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 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
