6.34 Optimal designs of full-load cases GISFC (g/kW h) SOI (ATDC) Swirl ratio (-) Pboost (bar) Pinj (bar) Design IV Case A 232.3 Optimum A1 228.9 (1.5%;) Design IV Case B 217.9 Optimum B1 215.4 (1.1%;)

-15.1 -15.5 -7.1 -8.3

1.73 1.81 1.73 1.78

3.57 2.45 3.2 3.65

1,600 1,790 1,600 1,616

The two full-load cases, Cases A and B, were optimized at first. Only GISFC was considered as an objective.2 Performance and design parameters of Design IV and optimal designs A1 and B1 are compared in Table 6.34. It can be seen that more than 1% additional improvement in fuel consumption can be achieved by optimizing the controllable design parameters. Note that the GISFC in Table 6.34 is based on the computation using the AMC model, and therefore it is slightly different from the value in Table 6.33 which was computed using the KIVA-CHEMKIN model. The same method was extended to optimize the controllable parameters for a new Case C. Case C represents a medium-load case whose engine speed is 2,400 rev/min and IMEP is about 15 bar. Objectives in this case include GISFC, NOx and soot emissions. Figure 6.64 shows all citizens and Pareto solutions from the optimization, and the baseline design. All data is based on computations using the AMC model. Selected optimal designs, which simultaneously reduce fuel consumption and pollutant emissions, as well as the baseline design are listed in Table 6.35. Optimal design C1 represents the best fuel consumption design which has 5% improvement in GISFC compared to the baseline design. Optimal design C2 has good NOx reduction with acceptable fuel consumption and soot emission: 46% reduction in NOx emission is achieved in Design C2. While optimal design C3 represents the lowest soot design, with 26% reduction in soot emission. Case D is a medium-load case whose engine speed is 2,280 rev/min and IMEP is about 9 bar. The optimization objectives were set to GISFC, soot and NOx emissions. Figure 6.65 shows all citizens and Pareto solutions from the optimization, and the baseline design. Selected optimal designs as well as the baseline design are

2 According to NEDC emission tests (Schmidt 2008), NOx emissions are not considered under full-load conditions. Since soot emission is usually proportional to GISFC, only GISFC was considered.

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Table 6.35 Selected optimal designs of Case C (medium-load, 15 bar) NOx (g/kgf) Soot (g/kgf)

GISFC (g/kW h)

Baseline Optimum C1 Optimum C2 Optimum C3

217.2 206.6 (5%;) 213.2 (2%;) 210.3 (3%;)

32.5 28.0 (14%;) 17.4 (46%;) 30.4 (6.5%;)

1.28 1.15 (10%;) 1.23 (4%;) 0.95 (26%;)

Fig. 6.64 All citizens and Pareto solutions from optimization and the baseline design: Case C (medium-load, 15 bar)

Fig. 6.65 All citizens and Pareto solutions from optimization and the baseline design: Case D (medium-load, 9 bar)

listed in Table 6.36. Optimal design D1 has very good fuel consumption and low soot emissions. Compared to the baseline design, 3% reduction in GISFC and 10% reduction in soot emissions were achieved. Optimal design D2 has very good reduction in NOx emission, with 7% reduction compared with baseline engine. Both of them simultaneously reduce fuel consumption and engine-out emissions. Case E is a low-load case whose engine speed is 1,500 rev/min and IMEP is about 7 bar. The same optimization was performed on Case E, with objectives of GISFC, NOx and soot emissions. Figure 6.66 shows all citizens and Pareto

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Fig. 6.66 All citizens and Pareto solutions from optimization and the baseline design: Case E (low-load, 7 bar) Table 6.36 Selected optimal designs of Case D (medium-load, 9 bar) NOx (g/kgf) Soot (g/kgf)

GISFC (g/kW h)

Baseline Optimum D1 Optimum D2

198.8 192.9 (3%;) 194.1 (2%;)

23.2 22.1 (5%;) 21.6 (7%;)

1.03 0.93 (10%;) 0.99 (4%;)

Table 6.37 Selected optimal designs of Case E (low-load, 7 bar) NOx (g/kgf) Soot (g/kgf)

GISFC (g/kW h)

Baseline Optimum Optimum Optimum Optimum

253.7 229.4 231.7 252.3 229.7

E1 E2 E3 E4

30.7 24.6 29.5 16.7 28.3

(20%;) (4%;) (46%;) (8%;)

0.977 0.755 (23%;) 0.436 (55%;) 0.97 (1%;) 0.493 (50%;)

(10%;) (9%;) (1%;) (9%;)

solutions from the optimization, and the baseline design. Again, all data is based on computations using the AMC model. Selected optimal designs, which simultaneously reduce fuel consumption and pollutant emissions, as well as the baseline design are listed in Table 6.37. Optimal design E1 represents the best fuel consumption design, which has 10% reduction in GISFC compared to the baseline design. Optimal design E2 has the lowest soot emission, with 55% reduction compared with the baseline engine. Optimal design E3 has good NOx reduction with acceptable fuel consumption and soot emission: 46% reduction in NOx emission, and 1% reduction in GISFC and soot emission. Optimal design E4 has similar reduction in GISFC and soot emission as Design E2, but much better NOx reduction (8%). Figure 6.67 shows some selected response surfaces from this optimization. It can be seen that SOI and boost pressure are the dominant parameters for both

6.3 Strategies for Simultaneous Optimization of Multiple Engine Operating Conditions

267

Fig. 6.67 Selected response surfaces: Case E (low-load, 7 bar)

