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ANALYSIS OF BLAST FURNACE LINING/COOLING SYSTEMS
USING COMPUTATIONAL FLUID DYNAMICS
by
HUGO JOUBERT
THESIS
submitted in partial fulfilment of the requirements for the degree
MAGISTER IINGENERIAE
in
MECHANICAL ENGINEERING
in the
FACULTY OF ENGINEERING
at the
RAND AFRIIKAANS UNIVERSITY
SUPERVISOR: PROF. L. PRETORIUS CO-SUPERVISOR: DR. G. COETZEE
NOVEMBER 1997
ACKNOWLEDGEMENTS
To Iscor Steel, Flat Products, Vanderbijipark, and more specifically Blast Furnaces, for the opportunity to do this study.
To my wife Ria, for enduring our absence from social life and her continuous support during the past few years.
ACKNOWLEDGEMENTS
SUMMARY
In this study it is shown that numerical analysis, and more specifically computational
fluid dynamics, can be used to investigate, compare, predict and design
lining/cooling system combinations for blast furnaces in order to ensure longer
campaign life and better performance. Three currently available cooling systems,
namely copper flat plate coolers, cast iron staves and copper staves, are
investigated. -These are -combined with-four different refractory materials, -namely
high alumina, silicon carbide, semi-graphite and graphite, stated in order of increasing thermal conductivity.
First of all, it is found that, in the bosh, belly and lower stack regions of the blast
furnace, the cooling system is of utmost importance since the wear reactions depend
strongly on the lining temperatures. Secondly, a higher heat conductivity is found
to be a superior property for refractory materials since it also helps lower the lining temperatures.
It is shown that silicon carbide is the better refractory material to combine with cast
iron staves, while semi-graphite is successfully combined with both copper flat plate
coolers and copper staves. Cast iron staves and silicon carbide, as a lining/cooling
system combination, is found to be less suitable for the high temperature bosh, belly
and lower stack regions of the blast furnace. Copper flat plate coolers and copper
staves combined with semi-graphite are found to be better suited for these regions for the following basic reasons:
• Lining temperatures as well as the iron and ash content are very low. Hence,
chemical wear mechanisms as well as the kinetics of the reactions are limited and
slow in their occurrence. Mechanical wear is reduced due to lower thermal expansion.
• Hot face temperatures are low hence promoting the formation of a stable skull or
accretion layer. Cooling losses are kept low while erosion of the lining is limited.
• If temperature fluctuations occur in periods of irregularity, the lining/cooling
system can deal with this. Lining wear in these periods is minimised.
It is also found that copper flat plate coolers have the following advantages over copper staves:
SUMMARY -- li
• Steam formation in the cooling water channels is less likely to occur, and
• better physical support is given to the refractory brickwork.
Copper staves have the following advantages over copper flat plate coolers:
• Hot face and lining temperatures are lower and thus skull formation should be better,
• high heat fluxes and temperature fluctuations can better be dealt with, and
• temperature differences on the hot face are lower. This will result in less tension
in the brickwork as well as a more uniform skull or accretion layer.
Considering the strengths and weaknesses of both copper flat plate coolers and
copper staves, it is recommended to use a combined solution, together with a high
conductivity refractory material, such as semi-graphite. The investigation of this proposal is left for possible future work.
SUMMARY
OPSOMMI1G
In hierdie studie is aangedui hoe numeriese analitiese metodes, en meer spesifiek
berekeningsvloeimeganika, aangewend kan word vir die ondersoek en ontwerp van
kombinasies van vuurvaste steenwerk en verkoeingsstelsels vir hoogoonde. Drie
huidiglik beskikbare verkoelingsstelsels is ondersoek, naamlik koper platplaatver-
koelers, gietyster staafverkoelers, en koper staafverkoelers. Die verkoelingsstelsels
is met vier verskillende vuurvaste materiale-gekombineer-om -die bestekombinasies
te bepaal, naamlik hoe-alumina, silikon karbied, semi-grafiet en graflet. Die
vuurvaste materiale is gerangskik volgens toenemende hitte geleidingsvermoe.
Eerstens is gevind dat, in die onderste tot middeiste gedeelte van die hoogoondskag
wat ondersoek word, die verkoelingssisteem van uiterste belang is aangesien die
verweringsreaksies nou saamloop met die temperatuur van die vuurvaste materiaal.
Tweedens, 'n hoer hitte geleidingsvermoe is gevind om 'n positiewe eienskap te
wees vir vuurvaste materiale, aangesien dit help om die temperature laag te hou.
Dit is ook aangedui dat silikon karbied die beter vuurvaste materiaal is om met
gietyster staafverkoelers te kombineer, terwyl semi-grafiet beter geskik is vir beide
koper platplaatverkoelers en staafverkoelers. Gietyster staafverkoelers, gekombi-
neer met silikon karbied, is gevind om nie geskik te wees vir die gedeelte van die
hoogoondskag wat ondersoek word nie, vanweë die hoe temperature. Dit is gevind
dat koper platplaatverkoelers en staafverkoelers beter pas in die hoe temperatuur areas van n hoogoond na aanleiding van die volgende redes:
• Temperature, asook yster- en asinhoud, van semi-graflet is bale laag. Dus,
chemiese verwering asook die kinetika agter die reaksies word vertraag.
Meganiese verwering word ook beperk vanweë Iaer termiese uitsetting.
• Warmkant temperature is laag wat die vorming van 'n stabiele skil bevorder.
Hitte verliese word hierdeur beperk terwyl die temperature in die vuurvaste steenwerk laag bly.
• As skielike veranderinge in die oond temperature voorkom, kan die verkoelings-
sisteem, tesame met die vuurvaste steenwerk, die veranderende hittevloed hanteer.
Daar is ook gevind dat koper platplaatverkoelers die volgende voordele bo koper staaf rerkoelers het:
OPSOMMING
• Die kans is skraler vir die vorming van stoom in die verkoelingswaterkanale, en
• beter fisiese ondersteuning word verleen aan die vuurvaste steenwerk.
Koper staafverkoelers het die volgende voordele bo koper platplaatverkoelers:
• Warmkant en vuurvaste temperature is laer en dus behoort skilvorming makliker plaastevind,
• hoe hittevloede en temperatuur skommelings kan beter hanteer word, en
• temperatuur verskille in die vuurvaste steenwerk is laer. Dit het minder
spannings in die steenwerk en 'n meer eweredige skil tot gevoig.
Indien die sterk- en swakpunte van beide die verkoelingsstelsels in ag geneem word,
word aanbeveel dat 'n kombinasie van die twee stelsels, tesame met 'n hoe
geleidingsvermoe vuurvaste materiaal, soos semi-grafiet, aangewend word. Die
ondersoek van hierdie voorstel is geIdentifiseer as moontlike verdere studie.
OPSOMMING v
INDEX
PAGE
ACKNOWLEDGEMENTS SUMMARY ii OPSOMMING iv INDEX vi
LIST=OF-SYMBOLS -- - -- -----1- --
CHAPTER 1 HIGHER PRODUCTIVITY AND LONGER CAMPAIGNS DEMAND
IMPROVED BLAST FURNACE LINING/COOLING SYSTEM DESIGNS
1.1 Introduction 4 1.2 Variables influencing blast furnace campaign life 4 1.3 Conclusion 7
CHAPTER 2: BLAST FURNACE DEVELOPMENT: REFRACTORY LININGS AND
COOLING SYSTEMS
2.1 Introduction 8 2.2 Wear mechanisms in the blast furnace 8 2.3 Development of blast furnace refractory linings 12 2.3.1 High-alumina, corundum and variants 14 2.3.2 Silicon carbide and variants 16 2.3.3 Carbon, graphite and semi-graphite 18 2.4 Development of blast furnace cooling systems 21 2.4.1 Copper flat plate coolers 22 2.4.2 Cigar coolers 23 2.4.3 Cast iron staves 24 2.4.4 Current design data for flat plate coolers and cast iron staves 27 2.4.5 Mantle or lintel staves 28 2.4.6 Copper staves 29 2.4.7 Current layout of cooling systems 29 2.5 Conclusion 30
CHAPTER 3 COMPARISON BETWEEN COMBINATIONS OF REFRACTORY
LININGS AND COOLING SYSTEMS
3.1 Introduction 31
3.2 Measuring the performance of refractory linings and cooling 31 systems
3.3 Comparison of known performances by cooling systems and 36 refractory linings in the bosh, belly and lower stack area
INDEX vi
3.3.1 Copper flat plate coolers 36 3.3.2 Combination offlat plate coolers and cast iron staves 39 3.3.3 Cast iron staves 40 3.3.4 Copper staves 41 3.4 Predicting the performance of refractory linings and cooling systems 43 3.5 Conclusion 46
CHAPTER 4 OVERVIEW OF COMPUTATIONAL FLUID DYNAMICS
4.1 Introduction 48 4.2 Applications of computational fluid dynamics 48 4.3 Governing flow and heat transfer equations 51 4.3.1 Continuity equation 52 4.3.2 Momentum equation 53 4.3.3 Energy equation 55 4.4 Discretisation and grid generation. 59 4.5 Conclusion 63
CHAPTER 5 NUMERICAL MODELS OF LINING/COOLING SYSTEMS
5.1 Introduction 64 5.2 The theory of skull formation 64 5.3 Influence of high conductivity differences in two-dimensional heat 69
conduction problems on solutions obtained by different methods 5.4 Numerical solution of forced convection heat transfer 78 5.5 Heat transfer from the furnace to the lining/cooling system 86 5.6 Heat transfer through the lining/cooling system 88 5.7 Two-dimensional analysis of variables influencing skull formation 90 5.8 Three-dimensional numerical models of lining/cooling systems 99 5.8.1 Copper flat plate coolers 100 5.8.2 Cast iron staves 104 5.8.3 Copper staves 107 5.9 Conclusion 108
CHAPTER 6 RESULTS, DISCUSSIONS AND SOME CONCLUSIONS
6.1 Introduction 109 6.2 Verification of fluid dynamics results 109 62.1 Copper flat plate coolers ii 0 62.2 Cast iron and copper staves 119 6.3 Variables influencing skull formation 123 6.4 Heat transfer results for the three different cooling systems 131 64.1 Copper flat plate coolers 131 64.2 Cast iron staves i 64.3 Copper staves 137
ITDEX
6.5 Comparison of results for different lining/cooling system 139 combinations
65.1 Possible skull formation 139 65.2 Chemical and mechanical wear mechanisms 143 65.3 Possible steam layer formation 148 6.6 The influence of skull formation on heat losses and hot face 151
temperatures 6.7 Conclusion 158
___ ___ - -- ___ - ___ FINAL CONCLUSIONS, RECOMMENDATIONS AND POSSIBLE
FUTURE WORK
7.1 Introduction 164 7.2 Summary of conclusions 164 7.3 Final conclusions 170 7.4 Possible future work 172 7.4.1 Transient solutions 172 7.4.2 Simulation of skull formation 173 7.4.3 Combination offlat plate coolers and staves 173
REFERENCES 175
APPENDIX A: INPUT FILE FOR TWO-DIMENSIONAL CONDUCTION 179 MODEL WITH HIGH CONDUCTIVITY DIFFERENCES
APPENDIX B: INPUT FILE FOR TWO-DIMENSIONAL MODEL OF 181 CONVECTION HEAT TRANSFER ON A FLAT PLATE
APPENDIX C: INPUT FILE FOR TWO-DIMENSIONAL MODEL FOR 183 INVESTIGATING THE INFLUENCE OF DIFFERENT VARIABLES ON SKULL FORMATION
APPENDIX D: INPUT FILE FOR THREE-DIMENSIONAL MODEL OF 185 COPPER FLAT PLATE COOLER ARRANGEMENT WITH A 300 mm VERTICAL PITCH
APPENDIX E: INPUT FILE FOR THREE-DIMENSIONAL MODEL OF 199 CAST IRON STAVE ARRANGEMENT
APPENDIX F: INPUT FILE FOR THREE-DIMENSIONAL MODEL OF 204 COPPER STAVE ARRANGEMENT INCORPORATING AN ACCRETION LAYER
INDEX
LIST OF SYMBOLS
A m2 Cross sectional area of model hot face. m2 Indicates the shell area coverage by the cooling system
and depends on type of cooling system, vertical and horizontal spacing of cooling elements as well as the contact area for the cooling water in the cooling channels.
- - Ad m2 Cross sectional area of skull - equals x., times unit depth.
C, J/kgK Specific energy (volume)
d m Tube diameter. E N/rn2 Young's modulus Et Jim3 Total energy per unit volume e Jikg Internal energy per unit mass
fM/S2 Body force in Chapter 4 or friction coefficient in
Chapter 6.
g ff1/S2 Gravity. W/m2K Average heat transfer conductivity
ha W/m2K Convection heat transfer coefficient between air and shell.
h Convection heat transfer coefficient for cooling water. hf W/rn2K Furnace inside convection heat transfer coefficient. k W/mK Thermal conductivity
k1 W/mK Conductivity of cast iron as used for cooling element. kk W/mK Conductivity of copper as used for cooling element. km W/mK Conductivity of different mouldable refractory materials kr W/mK Conductivity of different refractory materials.
W/mK Conductivity of skull. k. W/mK Conductivity of carbon steel furnace shell. L m Length of section or plate.
NuL - Nusselt number
Ph m Horizontal pitch between flat plate coolers. m Vertical pitch between rows of flat plate coolers.
Pr - Prandtl number
P Pa Pressure
Q Jim3 Total heat per unit volume
q W Heat transfer rate
W/m2 Heat flux.
LIST OF SYMBOLS
R KJW Thermal resistance between cooling element and cooling water.
Rf K/W Thermal resistance between furnace inside and skull or refractory lining.
Rp K/W Equivalent resistance for parallel resistances.
Rr K/W Thermal resistance across refractory lining.
R K/W Thermal resistance across skull. RT K/W Total thermal resistance. -
Re1 - Critical Reynolds number indicating initiation of turbulent flow.
Red - Reynolds number for cylindrical tube section with diameter d
ReL - Reynolds number over flat plate with length L
Re - Reynolds number over flat plate with length x S W/m3 Rate of heat generation per unit volume
T °C (K) Temperature
T. °C (K) Air or ambient temperature on outer face of furnace
shell.
T Jk °C (K) Cooling water temperature used for determining water properties.
T °C(K) Cooling water temperature.
T. °C (K) Temperature between shell and cooling element. Tf Furnace inside temperature.
Tiniet = Ti °C (K) Temperature of water at inlet of cooling element. T °C (K) Temperature of furnace shell on the outside.
T1 Temperature between cooling element and refractories. T2 Refractory lining hot face temperature.
T2,, °C(K) Maximum hot face temperature T3 °C (K) Skull initiation temperature, if applicable.
AT1 °C(K) Total temperature difference across thermal resistance model.
sec Time
td m Depth of flat plate coolers sticking into furnace.
th m Thickness of flat plate cooler - height
Im m Thickness of mortar type refractories.
tP m Width of flat plate coolers. m Furnace shell thickness.
U m/s Magnitude of velocity vector V
u,v,w m/s The x,y,z components of V
LIST OF SYMBOLS 2
U inlet = Ui rn/s Inlet velocity of cooling water.
m/s Free stream velocity
- Non-dimensional velocity for turbulent boundary layer. V rn/s Velocity vector
Xk m Copper thickness. x,. m Refractory lining thickness.
m Skull thickness. - Nondimensional-distance for turbulentboundary layer.
z m Depth a 1/K Coefficient of thermal expansion
S m Boundary layer thickness. - Kronecker delta
0 - Represent variables to be discretisized
It kg/ms Dynamic viscosity
V m2/s Kinematic viscosity
V - Poisson constant
- Stress tensor
Pkg/M3 Bulk density
UB N/rn2 Tensile strength
- Viscous stress tensor
TW N/rn2 Shear stress at the wall
LIST OF SYMBOLS 3
CHAPTER 1
IIIGBIER PRODUCTIVITY AND LONGER CAMPAIGNS DEMAND IMPROVED BLAST FURNACE LINING/COOLING SYSTEM DESIGNS
1.1 Introduction
Blast furnace performance increased dramatically over the past 15 years due to the hightOthetitiwn of th globatstel costly-
alternatives to steel. Productivity and daily output must be high and downtime must
be minimal. The operating and maintenance costs must be as low as possible
without influencing the campaign life which is extended up to 15 years nowadays.
Due to this, the number of blast furnaces in the world is decreasing year by year
although the cumulative output of all the furnaces in operation remains relatively
stable. For example, in the Federal Republic of Germany, there were 130 blast
furnaces in operation in 1960 compared to 30 in 1993. The total annual hot metal
production over the same period remained stable and fluctuated between 25 and 35 million tonnes per annum [1]. Hoogovens of the Netherlands showed a 74%
increase in productivity for the period 1981 to 1995. This is illustrated in Table 1.1 [2].
Table 1.1 Productivity improvements at Hoogovens [21 1981 1995*
Number of operating furnaces 4 2 Total working volume (m) 8575 6118 Annual hot metal production (million tonnes) 4.61 5.72 Average productivity (tonnes/m 3/day) 1.47 2.56
* Annual production by extrapolation of Jan. to Aug. 1995 data.
Despite the increase in productivity world wide, which inevitably means greater
stress on the furnace itself, campaign life also needs to be increased to ensure a higher return on investment.
1.2 Variables influencing blast furnace campaign life
With higher productivity and longer campaigns, the demands placed on the blast
furnace lining/cooling system are considerable. The campaign life of a blast furnace
CHAPTER 1 ----- 4
is usually ended when the refractory lining, combined with the cooling system, is
beyond the point of repair and the furnace needs to be relined. Therefore, it is of
utmost importance to minimise the wear rate of the lining/cooling system. In Figure
1.1 an cross section of a typical blast furnace lining/cooling system is shown as incorporated in the furnace shell.
Throat
Upper stack
Middle stack
Lower stack
Belly
Bosh
Tuvere zone
Hearth
Figure 1.1 Cross section of typical blast furnace lining/cooling system.
The wear rate of the lining cooling system can be minimised by altering three
variables, each during a different stage starting at the design phase. The first is the
quality of the lining/cooling system design which can be altered only during the
design phases before the actual reline starts. The second is the quality of the
installation of the lining/cooling system which can only be altered during the reline.
The third is the operation of the blast furnace which can be altered during the
campaign life that commences with start up after the reline.
