Mineral Wool
i
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ii
Mineral Wool Production and properties
B. Širok, B. Blagojevic and P. Bullen
Cambridge International Science Publishing Limited in association with Woodhead Publishing Limited CRC Press Boca Raton Boston New York Washington, DC
WOODHEAD
PUBLISHING LIMITED
Cambridge, England
iii
Published by Cambridge International Science Publishing Limited in association with Woodhead Publishing Limited Cambridge International Science Publishing Limited, 7 Meadow Walk, Great Abington, Cambridge CB21 6AZ, England www.cisp-publishing.com Woodhead Publishing Limited, Abington Hall, Granta Park, Great Abington, Cambridge CB21 6AH, England www.woodheadpublishing.com Published in North America by CRC Press LLC, 6000 Broken Sound Parkway, NW, Suite 300, Boca Raton, FL 33487, USA First published 2008, Cambridge International Science Publishing Ltd, Woodhead Publishing Limited and CRC Press LLC © 2008, Cambridge International Science Publishing Limited The authors have asserted their moral rights. This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. Reasonable efforts have been made to publish reliable data and information, but the authors and the publishers cannot assume responsibility for the validity of all materials. Neither the authors nor the publishers, nor anyone else associated with this publication, shall be liable for any loss, damage or liability directly or indirectly caused or alleged to be caused by this book. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming and recording, or by any information storage or retrieval system, without permission in writing from Cambridge International Science Publishing Limited and Woodhead Publishing Limited. The consent of Cambridge International Science Publishing Limited and Woodhead Publishing Limited does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from either Cambridge International Science Publishing Limited or Woodhead Publishing Limited for such copying. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. Library of Congress Cataloging in Publication Data A catalog record for this book is available from the Library of Congress. Woodhead Publishing ISBN 978-1-84569-406-7 (book) Woodhead Publishing ISBN 978-1-84569-445-6 (e-book) CRC Press ISBN 978-1-4200-7045-3 CRC Press order number: WP7045 The publishers’ policy is to use permanent paper from mills that operate a sustainable forestry policy, and which has been manufactured from pulp which is processed using acidfree and elementary chlorine-free practices. Furthermore, the publishers ensure that the text paper and cover board used have met acceptable environmental accreditation standards. Typeset by Thymus Solutions Ltd, Mumbai, India Printed by TJ International Limited, Padstow, Cornwall, England
iv
Contents
Contents
1.
PREFACE ...............................................................................ix INTRODUCTION ..................................................................1
2.
MELTING THE RAW MATERIALS ...................................8
2.1
Cupola furnace operation .............................................................................. 8
2.1.1
2.2 2.3
Processes and chemical reactions in the cupola furnace ...................................... 10
Influence of underdraft on cupola furnace operation ................................... 12 Measuring temperature and concentrations in the cupola furnace .............. 15
3.
MULTIPLE REGRESSION ............................................... 19
3.1
Hypothesis testing in multiple linear regression .......................................... 21
3.1.1 3.1.2 3.1.3
Coefficient of determination .................................................................................. 22 Other linear and non-linear models ..................................................................... 23 Computer printout ................................................................................................ 23
4.
PHYSICAL CHARACTERISTICS OF MINERAL WOOL MELTS .................................................................................. 28
4.1
Density ......................................................................................................... 29
4.1.1
4.2 4.2.1 4.2.2 4.3 4.3.1 4.3.2
4.4
Density of silicate melts ........................................................................................ 30
Viscosity ....................................................................................................... 32 Viscosity of silicate melts ....................................................................................... 34 Methods for measuring viscosity of silicate melts ................................................. 36 Surface tension ...................................................................................................... 40 Surface tension of silicate melts ............................................................................ 41 Methods for measuring surface tension of silicate melts ..................................... 41
Computing algorithm for calculation of density, viscosity and surface tension of mineral wool melts ....................................................................... 45
5.
DIMENSIONAL ANALYSIS ............................................. 48
5.1
Foundations of dimensional analysis ........................................................... 48
5.1.1
Full set of dimensionless numbers ........................................................................ 50
6.
FIBERISATION PROCESS ............................................... 54
6.1
Dimensional analysis of the fiberisation process on a double-wheel spinning machine ......................................................................................... 55
6.1.1 6.1.2
6.2 6.3 6.3.1
Experimental results ............................................................................................. 59 Statistical analysis of experimental results ............................................................ 60
Simulation of chemical composition’s influence on fibre thickness ............. 61 Regression model of mineral wool fibres on a four-wheel spinning machine ........................................................................................................ 65 Regression model of fibre formation in a four-wheel spinning machine ............... 68 v
Contents 6.3.2 6.3.3
6.4 6.4.1 6.4.2
Experimental results ............................................................................................. 69 Statistical analysis of experimental results ............................................................ 70
Cooling of glass fibres ................................................................................. 71 Trajectories of mineral wool fibres ....................................................................... 74 Numerical analysis ............................................................................................... 77
7.
VISUALISATION METHOD IN REAL PRODUCTION PROCESSES ........................................... 81
7.1
Monitoring the production process ............................................................. 83
7.1.1 7.1.2 7.1.3 7.1.4
7.2 7.2.1 7.2.2 7.2.2.1 7.2.2.2 7.2.2.3 7.2.2.4
Identifying the jet image ........................................................................................ 85 Detection of boundaries ........................................................................................ 86 Gradients at jet boundaries .................................................................................. 88 Gradient establishment ......................................................................................... 89
Reconstruction of the jet and its trajectory .................................................. 91 Observation of jet centre line between wheels ....................................................... 95 Experimental results ............................................................................................. 96 Centre line ............................................................................................................. 97 Fluctuation and centre line .................................................................................... 97 Fluctuation of grey levels in the selected field ....................................................... 98 Evaluation of mass flow of melt ............................................................................ 99
8.
APPLYING THE VISUALISATION METHOD TO MEASURING THE THICKNESS OF MINERAL WOOL FIBRES .................................................................. 106
8.1
Experimental results of fibre diameter on a double-wheel spinning machine ...................................................................................................... 110
9.
INFLUENCE OF MELT FILM TEMPERATURE ON THE FIBRE DIAMETER DISTRIBUTION IN MINERAL WOOL PRODUCED BY A DOUBLE-WHEEL SPINNING MACHINE ....................113
9.1
Thermovision of the spinning wheel melt film ............................................ 114
9.1.1
Experimental results ........................................................................................... 116
10.
FORMATION OF THE PRIMARY LAYER .................. 121
10.1
Influence of blow away velocity field on the primary layer fibre structure in the mineral wool production process ...................................... 124
10.1.1 10.1.2
10.2 10.2.1 10.2.2 10.2.3
Velocity field measurements on the nozzles of a four-wheel spinning machine ............................................................................................................... 125 Velocity field structure in the transition region through the perforated mesh of the collection chamber ........................................................................... 131
Visualisation method for measuring the primary layer ................................ 133 Regression model of mineral wool primary layer homogeneity .......................... 137 Experimental results ........................................................................................... 138 Statistical analysis of experimental results .......................................................... 138
vi
Contents
11.
NUMERICAL ANALYSIS OF FLOW PROPERTIES IN THE COLLECTION CHAMBER ............................. 141
11.1
Numerical analysis ..................................................................................... 142
11.1.1 11.1.2
11.2 11.3 11.4
Simulation set-up ................................................................................................ 146 Experimental determination of boundary conditions .......................................... 147
Numerical results of flow properties in the operating collection chamber ...................................................................................................... 147 Numerical simulation of modified geometry of the collection chamber .... 150 Local distribution and spectral analysis of the primary layer structure ...... 152
12.
QUALITY OF THE PRIMARY LAYER AND ITS INFLUENCE ON THE FINAL PRODUCT .................... 157
12.1
Experiments ................................................................................................ 158
12.1.1
12.2 12.2.1
Measurement of the specific density of the final product ..................................... 158
Regression model of the specific density of the final product ................... 160 Statistical analysis of experimental results .......................................................... 160
13.
CURING CHAMBER ....................................................... 163
13.1
Measurements of mineral wool layer temperature characteristics along the curing chamber ........................................................................... 167 Measurements of aerodynamic resistive characteristics of mineral wool layer ................................................................................................... 170 Diagnostics of local homogeneities in the mineral wool layer .................... 173
13.2 13.3
REFERENCES ................................................................................179 INDEX ..........................................................................................184
vii
Contents
viii
Preface
Preface This book is one of the small number of publications in the field of mineral wool production. The authors concentrate on the monitoring of the mineral wool production process and on the experimental modelling of key production phases. A major portion of the book draws on the authors’ past research work. It shows original experimental–measuring methods developed on real processes with all the limitations and specific characteristics of mineral wool production taken into account. This alone ensures the applicability of the methods to similar production lines or broadly similar production processes, such as the production of glass wool, etc. Some of the material in this book has already been published in scientific papers and as patents and patent applications. We logically combined the contents into book in accordance with the course of the production process. The majority of the experimental methods have been tested at the Termo Company in Slovenia which enabled graduate and postgraduate research activities within the framework of mineral wool production process diagnostics. Furthermore, the book presents the research results in relation to issues dealt with by general experimental methods, such as dimensionless analysis, multiregression models and computer-aided visualisation. For this reason, the book is suitable for engineers, researchers and for graduate and postgraduate students who wish to broaden their knowledge of experimental methods. The structure of the book is based on the size and scale of the observed technological process and, consequently, on the use of integral and differential analysis methods. The initial part of the book describes the technological process of mineral wool production. It is followed by the presentation of the physical characteristics of the melt and theoretical bases of multiregression and dimensionless theory which represents the basic tool for the formation of phenomenological models of mineral wool fiberisation. This is followed by the introduction of the fibre cooling model in the blow-away flow and the influence of temperature in the melt film (on the rotating centrifuge wheels) on the thickness of forming fibres. ix
Preface
The second part of the book is predominantly based on the use of computer-aided visualisation: tools for the diagnostics of fibre and primary layer formation. Special attention is given to the study of the aerodynamic characteristics of the airflow which significantly influences the quality of the final product. In conclusion, the authors describe the polymerisation process in the curing chamber and present the procedures for measuring the temperature profiles along the curing chamber and for estimating the homogeneities of mineral wool density in the final product. The authors wish to thank their colleagues at LVTS – Faculty of Mechanical Engineering, University in Ljubljana and their colleagues at the Thermo Company in Slovenia who with their devoted work greatly contributed to the publication of this book. `
B. Širok, B. Blagojevic and P. Bullen Ljubljana
`
B. Širok and B. Blagojevic – University of Ljubljana, Slovenia P. Bullen – University of Hertfordshire, Hatfield, UK
x
Introduction
1 INTRODUCTION The relation to the energy sources, their use and the burdening of environment with by-products are undergoing a significant change. With the new perspective a change of attitude towards the efficiency of all energy conversion processes in production and consumption has taken place. A large part of energy conversions is tightly connected with heat transfer, where the process efficiency is influenced by introducing insulation materials. The use and development of the latter has significantly increased, and the amount of those which are based on classical technologies with modified technological procedures is also increasing. The technology of mineral wool also belongs to such procedures. It is composed of particular complex technological subsystems. Mineral wool is a general name for many inorganic insulation materials made of fibres. It is usually divided into different subgroups depending on raw materials it is made of, such as rock wool, glass wool and slag wool. There are several methods for mineral wool fibre production with a wide variation in the quality and quantity of the final product, Ohberg [1,2]. The main process areas which are also shown in Fig. 1.1 are: z supplying raw materials and energy sources, z melting, z fiberisation and collecting, z primary layer formation, z finishing (binder application, curing, cutting, packing, etc.) Supplying raw materials and energy sources The most frequently used raw materials for mineral wool production are diabase, dolomite, granite, basalt, limestone, etc. Because of its amorphous structure, mineral wool has excellent sound and 1
2
binder
air
2
1
oxygen
raw materials + energy sources (cox)
3
air 4
5 6
7
Fig. 1.1. Production process of mineral wool.
blast air
to abolement plant
8
air
9
10
gas
11
Mineral Wool
Introduction
thermal insulation properties. The energy source is coke. Raw materials and coke are charged into a silo from which they are weighted on a conveyor belt that transports them to the top of the cupola furnace. 1. Melting and fiberisation sources: Pos. 1 Cupola Pos. 2 Spinning machine – centrifuge 2. Primary layer formation: Pos. 3 Collection chamber Pos. 4 Conveyor belt Pos. 5 Primary balance 3. Mineral wool layer formation: Pos. 6 Pendulum system – transversal layer arrangement Pos. 7 Superficial and loading balance Pos. 8 Squeezer Pos. 9 Curing chamber 4. Finishing: Pos.10 Cooling zone Pos.11 Suction from the cooling zone Melting In the cupola (Fig. 1.1 – pos.1), coke is combusted releasing heat that is utilised for heating and melting raw materials. Most rock melts have temperatures in the range from 1300–1600°C. The cupola furnace is a system for melting magma rocks and supplements. In the cupola furnace, several chemical and thermodynamic processes take place. Coke is most frequently used as an energy source; however, electric and gas furnaces are also used for melting rocks. Melting furnaces serve not only for melting rocks, but also for reaching the homogeneity of melts in the temperature range 1400–1600°C. In the melting process it is intended to acquire the desired chemical substances which influence the material characteristics, such as viscosity and surface tension of the melt. Fiberisation – Centrifuge The most commonly used mineral wool production process is the fiberisation process (Fig. 1.2) of molten rock on fast rotating spinning machines (wheels) (Fig. 1.1 – pos.2) where the melt is spun into fibres. This machine uses several cylindrical rotors onto 3
Mineral Wool
Fig. 1.2. Fiberisation process of mineral wool.
which the melt is directed and which fiberise the melt with or without the help of stripping air. The fibres are mixed with an organic binder and collected on the conveyor belt as wool. The literature [1] also provides the description of other methods which can be used for fiberisation. These methods are V-shaped blowing nozzle, the Downey method and the Sillan process. The V-shaped blowing nozzle, giving a high percentage of unfiberised material and the fibre diameter distribution, was very broad. This led to the development of the Downey rotor which provides a controlled distribution of the melt. The most commonly used mineral wool production process is the fiberisation process of molten rock on fast rotating spinning wheels (Trdic et al. [3], Angwafo et al. [4] and Westerlund et al. [5]). Molten rock enters through a siphon neck in a homogenisation reservoir. Over the weir and the directing channel, the molten rock falls under gravity onto the rotating wheel of the spinning machine. With blow-in air led coaxially over the wheels, the fibres are transported away from the spinning machine and are thrown into the collection chamber where they solidify into fibres which have the diameter of about 5 mm and length of approx. 10 mm. The formation mechanism, as mentioned in reference [5], was
ˆ
4
Introduction
described by Eisenklam [6]. Fibres are formed from the molten film on spinning wheels. The forming and motion of fibres depend on inertial, viscous and surface tension forces, whereas the solidification process depends on thermodynamic and mass properties of the melt. The quality of the final product depends on the structure of fibres and on the proportion of solidified shots in the mineral wool. The fibre structure is characterised by its thickness (diameter), its length, and the variation of both respective quantities. Material that did not transform into fibres remains in the form of solidified shots which arise from an incomplete fiberisation process [3,4]. Primary layer formation – collection chamber The fibres formed on the centrifuge are transported by the air flow of the nozzle outlet into the interior of the collection chamber (Fig. 1.1 – pos.3), where the primary layer of mineral wool is being formed on the perforated conveyor belt. A homogenous turbulence field forms a thin layer of intertwined fibres (Fig. 1.3) which are damped with phenol formaldehyde pitch. As the dispersed drop flow, the pitch is added into the outlet flow in the area of fibre formation. The geometrical structure of intertwined fibres and the homogenous binder distribution on the fibre surface significantly influence the quality of the final product. Conveyor belt and primary balance The primary layer leaves the collection chamber and passes over the intermediate belt (Fig. 1.1 – pos.4) onto the primary balance (Fig. 1.1 – pos.5) which measures the mass flow of mineral wool. Apart from performing this measurement, the basic function of the primary balance is to diagnose the transversal distribution of mineral
Fig. 1.3. Primary layer formation in the collection chamber. 5
Mineral Wool
wool surface density in the primary layer. The balance is designed to enable the combination of four independent simultaneously measured values of gravity force of the primary layer and to detect the density fluctuations of mineral wool in the primary layer [7,75]. Pendulum The function of the pendulum (Fig. 1.1 – pos. 6) is to periodically fold and load the primary layer into a stack of mineral wool, which moves in the process direction. The pendulum oscillation frequency, the velocity of the primary layer and conveyor belt velocity (Fig. 1.1 – pos.7) form a multilayered structure of mineral wool which then enters the area of the process balance where the measurements of mineral wool mass are performed corresponding with the surface density of the final product. Squeezer The squeezer (Fig. 1.1 – pos. 8) reduces the primary layer thickness at the curing chamber inlet (Fig. 1.1 – pos. 9). When the primary layer passes through the squeezer, the reduction of the layer thickness causes mineral wool to compress and to change its specific density. The redistribution of mineral wool in the primary layer also causes the re-formation – re-direction of fibres in the layer and changes the insulation characteristics of the final product. Curing chamber In the curing chamber, binder polymerisation takes place on the surface of mineral wool fibres. The polymerisation process, which reflects on the macroscale as hardening–lacing of the mineral wool, proceeds at approximately 240–280 oC. The heating process of the mineral wool layer is performed convectively by blowing smoke gases through the layer with smoke gas. The holding time of mineral wool in the area above the activation temperature of the polymerisation has to be sufficiently long to enable the execution of the whole chemical process. The cooling zone (Fig. 1.1 – pos. 10) is located at the outlet of the curing chamber. It serves to cool the mineral wool layer before the layer enters the area of the line, where the mineral wool is cut into dimensions of the final product.
6
Introduction
This book aims to tackle the most important segments of the technological process of mineral wool production. It presents the physical and chemical characteristics of mineral wool fiberisation and primary layer formation, and describes the basic variables of the process as well as their reciprocal phenomenological dependences. It describes the applied experimental procedures and the adapted methods which are appropriate for monitoring of real technological procedures of mineral wool production.
7
Mineral Wool
2 MELTING THE RAW MATERIALS The cupola furnace is an aggregate for melting of magma rocks and supplements where coke is used as the energy source [8–12]. The furnace is being filled downwards with preliminary prepared packages of magma rocks and coke. There, several chemical and heat processes occur. The melting process is controlled by the composition and the amount of inserted materials and by the underdraft. The underdraft is essential for proper operation of the cupola furnace and is used as a melting velocity regulator, and it directly influences the melt characteristics. It is enabled by concentrically displaced nozzles across the furnace periphery, through which the air is supplied at an exactly determined amount and temperature. The air can be enriched with oxygen. Because of the underdraft, coke burns out more intensively. As a result, extremely hot gas is created which travels through the cupola furnace upwards passing the heat energy over to the magma rocks and coke. The gas leaves the cupola furnace cooled down to approx. 400°C. Because of heat transfer, the inserted materials in the zone above the nozzles begin to melt and flow towards the bottom of the cupola. The melt level is controlled with a siphon. 2.1
Cupola furnace operation
According to its operation, the cupola furnace can be divided into several zones. This is shown in Fig. 2.1 [8]. The first zone can be characterised as the heating zone. There, the raw materials are heated losing damp and flame-loss. At 300–400°C, the indirect reduction of iron oxide starts. This zone is located in the temperature range 200–800°C. The second zone can be designated as the zone of re-formation of the inserted materials, Fig. 2.1. The temperature in this zone varies from 800°C to 1250°C. In the zone, dolomite (CaCO 3 , 8
Melting the Raw Materials Gas Gas output output
RawInput input materials raw materials
Gas temperature Raw material temperature
Heating zone
Reduction zone Oxidation zone Melting zone 500 1000 1500 2000
°C
Fig. 2.1. Cupola furnace scheme (mineral wool production) [8].
MgCO 3 ) decays, and CO 2 is released. Amphibolite can be crushed because it becomes more fragile at high temperatures. Also, further reduction of iron oxide takes place. Casting coke is inactive until it reaches the temperature of 1000°C. Direct reduction of iron oxide (FeO) is possible. The third zone is thin. It includes only the melting of the inserted materials, Fig. 2.1. One could say that magma rocks and dolomite melt in the temperature range from 1250 to 1350°C. The melting of magma rocks depends on minerals and granularity. With temperatures so high, the solidity of amphibolite decreases. Because of considerable loading at the top of the furnace, the material underneath crushes and becomes easier to melt. Something similar occurs to dolomite which decomposes at ~800°C. CO 2 is released. Grains of CaO and MgO burn at up to ~1200°C and then melt at higher temperatures. When melting the briquettes, more unknown quantities occur. They include thin calcinated bauxite and crushed melt that is not fiberised. All these substance together, bound by cement, build a compact structure. Briquettes consist mostly of waste material that is formed in the production process. The larger part is composed of the already fiberised mineral material and fiberisation products which form in the fiberisation process under 9
Mineral Wool
the furnace. The cement phases are bonded to each other and sublimate at ~600°C. The fourth zone is the zone of coke burning. It is located above the nozzles (shown in Fig. 2.1). It ends in the melting bed. In this zone, the coke reaches the temperature at which it starts to burn out with oxygen, ~600–700°C. The underdraft can be cold, or it can be heated which additionally speeds up the burning of coke. It is known that coke can burn into carbon dioxide CO 2 and carbon monoxide CO. In the first case, much more heat energy is being released. This burning is called full oxidation and is possible in the parts where the base coke receives more underdraft. This means that there is enough oxygen for combustion, Fig. 2.1. At high temperatures above 600°C, the thermodynamic balance favours the formation of CO. Out of CO 2, CO can form on the way through the base coke. The reaction depends on temperature, the CO 2 /coke contact surface and on the time the gases stay in the area of base coke. From the thermic point of view, this reaction is undesired since it consumes fuel (casting coke) and is endothermic. More CO increases the atmosphere reduction and therefore the capability of Fe 2 O 3 to reduce into pig iron. Casters and mineral wool manufacturers use casting coke in their cupola furnaces because it is less reactive. CO forms more easily and the thermic effect of casting coke is greater. In the fourth zone, the temperature is at its highest right above the melting bed. We distinguish between the peak temperature of gases, of coke and of the inflowing melt. Danish researchers [8] show the following peak temperatures of: melt ~1500°C, coke ~1800°C and gas above 2000°C. It has been known that the melt heats up to 1300–1500°C when crossing the zone, and preserves the temperature at the exit from the cupola furnace (Fig. 2.1). The fifth zone is at the bottom of the cupola furnace. It is also called the zone of separation. In this part, because of the physical principles, pig iron is separated from the rest of the silicate melt (slag) and sinks because of its high density. 2.1.1 Processes and chemical reactions in the cupola furnace The cupola furnace works as an oriented heat transformer. The inserted rocks and coke that heat up and melt travel downwards. The melt flows out of the siphon. Occasionally, pig iron is drained at the bottom of the cupola furnace. Combusted gases travel in the 10
Melting the Raw Materials INPUT
OUTPUT
stone dolomite briquette coke
melt cupola furnace
pig iron smoke gas
blow away oxygene
Fig. 2.2. Scheme of cupola furnace operation.
opposite direction. They heat up the inserted materials at the mouth of the cupola furnace. Materials entering and leaving the cupola furnace are schematically presented in Fig. 2.2. Several chemical endothermic and exothermic processes take place in the cupola furnace at the same time. Multiphase systems with phase transitions of aggregation are present. These processes consist of the heating, melting and overheating of inserted materials above the melting point of mineral compounds. In mineral material, Fe 2O 3 appears as the oxide with the highest valency. The reduction of this oxide produces oxides with lower valency and pig iron. The carbon from hard coke and carbon monoxide serves as a reducer. Iron oxides appear as Fe 2 O 3 , Fe 3 O 4 and FeO. In theory, the reduction can occur with hydrogen H 2 which enters the furnace with the aid of damp in cold underdraft. At high temperatures, steam dissociates into H 2 and CO. In terms of quantity, the first two reducers (coke and CO) dominate. Air humidity is negligible. The humidity of the inserted coke evaporates immediately after its insertion and mixes with smoke gases. This is why the reduction with hydrogen normally does not occur or is negligible. In the cupola furnace, the reductions of all three oxides, Fe 2 O 3 , Fe 3 O 4 , FeO, can take place with help of CO and C. But carbon in the form of hard coke at temperatures lower than 1000°C is relatively inactive. Up to this temperature, the reduction happens only with CO. More relevant reactions that influence the reduction are [8]: Warm-up pre-reduction zone ~350 to 900°C 1) 3Fe 2 O 3 + CO = 2Fe 3 O 4 + CO 2 11
Mineral Wool
2)
Fe 3 O 4 + CO = 3FeO + CO 2
Reduction zone (indirect reduction) ~800 to 1100°C 3) FeO + CO = Fe + CO 2 4) CaMg(CO 3 ) 2 = MgO + CaO + 2CO 2 Reduction zone (direct reduction) >1000°C 5) FeO + C(coke) = Fe + CO 6) FeO n + C(coke) = Fe n + CO 7) C(coke) + CO 2 = 2CO Underdraft with air, oxygen (base coke) 10) C(coke) + ½ O 2 = CO 11) C(coke) + O 2 = CO 2 2.2
Influence of underdraft on cupola furnace operation
Gases are the main heat carriers in the cupola furnace. They transfer heat convectively as they flow in the opposite direction through the porous inserted materials. It would be ideal if the gas would flow through the homogenous deposit of materials. However, it turns out that a homogenous deposit cannot be produced. The structure of deposition is influenced by a wide granulation range of coke in mineral rocks. The difference in density between coke and mineral materials causes different pouring (trajectories) and loading as well constructional form of the feed shaft. Gases flow through the part of the deposit where resistance is at its lowest or where respectively the permeability is the highest. If the granulation of the deposit is too small, this can cause a significant drop of pressure in the gas flow and force the gases to stop in the middle of the deposit. To prevent this, the underdraft system has to induce an overpressure at the bottom of the cupola furnace. The gases in the cupola furnace are the main factors of the melting process. The amount of blown-in air enables the inserted coke to combust into the determined ratio CO/CO 2 . This gas ratio shows the amount of heat released by coke in the cupola furnace. Large quantities of CO mean that the heat released by coke has been significantly reduced. The ratio of these two gases depends on the underdraft through the base coke. Here, the most CO/CO 2 smoke gases are formed. The flow through the deposit of base coke is determined by the 12
Melting the Raw Materials
overpressure, underdraft amount and by the temperature and permeability of base coke. The amount of underdraft plays an interesting part in the capacity or efficiency of the furnace. According to the given amount of inserted coke, increased underdraft enhances the melting efficiency. Exaggerated underdraft increase can cause rapid melting. As a result, bigger chunks of rock stay in the melting bed, and the melt leaving the cupola furnace is not hot enough. This has a detrimental effect on the fiberisation process. The underdraft reduction leads to reduced efficiency. Temperatures in the cupola furnace and, above all, the highest temperature can be changed with the heated and oxygen-enriched underdraft. We can simply imagine that the increase of underdraft temperature and higher percentage of oxygen O 2 in underdraft result in a rise of maximum temperature in the cupola furnace. This temperature is higher than the melt temperature. The oxidation zone is located in the vicinity of nozzles in the cupola furnace (Fig. 2.1). Intensive burning takes place in the empty space around the nozzles which formed after the combustion of base coke. This space is also known as the combustion space. From the walls surrounding the combustion space, pieces of coke flake off. Because of the turbulent underdraft, the pieces of coke whirl and combust with oxygen enriched smoke gases, and CO 2 forms. C(casting coke) + O 2 → CO 2 An enormous amount of heat is released. The temperature in the combustion space reaches 2000–2500°C [12]. The combustion space and the vortex flow of gas are schematically shown in Fig. 2.3. Figure 2.3 [12] shows the oxidation zone around the nozzles and towards the centre of the furnace. This zone is similar to the combustion space. In these two zones, the amount of oxygen is sufficient for coke to burn into CO 2 . A rich layer of CO 2 forms and passes through the deposit of base coke. The oxidation zone can expand across the combustion space if the underdraft has a high enough pressure and if the permeability of the base coke deposit allows for it. Figure 2.4 [10] shows the profile of smoke gases in relation to the distance from the nozzles. At the distance of 0.6 m, the oxygen concentration is negligible and that of CO 2 is maximal. The distance to which the oxygen can penetrate into the interior of the cupola furnace depends on the distribution of the nozzles, their form, the pressure and amount of underdraft. 13
Mineral Wool
Fig. 2.3. Combustion space in the vicinity of the nozzles [10].
Concentration % 50 CO CO2
40
O2
30
T °C 2400 CO
2200
T
20
2000 1800
O2
CO2 1600
10 0
1400 0
0.5
1.0 1.5 Distance from the nozzle
2.0 mm
2.5
Fig. 2.4. Smoke gas profile according to the distance from the nozzles [10].
The formed CO 2 passes through the deposit of base coke. The passing CO 2 reacts with the white-hot coke and its surface and CO forms: C(cast coke) + CO 2 → 2CO The oxygen enriched underdraft makes the base coke combust more intensively which causes an enormous rise of temperature in the lower part of the cupola furnace. The level of base coke is therefore connected with the 14
Melting the Raw Materials
sufficiency of the outlet temperature and the efficiency of the cupola furnace. If this level is not high enough, the melting zone can reach the area of highest temperature. For this reason, the melt running through the rest of the base coke deposit can not heat up properly and leaves the cupola furnace ‘cold’. This has a negative influence on the viscosity which is an important factor of melt fiberisation. If, however, the level of base coke is too high, the melting process is slowed down because the melting zone is higher and therefore somewhat cooler. The melt at the furnace exit is well heated. 2.3
Measuring temperature and concentrations in the cupola furnace
Chemical processes and phase transitions from solid rock materials into the melt depend on the temperature. It is most important to know the local temperature distributions in order to understand the processes in the cupola furnace. To determine the vertical temperature distribution of gases in the cupola furnace, we measured: z temperatures of smoke gases; z carbon dioxide concentration in dry smoke gases; z carbon monoxide concentration in dry smoke gases; z oxygen concentration in dry smoke gases; z pressure difference between the exterior and interior of cupola furnace. Figure 2.5 shows the measuring positions and the measuring probe for measuring the concentration of O 2, CO, CO 2, depth, temperature and pressure. In our case, the measurements of the temperature–gas profile have been performed at the wall of the cupola furnace. In the narrowest part of the furnace, the so-called belly, the distance between the probe and the furnace wall was 70 mm. Figure 2.6 shows the gas temperature vertically along the cupola furnace. It also shows how melt temperature depends on the vertical distance from the nozzles. One can see that by closing the inlet nozzles, the temperature rises monotonously. At a distance of 120 cm from the nozzles, the first temperature fluctuations appear (local temperature fluctuations) and the temperature gradient increases. The measured maximum temperature is reached in the area of ~60 cm above the nozzles. The temperature curve then starts to decrease monotonically to the point where the 15
Mineral Wool
temperature
pressure concentration
depth
Fig. 2.5. Measuring probe.
Distance from the nozzle
cm
250
200
150
100
50
0
400
500
600
700
800
900
Temperature
1000 1100 1200 1300 1400 1500 o
C
Fig. 2.6. Temperature profile of the cupola furnace.
measurement was terminated, i.e., 40 cm above the nozzles. The temperature profile helps to determine the zones of the furnace on theoretical grounds. The highest temperature of 1367°C was measured 570 mm above the nozzles. The temperature decreased with depth to 1142°C when the temperature sensor was destroyed 16
Melting the Raw Materials
25 CO2 CO O2
Concentration
%
20 15 10 5 0 0
25
50
75
100
125
Distance
150
175
200
225
250
275
cm
Fig. 2.7. Gas profile of the cupola furnace.
and the measurement terminated. This happened 330 mm above the nozzles. In the case where the probe was going deeper, the temperature reduction is possible only if the probe enters the area of increased air flow which could have caused local cooling. The temperature measurements were carried out simultaneously with the measurements of the chemical concentration of smoke gases. Figure 2.7 shows the distribution of O 2 , CO 2 and CO concentrations in the cupola furnace. These concentrations also depend on the distance from the nozzles. The results of the measurements show that O 2 and CO 2 have the highest concentration. In the area from 0 to 200 cm, the concentration of O 2 increases in direction towards the nozzles and stabilizes somewhere at 18 vol.%. The concentration distribution of CO 2 seems to be the mirror image of oxygen concentration. The CO 2 concentration stabilizes at 1.5 vol.%. The CO content at a distance of 110 cm from the nozzles is hardly noticeable. From 110 cm to 130 cm above the nozzles, CO rises to its maximal level of 1.69 vol.%. This result tells us that, during the measurement, the cupola furnace operated with good efficiency. Figure 2.8 shows the concentration of O 2 , CO 2 and CO in relation to the temperature in the cupola furnace. Structurally, the diagram is similar to the one in Figure 2.7. Besides the chemical concentration of smoke gases, the static 17
Mineral Wool
cm
300
Distance from the nozzle
350
250
measured
200 150 100 50 0 -5
0
5
10
15
Pressure loss
20
25
Pa
Fig. 2.8. Concentrations shown according to the temperature in the cupola furnace. 25
Concentration
%
20
15
CO2 CO O2
10
5
0 400
500
600
700
800
900
Temperature
1000
1100
1200
1300
1400
o
C
Fig. 2.9. Pressure relation to the distance from the nozzles.
pressure in the vicinity of the measuring probe has been simultaneously measured. The pressure conditions in the cupola furnace are shown in Fig. 2.9 as the relation of pressure to the distance from the nozzles. One can see that the pressure created by the underdraft and the negative suction pressure influence the pressure in the cupola furnace. The negative pressure passes over to an overpressure of 248 cm above the nozzles. The dynamics of pressure relation to the position – layer depth lead us to conclude that the course of the curve is typical for a turbulent flow through the porous layer with the stressed square law of pressure relation to the depth.