GISFC and soot emissions. Correlations among the controllable parameters were not found in the optimization of all these cases. This implies that these controllable parameters can also be optimized separately. These observations were also true for the other cases whose response surfaces are not shown for brevity. Finally, Case F is a very-low-load case whose engine speed is 1,500 rev/min and IMEP is about 4 bar. Besides GISFC, NOx and soot emissions, CO and UHC emissions were taken into account in objectives. Figure 6.68 shows all citizens and Pareto solutions from the optimization, and the baseline design. It can be seen from Fig. 6.68 that the baseline engine represents one of the optimal designs compared to the citizens from the present optimization (c.f., plots of GISFC and NOx emission). Designs that simultaneously reduce GISFC and all pollutant emissions were not found in the present optimization. One of the major reasons is that the hardware design was optimized under the full-load condition. As shown in (Shi and Reitz 2008b; Ge et al. 2009a, b), full-load conditions have different preferences from the low-load conditions. For instance, full-load cases prefer a large bowl design while low-load cases prefer a small bowl design (Ge et al. 2009b). Selected optimal designs, which simultaneously reduce fuel consumption and UHC and CO emissions, as well as the baseline design are listed in Table 6.38. Optimal design F1 represents the best fuel consumption design, which has 3% reduction in GISFC compared to the baseline design. Significant reductions in CO and UHC emissions were achieved—80% and 48% reductions

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Fig. 6.68 All citizens and Pareto solutions from optimization and the baseline design: Case F (low-load, 4 bar)

Table 6.38 Selected optimal designs of Case F (low-load, 4 bar) NOx (g/kgf) Soot (g/kgf) CO (g/kgf) UHC (g/kgf)

GISFC (g/kW h)

baseline 9.1 Optimum F1 56.1 (516%:) Optimum F2 54.4 (498%:) Optimum F3 8.11 (11%;)

252.9 246.0 (3%;) 246.8 (2.4%;) 255.8 (1%:)

0.529 13.1 2.67 0.787 (48%:) 2.65 (80%;) 1.39 (48%;) 0.410 (22%;) 1.53 (88%;) 0.9 (93%;) 1.664 (215%:) 5.82 (56%;) 0.958 (64%;)

in CO and UHC, respectively. Optimal design F2 has considerable reduction in soot, CO, and UHC emissions, with 22, 88, 93% reduction compared with baseline engine, respectively. Besides, more than 2% improvement in GISFC was obtained. Optimal design F3 has improved NOx emission with similar fuel consumption. CO and UHC emissions were reduced by around 60%. However, soot emission increased by 2 fold. Overall, the current hardware design is good at CO and UHC reduction but not NOx reduction, indicating that other methods, such as the use of increased EGR levels might be needed at low-load. Figure 6.69 summarizes averaged design parameters as a function of engine load. The averaged values were evaluated by averaging over all the Pareto

6.3 Strategies for Simultaneous Optimization of Multiple Engine Operating Conditions

269

Table 6.39 Scaling laws for the specification of the 450 cc optimal and down-scaled 400 cc engines Parameter 450 cc 400 cc Scaling factor Bore (cm) Stroke (cm) Displacement volume (cm3) Volume@TDC (cm3) Squish height (cm) Compression Ratio Conrod length (cm) Bowl diameter (cm) IVC (ATDC) EVO (ATDC) Twall/Thead/Tpiston (K)

8.1 8.8 453.23 31.66824 0.07 15.313 16 4.836 -129.5 120 379/385/441

7.788 8.461 402.88 28.18 0.0673 15.295 16 4.65

L L L3 L3 L Equal – L Equal Equal Equal

Fig. 6.69 Averaged design parameters from Pareto solutions as a function of engine load

solutions for each operating condition. Since only GISFC was taken as the objective in the optimizations of Cases A and B, there is no Pareto front from these two optimizations and therefore these two cases were not considered here. There is no evident trend in SOI, since either early injection or late injection may lead to certain benefits such as NOx and GISFC reduction. This is true particularly for the very low-load case (Case F, IMEP = 4 bar). The very late injection condition shows similar features as those of MK combustion, which has very low NOx emissions and good fuel consumption. Very early injection may lead to a similar combustion event as in HCCI combustion. Additionally, CO and UHC emissions and a wider search space of SOI were considered in the optimization of Case F. Therefore, Case F has a large variance in SOI of the Pareto designs. Case D also considered a wider search space of SOI than Cases C and E, which results in a larger variance in SOI, too. The boost pressure increases with the engine load. Higher load requires more injected fuel, and the corresponding amount of air, therefore necessitating higher boost pressure to

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trap more air in cylinder. It can be seen that the averaged injection pressure increases as engine load increases. The ambient density and temperature in the high-load cases are higher than the ones in the low-load cases. Plus the global equivalence ratio is higher in the high-load cases. Therefore, mixing with available oxygen is essential for engine performance, and the key issue for spray control lies in keeping spray penetration as long as possible while avoiding spray wall impingement. Higher injection pressure needed for the high-load condition increases spray penetration and enhances mixing with oxygen near the cylinder wall and piston bottom. There is no evident trend in the averaged swirl ratio with engine load as well. Although the same search space was used for the swirl ratio, the variance in the Pareto designs is larger in the low-load cases than the high-load cases. This implies that the high-load cases have a clear preference in swirl, while engine performance is less sensitive to the swirl for the low-load cases.

6.3.1.3 Summary The following conclusions can be drawn from the present section: • The present study demonstrated that the proposed hardware optimization method is feasible for CFD-based engine optimization. • With the fixed optimal hardware design and optimal sets of controllable parameters for each case, optimal designs which simultaneously reduce fuel consumption and pollutant emissions were obtained in all cases except for the very low load case. The reason is that different engine loads have different preferences in hardware design, for instance, bowl radius, which is smaller at low load. • Strong correlations among the controllable design parameters were not observed, which implies that these controllable parameters can be optimized separately. • Optimal injection pressure and boost pressure increase with engine load, but no evident trend in SOI and swirl ratio is observed. With small modifications, the present method could be applied to other engine development procedures.