According to Tijhuis et al [3], the least important of the above is the installation
quality, which leaves the quality of lining/cooling system design and operation of
CHAPTER 1 5
the blast furnace. In particular the operation of the blast furnace is of paramount
importance to ensure long furnace campaigns.
Lately, much progress has been made in improving raw materials quality as well as
distribution of the burden inside the furnace. A modern furnace will be operated
today in such a way that the process is as stable as possible. This includes the
burden quality, burden distribution, continuous tapping, minimum number of stops
-to do maintenance (shutdowns), etc. Deviation- from what could be described-=as
"normal operation" occurs all the time and can never be prevented. First of all,
during stable or normal operation, minor fluctuations in pressure drop and heat flux
to the wall occur all the time. Obviously the design of the furnace must be able to cope with this.
Extreme operating conditions or extreme deviations however are more important to
keep in mind in the design stages of the lining/cooling system. For example,
different coke quality, problems with distribution, change in burden composition, a
long furnace stop, or furnace stops at a too frequent interval, can all have a
dramatic impact on the lining/cooling system. In particular the heat flux level and
temperature fluctuations in the bosh and lower stack increase with these changes, causing increased lining wear.
As an example it could be seen that many shutdowns are not advantageous for the
preservation of the refractory materials and a long campaign life. Wilms et al [4]
show in their paper that a long campaign life could be reached if the blast furnace
has a mostly continuous operation with less shutdowns. The results are summarised
in Figure 1.2. The specific iron production per useful volume (m) of a furnace is
shown, depending on the percentage of shutdown time during the campaign.
Therefore, campaign life and performance of a blast furnace is not determined by
the normal operation mode, but by the extreme operating conditions the furnace
experiences. The lining/cooling system of a blast furnace must be able to cope with
the worst deviations one can expect during the campaign. For each and every blast
furnace the conditions for which to design a refractory lining and cooling system are different.
CHAPTER 1 - 6
10
0
CL 410 No
'S 5- ON E M 11
0 10 20 30 40 50
Percentage shutdown time during campaign
Figure 1.2 Specific pig iron output per blast furnace campaign depending
on the percentage of shutdown time [4].
1.3 Conclusion
The aim of this study is to compare available lining/cooling system designs in order
to determine the best option for the area of the blast furnace experiencing the
highest temperatures and temperature fluctuations. As indicated in red in Figure
1. 1, these areas include the bosh, belly and lower stack regions. As discussed in this
chapter, to have the right design for the lining/cooling system, is one of the three important variables in determining the campaign life of a blast furnace.
From this chapter it is also concluded that the extreme operating conditions of a
blast furnace must be used as boundary values when designing or determining the
best lining/cooling system. Furthermore, it is important to have sufficient
knowledge and information regarding available refractory materials and cooling
methods or systems. In Chapter 2 the latest developments regarding refractory
linings and cooling systems for blast furnaces are investigated and summarised. In
Chapter 3 some actual performances reported in literature for the different blast furnace lining/cooling systems are compared.
A further aim of this study is to show that a numerical solution method, such as
computational fluid dynamics, can be used to evaluate and compare blast furnace
lining/cooling systems. An overview of the applications as well as the theory of
computational fluid dynamics are also included for this purpose.
I.
CHAPTER! 7
CHAPTER 2
BLAST FURNACE DEVELOPMENT: REFRACTORY LININGS AND COOLING SYSTEMS
2.1 Introduction
Before the lining/cooling system as such is discussed, it is necessary to take a closer
look at the wear mechanisms active in the blast furnace. Knowledge of physical and - - chemical wear mechanisms in the blast furnacei required for the designer tomakè
the right choice of refractory materials and cooling methods. What kind of wear
mechanisms are active in which part of the furnace and what type of damage they
cause is also important information.
With this information refractory linings and cooling systems for the blast furnace
will be investigated with regard to recent developments and what is available. More
attention will be given to the bosh, belly and lower stack areas as these areas are
subjected to the highest temperature fluctuations and subsequent wear mechanisms at extreme operating conditions.
2.2 Wear mechanisms in the blast furnace
The blast furnace is refractory lined to protect the furnace shell from the high
temperatures and abrasive materials inside the furnace. The refractory lining is
cooled to further enhance the protection against and dispatch of excess heat that
could destroy the lining itself. Thus, knowledge of the physical and chemical wear
mechanisms in a blast furnace is of decisive importance for the design of the
refractory lining and cooling system. Lining wear is a complex phenomena as
different attack mechanisms are active in different zones of the furnace. In Table
2.1 a summary is given of the different attack mechanisms according to the furnace
zones, as proposed by Van Laar et al [5].
Mechanical wear or abrasion occurs mainly in the upper stack region and is caused
by the descent of the charge materials and by the dust laden gases. High thermal
loads are a major factor in the lower stack and the belly regions. In the hearth
region, horizontal and vertical flows of hot metal combined with thermal stresses
often form undesirable elephant foot shaped cavitations.
CHAPTER 2 8
Table 2.1 Different attack mechanisms according to different furnace
zones 1131.
Area Principle attack phenomena Resulting damage
Upper stack Abrasion Abrasive wear
Medium temperature fluctuations Spalling
Impact Loss of bricks
Middle stack Abrasion Abrasive wear
eavy - temperature - fluctuations
Gas erosion Wear
Oxidation & alkali attack Deterioration
Lower stack Heavy temperature fluctuations Severe spalling
Erosion by gas jets & Abrasion Wear
Oxidation & alkali attack Deterioration
Thermal fatigue Shell damage and cracks
Belly Medium temperature fluctuations Spalling
Oxidation & alkali attack Deterioration
Abrasion, gas erosion & high Wear temperature
Bosh High temperature Stress attack
Slag & alkali attack Deterioration & wear
Medium temperature fluctuations Spalling
Abrasion Wear
Raceway & Very high temperature Stress cracking & wear tuyere zone
Temperature fluctuations Spalling
Oxidation (water & 02) Deterioration
Slag attack & erosion Wear
Damage from scabs Loss of cooling elements and tuyeres
Hearth Oxidation (water) Wear
Zn, slag & alkali attack Deterioration
High temperature Stress build up and cracking
Erosion from hot liquids Break Out risk
Iron notch Heavy temperature fluctuations Spalling
(Taphole) Erosion (slag & iron) Taphole wear
Zn & alkali attack Deterioration
Gas attack & oxidation (water) Wear & deterioration
CHAPTER 2 9
The main chemical attack mechanisms are alkali attack, CO disintegration and
oxidation. These are important for wear in the long term. The reactive kinetics
involved depends on the temperature of the lining and on the presence of catalysts
in the refractory, which are found as impurities in the materials, such as the ash of
carbonaceous products. The heat load determines the temperature distribution in
the lining, which in turn is determined mainly by the operation of the blast furnace.
In Table 2.2 a summary is given of approximate temperature levels promoting - - -- -- -- - --- --- -------
Table 2.2 Temperature levels that promote chemical attack mechanisms 161
Mechanism Temperature (°C)
CO disintegration 450 -850 Alkali and zinc attack 800-950 Oxidation by 02 >400 Oxidation by CO 2 and H2O >700
Apart from the fact that temperature plays an important role in the chemical attack
mechanisms, there is also the relation with the thermal expansion of the lining
materials. If the lining material has a high thermal expansion, the thermal stresses in
- the bricks may exceed the critical crushing values, or more specifically, the
material's cold crushing strain value. Bricks will then start to crack. Materials with
a higher thermal conductivity, on the other hand, will have lower steady-state lining
temperatures, and thus lower thermal expansion will occur. This is because of the
more effective removal of heat from the lining, assuming the same cooling system is used.
Hoogovens Technical Services (HTS) [3] from the Netherlands combined these two
properties, the cold crushing strain and thermal expansion at 1000 °C, to form a
theoretical value which they call the "critical crushing temperature". This is
obtained by dividing the cold crushing strain with the thermal expansion at 1000 °C,
times 1000, to obtain an answer in degree Celsius. In Table 2.3 the results for the
different refractory materials are shown. It shows that semi-graphite and full
graphite have very low thermal expansion and that they are very compressible
relative to the other refractory materials.
CHAPTER 10
Table 2.3 Comparison of crushing resistance for blast furnace refractory
materials 131.
Material Cold crushing Thermal expansion Critical crushing strain (%) at 1000 °C (%) temperature (°C)
Silicon carbide 0.05 0.3 170 High duty 0.1 0.5 200 High alumina 0.1 0.7 140 Amorphous carbon 0.4 0.5 800 Semi-graphite- ---0.4 2500--Graphite 1.0 0.3 3300
Table 2.4 Critical temperature fluctuations for spalling [3].
Material Maximum allowable temperature rise ('C/min)
Graphite 500
Semi-graphite 250
Silicon carbide 50 Cast iron 50 85% Al203 (alumina) 5
Chrome corundum 5
44% A103 (alumina) 4Actual measured: Sinter pellets 50/50
I1il Sinter pellets < 10% 50
One of the most problematic wear mechanisms in the blast furnace arises from
temperature fluctuations giving rise to the formation and breaking away of scabs on
the furnace wall. Apart from the mechanical wear or physical damage caused by
scabs sliding down the furnace lining, the rapid change of the thermal resistance in
front of the lining causes further temperature fluctuations in the refractory materials.
These fluctuations leads to spalling of the refractory materials. Hence, spalling
resistance is an important requirement apart from properties like cold crushing strain and thermal expansion.
In particular in the belly and the lower stack, large temperature fluctuations may
occur. Practise shows that the amount of pellets, like sinter pellets, in the burden
also plays an important role. More severe temperature fluctuations occur if more
pellets are used. According to Tijhuis et al [3], a temperature rise as high as 150
°C/min has been measured, and necessarily the refractory materials should be able
CHAPTER2 ---- 11
to cope with this. Table 2.4 shows the maximum temperature rise for different
refractory materials [3]. It also shows that semi-graphite and graphite are the only
materials that can withstand such a temperature rise.
From the above overview of attack mechanisms, the ideal refractory material (or
combinations of materials) should meet the following requirements:
• - For the best—resistance against chemical attack, two parameters could--be
changed. Firstly, the ash and iron content of the material should be very low.
Secondly, the design of the lining/cooling system should be such that the
temperatures in the lining are below the critical reaction temperatures for any of
the chemical reactions mentioned. The lowest threshold values are for CO-
disintegration (450°C) and the oxidation by oxygen (500°C).
• The heat load, or cooling losses, for each furnace zone, are determined by the
operating mode of the furnace. Hence, this is not determined by the choice of
refractory material or cooling system used. The temperature level in the lining
can be decreased by increasing the thermal conductivity of the refractory
material. By doing so, the hot face temperature of the lining will also be lower.
With these low hot face temperatures, a uniform and stable skull could be
formed on the lining. This not only protects the lining from mechanical wear,
but also reduces heat losses further as the thermal resistance to the cooling
system is increased without an increase in lining temperatures.
• The consequence of the operating mode selected by the operators is that certain
temperature fluctuations will occur. Materials with a high thermal conductivity
can deal with severe temperature fluctuations.
2.3 Development of blast furnace refractory linings
In Table 2.1, the different attack mechanisms are summarised according to the
different blast furnace zones or areas. With regard to the bosh, belly and lower
stack the following attack phenomena are highlighted:
• Medium to heavy temperature fluctuations,
• high average temperature,
• gas erosion,
• abrasion,
CBAPTER2 12
• oxidation, alkali and slag attack, and
• thermal fatigue.
A refractory lining in this area consisting of materials able to withstand these attack
mechanisms is of utmost importance for the stable and continuous operation of the
blast furnace. According to Hebei et al [7], this could be done by selecting
refractory materials with the correct thermochemical and thermomechanical
properties and behaviour. -These include
• pig iron resistance,
• slag resistance,
• alkali resistance,
• zinc and lead resistance,
• thermal conductivity,
• heat transfer to cooling system,
• pig iron infiltration behaviour,
• micro porosity,
• pore size distribution,
• apparent porosity,
• bulk density,
• thermal expansion,
• abrasion,
• permeability,
• thermal shock resistance,
• modulus of elasticity,
• modulus of deformation,
• modulus of tensile and compressive strength
• cold and hot crushing strength,
• modulus of rupture, and
• suppressed expansion.
For the above several property standards have been drawn up by different
companies using different data sets and test methods. Therefore it is sometimes
difficult to compare materials considering only the properties while on the other
hand, comparisons based on experience are very important as will be discussed in Chapter 3.
CHAPTER - 13
According to an European study conducted by Burteaux et al [8], the development
of the refractory linings and structures in blast furnaces is substantially divided into
two groups. The first group is the "white" or "oxide ceramic" solution and this
predominantly employs further developed conventional refractories. These
refractories possess very low to medium thermal conductivities and the idea of
insulating the furnace to minimise heat loss is a dominant design factor in the "white" solution.
The second is the so-called "black" or "thermal" solution which is mainly based on
the lower reaction limit temperature and is clearly identified by working with
refractories that have a medium to high thermal conductivity. The lower reaction
limit temperature of a refractory material is the temperature at which the material
becomes chemically reactive in the furnace and thus chemical wear starts taking place.
It must be noted that although two totally different approaches have been presented
here, there are "grey" solutions which incorporate both the "black" and "white"
solutions in furnace design. Currently the following refractory materials, arranged
from "white" to "black", are most commonly used in the bosh, belly and lower
stack:
High-alumina, corundum and variants,
• silicon carbide and variants, and
• different grades of carbonaceous products like graphite and semi-graphite.
23.1 High-alumina, corundum and variants
High-alumina and corundum (extremely hard crystallised alumina) refers to refractory brick having an alumina (Al 203) content of 47.5% or higher. They are
distinguished from brick made predominantly of clay or other alumino silicates that
have an alumina content of less than 47.5%. Several special types of high-alumina products are available for refractory use [9]:
• Mullite brick: Contains primarily the mineral phase 3Al 203.Si02 (mullite) that, on weight basis, is 72% Al203 and 28% Si02.
• Chemically bonded brick: Normally phosphate-bonded in the 75 to 85%
Al203 range (an aluminum orthophosphate [AIPO 4] bond is formed at relatively low temperatures).
CHAPTER 2 14
• Alumina-chrome brick (chrome-corundum bricks): According to
manufacturers, this is made of high-purity, high-alumina materials and chromic
oxide (Cr203) that form a highly refractory solid solution at high temperatures.
• Alumina-carbon brick: This is a resin-bonded high-alumina brick that contains
a carbonaceous additive such as graphite. The bonding by thermosetting of
resins produce a carbonaceous bond on pyrolysis (subjection to very high
temperatures).
For alumina-silica refractories, refractoriness (resistance to heat and corrosion) is a
function of alumina content. For instance, a 50% alumina brick is more refractory
than a fire clay brick. Refractoriness increases with increasing aluminium oxide
content up to 99% Al203 . It is important to recognise that the presence of certain
impurities, like oxides, affects refractoriness. Naturally occurring minerals, as
mined, may contain alkalis (Na2O, K20, Li20), iron oxide (Fe203), and titania (Ti02). Alkalis are harmful, because they may react with silica to form a low-
melting glass when bricks are fired or are exposed to high temperatures in service.
Both Fe203 and Ti02 have been observed to react with Al203 and Si02 to form low-melting phases.
Important properties of these bricks can be altered dramatically by chemical
composition and impurities. For instance, alkalis and lime affect creep resistance.
On the other hand, basic components in any slag (MgO, CaO, FeO, etc.) react with
high-alumina brick. As the Al203 content increases, resistance to acid slags (those
high in silica) increases.
Development of high-alumina and/or corundum bricks has been in two directions,
namely, improvements in the chemical and in high temperature properties. With the
corundum qualities mention should be made of the improvement in quality of pre-
cast concrete blocks and tiles by chromic oxide addition [10,11]. These blocks are
particularly resistant to attack by liquid slags and alkalis. The thermal
characteristics and especially the resistance to fluctuating temperatures have been
improved by the addition of SiC in chrome-corundum bricks and through the
improvement of the bonding phase with nitride in the corundum qualities.
CHAPTER 2 15
Al203 100
SiO2 3Al203 + 2 Si02
80
60
40
Si2N2C
20
0 100
AIN 0 20 40 60 80
Si3N4 1760°C
23.2 Silicon carbide and variants
Silicon carbide (SiC) bricks were first used in the blast furnace about 20 years ago.
Since then silicon carbide was developed into a refractory material that not only has
good wear but also good temperature resisting characteristics. Different bonds
were and are still investigated in order to increase the quality of the SiC bricks. The
development went from oxide to oxinitride bonded bricks and ended in pure nitride
bonded and self-bonded SiC bricks. The iast==two types are currently widely used.-
The latest development is the sialon bond, which is a 4-phase system [8,12].
Sialon is a continuous solid solution consisting of Si, Al, 0 and N, as an end
member of silicon nitride Si3N4 (Z=0), and its chemical formula is written as
Si6A1ON8 (0 <Z <4.2), as shown in Figure 2.1 [12].
Figure 2.1 Phase diagram of the Si 3N4-AIN-Al203-Si02 system 1121.
CHAPTER 2 16
Sialon solid solution may be formed in the matrix of the SiC brick by the reaction
between Si3N4 and Al203 during sintering at elevated temperature in carbon
powder.
Si3N4 + Al203 + 13-sialon
The strength of the brick increases as bonding force increases between SiC particles
by the formation-of sialon until- the Z number reaches I- However, when the -Z
number reaches 3, Al203 becomes excessive for the formation of sialon in this
condition, and the residual Al203 remains in the matrix of the sialon-bonded SiC
brick.
Table 2.5 shows that this bonding produces particularly good property values not
only for porosity but also for the hot bending strength after the alkali test [8,13].
At this point, attention should be drawn to an SiC type of brick developed in the
Netherlands. The bevelled heads on the hot side, so-called "cat heads", should
satisfy the expansion conditions at this particularly hazardous area in the furnace
and avoid spalling (Figure 2.2) [14].
Table 2.5 Resistance of various bond types of SiC refractories [8,13].
Property Oxide Si3N4 f3-SiC Sialon
SiC content % 85-90 75 90 75
Porosity % 18-20 16-18 15-18 15
Hot MOR* (1400°C) N/mm2 22 44 52 62
Hot MOR alkali test N/mm2 0 21 32 36
CCS N/nun2 100 182 155 215
CCS after thermal shock test*** N/mm2 n.d. 177 180 245
Oxidation weight loss (steam test) 0.65 1.7 1.2 2.4
*MOR = Modules of rupture (= hot bending strength) **CCS = Cold Crushing Strength = water test
CIIAPTER2 17
_
Figure 2.2 Tapered SiC bricks for increased spalling resistance 1141.