18
Multiple Regression
3 MULTIPLE REGRESSION This section sums up Douglas Montgomery’s [13] work on multiple regression and basic definitions and deductions in the bases of statistics [14]. The aim of curve fitting is to express the relationship between two or more variables in mathematical form by determining the equation connecting the variables. If we feel that there is a linear relationship between the dependent variable y and independent variables x i (i=1,2,…m), then we would seek the equation connecting the variables which has the form:
y = a0 + a1 ⋅ x1 + a2 ⋅ x2 + K + am ⋅ xm + ε ,
(3.1)
where the unknown parameters {a i } are regression coefficients, and ε represents the random errors. The regression coefficients {a i } are obtained with the least squares method. Equation (3.1) represents the plane in the m-dimensional rectangular coordinate system. Our assumption is that the number of equations is greater than the number of regressor variables n > m, x ij . The data are shown in Table 3.1. The estimation of the procedure requires the mathematical expectation of random errors to be E[ ε ]=0, the variance to be E[ ε ] 2 = σ , and that { ε } are not correlated with each other. In this Table 3.1. Data for linear multiple regression [13]
Y
x1
x2
…
xk
y1
x11
x21
…
xm1
y2
x12
x22
…
xm2
M
M
M
M
M
yn
x1n
x2n
…
xmn
19
Mineral Wool
case, we can write a model with the form:
y = a0 + a1 ⋅ x1 j + a2 ⋅ x2 j + K + am ⋅ xmj + ε j
(3.2)
Equation (3.2) can be written also in the matrix notation:
y = xa + ε (3.3) where y is (n x 1) vector, x is (n x m) matrix, a is (m x 1) vector of regression coefficient and ε is (n x 1) vector of random errors. ⎡ y1 ⎤ ⎢y ⎥ y = ⎢ 1⎥ ⎢ M⎥ ⎢ ⎥ ⎣ yn ⎦
⎡1 x11 ⎢1 x 12 x=⎢ ⎢M M ⎢ ⎣1 x1n
xm1 ⎤ xm1 ⎥⎥ M M⎥ ⎥ L xmn ⎦
x21 K x22 L M x2 n
⎡ε 0 ⎤ ⎢ ⎥ ε ε=⎢ 1⎥ ⎢ M⎥ ⎢ ⎥ ⎢⎣ε m ⎥⎦
⎡ a0 ⎤ ⎢ ⎥ a a=⎢ 1⎥ ⎢ M⎥ ⎢ ⎥ ⎢⎣ am ⎥⎦
The vector of the regression coefficient a is found by the least square method: n
L = ∑ ε 2j = εT ε = (y − xa)T (y − xa) j =1
(3.4)
The notation T denotes a transpose matrix or a vector, for example vector a and its transposing vector a T :
⎡ a0 ⎤ ⎢ ⎥ a a=⎢ 1⎥ ⎢ M⎥ ⎢ ⎥ ⎢⎣ am ⎥⎦
and aT = [ a0 , a1 , a2 ,L am −1 , am ]
The least squares estimators must satisfy the equation:
∂L = −2xT y + 2xT xa = 0 , ∂a
(3.5)
which simplifies to
xT xa = xT y ,
(3.6)
20
Multiple Regression
To solve the equation (3.6), we multiply both sides by the inverse of the matrix product xT xa = (xT x) −1 xT y . The least square estimator of a is:
xT xa = (xT x) −1 xT y ,
(3.7)
or in the explicit matrix form:
⎡n 0 ⎢0 S 11 ⎢ ⎢ 0 S12 ⎢ ⎢M M ⎢⎣ 0 S1m 3.1
0 S12 S22 M S2 m
⎡ n ⎤ 0 0 ⎤ ⎡ a0 ⎤ ⎢ ∑ yi ⎥ i =1 ⎢ ⎥ ⎥ L S1m ⎥⎥ ⎢ a1 ⎥ ⎢ ⎢ S1 y ⎥ L S2 m ⎥ ⎢ a2 ⎥ = ⎢ ⎥ ⎥ ⎢ ⎥ ⎢ S2 y ⎥ M M ⎥⎢ M⎥ ⎢ M ⎥ L Smm ⎥⎦ ⎢⎣ am ⎥⎦ ⎢ ⎥ ⎢⎣ Smy ⎥⎦
(3.8)
Hypothesis testing in multiple linear regression
In multiple linear regression, we wish to test hypotheses about model parameters a. It is important to consider testing for the significance of regression. In multiple linear regression, this is accomplished by testing [13]:
H 0 : a1 = a2 = L = am = 0 H1 : ai ≠ 0
(3.9)
at least one i
The rejection of H 0 in equation (3.9) implies that at least one variable in the model contributes significantly to the fit. The total sum of squares is portioned into regression and error sums of squares S yy = SS R + SS E where SS R and SS E are: m
m
SS E = ∑ ( yi − yest ) 2 ;
SS R = ∑ ai yi ( xij − x) 2 ,
i =1
i =1
(3.10)
The test procedure for H 0 : a i = 0 is the computation:
F0 =
SS R ( n − m − 1) MS R = m SS E MS E
(3.11)
and the rejection of H 0 if F 0 > F a,m,n–m-1 . The procedure is usually summarized in the analysis of variance tables, such as Table 3.2 [13]: We are frequently interested in testing hypotheses on individual regression coefficients. The hypotheses for testing the significance 21
Mineral Wool Table 3.2. Analysis of variance table S o urc e o f Va ria tio n
S um o f S qua re s
D e g re e s o f Fre e do m
M e an S qua re
Le ve ls
Fis he r Sta tis tic s F0
Re gre ssio n
SSR
K
MS R
Erro r o f re sid ua l
SSE
n -m -1
MS E
To ta l
S yy
n -1
M S E /M S R
of any individual coefficient, for example a i , are:
H 0 : ai = 0
(3.12)
H1 : ai ≠ 0
The appropriate test statistics are:
ai MS E Cii .
t0 =
(3.13)
Hypothesis H 0 : ai = 0 is rejected if t0 > tα / 2,n − m−1 . 3.1.1 Coefficient of determination The coefficient of determination is the quadratic value of the correlation coefficient r and is defined as [13, 14]: m
r2 = 1−
∑(y − y i
i =1
( est ) i
m
∑ ( y − y) i =1
m
)2 =
2
i
∑(y i =1 m
est
− y )2
∑ ( y − y) i =1
= 2
Explained variation Total variation .(3.14)
i
The coefficient of determination r 2 can be interpreted as the fraction of total variation which is explained by the least squares regression line. This means that r measures how well the least squares regression line fits the sample data. r 2 lies between 0 and 1, r 2 ≥ 0. The definition (3.14) holds for non-linear correlation as well. Important statistics are also the adjusted statistics r 2 :
⎛ n −1 ⎞ 2 2 radj = 1− ⎜ ⎟ (1 − r ) ⎝n−m⎠ The advantage of adjusted statistics r 2 is that they do not 22
Multiple Regression
automatically increase if a new variable is added to the model. 3.1.2 Other linear and non-linear models The linear model y = xa + ε is a general model. It can be used for adapting the linear relations of unknown parameters a. By transforming the equations, it is in many cases possible to form a linear model. The most frequent expression in empirical correlations is the non-linear relation which represents the product of particular non-linear connections.
Y = a0 X 1a1 X 2a2 L X iai X ia+i1+1 X mam ,
(3.15)
The equation (3.15) can simply be transformed into a linear model. If the variables X 1 , X 2 , ... X m are independent of each other, we can take the logarithm of the equation (3.15).
y = log Y = log(a0 X 1a1 X 2a2 L X mam−−11 X mam ) = = a0 + a1 log X 1 + a2 log X 2 + L + am−1 log X m−1 + am log X m = (3.16) = a0 + a1 x1 + a2 x2 + ... + am−1 xm−1 + am x6 m Final form of the equation (3.16) is simple and represents the linear relation of the transformed value y to the transformed values x 1 , x 2 , .... x m . Indeed, the equation (3.15) can be solved also as a non-linear equation. In this case, we use the gradient methods, most frequently the Levenberg–Marquardt method. In order to successfully solve a non-linear system of equations, properly chosen values of parameters a i are essential. The latter can more easily be determined by the solution of a linear problem. 3.1.3 Computer printout Computer programmes are used extensively in regression analysis. The output from such a programme, SPSS [15], is shown below. First, we have to determine the input variables. A computer printout can appropriately be presented with the practical example of six independent variables. A regression equation can be expressed as:
dV = a0 Π1a1 Π a22 Π 3a3 Π 4a4 Π 5a5 Π 6a6 .
(3.17)
The regression equation (3.17) can be transformed into the form of equation (3.16). In this manner, a linear model can be acquired: 23
Mineral Wool y = log dV = log( a0Π1a1 Π a22 Π 3a3 Π 4a4 Π 5a5 Π 6a6 ) = = a0 + a1 log Π1 + a2 log Π 2 + a3 log Π 3 + a4 log Π 4 + a5 log Π 5 + a6 log Π 6 = (3.18) = a0 + a1 x1 + a2 x2 + a3 x3 + a4 x4 + a5 x5 + a6 x6
We can designate the equation (3.18) as Model 1. Table 3.3. M ode l
Variable s Ente re d
Variable s Re move d
1
X6, X1, X5, X4, X3, X2
M e thod Enter
All requested variables entered. Dependent Variable: Y Let us take a look at the computer printout of six independent variables. On the basis of the computer printout we first obtain information about the correlation coefficient r, coefficient of determination r 2 , adopted coefficient r 2 and the standard error of estimate (SEE). This is presented in the table below. r 2 shows that the model explains almost 88 % of joint variance because it amounts to r 2 = 0.878. Model summary Table 3.4. M o de l
R
R S qua re
Adjus te d R S qua re
Std. Erro r o f the Es tima te
1
0.938
0.878
0.852
2 . 2 6 7 E- 0 2
a Predictors: (Constant), X6, X1, X5, X3, X2, X4 b Dependent Variable: Y The variance of analysis helps us to ascertain if the regression model is statistically significant. Table 3.5. M ode l Regression Residual Total
Sum of Square s
De gre e s of Fre e dom
M e an Square
F
Sig.
0.107
6
1.781E- 02
34.647
.000
1.491E- 02
29
5.141E- 04
0.122
35
a Predictors: (Constant), X6, X1, X5, X3, X2, X4 b Dependent Variable: Y 24
Multiple Regression
At the end, we check the importance of particular predictors for explaining the regression criterion. For this purpose, we use the statistic t-test. Since the t-test can be misleading in individual cases, we perform regression analysis in stages by adding variables one after another untill they can contribute to explaining the criterion. Data in the table below leads us to the conclusion that all predictors are statistically characteristic and very important. Least important are coefficients a 4 and a 6 , but their importance is still great. Coefficients Table 3.6.
N o ns ta nda rd Co e ffic ie nts
Sta nda rd Co e ffic ie nts
t
S ig .
1.995
0.056
a
Std. Erro r
Co ns ta nt
a0 = 145.789
73.085
X1
a1 = –0.353
0.167
–0.532
–2.106
0.044
X2
a2 = –0.266
0.162
–0.422
–1.641
0 . 11 2
X3
a 3 = 2 11 . 11 3
104.867
0.384
2.013
0.053
X4
a 4 = – 9 . 6 9 7 E- 0 2
0.099
–0.181
–0.983
0.334
X5
a5 = –25.781
7.754
–0.404
–3.325
0.002
X6
a6 = 0.103
0.093
0.147
1.108
0.277
β
a Dependent Variable: Y The importance can most easily be presented graphically, Fig. 3.1. Equation (3.15) can be tackled with the help of solving nonlinear equations. In this case, we are trying to solve a system of equations with the Levenberg–Marquardt method. It is necessary to determine the initial values a 1 , a 2 , … a k . Because this is an iterative procedure, the precision of iterations is necessary as well and should be 1× 10 –10 . First, the variance of the analysis helps us to ascertain if the regression model is statistically significant. The table below clarifies this because we see that the determination coefficient is very high. 25
Mineral Wool
The following table leads us to conclude that all parameters are of great importance. A special demand has been made that this time the coefficient be a 0 = 1. Caution is required when interpreting r 2 for the linear and non-linear model. In the linear model, the value of the correlation coefficient r 2 holds for the transformed value of the dependent variable log Y. Scatterplot Dependent Variable: LOGY Dependent variable: log Y
Regression standardized Regression standardized predicted value predicted value
3
2
1
0
-1
-2
-3 .6
.7
.8
.9
log Y
LOGY
Fig. 3.1. Comparison between the measured and the regression model (SPSS graph). Table 3.7. D e g re e s o f Fre e do m
S um o f S qua re s
M e an S qua re
F
S ig .
Re gre ssio n
6
1206.33906
201.05651
2 2 11 . 11
0.000
Re sid ua l
30
2.72794
0.09093
Unc o rre c te d To ta l
36
1209.06700
( C o r r e c te d To ta l)
35
21.80512
S o urc e
r2 = 1 - Re sid ua l S S /C o rre c te d S S = 0 . 8 7 4 8 9
26
Multiple Regression Table 3.8.
N o ns ta nda rd Co e ffic ie nts Va ria ble
ai
t
S ig .
Std. Erro r
9 5 % Co nfide nc e Inte rv a l fo r B Lo we r B o und
Uppe r B o und
a0 = 1 X1
a 1= – 0 . 3 5 8
0.158
–2.272
0.03039
–3.680
–0.036
X2
a 2= – 0 . 2 4 5
0.155
–1.585
0.12342
–3.561
0.071
X3
a 3= 2 . 1 8 9
1.050
2.085
0.04568
0.045
4.334
X4
a 4= – 0 . 2 5 5
0.073
–3.492
0.00151
–3.404
–0.106
X5
a 5= – 3 6 . 7 5 3
5.672
–6.480
3 . 7 E- 0 7
–48.337
–25.170
X6
a6 = 0.144
0.096
1.490
0.14662
–0.053
0.340
27
Mineral Wool
4 PHYSICAL CHARACTERISTICS OF MINERAL WOOL MELTS Knowledge of material char acteristics of melt has a significant impor tance for the pr ocess of fiber isation and for achieving the desired insulation properties of mineral wool. The understanding of qualities, such as density, vis cosity and sur face t ension, is historically bound to the development of glass production. Mathematical descriptions and calculation experiments of glass cha r a cter is tics a r e a s old a s moder n gla ss r esea r ch [16]. T he following section does not include a vast mathematical description of glass pr oper ties. However, it offer s a limited selection of pr actica l mathematical expr essions, which ar e r elevant for the production of mineral wool. Among the physical characteristics of silicate melts, most r elevant ar e densit y, viscosity and sur face tension. Vogel [16] also considers the index of refraction, dispersion, Abbe number, molar r efr action, heat dilatation, tension, heat conductivity and electr ic conductivity. T he fir st thr ee physical cha r a cter istics a r e by far most impor ta nt for miner a l wool production. For this r eason, we are going to concentrate on the density, viscosity and surface tension of mineral wool. The term ‘miner al wool’ is often used to r efer collectively to rock wool and slag wool, though glass wool is sometimes included in this ter m as well [17]. Because the r ock and slag wool have differ ent or igins and differ chemically, they should be identified individually whenever possible. Like the other fibres, rock and slag wool ar e p r edominantly calcium and aluminium silicates. As a group, however, these wools tend to be richer in the alkali earth metal oxides (i.e., Ca, Fe, Mg, Ti), and tend to ha ve smaller amounts of alkali metal oxides (i.e., K, Na) than the other manmade fibres. In nature, rock wool is formed by igneous rocks such as diabase, basalt or olivine. These natural rocks consist 40–60 % of calcium and magnesium car b onate. Rock wool dissolves in 28
Physical Characteristics of Mineral Wool Melts Table 4.1. Chemical composition of typical rock and slag wool [17]
Component
Slag wool
Rock wool
SiO 2
32–41
40–52
CaO
27–40
10–12
MgO
4–13
8–15
Al2O 3
8–15
8–13
K 2O
0–0.5
0.8–2.0
Na2O
0–0.2
0.8–3.3
TiO 2
0–0.5
1.5–2.7
Fe 2O 3
0–2
5.5–6.5
S
0–2
0–0.2
P 2O 5
0–1
MnO
0.1–0.5
0.1–0.3
hydrochloric acid. Slag wool is produced by recycling certain blast furnace waste. Naturally, the final product composition varies with the metallic content of the slag originally used. Slag wools typically lack significant amounts of sodium. They are usually slightly soluble in hydrochloric acid. The chemical composition of typical rock and slag wools is shown in Table 4.1 [17]. The final chemical proportions of wool products are controlled by balancing the acid to the base ratio of the melt [17]. The total percentage of silicon dioxide and aluminium oxide forms the acid portion, wher eas the base is the sum of calcium and magnesium oxides. T he acid–base r atio is impor tant for deter mining the viscosity of the melt. 4.1
Density
The density of silicate alloys is often necessary for calculating other quantities such as molar volume and molar r efra ction. The first empirical relation was derived by A. Winkelmann and Schott [16]
100
p1
U
U1
p1
U2
p1
U3
pn
Un 29
(4.1)
Mineral Wool
where p is the portion of the particular silicate alloy component in mass% and U are the densities of particular glass components. In his book, Vogel [16] states that this expression is in some particular cases applicable, but on the other hand it does not apply to the general area of glass production. Considering this, let us remember the density curve of intersecting binary alkali–silicate systems and the inflection points on the density curves of simple boron–silicate glasses. Vogel [16] continues that some other authors, such as Gilard and Dubral, tried to harmonise the deviation of measuring curves from the linearity by considering the square estimator:
1
U
1 N § pi pi2 · ¦¨ ¸ 100 i 1 © Ui' Ui" ¹
(4.2)
4.1.1 Density of silicate melts To a great deta il, high temperatur e dependencies of silicate melt densities wer e tackled in many experimental studies (Bockris et al.,1956; Riebling, 1966; Lange and Carmichael, 1987; Dingwell and Brearley 1988; Dingwell et al. 1988). Empirical predictive schemes were dealt with in (Bottinga in Weill, 1970; Bottinga et al., 1982; Lange and Carmichael, 1987, 1990; Kress and Carmichael, 1991) [18]. Ver y precise experimental studies focused on determining the melt densities under pressure of 1 atm of super fluid temperatures. T hey used double-bob Ar chimedean methods ( Dingwell et al. 1988), Stokesian failing sphere or sink-float densitometry (Shaw, 1963; Kushiro, 1978; Scarfe et al., 1987) [18]. Mor e noticeable studies also applied shock-wave Hugoniot density (Rigden et al., 1984, 1988, 1989), ultrasonic compressibility studies (Rivers and Carmichael, 1987; Kress et al., 1988; Webb and Dingwell, 1994) as well as interferences from the slopes of melting curves (Lange, 1994) [18]. In their article [18], R. Knoche, D.B. Dingwell and S.L. Webb presented the melt density of leucogranites and granitic pegmatites. T hese author s studied 38 haplogr anitic silica te melts. T he compositions r epr esent the addition of 5, 10 a nd 20 wt.% of selected oxide components Al 2 O 3 , Na 2 O, K 2 O, Li 2 O, Rb 2 O, Cs 2 O, MgO, CaO, SrO, BaO, TiO 2 , Nb 2 O 5 , Ta 2 O 5 and WO 3 to the basic haplogr anitic melt (HPG8). Melt densities wer e obtained by 30
Physical Characteristics of Mineral Wool Melts
combining the scanned dilatometr ies and using the Ar chimedes densities together with the scanned calorimetries. The authors also determined the temperature expansions. R.A. Lange and I.S.E. Carmichael (1987) [19] presented the densities of Na 2 O–K 2 O–CaO–MgO–FeO–Fe 2 O 3 –Al 2 O 3 –TiO 2 –SiO 2 melts by applying the double-bob Archimedean measuring method. The results showed that multi-component silicate fluid volumes are linearly dependent on the composition with the exception of TiO 2 . The equation: N
V (T )
¦ X (T )V (T ) X i
i
Na 2 O
i 1
X TiO 2 V
Na2O TiO2
(4.3)
is used for the derivation of oxides with partial molar volumes V i with the aid of the least squares method. T he r egr essions wer e made separately at 1573 K, 1673 K, 1773 K and 1873 K. The goal of this contribution was to give reliable data on the densities of silicate melts. So, the best measuring techniques were used (doublebob Archimedean measur ing method). The authors both presented the 27 melts and measured their density. The experimental double-bob Archimedean measuring method is well described in (Nelson and Carmichael, 1979) [19]. They used the MoSi 2 device with electr onic temper at ur e r egulation up to 1873 K. In this furnace, a sample of a silicate melt is heated up in a platinum crucible. For measuring the temperature at the top of the cr ucib le, the author s us ed the S-type ther mocouple. An electronic balance with 0.0001 g pr ecision was mounted onto a massive plate and used for measuring the weight of the melt. The melt density was calculated with the following equation:
U (T )
B(T ) S (T ) V (T )
(4.4)
wher e B(T) is the buoyancy at temper atur e T; U(T) is the melt density at temperature T; S(T) is the sur face tension of the melt on the holder of the cr ucible; V(T) is the submer ged volume at temperature T. Cour tial and Dingwell [20] also took into consider ation the temper atur e gr adient of mola r volumes based on their own measur ements of density in a CaO–MgO–Al 2 O 3 –SiO 2 system N
VL (T )
¦x
i
i 1
ª¬Vi ,1873 wVi / wT T 1873 º¼ ,
31
(4.5)
Mineral Wool
wher e the par tial molar volume V i ,18 73 is deter mined a t the temperature of 1873 K, and x i is the molar part of i oxide. Blagojeviü, Širok and Štremfelj, 2004 [21] used the gathered data on molar volumes of silicate melts as pr esented in [19]. In the analysis, only 67 multi-component silicate melts from the paper [19] were taken into account. The molar volumes V L (T) in cm3 /mol were approximated by the equation: N 9
VL (T )
N 9
¦ x V i
i ,1773
i 1
UL
¦ xi (wVi / wT )(T 1773) i 1
N 9
¦ x H i
N 9
i ,1773
i 1
¦ xi Pi (T 1773) i 1
,
ML , VL
(4.6) where, U L is the density and M L the molar mas. The values of linear r egr ession coefficients H i and gr adient coefficients P i wer e obtained, as given in Table 4.2. Table 4.2. Coefficient values of regression equation (4.6) to calculate the molar volume of silicate melts Oxide
SiO2
TiO2
Al2O3
Fe 2O3
FeO
MgO
CaO
Na2O
K2O
Hi
25.178
24.227
39.126
44.457
11.731
14.110
18.677
35.872
49.978
Pi
–0.0025
0.0027
–0.0096
–0.0229
0.0138
0.0041
0.0081
0.0158
0.0190
Based on r egr ession analysis , a ver y good agr eement was obtained b etween the measur ed molar volumes of ex per imental liquids at different temperatures from 1300 K up to 1896 K and those predicted by regression, as shown in Fig. 4.1. 4.2
Viscosity
Two layers in the melt can move in relation to each other only if a force is exerted. For such a force, the following relation holds [16]:
ww , (4.7) wx where: K is force; K is viscosity (proportionality factor); q is the ww is velocity gradient w in contact surface between two layers; wx layer thickness x. K
K q
32
34
2
r =0.994
m
3
Physical Characteristics of Mineral Wool Melts
3
SEE=+0.271 m
molar volume (measured, predicted)
32 30
predicted measured
28 26 24 22 20 20
22
24
26
28
molar volume - measured
30
32
34
3
m
Fig. 4.1. Comparison between measured and predicted values of molar volume.
The proportionality factor in equation (4.7) is also called dynamic viscosit y which r epr esents the coefficient of inter nal fr iction between the la yer s of the fluid. Viscosity is one of the most important quantities for glass production. It plays an important role in all mixing processes in glass; in the clarification process (bubble elimination), in the pouring and pressing process, in the process of crystallization and in all processes of microstructure formation. It took many experiments to find out and determine the correct mathematical expression for the relation between the temperature and viscosity of glass melt. This relation can be described by the Boltzmann law [16]:
K
K exp ( EK / RT ) ,
(4.8)
where K is dynamic viscosity; K is the proportional constant; E P is the activation energy for viscosity; R is the ga s constant; T is absolute temperature. The Boltzmann law strictly holds only for fluids with spherical particles and drifting ties which is not the case with glass melts. That is why E P activation energy for viscosity is not constant. In his book [ 16], Vogel states that if we dr aw the diagr am log P –(1/T), the inclination of straight lines represents the activation energy for viscosity. T he pr eliminar y condition for viscosity incr ease, e.g. temper atu r e incr ease, is weakening or fr eeing of chemical bonds in glass. 33
Mineral Wool
There were numerous attempts to develop an equation that could successfully be used in pr actice. T he best known is the VogelFulcher –Ta mma nn (VFT ) equation wher e a thir d constant that represents temperature T is introduced into the Boltzmann equation (4.8):
K
K exp( EK /(T T0 )) ,
(4.9)
or in logarithmic expression:
logK
B0
T T0 B1
(4.10)
where B 0 , B 1 and T 0 ar e constants. The VFT equation gives results which agree with practice above the transformation point of the adequate glass [16]. 4.2.1 Viscosity of silicate melts The viscosity and temperature dependences in mineral wool melts in SiO 2 –Al 2 O 3 –CaO–M gO–alkali–F eO–Fe 2 O 3 syst ems ar e ver y well described by T. Lakatos, L.G. Johansson, and B. Simmingsköld, 1981 [22]. Mineral wool fibres usually represent a four-phase SiO 2 – Al 2 O 3 –CaO–MgO diagram. T his diagram informs us ab out the viscosity. Low melt temper atures do not automatically mean low viscosity. The inverse proportion of these quantities appears in many cases. In p r actice, two for mula s ar e used for deter mining the appropriate melts for the production of insulation fibres:
BNo
AM
100 ( xSiO2 xAl2O3 ) xSiO2 xAl2O3
,
(4.11)
xSiO2 xAl2O3
xCaO xMgO ,
(4.12)
where: B No is the basicity number; A M is the acidity module; x i is mass weight %. Lakatos et al., 1981 [22] give the basic data on the basicity number for basalt/diabas melts of B No | 0.65–0. 75 and for slag melts of B No | 0.70 to 0.75. Similar is the estimation of the acidity module. Its size for basalt/diabase melts is A M | 2.6–3.0 and for slag melts fr om A M | 1.2 to 1.4. The acidity module is a r ough approximation because is based on supposition that the influence of SiO 2 and Al 2 O 3 portions on the portions of CaO and MgO is the 34
Physical Characteristics of Mineral Wool Melts
same. In these cases, the effects of alkali and ir on ox ides ar e disr egarded. La katos et al. [22] intended to deter mine separ ate factors for all important components of alkali oxides and di- and trivalent iron oxides. Therefore, 16 different chemical melts were analysed in the melting furnac e with an air atmos phere. Raw mater ials wer e: kaolin, silica flour, dolomites, MgCO 3 , CaCO 3 , sodium ash, pla nt ash. T he melting point was between 1450 and 1500°C, depending on the viscosity of the melt. Viscosities were measur ed with a Pt10%Rh alloy r otational viscometer. Initial temperature was 1550°C. The cooling proceeded to the beginning of crystallization. Lakatos’ regression model [22] can be used for the calculation of the temper a tur e dependence of viscosity on the chemical composition. T he model is designed on the basis of temper atur e calculat ions of silicat e melts at thr ee differ ent viscosities: log K = 1.5; log K = 2; log K = 2.5. The viscosity K is entered into deka Pas. Based on the known composition, the melt temperature T in °C can be determined with the aid of Lakatos’ equation:
T
ª º b0 SiO 2 b1·Al2O3 A« » , (4.13) ¬ b2 ·CaO b3 ·MgO b4 ·Alk b5 ·FeO b6 ·Fe 2O3 ¼
where b 0 , b 1 , b 2 , b 3 , b 4 , b 5 , b 6 and A are Lakatos’ approximation constants (Table 4.3) while the fractions of individual oxides are enter ed in weight %. Constants B 0 , T 0 and B 1 in equation (4.10) ca n be calculated Table 4.3. Lakatos’ approximation constants for logK=1.5, logK=2.0 and logK=2.5.
Coefficient
log K= 1.5
log K= 2.0
log K= 2.5
A
1375.76
1272.64
1192.44
b0
122.29
117.64
112.99
b1
1.06247
1.05336
1.03567
b2
1.57233
1.42246
1.27336
b3
1.61648
1.48036
1.43136
b4
1.44738
1.51099
1.41448
b5
1.92899
1.86207
1.65966
b6
1.47337
1.36590
1.20929
35
Mineral Wool
from the obtained temperatures T(log K =1.5), T(log K =2.0) and T(log K =2.5), and with the aid of the VFT equation which enables the calculation of dynamic vis cosity of the melt at var ious temperatures. The constants can be expressed in a simple manner. If y 1 = log K 1 =1.5, y 2 = log K 2 =2.0 and y 3 = log K 3 =2.5 and the corresponding temperatures according to Lakatos’ equation (4.13) designate with T 1 = T(log K 1 =1.5), T 2 = T(log K 2 =2.0) and T 3 = T(log K 3 =2.5), we can express the constants B 0 , T 0 and B 1 explicitly with:
b ( y3 y1 ) c T0 B1 B0
y1 y2 y y (T2 T3 ) 1 2 (T1 T2 ) T2 T1 T2 T1
( y3 y1 ) T3
y1 y2 y y T2 T3 1 2 T1 T2 T2 T1 T2 T1
c b y1 y2 T1 T0 T2 T1 T2 T0
y1
(4.14)
B1 T1 T0
The applicability of Lakatos’ model was verified in practice for the following chemical comp osition of the s ilicate system given in weight %: SiO 2 35 up to 42 %; Al 2 O 3 15 up to 20 %; CaO 16 up to 20 %; Fe 3 O 4 2 up to 6 %; MgO up to 12 %; and Na 2 O up to 4 %. Ver y good agr eement was found between the viscosities measured in laboratory and the measurement results, as shown in Fig. 4.2 (Blagojeviü, et al., 2004 [21]). Comparisons have shown that the dynamic viscosity values of the melt, calculated in accordance with the model, do not differ from the measur ed values by mor e than ±35 %. However, if the last measurement results at the temperature of 1100°C were not taken into account, the r elative er r or would only be ±18 %, a nd the standard approximation error only ±9 deka Pas. 4.2.2 Methods for measuring viscosity of silicate melts Shelby [23,24] gives a fine presentation of measuring methods. In practice, there are many significant reference points which describe 36
predicted measured
100
er < + 18 (35) % deka Pas Pa s SEE + 9 9(76) SEE <<+ (76) deka
K
dekadeka Pa Pas s
Physical Characteristics of Mineral Wool Melts
10
1100
1150
1200
1250
1300
1350
Temperature
1400
1450
1500
1550
°C
Fig. 4.2. Com parison between the measured and calculated viscosity values of melt as a function of temperature.
the viscosity–temperature relation as shown in Fig 4.3. 1. Practical melting temperatures: ( K d 10 Pa s): the melt is hot enough for homogenisation which occurs in real time. These temperatur es do not coincide with the phase transition from the crystal to the liquid phase. 2. Wor king temper atur e: ( K =10 3 Pa s): is the temper atur e at which the molten glass ca n b e moulded. Viscosity is low enough to enable some refinement processes such as pressing, blowing…, and yet it is high enough for the glass to preserve its form after refinement has taken place. 3. Softening point: ( K =10 6.6 Pa s): is the temperature at which glass will deform due to its own weight. 4. Hardening point: ( K =10 12 –10 12.4 Pa s): is the temperatur e at which the tensions loosen after a few minutes. 5. Tension point: ( K = 10 13.5 Pa s): is the temperature at which the tensions loosen after several hours. 6. Glass transformation temperature Tg: ( K = 10 11 –10 12 Pa s); 7. Point of softening and extending Td: ( K = 10 8 –10 9 Pa s). At high temperatures, glass melts behave as Newtonian fluids where the defor mation is time-dependent. At low temper at ur es, they behave as ela stic solid bodies. In the inter mediate ar ea: ( K = 10 8 d10 13 Pa s) they behave as Maxwell elastic elements. 37
Mineral Wool 16 strain point
14
annealing point
Viscosity Viscosity Pa Pas s
12 10
softening point
8 6
working point melting temperature
4 2 0 500
600
700
800
900
1000
Temperature
1100
1200
1300
1400
1500
o
C
Fig. 4.3. Important reference temperatures, Shelby [23]. Table 4.4. Methods for measurin g viscosity of silicate melts [23,24]
Methods for measuring viscosity Area
Method
Viscosity
Failing sphere or bubble elevation
K<10 4 Pa s
Margules' rotational cylinder
K<10 6 Pa s
Parallel plates
10 5 Pas< K < 10 9 Pa s
Penetration viscometer
10 ` Pa s < K <10 9 Pa s
Fibre extension
10 5 Pa s < K < 101 5.5 Pa s
Shaft bending
10 7 Pa s < K < 10 12 Pa s
Decreasing tension
10 11 Pa s < K < 10 14 Pa s
Melting
Softening and annealing
Shelby pr esents the over view of the following methods for measuring viscosity as shown in Table 4.4:
38
Physical Characteristics of Mineral Wool Melts
1. Rotational viscometer (10–10 6 Pa s) Of all mea sur ing methods, most ly r otational viscometer s (10– 10 6 Pa s) are used. They operate according to the following physical principle:
K
1 §1 1 ·T ¨ 2 2¸ , 4S L © r R ¹Z
(4.15)
where T is the moment of rotation, L is the length of the spindle, R is the cylinder radius, r is the spindle radius and Z is angular velocity. It is important to measure the moment of rotation which maintains the constant velocity of the spindle, or to measure the velocity at constant moment of rotation. High temperatures of glass melts r equ ir e a Pt alloy spindle. T his measur ing method is schematically shown in Fig. 4.4. 2. Falling sphere (from 10–10 6 Pa s) T his method repr esents the second possibility for measur ing the viscosity of the melt where the force of viscosity depends on the gravitational force.