6.3.2 A Consistent Method for Simultaneous Optimization of Multiple Operating Conditions The second method is a general method for the optimization of multiple operating conditions. Design parameters cover a common set of hardware parameters, as well as sets of controllable parameters for each individual

6.3 Strategies for Simultaneous Optimization of Multiple Engine Operating Conditions

271

Fig. 6.70 Flowchart of consistent multi-mode optimization

condition. We take a computational optimization of IC engine with KIVA CFD code and genetic algorithms for example. The optimization objectives include GISFC and the pollutant emissions (soot and NOx emissions) of all the operating conditions. The concept of this optimization methodology as depicted in Fig. 6.70, indicates that each GA population invokes two KIVA runs (e.g., for 2,000 and 4,000 rev/min cases, respectively). Each run generates a set of objectives that include GISFC, NOx and soot emissions. Thus, there are six objectives in. This optimization method avoids conflicts in hardware designs from independent optimization for each individual case, and offers a systematic method for engine optimization. Considering that the computational cost of one optimization is proportional to its total number of design parameters, the computational cost of the present method is cos t / Nhw þ Ncase  Ncontr which will usually be lower than the total cost of the conventional individual optimization where cos t / Ncase  ðNhw þ Ncontr Þ. Here Ncase is the total number of considered operating conditions, and Nhw and Ncontr indicate the number of hardware parameters and controllable parameters, respectively. This method will be practiced in the next section.

6.4 Coupling of Scaling Laws with Computational Optimization The scaling laws discussed in Chap. 5 were applied to down-size an optimal design in Sect. 6.1.4 from 450 to 400 cc. The scaling laws were validated by comparing the two engines under six operating conditions, which cover full-load, mid-load,

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and low-load conditions. The down-scaled optimal design is then taken as the starting point for engine development of this class, and is further optimized using the second method described in Sect. 6.3.

6.4.1 Downsizing of a HSDI Diesel Engine Scaling laws are desired to produce identical performance and emission levels of engines of different sizes. However, it is very difficult to achieve this aim in reality. First of all, geometric similarity is needed, such that the two scaled engines have similar boundary conditions. This includes scaling the bore, stroke, squish height, and piston bowl shape. The resulting compression ratio should be the same in the two engines. By setting the same boost pressure and temperature,3 the same wall temperatures, and the same initial flow conditions, such as the swirl ratio, similar initial thermodynamic and fluid dynamic conditions prior to spray injection can be achieved in the combustion chamber. Secondly, similarity in spray dynamics should be considered. Spray development has a primary effect on engine performance and pollutant emissions as it determines the mixing of the fuel and air. The aim is to have similar fuel distributions before the combustion event. This is usually quantified in terms of spray penetration, which is the essential parameter determining the fuel distribution. Finally, similarity in the combustion characteristics in the scaled engines should be maintained in order to provide similar engine performance and emissions. In the following, a 450 cc HSDI engine is down-scaled to a 400 cc engine following the procedures described above. The 450 cc HSDI diesel engine was optimized in a previous computational optimization study (Ge et al. 2009b, 2010). The scaling factor is based the ratio of the displacements: V ¼ 400=450 ¼ 0:8889 and the corresponding length scaling factor is: L ¼ ð400=450Þ1=3 ¼ 0:9615: Based on the scaling relations listed in Table 5.1, the two scaled piston geometries of the two engines are depicted in Fig. 6.71 and the engine specifications are listed in Table 6.39. Valve opening and closing timings, wall temperatures,

3

In Chap. 5, different initial temperatures were used to take into account the different heat transfer between engines of different sizes. Since the scaling factor in this section is close to unity, the corresponding volume-to-area ratios of the two engines are similar and thus the same initial temperatures were used in this section.

6.4 Coupling of Scaling Laws with Computational Optimization

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Fig. 6.71 Schematic of the piston geometries of the 450 cc (left) and 400 cc (right) engines

Table 6.40 Scaling laws for the nozzle design of the 450 cc optimal and down-scaled 400 cc engine 450 cc 400 cc Scaling factor Nozzle diameter (lm) Nozzle hole number

121 8

116 8

Table 6.41 Scaling laws for full-load cases: 2,000 and 4,000 rev/min 450 cc 400 cc 450 cc Engine speed (rev/min) Temperature@IVC Pressure@IVC (atm) Swirl@IVC SOI DOI Injected fuel mass (mg) Injection pressure (bar) EGR

2,000 358 3.2012 1.73 -7.06 32.5 0.063 1,600 0.13%

2,026.3

0.056 1,518

4,000 482.42 3.57 1.73 -15.1 42.4 0.0556 1,600 0.16%

L Equal

400 cc

Scaling factor

4,052.7

L1=3 Equal Equal Equal Equal Equal L3 L4=3 Equal

0.0494 1,518

boost pressures and temperatures were kept the same, so that the thermodynamic conditions before spray injection are similar between the two engines. The scaling relations described in Chap. 5 were applied to the 450 cc and 400 cc engines. Parameters concerning the nozzle design are listed in Table 6.40. Operating parameters, including engine speed, boost pressure and temperature, swirl ratio, injection timing and duration in crank angles, injected fuel mass, injection pressure, and EGR, are listed in Table 6.41 for two full-load operating conditions. The same scaling laws can be applied for mid- and low-load operating conditions as well (Ge et al. 2011). All of the six cases for both engines were simulated using the same CFD code and include full-, mid- and low-load cases, at different speeds. Pressure traces, HRR, averaged and peak temperatures, NOx and soot emissions for the two full-load cases are plotted in Fig. 6.72. Since HRR is not a volume-specific variable, the HRR of the down-scaled engine is multiplied by the scaling factor V. It is seen that all of these cylinder averaged quantities match very well, which implies the applicability of the scaling laws. Figure 6.73 shows the comparison of the GISFC and engine-out emissions of the six operating conditions between the two engines. Slight discrepancies are observed only in the two low-load cases.