2.3.3 Carbon, graphite and semi-graphite.
Carbon has certain definite characteristics or properties as an element which are
established by nature and which are unchangeable. In industry the terms carbon,
formed carbon, manufactured carbon, amorphous (non-crystalline) carbon or baked
carbon refer to products that result from the process of mixing carbonaceous filler
materials such as calcined anthracite coal, petroleum coke or carbon black with
binder materials such as petroleum pitch or coal tar pitch, forming these mixtures by
moulding or extrusion and conventionally baking these formed pieces in furnaces at
temperatures from 800°C-1400°C to carbonise the binder. The resulting product
contains carbon particles with a carbon binder.
Conventionally baked carbon can be densifled and permeability reduced by the
introduction of additional binders, impregnated into the baked carbon under
vacuum, and the resultant product rebaked to carbonise the impregnation pitch.
Multiple impregnations are also possible to double or triple the density of the end
product called microporous carbon. Each densification, however, adds additional
cost and results in a high priced product [15].
The term "graphite", also called synthetic, artificial or electro-graphite, refers to a
carbon product that has been further heat treated at a temperature of between 2400°C - 30000C. This process of graphitisation, changes the structure of carbon
as well as the binder to a crystallographic structure which also changes the physical
and chemical properties.
CHAPTER 2 18
The term "semi-graphite" is used to describe a product which is composed of
synthetic graphite particles, mixed with carbonaceous binders such as pitch or tar,
and baked at carbonisation temperatures of 800°C - 1400°C. The resulting product
is composed of graphite particles which were produced at temperatures close to
3000"C, bonded together with amorphous carbon binders which have been baked at
800°C - 1400°C. The resulting product, a true carbon bonded graphite, exhibits
higher thermal conductivity than the carbons, but because of the carbon binder, not
as high as -100%- graphite. Thermal conductivities'-=will vary withbaking
temperature and can be increased by rebaking at higher temperatures [15].
Manufactured carbon and graphite can be modified with additives and coatings, but
one cannot appreciably change such fundamental characteristics of the element carbon as [15]:
• Oxidation: Starts occurring at approximately 400°C and higher in the presence of free oxygen.
• Melting: Carbon does not melt, slump or deform at high temperatures in the manner of most materials with which it competes. It evaporates without
melting above 3600°C (sublimation).
• Stability: Carbon is the highest temperature-stable elemental solid known to man.
• Non-wetting: Most molten metals will not cling to or adhere to a carbon body.
• Strength: The strength of graphite increases with temperature up to 2500°C, primarily because graphite is quite brittle at lower temperatures, as there is no
mechanism to relieve stress concentrations where particles are bonded.
• Thermal expansion (Graphite): Very low. Only 10% to 16% of that of stainless steel and much lower than the best refractory ceramics. It also
possesses great thermal shock resistance. Thermal expansion is kept low by
control of the individual crystal orientation in a brick.
Conductivity - Electrical and thermal: Both carbon and graphite conducts electricity and heat while graphite has a higher thermal conductivity than most metals.
• Corrosion resistance: Carbon is inert to the action of most chemicals and
chemical compounds, except those of a highly oxidising nature.
With the graphite brick qualities the development in Germany is particularly
characterised by the production of high quality electro-graphite and the single or
multiple impregnation with pitch or phosphate [16]. These measures make the
CHAPTER 2 19
normally wear-sensitive graphite harder and more resistant to oxidation. Semi-
graphite qualities have also been further developed to harden graphite by means of
compaction. This reduces the porosity and increases the thermal conductivity.
In Japan, also in the UK and France, carbon bricks have been developed to the
extent that an extremely fine structure or fine porosity is produced through metallic
additions [17,10]. Consequently, these bricks have a very low permeability and are
therefore more -resistant to alkalis, hot metal -and =slag infiltration. Lessthan 10% of
the open pores are larger than 41.tm. With conventional bricks this value is at least
70%. Table 2.6 is a summary of properties for carbon refractory products from
results obtained by Hebel et al [7]. This is only a comparison between
carbonaceous materials and in most cases all of them have better properties than other refractory materials.
Table 2.6 Properties of carbon refractory materials 1711
Type of carbon Raw material J1icr'p' Pig iron I'Jwrnñ,l Cold material basis r .iii and slag 'nrh...n- crushing
resistance strength
amorphous carbon anthracite + mine low medium coke
amorphous carbon anthracite IONN, medium medium
microporous carbon
anthracite + SiC high medium !. high
super microporous anthracite + SiC er, Iii h very high v. very high carbon + Al203
semi-graphite electrographite + li:h :: low 111cdjuñi•. medium calcined coke powder
microporous semi- electrographite + vr liih high hj!; high graphite calcined coke
powder + SiC + Al203
graphite pure graphite hi low very high low
Hoogovens of the Netherlands is in the forefront in the development of the so called
"black" solution [3,5,18]. The philosophy behind this solution is based on the fact
that the heat load on the lining/cooling system is determined by the operating mode
of the furnace. As stated previously, the operation of the furnace is one of the
factors that has an important influence on the campaign life of a furnace. Because
the hot gas flow to the top of the furnace, through the burden, can cause high hot
CHAPTER 2 20
face temperatures on the lining/cooling system, it is preferable to have the gas flow
through the middle and not along the sides of the burden.
Thus, by changing the operating mode of the furnace from wall working to central
working, the thermal load on the lining/cooling system is changed accordingly. This
can reduce the heat loss from the furnace up to 40%. Hence, the heat loads the
lining is subjected to are independent of the design of the refractory and cooling
systems. This with high thermal conductivities
does not necessarily have high cooling losses as a consequence.
As can be seen there are many different refractory materials available currently. All
of these have reason to exist and are best suitable for one or more applications. In
the next section the current developments regarding cooling systems will be
discussed.
2.4 Development of blast furnace cooling systems
"Irrespective of the use of so called refractory materials, the best
means of maintaining the walls of the blast furnace is with cooling
water."
These words were spoken in 1892 by Fritz W Lurman [8], a well-known blast
furnace man from the time shortly before the turn of the century. The main function
of the cooling system is to cool the furnace shell and prevent it from over heating
and subsequent burn through. To accomplish this, the cooling system must be able
to take up the excess heat generated by the furnace and loaded on to the shell. This
heat will lift the shell and lining temperature too high if the cooling system is not
effective in dispelling it.
Over the years, the development of cooling systems has received a great deal of
attention, especially in the last two decades. Two main competitors emerged for
shell cooling, with still no clear advantage evident. The first of these is the so called
cooling boxes, or sometimes better known as flat plate coolers. The second is the
cast iron staves, which receive great attention especially in Japan. Where flat plate
coolers, as the name describes, are flat plates that are arranged horizontally into the
furnace shell, staves can be described as flat plates stacked parallel and flush to the
inside of the shell and are cooled by a built in piping arrangement.
CHAPTER 21
An investigation of 1984 established that there was still a predominance of blast
furnaces equipped with cooling boxes but that there was an increasing number being
equipped with cast iron staves. Figure 2.3 shows that in Japan over 70% of blast
furnaces are fitted with staves, less than 5% in America and over 20% in Europe [19].
2.4.1 Copperfial plate coolers -
Nearly all the large European furnaces with cooling boxes use copper flat plate
coolers (Figure 2.3). The usual plate sizes are 500 - 1000 mm long, 400 - 800 mm
wide and approximately 75 mm high. Copper flat plate coolers are either welded or
cast in electrolytic copper. With the latter, there are then no problems at the weld
seams and there is a greater uniformity of the material properties over the complete
cooling element.
In the regions of the furnace which are subject to mechanical damage the front sides
of the cooling elements are frequently reinforced with special materials. To ensure
gas tight sealing the flat plate coolers are mostly welded to the shell. The copper
flat plate coolers generally have multiple channels with one or two independent
chambers. Minimum losses of water pressure are ensured in both the piping and the
element itself [20]. Figure 2.4 shows a typical copper flat plate cooler design.
Figure 2.3 World distribution of blast furnaces with stave cooling and plate
cooling in 1984 [191
CHAPTER 2 22
Welded in shell
Flanged
Figure 2.4 Typical copper flat plate cooler [201.
The vertical spacing of the flat plate coolers is usually selected at between 300 and
600 mm. In the zones with the highest heat loads, especially the lower stack and
bosh, the spacing today is sometimes reduced to 250 mm. The most recent design in copper flat plate coolers is the six pass, single chamber cooler as shown in Figure
2.4. This type of cooler is usually used in the area from the bosh up to and
including the lower stack. It has been designed to maintain high water velocities
throughout the cooler, thus giving both an even and high heat transfer coefficient [20].
2.4.2 Cigar coolers
For still more intensive cooling or with insufficient existing spacing of the flat plate
coolers, separate so-called copper jackets or cigar coolers are used in the open
areas between the plate coolers. These are sometimes also utilised for
improvements to existing cooling systems during a campaign. Cigar coolers are
usually machined from a solid copper bar to form a cylindrical core and a single
channel is added by drilling and plugging. A typical cigar cooler is shown in Figure 2.5.
The cigar coolers are usually inserted on the centrelines between adjacent flat plate
coolers on a horizontal and vertical plane. For installation a cylindrical hole is
drilled through the furnace shell and existing refractory lining with a core drill. In
Figure 2.6 the positioning of a cigar cooler between flat plate coolers is shown as
seen from the outside of the furnace shell.
CHAPTER 2 23
Plugged and
I f
machined
= water -
Figure 2.5 Typical cigar cooler.
Horizontal pitch 4
Flat plate cooler
0 cooler Vertical pitch
Figure 2.6 Position of cigar cooler between flat plate coolers.
The use of cigar coolers in the bosh, belly and lower stack areas will increase the
cooling system area. Because this area of the furnace has the highest temperature
and temperature fluctuations, the use of cigar coolers could increase the refractory
linings resistance to chemical as well as mechanical attack mechanisms. If cigar
coolers are to be used, the shell strength should also be considered due to the increase in apertures.
2.4.3 Cast iron staves.
Currently used cast iron staves have the following typical dimensions [8]: Length = 1.8 - 2.4m (average 2m) Width = 0.8 - 1.1 m (average I m) Thickness = 0.250- 0.6m (0.6m only on staves with noses)
CHAPTER 2 24
a) b) c) d) "Dogleg" pipes "Dogleg" pipes Straight pipes Straight pipes
Lug at upper end Lug at upper end
Figure 2.7 Different stave designs [8].
In the past the material used for cast iron staves was alloyed perlitic lamellar grey
iron, but nowadays this is frequently replaced by SG iron, which is less subject to
cracking at temperatures above 760°C [20]. Successful tests have also been carried
out with cast steel. The higher melting point makes these staves less susceptible to
attack by hot metal and slag. Instead of the originally used marschalite coating on
the tubes, there is some test use of either flame sprayed ceramic or metal-ceramic
multi-layer coatings. Non-coated Ni base alloy tubes are also under development.
The cooling effect of the staves are determined by the size and shape of the cooling
water tubes inside the stave. For this reason, ever larger tube diameters and/or oval
cross-sections are being used. For the same reason, development is aimed at staves
with four to six vertical tubes. In Japan, Nippon Steel Corporation (NSC), has
developed their fourth generation stave cooler with four vertical running tubes [21].
They are characterised by the fact that they have two cooling planes, four vertical
tubes in the hot side plane and one serpentine tube on the cold side. Some of the
staves are equipped with cooled noses and/or brackets for the support of the
refractory materials. Furthermore, the corners of the staves are intensively cooled.
As can be seen in Figure 2.8, the refractory materials are cast into special support
holes in the staves. Type C can be seen to be much thinner and is designed to save
space inside the furnace and hence enlarge the working volume of the furnace.
CHAPTER 2 25
Type A
g pipe -
Lug portion
Co
E.. Serper
pipe
entine pipe
Vertical pipe
1 omer pipe
Cast-in wall Cast-in brick
brick
Type B
Corner pipe
S S Lug pipe
Lug portion :'S. Serpentine pipe
Vertical pipe
omer pipe
7 Cast-in wall Cast-in brick
brick
8E:_.oE
:0
Type C
Corner pipe
Serpentine pipe
Vertical pipe
' omer pipe
Cast-in wall Cast-in brick brick
Figure 2.8 The latest stave designs from NSC, Japan 1211.
One of the claimed advantages of stave cooling over flat plate cooling is the so-
called blanket cooling effect of the staves, in contrast to the point-by-point cooling
achieved by flat plate coolers. This ensures a more uniform cooling performance.
Kawasaki Steel of Japan has adopted a combined strength solution [22]. According
to Kawasaki Steel, the main advantage of the combined use of staves and flat plate
coolers, is the additional refractory support achieved with the flat plate coolers.
In the past staves with lugs at the top were used (see Figure 2.7) to support the
brickwork in the shaft, but the service life of these staves were found to be too
short. Damage to the staves may occur within several years after blow-in, thus
failing to provide an adequate brick support function. For this reason, flat plate
CHAPTER 2 26
coolers were inserted between the stave coolers in order to maintain the brick
support function over the long term. (See Figure 2.9).
Stave cooler
Refractory lining
Copper fiat plate cooler
Figure 2.9 Blast furnace stack with flat plate coolers inserted between rows
of stave coolers 1221.
2.4.4 Current design data for flat plate coolers and cast iron slaves.
A comparison of the two cooling systems with respect to the specific cooling areas (expressed as m 2 cooling area/M2 furnace shell), the specific water volumes and water velocities, produces the picture shown in Table 2.7 [20]. The specific cooling
area with cooling plates is usually 1-2 M2/M2; extreme values of 2.5 m2/m2 occur with very close spacing of the cooling boxes, especially in the belly and the lower stack.
The values achieved with staves lie within a close range of 0.8 to 1.1 m 2/rn2 . This value doubles for intensive cooling staves. Water volumes for copper flat plate cooler systems are between 5 and 10 M3 /h per m2 of shell and about half these volumes for staves. The water velocities for both copper plate coolers and staves are an average of 1.3m/s.
Table 2.7 Design data for cooling systems 1201.
Copper plate coolers
Average Max.
Cast iron staves
Average Max.
Specific surface area of cooling 1-2 2.5 0.8-1 1-2 element per m2 shell (m2/m2)
Specific cooling water flow per m2 5-10 3-5
shell (m3Ih)
Typical cooling water velocity (m/s) 0.5-1 2-2.5 1-1 2.5-3
It can generally be said of these values that, with both systems, a greater intensity of
cooling is achieved through an increase in specific cooling areas. Close spacing of
CHAPTER2 27
Furn colui
Plat
Lint t1e
factory rt
flat plate coolers and intensive cooling staves aim in this direction. The result of
this is not only to be seen in the higher capital costs for the cooling elements but
also in the problems arising in the strength requirements of the furnace shell and
there could also be unfavourable effects on the current pumping costs, but the need
to achieve long campaign lives depends upon this more intensive cooling.
2.4.5 Mantle or lintel staves.
While most blast furnaces designed in Europe are of the free standing type with no
upper supports on the furnace shell, some American furnaces incorporate a mantle
where the furnace is supported from ground level with steel and concrete columns.
The use of a mantle usually eliminates the belly area. The mantle is an integral part
of the furnace design and must be protected against overheating under the same conditions experienced in the belly area of other furnaces.
Cooling of the furnace lining in the mantle area using copper plates is difficult due
to limited access for changing and the length of plate coolers that must be used.
The use of staves in this area has the advantage of giving a complete cooling
coverage of the mantel. The stave arrangement at the mantle on most modern
furnaces using cooling plates otherwise is shown in Figure 2.10 [23].
Figure 2.10 Mantle stave in plate cooled furnace [231.
CHAPTER2 28
24.6 Copper staves.
In the region of the bosh, belly and lower stack a good cooling system design is of
utmost importance to be able to cope with high heat loads and high temperature
fluctuations. A recent development aimed specifically at this area is the use of
copper staves. MAN GHH from Germany [24], in collaboration with Thyssen Stahl
AG, selected copper staves for development and testing on the basis of trials performed-in Japan with cast-copper staves. =
Since the MAN GHH copper staves are rolled rather than cast, the outer
dimensions can be held to close tolerances. In addition, by boring the cooling
passages directly into the rolled copper plates, the cooling water is directly in
contact with the stave body, thus eliminating the thermal barrier of the coating on
the cast-in pipes used in cast iron staves. These techniques, in conjunction with the
high conductivity of copper, lead to much lower stave operating temperatures under all operating conditions.
2.4.7 Current layout of cooling systems.
Water cooling systems are designed to operate in a closed loop rather than the
conventional open systems. This allows the pipe work to be chemically cleaned,
and by controlling water chemistry throughout the campaign this clean surface can
be maintained, thus ensuring maximum heat transfer. The development of the
sealing of the cooling tubes to the shell is towards the use of ever thinner, 'softer'
metallic expansion joints. For both systems, i.e. flat plate coolers or staves, there is an increasing use of rubber bends and hoses [8].
Independent series are typical for water distribution in flat plate coolers (Figure
2.11). With staves it is usual to provide a number of independent flow and return
headers in accordance with the number of tubes. This ensures that in the case of
failure of one feed system, the remaining stave tubes receive sufficient cooling.
Nose and corner tubes are connected to additional water circuits.
CHAPTER 2
Inlet
jii uiu• iiu iuu
.Li
a) Horizontal series - - -- b) Vertical series - - -
Figure 2.11 Typical series of flat plate coolers.
2.5 Conclusion
First of all in Chapter 2, the chemical and mechanical wear mechanisms that may
attack the blast furnace lining were discussed. The main requirements for the
initiation of the different mechanisms were identified. These initiation requirements
will be used later in the study for the evaluation of results. Secondly, the currently
available and most commonly used refractory materials as well as cooling systems were discussed.
To conclude the discussion on what is currently available regarding refractory
linings and cooling systems, Table 2.8 shows combinations of refractory linings and
cooling systems currently used. This will also be useful in the comparison between
performances of existing refractory linings and cooling systems in the bosh, belly
and lower stack area to be discussed in Chapter 3.
Table 2.8 Current combinations of refractory linings and cooling systems used.