K
2 r2g Us Um , 9 v
(4.16)
where r is the radius of the sphere, g is gravitational acceleration, v is terminal velocity, U m is the density of the melt, and U s is the viscometer
crucible
insulation
spindle
temperature measurement Fig. 4.4. Rotational viscometer.
39
Mineral Wool
counterweight
falling sphere (Stokes’ Law) Fig. 4.5. Falling sphere.
density of the sphere. Figure 4.5 shows this method schematically. If the pattern is cylinder-shaped, then we have to consider the influence of the finiteness of the cylinder F and the finiteness of length K:
K
2 r2g F Us Um , 9 v K
(4.17)
the correction factors F and K can be calculated as follows: 3
5
F
r §r · §r · 1 2.104 s 2.09 ¨ s ¸ 0.95 ¨ s ¸ , r ©r¹ ©r¹
K
1 3.3
rs . h
(4.18)
(4.19)
where r s is the pattern radius and h is the pattern height. On the basis of scientific knowledge, we know that the movement of the sphere can be observed with X-rays, radiometer. It is also possible to use a counter balance which then enables the elevation of the sphere to be measur ed. 4.3
Surface tension
The molecules on the surface of the melt and r ight underneath it ar e influenced by the inter nal molecules with the r esultant rectangular to the surface and directed into the interior of the melt [16]. The thin upper layer of the melt is in a condition resembling a stretched elastic membr ane. The forces try to keep any par t of the upper layer in the tensioned condition. The upper layer exerts equal but opposite forces on its surrounding. This force which the molecules exert on each other is: 40
Physical Characteristics of Mineral Wool Melts
'F V 'l
(4.20)
Coefficient V is surface tension. 4.3.1 Surface tension of silicate melts When mea sur ing the sur fa ce tension of a melt in vacuum or in contact with a gas that contains dipolar molecules [16], different values a r e obta ined. T he differ ence is a r esult of accumulated dipolar molecules with different energy. On the surface of the melt, one-sided extension towards the interior is somewhat compensated. T her eby, t he sur face tension may change. T his phenomenon is essential for the melting process. The tension of the melt and its temperature are important as well. By increasing the temperature, the surface tension reduces. It is well known that the su r face tension influences the pr oduction and for m of glass. Accur ate knowledge of sur face tension of glass melts as a function of chemical str ucture would enable bett er contr ol over r efinement, foaming and r efr action corrosion in glass tanks. Understanding the variables that influence the sur f ace tension of glass and glass melts ca n contr ibute to improving the glass formation processes such as fibre drawing and mould form. A lot of information on different high temperatures of physical char acter istics of melts such as density, viscosity and sur face tension is already available. Based on chemical analysis, the surface tension value was indirectly determined in accordance with Kucuk’s equation [ 25] for calculat ion of sur face tensions V[mN/m] of silicate glass melts at 1400 °C:
V
271.2 1.48v > Li 2O @ 2.22v > K 2O @ 3.43v > Rb 2O @ 1.96v > MgO @ 3.34v > CaO @ 1.28v > BaO @ 3.32v >SrO @ 2.68v > FeO @ 2.92v > MnO@ 1.38v > PbO @ 2.86v > B2O3 @ 3.47v > Al2O3 @ 24.5v > MoO3 @ ,
(4.21) wher e v[X i O i ] is t he molar concentr ation of the oxides. T he r egr ession equa tion (4.21) was obtained on the ba sis of 350 different chemical compositions, and it excels in a high regression coefficient r 2 > 0.97 [25].
41
Mineral Wool
4.3.2 Methods for measuring surface tension of silicate melts The following methods are used for measuring the surface tension on the abutting surface: • classical measuring methods; • dynamic methods for measuring surface tension; • microtensometry. This division of methods is taken from Encyclopaedia of Surface and Colloid Science by J. Drelich, Ch. Fang and C.L. White [26]. Classical methods are used in chemical laboratories for research of abutting surfaces. Dynamic methods are applied when measuring ultra-low surface tensions (< 0.001 N/m). Microtensometry is used for research on micro-abutting surfaces or of micron drops which ar e ver y impor tant for r esear ch of nanomater ia ls. M ethods for measuring the surface tension can be divided into several groups: 1. Group: direct measuring of surface tension with micron scales (Wilhelmy plate, Du Noüya ring); 2. Group: direct measuring of surface tension on the surface of capillary pressure (maximum bubble pressure, growing drop); 3. Gr oup: levelling of sur face tension for ces and changeable volume (capillary rise, drop volume); 4. Group: measuring the fix drop volume and drop distortion on the basis of gr avitational influence (pendent dr op, sessile drop); 5. Group: measuring ultra-low surface tensions at drop distortion Table 4.5. Adequacy of methods for measuring the surface tension [26] Accuracy mN/m
Ade quacy for Surface Solutions
Ade quacy for Fluid-fluid System
Adequacy for Viscose Fluids
Adequacy for Fluid Metals
Commercial Chance s
Wilhelmy plate
~0.1
Limited
Good
Very good
Not recommended
YES
Du No ya ring
~0.1
Limited
Smaller accuracy
Not recommended
Not recommended
YES
0.1–0.3
Very good
Very good
Not recommended
YES
YES
Capillary rise
<<0.1
Very good
Very good, experimentally complicated
Not recommended
Not recommended
NO
Drop volume
0.1–0.2
Limited
Good
Not recommended
YES
YES
Pendent
~0.1
Very good
Very good
Not recommended
YES
YES
Sessile drop
~0.1
Good
Very good
Very good
YES
NO
Method
Maximum bubble
42
Physical Characteristics of Mineral Wool Melts
because of centrifugal forces (spinning drop, micropipette). Table 4.5 presents the adequacy of particular methods for measuring surface tension in different fluid–fluid systems. The data show that in the case of high viscose fluids and fluid metals, the sessile drop method is most appropriate. During the course of this section, we are going to concentrate on this particular method. As it tur ns out, the most appr opriate is the sessile dr op and pendent drop measuring method. For the calculation of surface tension, two formalisms are used [26]: 1 . Blaisdell’s formalism. T his equation considers the sessile drop (Fig. 4.6 shows the maximal diameter of the drop r e – equator) and the distance between the flat bottom and the top of the drop. The relation of both values is then entered into the empirical function F from which the surface tension can
h re Fig . 4.6. Blaisdell’s formalism of the sessile drop.
be calculated:
V
U U2 §h· F ¨ ¸ re2 g 1 . 2 © re ¹
(4.22)
2 . Dorsey’s f ormalism. After ha ving deter mined the largest diameters of height and length (2 r e ), we mark the tangents at a 45° angle on both sides of the drop form. Where these tangents t ouch the dr op for m, we calcula te the diameter (2r 45 ), Fig. 4.7. Sur face tension is then calculated with the following equation:
r45
h
re
Fig. 4.7. Dorsey’s formalism of the sessile drop.
43
Mineral Wool
V
§ 0.052 · 0.12268 0.0481 f ¸ re2 g U1 U 2 , ¨ © f ¹
(4.23)
where f is defined by the equation:
f
r45 h45 U1 U 2 . re
Surface tension can be measured from the profile of the drop by using the equation system and considering the La place equation. This model is taken from Arthur Adams [27]. The process of solving starts with the Laplace equation, which supposes the pr essure difference 'p across the boundar y surface because of surface tension and the radii of curvature R 1 and R 2 :
§ 1 1 · ¸. © R1 R2 ¹
'p V ¨
(4.24)
Within the drop or capillary which is positioned symmetrically to the ver tical axis, the pressure difference 'p can be expr essed as the function of gravitational acceleration, difference of drops’ density and the su r r ounding medium. T his pr essur e differ ence can be expr essed as: (4.25) ' p 'U gh , where h is the height of the drop. Combination of equations (4.24) and (4.25) is known as the Laplace–Young equation:
§ 1 1 · ¸. © R1 R2 ¹
'U gh V ¨
(4.26)
Height h is normally measured from the top of the drop (summit). The difference of densities ' U and the gravitational acceleration are known. V is the desired quantity. R 1 and R 2 are acquired from the drop profile which, however, is not a trivial solution. If we express the r adius of curvature in the x–y coor dinate system, we get for a dr op of height h in the dir ect ion of the y axis the following differential equation with no analytical solution:
§§
y"
· §
y'
··
'U gh V ¨ ¨ 2 3/ 2 ¸ ¨ 2 1/ 2 ¸ ¸ , © © (1 y ' ) ¹ © (1 y ' ) ¹ ¹
(4.27)
wher e y' = dy/dx and y'' = dy 2 /dx 2 . It can only be solved with numeric approximation. Since this is a differ ential equation, the appr oximation pr ocess is called the 44
Physical Characteristics of Mineral Wool Melts
integration of the Laplace–Young’s equation.
4.4
Computing algorithm for calculation of density, viscosity and surface tension of mineral wool melts
On the basis of the described algorithms for calculating the density, viscosity and surface tension of mineral wool melt, we can create a Microsoft Excel computer programme which can also be found in the following figure on pages 46 and 47. General instructions for using this programme are described in the following section [28,77].
45
Mineral Wool
SURFACE TENSION, VISCOSITY, DENSITY AND FIBRE THICKNESS OF SILICATE MELTS
INSTRUCTIONS i. In general Worksheet: SigmaEta Worksheet: FIBRES Hidden list: Vissigma and ro. Viscosity: from 1150 to 1550°C; Surface tension: |1450 °C; Density: from 1350 to 1800 °C. 0. Instructions for use: 1. Choose the worksheet SigmaEta. 2. Enter chemical composition into the worksheet SigmaEta. Move through cells with TAB. Chemical composition [ must be in weight %. Entry cells from E10 to E26 are coloured with
[ % Li 2O=
E10
K 2O=
E11
Rb2O=
E12
MgO=
E13
CaO=
E14
BaO=
E15
SrO=
E16
FeO=
E17
MnO=
E18
PbO=
E19
B2 O3 =
E20
46
.
Physical Characteristics of Mineral Wool Melts Al 2O 3 =
E21
MoO 3=
E22
SiO 2=
E23
Na2 O=
E24
TiO 2=
E25
Fe 2O 3 =
E26
3. Enter the melt temperature into the worksheet SigmaEta. Enter the melt temperature into cell K9. K9 °C
MELT TEMPERATURE T=
Melt temperature K9 should not exceed the temperature in cell K19. 4. The calculation results are in cells: K10, K11, K12, K13: viscosity=
K11
deka Pa s
surface tension=
K12
mili N/m
density=
K13
kg/m 3
47
Mineral Wool
5 DIMENSIONAL ANALYSIS Dimensional analysis is thoroughly and with rich references described in Zlokarnik’s book [29]. Based on this book, the following presentation starts with main characteristics of dimensional analysis: • Reduction of the number of parameters required to define the problem; • Reliable scale-up of desired operating conditions from the model to the fill-scale plant; • A deeper insight into the physical nature of a process; • Flexibility of the selection of parameters and their reliable extrapolation within the range covered by dimensionless numbers. 5.1
Foundations of dimensional analysis
In his book, Zlokarnik states the following fundamental characteristics of dimensional analysis [29]: • Physical quantities and their mutual relationships; • Consistency of secondary units and invariance of physical relationships; • Physical dimensions, system of dimensions, dimensional constants; The dimensions are not inherent properties of physical quantities, but merely expressions of laws which define them; • The dimensional matrix and its linear dependence. Our example supposes the pressure difference Δp = ρ ·g·h across the boundary surface of the sessile drop because of surface tension σ and radii of curvature R 1 and R 2 of the sessile drop. We begin by assembling the dimensional matrix: We see that rank r of this matrix is 3, therefore we obtain three dimensionless numbers which are: 48
Dimensional Analysis
'U
g
h
ı
R1
R2
M
1
0
0
1
0
0
L
-3
1
1
0
1
1
T
0
-2
0
-2
0
0
'U
g
h
ı
R1
R2
Z1=M
1
0
0
1
0
0
Z2=3M+L
0
1
1
3
1
1
Z3=2Z2+T
0
0
2
4
2
2
'U
G
h
ı
R1
R2
Z1=M
1
0
0
1
0
0
Z4=-Z3/2+Z2
0
1
0
1
0
0
Z4=Z3/2
0
0
1
2
1
1
31
V U g h
2
;
32
R1 ; h
33
R2 h .
The solution is found in this form:
31
f ( 32, 33) .
The solution is equivalent to the Young’s equation (4.26). If one of the rows is simply any sum of two other quantities, then it can be descr ibed as a linear combination of these two and is independent of them. In this case, the rank of the matrix is lower than the number of rows it contains. The number of elements in the ma in diagonal which do not disappear but for m a continuous sequence is rank r, of the matrix. • The 3 theorem: T his theor em for ms the basis f or the discussion of physical relationships within the framework of the theory of similarity. Every physical relationship between n physical quantities can be reduced to a relationship between m = n–r mutually independent dimensionless gr oups, wher eby r stands for the r ank of the dimensional matrix, made up of the physical quantities in question and generally equal to the number of the basic quantities contained in them [29]. 49
Mineral Wool
dimensional matrix unity matrix xi ª1 « 1 « « 1 « 1 « «¬ 1 r
residual matrix xj
º » » » » » »¼
m n
Fig. 5.1. Dimensional matrix [29].
T he classif ication of the physical quantities involved in the process in consideration is illustrated by the following dimensional matrix [29]: 5.1.1 Full set of dimensionless numbers The relevance list represents the starting point for the determination of the complete set of dimensionless number s. T he process uses matrix calculation and consists of the following steps [29]: – construction of the dimensional matrix; – application of the Gaussian algorithm in order to determine rank r of the matrix; – formation of the unity matrix; – formation of dimensionless numbers; – possible transformation of formed dimensionless numbers to provide more common expressions. Relevant physical variables that define the target quantity can be divided into three groups: 1. geometrical characteristics 2. material (physical) characteristics 3. process variables T he pr ocedur e for constr ucting the dimensional matr ix and deter mining t he complete 3 set can be demonstr ated with the following example: Fluid dispersion on the rotating wheels. In this example the fluid is flowing onto two rotating wheels. Dia met er s R and widths B of both wheels ar e the s ame. T he number of wheel rotations, however, is Z1 and Z2 . The volume flow 50
Dimensional Analysis
of the fluid is q V and the volume air flow that blows across the wheels is q VG . Physical properties of the fluid and air are: densities U and U G , viscosities K and K G , and surface tension between liquid and air V. The dispersion process is isothermal. The target function is to determine the diameter of the droplet d v . • Target variable: d v • Geometric parameters: R, B • Physical properties: U , V, K , U G , K G ; • Process parameters: Z 1 , Z2 , q V , q VG ; • Dimensional system: (M, L, T); • n = 12; • r = 3.
m
n r 12 3 9
reservoir of fluid
fluid jet
w flo low air airf fil m of
Z2
Z1
id flu
droplets rotating wheels Fig. 5.2. Fluid dispersion on the rotating wheels.
51
Mineral Wool
• Dimensional system (M, L, T):
ȡ
R
Z1
K
V
qV
B
qVG
Z2
KG
UG
dv
M
1
0
0
1
1
0
0
0
0
1
1
0
L
-3
1
0
-1
0
3
1
3
0
-1
-3
1
T
0
0
-1
-1
-2
-1
0
-1
-1
-1
0
0
Z1 = M Z2 = 3M+L Z3 = -T ȡ
R
Z1
K
V
qV
B
qVG
Z2
KG
UG
dv
Z1
1
0
0
1
1
0
0
0
0
1
1
0
Z2
0
1
0
2
3
3
1
3
0
2
0
1
Z3
0
0
1
1
2
1
0
1
1
1
0
0
• Dimensionless numbers are:
N1
K 2
U R Z1
;
N2
V ; U R3Z12
N3
qV ; R 2Z1
N4
B ; R
N5
qVG ; R 3Z1
N6
Z2 ; Z1
N7
KG ; U R 2Z1
N8
UG ; U
N9
dV ; R
In this manner we have obtained nine dimensionless numbers. The regression equation can be written as follows:
N9
dV R
f ( N1 , N 2 , N 3 , N 4 , N 5 , N 6 , N 7 , N8 )
• Readjustment of dimensionless numbers: The readjustment enables to obtain dimensionless numbers that are more known in the specialised literature. Walzel [30] engaged in the 52
Dimensional Analysis
r esearch of liquid atomisation by film splitting. The influencing parameters and characteristic dimensionless number s for atomisation of liquids with cam rollers are: U , K , V , R, Z, S 0 , R S :
dV R
dV * * Z , qV , Z , R / S0 , RS / R R
dV ( M 3 , M 2 , M 1 , R / S0 , RS / R ); R
The influence of air on drop formation is neglected. For this reason, some acquired dimensionless numbers are going to be transformed into numbers that are known from the specialised literature: M 1 , M 2 and M 3 [30]. M1
N12 N2
K2 ; RV
M4
N4
B ; R
M5
N3 N6
qV ; qVG
M7
N1 N8
K ; KG
M8
N9
UG ; U
M2
N3 1 N2 N4
qV B
53
U ; VR
1 N2
Z R 3/ 2
M6
N7
Z2 ; Z1
M9
N9
dV ; R
M3
U ; V
Mineral Wool
6 FIBERISATION PROCESS A schematic presentation of the fiberisation process on a doublewheel spinning machine is given in Fig. 6.1 [21,31]. The molten material flows over a system of adjustable channels onto the first spinning wheel. At the impingement point of the free jet and the first spinning wheel, a thin melt film is formed which is transferred via the droplet non-uniform flow onto the second wheel. Melt droplets – connected by surface tension and viscous for ces with the melt film on the spinning wheel – ar e dr awn out of the film and cylindrically-shaped mineral wool fibres are formed. These fibres are picked up by a coaxial air flow which emanates through coaxial nozzles placed at the perimeter of the spinning wheels. The coaxial
reservoir of melt
melt jet
reservoir adjustment
a
w folwo aiirrfl Z1
fib res
ilm tf el m
Z2
rotating wheels Fig. 6.1. Schematic presentation of the fiberisation process on a double-wheel spinning machine.
54
Fiberisation Process
air flow transforms the radial motion of fibres into axial motion, and the fibres are driven into the collection chamber where the primary layer of mineral wool is formed. 6.1
Dimensional analysis of the fiberisation process on a double-wheel spinning machine
The centrifugal process of mineral wool fiberisation depends on the parameters important for rotational fluid spraying, where the fluid flow falls in a coaxial, cylindrically-shaped form onto the first wheel. The parameters which influence the fiberisation process of the melt that is sprayed on the selected spinning wheel are [21,31]: • melt density: ρ (kg/m 3 ); • dynamic viscosity of the melt: η (kg/(ms)); • surface tension of the melt: σ (kg/s 2 ); • radius of the first wheel: R (m); • width of the wheel B (m); • rotational speed of the first wheel: ω 1 (rad/s); • rotational speed of the second wheel: ω 2 (rad/s); • melt flow rate: q V (m 3 /s). Physical properties ρ , η , σ are considered at melt temperature T L . Very important are also the physical properties of air: • air density: ω G (kg/m 3 ); • dynamic viscosity of air: η G (kg/(ms)); Physical properties of air are considered at air temperature T G . Very important are also temperature differences between melt and air ΔT = T L–T G . The thickness of a mineral wool fibre d V depends also on the air flow rate q VG . According to section 5, we are going to form dimensionless numbers and the regression model. • The target variable: d v • Geometric parameters: R, B • Physical properties: ρ , σ , η , ρ G, η G ; • Process parameters: ω 1 , ω 2 , ΔT, T L , T G, q V , q VG ; • Dimensional system: (M, L, T, Θ); • n = 15; • r = 4.
m
n r 15 4 11
• Dimensional system (M, L, T, Θ):
55
Mineral Wool ȡ
R
Z1
TL
K
V
qV
B
'T
qVG
M
1
0
0
0
1
1
0
0
0
0
0
L
-3
1
0
0
-1
0
3
1
0
3
0
T
0
0
-1
0
-1
-2
-1
0
0
-1
-1
4
0
0
0
1
0
0
0
0
1
0
ȡ
R
Z1
TL
K
V
qV
B
'T
Z1
1
0
0
0
1
1
0
0
Z2
0
1
0
0
2
3
3
Z3
0
0
1
0
1
2
1
Z4
0
0
0
1
0
0
0
UG
TG
dv
1
1
0
0
-1
-3
0
1
-1
0
0
0
0
0
0
1
0
qVG
Z2
KG
UG
TG
dv
0
0
0
1
1
0
0
1
0
3
0
2
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
Z2
KG
Z1 = M Z2 = 3M+L Z3 = -T Z4 = 4
• Based on the dimensional analysis [29], char a cter istic dimensionless numbers N can be found:
N1
K 2
UR V
;
N2
V ; U R 3Z12
N3
qV ; R 2Z1
N4
B ; R
N5
'T ; TL
N6
qVG ; R 3Z1
N7
Z2 ; Z1
N8
KG ; U R 2Z1
N9
UG ; U
N10
TG ; TL
N11
dV ; R
We can a sc er ta in tha t the a cqu ir ed dimensionless number s a r e similar to those numbers which were acquir ed when dealing with fluid disper sion on the r otating wheels (section 5) . T hey ar e expanded due to heat transfer between melt and air. • Readjustment of dimensionless numbers: By combining basic dimensionless numbers according to Walzel [30], the following characteristic dimensionless numbers can be defined: 56
Fiberisation Process
M1
N12 N2
K2 ; U RV
M2
N3 1 N2 N4
M4
N4
B ; R
M5
N5
'T ; TL
M7
N7
Z2 ; Z1
M8
N1 N8
K ; KG
M 10
N10
M 11
N11
TG ; TL
qV B
U ; VR M6 M9
M3
1 N2
N3 N6
qV ; qVG
Z R 3/ 2
U ; V
UG ; U
N9
dV ; R
• The basic aim of the regression model, which is presented in [21], is to determine the diameter of mineral wool fibres d v . General prediction of the regression model:
M 11
dV R
dV M 1 , M 2 , M 3 , M 4 , M 5 , M 6 , M 7 , M 8 , M 9 , M 10 ; R
(6.1)
Simplification of the regression model: When performing the experiment (constant geometry), some simplifications will be taken into consideration: • In this case B = const . and M 4 is not impor tant in the analysis. • Temper a tur e T G is included in the t emper atur e differ ence 'T = T L –T G , M 10 is expressed as number M 5 . N12 N2
M1
M7
N7
K2 ; U RV
Z2 ; Z1
M2
N3 1 N2 N4
qV B
M5
N5
'T ; TL
M8
N1 N8
K ; KG
M 11
N11
U ; VR
M3
M6 M9
N9
N3 N6
1 N2
Z R 3/ 2
U ; V
qV ; qVG
UG ; U
dV ; R
• We get the equation:
M 11
dV R
dV M1, M 2 , M 3 , M 5 , M 6 , M 7 , M 8 , M 9 ; R
(6.2)
If we consider the constant geometrical parameters, we have 57
Mineral Wool ȡ
R
Z1
TL
K
V
qV
'T
qVG
Z2
KG
UG
dv
Z1
1
0
0
0
1
1
0
0
0
0
1
1
0
Z2
0
1
0
0
2
3
3
0
3
0
2
0
1
Z3
0
0
1
0
1
2
1
0
1
1
1
0
0
Z4
0
0
0
1
0
0
0
1
0
0
0
0
0
only 13 variables. The fibre thickness diameter is the function of the following variables: d v = d v ( U , R, Z1 , T L , K , V , q V , 'T, q VG , Z2 , K G , U G ) m = n–r =13–4 = 9 T he fibr e thicknes s diameter can be deter mined with nine dimensionless numbers. • In our model we want to keep the first three numbers M 1 , M 2 , M 3 and also consider the mechanism of jet disintegr ation. Lubanska [32] investigated the droplet formation in the gas jet: 1/ 2
d50
ª§ q · Q º C1 «¨1 m ¸ » We1/ 2 D , ¬© qmG ¹ QG ¼
where d 50 is the average diameter of melt droplets, q m is the mass flow of the melt, q mG is the mass flow of gas (air), Q and Q G are the kinematic viscosities of the melt and the gas, We is the Weber number, D is the nozzle diameter and C 1 is the nozzle constant, respectively. The influence of the air jet – induction on the diameter of melt
§
droplets – can be expressed with: ¨ 1 the combination of the numbers:
Lu
ª§ qm · Q º «¨ 1 ¸ » ¬© qmG ¹ Q G ¼
©
qm · Q . This term is ¸ qmG ¹ Q G
ª¬ 1 M 6 M 7 M 8 M 9 º¼
• In our model, we wish to keep the Lubanska–Walzels model: ¾ char acteristic dimensionless r otational speed number :
31 ¾
M3
Z1 R 3/ 2
U , V
characteristic dimensionless flow
58
Fiberisation Process
number: 3 3 ¾
U ; VR
Z
K2 ; URV
M1
characteristic dimensionless temperature number:
35 ¾
qV B
characteristic dimensionless viscosity number:
34 ¾
qV * M 2
T* M5
'T ; TL
characteristic dimensionless flow number:
ª§ qm · Q º «¨ 1 ¸ » ª¬ 1 M 6 M 7 M 8 M 9 º¼ . ¬© qmG ¹ Q G ¼ Instead of dimensionless number M 7 , we introduce, according to P. Walzel [30], the number 3 2 : • characteristic dimensionless rotational second speed number: 36
Lu
§ qV U · Q ¨1 ¸ © qVG UG ¹ QG
32
Z2 R 3/ 2
U . V
Accor ding to the r egression method, we got the equation which predicts the thickness of mineral wool fibres:
dV
a0 31a1 3 a22 3 3a3 3 a44 3 5a5 3 6a6 ,
(6.3)
where a i (i = 0 to 6) are the parametric constants of the multiple regression model. If we compare the equation (6.3) with the equation (6.1), we can see that the number of dimensionless number s M i (i = 1,2,3,5,6,7,8,9) on the right side of equation (6.2) is still 8:
M 11
dV R
dV M1 , M 2 , M 3 , M 5 , M 6 , M 7 , M 8 , M 9 . R
(6.4)
6.1.1 Experimental results T he exper iments wer e per for med on a double-wheel spinning machine in real production process, Fig. 6.1 [21]. The diameter of both cylindrically-shaped wheels, which were 120 mm wide, was 385 mm. The experiments, 36 in total, carried out in two different seasons (summer and autumn), were performed at varying air mass flow q mG a nd r ota tiona l speed of both wheels, Z 1 and Z 2 . T he 59
Mineral Wool
above-mentioned variables were independent process variables and their selection was optional. During the variation of each parameter, the other parameters remained constant. The mass flow of the melt q m , its temp er atur e T, chemical composition, and a mbient parameters, all of which could not be selected, and which affected the experiment, were measured. In the presented exper iments, the distance between the axes of both wheels was not modified. At each repetition, samples of melt and mineral wool were taken. T he viscos ity and density of melt samples wer e mea sur ed, and thickness of mineral wool fibres was determined. Built-in inductive meter s measured the rotational speed of the spinning wheels. The rotational speed of the first wheel varied in the range fr om 1800 min –1 to 5500 min –1 , and that of the second wheel in the r ange fr om 2 000 min –1 to 530 0 min –1 . D ur ing the exper iment s, the r atio between both r otational speeds was approximately constant. The air flow rate in the spinning machine was determined directly by measur ing the velocity field with a vane anemometer, and indirectly on the basis of the pressure difference on the filter of the collection chamber, which directly depends on the air flow rate of the spinning machine. During the exper iments, the measured air flow velocities in the spinning machine were 1.2 m/s minimum, and 2.2 m/s maximum. T he mass flow of the melt was measur ed with t he aid of computer weighing of input materials in the cupola furnace. The melt temper atur e in the jet was measured with an optical pyr ometer. T his instr ument wa s dir ected at the axis of the jet. Time-aver a ged temper a tur e values wer e r ecor ded f or fur ther ana lysis. The aver age temper atur e of the melt impinging on the wheel was 1450 o C. Following ambient par ameter s wer e measur ed dur ing the experiments: ambient air temperature, ambient pressure and relative air humidity. In the laboratory, the fibre diameters of mineral wool samples were deter mined with the aid of computer microscopy. Dia meter values var ied between 4.4 and 7.5 mm. T he descr iption of this method can be found in section 8. 6.1.2 Statistical analysis of experimental results Using experimental data, the parameters of the regression model and equation (6.1) wer e deter mined by multiple r egr ession analysis. 60
Fiberisation Process Table 6.1. F-test results of agreement between the model and the measured values Source
Degree of Fre edom
Sum of Squares
Mean Square
F statistics
Regression
6
1206.3391
201.0565
2211.11
Residual
30
2.7279
0.09093
Total
35
21.8051
Prob > F
<0.0001
Table 6.2. Regression model parameter values according to equation (6.1 ) along with the resu lts of the t-test
Values Prob > |t|
a0
a1
a2
a3
a4
a5
a6
1
–0.358
–0.245
2.189
–0.255
–36.753
0.144
0.034
0.128
0.049
0.002
0.000
0.151
Agreement between the measured and calculated fibre par ameter values was examined with the F-test [15 ]. T he test r es ults ar e presented in Table 6.1. The F-test estimates the hypothesis that regression is not significant. The probability that this hypothesis is valid was less than 0.0001, hence the r egr ession was ver y significant. Good agreement between the model and the measured values of fibr e par a meter s was also conf ir med by the high va lue of the multiple cor r elation coefficient r 2 = 0.88, which indicates good quality of the regression fitting and the measured values. Values of the regression model parameters are presented in Table 6.2. Their significance was checked with the t-test. The test results pr esented in Table 6.2 show a significant influence of all parameters a 1 to a 6 . The results of the comparison between the measured parameters of fibres and the calculated ones on the basis of a six-parametric model are shown in Fig. 6.2. In Figure 6.3, 95 % confidence levels for model approximation are given for the six-parametric model. 6.2
Simulation of chemical composition’s influence on fibre thickness
T he availability of the r egr ession model coefficients ma kes it 61
Mineral Wool
Fibre thickness (predicted, measured)
Pm
8.0 2
r 6-param=0.88
7.5 7.0 6.5 6.0 5.5 5.0
6-parametric model measured
4.5 4.0 4.5
5.0
5.5
6.0
6.5
Fibre thickness (measured)
7.0
7.5
Pm
Fibre thickness
Pm
Fig . 6.2. Comparison between experimentally measured fibre diameters and the valu es predicted with the aid of statistical analysis. 10,0 9,5 9,0 8,5 8,0 7,5 7,0 6,5 6,0 5,5 5,0 4,5 4,0 3,5 3,0
95 % confidence fitting levels 6-parametric model measured
0
2
4
6
8
2
r 6-param=0.88
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 Number of experiment N
Fig . 6.3. Comparison between experimentally measured fibre diameters and the predicted values of regression model with 95 % confidence fitting levels.
possible to simulate the calculation of mineral wool fibre thickness by changing the chemical composition of input raw materials. The regression equations for the calculation of: density, equation (4.6); 62
Fiberisation Process Table 6.3. Predicted chemical compositions of silicate melts in weigh t % No.