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Fig. 6.72 Pressure, heat release rate, average temperature, peak temperature, and NOx and soot emissions of the full-load cases: 2,000 (left) and 4,000 rev/min (right)

6.4.2 Optimization of Downsized Engine It was of interest to explore whether the 400 cc engine downsized from the previous optimized 450 cc engine using the scaling laws could be further optimized. Thus, the downsized engine was further optimized using a multi-objective genetic algorithm methodology. Since full-load cases are the more representative conditions, only the two full-load cases (2,000 and 4,000 rev/min) were considered in

6.4 Coupling of Scaling Laws with Computational Optimization

275

Fig. 6.73 Fuel consumption and engine-out emissions of the 450 and 400 cc engines

the optimization. The consistent optimization method described in Sect. 6.3.2 was employed to optimize the down-sized engine operating under two full-load conditions. The hardware parameters considered in the present optimization include nozzle design (spray angle and number of nozzle holes), 12 parameters describing the piston bowl shape, and one parameter describing the relative bore size, Xb. An Xb of unity corresponds to the ratio of bore and stroke of the down-sized 450 cc engine design. When the bore size is changed, the volume at TDC and BDC is kept as the same, so that the compression ratio is the same, i.e.,: VBDC ¼ Vbowl þ Vsquish þ Vcrevice þ Vdisplacement ; VTDC ¼ Vbowl þ Vsquish þ Vcrevice : Thus, the corresponding thermodynamic conditions are guaranteed to be the same, too. In this case, Vdisplacement ¼ p4  Bore2  Stroke and Vsquish ¼ p4  Bore2  hsquish were kept the same. The stroke and squish height hsquish can then be determined from the bore size. The width and depth of the piston-liner crevice were kept the same. This implies that the crevice volume changes with the bore size as, Vcrevice ¼ pðBore  dcrevice Þdcrevice hcrevice : The difference in crevice volume was accounted for by adjusting the piston bowl volume. The piston bowl shape was kept the same except that the radius and depth of bowl were adjusted to match the volume at TDC and BDC (by keeping Vbowl þ Vcrevice ¼ const:). The mesh was generated using the automated mesh generator—Kwickgrid (c.f., Sect. 4.1)—based on the inputs of these hardware parameters. Figure 6.75 shows an example of a mesh generated using Kwickgrid. Controllable parameters include SOI and swirl ratio. Each population invokes two KIVA runs (for the 2,000 and 4,000 rev/min cases, respectively). Each run generates a set of objectives that

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Fig. 6.74 Automated mesh generator. Bezier curvature parameters: 1 Xab; 2 Xba; 3 Xbc; 4 Xcb; 5 Ycb; 6 Ycd

Fig. 6.75 Implementation of baseline design into optimization methodology

include GISFC, NOx and soot emissions. Thus, there are in total six objectives in the present work. This optimization method avoids conflicts in hardware designs from independent optimization for each individual case, and offers a systematic method for engine optimization. All the optimizations were conducted through CONDOR–the high throughput computing system (Thain et al. 2005). In usual practice, the optimization starts from a set of randomly generated designs by default. In other words, the optimization starts from scratch. This implies that the down-scaled optimal design is not utilized. To deal with this problem, one of the randomly generated designs in the first generation was replaced by the down-scaled optimal design (c.f., Fig. 6.75), which means that the evolution was seeded with the optimal design. Figure 6.76 shows a comparison of the early stage optimization results without and with the seed of the down-scaled optimal design. The left plot in Fig. 6.76 shows the distribution of initial citizens (1st generation) in terms of NOx and GISFC for the two optimizations. The blue solid star indicates the down-scaled optimal design. The red hollow star indicates the citizen that is randomly generated in the

6.4 Coupling of Scaling Laws with Computational Optimization

277

Fig. 6.76 Influence of initial design parameters. Left: 1st generation, right: 10th generation citizens with and without seeded 400 cc case from the scaled 450 cc optimum

first optimization (without the seed) but is replaced by the down-scaled optimal design in the second optimization (with the seed), while the other citizens are retained. The right plot in Fig. 6.76 illustrates the Pareto designs from the two optimizations at the 10th generation. Comparing to the optimal design, the random one has higher GISFC and lower NOx emission ranges. This initial difference causes the evident difference in the Pareto front at the 10th GA generation. The Pareto solutions from the optimization starting with random seeds in general have lower NOx emissions, while the optimal solutions from the optimization with an initial optimal design have lower GISFC. Especially, it is seen that there are more designs near the optimal design (blue solid star). It then can be concluded that the initial seeds are important for the evolution of optimization. The resulting citizens have more good features that the initial seeds have, i.e., seeded with a design that has good GISFC will lead to more citizens that have good GISFC. Figure 6.77 shows the final response functions with respect to bore size. The left column is for the 2,000 rev/min case and the right column is for the 4,000 rev/ min case. In general, the shapes of the response functions are similar and a sweet spot can be seen in the response function of GISFC for both cases. The optimal bore parameters are very close to unity, which indicates that the original bore/ stroke ratio is in the range of the optimal design. The response functions of the NOx emissions are similar in shape but different in magnitude for the two cases. A smaller bore benefits NOx reduction in general. For the soot emissions, both the shape and magnitude are quite close and a larger bore is preferred for soot reduction. Figure 6.78 shows multi-parameter response surfaces indicating the effect of bore size on GISFC for the 2,000 rev/min case. The correlation with SOI is seen to be minor. However, the bore size strongly correlates with spray angle. When the bore size is changed, spray targeting needs to be changed to maintain the optimal fuel distribution in the bowl and squish regions. Thus bore size is found to be correlated with the radius of the piston bowl and Xcb (the most influencing parameter for piston bowl shape). When bore size is changed, the absolute radius and depth of the piston bowl are changed accordingly. This affects the flow

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Fig. 6.77 Response functions with respect to bore size. Left: 2,000 rev/min, right: 4,000 rev/min

structures in the piston bowl and, consequently, the fuel and air mixing. Eventually, it has an impact on engine performance. Figure 6.79 shows multi-parameter response surfaces indicating the effect of bore size on soot emissions for the 2,000 rev/min case. Similar to the GISFC results, there is no correlation between SOI and bore size, but there are strong correlations between bore size and spray angle, bowl radius, and Xcb. Figure 6.80 shows the corresponding response surfaces indicating the effect of bore size on GISFC for the 4,000 rev/min case. The observations are similar to those of the 2,000 rev/min case. Compared to the 2,000 rev/min case, GISFC is more sensitive to SOI. For the high speed case, the real time per crank angle is shorter. Therefore, the time for mixing and reaction becomes more crucial, especially for chemical reactions, which mainly depend on the chemical properties of the reactants. Bore size is found to be correlated with the swirl ratio, e.g., small