Area Copper flat plate Cast iron staves Copper slaves (rolled coolers and machined)
Bosh Silicon carbide Silicon carbide Not as yet used High-alumina High-alumina Graphite
Semi-graphite
Belly Silicon carbide Silicon carbide High-alumina High-alumina High-alumina Graphite Graphite-silicon
Lower stack Silicon carbide Silicon carbide High-alumina High-alumina High-alumina Graphite Graphite-silicon
CHAPTER 2 30
CHAPTER 3
COMPARISON BETWEEN COMBINATIONS OF REFRACTORY LININGS AND COOLING SYSTEMS
3.1 Introduction
In the previous chapter the latest developments in refractory linings and cooling
systems werediscussed. Iff this chapter refractrily lininihd cooling- systems specifically for the bosh, belly and lower stack areas will be investigated with regard
to measurement, comparison and prediction of performances.
In order to measure the performance of a blast furnace during operation it is
necessary to install a great number of measuring or instrumentation devices. For
the lining/cooling system it is also necessary to take measurements during the
campaign for two basic reasons. The first is to enable the operators to operate the
furnace in such a way as to minimise wear on the lining/cooling system. The second
is to warn operators of a possible break out or burn through, as well as to indicate
when the furnace will need to be relined.
A third reason for measurement of performance on the lining/cooling system is for
comparison of performances. This enables designers to select the best systems and
improve on current systems. Two of the best parameters of performance are the
length of the campaign life and the productivity of the furnace during the campaign
life. These are good parameters because, as noted before, the campaign is usually
ended due to the need to replace the lining/cooling system.
Due to the length of campaigns and the enormous cost involved with replacing the
lining/cooling system, the designer has limited freedom in experimenting with new
ideas and systems. The designer therefore has to turn to alternative methods to
accurately predict the performance of a lining/cooling system. New possibilities in
this regard were created due to the accelerating development of computers the past few years.
3.2 Measuring the performance of refractory linings and cooling systems
Later in this chapter the use of numerical computer models to predict the
performance of different combinations of refractory linings and cooling systems will
CHAPTER3 31
be discussed. In addition to good models for prediction, it is also necessary to
equip the furnace with measuring devices in order to observe the wear processes.
The information on the progression of wear opens up the possibility of being able to
change or optimise the mode of working in order to thereby retard the wear.
Longer campaigns can be achieved in this way. Furthermore, the knowledge gained
from such measurements permits the refining of the above mentioned models and
this is very important for the designing of future linings.
In practice, individual methods of measuring come up against various problems and
limitations. The accessibility and availability from the outside is often impeded and
measuring devices can sometimes only be installed during furnace relining or
shutdowns. Also, on account of very small differentials the accuracy of some
measurements is limited. Table 3.1 [8] presents the advantages and disadvantages
of various measuring methods.
Table 3.1 Inspection and measuring techniques for furnace lining
conditions [81
Driff1fine , Isotopes HtFmonie Thermo Heat flux • Biri ug F4il, -couples
r.Jrts / r cooling
el water
Area -+ hearth
-> stack
not used yes —
yes L 'es S ',es
Measured area Pil II small point Ali all panel
Continuous record no no pusible '.cs cs
Direct relation with no no no es ni:diuw good B.F. operation
Accuracy Li rly bad g'iod — uod good
Significant inf. on yes yes yes no no no lining thickness
Replacement - no yes es cs yes possible
Maintenance - no yes yes VCS YCS
possible.
Drilling of the blast furnace shell is mostly only carried out above the tuyere level.
Usually, it is only the local progress of wear that is to be measured. If cylindrical
cores are bored out this not only enables the identification of the degree of wear but
CHAPTER 3
the sample can also be used for chemical and physical structure tests in order to reconstruct the wear mechanisms.
Radioactive isotopes are normally used for the measurement of wear in the bosh,
tuyere and hearth regions. These can generally only be installed at three interrelated
depths during reining of the corresponding region. On account of their
radioactivity, they are subjected to strict regulations. The information from the - -
With steel or ceramic rods that pass through the refractory brickwork it is usually
only possible to use the bum-off as a more or less accurate determination of wear
on shutdowns. Tests with the introduction of impulses in order to determine the
length of the return path in the rod, by measurement of the time differential, run up against considerable difficulties. The time differentials are very small so that any
conclusion on the progress of wear become inaccurate.
Thermocouples permit continuous and reliable measurements to be made up to
around 1000°C. With a corresponding arranged grid pattern they are an especially
suitable basis for the continuous examination of wear in the underhearth region. On
account of the easy positioning of the thermocouples, these should be inserted into
gas tight ceramic tubes up to a depth of 1.5 m and can therefore be changed at any
time. In the stack region thermocouples can be used in the refractory brickwork or 50-80 mm from the hot face of staves. This enables the continuous acquisition of information on local temperatures.
The last method discussed is the measurement of the heat loss or heat extraction.
Two methods can be used here, namely, direct or indirect measurement. In the
direct method the amount of extracted heat is determined by two successive
thermocouples. The heat flow is calculated on the basis of the temperature
difference, a constant heat conductivity of the refractory material and the known depth of the thermocouples.
The problem here is that the heat conductivity of the refractory material can
incalculably vary, and so introduce errors. In Figure 3.1 an arrangement of
thermocouples for investigation and monitoring of the hearth lining is shown [25].
The thermocouples are arranged with a known horizontal distance between each
other and are slightly spaced vertically for installation purposes.
CHAPTER 3
Gas tight sealing
f— Thermocouple - wire
Another application for the direct method of determining the heat flux with the use
of thermocouples is in the furnace bottom under the hearth. Because of the circular
flow of molten metal in the hearth around the so-called "dead man", erosion in the
bottom corners of the hearth becomes a problem. (The "dead man" is a lump of
non-reduced material forming on the vertical centre of the hearth). As a measure to
prevent this circular flow, the vertical temperature difference at the centre of the
—=-=-hearth bottom-is- controlled to-avoid inactivity in--the "dead man" :-
A lower temperature difference will indicate a low thermal heat flux at the hearth
bottom and promote circular flow by forming a solidified layer at the hearth centre.
At Chiba No. 6 blast furnace [22], the temperature difference was kept low enough
by effective burden distribution to ensure a central gas flow through the furnace. In
other words, the "dead man" was reduced and this could be monitored by the
continuous measurement of the temperature difference.
Carbon type Section A II] refractory blocks
Sillimanite ermocoup1e
rangement Fire clay
Sect inn A
Carbon block Carbon Blast furnace ramming mix shell
Figure 3.1 Arrangement of thermocouples in blast furnace hearth wall 1251
C}IAPTER3 34
With the indirect method of determining heat loss the heat extracted from a
complete furnace zone is determined by the increase in temperature of the cooling
water from that zone. The zonal pattern coverage of such measurements provides a
good opportunity for the estimation of the thermal state of the furnace. However,
the accuracy is limited on account of the small temperature differentials measured in the cooling water.
When-using thermocouples-for-=determining the state of a furnace refractory lining,
the spacing between measuring can be up to several meters. It cannot be excluded
that the state of the refractory lining or heat load on the lining is worse between
measuring points. For this reason infra-red pictures are used to scan whole areas of
the furnace shell where few or no thermocouples are installed [25].
This is particularly useful on the hearth, although the shell must be dry and could
therefore only be done during a furnace stop if spray cooling is employed. During
the stop the spray cooling could also only be stopped for short periods due to the
sharp rise in shell temperatures. These boundary conditions have to be respected and theoretical calculations with the measured results are required.
The measurement of gas composition and temperatures within and above the
burden permits new knowledge to be gained concerning the factors that influence
the heat loss and the wear of refractory in a furnace. All these measurements need
to be monitored by computers. In doing so, it should not only be possible to make
long term calculations but, through easy to survey presentations of the current
operating conditions in the measuring station, it should also enable improved day to day control of the furnace.
Whether it be the improvement of the refractory qualities, the methods of lining, the
cooling elements, the cooling system for the measurements and their evaluation, the
aim of all these measures is the further improvement of the economics of the blast
furnace process through long campaigns with optimal furnace capacities and less use of energy.
CHAPTER 3 35
3.3 Comparison of known performances by cooling systems and refractory linings
in the bosh, belly and lower stack area
3.3.1 Copper flat plate coolers.
The progression and development of the bosh, belly and lower stack lining during
the engineering of four furnaces at POSCO's Kwangyang works is summarised in Table 3.2 [2=3] All four furnaces make-use of intensive plate cooling in this area.
From the alumina-based stack refractories used in No. 1 furnace has evolved the
latest design of No. 4 furnace which extensively uses silicon carbide. This reflects
the general approach that has been adopted by the industry since the mid 1980's.
Table 3.2 Progression of refractory design for POSCO's Kwangyang blast
furnaces. [23]
Blast furnace Furnace zone No. 1 No. 2 No. 3 No. 4
Lower stack 92% Al203 sic sic sic
Belly 92% Al203 sic sic sic
Bosh 92% Al203 92% Al203 92% Al203 sic
A trend toward the higher thermal conductivity material in the bosh is also illustrated in Table 3.2. The change from high alumina to silicon carbide at
Kwanyang No. 4 furnace was a measure of the growing acceptance of this material,
together with the recognition that high levels of coal injection result in increased
thermal loads in the bosh. As the belly/lower stack area is the highest heat zone of
the furnace, it is most dependent on cooling to preserve the lining. The main reason
for the increasing use of silicon carbide (sialon bond) at kwanyang, are its alkali,
oxidation and abrasion resistance, combined with a relatively high thermal
conductivity to make use of the intensive plate cooling.
Kawasaki Refractory Corporation also did some extensive testing and development
of silicon carbide bricks, recently with the sialon bond, specifically for use in the
bosh, belly and lower stack areas [12]. For an actual blast furnace test, two types of SiC bricks, silicon nitride (Si3N4) bonded silicon carbide bricks and the sialon
bonded silicon carbide bricks with Z = 2 (see Figure 2.1) and one type of alumina,
Al203, bricks were used for the lining of the lower stack area of No. 1 blast furnace,
Mizushima works, Kawasaki Steel Corporation.
CHAPTER 3 --- 36
I Upper stack
( I Middle stack
Lower stack
W
Sialon bond SiC brick
E Si3N4 bond SiC brick [J Alumina brick
After nine months of operation and testing, the samples were collected and investigated. Figure 3.2 shows the lining positions of the two types of SiC bricks and Al203 bricks, and Figure 3.3 illustrates the wear profile after the nine month period. Both residual SiC bricks were thicker than the Al 203 bricks. Table 3.3 lists the wear rate experienced by the silicon carbide bricks as measured per ton of hot metal produced. The hot surface of the sialon bonded SiC brick was smooth and its
------wear rate=was smal1erthan that-of Si3N4 bonded SiC—brick. -- - --
BoshSialon bond SiC brick
I Tuyere zone Si3N bond SiC brick
!earth [J Alumina brick
Figure 3.2 Area of test lining in lower stack of blast furnace. 1121
S
Figure 3.3 Wear profile after nine months test period. 1121
CHAPTER 3 37
Table 3.3 Comparison of wear rate of used silicon carbide bricks. 1121
Si3N4 bonded Sialon bonded
Wear rate (x 10 5mmtthm) 9.79 8.42
Blast furnace No. 6 of Hoogovens at Ijmuiden, the Netherlands, is equipped with
copper cooling boxes and represents a particularly interesting variant of refractory lining. -The furnace was relined-in 1986 for at leisfãthn year campaiFIriFigüre
3.4 the refractory lining from the bosh up to and including the middle stack is shown [8].
Hoogovens adopted a dense plate cooled bosh in combination with a sandwich
refractory construction consisting of graphite and semi-graphite. The refractory
construction is designed, from a thermal and mechanical point of view, as small
independent panels around each cooler. In the belly and lower stack plate cooling is
used in conjunction with a combination of graphite and silicon carbide. The actual
construction of the refractory around the cooler plates, however, differs from zone
to zone. Following the research carried out by Hoogovens with regard to the
mechanisms that cause lining failure, it is noted that the most dense area of lining
cooling has now moved from the bosh to the lower stack area.
Middle stack
800mm[::. 1 Sialon bonded SiC
Lower stack I I Graphite
111111111 Semi-graphite
Belly I I Blow in lining
Bosh
Figure 3.4 Hoogovens B.F. 6, Ijmuiden, 1986 lining. 181
CHAPTER 3 38
The silicon carbide in the stack area is of sialon bonded quality which have better
combined alkali and oxidation resistance compared to the silicon carbide qualities
used previously. This is in accordance with the results as discussed previously [12].
The ratio between silicon carbide and graphite is carefully balanced for each zone to
optimise between spalling resistance, chemical attack, oxidation and abrasion. The
percentage of silicon carbide in the stack increases with elevation until nearly a
complete hot face of silicon carbide is utilised in the upper portion of the middle
stack. -=
Since the blow in of Blast furnace No. 6 at Ijmuiden the wear of the refractory
lining was monitored. Incorporated in the lining on different levels are ceramic
rods, which wear with the lining [3]. The length of these rods are measured
ultrasonically. These measurements showed that after three years of campaign life
the wear stabilised at an approximate lining thickness of 400 mm in the lower stack area.
After nine years of campaign life and over 17.5 Mt of iron production, the original
lining thickness of 600 mm in this area (excluding blow in lining) diminished to
approximately 380 mm. This represents 70% of the lining thickness up to the
copper flat plate cooler noses. Over the last few years, the productivity of B.F. 6 was 2.7t/24h.m3 (working volume). This performance of the blast furnace and the
measured results show that this lining/cooling concept is very powerful. In 1995 no relines had as yet been planned for this furnace.
3.3.2 Combination offlat plate coolers and cast iron staves.
All furnaces discussed regarding performance so far were equipped with copper flat
plate coolers. A good example of the use of both cast iron staves and copper
coolers is Kawasaki Steel's Chiba No. 6 blast furnace [22]. In July 1993 it became
Kawasaki Steel's longest continuously operating furnace with a campaign life of
over 16 years since its blow in on June 17 1977. Up to that date its operating
results include a cumulative pig iron output of approximately 48.2 million tons, or
in terms of output per unit of inner volume, more than 10 700 t/m3.
Chiba No. 6 is a large scale blast furnace with an inner volume of 4 500 m 3, a throat
diameter of 10.5 m, a hearth diameter of 14.1 m, four tap holes, and 40 tuyeres, and
is capable of producing 10 000 t/day of iron. It was blown in in 1977 as Kawasaki
CHAPTER 3 39
Steel's largest blast furnace. During the engineering study prior to the reline, a goal
was set to achieve a campaign life longer than the average 8-10 years prevailing at
the time.
As discussed in Chapter 2 and shown in Figure 2.9, the use of copper flat plate
coolers between rows of staves, are mainly for the increased support of the
refractory lining to ensure a long campaign life. Chiba No. 6 blast furnace has
twelve rows of staves= and Three rows of-copper flat=plate-coolers; of which-one is--- -
situated between the belly and lower stack areas. Only the top row of staves are of
the upper ledge type (See Figure 2.7).
The refractories in the bosh, belly and lower stack areas were the first SiC bricks to
be adopted by Kawasaki Steel. In the past, high alumina bricks were used in these
positions in consideration of oxidation resistance and strength characteristics, but at
No. 6 blast furnace, SiC bricks were adopted, again, for their outstanding hot
modulus of rupture, heat conductivity, and resistance to alkali corrosion.
3.3.3 Cast iron staves
The design of Nippon Steel Corporation cast iron stave coolers was revised many
times to improve the performance to current levels. [21]. With the latest fourth
generation pattern, the wall bricks are cast into the ductile iron base casting and are
held tightly between tapered ribs ensuring that they can not be displaced during
operation. Cooling pipe configuration now gives improved cooling in the corner
regions of the stave, and refractory quality has been changed.
The wall facing is now a graphite-silicon brick, with the back-up bricks of alumina-
SiC. Overall thickness has been reduced resulting in increased furnace operating
volume. The stave upper ledge of the third generation has been dispensed with as
this has been found to reduce stave lifetime. The present stave design can be seen in Figure 2.8.
A recent mid-campaign installation of 150 fourth generation stave coolers in three
rows out of 50 at Nippon Steel Corporation's Kimitsu No. 3 blast furnace was
accomplished in 280 hours. This involved 127 hours of preparation work, 74 hours
of stave cooler installation and 79 hours of castable gunning, grouting and sealing,
and weld repairs. This represents a furnace shutdown of just under two weeks.
CHAPTER3 40
Improvements recorded at Kimitsu No.3 blast furnace after replacement of its
copper flat plate cooling system by fourth generation stave coolers is shown in
Table 3.4.
Table 3.4 Improvements in productivity at Kimitsu No. 3 after installation
of 4th generation stave coolers. 1211
Before After
Production rate (t/day)
CO utilisation (%)
Fuel consumption (kg/t)
8 290
48.9
505
8 260
51.2
487
Cast iron stave cooled furnaces have, in the past, had both low conductivity linings
and high conductivity linings. However, it is generally accepted that higher
conductivity materials such as silicon carbide give better results. This is
demonstrated by the two campaigns of the British Steel Redcar furnace which used
sillimanite (an aluminium silicate) bricks in the first campaign [23]. The majority of
the sillimanite bricks disappeared within two years. In the second campaign, a
nitride bonded silicon carbide lining was adopted, which out-performed the alumina
brick lining.
3.3.4 Copper staves
Copper stave cooling, as stated before, is the most recent development in furnace
cooling systems. MAN GM is on the forefront of development on copper staves
[24]. In 1979 they installed two copper staves in the mid-stack of No. 4 blast
furnace at Thyssen, Hamborn. Nine years later, in July 1988, the furnace was
blown down and all of the staves were inspected.
While the neighbouring cast iron staves showed heavy signs of process exposure
with several cracks and exposed pipes, the copper staves looked new. The final
thickness measurements of the copper staves which were initially 150 mm thick,
yielded a maximum loss in thickness of only 3 mm after nine years of campaign life.
This gave credence to the possibility of achieving a longer campaign life.
CHAPTER 3 41
Two copper staves of similar design were installed in the lower stack region of No.
6 blast furnace at Thyssen, Ruhort in 1988 [24]. The staves were visually inspected
several times since blow-in and after shutdown in 1994. Due to unusual operating
conditions, the cast iron staves showed signs of cracking and, in some cases,
cooling pipes were exposed. In comparison, the copper staves again looked new.