K2 O %
Na 2O %
MgO %
CaO %
Fe 2O3 %
TiO2 %
MnO %
Al2O3 %
SiO2 %
1
0.5
2.0
11.5
23.0
3.6
1.3
0.1
19.5
38.5
2
0.5
2.0
11.5
23.0
3.6
1.3
0.1
14.5
43.5
3
0.5
2.0
11.5
23.0
3.6
1.3
0.1
24.5
33.5
4
3.0
2.0
6.5
23.0
6.1
1.3
0.1
19.5
38.5
5
0.0
0.0
11.5
23.0
6.1
1.3
0.1
19.5
38.5
6
0.5
2.0
16.5
23.0
3.6
1.3
0.1
19.5
33.5
7
0.5
2.0
16.5
18.0
0.1
1.3
0.1
19.5
38.5
Table 6.4. Simulated calculation of density, surface tension and viscosity of silicate melts based on data from Table 6.3 at 1450°C Compositions
1
2
3
4
5
6
7
U, kg/m3
2617
2606
2628
2592
2659
2644
2610
Kdeka Pa s
10.94
11.41
10.53
15.34
8.57
5.20
9.03
440
425
455
430
441
451
432
V miliN/m
viscosity, equations (4.10), (4.13), (4.14); and sur face tension, equation (4.21), of silicate melts as a function of temperature were taken into account. The chemical compositions of the silicate melts pr esented in Table 6.3 were chosen for the simulation [21]. T he chemical composition 1 in Tab le 6.3 r epr esented the basic composition; it was determined on the basis of the analysis of the samples obtained by the experiment described in section 6.1.1 in a real mineral wool production process. Table 6.4 shows the influence of individual chemical compositions of silicate melts on density, viscosity and surface tension at 1450°C. When simulating the influence of chemical composition on the size of mineral wool fibres, the constants of the regression model, as gathered in Table 6.2, were taken into account in all calculations. Other quantities (melt temperature, rotational speed, etc.) were the same as in the experiment described in section 6.1. The obtained results are shown in Fig. 6.4. It is evident from Fig. 6.4 that chemical compositions 4, 6 and 63
Mineral Wool 5 composition 2; composition 4; composition 6;
Pm
4
composition 3; composition 5; composition 7.
3
'dV=dVi-dV1
2 1 0 -1 -2 0
2
4
6
8
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 Number of experiments
Fig . 6.4. Influence of chemical compositions on the size of mineral wool fibres.
7 affect the size of mineral wool fibres, whereas the influence of chemical compositions 2, 3 and 5 is similar to that of the basic chemical composition 1. The above simulations provide proof that changes of SiO 2 and Al2 O 3 fraction within ±5 % in combination with other oxides can have a higher or lower influence on fibr e thickness. When the influence of chemical compositions on the magnitude of dimensionless numbers in equation (6.3) is analysed, the logical conclusion is that number 3 4 , containing substance characteristics, U K V , has by far the str ongest influence. T he inf luence of chemical composition is also apparent in numbers 3 3 and 3 6 . The relative errors of chemical composition’s influence on the size of dimensionless numbers with respect to the composition 1 are also shown in Fig. 6.5. T he obtained results have confir med the pr oposed r egr ession model for pr edicting fibr e thickness on a double-wheel spinning machine. The model demonstrates good agreement with measured values which is as well suppor ted by a high multiple correlation coefficient. The knowing of the constants of the regression model also makes it possible to carry out simulations of mineral wool fibre thickness by changing the chemical composition of input r aw materials. All the measur ed quantities featuring in the model can easily be measured in the experiment. By using the model in a real production process, essentially better repeatability of product quality 64
er
%
Fiberisation Process 60 55 50 45 40 35 30 25 20 15 10 5 0 -5 -10 -15 -20
composition 2; composition 4; composition 6;
a1
31
composition 3; composition 5; composition 7.
a2
32
a3
33
a4
34
a5
35
a6
36
Dimensionless 3 number
Fig. 6.5. Simulation of the influence of chemical composition on the magnitude of characteristic dimensionless numbers in equation (6.3).
can be achieved. This model can also be designed for processes on a four -wheel spinning ma chine, which is mor e oft en used in practice and is described in the following section. 6.3
Regression model of mineral wool fibres on a four-rheel spinning machine
The quality of the final product on the microscale depends on the str uctur e of fibr es and on the p r opor tion of solidified shots in mineral wool. The fibre structure is characterised by its thickness (diameter), its length and the variation of both respective quantities. Material that has not been transformed into fibres remains in the form of solidified shots, which arise from an incomplete fiberisation process [3,4]. In [3] it was experimentally determined that solidified shots are principally formed by splashing of the melt jet on impact with the first wheel due to inappropriate impingement position of the jet. T he regr ession model for a two-wheel spinning machine was briefly described in section 6.1. For the development of a regression model for pr imar y layer evalua tion on a four -wheel spinning machine, the same char acteristic dimensionless number s will be used and s ome will be added. T he par ameter s influ encing the pr ocess of miner al wool pr oduction on the selected wheel of 65
Mineral Wool
reservoir of melt
melt jet 'M
reservoir adjustment ai
impingement
w lo w r f irflo a
air
R1
Z
flo
R2
Z
w R3
Z R4
Z
rotating wheels Fig . 6.6. Continuous measurement of jet position on the first spinning wheel.
spinning machine ar e: melt density U , melt dynamic viscosity P , sur face tension V , wheel radius R, width of the melt film on the wheel B, rotational speeds of the four wheels Z and melt volume flow q V . T he melt with mass flow q m and temper atur e T L measured on the surface of the melt jet is falling on the first wheel of the fourwheel centrifuge, as shown in Fig. 6.6. The repeatability of the process depends on the repeatability of the impingement position of the jet (wheel 1) at angle M as shown in Fig. 6.6. In this four-wheel centrifuge, the radii of all wheels are the sa me: R 1 =R 2 =R 3 =R 4 =R as well as the widths of all wheels B 1 =B 2 =B 3 =B 4 =B. However, the rotational speeds of the four wheels Z1 , Z2 , Z3 and Z4 differ. We a lso have two differ ent air flows: volume rate of outlet flow q VOutlet and volume rate of suction flow q VSuction . The outlet flow is divided into left q VOutletL and right flow q VO utletR which enter the centr ifuge. T he air inlet temperatures of left and right outlet flow, T ol and T od , are basically nearly the same. Because of the temper atur e difference between the air flow and the melt flow, an intensive hea t transfer occur s. The suction air flow that enters the collection chamber with temperature T sucti on and directs the flow of formed fibres towards this chamber also plays an important role. In the process of fibr e for mation in the fourwheel centrifuge, the binder is injected with volume flow q Vbin der and 66
Fiberisation Process
temperature T binder . Because the centrifuge wheels have a great heat loa d, they have to be cooled by water with volume flow q V and cooling temper atur e T hl . T he intensive hea t and mass t r ansfer between the fluids cause the air leaving the centrifuge to heat up to temperature T can . This temperature depends on mass flows and on the inlet temperatures of airflows, melt, cooling water and binder. Since the inlet suction flow has the temperature of the surrounding air, temperature T can depends on the conditions of the surroundings (ambient temper atur e T o , amb ient pr ess ur e p o and r elative air humidity M ). As we have already established in the case of fibre formation in the two-wheel centrifuge, the following thermodynamic and physical characteristics of fluids (air, melt, water, binder) are very important: density, viscosity, surface tension and specific heat. On the basis of the analogy with the two-wheel centrifuge, we will consider the following characteristic dimensionless numbers: • The characteristic dimensionless numbers of rotational speeds of all wheels: 311
Z1 R 3/ 2
U ; 312 V
Z2 R 3/ 2
U ; 313 V
Z3 R 3/ 2
U ; 314 V
Z2 R 3/ 2
U ; V
• The characteristic dimensionless number of melt volume flow:
33
qV B
U RV
qm B
1 ; U RV
• The characteristic dimensionless viscosity number:
34
3 2I 3 II
K2 ; VUR
• The characteristic dimensionless temperature number:
3 51
TL TOl , 3 52 TL
TL TOd , TL
wher e T L is t he melt temper atur e and T Ol and T Od the air temperatur e; • The characteristic dimensionless number of volume flow ratio:
36a
§ qm ¨1 © qmG
· Q ¸ ¹ QG
§ · Q qm ¨1 ¸ , © qVodLUodL qVodDUodD qVodsesUodses ¹ QG
where mass flow of air q mG is the sum of outlet mass flows (left and r ight) and of suction flow, and Q G and Q a r e kinematic viscosities of air and melt flow; 67
Mineral Wool
• The characteristic dimensionless number of melt flow impact position:
37
'M ,
where ' M is the distance between the impingement point of the melt jet and the vertical line of the first wheel axis. 6.3.1 Regression model of fibre formation in a fourwheel spinning machine On the basis of experience with the regression model of the twowheel spinning machine, the model was extended to a four-wheel spinning machine. Besides the above descr ibed dimensionless number s, such char acteristic dimensionless number s wer e added that take heat flows in the process of mineral wool primary layer formation into consideration, and numbers that consider the ratios of mass flows: • The characteristic dimensionless numbers of heat flows are:
3 81
qVblowL UblowL cpblow tblowL qVblowR UblowR cpblow tblowR ; qm cp t L
3 82
qVsuck Usuck cpsuck tsuck qVsuck Usuck cpsuck tambient = ; qm cp t L qm cp t L
3 83
qVbinder Ubinder cpbinder tbinder qVbinder Ubinder cpbinder twaterHL = ; qm cp t L qm cp t L
3 84
qVwaterHL UwaterHL cpwater t waterHL , qm cp t L
where 3 81 is the ratio between the heat flows of outlet flow and the melt, 3 82 is the ratio between the heat flows of suction flow and the melt, 3 83 is the ratio between the heat flows of phenol solution and the melt, and 3 84 is the ratio between the heat flows of cooling water and the melt; cp is the specific heat of the melt and t is temperature in °C. • The dimensionless number of fluid flows: The dimensionless number 3 62 is defined by the ratio between the sum of mass flow of air, mass flow of phenol (binder) solution and the mass flow of the melt 68
Fiberisation Process
3 62
qVblowUblow qVsuck Usuck qVbinder Ubinder qm
• The dimensionless temperature number: The dimensionless number 3 9 is defined by the difference of temper atur es between the melt temper atur e T L and t he air temper atur e in the channel T c an divided by t he absolute temperature of the melt:
39
TL Tcan . TL
The target function of fibre thickness can be written in parametric form with the regression model as:
dV
a3 h3 a1 a2 a4 e1 e2 h1 h2 h4 a0311 312 313 314 3 3c1 3 d41 3 51 3 52 3 61f1 3 62f2 3 7g 3 81 3 82 3 83 3 84 3 i9 (6.5)
where nine gr oups of dimensionless numbers are considered. The left side of the equation represents the measured fibre thicknesses of mineral wool. 6.3.2
Experimental results
The experimental set-up The experiments were performed on a four-wheel spinning machine in production. The schematic of the four-wheel spinning machine is presented in Fig. 6.6. The experiments, 61 in total, were performed by varying the air mass flow q mG (outlet flow and suction flow), the rotational speed of wheels Z1 , Z2 , Z3 , Z4 and the volume flow of binder. T hese wer e independent pr ocess var iables and their selection was optional. During the variation of each parameter, the other parameters remained constant. The mass flow of the melt q m , its temperature T, chemical structure, the melt flow impact position of the jet on the first wheel and ambient parameters all of which could not be selected and which influenced the exper iment wer e measured. At each operation point, samples of melt and successive images of the primary layer of mineral wool were stored. The rota tiona l speed of wheels was va ried in the r egion fr om 100 % to 60 %. The air flow rate was determined on the basis of the pressure difference on the nozzle of the spinning machine. The impact pos ition of the melt flow against the fir st wheel was measured with the aid of computer visualisation equipment [3]. The mass flow of the melt was measured with mass scales in regular 69
Mineral Wool
time intervals. The melt temperature in the jet was measured with the optical pyrometer. The instrument was directed towards the jet axis. The average temperature of the melt impinging on the wheel was 1448°C. The temperatures of the air flow, the binder flow and cooling water were measured with thermocouples and Pt-resistance thermometers. The following ambient par ameters wer e mea sured during the experiment: ambient air temperature, ambient pressure and relative air humidity. 6.3.3 Statistical analysis of experimental results Ba sed on the exper iments and multiple r egr ession analysis, the parameters of the regression model are set in the following equation: h3 a1 a2 a4 c2 d1 h1 h2 h4 a0 311 312 314 3 32 3 41 3 61f1 3 62f2 3 7g 3 81 3 82 3 83 3 84 3 i9 .
dV
(6.6)
T he r egr ession analysis gives us the significance of impor tant dimensionless numbers and the values of their coefficients which are assembled in Table 6.5. We can conclude that only 13 dimensionless numbers significantly influence t he quality of fibr e thickness. Other dimensionless number s ar e negligible. T he multiple r egr ession coefficient r 2 according to the model of equation (6.6) was r 2 =0.817. This speaks for good correlation between the model and the measured results. Comparison of calculated and measured results is shown in Fig. 6.7. 2
r 12-param=0.817
Fibre thickness
Pm
7
6 measured model
5 5
6
7
Fibre thickness
Pm
Fig. 6.7. Regression model of mineral wool fibre thickness on the four cen trifuge wheels. 70
Fiberisation Process Table 6.5. Significance of dimensionless numbers
6.4
Variable
Coefficients
t-test
Significance
Range of Significance
a0
0.2070
–0.832
0.411
IX.
3 11
–1.8086
–2.600
0.013
IV.
3 12
1.6869
2.375
0.023
VI.
3 14
–0.0503
–0.533
0.597
XII.
3 32
–3.3113
–3.174
0.003
III.
3 41
0.0313
0.668
0.508
X.
3 61
–2.6344
–0.525
0.603
XIII.
3 62
7.7906
0.964
0.341
VIII.
37
0.0440
0.653
0.517
XI.
3 81
–0.0031
–0.165
0.870
XIV.
3 82
0.0970
3.271
0.002
II.
3 83
–0.3662
–1.966
0.056
VII.
3 84
0.7025
4.070
0.000
I.
39
–5.3521
–2.555
0.015
V.
Cooling of glass fibres
For a better understanding of the fiberisation process in addition to the presented phenomenological relations, it is also appropriate to present the dynamic and thermodynamic laws of heat transfer in the process of fibre formation [33]. Let us suppose that a fibre with mass m, volume V, surface A, specific heat at JGa constant pressure cp and temperature T is moving with velocity w . If this fibr e enter s the air flow which ha s the JG velocity U and temperature T a (TzT a ), the boundary layer is formed around the surface of the fibre. Because of the relative movement of the fibre according to the surrounding air flow, only convective heat transfer prevails.
71
Mineral Wool
w (m c p T ) D A (T Ta ) , (6.7) wt wher e D is the convective hea t tr ansfer coefficient. In the melt spinning process of inorganic melts where extrusion temperatures reach 900–1500 K, the contribution of radiative heat tr ansfer is considerable. The apparent heat transfer for radiation Q r is: (6.8) Qr H V A ((T 273.15) 4 (Tamb 273.15) 4 ) , where H is emissivity, H is the Stefan–Boltzmann constant and T amb is the absolu te ambient sur fa ce temper atur e and T is fibr e temper at ur e in °C. If the mater ial and ther modynamic cha r acter istics of a miner al wool fibr e ar e constant a nd if we consider r adiation, then equation (6.7) is tr ansfor med into an ordinary differential equation with constant coefficients:
HV A dT D A (T Ta ) ª(T 273.15) 4 (Tamb 273.15) 4 º¼ 0 .(6.9) dt m cp m cp ¬ Convective heat transfer coefficient D can be expressed with the aid of Nusselt number Nu, which is dependent on the heat conductivit y of air O a and the char acter is tic length (cylinder diameter) of a fibre d:
Nu
D d Oa .
(6.10)
The differential equation of convective fibre cooling can be written as follows: dT Nu O a A HV A (T Ta ) ª(T 273.15) 4 (Tamb 273.15) 4 º¼ dt m cp d m cp ¬
0 .(6.11)
If we suppose that the cylinder -shaped fibr es have diameter d, length l f and density U, equation (6.11) can be simplified as follows: Nu O a dT HV 4 (T Ta ) 4 ª(T 273.15) 4 (Tamb 273.15) 4 º¼ 2 U d cp U cp d ¬ dt
0 .(6.12)
In order to solve the equation (6.11), we have to know the velocity field around the fibre. If the effects of radiation are appreciable only in the initial period of the cooling process and if we suppose tha t air temperature is constant, in this case equation (6.11) can simply be solved by considering the initial conditions T(0) = T f and T a = const.
72
°C °C
Fiberisation Process
Tf
Temperature Temperature
0.623(Tf-Ta)
Ta W
Time
Time s
s
Fig. 6.8. Dynamic temperature response of the cylinder-shaped fibre.
T Tf Ta Tf
1 exp(t / W) .
(6.13)
wher e T f is the initial temperature of the fibre and W is the time constant of the fibre which is:
W
m cp D A
U cp d . 4D
(6.14)
Time constant W represents 63.2% of the whole temperature change as shown in Fig. 6.8. T he calculation of heat tr ansfer coefficient is in the case of convective heat tr ansfer mostly dependent on velocity conditions. For lamina r flow ar ound a cylinder -shaped fibr e, t he Nusselt number can be calculated on the basis of the following empirical correlation [5, 34]:
Nu
0.4 Re r 0.3 ,
(6.15)
where Reynold’s number can be defined according to the radius of the cylinder-shaped fibre:
Rer
JG JG w U r Qa
,
(6.16)
where Q a is the kinematic viscosity of air. Equation (6.15) is valid
73
Mineral Wool
for Re r < 10 2 and Re l > 10 5 where Reynold’s number Re l refer s to the length of the fibre l [34]. There are several expressions for the calculation of heat transfer coefficient. Ziabacki [34] gave several expressions on the basis of which we can conclude that Nu = Nu(Re). Hoikka and Westerlund [5] have with experimental work developed the following expression for calculating the Nusselt number: (6.17) Nu 0.226 Re d 0.611 0.469 . Since thes e author s could not simulate the velocit y of up to 100 m/s, they had to extrapolate the equation. Lindqust’s equation is also very similar: (6.18) Nu 0.48Re d 0.5 0.43 . Next, we present Sano’s model [35]: (6.19) Nu 0.15Re d 0,36 0.25 . In our model we used equation (6.17). 6.4.1 Trajectories of mineral wool fibres In the process of mineral wool production, the melt jet is flowing onto the centrifuge. Small fibres form out of the thin melt film on the rotating wheels. Thin fibres intertwine in the turbulent air flow and go over fr om the r adial into axial dir ection of the ca rr ying coaxial airflow. This air flow usually surrounds the circumference of the r ot ating wheels. At the nozzle outlet it r eaches high velocities (higher than 100 m/s). In this section we are going to descr ibe the kinematics of the two-phase jet of glass fibr es and axial airflow. Our model is based on the following suppositions: • the jet flow of fibres and the air flow are stationary and onedimensional; • when deter mining the flow, we obser ve only the fibr e trajectories which define the outer envelope of the jet y e and tangentially leave the rotating wheel, as shown in Fig. 6.9; • the r adius of cur vatur e of fibr e flow changes along the x axis; • air enters into the jet with constant velocity rectangular to the jet envelope [36, 37]; • temperature of the air T a is constant; • fibr es ar e cylinder -shaped and have diameter d f , length l f ; and temperature T f ; • the initial fibre temperature is constant and equal to T f ; 74
Fiberisation Process
y F ut
envelope
wr
f
E
fibre
dy
w ft
y
U
JJG wf
D
J
JG U
rotating wheel
F un
g
dx x
Fig. 6.9. Fibre trajectory on the jet envelope.
• density of the melt is calculated according to [21, 19, 20, 22]; • thermophysical properties for humid air are also considered. Momentum equation and envelope diameter: The jet envelope is determined by the outer trajectories of fibres. The movement of JJG fibres along the envelope is mostly influenced by the drag force Fu , which is a result of relative movement between the fibres and air [37]:
JJG Fu
JJJG JJG JJJG JJG 1 c f Ak Ua w fe U e w fe U e , (6.20) 2 wher e c f is dr ag coefficientJJJGof a fibre, A k is the fr ont surface of a fibre, JJG U a is air density, w fe is fibre velocity on the jet envelope and U e is the velocity of the a ir flow entering rectangula r to the envelope. Besides the resisting force that drags JJ the G fibre movement, we alsoJJGconsider the gravity force of the fibre Fg and the buoyancy force Fb [37]. JJG JJG JG Fg Fb U f U a V f g , (6.21) JG where U f is fibre density, V f is fibre volume and g is gravitational
acceleration. The momentum equation for fibre movement along the envelope is: 75
Mineral Wool
JJJG d mw fe
dt
JJG JJG JJG Fu Fg Fb .
(6.22)
If we consider that fibres, moving along the envelope, are cylindershaped and have diameter d f and length l f , the equation (6.22) can be expressed as [37]: JJJG d mw fe JJJG JJG JJJG JJG JG 1 cd Ak Ua w fe U e w fe U e U f U a V f g . (6.23) 2 dt Supposing the air enters rectangularly to the jet envelope [36,37]
JJJG
(see Fig. 6.9), the absolute value of relative velocity vector w fer is:
JJJG w fer
JJJG JJG w fe U e
w2fe U e2 .
(6.24)
By considering the stationary flow and the projections of momentum equation (6.23) onto the tangent of the jet envelope, we get:
U f Ua g cos(E) 1 1 U c ft a w2fe U e2 B , 2 l f Uf w fe Uf
dw fe dx
(6.25) where the upper or the lower envelope determines the sign B . The curvature radius of jet envelope R is defined as follows [36]:
1 R
an w2fe
yecc 2 3
1 yc
,
(6.26)
e
where the upper or the lower envelope deter mines the sign. The curvature radius of jet envelope R is defined as follows
U f V f an
Fun Fg Fb sin(E) ,
(6.27)
where the following was taken into consideration:
sin(E)
dx 2
dx dye
2
.
(6.28)
Fun is the component of the drag force rectangular to the direction of the tangent. If we consider the cur vatur e sign, the second derivation can be expressed as:
76
Fiberisation Process
yecc
d 2 ye dx 2
U 1 1 U 1 U f Ua 1 1 c fn a w2fe U e2 3 e 2 B g 2 ,(6.29) Uf l f Uf 2 sin (E) w fe sin (E) w2fe
where the upper or the lower envelope determines the sign B . The resistance coefficient of the fibre in the air flow depends mostly on the Reynold’s number. In or der to calculate the r esistance coefficient in direction of the tangent, Glicksman in [5] offers the following expression:
c fT
0.4 Rer0.7 , Re 100 ,
(6.30)
where Reynold’s number refers to the radius of the cylinder-shaped fibre:
Rer
wret d , 2Q
(6.31)
where wret is the relative velocity of the fibre in the tangentially directed air flow, d is fibre diameter used for calculating the drag coeffic ient c fT , Q is the kinematic viscosity of air. T he dr ag coefficient of the fibre c fn in rectangular direction can be calculated from the following empirical expression [34]:
c fn
1.018 1.458 Re 0.5 8.151 Re0.8 , Re ! 0, 06 ,
(6.32)
where Reynold’s number is defined as:
Re
wren d , Q
(6.33)
where wret is the relative velocity of the fibre in the tangentially directed air flow. 6.4.2 Numerical analysis When determining the fibr e tr a jector ies along the envelope, the following supposition was taken into consideration:
dw fe dt
w fe
dw fe dx
.
(6.34)
A similar supposition can be used when observing the fibre cooling:
dT dt
w fe
dT . dx
(6.35)
77
Mineral Wool
With r egar d to equation (6.34) , equation (6.11) ca n aga in be expr essed as: dT dx
4
D HV (T Ta ) 4 ª(T 273.15) 4 (Tamb 273.15) 4 º¼. U f w fer d f cp f U cp d w fer ¬
(6.36) If we want to describe the fibre trajectory on the jet envelope and fibre cooling, we have to simultaneously solve the following system of equations: (6.25), (6.29) and (6.36). This system of equations can be solved with the Runge–Kutta method of 4 th order. The optimum step is determined according to the initial and boundary conditions. For the calculation we used the following settings: average fibre thickness of 5 μm and three different lengths of the fibres: 1 mm, 10 mm and 100 mm. The initial temperature of fibres is 1450°C, aver age air temper atur e wa s 30°C. Fibr es formed a t the circumference of the wheel and started to move in the direction of the y axis. The air flow was moving in the direction of the x axis rectangular to the fibre with velocity of 100 m/s. The emissivity was equal 0.85. The optimum step (0.1 mm) for solving the system of equations was chosen accor ding to the initial and boundar y conditions. Upper fibre trajectory 2.6 2.4 2.2
m
2.0 1.8 1.6 1.4
wf=30 m/s wa=100 m/s Tf=1450 °C Ta=30 °C J=89.5 ° df=5 Pm
lv = 1 mm lv = 10 mm lv = 100 mm
Step=0.000001 m
1.2
y
1.0 0.8 0.6 0.4 0.2 0.0 0.00
0.05
0.10
0.15
0.20 x
0.25
0.30
0.35
m
Fig. 6.10. Fibre trajectory on the jet envelope.
78
0.40
0.45
Fibre temperature °C°C Temperature of fibre ºC Fibre temperature
Fiberisation Process 1500 1400 1300 1200 1100 1000 900 800 700 600 500 400 300 200 100 0
wf=30 m/s wa=100 m/s Tf=1450 °C Ta=30 °C J=89.5 ° df=5 Pm Step=0.000001 m
0.00
0.05
0.10
0.15 xx
lv=1 mm lv=10 mm lv=100 mm
0.20
0.25
m
m
0.30
0.35
0.40
Fig. 6.11. Fibre temperature along the trajectory on the jet envelope.
1.0
measurement lf=60 mm; d=0,006 mm; lf=10 mm; d=0,005 mm; lf=10 mm; d=0,004 mm;
(T–T 0 )/(T f–T a)
0.8
0.6
0.4
0.2
0.0 0.000
0.025
0.050
0.075
0.100
0.125
Distance from wheels Distance from wheels
0.150
0.175
0.200
m m
Fig . 6.12. Comparison between experimental and numerical prediction results of the temperature along the trajectory on the jet envelope.
79
Mineral Wool
Numerical results of fibre trajectory and fibre temperatures along the trajectory on the jet envelope are shown in Fig. 6.11 and 6.12. On the way along the jet envelope, the fibr e was constantly cooling. Figure 6.11 shows the temperature of a fibre on its way along the jet envelope. Compar ison between exper imental and numer ical pr ediction results of the temperature in the two phase fibre and air flow are seen in Fig. 6.12, which pr esents the dependence b etween the dimensionless temperature
T
T Ta T f Ta ,
(6.37)
and the dis tance fr om the wheels, wher e T f is the initia l fibr e temper a tur e. T he mea sur ement r esult s ar e obtained using an infrar ed camer a.
80
Visualisation Method in Real Production Processes
7 VISUALISATION METHOD IN REAL PRODUCTION PROCESSES The manufacturing process is influenced by the fluctuation of key pr ocess par ameter s with time. In par ticular fluctuations in the trajectory of the falling jet of molten rock, variations occur in the jet’s impingement point on the rotating wheels. T he impingement position must be controlled because it has been found to be critical to the production of good quality mineral wool and to the overall quality of the final product. In the past, this control was achieved by an experienced oper ator viewing the pr ocess and adjusting it accor dingly. T herefore, a visualisation system has been designed, developed and installed in order to monitor the production process and ultimately to provide control [38]. The system is based on low cost hardware such as standard personal computer s and standard video cameras. Real time software has been developed in order to observe key features of the process, for instance the fluctuation of the jet tr ajector y, and to offer contr ol of the jet imp ingement position. Figur es 7. 1 and 7.2 pr ovide a compar ison between the two operating conditions. Figure 7.1 shows the fibre structure resulting from jet position x t ≈ R, where R is the wheel radius, and Fig. 7.2 shows an undesirable structure resulting from jet position x t << R where sufficient shots are present to cause unacceptable quality. The shots, shown in Fig. 7.2, cause a reduction of the thermal insulation ability of mineral wool. The statistical distribution of the fibr e diameter is also impor ta nt with r espect to t he ther mal pr oper ties of mineral wool. T he Figures also show typical shots having a diameter of the order of 10 to 100 times the diameter of fibres in the range from 0.1 to 2 mm. When the jet is located to the left (Fig. 7.1 and 7.3a), most of the fluid fr om the jet falls directly between the wheels and the formation of the film on the wheels is reduced to a minimum. This 81
Mineral Wool xt jet FR wheel
FT
Fig. 7.1. Fibres in mineral wool mat (average fibre diameter 12 μm, magnification ×200).
jet
xt
FR FT
wheel
Fig. 7.2. Poor fibre structure showing presence of solidified shots (average fibre diameter 10 μm, magnification ×200).
leads to a minimal quantity of the final product. If the jet is located to the right (Fig. 7.2 and 7.3b), shot formation is then significantly increased, and thermal quality of the product is reduced. Figures 7.3a and 3b show very significant differences. Image (a) shows a largely undisturbed jet and a small amout on the melt film on the wheel peripheries, while image (b) shows a high number of shots. In the particular operating condition shown in image (b), most of the shots appear to originate from the surface of the upper left hand wheel. This is because the jet has been deflected relatively cleanly by the initial impact to strike this wheel in a direction normal to its sur face. The position of impingement in real process changes with time for a number of reasons: • solidified material at the orifice from the reservoir is formed, from time to time due to local freezing of the melt, 82
Visualisation Method in Real Production Processes
a)
b)
Fig. 7.3. Images of real process showing the effects of two different impingement posit ion s.
• the liquid level in the reservoir varies with time, • the jet trajectory changes due to changing properties of melt caused by fluctuations in temperature. T hese par a meter s cannot be st abilised in the r ea l pr ocess. Therefore, it is necessary to regulate the jet position so that the jet can fall onto the required impingement point. As described above, the parameters of the production pr ocess (temper atur e, jet position a nd pr oper ties of the melt) have a significant influence on the visual form of the process. Thus, image analysis can be used for quality estima tion and for contr ol or monitoring purposes (see references [38, 39]). 7.1
Monitoring the production process
Computer or machine vision is a very complex technique, especially when decis ions must be made in r eal time. T his means that a par ticular decision must be made faster than the changes in the monitored process can occur. Some of the observed changes in the monitor ed process are nevertheless quicker than the r eactions of the machine vision technique. However, it appear s that these particular featur es are not significantly associated with the final quality of the product. T he impor tant visual featur es of the mineral wool production pr ocess are associated with fluctuations of the molten material directly after its impingement on the rotating wheel, together with the melt film distribution on the wheel peripheries. These features ar e obser ved by a video ca mer a mounted at the b ack of the collection chamber, at an angle to the z axis, as shown in Fig. 7.4. T he camer a inclination α is appr oximately 20 o . T his allows for simultaneous observation of the film position in the z direction (top side of the first wheel) and the fluctuating jet motion between the wheels. 83
Mineral Wool
data acq. system
reservoir of melt
video camera
melt jet
PC
primary layer
angle of camera
visible area spinning machine
suction channel
blow away flow
perforated mesh
secondary air flow (suction)
Fig. 7.4. Monitorin g the fibre production process.
video camera
airflow air flow
plexiglas
tube
Fig. 7.5. Video camera installation principle.