6.4 Coupling of Scaling Laws with Computational Optimization

Fig. 6.78 Response surfaces of GISFC as a function of bore size: 2,000 rev/min

Fig. 6.79 Response surfaces of soot as a function of bore size: 2,000 rev/min

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Fig. 6.80 Response surfaces of GISFC as a function of bore size: 4,000 rev/min

bores prefer strong swirl and large bores favor low swirl ratio. As discussed in Ge et al. (2009b), spray penetration should be as long as possible but without spray wall impingement for full load cases. Since swirl flow adds a tangential velocity component to the spray and vapor trajectory and increases the relative velocity between the spray and air flows, swirl reduces spray and vapor penetration. When the bore is small, the spray and vapor penetration should be reduced accordingly to ensure a more homogeneous distribution of fuel vapor. Increasing swirl ratio can achieve this aim. Therefore, a high swirl ratio is preferred in this case, and a low swirl is preferred when the bore is large.

6.5 Summary In the present example, a HSDI diesel engine was downsized from 450 to 400 cc using scaling laws based on spray penetration and flame lift-off length similitude. The scaling laws were validated by comparing the two engines’ performance. A consistent optimization method was applied that is able to simultaneously optimize multiple operating conditions without conflict. The following conclusions were drawn from the study:

6.5 Summary

281

• The extended scaling laws work well for a wide range of operating conditions. But it is noted that the range of scaling factor considered in the present work is relatively small. • Initial seeds have significant effects on the final citizens. Good features of the initial seeds will be retained. Thus, seeded with optimal designs from previous optimization will speed up convergence of optimization. • The optimization results show that bore size can be correlated with spray angle, swirl ratio, radius of the piston bowl, and the bowl shape Bezier curvature parameter Xbc (reentrancy). • When the engine speed is high, fuel efficiency depends more on injection timing, because the time for mixing and chemical reaction becomes shorter and is thus more critical.

Chapter 7

Epilogue

We began this book by stating the important role of internal combustion engines in the transportation sector and the fact that this role is projected to not diminish in the next few decades. However, increasing fuel prices and escalating environmental concerns due to vehicle emissions are forcing engineers to look for better solutions to improve existing IC engine designs. Modeling IC engines provides a cost-effective and time-efficient way to study engine performance and pollutant formation. With increasing capacity and improved prediction accuracy of IC engine modeling tools, numerical simulations have become more important in assisting IC engine design and optimization. More than 30 representative papers that focus on computational engine optimization were reviewed to describe the recent progress in the relevant research areas in Chap. 1. In Chap. 2, the performance of non-evolutionary optimization, evolutionary optimization, single-objective and multi-objective optimization methods were compared with several particularly designed mathematical test problems. It was concluded that multi-objective evolutionary optimization methods are more suitable for real-world IC engine design problems, which are multi-objective optimization problems in nature. Another focus of Chap. 2 was an overview of engine computational fluid dynamics (CFD) modeling methods. A detailed review of each sophisticated model is beyond the scope of this book. Instead, the framework of engine CFD modeling and the basic concepts of the governing equations, physical models, and numerical methods were covered. In addition, the applicable ranges, advantages and disadvantages of existing physical models were also briefly discussed. The last part of Chap. 2, describes the fundamental ideas of several regression methods. The component selection and smoothing operator (COSSO) method was discussed in more detail because it was the main regression analysis tool used in this book. How to improve the efficiency of engine CFD modeling tools remains one of the main challenges in computational optimization of IC engines. This issue was tackled in Chap. 3 with methods that fall into four categories. First, methods were presented for reducing mesh- and timestep-dependency for spray modeling, which enables engine simulations using coarser meshes and larger timesteps while Y. Shi et al., Computational Optimization of Internal Combustion Engines, DOI: 10.1007/978-0-85729-619-1_7, Ó Springer-Verlag London Limited 2011

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adequately resolving spatial and temporal information of the modeling without using finer meshes and smaller timesteps. Second, reducing the size of reaction mechanisms has been an active subject in reacting flow simulations. An automatic approach for mechanism reduction that is based on the directed relation graph with error propagation (DRGEP) and principal component analysis (PCA) methods was proposed. It was shown that reaction mechanisms of significantly reduced sizes are obtainable by performing a two-stage reduction approach to the detailed reaction mechanisms while maintaining their major characteristics. Third, multi-grid techniques in reacting flow simulations were discussed. The idea is to approximate the solution over the entire computational domain by grouping thermodynamically-similar computational cells to reduce the calling frequency of the CFD solver to the chemistry solver. An adaptive multi-grid chemistry (AMC) solver for engine simulations was developed, and it showed significant speed-up in both homogeneous charge compression ignition (HCCI) and direct-injection (DI) engine simulations. The fourth approach is an extension to the mechanism reduction method, which dynamically applies efficient mechanism reduction methods, such as the DRGEP method, on-the-fly to engine CFD simulation so that each computational cell solves a small reaction mechanism at every timestep. It was demonstrated that cumulative benefits are achievable by combining all these approaches to further speed-up engine simulations. To extend the comparative study of optimization methods conducted in Chap. 2 with mathematical test functions, three widely used multi-objective genetic algorithms were compared, namely, micro-GA, non-dominated sorting genetic algorithm II (NSGA II), and adaptive range multi-objective genetic algorithm (ARMOGA) for a real-world engine optimization problem in Chap. 4. To assess their performance, four quantities were defined to quantify the optimality and diversity of the optimization methods. It was concluded that NSGA II performed the best with a large population size, and it thus was extensively used in the case studies of this book. Then, the NSGA II with different niching techniques was further investigated and the convergence and diversity metrics were proposed to assess its performance. A dynamic learning strategy was proposed based on the assessment of regression methods for an engine optimization problem. Engine-size scaling is an efficient way to expedite prototype engine development and optimization by utilizing existing design information of either larger or smaller-scale engines. In Chap. 5, such size-scaling relationship between IC engines of different dimensions is discussed. The scaling laws were proposed based on the spray liquid penetration and flame lift-off lengths in diesel engines. The scaling laws were then applied in a light-duty and a heavy-duty production diesel engines. The engine simulation results illustrated that such scaling laws can indeed lead to similar performance and emissions between the two engines. To demonstrate the applicability of the engine optimization tools that have been developed, Chap. 6 summarizes seven cases that include optimization studies of spark-ignition (SI) and compression-ignition (CI) engines, light-duty and heavyduty engines, and engines fueled with gasoline and diesel. The use of CFD simulations was first demonstrated with simple combustion models for engine