The daily average temperature of the copper staves were between 70 and 80°C.
This indicates that, during operation, the staves were either protected by some of - - the originaFrefractory-orbyastableskulForaccretioniayer
On the basis of these findings, Preussag, Salzgitter ordered three full rows of
copper staves for their blast furnace B. Thyssen also purchased a full row for
Schwelgern No. 2 blast furnace. Two of the rows for Salzgitter B were installed in
the belly and the other row in the lower stack as shown in Figure 3.5.
The copper staves operate at a much lower average temperature than the cast iron
staves. Temperature fluctuations in the cast iron staves occurred immediately after
blow-in of the furnace, which suggest that a aggressive process and operating
condition has a significant effect on the cast iron stave but has only a minimal effect
on the copper stave. The average temperature over the first two months of
operation was 107°C for the cast iron staves and 44°C for the copper staves. This
include a maximum temperature for the cast iron staves of about 380'C and about
50°C for the copper staves.
Castironstavesl\\\
Lower stack
Copper stave
Copper staves I W1 Belly
Cast iron staves
/ - 3h
Figure 3.5 Blast furnace B, Preussag Stahl, Salzgitter; copper stave
positioning. [241
C}IAPTER3 42
In order to design the cooling system for Preussag, Salzgitter B furnace, the heat
flux for each row of staves had to be estimated. This was done by using previous
values experienced with cast iron staves as shown in Table 3.5 [24]. The estimation
of the heat loss for the five rows of staves totalled 19000 kW. A total flow rate of
3600 M3 /hr was necessary to achieve the maximum allowable temperature rise in the
cooling water of 5.5°C.
Also shown in Table 3.5-is-the heat flux-measured to the--staves-since the furnace-
was put into operation. The cast iron staves reached 49% of the design heat flux
level, while the copper staves reached only 19% of the design heat flux level.
Although this is still early in the campaign, MAN GHH points out that according to
previous experience, heat flux to the cast iron staves will increase with time, while
the heat flux to the copper staves will only increase slightly.
Table 3.5 Designed and measured heat flux for blast furnace B, Preussag,
Salzgitter [24].
Stave row Design heat Measured Design heat Measured
flux, heat flux, load, heat load,
kW/m2 kW/m2 kW kW
Row no. 1, 46.4 24.0 3370.3 1729.1 cast iron staves
Row no. 2, 51.1 24.0 3868.5 1817.0 cast iron staves
Row no. 3, 52.4 9.9 3956.5 762.0 copper staves
Row no. 4, 52.4 9.9 3868.5 732.7 copper staves
Row no. 5, 52.4 9.9 3897.8 732.7 copper staves
3.4 Predicting the performance of refractory linings and cooling systems
In designing a new blast furnace refractory lining and cooling system, the wear
mechanisms, as discussed in Chapter 2, must be used as a starting point. After the
correct type of refractory lining as well as cooling system for the area of application
are chosen, the refractory lining thickness and design as well as the cooling system
intensity and design must be decided on.
CHAPTER 3 43
For this purpose, the designer must, from a metallurgical and furnace operation
point of view, predict the maximum heat load, temperatures and temperature
fluctuations to be expected. From this, the lining and cooling system must be
designed to ensure that hot face temperatures stay below the critical reaction
temperatures for any of the chemical reactions causing wear.
The hot face temperatures should also be low enough to enhance the possibility of
-stable skull or accretion layer formation= Skull formation is--most likely to take -
place at temperatures below 1150°C. As far as refractories are concerned, the
threshold values for CO disintegration and for oxidation by oxygen are the lowest
ones at 450°C and 500°C respectively [18].
In the bosh, belly and lower stack area, specific consideration should also be given
to the spalling of refractories. Here the designer must use the calculated maximum
temperature fluctuations expected combined with the critical spalling rates for
different materials, as shown in Table 2.4, to decide on the best lining material and
design for the application. The critical spalling rate is determined by several
material properties [2]:
Critical spalling rate oc k(1- v) cr81[pcEa]
where c = specific heat, J/kgK,
E = Young's modulus, N/mm2,
a = coefficient of thermal expansion, 1/K,
k = thermal conductivity, W/mK,
V Poisson constant,
P = bulk density, kg/rn 3, and
c.TB = tensile strength, N/mm2.
This relation shows that a high thermal conductivity, high strength, low Young's
modulus and low coefficient of thermal expansion increase the critical spalling rate.
It is then possible to calculate a relative spalling rate by dividing the maximum
expected temperature fluctuation per minute by the critical spalling rate. If this
critical spalling rate has a value over 1.0, the temperature increase is exceeding the
allowable value and the material will spall.
CHAPTER 3 44
The main function of the cooling system is to help preserve the refractory lining as
long as possible. After the blow in of the furnace the refractory lining usually wears
rapidly to a level where the nose end or front face of the cooling elements are
exposed. The cooling elements themselves must now be able to withstand the
predicted maximum temperatures and temperature fluctuations.
For cast iron as used in cast iron staves, the perlite structure will start breaking
disastrous, but the perlite structure is known to be harder and have better wear
resistance than the transformation structure. Melting of the cast iron stave, or parts
thereof, can be expected above 1100°C. Copper, as used for flat plate coolers and
copper staves, starts melting above 1000°C.
Designers are more frequently using mathematical models for the calculation of
isotherms and wear as far as possible to reproduce the actual conditions to be
expected in the blast furnace. In the past, calculation models were mostly worked
out by the finite difference method, generally analysing one dimensional problems.
It has been possible to improve these models considerably in recent years by
employing the computer intensive finite and boundary element methods as well as
the finite volume method.
The planning of new refractory linings and cooling systems is mostly undertaken in
two stages. The coarse structures are firstly investigated with axi-symmetrical
models. If a variant shows a particularly advantageous result the fine structures are
then determined by a computer intensive three dimensional analysis [25].
The advanced models of today are capable of accepting not only refractory bricks
but also monolithic materials. The laboratory measured conductivities of different
refractory qualities can be modified in the light of operating experience. Depending
on which furnace zone is being examined in the model the heat transmission can be
matched to the local conditions in accordance with the estimation of within furnace
temperature and gas velocity. Moreover, empirical coefficients for erosion and for
the heat conduction across joints can be worked into the dynamic interactive model,
which has a decisive influence on the quality of the model and the results obtained.
In Table 3.6 different methods used for calculation of the temperature distribution
in different areas of the blast furnace lining and cooling system are summarised [25].
-
CHAFFER 3 45
Table 3.6 Different methods of calculation of temperature distribution in a
blast furnace lining. [25]
Finite differential Finite and boundary Finite and boundary method element method element method
Zone/cooling system One dimensional Two dimensional Three dimensional
Stack / no cooling Possible I very small Possible I higher CPU Not necessary CPU time time
Stack, belly and bosh Not possible Only for estimation Necessary / high CPU / cooling plates time
Stack, belly and bosh Not possible With assumptions Advantages I high / Staves possible CPU time
Mantel area with Not possible Not possible Necessary / high CPU cooling system time
Hearth wall Possible I very sinall Possible I higher CPU Not necessars CPU time time
Hearth bottom I with Not possible Possible Advantages for
or without cooling special areas but higher CPU time
Normally, only steady-state analysis is employed and the focus is on long term wear
phenomena. Dynamic or transient analysis is employed for predicting wear due to a
single event. This includes thermal spalling due to a sudden temperature fluctuation
in the furnace. For example, a gas flow suddenly occurs in front of the refractory
lining or the protective skull disappears. As discussed in Chapter 2, it is usually this
abnormal furnace operation that will determine the campaign life.
3.5 Conclusion
From the comparison of known performances it is already possible to make some
conclusions. It is evident that SiC, graphite and semi-graphite are the superior
refractory materials used in the bosh, belly and lower stack area. Most of the
development on refractory linings are also aimed at these materials. Regarding
cooling systems, there is still no clear advantage for either cast iron staves nor
copper flat plate coolers. Copper staves is a promising new development,
specifically with regard to the high thermal loads experienced in the bosh, belly and
lower stack.
A comparative study between the different refractory materials and cooling systems
with the use of computational fluid dynamics, CFD, will be done in Chapters 5 and
CHAPTER 3 46
6. In Chapter 4 CFD will be discussed in some detail as well as applications
thereof This is finite volume method based software with the capability to calculate three dimensional models with regard to flow and heat transfer simultaneously. This includes the flow and convection heat transfer of the cooling
medium (water), as well as the conduction through different refractory grades and the cooling element.
CHAPTER 3 47
CHAPTER 4
OVERVIEW OF COMPUTATIONAL FLUID DYNAMICS
4.1 Introduction
The development of the high-speed digital computer has had a great impact on the
way in which principles from the sciences of fluid mechanics and heat transfer are
applied to problems of design - In modern -engineering practise. --Problems-can now
be solved at very little cost and in a fraction of the time it took twenty years ago.
The availability of previously impossible computing power has stimulated many
changes. These were first noticeable in industry and research laboratories where the
need to solve complex problems was the most urgent.
The increasing importance of a new methodology for solving the complex problems
in fluid mechanics and heat transfer, which has become known as computational
fluid dynamics (CFD), has been witnessed [27]. In this computational (or
numerical) approach, the equations (usually in partial differential form) which
govern a process of interest are solved numerically.
The evolution of numerical methods, especially finite-difference methods for solving
ordinary and partial differential equations, began at the turn of the century.
Although the automatic digital computer was invented by Atansoff in the late
1930's, the usage of computational solutions to numerical methods only became
popular after the general availability of high speed computers increased during the
1960's [27].
Traditionally, both experimental and theoretical methods have been used to develop
designs for equipment and vehicles involving fluid flow and heat transfer. With the
advent of the digital computer, a third method, the numerical approach, has become
available. Although experimentation continues to be important, especially when the
flows involved are very complex, the trend is clearly toward greater reliance on
computer based predictions in design.
4.2 Applications of computational fluid dynamics.
To most engineers, the mention of computational fluid dynamics conjures up
colourful images of sleek fighter aircraft surrounded by flow streams and pressure
CHAPTER 4 48
fields. Computational fluid dynamics is often thought of as a laboratory technique
that is too advanced for real world products. Though the imagery is correct, the
assumptions are not. Computational fluid dynamics now lets engineers effectively
look inside equipment such as pumps and heat exchangers to better predict and
enhance their performance [28].
Computational fluid dynamics can reveal comprehensive information on flow
----velocities, pressures; temperatures- and even--combustion reactions in a range--of
designs and well before the physical prototype stage. Computational fluid dynamics
software is no longer the domain of researchers. It lets design engineers solve
practical flow problems within reasonable time and cost investments.
For example, previously, when engineers at steel companies encountered a
production problem with molten metal, they turned to Plexiglas scale models of
their equipment and substituted water for liquid steel [29]. Within limits, water
models worked well. But complicated processes and high quality requirements
present analytical challenges beyond the scope of water models.
For instance, in continuous casting operations, a vessel called a tundish, with a slide
gate to throttle flow, directs molten steel to a water cooled copper mould through a
dual exit nozzle. Process conditions are critical for a successful flowing operation
to take place. Turbulence inside the nozzle from the slidegate's position as well as
clogging by aluminum oxide, a thermal insulator, produces more flow at one exit
than the other.
Also, the uneven flow produces shearing in the process which may remelt the
solidifying shell around a liquid core. Visual observation to understand what has
occurred in the system is difficult. Computational fluid dynamics can help pinpoint
conditions, temperature distributions, and inclusion behaviour in the molten steel. It
helps evaluate proposed modifications to reduce problems and produce better steel
[29,30,31,32].
Another application of computational fluid dynamics in the steel industry is the
modelling of fluid flow, heat transfer and solidification phenomena in the continuous
casting of steel. Choudhary et al [33] developed a two dimensional model for the
continuous billet casting operation. The effect of various assumptions and
procedures applied to modelling of turbulence phenomena, thermal buoyancy, flow
CHAPTER 4 49
through the so-called mushy zone, free surface conditions etc., on the sensitivity of
the computed results was investigated computationally.
Of all these, the heat and fluid flow phenomena in the mushy region was found to
have the highest effect on the predicted results. In addition to these, a set of three
different billet casting operations were simulated and direct comparisons were made
between predicted and observed solidified shell profiles. Such comparisons
demonstrated reasonable to excellent agreement between-theory and- experiments.-
Zhu et al [34], investigated the flow pattern and mixing phenomena in argon-stirred
ladles with six types of tuyere arrangements using water model experiments as well
as computational fluid dynamics. It was found that the arrangement of tuyeres has
a great effect on the flow patterns and mixing in the ladle.
The placement of single tuyere at an off-centric position gave the shortest mixing
time, whereas double tuyeres placed opposite to one another at half radii, was
found to be the best arrangement considering the aspects of blowing, mixing,
inclusion flotation and splashing. An empirical correlation for mixing time in the
ladle considering the number of tuyeres was proposed. The predicted and measured
results showed quantitatively good agreements.
Other industry applications of computational fluid dynamics include:
Computational modelling of mine and other fires [35],
• multi-phase flow,
• combustion and chemical reactions,
• mixing phenomena,
• complicated ventilation designs,
• condenser analysis and design [36],
complicated heat and mass transfer problems combined with flow fields,
• turbulent flow,
• particle tracing, as well as
• different combinations of the above.
All of these can be considered together in the application of computational fluid
dynamics, a powerful technique that frees the engineer from many of the restrictions
hampering traditional analysis. The user's understanding of the basic physics and
chemistry of the process becomes the limiting factors.
CHAPTER 4 50
4.3 Governing flow and heat transfer equations
The fundamental equations of fluid dynamics are based on the following universal
laws of conservation:
1. Conservation of mass.
-= - - 2. -Conservation of momentum-. - - --- -
3. Conservation of energy.
The equation that results from applying the Conservation of mass law to a fluid
flow is called the continuity equation. The Conservation of momentum law is
nothing more than Newton's Second Law. When this law is applied to a fluid flow
it yields a vector equation known as the momentum equation. The Navier-Stokes
equations are a special form of the momentum equations for Newtonian viscous
flows which include those for air and water [28].
The Conservation of energy law is identical to the First Law of Thermodynamics
and the resulting fluid dynamic equation is named the energy equation. In addition
to the equations developed from these universal laws, it is necessary to establish
relationships between fluid properties in order to close the system of equations. An
example of such a relationship is the equation of state which relates the
thermodynamic variables pressure (p), density (p), and temperature (7) [28].
During fluid flow, momentum is transported by streamwise advection of fluid mass,
and by diffusion through rapid molecular interactions. Consequently, the Navier-
Stokes equations are called advection-diffusion transport equations. They state a
balance between the net forces acting on the fluid and changes in fluid momentum.
These forces include centrifugal, gravitational, and buoyancy body forces, and flow
related pressure gradients [27].
An exact solution to a flow problem would yield a continuous description of the
field variables like velocity components, pressure, and temperature throughout the
flowfield. However, the Navier-Stokes equations are highly non-linear, and closed
form solutions exist for only a handful of idealised cases. Instead, engineers must
rely on computer based flow simulations which calculate approximate values of the
field variables at discrete points in the flowfleld [28].
CHAPTER 4 51
1 surface
- - - -- - - - - expansions and modifications as found necessary, taken from Anderson [27].
4.3.1 Continuity equation
The Conservation of mass law applied to a fluid passing through an infinitesimal,
fixed control volume (Figure 4.1) yields the following equation of continuity
o
(4.1) 0
wherèj51s The fluid density and -- V is the fluidvelocity. The first tehifln this
equation represents the rate of increase of the density in the control volume and the
second term represents the rate of mass flux passing out of the control surface,
which surrounds the control volume, per unit volume. Equation (4.1) was derived
using the Eulerian approach. In this approach, a fixed control volume is utilised and
the changes to the fluid are recorded as the fluid passes through the control volume.
In the alternative Lagrangian approach, the changes to the properties of a fluid
element are recorded by an observer moving with the fluid element. In general, the
Eulerian viewpoint is the appropriate choice for fluid mechanics.
Figure 4.1 Control volume for Eulerian approach.
For a Cartesian co-ordinate system, where u,v,w represent the x,y,z components of
the velocity vector, Equation (4.1) becomes
CHAPTER 52
ap + o (pu) + a (PV) + -- (pw) - 0. (4.2)
a ax- - -
Note that this equation is in the conservation-law (divergence) form. A flow in
which the density of each fluid element remains constant is called incompressible.
Mathematically, this implies that
p=constant, thus =0 (4.3) a
which reduces Equations (4.1) and (4.2) to
V.V=O (4.4)
or
auav —+--+ aw --=0 (4.5)
0-Y &Z
for the Cartesian co-ordinate system.
4.3.2 Momentum equation
Newton's Second Law of motion applied to a fluid passing through an infinitesimal,
fixed control volume yields the following momentum equation:
-(pV)+V.pVV=pf+V.11, (4.6) at
The first term on the right hand side of Equation (4.6) is the body force per unit
volume. Body forces act at a distance and apply to the entire mass of fluid. The
most common body force is the gravitational force. In this study only forced flow
will be considered where body forces are omissible and will therefore not be
considered further.
The first term on the left hand side of Equation (4.6) represents the rate of increase
of momentum per unit volume in the control volume. The second term represents
the rate of momentum lost by convection (per unit volume) through the control
CHAPTER 4 53
surface. Note that pVV is a tensor so that V.pVV is not a simple divergence. This
term can be expanded, however, as
V.pVV=pV.VV+V(V.pV) (4.7)
When this expression for V.pVV is substituted into Equation (4.6), we can simplify
it to [49]
(pV)+pV.VV±V(V.pV)=V.fI at
pV+V-p+ PV* VV+V(V.pV)=V.H at at
V(P+ V. PV) + p-V+ PV 0 VV= V.
at Ot
(v+v.vvJ=v. 7 (4.8)at
by utilising the continuity equation (Equation (4.1)). Equation (4.8) can be further
simplified through the convenient use of the substantial derivative [49]
Do=U +v.v() (4.9) Di - at
to give
DV p—=V.lT.
Di(4.10)
The term on the right hand side of Equation (4.10) represents the surface forces per
unit volume. These forces are applied by the external stresses on the fluid element.
The stresses consist of normal stresses and shearing stresses and are represented by
the components of the stress tensorny. The momentum equation above is quite
general and is applicable to both continuum and non-continuum flows.