The collection chamber is filled with fibres and perls moving fast in all directions which can destroy the camera optics. To overcome this problem, the video camera is mounted in a tube, see Fig. 7.5. Air flows through the tube at the speed several times higher than the average speed of the air flow in this part of the chamber. This air both provides cooling and keeps the optics clear of fibres. It does not influence the production process because the volume of air flow ar ound the camera is relatively small compar ed with the main air flow. On-line observation of the fibre production process 84
Visualisation Method in Real Production Processes
is achieved using only one video camer a. T he video camer a is connected to a video fr ame gr a bber that is connect ed to a PC compatible computer. 7.1.1 Identifying the jet image In or der t o monitor the jet motion with r easonable computing economy, it is necessary to restrict observation to specific areas or windows (6). These areas will be r eferr ed to as control windows or regions of interest (ROI). The first window is applied to a region which is close to the impact point of jet flow on the fir st wheel (Fig. 7.6a). The second window is applied to the region between the wheels as shown in Fig. 7.6b. Further windows are also used to monitor the melt film distribution at the wheel peripheries. It is necessary to identify the jet image so that the jet position can be deter mined. T his step is needed because the ver y high fluctuation in grey levels over the image makes detection of the jet boundary very difficult due to the noise caused by moving shots and fibr es. Initially, tests wer e per for med using a number of techniques, such as active contour tr acing [40]. T he effect of noise can be reduced by moderate smoothing, but this smoothing depends on the direction of observation, and is different for the horizontal and for the vertical direction. Smoothing is carried out on the first window, where the trajectory of the jet can be expected. T he image fr om the first window (ROI 1 ) is divided into a new matrix (M × N) of equal cells. T he cells have typically the r ectangular for m shown in Fig. 7.7. Two contrasting criteria are applied depending on the width of the cell (dx c ). If t he width of t he cell is s mall, the eff ects of smoothing are minimal, and if the width of the cell is large, the
a)
b)
Fig. 7.6. The position of control windows: a) impact point, b) jet flow through the wheels. 85
Mineral Wool ideal profile of jet y
control window
dyc dxc
single cell x
Fig. 7.7. Rectangular form of cells.
boundar y detection will be inaccur ate. T he cell height can be increased without significant loss of accuracy because the expected boundaries are mostly vertically oriented. Horizontal precision is required for the correct detection of the jet position and the size of cells (dx c , dy c ) has, ther efor e, been determined by visual inspection, where dx c is usually set to around 2 or 3 pixels and dy c is set between 5 to 7 pixels. From this M and N are defined as: M = width(ROI1)/dx c and N=height(ROI1)/dy c . The average grey level (f c ) is calculated for each cell from:
f c ( x, y ) =
1 1 dy dx ∑ ∑ f p ( xc + i p , yc + j p ) dyc dxc i =1 j =1 c
p
c
(7.1)
p
wher e f p (x c +i p ,y c +j p ) pr esents the value of the obser ved pixel at cell position (x c , y c ) and relative position (i p , j p ) of pixel within the position of the cell. Observation of grey levels in the first window (from Fig. 7.6a) through the matrix of cells gives a three dimensional diagram, as is shown in Fig. 7.7, where the average grey level of each cell is plotted in the z direction. 7.1.2 Detection of boundaries In order to establish the centre line of the jet trajectory, we decided to first detect the jet boundaries and then reconstruct the jet from these results. Visual observation of Fig. 7.7 shows that the jet consists of a higher amplitude of gr ey levels than the backgr ound (at ideal visibility of the jet), and that there is a sudden transition in grey levels from low to high value. T he intensity of this tr ansition is 86
Visualisation Method in Real Production Processes level caused by jet
background around the jet
z=fc y
x
Fig. 7.8. Three-dimensional diagram of grey levels in the first window.
described by a gradient [42] ideally given by:
∇f ( x , y ) =
∂f ∂x
(7.2)
or by a two-component gradient:
⎡∂ f ⎤ ∇ ( , ) f x y ⎡ x ⎤ ⎢∂x ⎥ ⎥ ∇f xy ( x , y ) = ⎢ ⎥=⎢ ⎣∇f y ( x , y ) ⎦ ⎢ ∂ f ⎥ ⎢⎣ ∂ y ⎥⎦
(7.3)
where f repr esents the observed phenomena in the position x,y in the image. Because the pixels in the digital image are distributed in space, based on discrete values of x,y co-ordinates (because of the digital nature of the image), the gr adient over the image can be written approximately as:
⎡ f c ( x , y ) − f c ( x + di , y ) ⎤ ⎢ ⎥ di ∇f xy ( x , y ) = ⎢ ⎥ ⎢ f c ( x , y ) − f c ( x , y + di ) ⎥ ⎥⎦ di ⎣⎢
(7.4)
T he par a meter d i is the dista nce over which the gr adient is calculated, wher e (i) is the index of the r ow. Because the orientation of the jet is predominantly vertical, the jet edges can be detected using two gradients in the horizontal direction, where these 87
Mineral Wool
normalised gradients (referred as gradient G) are given by:
G( x , y ) = f c ( x , y) − f c ( x + d i , y )
(7.5) with the left hand gradient being calculated first, followed by the right hand gradient:
G L ( x L , y ) = − G( x , y )
with d i = d i L
with d i = d i R (‘L’ indicates the left boundary and ‘R’ the right boundary of the jet) where f c (x,y) repr esents the gr ey level of one cell, x L and x R r epr esent the left and the r ight x position at r ow y wher e the calculation of gradient is per formed. The distance d i is the most important factor in establishing the real gradient. Generally, the parameter d i can be determined in two ways: 1. Its value can be fixed: This is possible only when the light properties of the image are constant in time and space, and when the characteristics of the gr ey levels ar e established befor e the a nalysis is per for med. 2. It can be calculated adaptively: Adaptive establishment of the distance on which the gradient must be calculated can result in the correct establishment of the gradient for images where the fluctuation in contrast is very high, but this is not a straightforward matter.
GR ( x R , y ) = G( x , y )
7.1.3 Gradients at jet boundaries In the r ea l image the optimum length, on which the gr adient calculation should be based, changes as a consequence of changing visual pr operties of the image in time and space. This is due to different optical conditions (e.g. reflection of light in the plane of the camera at different angles) and unfocused objects (the object is three-dimensional and only part of it is correctly focused). For example, Fig. 7.8a and 7. 8b show differ ent gr ey level profiles (top part of diagram) and observed segments of the image (bottom part of diagram). It is evident that the ‘boundary’ of the jet is ‘spread’ over very different lengths. This is described ‘theoretically’ in Fig. 7.9 where a and b show ‘theoretical’ pr ofiles for the images pr esented in Fig. 7.8. Each image contains a similar difference of grey levels Δf c between high (f 2 ) and low (f 1 ) level, but ther e ar e differ ent lengths d i over which Δf c was obser ved. 88
Visualisation Method in Real Production Processes shot
jet
grey profile
a)
b)
Fig. 7.9. Flow image at different times, top part: grey level profile; bottom part: observed image.
This shows that the parameter d i cannot be pr e-set as a fixed value and that adaptive calcu lation of gr adient distance d i is necessary to correctly establish the relevant gradient. 7.1.4 Gradient establishment It is necessar y to calcu late all positive and negative gr adients bor der ing the image of the jet so that its boundar y can be established. Both left and right gradients must be detected for each row of the selected window, so that the jet can be reconstr ucted (as described in the next section). T he gr adient on the left boundar y of the jet is calculated as follows:
G L ( x ) = f c ( x + ni ) − f c ( x + ni + d i ) and similarly for G R . The maximum gradient max(G) is determined for both the left and right hand boundaries, as shown in Fig. 7.10 f2
f2
Δfc
Δfc
f1
f1 di x1
di x2
x1
a)
x2 b)
Fig. 7.10. Different ‘theoretical’ profiles of gradients at the left boundary of the jet. 89
Mineral Wool
because the profile of grey level can contain more gradients formed by the shots. Because the jet grey levels are higher than the background grey levels G L < 0 and G R > 0, the gradients must satisfy the appropriate condition G L > Gmin or G R > Gmin , where G min is preselected based on the ratio between grey levels of the jet and grey levels of the background. If the test is true, the width of the jet is given by l = x R –x L , where x L represents the position where the left gradient has been calculated, and x R represents the position where the right gradient has been calculated (Fig. 7.11). Both, x L and x R , therefore define the probable boundaries of the jet for this row of cells (Fig. 7.10 and 7.11).
x L = xi + ni + d i L / 2
and
x r = xi + ni + d i L + n k + d iR / 2
GL(3) =max GR
GL(2)
GL(1)
fc(x) grey level
shots
GR(3) = max GR
The parameter l is also tested to ensure that l min < l < l max where the limits are set from the knowledge of the actual jet dimension and expected variation in this dimension. Because of large fluctuations in grey levels at the boundary of the jet, the gr adients detected in one r ow of cells cannot be a representative of the whole image. Thus, a further test is required. Detection is carried out on two neighbouring rows (y–1) and (y+1) giving left and right boundaries as x L (y–1), x R (y–1) and x L (y+1), x R (y+1) (Fig. 7.12). Var ia tions of the boundar y in the ver tical direction are expected to be small in the real jet so that x L ( y − 1) ≈ x L ( y ) ≈ x L ( y + 1) and x R ( y − 1) ≈ x R ( y ) ≈ x R ( y + 1) .
jet
shots
xL(1) xR(1) xL(2) xR(2) xL(3)
xR(L)
x
Fig. 7.11. Row profile of grey levels; peaks formed by the jet and shots. 90
Visualisation Method in Real Production Processes
L
fc(x)
xL xi+ni
diL
xR xi+ni+diL+nK
diR x
Fig. 7.12. Expected positive and negative gradients within the grey level pro file.
An additional test is therefore included to compare the grey levels in 3 adjacent rows between positions x L and x R , expecting that: xR ( y)
x R ( y −1)
x R ( y + 1)
c x = x L ( y − 1)
c x = x L ( y + 1)
∑ f ( y, x) ≈ ∑ f ( y − 1, x) ≈ ∑ f ( y + 1, x) c
x = xL ( y)
(7.7)
The difference between these values must be very small and less than the minimum accepted pr e-s et level ( ε S ), wher e the determination of ( ε S ) is based on the knowledge of the fluctuation of jet width in the vertical direction. x R ( y −1) ⎛ xR ( y ) ⎞ ⎜ ∑ f c ( y , x ) − ∑ f c ( y − 1, x ) ⎟ < ε S ⎜ ⎟ x = x L ( y −1) ⎝ x= xL ( y) ⎠
(7.8)
In this case the boundaries are classified as valid. This process is repeated for all lines of the diagram from the top to the bot tom of the window. E ach valid r esult (p osition of boundaries (x L , x R )) is saved into the buffer R(y) where each y line of the buffer consists of a valid or an invalid result. In the next section, the method for jet reconstr uction from the results stored in array R(y) is presented. 7.2
Reconstruction of the jet and its trajectory
It is necessary to connect the results from the array R(y) so that the jet trajectory can be established. Conventional methods, such as linear regr ession or polynomial regr ession, cannot be applied because the boundaries of the jet image are highly fluctuating in the vertical direction. An optimum boundary line must be drawn over the detected points x L (y) and x R (y) as indicated in Fig. 7.13. 91
Mineral Wool fc(y+1) y
xL(y+1)
∑(y+1)
xR(y+1)
row: y+1
fc(y) xL(y)
∑(y)
xL(y-1)
∑(y-1)
fc(y-1)
xR(y)
xR(y-1)
row: y
row: y-1 x
Fig. 7.13. Comparison of 3 adjacent rows.
A technique of ‘minimum allowable fluctuation’ of the detected points in the vertical direction has been developed for this purpose. If the fluctuation is greater than the minimum, the detected point is ignored and interpolation through this point is carried out. This technique requires a ‘starting’ or reference point (y 0 ) – y, a position from which the reconstruction starts. This technique is not straightforward because the fluctuation in the boundaries of the image of the jet does not necessary coincide with the fluctuations in the boundaries of the real jet. Based on the experiment and visual obser vation, the reference point can be calculated from the first (t L = 4) rows which contain very similar values of x L and x R . Index x L at t L is r elated to the lines and not to the left position. Also, t L is always even because of the computing method. At the left jet boundary (Fig. 7.14) the quantity
Δ Lmax = max x L max − x Lmin is calculat ed, wher e x Lmax = max( x L ( y 0 + i )) and x Lmin = min( x L ( y0 + i )) and at the right boundary
Δ Rmax = max x Rmax − x Rmin
wher e
xRmax = max( xR ( y0 + i ))
and
x Rmin = min( x R ( y0 + i )) where i=1,2,...,t L . If for the vertical region from y 0 to y 0 +t L :
Δ Lmax < Δ X max and Δ Rmax < Δ X max wher e Δ Xmax defines the maximum allowable fluctuation in the x direction, then y 0 is taken as the starting point of the jet (reference point) as shown in Fig. 7.14 . Other wise, the value of y 0 is 92
Visualisation Method in Real Production Processes
fc
left centre boundary line
right boundary
y
xL
xt
xR
x
Fig. 7.14. Reconstructing th e jet from data in the buffer R(y).
incr emented by 1 and the test is r epeated until the cr iter ia mentioned above are satisfied. T he validity of the por tion of the jet pr ofile detected by the above method is established by an additional test. Two horizontal groups of rows (y 0 ,...,y+t L /2) and (y+t L /2,...,y+t L ) are compared (where one group consists of t L /2+1 rows) to determine whether: y0 + t L / 2 x R ( y )
∑ ∑
y = y0
y0 + t L
f c ( y, x) ≈
x= xL ( y)
∑
xR ( y )
∑f
c
( y, x)
y = y0 + t L / 2 x = x L ( y )
(7.9)
If this condition is tr u e, the r efer ence for the jet bou ndar y is considered to be successfully established and the aver age values of x L and x R over t L rows are taken as the jet boundary positions at the mid point of this interval:
xL =
1 y0 + t L 1 y0 + t L x ( y ) x = x R ( y) ∑ L and R t + 1 y∑ t L + 1 y = y0 = y0 L
(7.10)
This is then taken as the reference for the next y row (Fig. 7.14). y
xLmax y0 y0+1
xL(y0)
y0+tL
xLmin ΔLmax< ΔXmax
x Fig. 7.15. Determination of the reference of the jet.
93
Mineral Wool
Fluctuation of the next row position y 0 +t L +1 is tested as:
Δ Lmax 1 = x L ( y0 + t L + 1) − x L
(7.11)
and for the right boundary:
Δ Rmax1 = xR ( y0 + t L + 1) − xR
(7.12)
If Δ Lmax1 and Δ Rmax are less than Δ Xmax , the process is continued by 1
testing that: y0 + t L 1 ∑ t L / 2 + 1 y = y0 + t L / 2
xR ( y )
∑
f ( y, x) ≈
x= xL ( y)
x R ( y0 + t L +1)
∑ f ( y, x)
x = x L ( y0 + t L +1)
(7.13)
This comparison gives the relation between the current grey level profile and the average value of previous grey levels. If the result of this operation is true, points x L and x R are added to the buffer of real boundaries. If the observed y row is invalidated, then the programme jumps to the next y. If the next row has a valid result, then linear regression is performed from y–1 to y+1, otherwise the next row y+2 is checked. If, for example, x L exists and x R not, then x R is established by interpolation through previous and next row. In this way, the pr ocess is continued from the top part to the bottom part of the control window. Connections through points x L (i),...,x L (n L ) where i=1, 2,...,n L and x R (i),...,x R (n R ) where i=1,2,...,n R are made, where n L and n R represent the number of detected points for the left (x L ) and the right (x R ) side of the boundary. The process gives two near vertical lines which represent the boundaries of the jet. The centre of the jet is located at x T (y) where: (7.14) x T ( y ) = ( x L ( y ) + x R ( y )) / 2 The trajectory is generated as:
{
}
ℜ T = ( xT1 , yT1 ), ( xT2 , yT2 ),...( xTn , yTn )
(7.15)
where y Ti = yi and T n represents the number of points from which the trajectory has been detected. To reduce the fluctuation of the boundar y, linear regression is performed on ℜ T , where the slope of the jet is defined as:
94
Visualisation Method in Real Production Processes nT
b=
∑x i =1
Ti
nT
yi − nT xT y
∑x i =1
2 Ti
(7.16)
− nxT2
where the check of expression 0/0 is tested by software. The angle β = 90–arctan (b) (Fig. 7.16) gives the current slope of the jet. Because the attachment point is always under the area where the jet is detected, its x t position is calculated as a straight line fitted through the detected points to the attachment point on the wheel, as shown in Fig. 7.16, while the detection of jet flow in the real image is shown in Fig. 7.17. x t is the main control parameter for this production process. It r egulates the jet position so that the jet impinges on a constant position in time. The system can analyse more than six images per second which gives a sufficiently fast response for the monitoring system the r esponse r ate of which is limited mainly by the mechanical components in the control loop. 7.2.1 Observation of jet centre line between wheels The area of the jet between the wheels is analysed using the same pr inciple as used in the case of the jet above the wheels. T his analysis is applied to the area selected by the window shown in Fig. 7.6b. Bigger fluctuation of the boundar ies of the jet is allowed because these r esults ar e used only for tr ajector y analysis. In comparison with the previous section, a single linear connection is used for the reconstruction of the jet between the wheels because β
angle of trajectory
calculated points of jet extrapolated zone
trajectory of jet attachment attachement poin t point
xt
wheel
Fig. 7.16. Attachment point.
95
Mineral Wool detected boundaries of the jet jet centre line
wheel Fig. 7.17. Detection of jet flow in a real image.
there is less noise from shots and fibres. The middle point of the jet is taken as the mid point of left and right boundaries of the jet image. This is shown in Fig. 7.18. The trajectory centre line is then used to characterise the flow pattern between the wheels. 7.2.2
Experimental results
A r eal time visualisation system has been developed and implemented directly into the industrial production of mineral wool. The presented computer-aided visualisation method can be applied for several purposes. It is based on the fact that visual information contained b y the kinematics of melt in the zone wher e the jet impinges on the r otating wheels is of essential impor tance for : formation of fibres of cer tain thickness and length and for pearl formation (material that does not fiberise). The basic information includes: – time variation of the centre line of the melt flow in the zone of impingement and between the centrifuge wheels, – time variation of boundary lines (left and right boundary line) from the visual edge at the top to the impingement point on the first wheel of the centrifuge and
boundaries of jet flow centre line wheel
Fig. 7.18. Boundaries of the jet flow and its centre line between the wheels. 96
Visualisation Method in Real Production Processes
– time variation of grey levels in selected active windows outside the area of continuous melt flow; this is intended for the evaluation of non-fiberisation (pearls). 7.2.2.1 Centre line One of the most impor tant var iables that influence the fibr e thickness of mineral wool is the time-averaged centre line of the melt impinging on the rotating wheel. The current centre line as shown in Fig. 7.19 is expressed with vector ℜ T (t ) :
{
}
ℜ T (t ) = ( xT1 , yT1 ), ( xT2 , yT2 ),...( xTn , yTn )
The time-averaged centre line is expressed with average of current lines in the series of captured images:
〈ℜ T (t )〉 =
1 N
N
∑ℜ i =1
T
(i )
(7.17)
where N is the number of digitized shots that were considered when calculating the time averaged centre lines of the impinging melt flow. The acquired centre line can directly be used as input data for the empirical model of fibre thickness, and can indirectly via this model be included into the r egulation algor ithm of fiberisation process control. 7.2.2.2 Fluctuation and centre line Besides the centre line, it is also important to stress its fluctuation according to the time aver aged value expressed with (7.17). T he statistical estimator of centre line variation is expressed as follows:
Fig. 7.19. Current centre line between the wheels.
97
Mineral Wool
σℜ = T
N 1 (〈ℜ T (i )〉 − ℜ T (i )) 2 ∑ N ( N − 1) i =1
(7.18)
The fluctuation intensity of the centre line significantly influences the quality of the fiberisation process; therefore, it is often used as stability estimator of the fiberisation process and is similarly as the time averaged centre line included into the regulation system of melt impingement on the rotating wheels. 7.2.2.3 Fluctuation of grey levels in the selected iield In order to estimate the effects of the jet on the fiberisation in the vicinity of the r otating wheels, the computer-aided visualisation enables the quantification of pearl formation – i.e. of melt droplets that leave the ar ea of centr if uge wheels as unfiber ised dr op structures. Drop structures are significantly bigger as melt droplets out of which mineral wool fibr es are formed. Besides, fibres are formed in the direct vicinity where melt film impinges on the rotating wheels. In this manner, it is possible to estimate the intensity of unfiber ised melt by obser ving the fluct uation of gr ey levels in selected active windows as shown in Fig. 7.20. Here, the algorithms of time-averaged grey intensity calculation were used, and the algorithms of corresponding time fluctuations of grey levels in selected partial windows as shown with the example in Fig. 7.20. For evaluating the grey levels, we can use the equation (7.1):
f c ( x, y ) =
1 1 dy dx ∑ ∑ f p ( xc + i p , yc + j p ) dyc dxc i =1 j =1 c
p
c
(7.19)
p
wher e f p (x c +i p ,y c +j p ) pr esents the value of the obser ved pixel at cell position (x c , y c ) and relative position (i p , j p ) of the pixel within the position of the cell. Time fluctuations in the selected window can be evaluated with the standard deviation expressed as:
σ c ( x, y ) =
N 2 1 〈 f c ( x, y )〉 − f c ( x, y, i ) ) ( ∑ N ( N − 1) i =1
(7.20)
wher e the time-aver aged gr ey level in the selected window is expressed with:
98
Visualisation Method in Real Production Processes
Fig. 7.20. Melt droplets in selected active windows.
〈 f c ( x, y )〉 =
1 N
N
∑ f ( x, y , i ) i =1
(7.21)
c
The coefficient of both expressions gives the normalised estimator of grey level fluctuations. T he grey level is pr opor tional to the occurrence intensity of unfiberised pearls in the observed area, and r epr esents, besides the fluctuation of t he centr e line, the most important estimator of the mineral wool fiberisation process.
ε ( x, y ) =
σ c ( x, y )
(7.22)
〈 f c ( x, y )〉
7.2.2.4 Evaluation of mass flow of melt Computer-aided visualisation also enables to estimate the volume or mass flow of the melt flowing onto the r otating wheels. T he calculation is based on the supposition that the cross section of melt jet is approximately cylinder-shaped and on the supposition that the scalar distur bances that occur as gr ey level var iations or local perturbations of jet surface move, together with melt, with the same terminal velocity. If the suggested suppositions are adopted, the cor r elation method makes it pos sible to deter mine t he ter minal velocity of the melt and to determine the average diameter of jet melt which can be normalised to the actual size. Figure 7.21 presents two successive digitalised images of melt impinging on the wheel, where a local disturbance can be observed. Because of jet movement and time increment between the images, the local disturbance changes and moves with the melt flow. These images also present one of possible methods for evaluating local disturbances. The following procedure is valid for the determination of vertical velocity component of the melt flow. Inside the area outlined with a solid line (ar ea ‘a’, Fig. 7.21), the mean value of gr ey level intensity A is calculated using equation (7.22): 99
Mineral Wool
h a b(h)
Fig. 7.21. Two consecutive images of the jet melt flow with areas of interest, indicated.
A(i ) =
1 N ⋅ ∑ E p (i, j ) , N j =1
(7.22)
where E p denotes the grey level intensity of the j-th pixel inside the outlined area of the i-th image, N is the number of all pixels inside the outlined area ‘a’. The grey intensity of variable E p (i, j) has 256 levels, which vary from 0 (black) to 1 (white). In the same procedure equation (7.22) is adopted on the consecutive image, but the area of interest, which is outlined with a dashed line (area ‘b(h)’, Fig. 7.21) and is of the same dimensions as the area ‘a’, is in this case moved in the direction of melt flow movement due to buoyancy with respect to the area ‘a’ in Fig. 7.21 for a certain (arbitrary) value h. This procedure is repeated on many pairs of consecutive images in order to get the mean value of grey level intensity inside the outlined areas of the numerous images. The cross-correlation coefficient r between average grey level intensity inside area ‘a’ and the one inside area ‘b(h)’ is a function of h and is calculated using the following equation, [43, 44]:
r (h) =
∑ ( A (i) − A ) ⋅ ( A a
a
b(h)
i
∑ ( A (i) − A ) a
i
a
2
⋅
(i + 1) − Ab ( h ) )
∑( A
b (h )
i
2 (i + 1) − Ab ( h ) ) ,
(7.23)
where A a and A b(h) denote the mean grey level intensity on a single image inside areas ‘a’ and ‘b(h)’, respectively; Aa and Ab ( h ) denote the average grey level intensity inside areas ‘a’ and ‘b(h)’, respectively, of i consecutive images. i denotes the number of all consecutive images that were used for calculation of r. By changing (increasing) the value of h and calculating r(h) 100
Visualisation Method in Real Production Processes
accordingly, it is possible to detect the value of h, where r(h) has its maximum (Fig. 7.22). It can be seen fr om Fig. 7.22, which represents the corr elation function of the border line on the melt jet, that r(h) reaches its maximum at h r,max ≈ 170 pixels. Thus, the value of h r,m ax r epr esents the distance in pixels, which the disturbance of the border line of the melt jet has travelled between two succesive images. By knowing the relation between the number of pixels of the image and the size of the jet field of vision together with the acquisition fr equency of the camer a, it is pos sible to assess the mean melt flow. In Fig. 7. 23 we can see tha t the velocity of the melt flow increases as the gravitational force acts upon the flow. Therefore higher velocities were measured when the disturbance was in the bottom part of the image. For the measurement of the velocity of the melt flow it is therefore important that thickness is measured in the region only between two peaks of disturbance. T he mass flow was calculated using the default set tings for edge extraction. Proper settings can be only derived by calibration. The main measured parameter, which is influenced by settings, is the thickness of the melt flow. T he basic algor ithms for the calculation of left and right border is presented in chapter 7.2. The algor ithm has to find edges in the image, but the image can be brighter or darker due to aperture of the lens, selection of threshold
r (hr max)
hr max
Fig. 7.22. Correlation function of local disturbance. 101
Mineral Wool 225
3.00
a
b
200 2.75 measured m/s
150 125
2.50 2.25
100
Velocity
Distance
mm
175
75
measured
2.00
50 1.75
25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Image index
1.50
6
7
8
9
10
Image index
Fig. 7.23. Measurement of the melt flow velocity v TER with light external disturbances: a) distance of the maximum melt flow deflection from the upper part of each image in the sequence; b) calculated terminal velocity of the maximum melt flow deflection.
in edge extr action, etc. This is shown in Fig. 7.24. Besides, the cr oss section of the melt flow is pr opor tional to the squar e of thickness. To make ca libr ation easier, we can calibr ate the mass flow calculation after the installation. The calibration should then be performed over a longer per iod of time (more than one hour ) so that it is possible to adjust software settings in a way that the mass flow of the melt is equal to the mass flow on the secondary line balance. The melt flow cross section depends on software settings. Here, the same image is shown, only the settings of the steepness control wer e changed (left image 30 and right image 3). This should be arranged with online calibration. Figure 7.25 shows the grey level gradient of the melt flow as seen on the enlar ged image of the melt flow (br ight part of the image) and the background (dark part of the image). The line in Fig. 7.25 depicts a difference between the grey level intensity and the black background, where the intensity is close to zero (rightmost part of the line in Fig. 7.25), to the core of the melt flow (leftmost part of the line in Fig. 7.25), where the grey level 102
Visualisation Method in Real Production Processes
xL(h)
xR(h)
Fig. 7.24. Melt flow cross section.
intensity is the highest. A part of the line between points A and B in Fig. 7.25 denotes the region where the grey level on the image changes its value. Therefore, it is a matter of discussion whether a real margin (edge) of the melt flow is in point A, in point B or somewhere in between. Since there is a certain ‘glow’ present in the images, which results from the high contrast between the melt flow and the background, and since the pixels of the image with high grey intensity levels affect the neigbouring pixels by raising their grey level intensity (hence the so-called glow), point B in Fig. 7.25 is determined as the edge of the melt flow. The diameter (melt flow thickness) and consequently the cross section area of the melt flow are then calculated according to this specified melt flow edge. The cross section of the melt flow is assumed to be circular in shape. Based on the supposition that the cylinder-shaped cross section of the melt jet is determined with the left and right boundary of the
Grey level intensity
B B
A A
Fig. 7.25. Gradient of grey level intensity on the image of melt flow. 103
Mineral Wool
jet presented in Fig. 7.24, terminal velocity in position h shown in Fig. 7.24, the mass flow rate of the melt q m is expressed as follows: 2
⎛ x ( h ) − xL ( h ) ⎞ qm = k ⎜ R ⎟ π vTER ( x) 2 ⎝ ⎠
(7.24)
where k is the coefficient that connects the actual diameter of the melt jet with the dimension of the melt jet in digitized shots, ρ m is the melt density presented in section 4.1. The measuring uncertainty of the met hod for measur ing the volume r ate of the melt flow depends on calibration methods. Because of constant k, this method has to be calibrated with other available integral methods. If we suppose a simple model of a steady and isothermal liquid jet, the velocity and stress distribution have the exponential form [34]:
v = v0 ⋅ exp(ξ ⋅ x)
(7.25)
pxx ( x) = pxx ,0 ⋅ exp(ξ ⋅ x)
wher e ξ is the defor mation gr a dient. T he cor r esponding r adius variation R(x) is:
R( x) = R0 ⋅ exp(−ξ ⋅ x / 2)
(7.26) The break-up of the melt jet due to the capillary wave mechanism is schematically shown in Fig. 7.26. The mass rate of the melt flow of is given with equation (7.24). The jet diameters along the trajectory of the jet acquired with the visualisation method enable the prediction of the melt velocity along the jet. With the supposed exponential velocity field of the melt one can determine the deformation gradient ξ in advance:
ξ=
1 dv v dx
(7.27)
Taking into account equation (7.26), the melt velocity in relation to the position of the jet is:
⎛ x 2 R( x) ⎞ v( x) = v0 ⋅ exp ⎜ − ∫ ln dx ⎟ ⎜ x x ⎟ R0 ⎝ 0 ⎠
(7.28)
The condition necessary for the use of equation (7.28) is to know the velocit y in at least one point of the jet, Fig. 7.23. T he comparison between t he pr edicted and measur ed melt velocities is given in Fig. 7.27. T his method is extr emely a pplicable because it enables to 104
Visualisation Method in Real Production Processes
R(x)
qm melt jet
x
Fig. 7.26. Radius variation along the melt jet.
m/s
3.5
Melt velocity
3.0
2.5 measured velocity predicted velocity 2.0 -20
0
20
40
60
80
x
100
120
140
160
180
mm
Fig. 7.27. Predicted and measured velocity in the melt jet.
estimate the mass r ate of the melt flow in r eal-time pr oduction processes and to detect melt flow fluctuations. The detection of these fluctuations is indirectly used for regulating the mineral wool production process.
105
Mineral Wool
8 APPLYING THE VISUALISATION METHOD TO MEASURING THE THICKNESS OF MINERAL WOOL FIBRES The conventional method for measuring the thickness of miner al wool fibr es is based on microscopic obser vation and analysis of every single fibre. The fibres are inserted between two glass plates and pr essed together. Because of the shots and other thicker ma ter ial mixed with the fibr e, the specimen cannot be thinned enough to match the depth of the microscope field. The results are images like those shown in Fig. 8.1. They show only some fibres or par ts of fibr es, shar ply a nd cor r ectly focused. T her efor e, constant focus adjustments and oper ator ’s decisions to choose fibres suitable for analysis are required. For real-time analysis, this repr esents a major deficiency. A new, more automated method is needed. Such a method is presented in [42]. However, in addition to automation, a new method would have to ensure the same constant conditions and impartiality towards all shapes and forms of fibres
Fig. 8.1. Sample images of the classical measuring method. 106
Applying Visualisation Method to Measuring Thickness CCD camera
PC and software
microscope
monitor
glass substrate
frame grabber
positioning unit
series of images
I/O unit
statistical analysis
Fig. 8.2. Scheme of the experimental set-up.
during specimen preparation. Automatic analysis would also lead to measur ements on mor e specimens. Figure 8.2 shows a schematic of the experimental set-up that provided us with an automatic and less biased quantification of fibre thickness. T he fibr es wer e analysed with a micr oscope. A conventional CCD video camer a with 1/3" sensor was used to captur e the ima ges. T he computer -contr olled r otating platfor m was used to position the specimen under the microscope. The captured images were digitised and analysed on a PC with Neuro Inspector software [45]. The measuring procedure [78] with the described set-up consists of the following steps: 1. Taking samples of mineral wool from the production line. Captured samples must be statistically representative and must reflect the average quality of mineral wool for the operational set-up parameters. 2. Prepar ation of miner al wool samples for micr oscopic analysis. 3. The mineral wool is grinded in a rotating mill to the fibre length of 0.05–0.20 mm. 4. To ensur e the cor r ect focus, the fibr es have to be positioned on a glass substrate in a thin layer that does not exceed the height of 1–2 times the fibre diameter. Glycer ine oil is added to for m a compact, viscous suspension. When applying the suspension into the thin layer, the distribution of fibres has to be uniform and without any 107
Mineral Wool
sample of mineral wool fibres
grinded fibres 0.05 – 0.2 mm
suspension medium + fibres
Fig. 8.3. Steps in the preparation of a specimen for analysis.
glass substrate
air jet
redundant suspension
thin layer of suspension h = 1-2 d
Fig. 8.4. Process for the uniform spreading of the suspension.
5.
6.
bias towards the size or shape of the fibres. To ensure these r equir ements, the pr ocess of spr ea ding the suspension with a compressed-air jet was used as shown in Fig. 8.4. Captur ing images of the specimen. A r ound, glass substr ate with the specimen applied in a thin film is placed onto the computer -controlled rotating platform under the microscope. Neuro Inspector software controls the movements of the specimen and captures a sequence of 500 images of fibres for every sample. All images are pre-processed and analysed online. Pr e-pr ocessing and image analysis. T he complete pr ocedur e for the measur ement of fibr e thickness is based on the algorithm for the recognition and detection of fibr e- like str uctur es that was develop ed by FDS Resear ch and is pa r t of t he gener al-pur pose vision softwar e called Neuro Inspector [45]. T he images of miner al-wool fibr es that wer e captur ed under r eal conditions varied from the ideal fibre structures. T his means: to make the analysis possible, the images have 108
Applying Visualisation Method to Measuring Thickness
A captured image of specimen
B image with morphology closed structures
C normalised and brightness & contrast corrected image
Fig. 8.5. Three stages of image pre-processing.