7 Epilogue

285

optimization within conventional combustion regimes. Then, a heavy-duty CI engine fueled with diesel and gasoline-like fuels was optimized using advanced combustion models with efficient chemistry solvers. Strategies for simultaneous optimization of multiple engine operating conditions were discussed. Inspired by the engine size-scaling study in Chap. 5, engine size-scaling laws were also employed in an engine optimization study and the results showed how this methodology can be used for downsizing development of a high-speed directinjection (HSDI) diesel engine. Finally, it is noted that engine design and optimization is a sophisticated process that involves the optimization of different engine components and integrated system level optimization. The present book focuses on the in-cylinder combustion strategy optimization only. But we believe that the optimization methodologies and numerical models described throughout the entire book are generally applicable to other related areas.

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Index

A Acetylene, 46, 154, 174 see soot precursor, 44–46, 154 Adaptive Multi-grid Chemistry (AMC), 14, 94–95, 99–102, 104, 116, 122–123, 233, 235–236, 263–264, 266, 284 Arbitrary Lagrangian–Eulerian (ALE), 68 Arc, 41 Arrhenius equation, 29, 42, 45, 80 Atomization, 46, 49, 60, 180, 187–188

B Bezier, 126–128, 192, 219–220, 226–227, 233, 276, 281 Bio-diesel, 79 Boiling temperature, 60 Bottom Dead Center (BDC), 114 Boundary condition, 66 Box-Cox transformation, 139 Bray-Moss-Libby (BML), 40 Breakdown, 41 Breakup length, 50, 53–54 Breakup time, 50, 53–54, 150 Broyden–Fletcher–Goldfarb–Shanno (BFGS), 15

C Carbon monoxide (CO), 5, 8, 42, 88, 102, 104–109, 189 Caterpillar (CAT), 88, 126, 148, 153, 189 Characteristic Time Combustion (CTC) model, 22, 38, 127–128, 177, 189, 199, 260–261, 263 CHEMKIN, 38, 80, 85, 95, 154, 222, 261, 264 Chi-squared distribution, 48–49

Chrysler, 182 Coalescence, 57 Coherent flame model, 40 Cold start, 6 Collision, 56–58, 60, 70, 76–79, 101, 219 Compression ratio (CR), 5, 88, 126–127, 148, 154, 158, 161, 168–169, 183, 190–191, 211, 220, 255, 269, 272, 275 Compression-Ignition (CI), 2, 14, 234, 284 Computational Fluid Dynamics (CFD), 3, 27 Computational Singular Perturbation (CSP), 79 Conditional Moment Closure (CMC), 41 Continuous Droplet Model (CDM), 30 Continuous Formulation Model (CFM), 30 Contraction coefficient, 47 Controlled Random Search (CRS), 9 CONVERGE, 70 Convergence metric, 134 Courant–Friedrichs–Lewy (CFL), 69 Crevice, 63–64, 168, 232, 244, 249, 275 Crowding distance, 24–25, 132–133

D Depth First Search (DFS), 81 Design of Experiments (DoE), 139, 210 Detroit Diesel Company (DDC), 210 Diesel Particulate Filters (DPF), vi Diffusion combustion, 14, 39, 189 also see diffusion flame, 14, 39, 189 Direct Injection (DI), 2, 5, 7, 9, 71, 79, 149, 178, 181–182, 218, 234, 284 High Speed Direct Injection (HSDI), 9, 14, 71, 148, 218, 232, 272, 280, 285 Direct Numerical Simulation (DNS), 32

305

306

D (cont.) Directed Relation Graph (DRG), 80–81 Directed Relation Graph with Error Propagation (DRGEP), 80–81 Discharge coefficient, 46–47, 49 Discrete Particle Ignition Kernel (DPIK) model, 41–42, 180 see ignition, 41 Dispersion, 50–51, 54 Diversity metric, 135 Downsizing, 148, 272 Drag, 55 Droplet deformation, 55 Droplet size, 46, 48–49 Dual fuel, vii, 258 Dynamic Adaptive Chemistry (DAC), 105 Extended Dynamic Adaptive Chemistry (EDAC), 105

E Emissions see Nox emission model, 43 see Soot model, 44 Engine combustion phasing, 84 Engine Research Center (ERC), 42–43, 46, 95, 101, 114–117, 123–124, 127, 179, 210 Environmental Protection Agency (EPA), 1 Equilibrium constant, 29 equivalence ratio, 7, 10, 88, 94, 96–97, 104, 108–109, 113, 117, 126, 162, 169, 172, 176, 190–191, 205, 223, 235, 270 ESTECO, 15, 27, 211 Evaporation Model, 58 Exhaust Gas Recirculation (EGR), vi, 5, 9–10, 101–102, 104, 112, 117, 126, 154, 162, 169, 176, 190–191, 211, 220, 234–238, 268, 273 Exhaust Valve Opening (EVO), 5, 210 Extended Dynamic Adaptive Chemistry (EDAC), 105 see Dynamic Adaptive Chemistry (DAC), 105

F Federal Test Procedure (FTP), 88 Fiat, 102–105 FIRE, 70 Finite volume, 68, 179 Fitness value, 25 Flame kernel, 41