It is only when appropriate expressions are inserted for the shear stress tensor that it
loses its generality. For all gases which can be treated as a continuum, and most
liquids, it has been observed that the stress at a point is linearly dependent on the
CHAPTER 4 54
rates of strain (deformation) of the fluid. A fluid which behaves in this manner is
called a Newtonian fluid [42]. The stress tensor is frequently separated in the
following manner
(4.11)
where t, represents the viscous stress tensor given by
(ôu. ôu 2 ôul = t —A-]- pu'u . (i,j,k = 1,2,3) (4.12)
The first term on the right hand side of Equation (4.12) represents the average
viscous stresses, while the last term represents additional Reynolds stresses due to
turbulent motion. 6 represents the Kronecker delta. Upon substituting Equation
(4.11) into Equation (4.10), the Navier- Stokes equation is obtained
DV a(4.13)
Utilising Equation (4.6), without taking the body forces into account, Equation
(4.13) can be rewritten in conservation law form and tensor notation as [49]
-(pu)+_(puu1 +p_t,)=O (i,j,k= 1,2,3) (4.14) at CIXj
The tensor notation indicates in which co-ordinate system (ij,k) a vector in its
present position is to be evaluated. If the flow is assumed incompressible, Equation
(4.14) will reduce to
au. a
+p_)=o (i,j,k= 1,2,3) (4.15) at
4.3.3 Energy equation
The First Law of Thermodynamics applied to a fluid passing through an
infinitesimal, fixed control volume yields the following energy equation
CHAPTER 4 55
L+V.E tV = ô2—v.q+pf.V+V.(IIL .v) (4.116) at
where Et is the total energy per unit volume given by
-= -- E=pe ± _+ potential energy + ..... ) (4.17)
and e represents the internal energy per unit mass while U represents the magnitude
of the velocity vector V. The first term on the left hand side of Equation (4.16)
represents the rate of increase of total energy per unit volume in the control volume
while the second term represents the rate of total energy lost by convection (per
unit volume) through the control surface. The first term on the right hand side of
Equation (4.16) is the rate of heat produced per unit volume by external agencies
while the second term is the rate of heat lost by conduction (per unit volume)
through the control surface. Fourier's law for heat transfer by conduction will be
assumed so that the heat transfer q can be expressed as [40]
q= —kVT
(4.18)
where k is the coefficient of thermal conductivity and T is the temperature. The
third term on the right hand side of Equation (4.16) represents the work done on
the control volume (per unit volume) by the body forces while the fourth term
represents the work done on the control volume (per unit volume) by the surface
forces. According to the First Law of Thermodynamics, Equation (4.16) states that
the increase of energy in the system is equal to heat added to the system plus the
work done on the system.
The left hand side of Equation (4.16) can be replaced by the following expression
D(E 1) = aE,+ V • E V (4.19)
Di at
This follows from
CHAPTER 4 56
+V*VE,)p—E,
p't ____ LDi)j D(E/p) [.ai Di - p2
and, from the continuity equation, using the substantial derivative (Equation (4.9))
to change Equation (4.1) into the form
=-p(V.V) Dl ' Dl
it follows that
D(E Ip) = Di
+ • VE +E (V. v)
where
V.EV=V.VE, +E(V.V)
Equation (4.19) is thus obtained, which is equivalent to
D(E /p) De D(U2 /2) =p—+p (4.20)
Di Di Di
if only internal energy and kinetic energy are considered significant in Equation
(4.17). Forming the scalar dot product of Equation (4.10) (without omitting the
body forces) with the velocity vector V allows one to obtain
pj i . v=pf.v_vp.v+(v.t).v (4.21)
D DVDV DV As (V.V)=V.—+—.V-2V.— Di Di Di - Dl'
it follows that
D(U2/2)1D(U2) ID )=!f.v Di 2 Di 2 D Dr
CHAFFER 4 57
Using this and combining Equations (4.19), (4.20) and (4.21), the result can be
substituted into Equation (4.16) to obtain a useful variation of the original energy
equation
De(4.22)
DI at
S - -- ---
and Equation (4.22) will be the same if the body forces have been omitted from the
start. The last term in Equation (4.22) represents the work done on the control
volume and the stress tensor, H, can be split according to Equation (4.11) giving
v . (n 0V)=V.((_p8 +z-).v)
=V* (—P,50 0 V + 7- Or .v)
=_V. (p8 .v)+v.( .v)
=_V.(pV)+V.(r .v)
Substituting this in Equation (4.22) we obtain
p2 +p(V. v)-- V. q+ V. ( r . v)-(v. V (4.23) Dt
where
V.(pV)—Vp.V=p(V.V)
The last two terms in Equation (4.23) can be combined into a single term since
t..--=V.(t.. .V)—(V.t).V (4.24)
This term is customarily called the dissipation function 1) and represents the heat
equivalent of the rate at which mechanical energy is expended in the process of
deformation of the fluid due to viscosity. After inserting the dissipation function,
Equation (4.23) becomes
CHAPTER 4
-- P De + V.V V.q+t
a (4.25)
Di ai
If the flow is assumed incompressible, the coefficient of thermal conductivity
assumed constant and th heart neraion term neglected rewritten m conservation tensor notation, uin
substantial derivative for the first term, as
ae a( aT —k — +puj)=O (4.26)
axi
Using the definition of enthalpy [42]
h=e+ (4.27) P
and the continuity equation, Equation (4.25) can also be rewritten as
. p=!+_V.q+t11 au L (4.28) Dt Di at
If the thermal conductivity, k, is assumed constant, the dimensionless Prandtl
number can be used to determine the viscosity, p.. The Prandtl number is defined as
follows [40]
Pr= -- (4.29)
4.4 Discretisation and grid generation
Often elementary textbooks on heat transfer derive the finite-difference equation via
the Taylor-series method and then demonstrate that the resulting equation is
consistent with a heat balance over a small region surrounding a grid point. It is
also seen that the control volume formulation can be regarded as a special version
of the method of weighted residuals. The basic idea of the control volume
formulation is easy to understand and lends itself to direct physical interpretation.
CHAPTER 4 59
For this study the finite volume method is used for the discretisation of the
continuity, momentum and energy equations over the flow and heat transfer
domains [37,38]. In this method the flow and heat transfer domains are divided in
discrete cells, or non-overlapping control volumes, across which the equations are
integrated and approximated in terms of nodal cell centred values to obtain the
discretisation equation:
A±Amm =(430)
In Equation (4.30), 0 represents the variables to be solved, which, for the
incompressible case, include u, v, w, p, e and T. Each variable is then solved at a
point (or grid point) P in terms of the values of the neighbouring points m. The
coefficients A represent the effects of conduction as well as convection/diffusion in
the flow. Each of the variables 0 in Equation (4.30) can now be solved iteratively
at the internal points P. This is done by employing the SIMPLE algorithm
described by Patankar [37].
The discretisation of the governing equations can be best described with the use of
an illustrative example. The simple situation of steady one-dimensional heat
conduction will be used for this purpose. It is important to note that although this
is a simple example of discretisation, the method used and the form of the
discretisation equation obtained, is essentially the same for the more complex
situations. These more complex situations could include two- and three-
dimensional flow fields, convection, transient solutions, as well as source terms
and/or user functions that may be employed in the governing equations. Patankar
[37] and Anderson [27] give more detail on the discretisation of these equations.
Steady one-dimensional heat conduction is governed by [40]
dx' cfr) (4.31)
where k is the thermal conductivity, T is the temperature, and S is the rate of heat
generation per unit volume. To derive the discretisation equation, the grid point
cluster shown in Figure 4.2 will be employed. The discretisation equation will be
derived for grid point P in relation to its neighbours, grid points E and W. The
dashed lines show the faces of the control volume denoted by the letters e and w.
CHAPTER 4 60
T
W w e E
x
a)
W w P e E
x
b)
T
For the one-dimensional problem under consideration, unit thickness is assumed in
they and z directions. Thus, the volume of the control volume shown is Ax x 1 x 1.
If Equation (4.3:1) is now integrated over the control volume, the following is
obtained:
(dT" (dT\ Ik—I –1k—I +fScIx=O (4.32)
______I____________ AX
x
Figure 4.2 Cluster of grid points showing grid point P between
neighbouring grid points Wand E.
In order to evaluate above integration equation, a profile assumption or an
interpolation formula is needed. Two simple profile assumptions are shown in
Figure 4.3.
Figure 4.3 Two simple profile assumptions. a) Stepwise profile; b)
piecewise linear profile.
CHAPTER 4 61
The simplest possibility is the stepwise profile assumption where the value of T at a grid point is assumed to prevail over the control volume surrounding it (Figure 4.3
a)). For this profile, the slope dT/dx is not defined at the control volume faces. A
profile that does not suffer from this difficulty is the piecewise-linear profile as
illustrated in Figure 4.3 b). For this profile, linear interpolation functions are used
between the grid points.
profile, the resulting equation will be
ke (Tg - 7;,) - k. (T - T) -
(6x) (x+Sz\x=0 (4.33)
IC '. 1W
where S is the average value for S over the control volume. The discretisation
equation, Equation (4.33), will be cast into the following general form:
AT =AE TE +AT +b (4.34)
where
A -kk ,,- /
(x \ 'e
Aw=i (4.35) (6x) '. 1W
A = AE + A,
b=Szx.
From this example it is clear how the general form for the discretisation equation,
Equation (4.30), was obtained. As stated previously, this form can be applied to the
more complex situations, including the situations encountered in this study. Before
this form of the discretisation equation can be used blindly, there are certain rules
and guiding principles that must be adhered to for the successful solution of the
unknown variables. A detailed discussion of these rules and principles, as well as
examples of obtaining more complex discretisation equations, can be found in Patankar [37].
-- -
CHAPTER 4
4.5 Conclusion
Once the problem at hand has been thoroughly studied from a sound physical and/or
chemical background, it can be prepared to be solved by a CFD program. The
reason for this is to ensure that the results obtained will still be evaluated with the
same scrutiny as would have been the case with an analytical solution, if possible, of
the same problem. It is therefore important to have a sound knowledge and understanding-of thegovengflowandheattransferequationsasweWashowihe
numerical solution will be obtained.
For the purpose of this study, the general purpose CFD-code FLO++ [38]
employing the above mentioned procedures will be used for simulating the flow and
heat transfer in the blast furnace refractory lining and cooling system.
CHAPTER 4 63
CHAPTER 5
NUMERICAL MODELS OF LINING/COOLING SYSTEMS
5.1 Introduction
From the previous chapters, the different types and current available lining/cooling
systems, are now known. Furthermore, in Chapter 4 a powerful tool for the purpose 6 mu ing—diff6refit-lining/coo tés_ifd öniW thé résulf was discussed in some detail. This tool is computational fluid dynamics (CFD).
Although CID is a very powerful tool, it will first be verified in this chapter
whether or not it is the right tool for the purpose. In Chapter 1 the problem
statement or purpose of this study was set out to be a comparison between available
lining/cooling systems. In order to achieve this with CID, the parameters to be
compared must be identified, after which the solution values of the parameters must
be verified. Some of these parameters, for example the critical hot face
temperatures for chemical and mechanical attack initiation, have already been identified. In Section 5.2 these will be discussed again together with other parameters like skull formation and/or skull thickness.
The advantages of a numerical solution over an analytical solution regarding this
study will be discussed in Section 5.3, while the numerical solution of forced convection heat transfer will be verified in Section 5.4. In Sections 5.5 and 5.6
some common boundary values and material properties will be discussed. A
numerical two-dimensional analysis of variables that can influence the mentioned parameters follows in Section 5.7.
As the chapter's heading specifies, the end purpose is to create numerical models
necessary for the approximation and comparison of the different lining/cooling system combinations. Section 5.8 discusses and illustrates the three-dimensional
models created for determining the results to be discussed in the next chapter.
5.2 The theory of skull formation
During the past two decades skull formation on the hot face of a refractory lining
was the subject of many investigations [18,39,6]. The skull Consists of burden material forming a layer on the refractory lining as it cools down. This is due to the
CHAPTER 5 64
20(
15( Temperature
oc50(
Mouldable Pipe with refi
Skull Limit of cooling
removal of heat via the cooling system and refractory lining. The main advantages
of skull formation are, firstly, the wear protection it lends to the refractory lining.
This is accomplished by preventing the burden material that slides down the inside
of the furnace from making direct contact with the refractory lining.
The second advantage is the reduction of the temperature in the refractory lining.
As previously explained, the temperature plays a major part in chemical as well as
mechanical=attack-mechanisms=on=the-=refractory=Iining-==To='understand'-=the
reduction of the hot face temperature due to skull formation, it is necessary to
understand the theory of thermal resistance and skull formation.
In Figure 5.1 [18] a vertical cut through the 'furnace side is shown. This shows the
furnace shell with refractories and cooling system as well as part of the burden
sliding down along the refractory lining. The formation of a skull on the refractory
lining is also shown. Stave coolers are used with ribs and refractory inserts on the
hot face. The brickwork in front of the stave is assumed to be worn away.
Furnace Stave Refractory Furnace inside with shell with ribs inserts burden material
Figure 5.1 Model of actual heat transfer to a stave surface in the belly and
lower stack regions [18].
The heat transfer from the furnace to the cooling system can be best explained with
the use of an analogy to Ohm's law. Heat transfer is due to the temperature
difference between the burden and gas inside the furnace and the cooling medium
CHAPTER 5 65
(usually water) used in the cooling system. A series of thermal resistances are
formed by the skull, refractories, body and ribs of the stave cooler, as well as the
pipes inside the stave. There are also the resistances due to the heat transfer
coefficients to the cooling medium and from the burden and gas combination in the
furnace. According to Kramer et a! [39] the heat transfer from the furnace to the
lining is characterised by a number of processes which include
-=.heat-conductiondue-to-contact- -- - - -- - -
• solid state body radiation,
• gas radiation and
• convection of the furnace gas,
where the last process has on average the highest influence on the heat transfer
coefficient. A schematic diagram of the resistances and the overall temperature difference is shown in Figure 5.2. This forms the basis of the theory of thermal resistances
T1 T2 T3 _________ TI medium I A,h, I I k, • I k, j • f h furnace inside
cooling system refinstosy liningi I skull I furnace inside
- T2
Tf TI T1 T2T' F71 medium I A,h I - 1 k. I - I k. I I ,. furnace inside
Figure 5.2 One dimensional schematic diagram of the thermal resistances
encountered through the furnace shell.
For the situation as shown in Figure 5.2 the following are assumed:
• The furnace-inside situation stays constant for every scenario to be described. Thus, Tf and h are assumed constant.
• The area A is equal to unity accept for A.
• For the purpose of explaining skull formation, the heat transfer is assumed one-dimensional.
• T2 represents the hot face temperature on the refractory lining.
CHAPTER 5 66
• I'3 represents the temperature below which skull formation is most likely to
occur and is assumed constant for all scenarios.
• As T, hf and T3 are assumed constant, q is also constant for the whole system.
The heat transfer through the system is represented by the following equation analogous to Ohm's law [40]:
- ______ (5
where
R= 1 C
Ah
R =--= Ak,. kr
R = --
S Ak5k5
11
A/i1 h
The thicknesses of the refractory lining and the skull are indicated respectively by Xr
and x5. In the first scenario the influence of the refractory's thermal conductivity on
skull formation is investigated. All parameters are assumed constant accept ic,. and x5. In Equation (5.1) only R,. and R5 are not constant. But, as q is assumed constant, the sum Of A. and R3 should also be constant.
R5 + R,. = c = constant (5.2) Thus,
xS =ck. —k (5.3)
IC,.
From Equation (5.3) it could be seen that x5 increases as IC,. increases and vice versa. An increase in the thermal conductivity of the refractory lining will thus promote
skull formation. The next scenario to be investigated is the influence of the cooling system area A on skull formation. From equation (5.1) it follows that the sum of
R and R5 must be constant to ensure a constant heat transfer.
CIIAPTER5 67
R+ R5 = c = constant (5.4) Thus,
x =ck - k5
(5.5) S Ah
From equation (5.5) it follows that x . , the skull thickness, increases as the cooling system area A c increases. The same two resistances, Rc and R5, are affected when
cOeffiient;1i on skull-fi5ni—natiWn is investigated. From equation (5.5) it follows that the skull thickness increases as h
increases. The heat transfer coefficient, h, is mainly influenced by the velocity of the cooling medium. In section 5.7 and Chapter 6 the extent of influence by the
different parameters on skull formation will be investigated and compared.
The influence of the skull thickness on the hot face temperature, T2, can be shown by the use of equation (5.1). As the heat transfer is the same through the whole
system, the following holds for the heat transfer across resistance R5:
–I; 7;
q= R5
(5.6)
Only T2 and the skull thickness, x5, are not constant. Thus
(5.7) S
From equation (5.7) it follows that T2 decreases as x5 increases. As all three parameters (kr, A, h) can have a positive influence on skull formation, they can also have a positive influence on the hot face temperature, T2, by decreasing it.
Stable skull formation on the hot face of a refractory lining is influenced by other
factors as well, such as wear due to burden movement in the furnace, shut down
frequency and abnormal furnace operation. Two different techniques of furnace
operation called side working and centre working could also have different effects
on skull formation. During side working the burden distribution is of such a nature
as to allow more upward gas flow along the sides of the furnace than through the
centre. This could have a negative influence on skull formation due to the
temperature increase along the hot face of the lining.
CHAPTER 5 68
5.3 Influence of high conductivity differences in two-dimensional heat conduction problems on solutions obtained by different methods.
Some two-dimensional heat conduction problems can be solved analytically,
although in certain cases this is impossible or solutions are cumbersome and difficult
to obtain. An extensive study of analytical techniques used in conduction heat
40 and 41 for further references]. Fourier series are one example of orthogonal
functions, as are Bessel functions and other special functions applicable to different geometries and boundary conditions.
In this study there will not be concentrated on these analytical techniques to solve
complex two-dimensional heat conduction problems, as it is already an accepted
fact that numerical methods are relatively easy to use, quicker to obtain solutions
and becoming cheaper due to the higher availability of computing power. What is
of interest here is to see what are the limitations in solving two-dimensional heat
conduction problems via the use of the Ohm's Law analogy and thermal resistance
models. With one-dimensional heat transfer problems no limitations are encountered [40]. Figure 5.2 is an example of a one-dimensional heat transfer problem with all thermal resistances arranged in series.