7.
to be pre-processed. Because of round cross section of fibr es and their tr a nsparency, the fibr es can a ct as cylindrical lenses. Thicker fibres, in particular the ones shown on Fig. 8.5A, have dar ker edges a nd a considerably lighter ar ea in the middle as a result. To prevent the algorithm from detecting two thin fibres in such cases, morphology closing was used. Figure 8.5B shows the image after mor phology closing with filled areas in the middle of thicker fibres. To eliminate the effects of uneven illumination and incr ease the algorithm’s reliability, the pictures were normalised, and the brightness and contrast were corrected as shown in Fig. 8.5C. The detection pr ocedure consists of three phases. T he fir st pha se is to r ecognize linear object s in the background. These objects represent the basic elements of the fibr e. In the second phase, these ob jects ar e categor ised as fibres in ter ms of thickness, curvatur e and lengt h. T he thir d phas e is to check the fibr es’ consistency and ca lculat e the aver age length and thickness. The statistical analysis of the results includes the number of fibr es detected in the specimen, the st atistical distribution of these fibres, their mean thickness and the standard deviation of fibre thicknesses.
This method is suitable for online analysis of mineral wool fibres. However, it cannot be used a s the absolute method beca use it depends on many parameters that are linked to the preparation of the specimen and image analysis. 109
Mineral Wool
8.1
Experimental results of fibre diameter on a doublewheel spinning machine
The experiments were first performed on a double-wheel spinning machine in a real production process, Fig. 6.1. The diameter of both cylinder-shaped wheels, which wer e 120 mm wide, was 385 mm. The experiments, 17 in total, were performed at varying air mass flow q mG and rotational speeds of both wheels, ω1 and ω2 . Other par a meter s wer e simila r to the ones in exper iments described in section 6.1. The fibre diameters in mineral wool samples were determined in the labor ator y b y using both the classical met hod and the new method. For each operational set-up, four samples of mineral wool were taken from four different locations on the output production line of miner al wool. The volume of each sample measur ed is approximately 0.25 dm3 . After the appropriate specimen preparation, approximately 10 ml of suspension was applied on a glass substrate in a thin layer. For each operational set-up, a total of 500 images were captured and processed with the computer pr ogram [45]. T he analysis results represent the thickness of each detected fibre and the total count of fibr es. T he r esolution of the optical system was less than ±0.5 μm, but according to the algorithm for width detection based on the aver aging of multiple measurements, the resolution of the whole system was actually ±0.1 μm. Figure 8.6 shows the comparison between the classical and the new method. Each measuring point N (17 in total) represents the mean fib r e thickness that is obtained f r om the fibr e t hickness histogram. Such histogram for measuring point 6 is also shown in Fig. 8.6. It is evident from this figure that both methods exhibit a similar tr end. Only a deter ministic shift exists between these methods. T his shift can be r emoved by using a calibr ation pr ocedure that is based on the classical method. T he calibration constant is calculated with the formula:
K=
1 N
N
dVi ( new method )
i =1
Vi ( classic method )
∑d
(8.1)
where d Vi is the mean fibre thickness obtained both by the new and classical method. If we multiply the fibre thicknesses with the calibration constant K , we obtain results ‘without the shift’. These fibre thicknesses 110
Fibre diameter Fibre diameter
10.0 9.5 9.0 8.5 8.0 7.5 7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0
shift
µm μm
Applying Visualisation Method to Measuring Thickness
Classical method Classic method New method (with shift) New method (without shift)
0
1
2
3
4
5
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Number of ofexperiments Number experiments N N
Fig. 8.6. Comparison between the classical and the new (computer analysis measurement) meth od.
are also shown in Fig. 8.6 (the new method without the shift). The shift between the calibrated and uncalibrated thicknesses was less than 2 μm. The results in Fig. 8.6 show a large deviation between the classical and the new method only for the 7 th sample of mineral wool. T he significance of thickness differ ence Δd between the cla ssical d Vclassi c and the new method (with the shift) d V(new method)
Δdi = dVi ( classic method ) − dVi ( new method )
(8.3),
was checked with the t-test. This test estimates the hypothesis that the diff er ence Δd is not s ignificant. T he pr obability t ha t this hypothesis is valid was less than 0.89, and the new method is, therefor e, comparable to the classical method. The r esults of the t-test, which are at the 99 % confidence interval, are presented in Table 8.1. Ver y good agr eement between the classical and new method for measuring fibre thickness was also confirmed by the high value of linear correlation coefficient r which was 0.904. Based on the statistical analysis, a histogram of fibre thickness was made for each set of operational parameters. Figure 8.7 shows the histogr a m for the 7 th sample of miner al wool. Besides the differ ence in fibr e thickness distr ibut ion, Fig. 8.7 also shows deviation from the normal distr ibution of fibre thickness a nd the 111
Mineral Wool Table 8.1. The significance of thickness difference between the measuring methods Mean
Δd
1.075E-02
Standard
Standard
99% Confidence Interval of
Deviation
Error Mean
Difference
0.309
7.487E-02
Lower
Upper
–0.208
0.229
t
df
0.144
16
Sig. (2-tailed)
0.89
0.16 N7... number of sample _ d = 6.79 μm σ = +0.88 μm
0.14 0.12
Normal curve
Frequency
0.10 0.08 0.06 0.04 0.02 0.00
5
6
7 Thickness of fibres
8
9
μm
Fig. 8.7. Fibre thickness histogram for the set of parameters No. 7.
results of fibre thickness measurements that are multiplied by the calibration factor. Based on the obtained results, the following conclusions can be dr awn. The presented method is a relative method for measuring fibre thickness. The shift between the absolute and the relative method can be removed by the multiplying calibration constant. T he pr esented measur ing method for the detection of fibr e thickness can be used in r eal-t ime monitor ing of miner al wool production process. Therefore, it can help to increase the quality of the final pr oduct. T he adva ntages of the new method a r e its simplicity and quickly verifiable repeatability because this method makes it possible to analyse large numbers of experimental samples. T his method also ensur es higher statistical confidence and less biased measurements. Since the presented method makes it possible to analyse lar ge numbers of samples, statistical tools and higher statistical moments can be estimated. 112
Influence of Melt Film Temperature on Fibre Diameter Distribution
9 INFLUENCE OF MELT FILM TEMPERATURE ON THE FIBRE DIAMETER DISTRIBUTION IN MINERAL WOOL PRODUCED BY A DOUBLE-WHEEL SPINNING MACHINE In this section, we are going to present the influence of temperature on the geometrical fibre values, which are described in the experimental model [21, 76]. Experiments, using thermal vision, enabled the estimation of local temperatures on the surface of the melt film, where the fibres of mineral wool are formed. With the temperature dependence of the thermophysical properties [21] and the fibre thickness model [21, 31], we wish to make a comparison between the measured fibre thickness distribution and the modelled fibre thickness, which considers the temperature on the surface of the melt film. When the melt flows onto the first spinning wheel, a thin melt film is formed. Since the melt film forms around the rotating spinning wheel in non-isothermal conditions, we can expect that the melt temperature on the surface of the film is time and space dependent. This influences the mechanisms of the fiberisation of melt. The melt film does not have a uniform temperature; therefore, the temperature profile in the transverse direction of the wheel exists. The average temperature of the melt film in the transverse direction of the wheel is:
TL
1 l TL (l )dl l ³0
(9.1)
where T L(l) is the local temperature of the melt film and l is its width. The temperature dependence of density, surface tension and viscosity of silicate melts have a strong effect on the fibre diameter. 113
Mineral Wool
Also, the density, viscosity and surface tension of silicate melts play an important role in the proposed model equation (6.3) for the calculation of the mineral wool fibre diameter on the double-wheel spinning machine. Virtually all the characteristic dimensionless numbers in equation (6.3) depend on the density, viscosity and surface tension of the melt, except the fifth characteristic dimensionless number, in which temperature is dominant. The dependences of density, surface tension and viscosity on the chemical composition of silicate melts are considered in the model equation (6.3) for the prediction of mineral wool diameter. 9.1
Thermovision of the spinning wheel melt film
For the estimation of the melt temperature influences on the fiberisation and solidification of fibres, the melt temperature analysis has been performed on the surface of the melt film using the thermovision method [48]. The experiments were performed on a double-wheel spinning machine in real production process (Fig. 9.1). The diameter of both cylinder-shaped, 120 mm wide wheels was 385 mm. Because of experimental limitations, the temperature distribution on the first and second rotating wheel has been assumed to be equal and axisymmetrical. This assumption enables observations of the temperature field on a partial segment of the second centrifuge wheel. Measurements of the surface temperature of the rotating wheel were performed by an AGEMA 570 infrared (IR) sensitive camera which operates in the range of wavelengths between 7.5 μm and 13 μm. Its thermal sensitivity is < 0.15 K and its spatial resolution is 1.3× 10 –3 rad. The camera uses a Focal Plane Array (FPA) detector which consists of a matrix with 320×240 elements/pixels. The accuracy of the camera is ±2 % according to manufacturer’s specifications. The IR camera is placed at the angle of 45° to the second wheel’s longitudinal axis of the spinning machine. The position of IR camera is shown in Fig. 9.1. The distance between the IR camera and the second wheel is 1.8 m. Melt flow images are produced at a capture frequency of 2 Hz in a time period of 100 seconds. Images recorded by the IR camera are processed by using a PC with the ThermaCAM Researcher 2000 programme. This program transforms each picture into a 320×240 matrix of pixels, which consists of particular temperature values (one value for one pixel/element of the matrix). Such matrices can then be used to extract the temperatures on a 114
Influence of Melt Film Temperature on Fibre Diameter Distribution
melt reservoir melt jet ir
ow r fl ai
reservoir adjustmenta melt film
PC
data acq. system
IR camera Z2
fl
ow
Z1
rotating wheels Fig. 9.1. Schematic presentation of the fiberisation process in a double-wheel spinning machine.
B A
Fig. 9.2. Thermovision image of the temperature field on the melt film on the second centrifuge wheel.
selected line between points A and B of the melt film on the second wheel and to form a temperature profile time series. Matlab version 6.1 software package was used for this purpose. The line between points A and B in Fig. 9.2 represents the activity contour of the second wheel. The activity contour A–B in Fig. 9.2 is 100 pixels wide in the IR image. It is parallel to the axis of the second wheel. On this contour, each pixel in the length of 0.75 mm represents the local temperature.
115
Mineral Wool
9.1.1 Experimental results The quantitative analysis of the temperature field on the melt film is reduced to the temperature distribution on the surface of the film on the contour A–B as shown in Fig. 9.2. The temperature values at particular points on the contour A–B are time-averaged for the representative sample group of 200 successively recorded thermovision images. The corresponding standard deviations are also obtained. Figure 9.3 represents the time-averaged temperature distribution on the contour A–B. The temperature profile contains the melt film and parts of the second wheel next to the melt film, where the temperature gradients are significant. These gradients can also be seen in Fig. 9.3 on both the left and right part of the temperature curve in the temperature region between 700 and 1200°C. These regions can significantly contribute to nonhomogeneous fiberisation of mineral wool because the material characteristics in this temperature region change values and thereby influence the fiberisation process. The edge of the melt film is estimated according to maximal temperature gradients of temperature distribution to be approximately 1150°C. In the temperature region above 1150°C, the average temperature calculated with equation (9.1) is 1436°C. The measurement using the optical pyrometric method has shown a similar melt temperature, i.e. 1439°C. The visible surface of the 1600 o
TL = 1436 C
°C
1400
Temperature
1200
1000 measured by IR camera average temperature (10 mm < l < 110 mm) 800
600 0
20
40
60
Widthof of the the disc Width wheel
80
100
120
mm
Fig. 9.3. Temperature profile on the second spinning wheel measured by IR camera. 116
Influence of Melt Film Temperature on Fibre Diameter Distribution
second wheel has the temperature of approximately 700°C. The narrow transition area between the temperature levels of 1150 and 700°C lies between the free surface of the rotating wheel and the melt film. The melt characteristics in this area are not well defined because neither material characteristics nor modelled diameter of fibres can be experimentally simulated. If we assume that the temperatures in Fig. 9.3 are true, the diameter of mineral wool fibres can be calculated according to the regression model, equation (6.3). The other process quantities are: n 1 = 3833 min –1 , n 2 = 4451 min –1 , w z = 2.17 m/s, q m = 1311.25 kg/h, ρ z = 1.169 kg/ m 3 . The calculated fibre diameters are also shown in Fig. 9.4. Figure 9.4 shows that the calculated diameter of fibres ranges from 4.75 m to 6.46 m. 1600 1550
°C
1500 1450 1400 1350 Temperature
1300 1250 1200 1150
calculated (1150 °C < TL < 1550 °C) extrapolation line
1100 1050 1000 4.5
5.0
5.5
6.0 Diameter of fibre
6.5
7.0
7.5
8.0
Pm
Fig. 9.4. Correlation between the calculated fibre diameter and melt temperatures.
Since the temperature field in this experiment exceeds the temperature limits (700 to 1550°C) in the model, the validity of fibre diameter model equation (6.3), is expanded with the linear extrapolation as shown in Fig. 9.4. On the basis of the temperature profile, shown in Fig. 9.4, a temperature histogram can be created, Fig. 9.5. It is evident from Fig. 9.5 that more than 85 % of the presented temperatures are greater than 1200°C and lower than 1550°C. If we assume that the temperature distribution on the surface of melt 117
Mineral Wool 40
38,05
35 31,96
%
30 25
Frequency
20 15
12,77
10 6,38 4,65
5 0
1,91
1,95
2,33
800
900
1000
1100
1200
Surface temperature
1300
1400
1500
°C
Fig. 9.5. Temperature histogram according to the temperature profile on the second spinning wheel.
film on the second spinning wheel is equal to the distribution of the mineral wool diameter of fibres, then 85% of the calculated diameters of fibres range from 4.75 up to 6.45 μm. Frequency in Fig. 9.5 is calculated according to this formula: l (T Ti 1 )
³
Frequency (Ti )
T (l )dl
l (T !Ti 1 ) l
³ T (l )dl
,
(9.2)
0
where T i is equal to (T i–1 + T i+1 )/2. A computer-aided visualisation method is used for estimating the fibre diameter from numerous samples of mineral wool as described in section 8. Figure 8.2 shows a scheme of the experimental setup that allowed automatic unbiased measurement of fibre diameter. Based on statistical analysis, the histogram of fibre diameter was made and is shown in Fig. 9.6. This distribution is based on the number of fibres in the specimen. Fibre diameter d V calculated from equation (6.3) is the median value of the fibre diameter distribution:
118
Influence of Melt Film Temperature on Fibre Diameter Distribution M
¦O d i
dV
i 1 M
Vi
,
¦d i 1
(9.3)
Vi
where M is the total number of fibres in the specimen, λ i is the portion of fibres with diameter d Vi . Figure 9.6 shows that the fibre diameter ranges from 1 to 14 μm. If the calculated diameter of fibres according to the temperature distribution on the second spinning wheel is extrapolated from 1150°C to 700°C, Fig. 9.4, then the fibre diameter ranges from 4.75 to 10 μm. The extrapolation of the model in the higher temperature region could not be used because the temperature in the real process does not exceed the 1550°C. Fibre thicknesses down to 1 μm were also observed. The range of fibre thickness (1–4.5 μm) could not be explained by the temperature profile. The temperature profile allowed to predict more than 70 % of fibre thicknesses (extrapolated model, Fig. 9.6). Different fibre diameters can be predicted from the temperature distribution on the second centrifuge wheel. The measuring method provided by the infrared camera is suitable for measuring the temperature distribution on the second wheel in the real manufacturing process. 40
extrapolated model
35
33,42
%
30 26,56
25
Frequency
20
18,13
15
14,10
10 5,32
5 1,32
0
0
1,15
2
4
6
8
Fibre diameter
10
12
Pm
Fig. 9.6. Typical histogram of fibre diameter (measured). 119
14
Mineral Wool
The non-uniform temperature distribution can explain the different size of fibres in the real production of mineral wool. By knowing the magnitude of parametric constants in the regression model, equation (6.3), which consider temperature dependence of silicate melts’ density, surface tension and viscosity can help to predict the different fibre diameter due to the non-uniform temperature distribution on the second spinning wheel.
120
Formation of the Primary Layer
10 FORMATION OF THE PRIMARY LAYER T his chapter deals with fibre for mation in the pr imary layer of mineral wool in the case of a four-wheel spinning machine. During the mineral wool formation process, the fibres are usually formed on the first and the second wheel of the spinning machine, where besides fibr e for mation, also moistening pr ocess of fibr es with phenol solution takes part (structure: phenol for maldehyde pitch, urea, water). When the melt jet impinges on the first spinning wheel and a thin layer of melt is formed on all wheels, mineral wool fibres start to form as well, Fig. 10.1. For med fib r es enter into the coaxial blow away flow which spr eads ar ound the cir cumfer ence of the centr ifuge wheels. The shape of the coaxial nozzles in flow direction is shown in Fig. 10.2. A nozzle of constant 20 mm wide cr oss section is placed ar ound the cir cumfer ence of wheels 2, 3 and 4. Wheel 1, on which the molten rock jet impinges, is not usually surrounded by the nozzle. Figure 10.3 represents the construction of the centrifugal rotor on the spinning wheels’ front which, when r otating, gener ates radial
Fig. 10.1. Fiberisation process on a four-wheel spinning machine. 121
Mineral Wool
1 2 f 3 4 f
f Fig. 10.2. Shape of coaxial nozzle on the spinning machine front.
Fig. 10.3. Shape of front rotor on wheel 2.
vortex flow. The solution with built-in front rotors is comparatively analysed with a classic solution of the wheels with plane, smooth front surface. The shape of the front rotors on wheels 3 and 4 is equal, on wheel 2, however, the geometry of the rotor is arranged to fit to the outer diameter of wheel 2. The nominal velocity of blow away, defined by the volume flow and the outlet cross section area of coaxial nozzles, is in the range w ≈ 100 − 110 m/s. 122
Formation of the Primary Layer melt reservoir
B
primary layer
melt jet
formation of mineral wool primary layer
spinning machine
CCD camera suction channel
data acq. system
A
blow away flow
perforated mesh
secondary air flow (suction)
A
PC
B
Fig. 10.4. Scheme of the collection chamber.
T he coaxial air flow tr anspor ts miner al wool fibr es into the collection chamber which is pr esented in Fig. 10.4. Besides the basic blow away flow that transports fibres into the region of the moving perforated mesh, a secondary suction air flow is formed in the collection chamber which ensures the negative pressure in the collection chamber and dir ects the air flow onto the per forated mesh, Wicker et al. [49]. Consequently, this causes the subsiding of mineral wool fibres on the mesh and the formation of the primary layer. The nominal velocity of the blow away flow in the region of the per for ated sur fa ce is w ≈ 2–2.5 m/s. T he blow a way flow transfers through the side channel into the suction system filter and to the transport ventilator. The volume flow ratio of blow away and suction flows in the collection chamber is given by the boundary r a tio: V blo w : V suc ≈ 1:10 to 1:12. T he inclination angle of the perforated surface α is usually in the region 50 < α < 90°. In the obser ved process, the inclina tion angle of the per for ated sur face was 58°. The pr imary layer formation is also influenced by the structure of the perforated mesh as well as its velocity of movement towards the outlet aper ture on the top of the collection chamber, 123
Mineral Wool
wher e the pr imar y layer is ult imately for med, and exits the collection chamber. The velocity of the perforated mesh influences the thickness and specific surface density of the primary layer. With increasing velocity of movement at constant quantity of the fiberised mater ial, the specific density and pr imar y layer thickness ar e reduced. Simultaneously, the influences of non-homogeneous layer for mation in the entir e r egion of the per for ated sur face become significant. T hey ar e above all connected with the velocity characteristics of the spinning machine, blow away flow, suction flow and their interaction in the collection chamber. Present local velocity anomalies cause the rearrangement of fibres in the air flow, tearing of the already existing layer, and the formation of fibre rolls in the primary mineral wool layer. T his section deals with loca l pr oper ties of blow away and suction flows as well as with their influence on the primary layer structure experiment. Starting from the hypothesis that aerodynamic char acter is tics of pr imar y blow away flow out of the spinning machine and suction flow from the collection chamber significantly influence the str uctur e of pr imar y miner al wool layer, separ ate measur ements of the velocity field were perfor med on the blow away flow of the spinning machine nozzles, on the suction flow in the region of perforated sur face, as well as measurements of the velocity profile in the region of perforated surface at simultaneous oper ation of both systems (blow away and suction). Dur ing simultaneous operation of both flows, the velocity conditions were investigated with and without centrifugal rotors at the front of the spinning wheels. All velocity field measurements were per formed without the presence of the melt jet on the rotating wheels. 10.1 Influence of blow away velocity field on the primary layer fibre structure in the mineral wool production process In this section, the study of the influence of airflow kinematics on the formation of the primary mineral wool layer is performed. This is also described in [50]. The analysis of the blow away velocity field in the coaxial flow of a four-wheel centrifuge was performed as well as its inter action with the suction flow in the collection chamber and the influence of both flows on the formation of mineral wool pr imar y layer, as r epor ted by Ab litzer et al [51], on the per forated mesh in the collection chamber. The very heart of the matter is the ratio of the observed suction flow velocity fields of 124
Formation of the Primary Layer
low intensity level, w ≈ 2.5 m/s, and the velocity field in the coaxial flow blow away velocity fields of which the mean value exceeds w ≈ 120 m/s and forms an axial non-symmetric velocity distribution on the perforated, moving surface of lamellae on which the fibres that form the primary mineral wool layer are deposited. As reported by Wa r da et al. [52], t he r eduction in absolute values of the velocities of two flows while keeping the same velocity r atio constant made the coaxial jet decay faster along the centr e line. Interaction of both flows in the region of primary layer formation causes, since the local kinetic energy of the flow is exceeded, the deformation of the layer which is indicated by the for mation of ‘rolls of wool’ which are torn off by the local air flow from the primary layer. Formation of the rolls has a negative influence on the quality of the primary layer and, consequently, on the final product. T he technical solution r epr esents the introduction of centrifugal r otor s, Šir ok et al. [53], on t he spinning wheels’ fr ont which generate a radial vortex flow which diverts the basic coaxial flow of the spinning machine, reduces the intensity of the velocity field in the r egion of miner al wool pr imar y layer for mation and consequently homogenises the str ucture of the primary layer. The influence of the mentioned technical solution is evaluated with the comparative experimental study which includes measurements of the velocity fields of coaxial air flow and in the plane of the perforated mesh in the collection chamber. T he estimation of the effects on the pr imar y layer is based on the compar ative a nalysis of successively recorded images of the primary layer with and without centrifugal rotors. 10.1.1 Velocity field measurements on the nozzles of a four-wheel spinning machine The estimation of velocity distribution on the coaxial nozzles of a four-wheel spinning machine was performed with the aid of local axial velocity component meas ur ements via dynamic pr essur e measurements with a Pitot–Prandtl probe. The position of the probe was def ined with par a meter R (R = H + D/2), wher e D is the diameter of the wheel and H the axial distance fr om the wheel surface, and angle ϕ as shown in Fig. 10.5. Angle ϕ is the relative angle between the tube position and the upper position of the coaxial nozzle on the measured wheel of the centr ifuge. This angle was measur ed indir ectly via the measur ement of volt age on the measurement potentiometer. Throughout the experiment, the probe 125
Mineral Wool Pitot-Prandtl probe
p dyn B /2
ps
B /2
H R
Flow out of coaxial nozzles
Measurement potentiometer of position ϕ
f
B
Fig. 10.5. Measurement of axial velocity component and angle ϕ .
was located in constant distance B/2 from the nozzle whereas B is the width of the wheel. The movement of the measurement system is performed manually. The described measurement procedure of axial velocity component was accomplished on wheels 2, 3 and 4 in range H = 5–50 mm. Velocity measurements in the collection chamber were performed with a vane anemometer in the entire plane of the chamber. The distance of the anemometer from the perforated mesh was 100 mm. Velocity profiles were measured at three different operation regimes: at nominal suction flow of the collection chamber; at nominal suction and blow away flow; and at nominal suction and blow away flow with centrifugal rotors. Measurements were performed without the mineral wool layer at nominal volume flow rates of suction and blow away flows. According to ISO 3354 [54], in order to correct the non-stationary effects, the local reference velocity was measured and taken into consideration when correcting the respective velocities in the measurement plane. The vane anemometer and its installation on the perforated mesh are presented in Fig. 10.6. The characteristic measurement signal on the vane anemometer in transition across the collection chamber at constant distance from the perforated mesh and constant measurement plane height are presented in Fig. 10.7. In this figure, one can notice that measurements were performed at constant height on eight locations in the collection chamber cross section. The vane anemometer was moved to the desired position where 126
Formation of the Primary Layer
Perforated mesh Vane anemometer
U, V U (V)
Fig. 10.6. Installation of vane an emometer on the perforated mesh in the collection chamber.
6 5 4 3 2 1 0
B A
0
1000 2000 3000 4000 5000 6000
ii (-) A – selected signal B – correction signal selected signal correction signal Fig. 10.7. Characteristic measurement results at selected height of the collection chamber’s cross section.
the measur ement dur ation in a cer tain cr oss section location depended on the time in which the local steady state condition was achieved. After measurement in the quasi-steady state condition has been per for med, the anemometer is moved to a new pr eviously determined measuring point. Simultaneously, measurements of local velocity a t the outlet channel ar e per for med accor ding to ISO 3354, [54] (measurement signal is presented in Fig. 10.7). The measurement signal is applied as a correction factor for determining the local velocity in the obser ved position. T her efor e, the compar is on cr iter ion of loca l velocities is attained. T he local velocities are measured at different times in statistically stationary operational conditions. The cor rection signal is measured in the stationar y point on the outlet channel axis at the ou tlet of the collection chamber. The position of the outlet channel is presented 127
Mineral Wool
in Fig. 10.4. Local time stationary velocities, which in continuation serve for determining the velocity field on the perforated mesh at the mentioned operational regimes of the collection chamber, were calculated by averaging corrected local velocities in intervals where the anemometer locally reached the stationary state. In Figs. 10.8 and 10.9, two typical structures of primary layer at the collection chamber outlet with and without centrifugal rotor on the spinning wheels’ front are presented. The successive images of the primary layer are captur ed with the aid of a CCD camera (Fig. 10.4) at the outlet of the collection chamber. Installation positions of the camera and of the illumination system are selected so that the disturbing effects are reduced to minimum and remain constant during the observation phase. The experimental results of collection chamber ’s blow away and suction system flow pr oper ties ar e obtained with the aid of pr evious ly descr ibed pr ocedur es. With t he synthesis of par tial results, mutual influences of blow away flow on coaxial nozzles and of suction flow can be investigated. T he influence of centr ifugal
Fig. 10.8. Structure of the primary layer at the collection chamber outlet without the centrifugal rotor.
Fig. 10.9. Structure of the primary layer at the collection chamber outlet with the centrifugal rotor. 128
Formation of the Primary Layer
rotors on the rotating wheels’ front, on flow structures of coaxial spinning machine flow and consequently on perforated mesh of the collection chamber can be deter mined. T his analysis, which was performed without taking into consideration the fibres in the air flow and without formation of the mineral wool layer in the collection chamber, can be upgraded with the analysis of the influences of flow field fluctuations on the structure of the mineral wool layer. Consider ing the positions of t he Pitot–Pr andtl pr obe and the r espective measur ed dynamic pr essur e, local velocit ies in the measurement plane were calculated:
2 pd
w( R, ϕ ) =
ρ
,
(10.1)
where R is the distance of the measurement tube from the centre of the wheel. Considering the arrangement of the nozzles near the wheels 2, 3 and 4, the total velocity field on coaxial nozzles can be presented in the Cartesian coordinate system, Fig. 10.10. From the presented velocity distribution, one can conclude that the axial velocity profile is determined, above all, by the shape of coaxial nozzles. Transver sal velocity distr ibution on a nozzle is asymmetric. Velocity maximum, wmax = 120–140 m/s, is reached at about 1/3 H from the wheel surface, whereby H is the nozzle width. After reaching its maximum, the velocity profile is reduced in radial dir ection a way fr om the sur face of the wheel, and r eaches the distance of about 2H value between 10–0 m/s. In several regions around blow away nozzles, local anomalies are present. They are linked to local geometric and flow characteristics of the blow away-
800 700
y (mm)
600 500 400 300 200 100 0
100
200
300
400
500
600
700
800
x (mm)
Fig. 10.10. Velocity distribution (presented in flow direction) in coaxial blow away flow on the nozzles of a four-wheel spinning machine. 129
Mineral Wool
flow. If, however, space flow anomalies do not exceed typical length H, the influence of velocity anomalies is functionally negligible. The velocity field in the region of the first wheel is not intensive since the coaxia l nozzle beside that wheel is not pr esent and the measured velocities depend only on the air flows of other wheels. The same holds for the velocity field between the wheels. There, coaxial blow away nozzles also are not present. Measured velocity fields in the region between the wheels and next to the first wheel are in the region of w < 20 m/s. These velocities do not significantly influence the transfer of fibres from the wheels into the collection chamber. According to the fact that the axial velocity on blow away nozzles of the spinning machine was measured during the standstill of the centrifuge wheels, it can be expected that the velocity field, when the wheels ar e r otating, is differ ent since the momentum transfers across the boundary layer which is transformed when the wheels are rotating. Significant changes of the blow away flow can, however, b e expected with cent r ifugal r otor s on the spinning wheels’ front. Qualitative presentation of the influence of the centrifugal rotor on flow conditions on the spinning machine wheel is given in Fig. 10.11 which provides important visual information about the flow conditions on the wheels. In Fig. 10.11(a), the structure of the blow away flow from the wheel is presented without a centrifugal rotor. Fig. 10.11(b) presents the flow str ucture of the blow away flow combined with secondary flow through the centrifugal rotor. Flow visualisation was performed with added smoke marker in the blow away flow of wheel 3 of the observed spinning machine. From Fig. 10.11(a) one can recognise that the blow away flow is, according to expectations, coaxially or iented. Consequently, the gr adual, insufficient reduction of the velocity field intensity is achieved at the transition of the blow away flow to the collection chamber. Fr om the p r esented topological str uctur e of the f low in the constr uction with added centr ifugal r otor, the flow diversion in
a) A
b) B
Fig. 10.11. Influence of centrifugal rotor on flow conditions on the spinning machine wheel: a) without centrifugal rotor; b) with centrifugal rotor. 130
Formation of the Primary Layer
diagonal direction can obviously be linked to the secondary flow on the added centrifugal rotor according to the Flow through the turbo machine rotor theory, similarly reported by Wicker et al. [49]. From the coaxial blow away flow diversion, the reduction of the axial blow away flow velocity component in the collection chamber is expected at simultaneous counter flow gener ation which is the consequence of pumping in the centrifugal rotors inlet region. The comparison of both flow structures leads us to the hypothesis that with the inclusion of centrifugal rotors on the spinning wheel’s front, flow conditions in the collect ion chamber ar e significantly influenced. 10.1.2 Velocity field structure in the transition region through the perforated mesh of the collection chamber On the basis of the velocity field measurement pr ocedur e of the transition region of air flow through the perforated mesh, local flow anomalies can be assessed, and the study of the influence of added centrifugal rotors on the velocity distribution in the region of flow tr ansition thr ough the per for a ted mesh can be per f or med. T he measurement results are presented in Figs. 10.12 and 10.13. In both diagrams, the normal velocity distribution in the A–B plane, Fig. 10.4, is presented, where the abscissa and the ordinate present the exact location of the measurement spot. Isolines in the diagrams quantify the local velocities. The analysis is focused on the assessment of local anomalies such as asymmetry of the velocity field, counterflow r egions, location of local extremes and their r elation to the spinning machine blow away flow. Centr al is the compar ison of velocity distribution on both velocity fields in Figs. 10.12 and 10.13 accor ding to which one can es timate the influence of added centrifugal rotors on the normal velocity distribution in the A–A plane. Figures 10.12 and 10.13 show that in both observed cases the region of the velocity extreme can be observed and is, according to expectations, located on the spinning machine blow away axis (x = 1.2–1.5 m, y = 2.3–3.0 m). An impor tant differ ence exists between the intensity of the velocity extremes of which the one pr esented in Fig. 10.12 is mor e pr onounced. Reduct ion of the velocity extreme in Fig. 10.13 is a consequence of the transformation of the blow away flow with the secondary flow, generated by centrifugal rotors on the spinning wheels’ front. By comparing both diagr ams one can conclude that with the intr oduct ion of the 131
Mineral Wool 5 4.5 4
y-axis
m
3.5 3
2.5 2 1.5 1
0.5
1
x-axis
1.5
2
2.5
m
Fig. 10.12. Velocity distribution (m/s) (represented in flow direction) in the A-B plane of the spinning machine without centrifugal rotors. 5 4.5
m
4
y-axis
3.5 3
2.5 2 1.5 1
0.5
1
x-axis
1.5
m
2
2.5
Fig. 10.13. Velocity distribution (m/s) (represented in flow direction) in the A-B plane of the spinning machine with centrifugal rotors.