Index Flame lift-off length, 147, 150–152, 175 Flame propagation, 41–42 Flame surface density model, 40, 180 Flamelet, 39 Eulerian particle flamelet model (EPFM), 40 Representative Interactive Flamelet (RIF), 40 FLUENT, 70 FORTé, 70 Frossling correlation, 58 Fuel consumption, 192 see Gross indicated specific fuel consumption, 192

G G-equation, 40, 42, 70 Gas jet model, 77 Gasoline Direct Injection (GDI), 2, 5 Genetic Algorithms (GA), 10–12, 20–22, 24, 26–27, 178, 181, 210, 217, 221, 232 Adaptive Range Multi-objective Genetic Algorithm (ARMOGA), 11, 22, 25, 125, 128 Multi-objective genetic algorithm (MOGA), 22 Non-dominated Sorting Genetic Algorithm (NSGA), 11, 21, 24, 26, 125 Single-Objective Genetic Algorithm (SOGA), 9, 20 Micro-Genetic Algorithm (micro-GA, l-GA), 11, 20, 125 Glow, 41 GM, 102–105 Gradient-based method, 8 Gross Indicated Specific Fuel Consumption (GISFC), 192 see Fuel Consumption, 192 Grouping, 95–97 Growth rate, 50–52

H Heat Release Rate (HRR), 106 n-Heptane, 42, 46, 79 High Throughput Computing (HTC), 219 Homogeneous Charge Compression Ignition (HCCI), vii, 2, 10, 13, 75, 79, 84–88, 94–96, 99–101, 104–109, 113–117, 162–165, 234, 284 Hydrocarbons (HC), 63, 102 see Unburned Hydrocarbons (UHC), 63, 102

Index I Ignition, 41 discrete particle ignition kernel model (DPIK), 41, 180 Shell auto-ignition model (Shell model), 42 Ignition delay, 10, 163 Indicated Mean Effective Pressure (IMEP), 88, 101, 104, 148, 154, 162, 169, 220, 235, 261, 264–265, 267, 269 Indicated Specific Fuel Consumption (ISFC), 148, 182, 185, 187–188 Gross Indicated Specific Fuel Consumption (GISFC), 125, 129, 139–144, 192, 194–200, 206–207, 209, 212–213, 215–218, 222–231, 236–237, 239, 243, 248–249, 261, 264–269, 271, 273, 276–280 Iso-octane, 79, 180 Intake Valve Closing (IVC), 10, 88 Internal Combustion Engines, 1, 2, 14 Intrinsic Low-Dimensional Manifolds (ILDM), 79

K k-e model, 33, 35, 37 RNG k-e model, 37, 39 K-nearest neighbors (KN), 13, 72, 125 Kelvin-Helmholtz (KH) model, 51 Knock, 42 Kriging (KR), 13, 72, 125 Kwickgrid, 126, 191, 193

L Lagrangian-Drop Eulerian-Fluid (LDEF), 75 Large Eddy Simulation (LES), 33–34, 38, 40, 70 Latin Hypercube Sampling (LHS), 8 Law-of-the-wall, 66 Lawrence Livermore National Laboratory (LLNL), 114–116, 122–124, 236 Ligament diameter, 50 Linearized Instability Sheet Atomization (LISA) model, 49–50, 180 Locally Homogeneous Flow (LHF), 30

M Maximum merit function (MMF) see merit function Mean Deviation of the Distance between Neighbor Pareto Solutions (MDDNPS), 129–132

307 Mean Distance between Extreme Pareto Solutions (MDEPS), 129–132 Mean Distance to the Pareto Front (MDPF), 129–132 Mercedes Benz, 178 Mercury Marine, 182 Merit Function, 11, 20–22, 181, 183–184, 189 Maximum merit function (MMF), 184 Method of Characteristics (MOC), 179 Methyl Butanoate (MB), 79 Methyl decanoate (MD), 79, 83, 87, 89 Misfire, 236, 240 ModeFRONTIER, 11, 16, 21, 27, 73, 128, 144, 211 Modified Bessel function, 51–52 Modulated Kinetics (MK), 13–14, 234, 255, 269 Monte-Carlo, 34, 68 Multi-component, 6, 60 Multi-Objective Evolutionary Algorithms (MOEA), 24 Multi-step phenomenological soot model see soot Multi-zone, 13, 94, 96, 99 Multiple injection, 9–10

N Nagle and Strickland-Constable, 45 NEDC, 264 Negative Valve Overlap (NVO), 258 Neural Networks (NN), 13, 72, 125, 138, 140, 144–145 Non-differentiable Interactive Multi-objective BUndle-based optimization System (NIMBUS), 9 Non-Methane Hydrocarbons (NMHC), 239–240, 248–249 Non-Parametric Regression (NPR), 71, 210 non-premixed combustion, 107, 117 Niche, 25–26 Niching technique, 125, 131, 135, 284 Nitrogen dioxide (NO2), 43, 154 Nitrogen monoxide (NO), 3, 5, 10, 43–44, 107, 109, 112, 114, 154 Nitrogen Oxide (NOx), 3–11, 43–44, 71, 101, 104–109, 114–115, 118–125, 128–129, 176, 182, 185–218, 222–230, 233–242, 245–251, 255–257, 261, 264–277 Nozzle flow model, 46–48 Number of Pareto Solutions (NPS), 129–130 Nukiyama-Tanasawa distribution, 49 Nusselt number, 59