For a two-dimensional problem there could be a problem if some of the parallel
resistances differs too much as also mentioned by Holman [40]. This could be
illustrated best by use of an example and a comparison between the solution
obtained using the crude discretization technique of thermal resistances and the true
numerical solution obtained using computational fluid dynamics. Figure 5.3 gives an illustration of a possible two-dimensional heat conduction problem with Figure 5.4 showing the thermal resistance model.
The objective is to determine the heat flow, q (W), while varying the conductivity,
/c, from 0 to 350 WImK. The following values and boundary values are taken as constant for this comparison:
Tf = 1423 K = T3 , thus, the furnace inside temperature is applied
directly onto the skull and set equal to 1423 K. k., =IOW/mK
CHAPTER 5 69
x 0.05m
kk 350W/mK
Xr =0.4m
0.05m
= 3000 W/m2K
T =303K
z = unit depth-
A 1m2
Figure 5.3 Two-dimensional heat conduction problem.
IRk,! 2Xr
T3 J Akk 412 R • J
R HTC ^_^_ ___
TI1
xL I Xk i
I
AkR, I Aick
2Xr
Ak,. I > x
Figure 5.4 Thermal resistance model for 2-D heat conduction problem.
Analogous to Ohm's Law, the thermal resistance equation can be set up as follows:
RRtotai Rs + R + Rk + R (5.8)
CHAPTER 5 --
Rk
-j R Ff R
Rk I I R F-
-L:1--
1120
0.00547+1
1.25kr + 437.5
(5.12)
where R=1'1 (5.9)
Rr R,,
and the heat flow can be expressed as
RT (5.10)
where ATT=LJTO,Q!=TJ—TC (5.11)
Figure 5.5 illustrates how the problem has been changed from two-dimensional to
one-dimensional with the use of the analogy to Ohm's Law.
Figure 5.5 One-dimensional approximation of two-dimensional problem.
Substituting all fixed values and boundary values into Equation (5.10), we obtain an
expression for the heat flow in terms of the conductivity k:
The same heat conduction problem can now be modelled using the computational
fluid dynamics program, FLO++, to obtain the numerical solution. The model is
CHAPTER 5 71
Xr
illustrated in Figure 5.6, showing the different materials in different colours. The
model consists of 1750 cells and the input file created in and for Flo++ [38] is
included under Appendix A. This proved to be adequate for the determination of
the heat flow through and isotherms in the model.
Figure 5.6 Two-dimensional numerical model.
The two solutions of the heat flow are graphically compared in Figure 5.7 relative to the conductivity kr, shown as a percentage of conductivity kk. The percentage
difference between the two solutions is also shown. At k, = 0 W/mK or 0% of kk,
qanaiyricai is 65,2% higher than qn,,,ricaj. This reduces drastically to less than 10%
difference for k, = 70 W/mK or 20% of kk, 5% difference for kr = 105 W/mK or 30% of kk, and 1% difference for k,. = 200 W/mK or 57.1% of kk.
From a blast furnace lining/cooling system point of view, the highest differences to
be encountered in this study will be between high alumina (Al 203) = 2 W/mK [27]
and copper = 350 W/mK [40]. According to this comparison, the numerical
solution of the two-dimensional conduction problem using a thermal resistance
model, could lead to a 50% higher heat flow.
CHAPTERS
72
70.00%
krIk(%)
Figure 5.7 Difference between thermal resistance and numerical solutions of two dimensional problem.
The solution obtained using the thermal resistance model is not accurate since it
represents a one-dimensional approximation of the actual problem. This could best
be explained by creating a numerical solution obtained by performing fill
discretization, using Flo++, of the one-dimensional approximation and compare it
with the actual two-dimensional numerical solution.
From this comparison it should first be possible to explain the difference in heat
flow and secondly to create a better thermal resistance model of the actual problem.
From Figure 5.5 it could be seen how the thermal resistance model changes from
two-dimensional to one-dimensional. Equation (5.9) shows how the parallel resistances, Rr and R, are changed to a single resistance R, to form a one-dimensional model, or series circuit, with the rest of the resistances. A numerical
model, as shown in Figure 5.8, is set up with a single material P replacing materials Rand RK shown in Figure 5.6.
In order to make the comparison, kr is taken equal to 25 W/mK for both solutions.
This value represents ± 7% of kk and previously incurred a calculated heat flow, using the thermal resistance model, of 147 303.8 W or 25.2% higher than the actual
heat flow. It follows that material P will have a equivalent conductivity k = 187.5
W/mK and according to Equation (5.9) a resistance R = 0.00213 K/W. Figure 5.9
(a) and (b) show the numerical results obtained according to above values for the
two models respectively shown in Figure 5.8 and Figure 5.6.
CHAPTER 5 73
Figure 5.8 Numerical model of one-dimensional thermal resistance
equivalent.
IIL%Version 2.10
DATE: 28 May 1997 t.J CASE: d:\work\2Dan2 TEMPERATURE Kelvin
[TER 5 GMAX 1.4230e+003 GMIN 3.5159e+002
1.4230e+003 1.3125e+003 1.2020e+003 1.0915e-i-003 9.8100e+002 8.7050e+002
F7.6000e+002 6.4950e+002 5.3900e+002 42850e+002 3.1 800e+002
V
Figure 5.9 (a) Temperature field obtained for one-dimensional solution.
The heat flow through the one-dimensional model as shown in Figure 5.9 (a) is 147 230 W or 0.05% lower than the previously heat flow calculated using the thermal
CHAPTER 5 74
resistance model of 147 303.8 W. This small difference can be attributed to the
rounding off of results during calculation.
Flo++ Version 2.10
U DATE: 28 May 1997
A - CASE: d:\work\2Dana TEMPERATURE Kelvin
hER 5 GMAX 1.4230e+003 GMIN 3.1826e+002
1.4230e+003 I----.- --
1.3125e+003
X 1.2020e+003 1.0915e+003
.--...i 9.81 00e+002 8.7050e+002
-
Ad-Z X
Figure 5.9 (b) Temperature field obtained for two-dimensional solution.
For the two-dimensional model the heat flow is 117 650 W as indicated on Figure 5.7. From the differences between the isotherms shown in Figure 5.9 (a) and (b), it
is evident that the one-dimensional solution is not a very accurate approximation of
the actual solution to the two-dimensional problem. From the isotherms in Figure
5.9 (a) it follows that there are only temperature differences in the x-direction and
thus only heat flow in the x-direction. Figure 5.9 (b) on the other hand shows
temperature differences in both the x- and y-directions, or more accurately, over the whole x,y plane.
By using the temperature differences as shown by the isotherms, it is possible to
create a thermal resistance model that will be a better approximation of the two-
dimensional model. There could be many different models to achieve this but the
objective is to create a simple model with a good approximation. As illustrated in
Figure 5.9 (b), the heat is assumed to flow along four major routes, A to D. These
routes were selected as to run along the paths of greatest temperature differences
according to the isotherms. The routes are now translated into a thermal resistance
model as shown in Figure 5.10.
CHAPTERS 75
rWLh 2x
A/cs
IXX,. Xr
Adk AkkJ
Akk
I 4xS 4Xr _2Xr
IAS 2Akr
4xS 4Xr AS Akr
Figure 5.10 Improved thermal resistance model.
RkI IRc =xi= Akk
As shown in Figure 5.9 (b), two new variables or values are added to the existing
set. This is cross sectional area Ad and length x. Ad equals thickness x3 times unit depth and x is taken equal to 0.4m. The common area A, is the cross sectional area of the model and are equal to unity. R, the equivalent resistance of the resistance model can now be determined in terms of the unknown icr.
1 RT=
1
1 1 1
+
1 1
+R,2 Rci+1?c2
+-
RARB
1 + Rk + R +
RD1+RD,
(5.13)
= -
+ 0.000473 1 1
+
90.69025 +
1I
+ 0.00115 0.02 + 1.6k,-'
0.02 + 0.8k g'
From Equation (5.13) the heat flow can now be determined using Equation (5.10)
along with the different values of k. The results are graphically shown in Figure
5.11 as compared to the actual or numerical determined heat flow to be
CHAPTER 5 76
experienced. The percentage difference reaches a maximum of 2.75% and peaks at k equal to 350 W/mK. From this it can be concluded that this thermal resistance
model approximates the actual heat conduction experienced much better, because it
is in essence a crude discretisized or numerical model in two dimensions.
lçIk(%)
0.0% 20.0% 40.0% 60.0% 80.0% 100.0% ....---- ..-------- .----.--- - ____ --• . 170000
-2.50% ----.. - 160000 150000
Cr -2.00% 140000
-1.50% ..7..... . .— 130000
Difference (%) -1.00%- — 110000
..-q - refined analytical (
I 100000 -0.50% . - q - numerical (W) —
0.00% 1 . . . ----
90000
80000
Figure 5.11 Solution results for numerical and refined thermal resistance
models.
Another variable in this problem that can influence the difference between the
thermal resistance model solution and the numerical solutions, is the thickness x5.
Although the fundamental reason for the difference in the solution results stays with
the high conductivity difference, this can be blurred by increasing the thickness
Figure 5.12 is a graphical representation of the analytical and numerical heat flow
solutions as obtained with regard to a varying thickness x.
The percentage difference between the two solutions shows a slight increase before
it starts decreasing, although the actual difference shows no such initial increase.
The reason for this is that both the heat flow solutions decrease initially at a higher
rate together with the increasing thickness x than the rate at which the difference decreases.
The reason why the percentage difference between the refined thermal resistance
model solution and the numerical solution decreases along with an increase in
thickness x, is best explainable by referring to Figure 5.9 again. In Figure 5.9 (a), the one-dimensional solution, the resistance in all four indicated heat flow routes increases with an increase in thickness x8. Thus, the heat flow decreases. In Figure
5.9 (b), the two-dimensional solution, the resistances in routes A, C and D increases
CHAPTERS .---- -- 77
while resistance RB in route B decreases with an increase in thickness x. RB
decreases due to a increase in cross sectional area Ad. Thus, the heat flow will also decrease due to a increase in x, but at a slower rate than for the one-dimensional solution.
30.0%T - -I--
- 350000
Difference(%) 25.0% 300000
\ i-q - analytical(\AO
20.0% \ -- - --- -- -
q - numerical ('/J) 250000 -- -
I -Difference (V 200000 15.0% - \ - -- - ---
:i
10.0%-
\Ni-------------
0 100 200 300 400 500 x (mm)
Figure 5.12 Refined thermal resistance model solution and numerical
solution with regard to varying thickness x.
5.4 Numerical solution of forced convection heat transfer
In the previous section errors in the solution of two-dimensional heat conduction
problems due to high differences in heat conductivities were discussed. For the
purpose of this study it is also necessary to investigate forced convection heat
transfer. It is important to verify the results obtained by the numerical method to be used.
Again it is not always possible to obtain an analytical solution especially if complex
geometries are involved. Empirical and practical relations have been developed
from experimental results for some standard geometries. The numerical method can
thus be verified by comparing it with an analytical method incorporating
experimentally obtained coefficients. For this purpose a simple one-dimensional
thermal resistance model is used. The resistance due to turbulent forced convection
on a flat surface is determined by using a two-dimensional analytical empirical
relation for the convection coefficient.
CHAPTER 5 78
Figure 5.13 shows a solid material with a uniform heat conduction. On the left side
heat is put into the material via a constant resistance and temperature. On the right
hand side heat is removed from the material by water flowing at 1.5 m/s over the
face of the material. The water enters the system at 27°C or 300 K. Bulk
temperature is assumed at 320 K for determining the water properties to be used in
both the analytical and numerical solutions. These values are [40]:
Density - p - =989kg/m3
Viscosity - 'U = 5.8 x 10-4 kg/ms Conductivity - k = 0.642 W/mK
Prandtl number - Pr = 3.75
FRjf
Tf = 1773K hf = 230W/m2K
Rk
kk350W/mk Xk = O.45 m
11iniet = 1.5m/s T = Tinier = 300K L = im A=1m2 T ik = 320K
=?
Figure 5.13 One-dimensional conduction problem incorporating two-
dimensional forced convection.
The length, L, of the flat face equals I while unit depth is assumed. Thus, the area A is also equal to unity. The one-dimensional thermal resistance model is constructed as shown in Figure 5.14.
IRJI S IRkI lRdI 1 Xk
A/i1 Akk Ah
Figure 5.14 Thermal resistance model for 2-D turbulent forced convection.
The total equivalent resistance, R, can be written as
CHAPTERS 79
RT = R + Rk +R,
1 + +
Xk 1 (5.14) = -
A/i1 Akk Ah
and the total heat flow as
\TT q= R
T -
(5.15)
RT
The only unknown in Equation (5.15) is h, the convection heat transfer coefficient for the water flow. By substituting all known values into Equation (5.15), the heat flow can be expressed in terms of hc as
1473 q= 1
0.005634+— h
= 1473h 0.005634h ±1
(5.16)
For the purpose of determining h, the Colburn analogy between fluid friction and
heat transfer is utilised. Holman [40] derives an expression for the average Nusselt
number for heat transfer over flat surfaces using this analogy. This expression is
stated here as Equation (5.17):
NUL hL = Pr)'(O. O37Re 8 _ 850) (5.17)
where the Reynolds number, ReL, can be expressed as
ReL = piL
(5.18) Al
Equation (5.17) is valid for Reynolds numbers < i0 7 . The average heat transfer
coefficient, I,, can now be determined from the average Nusselt number, NUL, as
shown in Equation (5.19).
CHAPTERS 80
= kNu L
/ \ = k Pr
[0.0371L puL
0.8
_850](5.19)
p)
Substituting all values into Equation (5.19), an average heat transfer coefficient, h, -equal-to -
one-dimensional thermal resistance model yields a heat flow of 250 569 W. These
values are now to be compared with those obtained during the numerical solution.
For the numerical solution of turbulent flow and forced convection heat transfer,
the size of the cells or blocks forming the grid is important. Next to the wall where
the turbulent and thermal boundary layers are formed, the thickness of the cells are
constrained by the expected boundary layer thickness. If the boundary layer as a
whole lies within a single cell thickness, this could lead to errors in the heat transfer solution.
This is due to the procedure used for determining the non-dimensional distance
y together with the non-dimensional velocity u, are used to determine the velocity profile in the boundary layer. y is determined as [41]
y+=u*y(5.20)
V
where u * is the so called friction velocity depicted by
(5.21)
v is the kinematic viscosity, z the shear stress at the wall, and p the density. y is
the actual normal distance on the wall and is taken as half the cell thickness during
the numerical solution. Thus, if the cell thickness is too great, y will be wrong and
could influence the heat transfer solution through use of the wrong velocity profile.
According to Rohsenow et al [41], Anderson et al [27] and Holman [40], the
following general accepted constants and limits are to be applied:
CHAPTERS 81
Laminar sublayer : 0 <y < 5 u = Buffer layer : 5 <y4 <30 = 51n(y) - 3:05 (5.22) Turbulent layer : 30 <y <400 = 2.51n(y) + 5.5
Verification of a numerical solution can thus also be obtained by checking the y
values. If turbulent flow has been solved for instance, y must be between 30 and
400. As stated before, a precaution to ensure this, is to create a grid with all
thickness. If the boundary layer is assumed to follow a laminar growth pattern up to 5 x 105 and a turbulent growth thereafter, the following expression can be used to determine the thickness [40]:
8= x(o.381Re7_- 10256Re (5.23)
where x is the length of the flat plate after which the thickness is obtained. Thus, for x = L = 1 m, a boundary layer thickness of 0.016 m or 16 mm is obtained. If x = L12 = 0.5 m, 8 = 8 mm, and if x = 0.25 m, 8 = 4 mm. A cell thickness of approximately 3 mm should be adequate.
The Navier-Stokes equations discussed in Chapter 4 are usually applied in solving
turbulent flows. Due to the great number of grid points and small time steps
required to numerically solve the small effects of turbulent motion, the time-
averaged Navier-Stokes equations, also called the Reynolds equations of motion,
were developed. In these equations, turbulent motion is described in terms of time
averaged quantities rather than instantaneous. This procedure gives rise to new
terms called "apparent" stress gradients and heat fluxes, also known as the
Reynolds stresses and turbulent scalar fluxes. A so-called turbulence model is required to relate these new terms to the mean flow variables [27].
The turbulence model used by Flo±+ is the k-e model [38], which is the most widely used model in present day engineering calculations. The k-e model employs the "turbulent eddy viscosity" concept [27], to relate the Reynolds stresses and scalar fluxes to the mean flow variables.
The numerical flow model is constructed according to Figure 5.13 and all the values
and boundary values are used as for the analytical solution. Figure 5.15 shows the
CHAPTERS - 82
Version 2.10
- -DATE: 10 Jun 1997 - - CASE: d:\work\skull
V
z x
model with the cells clearly visible and the different materials indicated. The model
consists of 1650 cells and the input file created in and for Flo-H- [38] is included in
Appendix B. The numerical solution resulted in a heat flow of 246 670 W or 1.6% lower than the analytical solution.
Figure 5.15 Numerical model for solving two-dimensional convection heat
transfer.
In Figure 5.16 the temperature solution can be seen showing the isotherms. A two-
dimensional change in the isotherms can be clearly seen due to the changing heat
transfer to the water. This is due to the chanaine water temnerattire and chaninø
boundary layer thickness resulting in a changing heat transfer coefficient. The 1.6%
difference in the heat flow can be attributed to this two-dimensional effect not accounted for in the one-dimensional solution.
Figure 5.17 shows the numerical solution to the convection heat transfer coefficient h. It first increases and then decreases along the length of the flow path. An average of approximately 4100 W/m2K is obtained by visual inspection. This is also satisfactorily close to the analytical solution. According to the results for y shown in Figure 5.18, cell thicknesses are accurate enough as the values fall between 30 and 400 and indicates turbulent flow.
CHAPTER5 - 83
I7o++ Version 2.10
DATE: 10 Jun 1997 CASE: d:\workskuIl TEMPERATURE Kelvin
ITER 55 GMAX 7.0704e+002 GMIN 3.0000e+002
7.0704e+002 I I
5.8493e+002 5.4423e+002 5.0352e+002 4.6282e+002 4.2211e+002 3.8141e+002 3.4070e+002 3.0000e+002
Y
z x
Figure 5.16 Temperature solution showing isotherms.
lo++ Version 2.10
DATE. 10 Jun 1997 CASE: d:\workskuIl HEAT COEFFICIENT
ITER 55 GMAX 4.8155e+003 GMIN 0.0000e+000
4.8155e+003 4.7266e+003 4.6376e+003
I 4.5487e+003 F
.. 4.4598e+003 4.3709e+003 4.2819e+003 4.1930e+003 4.1041e+003 4.0151e+003
I 3.9262e+003
ly
L... ....