132
Formation of the Primary Layer
centrifugal rotors, the following is achieved: a more homogeneous velocity distribution, reduced local extreme on the perforated mesh surface on the spinning machine blow away axis and elimination of the recirculation flow, presented in the spinning machine version without centrifugal rotors on the spinning wheels’ front. T he presented differences influence the for mation of pr imar y layer in t he per for ated mesh. It can be expected t hat in the homogeneous velocity field, the fibre transport is performed with generation of surface homogeneous structure of the primary layer. Consequently, the r egions r educe, in which the tear ing of the primary layer caused by high local velocity and recirculation flow takes part. Since in the real process of primary layer formation the velocity fields in the collection chamber cannot be measured, the mentioned expectations can be monitored indir ectly by estimating the velocity field. Influence of the centrifugal rotor on the primary layer structure Beside the qualitative estimation which can be per for med on the images of the mineral wool primary layer at the collection chamber outlet (Figs. 10.8 and 10.9) already fr om the comparison of the primary layer (Figs. 10.8 and 10.9), a significant change of the layer structure can be seen. In the basic construction without centrifugal rotors (the primary layer is presented in Fig. 10.8), the structure is mor e ‘r ough’ and non-homogeneous. With added centr ifugal r otor s, Fig. 10.9, the str uctur e homogenises a nd becomes ‘smoother ’. With centr ifugal r otors on the wheels, the kinematics of blow away flow of the spinning machine is significantly modified and consequently causes modifica tion of the air velocity field in the collection chamber. Velocity modifications in the region of primary layer formation, however, influence the structur e of the primary layer in the collection chamber. With the introduction of centrifugal r otor s on a four -wheel spinning machine, a mor e homogeneous miner al wool pr imar y layer is obtained as a cons equence of homogeneous velocity distribution of the air flow at its transition thr ough the r ising layer and per for ated mesh in the collection chamber.
133
Mineral Wool
10.2 Visualisation method for measuring the primary layer Manufacturers of mineral wool are trying to improve the insulating pr oper ties of the pr oduct. We ar e witnessing impor tant impr ovements in the optimisation of homogeneity of the primary layer. Currently, the primary layer homogeneity is not monitored online dur ing the pr oduction pr ocess. T he contr ol is limited to operator ’s periodic observations. However, a visualisation method for the measur ements of pr ima r y layer homogeneit y has been developed [46]. The applicability of the method is pr esented by coupling t he method with a cor r esponding r egr ession model of primary layer homogeneity. T he method of computer -aided visualisation was used for quantitative description of the homogeneity of mineral wool primary layer [46]. This method is based on the acquisition of subsequent images of the primary layer immediately after its exit out of the collection chamber (Fig. 10.4). T he tar geted str uct ur e of the primary layer should be homogeneous and isotropic on local scales, and without inter r uptions on the sur face on lar ge s cales. T he primary layer of mineral wool should also be as thin as possible for pr oducts of small density. T his is consistent with the optically homogeneous isotropic str ucture of miner al wool samples in the primary layer. The structure can be measured by using computeraided visualisation, spatially and in time. Two pr imar y layer sample ima ges ar e shown in F ig. 10.14, corresponding to the production line parameters denoted as ‘good’ (Fig. 10.14, left) and ‘bad’ (Fig. 10.14, right), r espectively. The example shows significant influence of production line parameters on the structure and quality of the primary layer.
Fig. 10.14. Structure of primary wool layer, homogeneous (left) and non-homogeneous (right). 134
Formation of the Primary Layer
T he images were acquir ed by using the same camer a and software as in the case of the experiment described in section 8.2. The camera position and illumination were selected as shown in Fig. 10.4, and did not change during the experiment. Analysis was per for med on each image in a sequence in selected windows, ar ranged as shown in Fig. 10.15. 90 windows wer e selected in each image. F or each image in the sequence, average intensity A(k,t) in each window was calculated [46]:
A(k , t ) = ∑∑ E (l , m) . l
(10.2)
m
Here, k denotes the successive window number in each frame and t denotes the successive acquired images; the intensity of pixels E(l,m) ranges from 0 to 255, corresponding to the 8-bit resolution of the camera; l and m are the coordinates of the pixels inside the window (k,t); the s ize of the window was set to 3× 3 pixels according to the typical structure of the primary layer as shown in Fig. 10.15. Both the instantaneous geometry structure of the primary layer and its time variation were recognized as important characteristics in the monitoring of the process. This led to the introduction of a ‘pseudo time series’ [47]. In this variable p is defined by:
p = n ⋅ 90 + k where k ∈ {1....90} , n = int(t / t f ) and t f = 1 25 s (10.3) n being the number of the video fr ame in the sequence, and 90 pr oviding t he appr opr iate shift , on the p axis, between the successive images; k is the distance from the image, and is the time inter val at which images ar e acquir ed (i.e. fr aming speed). Fig. direction of primary layer movement
k=1 to 90
3x3
Fig. 10.15. Arrangement of windows for analysis in each image. 135
Mineral Wool
200
A
150 100 50 0
90
180
270
360
450
p
Fig. 10.16. Construction of a ‘pseudo time series’ A(p), [44].
1600 1400 Normal curve
1200
_ A = 131.94 RMS = 13.29 It-ex = 10.07 %
Frequency
1000 800 600 400 200 0
60
80
100
120 140 Variable A
160
180
200
Fig. 10.17. Histogram of variable A with respect to Fig. 14 – left.
10.16 shows the average grey level A plotted against p. A(p) is the a ver age gr ey level intensity used to der ive the expression for the mineral wool structure estimator. Histograms of variable A(p) for pr imar y layer str uctur es cor r esponding to the primary layer structures from Fig. 10.14 – left and Fig. 10.14 – right are shown in Fig. 10.17 and 10.18. Figures 10.17 and 10.18 show significantly different histograms, confirming the qualitative estimation of mineral wool primary layer in Fig. 10.14 – left and Fig. 10.14 – right. Besides the differences 136
Formation of the Primary Layer 1200 1000
Normal curve _ A = 132.31 RMS = 25.13 It-ex = 18.99 %
Frequency
800 600 400 200 0
60
80
100 120 140 160 _ Fluctuation of variable A - A
180
200
Fig. 10.18. Histogram of variable A with respect to Fig. 10.14 – right.
in histogr ams, the statistics of aver age value Ā and r oot mean squar e ( RMS) of aver age gr ey level int ensity A(p) can be established. As a statistical estimator, thus, the ratio between RMS and the average of A(p) can be selected:
I t −ex =
1 M ∑ ( Ai ( p) − A)2 M − 1 i −1 RMS ⋅100 % = ⋅100 % . A A
(10.4)
Statistical estimator I t-ex , equation (10.4), is the measur e of the primary layer quality which depends on the selected pr oduction parameters. 10.2.1 Regression model of mineral wool primary layer homogeneity A regression model for a four-wheel spinning machine was briefly descr ibed in section 6.3. For the development of the r egr ession model for pr imar y layer evalua tion on a four -wheel spinning machine, the same characteristic dimensionless numbers are going to be used, equation (6.5). T he tar get function of aver age gr ey level intens ity of the miner al wool pr imar y layer, equ ation (10.4), can be wr itten in parametric form with the regression model as: 137
Mineral Wool a3 h3 a1 a2 a4 e1 e2 h1 h2 h4 I t = a0 Π11 Π12 Π13 Π14 Π 3c1 Π 4d1 Π 51 Π 52 Π 61f1 Π 62f 2 Π 7g Π 81 Π 82 Π 83 Π 84 Π i9 . (10.5)
Here, a 0 and a 1 , a 2 , a 3 ,… d 1 ,… i are the par ametric constants of the regression model. 10.2.2 Experimental results The experimental set-up T he exper iments wer e per for med on an oper ating four -wheel spinning machine. They, 47 in total, were carried out by varying the air mass flow q mG (blow away flow and suction flow), the rotational speed of wheels ω1 , ω2 , ω3 , and ω4 , and the volume flow of binder. At each operation point, samples of melt and successive images of primary layer were stored. These successive images were acquired by the CCD camer a at miner al wool’s exit fr om t he collection chamber. O ther exper imenta l conditions wer e similar to the conditions described in section 6.3. 10.2.3 Statistical analysis of experimental results The regression analysis was performed on the measured data with the a id of commer cial sof twar e [15]. T he par a meter s of the r egr ession model and the most impor tant char a cter istic dimensionless numbers from equation (10.5) were determined: a31 a51 a52 a62 a82 a83 a84 a11 a14 a44 I t = a0 Π11 Π14 Π 31 Π 44 Π 51 Π 52 Π 62 Π 7a71 Π 82 Π 83 Π 84 Π 9a91 .
(10.6)
On the basis of the performed experiments and the analysis, it has been established that the homogeneity of miner al wool pr imar y layer depends on 12 dimensionless number s, while all other dimensionless numbers can be neglected. Good agreement between the regression model and the measured values of fibre parameters was also confirmed by a high value of correlation coefficient: r 2 =0.813 which indicates good quality of the regression fitting and the measured values. The agreement between the measured and the modelled average grey level intensity of the pr imary layer was examined with the F-test. T he test r esults are pr esented in Table 10.1. The F-test estimated the hypothesis that the regression is not significant. The probability of the validity of this hypothesis was less than 0.001, so the regression was very significant. T he values of r egr ession model par ameter s ar e pr esented in 138
Formation of the Primary Layer
Table 10.2. Their significance was checked with the t-test. T he test r esults pr esented in Table 10.2 show a s ignificant influence of all par ameter s a i j a nd cer ta in cha r a ct er istic dimensionless number s. T he r esults of compar ison between the measured parameters of grey level intensity of mineral wool primary layer and t he calculated ones on the basis of a 12- par ametr ic regression model are shown in Fig. 10.19. The presented measurement method enables the monitoring and quality contr ol of miner al wool pr imar y layer. T he sta tistical Table 10.1. F-test results of agreement between the modelled and measured values De gre e of Free dom
Sum of Square s
Me an Square
F Statistics
Prob > F
Regression
12
6183.93172
515.32764
702.857
0.001
Residual
35
25.66148
0.73319
Total
47
137.89773
Source
Table 10.2. Significance of parameters of the regression model according to Equation (10.6) along with the results of t-test
Order of of significance Variable Coefficients Variable t-t est Significance Significance Order Coefficients t-test Significance Π 11
a11 = –53.09
–3.48
0.00225
VII
Π 14
a14 = –116.66
–7.81
1.2E-07
I
Π 31
a31 = –1362.31 –7.67
1.6E-07
II
Π 44
a44 = –97.10
–6.19
3.9E-06
VI
Π 51
a51 = –890.02
–6.60
1.6E-06
III
Π 52
a52 = 1048.85
2.70
0.01341
VIII
Π 62
a62 = –1063.69 –2.65
0.01485
IX
Π 82
a82 = –4.74
–2.63
0.01579
X
Π 83
a83 = 889.84
6.59
1.6E-06
IV
Π 84
a84 = –869.25
–6.40
2.4E-06
V
Π7
a71 = –20.22
–0.77
0.4487
XII
Π9
a91 = –242.34
–2.31
0.03141
XI
139
Mineral Wool 20
Intensity (measured, predicted)
%
2
r
=0.81
12-param
18
16
14 experiment modelled
12
10 10
12
14 Intensity (measured)
16
18
20
%
Fig. 10.19. Comparison between the experimentally measured grey level intensity of the primary layer and the predicted values obtained with the aid of statistical an alysis.
estimator of pr imar y layer homogeneity is defined by the r atio between the RMS and the average value of grey level intensity in the selected windows of the image. We found out that the estimator is a good indicator of pr imar y layer quality. T he r esults of the regression model show good agreement with measured gr ey level intensit ies of the miner al wool pr imar y layer. Because all the var iables pr esented in the r egression model ar e measur ed, it is possible to establish which par ameter of the pr ocess should be adjusted to obtain the desired quality of the product. The presented measur ing method and r egr ession model pr ovide for automated control of the mineral wool production process.
140
Numerical Analysis of Flow Properties in Collection Chamber
11 NUMERICAL ANALYSIS OF FLOW PROPERTIES IN THE COLLECTION CHAMBER Miner al wool pr imar y layer for mation is influenced by the aer odynamic char acter istics of the blow away flow and the secondary, surrounding air flow. The computer-aided visualisation method, descr ibed in section 8 .2, was used for qu antitative description of the uniformity of the primary layer [46]. Images were acquir ed using the same black-and-white CCD camer a as in the experiments in section 8.2. The size of the window was set to 3×3 pixels according to the typical str ucture of primary layer as shown in Fig. 11.1. In the par ticular window, the var ia ble A(k,t) denotes the momentar ily present portion of mineral wool. In the case of a thin primary layer, the hypothesis describing proportional dependence between variable A(k,t) and the belonging local structure of the primary layer can be set:
ρ ( x, t ) ∝ A( x, t ) .
(11.1)
The distribution of mineral wool perpendicular to the primary layer movement is estimated by using the time-averaged local mass of the primary layer ρ (x,t):
ρ ( x) =
T
1 ρ ( x, t )dt . T ∫0
(11.2)
The mineral wool distribution in the final product can be determined fr om equ ation (11.2). T he distr ibution of miner al wool for the observed production process is shown in Fig. 11.1. Figure 11.1 shows the asymmetrical distribution of mineral wool 141
Mineral Wool 1.4 +σ
1.2 1
ρ (x )
0.8 - σ
ρ avg( x ) 0.6 0.4 0.2 0 0
0.52
1.04 x
1.56
2.08
2.6
m
Fig. 11.1. Mineral wool distribution estimated with the aid of variable
ρ ( x) .
which deviates fr om the unifor m distr ibution that assur es homogeneous mechanical and thermal insulation properties in the final product. This asymmetry is the result of combined flows (blow away flow and secondary air flow) as well as of the mineral fibre transport on the moving perforated mesh. 11.1 Numerical analysis In this section we present a simple numerical model of air flow aerodynamic char acter istics in the collection chamber. T he real aerodynamic conditions of the blow away flow from the centrifuge nozzles are entered into the numerical model. Using the numerical r esults, we calculate the miner al wool thickness at the chamber outlet. Numerical analysis is performed by using CFD software package, CFX-5, [56]. Its solver uses numerical methods for solving general conservation equations including continuity, momentum, and energy equations. All simulations were performed for steady-state cases only, so that the terms with time derivatives could be omitted [56]:
∇ • ( ρU ) = 0 ,
(
(
∇ • ( ρU ⊗ U ) = ∇ • − pδ + μ ∇U + (∇U )
∇ • ( ρUhtot ) = ∇ • (λ∇T ) + S E . 142
T
)) + S
(11.3) M
,
(11.4) (11.5)
Numerical Analysis of Flow Properties in Collection Chamber
Due to fluctuations in turbulent flows, the values of scalar variables need to be time averaged. The original conservation equations, from (11.3) to (11.5), are tr ansfor med to Reynolds aver aged NavierStokes (RANS) equations. In this case, the standard two-equation k– ε tur bulence model was used. Reynolds str esses are expressed in terms of turbulent viscosity by using certain presumptions [56]:
μt = Cμ ρ
k2
ε
.
(11.6)
T he value of constant C μ is 0. 09; ε is the tur bulence eddy dissipation; and k is the turbulence kinetic energy defined as [56]:
k=
1 2 u . 2
(11.7)
The local values of k and ε are obtained by solving the following two additional semi-empirical transport equations [56]:
⎞ ⎛ μ eff ∇ • ( ρUk ) − ∇ • ⎜⎜ ∇k ⎟⎟ = Pk − ρε , ⎠ ⎝ σk
(11.8)
⎞ ε ⎛ μ eff ∇ • ( ρUε ) − ∇ • ⎜⎜ ∇ε ⎟⎟ = (Cε 1 Pk − Cε 2 ρε ) . (11.9) ⎠ k ⎝ σε Effective viscosity μ eff is the sum of real and turbulent viscosity, μ + μ t ; P k is the production rate of turbulent kinetic ener gy as a
result of turbulence. The constants in equations (11.8) and (10.9) are σ k = 1.0, σ ε = 1.3, C ε 1 = 1.44 and C ε 2 = 1.92 [56]. T he t er m S M in equa tion (11.4) r epr esents the momentum sour ce/loss in contr ol volume. T his ter m was used t o simulate pressure loss within the primary layer. The mineral wool layer on the perforated mesh could be regarded as a porous layer which is offering certain resistance to air flow passing through. The resulting pr essur e dr op can be expr essed with the aid of the following expr ession for the friction factor of layers packed with spheres [57]:
f =
1 ⎛ D p ⎞⎛ Δpt ⎞ ⎟ ⎜ ⎟⎜ 4 ⎝ L ⎠⎜⎝ 12 ρ v 2 ⎟⎠ ,
(11.10)
wher e D p is fibr e diameter, L is layer thickness, ρ and v are the fluid density and velocity, respectively, and Δ p t is total pressure drop thr ough the layer. Equation (11.10) shows that pr essur e dr op 143
Mineral Wool
depends on velocity squar ed a s well as on layer thickness. Therefore, pressure loss was modelled by using an additional source ter m in the momentum equa tion (11.4) for each of the thr ee coordinate axes:
S M ,i = −C R 2 U U i .
(11.11)
The thickness of the primary layer is not uniform over the entire ar ea of the per for ated mesh. It incr eases towar ds t he exit of mineral wool from the chamber. Perpendicular to the movement of the primary layer, a parabolic thickness profile was assumed with maximum thickness in the cent r e. T he par abolic r esistance distr ibu tion was confir med exper imentally [46]. T her ef or e, the r esistance coefficient C R2 in equation (11. 11) could not be considered as constant and was defined as:
CR2 = K y −
with K y being
K y = K bot −
K y − K bot ⎛ B⎞ ⎜ ⎟ ⎝2⎠
(K
bot
2
(x − B 2 )
− K top )y Lo
2
,
,
(11.12)
(11.13)
where B is the width and Lo the active length of the collection chamber. Constants K b ot and K to p wer e s et to K bo t = 500 kg/m 4 and K top = 1000 kg/m 4 , which gave appr oximately the same pr essure losses as in the case of measurements. Variable y is the coordinate running alongside and x is the coordinate transversal to the motion of the pr imar y layer. Other constants in equations (11.12) and (11.13) wer e set with r ega r d to the actual geometr y of the collection chamber. By using these values, the resistance coefficient at the bottom of the perforated mesh is K bot , and K top at the top, Fig. 11.2. Additional scalar variable, ψ , was used to monitor the distribution of mineral wool in the calculation domain. In CFX, the additional var iable allows the distinction between the air car rying the wool fibres and ‘clean’ air, [58,59]. Therefore, it simulates the transport of mineral wool fibres by air flow. In gener al, the total amount of fluid in ever y contr ol volume consists of fluids that have entered through both inlet openings. 144
Numerical Analysis of Flow Properties in Collection Chamber
upper edge
Resistance
K top
lower edge
K bot 0
0.52
1.04
1.56
2.08
2.6
x, m Fig. 11.2. Resistance coefficient within the perforated mesh.
Variable ψ in a particular control volume V i depends on the amount of air that has r eached the contr ol volume x(m) fr om t he inlet nozzles.
ψ=
Vn ,i
. Vn ,i + Va ,i
(11.14)
Index i repr esents the particular control volume; Vi is the total volume flow through the selected control volume; Vn ,i are volume flows from the nozzle; and Va ,i are volume flows of ambient air that r eached the contr ol volume. Var iable ψ always has values between 0 and 1. Its value at the free opening and inlet nozzles is 0 and 1, respectively. Presuming that fibre distribution at the inlet nozzles is uniform, the assumption is that the value of variable ψ for mass flow rate of mineral wool at the inlet m w is uniform too. This presumption enables the modelling of proportional dependence between the local mineral wool mass flow rate in the control volume, the mineral mass flow rate at the nozzles’ inlet m w and the local value of variable
ψ
(11.15) m kv , i ∝ mw ψ . The scalar value ψ is transported through the computational domain
together with the main fluid flow. This value is determined by the following additional transport equation for steady-state cases:
145
Mineral Wool
⎛μ ⎛ψ ⎞⎞ ∇ • (Uψ ) = ∇ • ⎜⎜ t ∇ • ⎜⎜ ⎟⎟ ⎟⎟ . ⎝ ρ ⎠⎠ ⎝ St t
(11.16)
The distribution of scalar variable ψ near the perforated mesh can give an estimate of the amount of mineral wool that is added to the existing mineral wool layer in particular areas of the mesh. 11.1.1 Simulation set-up The computational domain, the surface grid of the domain and the perforated mesh are shown in Fig. 11.3. The entire grid consists of 111591–124745 nodes (depending on the geometry variations) and 602720–662030 volume elements. Since the grid was not structured, the volume elements wer e mos tly tetr ahedr al. T he maximum tetr ahedr on edge length was limit ed to 250 mm. T he gr id was fur ther r efined for cer t ain geometr ical details (inlet nozzles, perforated mesh). The values for fluid velocity at the inlet nozzles and mass flow in the suction duct were established by the measurements described in section 8.1 Steady-state solutions were achieved for two simulated cases where the convergence criteria required the maximum residuals to fall under 10 –3 . The air properties were taken at STP (0°C, 1.01325 bar), with constant density being 1.284 kg/m3 . Additional models such as gr avity and buoyancy wer e not included s ince their influence on the flow is negligible.
Fig. 11.3. Computational domain and grid. 146
Numerical Analysis of Flow Properties in Collection Chamber Inlet nozzles Boundary condition type
Inlet
Fluid velocity
100 m/s
Flow direction
Normal to the boundary surface
Free opening Boundary condition type
Opening
Relative pressure
0 Pa
(With regard to reference pressure of 1 bar) Flow direction
Normal to the boundary surface
Suction duct Boundary condition type
Outlet
Mass flow
46.39 kg/s
11.1.2 Experimental determination of boundary conditions The measurements of blow away flow, suction air flow and primary layer formation were performed earlier and are described in detail in [50]. Boundar y conditions for numer ical simulation wer e determined by using the experimental data. The air velocity field at the spinning machine nozzles’ outlet is pr esented in Fig. 11.4. In Figur e 11.4, the axial asymmetr y of velocity distribution can be seen. The velocity extremes are detected and their values can exceed 100 m/s. T hese loca l extr emes significantly influence the distribution of scalar variable ψ and the fibre distribution in the primary layer, respectively. 11.2 Numerical results of flow properties in the operating collection chamber The mesh presented in Fig. 11.3 and the boundary conditions were used for numer ical analysis of flow pr oper ties in an oper ating collection chamber. Figur e 11. 5 pr esents the r esu lts of the simulation. The local values of additional scalar ψ were used to estimate the intensity of the subsiding fibr es, Fig. 11.5. T he cumulative distr ibution of scalar var iable ψ in Fig. 11.5 was calculated by using the local values of the scala r over the perforated mesh area shown in Fig. 11.5. 147
Mineral Wool 800 700
mm
600 500
z
400 300 200 100 0
100
200
300
400
x
500
600
700
800
mm
Fig. 11.4. Experimental data on axial velocities from spinning machine nozzles.
Fig. 11.5. The results of numerical simulation for the collection chamber.
148
Numerical Analysis of Flow Properties in Collection Chamber
y
ψ ( x, y ) = ∫ψ (x, y )dy
(11.17)
0
Figure 11.5 shows the expected shape of the primary layer. Finally, the normalised relative thickness of primary layer at the chamber outlet, ψ ( x, y = Lo ) , is also shown in Fig. 11.5. Value 1.0 represents the nor malised value of cumulative function ψ at the chamber outlet. The result in Fig. 11.6 is comparable to the miner al wool distribution ρ (x) shown in Fig. 11.1. Similarity between numerical and experimental results is obvious. The subsiding of mineral wool fibres is more intensive on the left side of the primary layer. This reduces the quality of the final product. Figure 11.5 shows that the subsiding of mineral wool fibres on the perforated mesh is highly non-uniform. Hence, the thickness of the final product is not uniform over the entire width of its layer. The asymmetry of wool distribution shown in Fig. 11.6 is caused by the asymmetr ical blow a way flow of the spinning machine (inflow nozzles), as well as by the position of the suction duct. The properties of the blow away flow have a significant influence on the distribution of mineral wool fibres over the perforated mesh, and consequently also on the shape and quality of the final product. This was confirmed both by numerical simulations and experiments. Since the numer ical r esults ar e in good agr eement with measurement r esults, the pr esented numerical model can be used for the modification of the geometr y of the collection chamber. 1.4 1.2
ρ 1.0 ρavg 0.8
ρ ψˆ
ψˆ 0.6 ψˆ avg 0.4 0.2 0.0 0.00
0.52
1.04
1.56
2.08
2.60
x (m)
Fig. 11.6. Relative thickness of mineral wool layer at the chamber outlet ψ (x, y = Lo ) . 149
Mineral Wool
Based on the numerical and experimental studies, certain design changes were proposed which could reduce the non-uniformity of the primary layer. The geometry of the inlet part of the collection chamber was modified with a guide mask in order to change the properties of air flow within the chamber, and assure more uniform subsiding of fibres on the perforated mesh. 11.3 Numerical simulation of modified geometry of the collection chamber Numerical and experimental results show that the flow field in the collection chamber causes non-uniform mineral wool to subside. A modified geometry of the chamber, with a guide mask inserted in the front part of the chamber, was tested numerically. This solution is based on a patent application [60]. The guide mask directs the air flow onto the per for ated mesh and assur es a mor e unifor m distribution of fibres in the primary layer, Fig. 11.7. All bounda r y conditions wer e equal to those in the existing cha mber (section 11. 1. ). T he numer ical r esults for the modified collection chamber are presented in Fig. 11.8. T he compa r ison of the r esu lts for the exist ing and modified collection chamber in Fig. 11.9 shows significant improvement in the distr ibut ion of scalar va r iable ψ on the per for ated mesh. T he subsiding of mineral wool is expected to be mor e uniform. There are no regions of very intensive subsiding, or regions where only a few fibres would be caught by the perforated mesh. As a result, the thickness of the primary layer at the outlet is also more uniform.
Fig. 11.7. Collection chamber geometry with a guide mask. 150
Numerical Analysis of Flow Properties in Collection Chamber
Fig. 11.8. Numerical results for modified collection chamber geometry. 1.4 1.2 1.0
original modified
ψˆ 0.8 ψˆ a vg 0.6 0.4 0.2 0.0 0.00
0.52
1.04
1.56
2.08
x (m) Fig. 11.9. Relative thickness of mineral wool layer at the chamber outlet
2.60
ψ ( X , Y = Lo )
Deviations from the average thickness are below 10 %, while in the existing collection chamber, the deviations are up to 20 %. The flow field in the collection chamber with an additional guide mask, ther efor e, allows better distr ibution of miner al wool on the per for ated mesh and consequent ly better quality of the final product. 151
Mineral Wool
11.4 Local distribution and spectral analysis of the primary layer structure In order to investigate the dependence of the primary layer structure on the air flow velocity field inside the collection chamber, a study of the distribution of the primary layer structure at selected longitudinal regions on the perforated mesh is necessary [79]. For this purpose, a narrow window of 1 (length) × 14 (height) pixels was placed over the images of the mineral wool primary layer at different positions x using [45]. In this case, the intensity of individual pixels E was recorded for each pixel in the window individually rather than calculating the average value of intensity A for the whole window. Thus, from each image 14 different values of E (one for each pixel in the window) could be obtained. Since the whole sequence amounted to 250 images, there were 14×250 = 3500 values of E gathered for the primary layer structure assessment on the selected position x of the perforated mesh. When sorted in time-successive series, it was possible to calculate the power spectrum from the values of E at selected positions x using the Fast Fourier Transformation. Figures 11.10 to 11.12 represent histograms of primary layer structure distribution at different positions x on the perforated mesh. It is of interest that the distribution of the values of E (Figs. 11.10a, 11.11a and 11.12a) is similar to Gaussian distribution, but the peak is moved slightly to the left in each case. Figures 11.10b, 11.11b and 11.12b show the power spectrum of the values of E at the selected positions x. There is also a dashed straight line that represents Kolmogorov’s ‘cascade –5/3 law’ for turbulence decay
a)
b)
Fig. 11.10. Distribution (a) and power spectrum (b) of values E at x = 53.5 mm. 152
Numerical Analysis of Flow Properties in Collection Chamber
a)
b)
Fig. 11.11. Distribution (a) and power spectrum (b) of values E at x = 1286.5 mm.
a)
b)
Fig. 11.12. Distribution (a) and power spectrum (b) of values E at x = 2519.5 mm.
[76]. It can be seen from Figs. 11.10b, 11.6b and 11.7b that the slope of the power spectrum matches quite well with the slope of the dashed line representing the –5/3 law. This yet again indicates that the turbulent velocity field inside the collection chamber might significantly influence the structure of the primary layer. Figure 11.13 shows successive images of the primary layer structure inside the collection chamber. The time shift between two neighbouring images is 0.4 s. Figure 11.14 shows the velocity distribution on the plane positioned 50 mm in front of the perforated mesh. The images correspond to the boundary conditions (primary layer distributions) shown in Fig. 11.13. The core of the flow is in the middle section (as already seen 153
Mineral Wool 7
6
6
6
6
5
5
5
5
4
4
4
4
y (m)
y (m)
7
y (m)
7
y (m)
7
3
3
3
3
2
2
2
2
1
1
1
1
0
0
1
2
x (m)
T = 0 s
0
0
1
2
0
0
x (m)
1
2 x (m)
T = 0.4 s
T = 0.8 s
0
0
1
2 x (m)
T = 1.2 s
Fig. 11.13. Experimentaly modelled successive images of the primary layer inside the collection chamber.
Fig. 11.14. Time-dependent normal velocity component on the perforated mesh.
in the pathlines in Fig. 11.10) where higher velocities are predicted. It can be seen by comparison of mineral wool distributions and velocity magnitude distributions that velocities are lower in the regions where the primary layer is thicker (where grey levels in Fig. 11.14 are lower (darker regions)). The histograms in Figs. 11.15 to 11.17 represent the distributions of velocity fluctuations (local 154
Numerical Analysis of Flow Properties in Collection Chamber
Fig. 11.15. Distribution of velocity fluctuations at x = 53 mm.
Fig. 11.16. Distribution of velocity fluctuations at x = 1286 mm.
standard deviation of velocity magnitude σ (v)) on sections 50 mm in front of the perforated mesh. The qualitative similarity between histograms of velocity fluctuations in Figs. 11.15–11.17 and appropriate histograms of primary layer structure in Figs. 11.10–11.12 at specified transverse locations x can be observed. 155
Mineral Wool
Fig. 11.17. Distribution of velocity fluctuations at x = 2519 mm.
156
Quality of the Primary Layer
12 QUALITY OF THE PRIMARY LAYER AND ITS INFLUENCE ON THE FINAL PRODUCT Homogeneity of the primary layer in the mineral wool production pr ocess is r equir ed for high quality pr oducts. Miner al wool distribution along the pr imar y layer in the outlet section of the collection chamber is asymmet r ical and non-homogeneous. In addition, secondary effects such as the local tearing and rolling of miner al wool layer cannot be neglected. T hese effects ar e stochastic in character and r esult in tempor al a nd spatial perturbations of the velocity field in the collection chamber. Manufactur er s of miner al wool ar e tr ying to impr ove the insulating properties of the product. Optimising the homogeneity of the pr imar y layer is seen as an important aspect of such developments. Primary layer quality criteria were assessed on the basis of the homogeneity and isotropy of fibre distribution in the final product. The final product is a plate of mineral wool with different possible nominal thicknesses and fixed nominal density. Dis cr epancies between the local density of miner al wool and its nominal value present a major problem. A r egr ess ion model which r elates the pr imar y layer char acter istics to discrepancies between local density of miner al wool and their nominal values for the particular pr oducts is also pr esented in [61]. T he multir egr ession model pr esents the dependence between the statistical estimator RMS of mineral wool fluctuation in the final pr oduct and statistical estimator of the visualised signal. Other access ible par ameter s which might be related to mineral wool density distribution in the final product are also considered.
157
Mineral Wool
12.1 Experiments To investigate the phenomenological r elationships b etween the available visual infor mation about the pr imar y layer for mation, secondary parameters which are related to the transformation of the pr imar y layer and densit y distr ibution in the final pr oduct ar e consider ed. T he exper iment can be divided into computer -aided visualisation of the primar y layer at the outlet of the collection chamber and measur ement of secondary parameter s such as the speed with which the pr oduction line is oper ating, pendulum oscillation frequency, production capacity, recycled material content and the compression ratio of the layer at the inlet of the collection chamber. At the end of the production line, sampling of the final pr oduct wa s per for med. On selected samples, a loca l specific density mea sur ement of differ ent pr oducts was under taken. All parameters were measured at the same time. Computer-aided visualisation was used to obtain a quantitative description of the primary layer homogeneity, section 8.2 [44]. The method was based on the acquisition of images of the mineral wool primary layer immediately after it left the collection chamber (Figure 8.4). T he t ar get str uctur e of t he pr imar y layer is that it is homogenous and isotropic on local scales and has no interruptions on large scales. For low density products, the primary layer should also be as thin as poss ible. T his is consistent with optically homogeneou s isotr opic str uctur es that can be meas ur ed using computer-aided visualisation spatially and in time. Statistics based on the aver a ge value and r oot-mean-squar e (RMS) of average grey level intensity A(p) were also established. The ratio between RMS and aver age of A(p) was selected as the statistical estimator: M
I t −ex =
∑ε i −1
2 i
(12.1)
A
T he statistical estimator I t-e x , equation (8.7), is the measur e of pr imar y la yer quality which depends on selected pr oduction parameters.