308 O n-Octane, 79 Ohnesorge number, 52 OpenFOAM, 70 Ordinary Differential Equations (ODE), 80, 95, 106–107

P Pareto Pareto front, 19, 21–26, 128–136, 193–195, 212, 222, 236, 269, 277 Pareto design, 198, 261, 269–270, 277 Partially Premixed Combustion (PPC), 2, 14, 40, 234, 255, 259 Particulate Matter (PM), 1, 148, 239 Particle Swarm Optimization (PSO), 9, 11 Path Flux Analysis (PFA), 80–84, 106 Peak Pressure Rise Rate (PPRR), 236–242, 245, 247–257 Peclet number, 59 Perfectly Stirred Reactor (PSR), 38 Polycyclic Aromatic Hydrocarbons (PAH), 46 Port Fuel Injection (PFI), 6, 60 Prandtl number, 36–37, 59 Premixed Charge Compression Ignition (PCCI), 10, 13, 102–105, 255 Premixed combustion, 194, 233, 242, 245, 252, 255, 258 Primary breakup, 48–51 Primary Reference Fuel (PRF), 79, 101, 116, 236, 255 Principal Component Analysis (PCA), 79–80, 85–93, 284 Probability Density Function (PDF), 34, 40 Progress equivalence ratio, 96–97, 108–113

Q Quasi-Second-Order Upwind (QSOU), 68 Quasi-Steady-State (QSS), 80, 82

R R-value-based breadth-first search (RBFS), 82 Radial Basis Functions (RBF) see Regression analysis Radius-of-Influence (ROI) model, 57–58, 219 Rayleigh-Taylor (RT) model, 51–54, 70, 79, 101, 128 Ranz-Marshall correlation, 59 Reaction rate, 29, 38–40, 79–80, 107 Reaction mechanism reduction, 13–14, 79–84

Index Reactivity Controlled Compression Ignition (RCCI), vii Regression analysis COmponent Selection and Smoothing Operator (COSSO) method, 12, 71–73, 189, 195–196, 210, 218, 222, 283 k-nearest method, 13, 72–73, 125, 133, 138, 144–145, 211 Kriging method, 8, 13, 72–73, 125, 138, 144–145 Neural networks method, 13, 72–73, 125, 138, 144 Radial Basis functions method, 13, 72–73, 125, 138–141, 144–145 Remapping, 95, 98–99 Representative Interactive Flamelet (RIF) see flamelet Response Surface Method (RSM), 7–8, 12–13, 72, 138–140, 144, 195–200, 211–219, 227–230, 266–267, 277–278 Reynolds Stress Model (RSM), 34 Reynolds Averaged Numerical Simulation (RANS), 33–34, 38 RNG k-e model see k-e model Rosin-Rammler distribution, 149, 180

S Sauter mean diameter (SMD), 185 Sauter Mean Radius (SMR), 48 Scaling law, 147–177, 269, 271–274, 280–281, 284–285 Schmidt number, 37, 58 Secondary breakup, 51–54 Selective Catalytic Reduction (SCR), vi Semi-Implicit Method for Pressure-Linked Equations (SIMPLE), 68 SENKIN, 85 Sequential Quadratic Programming (SQP), 7 Sharing function, 25 Shell auto-ignition model (Shell model) see ignition Sherwood number, 58 Single-cylinder research engine, 153, 178, 182 Smoothing spline analysis of variance (SS-ANOVA), 71–72

Index Soot soot emission, 3, 11, 71, 105, 115, 123, 125, 139, 152–156, 163, 165, 173–176, 189–193, 196–198, 201–217, 222–234, 237, 248, 252, 261, 264–267, 271–278 soot formation, 10, 44–45, 150, 166, 175–176, 189, 204, 230, 244 soot precursor, 44–46, 101, 128, 154, 174–175 two-step soot model, 44–46, 101, 154 multi-step phenomenological soot model, 46 Spalding mass transfer number, 58 Spark Ignition (SI), 2, 5, 41, 177, 234, 284 spark-ignition direct injection (SIDI), 5 Spray angle, 6, 46, 103, 137, 161, 168, 184, 191–192, 195–199, 201–203, 205–206, 209–210, 212–213, 215–218, 220, 225, 229–230, 241–242, 250–251, 260–261, 275, 277–278, 281 Spray equation, 32, 68, 75 Spray tip penetration, 77–78, 147–152, 159, 164–165, 169, 175, 178, 203, 207–208, 215, 223–226, 229, 234, 249, 270, 272, 280, 284 Squish flow, 167, 170, 203 Star-CD, 70 Stratification, 5–6, 102, 178 Subgrid-scale (SGS), 33, 70 Surface-to-volume, 64, 163 Swirl, 5–6, 10, 49–50, 68, 149, 151–153, 159, 176, 178, 180, 182, 195–200, 204, 206–209, 225–226, 229–230, 236, 244, 247, 250, 254–258, 270, 280 swirl ratio, 9, 11–12, 14, 125–128, 137, 148, 151–154, 159, 161, 168, 176, 189–199, 202–211, 220, 226, 229–230, 241–246, 249–251, 254–255, 258–261, 264, 270–275, 278–281

T Taylor Analogy Breakup (TAB), 55, 180 Taylor number, 52

309 Top Dead Center (TDC), 6, 149, 156–157, 161, 168–173, 202, 252, 255, 275 Tumble flow, 5–6, 10, 149, 159–160, 178, 180, 185, 227, 230–232 Turbulence, 4, 6, 11, 30, 32–42, 54, 67, 95, 148, 151, 156, 158, 162–166, 171, 175–176 Turbulence correlation time, 54 Turbulent persistence time, 55 Two-step soot model see soot

U Unburned Hydrocarbons (UHC), 63, 102, 178–179, 187, 235 Hydrocarbons (HC), 42, 63, 85, 87–88, 96, 102, 107–110, 178–179, 182, 186–187, 235

V Variable Valve Timings (VVT), 5 Vapor pressure, 47 VECTIS, 70 Vena contracta, 47–48 Viscosity, 35, 38, 50–51, 53, 65

W Wall film, 60–62 Wall function, 67, 70 Wall heat transfer, 3, 67, 102, 148, 156, 158, 175–176, 178, 182, 185–187 Wall impingement, 60–63, 101, 128, 149, 178, 187, 191, 203, 205, 207–208, 215–216, 224, 229, 234, 270, 280 Wavelength, 51–53, 100 Wave number, 32, 50 Wave stability theory, 49–53 Weber number, 51, 52, 56, 60 Well stirred reactor (WSR), 95

Z Zel’dovich mechanism, 43, 128