158
Quality of the Primary Layer
12.1.1 Measurement of the specific density of the final product In order to determine the influence of the primary layer on the homogenous structure of mineral wool in the final product, we measured the mineral wool specific density in the final product. The measurements were performed in accordance with standards DIN 18156 [60] which are generally used in mineral wool production. Sampling at the production line outlet was synchronised with primary layer visualisation at the outlet of the collection chamber. The time synchronisation was executed using markers placed in the primary layer at the beginning of the acquisition of each image. Related samples of the final product were captured at the transition point defined by marker in the selected location at the outlet of the line. The times between sampling intervals of the final product and the image acquisition were identical. In the observed experiment, the final product is a plate with nominal thickness δ 0 , dimensions 1000 × 500 mm and nominal density ρ 0 . The nominal production line width, which was l 0 = 2000 mm, and the final product (a plate of material) were obtained by transverse cuts. Samples which measured 100 × 100 mm were cut by a band saw. The total measurement uncertainty of nominal sample volume was estimated to be ±2 % (DIN Standard No 18156) [62]. First, it is important to stress that the population of samples is created from elements obtained across the entire production line width, and secondly, particular samples are defined by their position in the cut plate and by related sample mass. Sample masses were measured with measurement uncertainty of ±1 % (DIN Standard No 18156, [60]). We defined the relative statistical specific density estimator as:
σ (12.2) ρ0 , where ρ 0 is the nominal density of the final product and σ is the ε=
related density standard deviation of the defined sampled population. The variable ε represents the basic dependent variable. In the following, this variable is treated as the function of the visualising signal in the primary layer forming point and also as the function of other secondary influences which are hypothetically included in the multiregression dependence of the observed variables. Other parameters from other production phases such as stratification of the primary layer and periodic conveyor belt in a 159
Mineral Wool
thicker multi-strata layer, which moves along the production line towards the collection chamber (polymerising furnace), also affect the final product. Polymerisation of phenol formaldehyde binder occurs in the curing chamber. The mineral wool layer curls and becomes the final product – thermal insulation material. The periodically stratified multi-strata structure of the conveyor belt depends on the production line terminal velocity, w, and oscillation frequency, f 0 , in the transverse direction. In addition to these factors, the influence of compressing the longitudinal conveyor belt of mineral wool is determined by using the ratio between velocity w and production line velocity reduction in the collection chamber w k : λ = wk / w . All of these variables were observed and simultaneously measured. In the subsequent analysis they appear as process variables and change in accordance with choice of nominal process parameters like nominal thickness and nominal density of final product. The secondary process parameters, acquired during the experiment on the production process, were: statistical estimator of mineral wool primary layer I t-ex , product capacity of mineral wool Q c in kg/h, line velocity w in m/s, volumetric binder flow rate q Vb and emulsion q Ve in l/h, recycling capacity Q R in kg/h and compression ratio K. The statistical estimator varied from 3.9 to 5.52; product capacity varied from 4550 to 5000 kg/h; line velocity varied from 8 to 10 m/s; volumetric flow rate varied from 900 to 1100 l/h; volumetric emulsion flow rate varied from 15 to 30 l/h; recycling capacity varied from 270 to 300 kg/h and compression ratio from 0 to 10, respectively. 12.2 Regression model of specific density of the final product Our aim was to find and to characterise the connection between the parameters stated at the end of the previous section and specific density fluctuation ε . Based on dimensional analysis [29], we introduce the following dimensionless numbers: Π A = I t −ex ; Π B =
QC q w ⋅ 1000; Π C = Vb ; Π D = ; QR qVe wmax
Π E = K.
(12.3)
The target function of average specific density fluctuation can be represented in a parametric form: 160
Quality of the Primary Layer
ε cal = a0 Π aAΠ bB Π Cc Π dD Π eE ,
(12.4)
wher e a 0 , a, b, c, d, e ar e t he par ametr ic constants of the regression model and subscript cal represents the calculated value. 12.2.1 Statistical analysis of experimental results The regression model was determined on the basis of measured data by using commercial software [29]. Good agreement between the r egr ession model and measur ed values of the miner al wool of average grey level intensity can be confirmed by the high value of correlation coefficient r 2 = 0.92. Fitting between the measured and modelled values of the aver a ge density wer e examined with the F-test. The results are presented in Table 12.1. The F-test estimates the hypothesis that the r egression is not significant. The probability that this hypothesis is valid was less than 0.005. Therefore, the regression is very significant.Values of Table 12.1. F-test results of agreement between modelled and measured values Degrees of Freedom
Sum of Squares
Mean Square
F Statistics
Prob > F
Regression
4
2.717E-2
6.792E-3
17.67
0.002
Residual
6
2.306E-3
3.843E-4
Total
10
2.947E-2
Source
Table 12.2. Significance of parameters of the regression model according to equation (12.4) together with the results of t-test
Parameters
t-test
Significance
Order of Significance
Constant
a 0 = 6.161
1.522
0.179
IV.
IIA
a = 1.262
724
0.000
I.
IIB
b = –1.427
–1.497
0.185
V.
IID
d = 1.099
1.951
0.099
II.
IIE
e = –0.105
–2.477
0.048
III.
>0.99
not significant
Variable
IIC
excluded variable
161
Specific density (measured, predicted)
/
Mineral Wool
8.5
2
r 4- para m=0.92
8.0 7.5 7.0 6.5 6.0
experiment - Eq. (12.4) measured predicted - Eq. (12.5) calculated
5.5 5.0 5.0
5.5
6.0 6.5 7.0 Specific density (measured)
7.5
8.0
8.5
/
Fig. 12.1. Comparison of measured and statistically predicted values of the mineral wool specific density in the final product.
the regression model parameters are presented in Table 12.2. Their significance was checked by the t-test. Values of the r egr ession model parameters are pr esented in Table 12.2. Their significance was checked by the t-test. Based on the presented results in Table 12.2, we can conclude that the statistical estimator of the average grey level intensity of the mineral wool primary layer Π A (I t ) has the greatest influence on the average fluctuation of specific density. Other dimensionless number s such as Π D (line speed w), Π E (compr ession K) and P B (capacity r atio Q C and Q R ) a r e also impor tant. On the basis of experiments, it is evident that dimensionless number Π C (the volume flow rate of binder q Vb and emulsion volume flow rate q Ve ) has no significant influence. Considering all these facts, the final equation of the target function can be expressed as:
ε cal = a0 Π aAΠ bB Π dD Π eE ,
(12.5)
The results of comparison between the measured parameters of the mineral wool specific density in the final product ε (12.4) and the ones (12.5) calculated on the basis of the four-parametric regression model are shown in Figure 12.1.
162
Curing Chamber
13 CURING CHAMBER T his section describes the polymer isation pr ocedur e in a tunnel furnace – curing chamber. In the curing chamber, smoke gases are blown through the moving layer between the perforated surfaces of the moving conveyor belt. These gases are heating up the mineral wool in the layer to the temperature which activates polymerisation. When the temperature of the mineral wool layer r ises above the activation temper atur e, the polymer isation pr ocess of phenolformaldehyde binder, located on the surface of mineral wool fibres in the form of water solution, is initiated. The binder is obtained from the reaction of monomer to wateralkali medium. For this, we usually use strong miner al bases as catalysts: N aOH, Ca(OH) 2 or Ba(O H) 2 . T he dir ection a nd the amount of chemical reaction depend on temperature and pH values. The ratio of phenol and formaldehyde is between 1.2:1 and 3:1. The cur ing r ea ctions of r esin include fur ther lacing of phenolformaldehyde resin structures. The resin pH is normally 9 and the r eaction t emper atur e does not exceed 180°C. In miner al wool production, it is important to know that phenol–formaldehyde resin starts to decompose at temperatures above 200°C. At such t emper atur es, the b inder star ts to har den and consecutively lacing of fibr es occur s. T his results in incr eased mechanical characteristics of the final pr oduct such as tensile stress, tensile strength and the elastic module of the final product. On the microscale, lacing is accomplished by the cohesive bonding of resin and mineral wool fibres where both meet and where hard mechanical bonds ar e for med pr oviding the final pr oduct with expected mechanical character istics. Figure 13.1 shows the str uctur e of laced mater ial with bonds. The detail, mar ked with position 1, displays a typical longitudinal bond between two parallel fibres. Position 2 represents the bond between the transverse fibres where the polymerised formaldehyde resin binds the fibres in one 163
Mineral Wool
3
1
2
Fig. 13.1. Lacing of mineral wool fibres with phenol-formaldehyde resin.
point. Position 3 shows the resin distributed on a single fibre. Fr om the t her modynamic point of view, pr ocesses of fibr e heating, evaporation and condensation of binder on the micro scales in the mineral wool layer also take place besides the lacing process. T he chemical pr ocess of polymer isation is also impor tant. It is endother mic in a par ticular phase of the thermodynamic process and exothermic in another. All mentioned processes are extremely significant and they inf luence the lacing pr ocess toget her with ener gy consumption which is commonly added to the pr ocess by natural gas combustion. Both lacing and energy consumption are key elements of an effective pr ocess. We ar e inter ested in the conditions, under which the lacing pr ocess in real pr oduction is effective. The selection of the significant process variables results fr om the basic descr iption of lacing that takes place in tunnel fur naces. Figur e 13.2 r epr esents the function scheme of flow of smoke gases passing through the mineral wool layer. The displayed segment includes t he basic components which ar e pr esent in a r eal polymerisation process. Mineral wool layer continuously enters the curing chamber which consists of two separ ated ar eas. The pr essur e in the upper area (position 1, Fig. 13.2) is higher than the pressure in the bottom area of the cha mber (position 2, Fig. 13.2). T hese two ar eas ar e separated by a layer of mineral wool that is located between two perforated conveyor belts which are moving together with the layer through the chamber. The pressure difference is generated by the cir culation fan that moves the smoke gases thr ough the mineral 164
Curing Chamber
1
p+
2
p-
mineral wool layer
redundant redundant smoke smokegasses gases circulation fan
gas burner combustion suction fan air
Fig. 13.2. Functional scheme of the curing chamber.
wool layer. At a given functional velocity of smoke ga ses, the pr essur e differ ence depends on the aer odynamic-r esistive char acteristics of miner al wool. Smoke gases fr om the chamber ar ea of negative pr essur e enter the gas bur ner wher e they ar e heated up by the combustion of fuel and controlled supply of air necessary for the combustion. The cir culation fan tr ansports the heated smoke gases into the upper chamber with overpressure. At nominal volume rate of flow, this fan has to overcome the pressure losses in the cir culation system and the aerodynamic losses that occur when the smoke gases pass through the mineral wool layer. Since the fuel combustion in the combustion chamber supplies the sufficient energy to heat up the mineral wool layer and polymerise the binder, the quantity of smoke gases in the cir culation system increases. The generated quantity of smoke gases mostly depends on the amount of fuel, supplied air and water that evaporates when the layer is heated up. In or der to remove the smoke gases, the negative pressure circulation system is connected to the suction fan. This fan sustains the stationary pressure conditions in the circulation system and transpor ts the redundant smoke gases into the system of smoke gas combustion and further through the filter s into the atmospher e. The oper ating r egime of the suction fan depends on pressure conditions in the circulation system and on the amount of newly formed smoke gases. Usually, the operating point of this fan is adaptively set so that the absolute pressure in the smoke gases is the same as the pressure in the atmosphere wher e the smoke gases are passing through the mineral wool layer. This ensures the minimal transition of smoke gases into the environment and optimal fuel consumption. 165
Mineral Wool
T he cur ing chamber enables continuous adjustment of layer thickness and velocity of the longitudinal movement of mineral wool layer. The transporter velocity at a given layer thickness, layer width and cur r ent capacity of fiber is ed miner al wool depends on the desir ed specific density of the final pr oduct. Since the capacity determined by the mass flow of the fiberised mineral wool changes and is dependant on the conditions in the cupola furnace and the spinning machine, per manent cor r ection of miner al wool layer velocity in the curing chamber is necessary. The mineral wool layer thickness, specific mass on the surface of the mineral wool layer and the velocity of the conveyor belt ar e inter dependent. T heir relation is expressed as follows:
qm
vlin (G * B) Ulayer ,
(13.1)
wher e q m is the mass flow of miner al wool measur ed in the transition phase of the process, v lin is the adjustable velocity of the conveyor belt (transporter) in the curing chamber, G is the thickness of mineral wool in the curing chamber, B is the width of mineral wool in the curing chamber, U layer is the density of mineral wool in the curing chamber. We can conclude that the conveyer belt velocity is the only regulative variable which enables the compensation of mineral wool capacity to change on demand for constant layer thickness and density. The mass of mineral wool layer is the relevant measured variable, on the basis of which the transporter velocity is corrected. We measure it with a custom balance (Figure 1.1, pos. 5). Besides, measuring procedures for measuring the mass of mineral wool are being introduced at the exit out of the collection chamber (Figure 1.1, pos. 3) [75]. This increases the flexibility and reliability of the regulation system which ensures smaller variations of mineral wool micro density in the final product. T he var ying velocity of the miner al wool layer changes the retention of the mineral wool layer in the curing chamber which influences the lacing process. This influence is not significant when compared to the variation of the retention time of the mineral wool layer in the curing chamber as a result of different nominal layer widths and densities. This is also evident in equation (13.1) because the transporter velocity v lin , layer thickness G and specific density U layer ar e linearly interdependent. With large thicknesses and high specific densities of mineral wool, the layer retention times become significantly longer, contrary to a layer with small thickness and specific density which is only for a short time retained in the curing 166
Curing Chamber
chamber. T his influences the r egimes of aer o-ther modynamic characteristics of the circulating smoke gases. Besides the density regulation of primary mineral wool layer, the regulation of aero-ther modynamic variables of the polymerisation process is also required. Since there are different constructions of curing chambers present in practice, it is hardly possible to form universal phenomenological relations which would lead to ensuring the functionality of the production process and the minimisation of fuel consumption. Quantities, such as circulation system sealing, amount of removed smoked gases, geometr ical characteristics of transporter perforations, etc. influence the formation of functional areas of tr ansition velocity of smoke gases thr ough the mineral wool layer and the cor r esponding pr essur e differ ences. To determine the functional parameters of the process, it is important to know the temperature conditions in the mineral wool layer along the curing chamber. 13.1 Measurements of mineral wool layer temperature characteristics along the curing chamber One of the important diagnostic parameters is also the knowing of temperatures in the mineral wool layer at its transition through the curing chamber. According to the possibilities of local temperature changes in the layer, periodical temper ature measur ement in the miner al wool layer turns out to be the appropriate method. This method requires the implementation of a thermally insulated PC unit (Fig. 13.3 ) with six connected NiCr –Ni ther mocouples. T he insulation of the PC unit prevents the temperature in the unit to rise Thermo insulation material
PC - computer
Thermocouples Thermo-couples type K K Type #1
#2
#3
#4
#5
#6
Fig. 13.3. Process unit for continuous capturing of local temperatures in the mineral wool layer. 167
Mineral Wool
above the allowed 70°C while the measurements of mineral wool transition through the cur ing chamber are performed. In order to install the PC unit, a short interruption of the production process is necessary. The installation scheme for the implementation of the measuring system is shown in Fig. 13.4. The installed experimental equipment is moving together with the mineral wool layer through the curing chamber. During this, the current measured temperature values cap tur ed by par ticular sensor s ar e saved on the PC. Because the movement velocity along the chamber is constant dur ing t he exper iment, the longitudinal position of the cur ing chamber accor ding to the measu r ed local temper atu r es in the miner al wool layer is also clear ly deter mined. In the discussed experiment, the capturing frequency on each channel was 10 Hz. The reference point of thermocouples was determined on the basis of temperature measurement inside the PC unit. Figure 13.5 pr esents the r esults of mineral wool temperatur e measur ement s. T he r esults a r e calculated for the longitudinal position in the chamber. T his enables the connection of local temperatures with local particularities inside the chamber. In our cas e, the chamber is divided into thr ee sections with exchanging dir ection of circulation flows. In the fir st zone, the smoke gas flow is directed from the bottom area towards the upper area of the chamber. It is followed by the flow in the second zone, wher e the smoke gases flow fr om the upper ar ea t owar ds the bottom area of the chamber. In the third zone, the flow is again r edir ected. T he cour se of temper atur e distr ibut ions shows differences in the distribution. In the third zone, the temperatures appr oach t he outlet temper a tur e which exceeds the activation temper ature of polymer isation. In the first zone, the temperature pr edominantly incr eases . T he intensity of temper atur e incr ease mostly depends on the location of the installed ther mocouples. LU
mineral wool layer
CU RU LB CB
PC n of directio
motion
RB
Legend: LU...left-upper; CU..centerline-upper; RU...right-upper; LB...left-bottom; CB...centerline-bottom; RB...right-bottom;
Fig. 13.4. Arrangement of temperature sensors in the mineral wool layer. 168
Curing Chamber
inflow
outflow
Te m p e r a t u r e Zone 2Zone 2
Zone12 Zone
pr o f i l e
Zone 3 3 Zone
25 0
300
qC
2240 00
1180 50
120
T
10 0
60
50
0 0
200 20 0
250 25 0
3300 00
3350 50
4400 00
T im e #1
#2
#3
4450 50
550 00 0
5550 50
6600 00
s #4
#5
#6
Fig. 13.5. Temperature distribution in the mineral wool layer along the curing chamber.
Thermocouples, installed in the lower part of the layer (LB, CB and RB), have steepest gradients of temperature incr ease as a result of pr esence of hot smoke gases that enter the layer. During their tr ansition thr ough the miner al wool layer, their t emper atur e decreases, and the temperatures measured in the upper part of the layer are lower (LU, CU and RU). In the second zone where the smoke gases flow in the other direction, the trends of temperature gradients change. These changes cannot be explained in a simple manner. The temperatures here differ strongly from each other. This implies that the miner al wool is non-homogenous. Local nonhomogeneities of mineral wool are: local specific density, presence of non-homogenous binder distr ibution and humidity part. T hese findings a r e also confir med b y the analysis of measur ement repeatability. The repeatability of results in the middle part of the chamber is relatively weak. The measuring uncertainty in this area is estimated to be ~15 % of the measured value. Moreover, it is important to explain the phenomenon of local temperature decrease in the mineral wool layer present mostly at sensors (LB, CB and RB) implemented in the lower part of the layer, as shown in Fig. 13.5. This phenomenon may be linked to the constructional solution of redirection of circulating smoke gases. At the transition from zone 169
Mineral Wool
1 into zone 2, the smoke gases enter the heated mineral wool layer. They give away heat in the upper part of the layer and cool down to the temperatur e lower than the fibr e temperatur e in the lower par t of the layer. T he pr esented explanation is one of sever al possibilities. The heating process of mineral wool layer is complex and connected with processes of polymerisation, water evaporation and heat transfer from the flow of smoke gases to the mineral wool fibres. Therefore, it is necessary to deal with the observed process from the point of view of achieving the activation temperature and the bigges t homogeneity of a xially symmetr ic t emper atur e distribution possible without the presence of temperature fluctuations along the cur ing chamber. T his can be achieved with optimal aerodynamic operational conditions and intensity of fuel combustion in particular zones. The problem of local anomalies, such as local non-homogeneity of layer specific density should be tackled in the preliminary phases of the process in the area of material fiberisation and primary layer formation. In order to evaluate local anomalies, it is necessar y to develop exp er imental methods which enable laboratory and production diagnostics of aerodynamic and material anomalies in the mineral wool layer. 13.2 Measurements of aerodynamic resistive characteristics of mineral wool layer The dependence of pressure differ ence on the air flow velocity is determined exper imentally for differ ent thicknesses and specific densities of the mineral wool layer. The characteristics are acquired experimentally according to standards. The experimental scheme is shown in Fig. 13.6. T he pr ess ur e differ ence and air flow temper a tur e wer e measur ed on the or ifice. At the outlet section, the differ ence of static pressure was measured on mineral wool samples of different width and density. T he size of a sample in the transverse cr oss section in the circulation channel was A = 0.5 × 0.5 = 0.25 m2 . The measur ement r esults ar e given in the for m of f unctional relations ' ps f (G , U , w) , where w is the air flow velocity calculated fr om the measured rate of air flow and the channel sur face A in the cross section plane A–A in which the static pressure difference was measur ed. Figur e 13 .7 shows an example of the cour se of pr essur e difference at the air flow tr ansition thr ough the layer at chosen 170
Curing Chamber specimen of layer
fan
A
orifice
A 'pv
'ps
T
Fig. 13.6. Measurements of resistive characteristics of mineral wool layers with different thicknesses G and specific densities U laye r t .
12
'p
mbar
10 8 type type type type type
6
9,1 9,2 9,3 9,4 9,5 -
55 x 8 0 M 55 x 8 0 M 55 x 8 0 M 55 x 8 0 M 55 x 8 0 M
4 2 0 0
0.1
0.2
v
0.3
0.4
0.5 m/s
0.6
Fig. 13.7. Relation between pressure difference and flow velocity.
thickness and density ( G = 55 µm, U layer = 80 kg/m3 ). This figure pr esents t he cur ves of thr ee differ ent samples wit h the same nominal characteristics. Mutual deviations of measured differences a r e a r esu lt of local a er odyna mic cha r a cter istics – sample anomalies which implies tha t r esistive char acter istics ar e nonhomogenous. On the basis of average values of measured sample characteristics, relevant resistive characteristics are calculated for par ticular mater ial types. It is also evident that the functional relation of pressure difference is almost linear. This means that the flow conditions in the gaps between the miner al wool fibr es are laminar on the microscale of fibre material. This is also confirmed by the estimation of Reynolds number on the microscale, where the characteristic dimension of fibre diameter is d v = 5–8 µm, and the flow velocity through the gaps is w = 0.2–1.0 m/s. 171
Mineral Wool
Re
wd v
X
, Re = (0.63–3.2), implies the balancing of viscosity
forces and inertia in the flow field in the gaps between the fibres. According to this, it is appropriate to choose the phenomenological relation between the pressure difference and flow velocity:
' p ] (G , Ulayer ) wn ,
(13.2)
where ] (G , Ulayer ) , the empirical aerodynamic resistance coefficient, is relative to thickness and specific density of mineral wool layer, and n is exponent which hardly differs from value n | 1. T he diagr a m in Fig. 13.8 shows the pr ogr essive incr ease of resistive coefficient with the increase of thickness and density of miner al wool layer. T he aer odynamic r esistance incr eases significantly with both parameters and presents a problem of blowthrough in the case of larger primary wool thickness and density. This finding requires analysis according to the residence time of mineral wool in the curing chamber. The increase of thickness and specific density results in the decrease of velocity of layer transport through the cur ing chamber. Despite the incr eased aerodynamic resistances, this provides a sufficient supply of heat to the mineral wool layer. Empirical relations based on the experimental testing of different curing chambers were used to provide general operational tr ends, fu nctional (empir ical) pr essur e differ ences and the cor r esponding functional blow-through velocities (Fig. 13.9 and 13.10). The diagram (Fig. 13.9) shows that the blow-thr ough velocity
]
Ukg/m3
Gmm
Fig. 13.8. Resistive characteristic 172
] (G , Ulayer )
of the layer..
Curing Chamber
m/s w
Gmm Ukg/m3 Fig. 13.9. Empirical flow velocity of smoke gases blowing through the mineral wool layer.
Pa 'p
Gmm
Ukg/m3
Fig. 13.10. Functional pressure difference in the mineral wool layer.
can monotonously decrease by increasing the thickness and specific density of the mineral wool layer. Contr ar y to the results in the diagram (Fig. 13.8), pressure difference in the layer decreases. This is useful when choosing the suitable circulation fans and optimising the energy characteristics of a curing chamber. It is important to str ess that t he empir ical velocities or pr essur e differ ences ar e par ticular for each cur ing chamber and mostly depend on constructional solutions such as: blow-through concepts, positioning of the suction of smoke ga ses, leakage, length of the cur ing chamber … The experimental optimisation is of great importance. 13.3 Diagnostics of local homogeneities in the mineral wool layer Non-homogenous distributions of mineral wool on the microscale present a big problem nowadays. There are standardised criteria for estimating the mineral wool irregularities in the primary layer. Local 173
Mineral Wool
density measurements are usually performed by measuring masses of mineral wool samples taken from final products. The weakness of such standar dised methods is that the measur ements of local specific densities are usually carried out in laboratories and have a distinctive time delay that renders quick correction of production pr ocesses impossible. T he IR t her movision method enables the estimation of local non-homogeneities in the mineral wool layer at the curing chamber outlet in real time. This method was developed in the labor ator y envir onment that enabled the for mation of the functional r elation between local anomalies in the miner al wool layer and its local specific density. T his method is based on the hypothesis that local non-homogeneities reflect in the temperature variation on the surface of the layer moving through the cooling zone.
U t v T (t )
(13.3) We performed an experimental study with the goal to research and confir m this mutual r elation. Temper atur e measur ements wer e per formed on the sur face of miner al wool samples while the air was flowing through the samples. Then, the mass of these samples was measured. The experiment is presented in Fig. 13.11. The air flow with ambient temperatur e enter ed thr ough a pipeline and a measuring orifice for measuring the volume rate of flow. In front
air flow airflow
fan orifice heater photo mineral wool specimen
video camera
data acq. system
PC
Fig. 13.11. Sch eme of the experiment. 174
Curing Chamber
of the entrance to the r adial fan, an electric heater was installed with purpose to heat up the air flow to a desired value. The heated air flow then passed through the diffuser on the pressure side of the radial fan into the area of the measuring plane in front of the mineral wool sample with size of 500 × 500 mm 2 . A measuring device for measuring static pressure is positioned on the pressure side of the sample and controls integr al pr essur e differ ences at measured volume rate of air flow. In the frontal position to the mineral wool layer, the IR camera is positioned 1.5 m away in order to capture thermovision shots. For temper atur e measur ements on the sur face of samples, we used ther movision camer a AGEMA 570 with the active wave length between 7.5 Pm and 13 Pm. The measuring camera resolution was 0.15 K and 320 × 240 pixels. The estimated measuring uncertainty was approximately ±2 %. In these samples, we can see distinctive anomalies of temper atur e fields on the la yer. T he str ongly non- homogenous temperature is connected with the anomalies of the velocity field which carries the hot air flow through the mineral wool layer. The non-homogenous convective heat flow can be linked to the nonhomogenous aer odynamic r esista nce char acter istics which ar e caused by the ir regular mass distribution of mineral wool in the layer. By consider ing the phys ical mechanism descr ibed with expr ession (13.2), we can conclude that at constant pr essur e difference measur ed on the mineral wool layer, following relation can be formed:
] ( Ulayer ) v Ulayer wn v
1 n w T
(13.4)
Proceeding fr om r elation (13.4), the experiment was oriented to comparing the temperature fields, acquired by the IR camera, and the cor responding sample masses which were obtained by slicing the samples into smaller, basic samples. After thermovision, basic samples (550 × 550) wer e sliced up into nine equal samples as shown in Fig. 13.13. Since the final goal of the p r esented method is to quickly diagnose the local anomalies, we concentrate on the estimation of local density fluctuations of miner al wool and temper atur e field fluctuations. As estimator s, we use histogr ams of par tial density distr ibutions of samples and histogr ams of the cor r esponding temperature intensities in the belonging segments as shown in Fig. 13.13. T he mean temper atur e va lues in selected fr ames of IR 175
Mineral Wool
Fig. 13.12. Temperature distribution on the seleeted mineral wool sample, type 550 × 550.
U plast v
1 T
1
2
3
4
5 1 5 0,0-5 5,0
2 5 5,0-60,0
3 60, 0-65,0
4
5
65 ,0-70,0
kg/m3 70 ,0-7 5,0
A – specific density of samples Ulay er (i, j)
B – temperature of samples T(i,j)
Fig. 13.13. Comparison of local min eral wool density and temperature distributions on the sample surface.
camera viewing field are calculated with the following algorithm:
T i, j
1 ¦¦X k , l KL k l
(13.5)
where X k, l represents the local temperatur e in frame (i,j) with dimension K×L in position (k,l). T(i,j) represents the corresponding mean temper atur e which is then used for the calculation of standar d deviation V T and for mation of temper ature fluctuation histogr am T(i,j) ar ound the mean value. Figure 13.14 shows the temperature distribution around the mean value
in the case of the performed experiment, where f is the frequency at a selected temperatur e domain. Analogous to the temperature distribution, Fig. 13.15 presents the distribution of specific densities U layer i, j . The presented results lead us to conclude that temperature and 176
Curing Chamber
120 100 80 60 40 20 0 13 .6 15 .0 16 .4 17 .9 19 .3 20 .7 22 .1 23 .6 25 .0 26 .4 27 .9 29 .3
Frequency
Frequency
Temperature Temperature
°C ºC
Fig . 13 .14. Temperatu re dist ribu tio n histogram n = 650 sam ples, = 22.5 °C, V T = 4.8 °C . 120
Frequency
Frequency
100 80 60 40 20 0 19 20 21 22 23 24 25 2627 2829 30 3132 3334 3536 3738 39 40 41 Density
Density
kg/m3
kg/m3
Fig. 13.15. Histogram of specific densities distribution: n = 650 samples, V T =6.6 kg/m 3 .
U layer =30,
specific density fluctuations are similar. The relative fluctuation is defined as:
Hl
Vl <x(i, j )>
;l
T or U .
(13.6)
In our case the fluctuations are: Temperatures H T = 22.6 % and the specific density of a layer H U = 22.1 % also imply tha t temper atur e and specific density anomalies in the mineral wool layer are connected with each other. In the production process it is possible to indirectly apply the IR ther movision method in order to diagnose local anomalies in the mineral wool layer. The most pr oper position of detection is the zone where the mineral wool layer is cooling. T he pr esentation of the ther movision diagnostics of local anomalies in the mineral wool distribution rounds up this book. It 177
Mineral Wool
is impor tant to emphasise that we pr esented only a por tion of methods for monitoring the mineral wool pr oduction pr ocess and that in the future these will improve and expand onto new areas with the a im of under standing the technological p r ocess and achieving higher quality in production.
178
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73.
Mineral Wool
Index double-wheel spinning machine 114 Downey method 4 Downey rotor 4 drag force 75 Du Noüya ring 42 dynamic viscosity 33
A Abbe number 28 acid–base ratio 29 acidity module 34 active contour tracing 85 Amphibolite 9 average temperature of the melt film 113
F F-test 60 falling sphere method 39 fiberisation 3, 54 four-wheel spinning machine 68 full oxidation 9
B basalt 1, 28 basicity number 34 bauxite 9 Blaisdell’s formalism 43 Boltzmann law 33 buoyancy 31
G granite 1
C
H
characteristic dimensionless flow number 59 characteristic dimensionless rotational speed number 58 characteristic dimensionless temperature number 59 characteristic dimensionless viscosity number 58 coefficient of determination 22 computer-aided visualisation method 118 convective heat transfer coefficient 72 cupola furnace 3, 8 curing chamber 6, 163
hardening point 37
I impingement position 81
K Kolmogorov’s ‘cascade 152 Kucuk’s equation 41
L lacing 163 Lakatos’ regression model 35 Laplace–Young equation 44 leucogranite 30 Levenberg–Marquardt method 23 limestone 1 Lindquist’s equation 74 Lubanska–Walzels model 58
D deformation gradient 104 density 29 diabase 1 dimensional analysis 48 dolomite 1, 8 Dorsey’s formalism 43 double-bob Archimedean method 30
M magma rocks 9 microtensometry 42 184
References Index minimum allowable fluctuation 92 multiple linear regression 21
squeezer 6 statistic t-test 25 statistical estimator 158 Stokesian failing sphere 30 surface tension 41
N Neuro Inspector software 108 normalised gradients 88 Nusselt number 72
T t-test 111 tension point 37 thermovision image 115 time-averaged centre line 97 time-averaged grey level 98 turbulence eddy dissipation 143 turbulence kinetic energy 143
O olivine 28 oxidation zone 13
P pegmatite 30 Pitot–Prandtl probe 125 primary layer 6, 121, 157 primary layer homogeneity 134
U underdraft 8, 13
R
V
Reynolds number 73 Reynolds stresses 143 rotational viscometer 39 Runge–Kutta method 78
vane anemometer 126 Vogel–Fulcher–Tammann (VFT) equation 34
W
S
Weber number 58 Wilhelmy plate 42
Sano’s model 74 sessile drop 43 Sillan process 4 sink-float densitometry 30 softening point 37
Z zone of separation 10
185