L.. .. .. ___
Figure 5.17 Convection heat transfer coefficient.
CHAPTER 5 84
Flo++ Version 2.10
DATE: 10 Jun 1997 CASE: d:work\skuII YPLUS
ITER 55 GMAX 2.2432e+002 GMIN 0.0000e+000
I I 2.2432e+002 I 2.1961e+002 I 2.1490e+002 I
2.1019e+002 2.0548e+002
I I 2.0078e+002 1.9607e+002 1.9136e+002 1.8665e+002 1.8194e+002 1.7723e+002
^Y
Figure 5.18 yf indicating turbulent flow.
Numerical solutions to the magnitude velocity and pressure distribution in the water
are shown respectively in Figures 5.19 and 5.20. Pressure shows a constant drop in
the direction of flow and cross-sectionally mirrors the velocity profile. The velocity
also mirrors the velocity profile as well as the increase in boundary layer thickness.
NFlo++ Version 2.10
DATE: 10 Jun 1997 CASE: d:\work\skull VELOCITY Magnitude rn/s hER 55 GMAX 1.5706e+000 GMIN 0.0000e+000
I I 1.5706e+000 1.41 35e+000 1.2565 e+000 1.0994e+000 9.4236e-001 7.8530e-001 6.2824e-001 4.7118e-001 3.1412e-001 1 .5706e-OO1 0.0000e+000
V
z x
Figure 5.19 Magnitude velocity in contour form.
CHAPTER 5 85
Ro++ Version 2.10
DATE: 10 Jun 1997 CASE: d:\workskul ) PRESSURE Relative N1m2
ITER 55 GMAX 1.1091e+002 GMIN -1.9404e+000
1.1091e+002 9.9629e+001 8.8343e+001 --
- 7.7058e+001 6.5772e+001 5.4487e+001
r, 4.3201e+001 1 3.1916e+001
2.0631e+001 - - -1.9404e+000
Y
z x
Figure 5.20 Pressure revealing pressure drop from inlet to outlet.
5.5 Heat transfer from the furnace to the lining/cooling system
Inside temperatures of blast furnaces are on average increasing as higher
productivity is required and new developments such as pulverised coal injection
(PCI) also increases combustion temperatures lower down. According to Kramer
et a! [39], maximum gas temperatures as high as
• 2400°C at tuyere level,
• 1700 to 23000C in the bosh,
• 1600 to 1700°C in the belly, and
. 1400 to 1600°C in the lower stack area could be expected.
However, these temperatures are not transferred directly nor with flitl intensity to
the lining/cooling system of the furnace. The heat transfer resistance from the
furnace interior to the lining/cooling system is responsible for keeping the hot face
temperature lower than the furnace interior temperature. In section 5.2 of this
chapter the most prominent processes by which the heat transfer from the furnace
inside to the lining/cooling system is characterised are listed.
Theoretically this combined heat transfer is not to be easily quantified.
Observations of different furnaces and indirect findings show that the common heat
CHAPTER 5 86
transfer coefficient for all participating mechanisms lies between 90 and 230 W/m2K
[18,39]. The ruling inside temperatures of the furnace for observing the
lining/cooling system lie between 1200 and 1800°C for the bosh, belly and lower
stack areas [39]. In order to ensure that the lining/cooling systems are evaluated at
extreme operating conditions as discussed in Chapter 1, both a high heat transfer
coefficient and a high furnace inside temperature is taken as the case of reference:
• effective temperature of furnace inside, T1 = 1500°C = 1773K, and • heat transfercoefficient to fumacelining, hf— 230WIK. -
According to Seligmuller [18], an accretion layer or skull of burden material could
start forming on the lining/cooling system at hot face temperatures between 1100°C
and 1200°C. This layer or skull usually has a thickness of up to 50 mm and a conductivity between 1 and 5 W/mK depending on the composition and density thereof [18,24]. For the purpose of this study a conductivity of 2 W/mK will be used.
This will be incorporated with the furnace inside heat transfer coefficient by
determining an equivalent resistance with the use of thermal resistances. A one-
dimensional thermal resistance model can be used as the resistances due to the
furnace inside heat transfer coefficient and due to the skull are arranged in series.
Thus, if no skull formation has taken place, the furnace inside heat transfer resistance to the lining/cooling system can be taken as
R =__=_=O.00435m2K/W (5.24) hf 230
If, for instance, a 50 mm skull has been assumed to have formed on the hot face of
the lining/cooling system, the heat transfer resistance from the furnace inside can be taken as
(5.25) h1 k8 230 2
The new hot face temperatures on the skull can also be determined for different
skull thicknesses if the skull is incorporated as a material in the model with a fixed conductivity of 2 W/mK.
CHAPTER 5 -- 87
5.6 Heat transfer through the lining/cooling system
Different combinations of refractory linings and cooling systems have been
discussed in previous chapters. Before the actual comparison between these
combinations can be done with the use of computational fluid dynamics, it is
necessary to establish certain constant values and boundary values. According to
Tijhuis [2], the conductivities for refractory materials as listed in Table 5.1 are - -- ---- -
Table 5.1 Conductivities of refractory materials [2].
Refractory brickwork Applicable mortar type and mouldable (W/mK) refractory materials.
(W/mK) High-Alumina 2 1 Silicon carbide 25 5
Semi-graphite 55 15 Graphite 135 15
For the respective cooling units investigated, as well as the furnace shell, different
metals are used with different conductivities as listed in Table 5.2 [40].
Table 5.2 Conductivities of different metals 1401.
Conductivity Temperature measured at (W/mK) (K)
Pure copper 350 900 Carbon steel 45 350
Cast iron 40 900
Water is used as the cooling medium in all cooling systems investigated. Water properties at Tjk = 320 K are assumed constant as listed in Table 5.3 [40].
Table 5.3 Properties of water at 320K (Saturated liquid) 1401.
Specific heat Density Viscosity Conductivity Prandtl number c,, p p k Pr
kJ/kgK kg/m' kg/ms W/mK -- - 4.174 989 5.8 x 10 0.642 3.75
Flow is assumed incompressible and thus the reference pressures at inlets or outlets
will have no effect on the heat transfer. The pressure drop through the cooling
CHAPTER 5 - 88
system will be observed and discussed. If any, possible steam formation will be
discussed in accordance to the relevant steam tables [42]. The wall functions and
turbulence model are applied as described in Flo++ [38]. On the outer face of the
furnace shell natural convection by air at Ta = 27°C or 300K and a heat transfer coefficient ha = 5 W/m2K are assumed [40].
Table 5.4 is a summarisation of all the material properties and boundary values to -- -
- -be used further on in this- study-for both the two- and three-dimensional numerical
models. In Figure 5.21 a two-dimensional thermal resistance model is used to
indicate and visualise the positioning of all these properties, values and variables.
This two-dimensional thermal resistance model is not to be used for any other
purpose as the problems to be discussed contain high conductivity differences.
Table 5.4 Summary of material properties and boundary values.
Designation Value Description
T. 300 K Air or ambient temperature on outer face of furnace shell. 5 W/m2K Convection heat transfer coefficient between air and shell.
T. Variable Temperature of furnace shell on the outside. Ic,,. 45 W/mK Conductivity of carbon steel furnace shell.
Te Variable Temperature between shell and cooling element.
kk 350 W/mK Conductivity of copper as used for cooling element. /c, 40 W/mK Conductivity of cast iron as used for cooling element.
Tiniet 300 K Temperature of water at inlet of cooling element.
h Variable Convection heat transfer coefficient for cooling water. Variable Indicates the shell area coverage by the cooling system
and depends on type of cooling system, vertical and horizontal spacing of cooling elements as well as the contact area for the cooling water in the cooling channels.
Tb,k 320 K See Table 5.3 for water properties according to Tik.
U inlet 3 or 6 m/s Inlet velocity of cooling water.
Variable Temperature between cooling element and refractories.
kr See Table 5.1 Conductivities of different refractory materials.
km See Table 5.1 Conductivities of different mouldable refractory materials Variable Lining hot face temperature.
k 2 W/mK Conductivity of skull, if applicable.
XS Variable Skull thickness - 50 mm for comparative study. 1'3 1423 K Skull initiation temperature, if applicable.
h1 230 W/mK Furnace inside convection heat transfer coefficient. T 1773 K Furnace inside temperature - also 1473 K used for
evaluation of skull formation.
CHAPTERS 89
T. T. i Te
ha k).T T3 T1
TITJ
kk or k,. k., 11/ km
Tbj,. h
-- - - _- -
Figure 5.21 Two-dimensional thermal resistance model only for purpose of
visualising positioning of variables, boundary values and
material properties.
5.7 Two-dimensional analysis of variables influencing skull formation
In Section 5.2 of this chapter, the theory of skull formation was discussed. From
this it was concluded that skull formation can be influenced by changing three
variables in the heat transfer solution of the lining/cooling system. This is apart
from other factors that influence skull formation. The three variables are the
refractory conductivity, the cooling system area and the cooling system heat
transfer coefficient. In this section the goal is to determine the degree of influence
of each of these variables by using a two-dimensional numerical model. The results
will be compared with actual three-dimensional solutions in the next chapter.
The three variables will not be compared, as expected, based on a percentage
change, but based on possible practical changes to each of them. Thus, one may be changed 50%, as this is how much is practically possible, while another may be changed 500%.
Table 5.5 shows the different values of the three variables for which the numerical
two-dimensional solution will be obtained. The underlined values will stay fixed for
that variable while the other variables are investigated. For the purpose of
investigating the influence of the convection heat transfer coefficient, the inlet velocity is to be varied.
CHAPTER 5 - 90
Table 5.5 Variable values investigated with regard to influence on skull
formation.
kr A, U inlet for h (W/mK) (% of hot face area) (MIS)
2 25 1.0
25 40 1.5
55 50 2.0
135 6O - 2.5
75 3.0
Skull formation as such will not be numerically simulated. Thus, the change in skull thickness, x3, as described in Section 5.2, can not be used as an indication of the influence by the different variables on skull formation. From Equation (5.6) and
(5.7) it follows that T2, the hot face temperature will lower due to a thicker skull.
This argument can be reversed as skull thickness will increase with a lower hot face
temperature. The hot face temperature, T2, can therefore be used as an indication of possible skull formation. From Equation (5. 1), if x5 is kept constant and equal to zero, it follows that
(5.26)
So, if one of the three variables is varied, there is no other variable other than the
skull thickness that can change to restore the total resistance to its original value. Thus, the heat flow q can not be constant anymore and the degree of change thereof
will give another indication of what should have been a change in skull thickness. From Equation (5.26) it follows that if a change in one of the variables lowers the
applicable resistance, the heat flow will increase. Previously, an increase in the skull
thickness would have been the net result. As the skull is not included in the
problem anymore, the following equation can now be used to describe the relation
between the two parameters q and T2:
T—T2 q=
(5.27) Rf
Thus, if q is increased due to a change in one of the other resistances, T2 will be
lower, and the possibility for skull formation will increase. Figure 5.22 is an
CHAPTERS 91
illustration of the two-dimensional model, consisting of 1650 cells, to be used to
obtain the numerical solutions. It depicts a cooling system area of 50% of the total hot face area and unit depth is assumed. The cooling medium is water and the flow
is assumed turbulent. Copper is the material used for constructing the cooling
elements. All boundary values and material properties are applied as stated in Table
5.4 unless otherwise noted. The input file for this model as used in Flo++ [38] can be find in Appendix C.
++ Version 2.10
Water DATE: 10 Jun 1997 CASE: d:work\skuU
Copper
kk = 350 W/mKUinier? T Tiniet = 300K
T1 =1773K L=lm h1 =230W/m2K
i
A=1m2 Tba = 320K h,= ?
Refractory
kr?
Y
z x
Figure 5.22 Two-dimensional numerical model.
For varying values of all three the variables, T2 and q will be determined and plotted on a graph. The scale for T2 and q on the graphs will be kept the same for all
variables so as to make a fair comparison. The first variable to be investigated is the refractory conductivity, icr. A is kept at 50% and U jnlet at 1.5 m/s while icr is varied. The results are illustrated graphically in Figure 5.23.
The maximum hot face temperature, T2mar, crosses the skull initiation temperature, T3 = 1423 K = 1150°C, at approximately 25 W/m2K, the conductivity related with silicon carbide. Both T2 arid q changes a great amount as icr is varied between the possible practical values. The conclusion is made that an improvement could be
expected in skull formation if higher conductivity refractories, such as semi-graphite and graphite, is to be used.
CHAPTER 5 92
1800 . . . 240000 I—T2max(K)
1700 .\T3 (K) 220000
1600 \ q(V\) 1500 \ •. 1— ___ ____ ____
1400180000e
1300i
do
1100—
_.. i6Q00O
140000
120000 900
_
i00000 0 20 40 60 80 100 120 140
Refractory conductivity, k, (WIm K)
Figure 5.23 Influence of refractory conductivity on heat flow and hot face
temperature.
It must be stated clearly though, that this is a two-dimensional exercise to compare
influences and not an approximation of heat transfer to be expected in practise. Thus, the intersection between T2m and T3 will only become important during the investigation of the three-dimensional approximation models. The next variable to be investigated is the cooling system area, A, as a percentage of the total hot face area. The results are illustrated graphically in Figure 5.24. The cooling water inlet velocity is kept constant at 1.5 m/s and refractory conductivity at 55 W/mK.
Because k,. was taken fixed at 55 W/mK, all the T2m values lie below T3.
According to Figure 5.24, the heat flow is affected much more than the maximum
hot face temperature, T2max, by the varying of the cooling system area. It is
concluded that skull formation is promoted by an increasing cooling system area A
relative to the hot face area.
The average hot face temperature may show a greater decrease than the maximum
hot face temperature relative to an increase in cooling system area, A. This is due to the great difference in conductivity between the refractory materials and the
cooling element material, in this case copper, which causes a great difference in the
hot face temperature profile. Figure 5.25 compares the isotherms for the cases 25% and 75%. It can be seen that in both cases there is still a great amount of refractory
material between the copper and the points marked where T2, is found.
CHAPTER 5 93
1800
1700- - - - -- 240000
1600
220000
1500 -__ __ __.200000
1400- _ _ _- 1
1300
1200 160000 ______
1100 1 ___ = ^Uinia flat plate arrang-n-,nt
900-- q (VV)- flat plate arrangement
800:; ____ ____ 100000 20 30 40 50 60 70 80
Cooling system area A as % of hot face area (%)
Figure 5.24 Influence of cooling system area on heat flow and hot face
temperature.
I
rno++ Version 2.10
DATE: 10 Jun 1997 CASE: d:\work 'skull TEMPERATURE Kelvin
ITER 55 OMAX 1.2337e+003 GMIN 3.0000e+002
• I 1.2350e+003 I 1.1415e+003
—] 1.0480e+003 • I I 9.5450e+002
• I 8.6100e+002 7.6750e+002
k : ! • 67400e-i-002 I- •I 5.8050e+002
4.8700e+002 3.9350e+002 3.0000e+002
Y
T2max z x
Figure 5.25 a) Temperature profile for cooling system area 25% of total area
According to the theory of stave cooling, this temperature profile can be levelled
out if more uniform cooling is applied. While the model used up to now represents
so called "point cooling" as associated with flat plate cooling systems, the model
CHAPTER 5 94
shown in Figure 5.26 incorporates so called "blanket cooling" associated with stave cooling.
i7o++ Version 2.10
DATE: 10 Jun 1997 CASE: d:\work\skull TEMPERATURE Kelvin
ITER 55 GMAX 1.1238e+003 GMIN 3.0000e+002
r . 1.2350e+003 1.1415e+003
9.5450e+002 8.6100e+002 7.6750e+002 6.7400e+002 5.8050e+002 4.8700e+002 3.9350e+002 3.0000e+002
T2maxJ'
Figure 5.25 b) Temperature profile for cooling system area 75% of total area.
Version 2.10
DATE: 11 Jun 1997 CASE: d:\work\skull
Figure 5.26 One-dimensional model with copper behind refractory material.
CHAPTER 5 95
The same volume of respectively copper and refractory material is used as in the
model shown in Figure 5.22. All the copper is now behind the refractory material
and thus forms a one-dimensional model. If the volume of copper and the volume
of refractory material are kept the same as for all the previous cases of varying area, the new results for T2m and q are graphically illustrated against these areas in Figure 5.27, together with the previous results.
Figure 5.27 Influence of cooling system layout on heat flow and hot face
temperature.
From Figure 5.27 it is concluded that the stave type arrangement can reduce the maximum hot face temperature while reducing the heat loss experienced. This is
done without changing the volume of copper or refractory material used. However,
overall it is clear that a practical possible change of the cooling system area does have a significant influence on T217,. and q and thus also the skull thickness, x3, but not as high an influence as the refractory conductivity.
The final variable to be investigated is the convection heat transfer coefficient of the
water as determined by the different inlet velocities. The model shown in Figure
5.22 and used to investigate the other two variables, is also used for investigating
the effect of the convection heat transfer coefficient on skull formation. A 0 is kept constant at 50% and k,. at 55 W/mK. Figure 5.28 shows the change in maximum convection heat transfer coefficient relative to the inlet velocity, while Figure 5.29
illustrates the results for q and T2max relative to the maximum convection heat
CHAPTER 5 - 96
1800
1700
1600
1500
1400
1300
F200
1100
1000
900
800
transfer coefficient. Figure 5.28 also shows the analytical average convection heat
transfer coefficient as calculated according to the method described in Section 5.4.
Figure 5.28 Influence of inlet velocity on convection heat transfer coefficient.
240000
220000
200000
1800000
160000 i0
140000
120000
100000 3000 4000 5000 6000 7000 8000 9000
Heat transfer coefficient, h (W1m21Q
Figure 5.29 Influence of convection heat transfer coefficient on heat flow
and hot face temperature.
Although there is a sharp increase in the convection heat transfer coefficient, h, due to an increase in the inlet velocity, U inlet, the decrease in T2,, and increase in q is
minimal. Thus, an increase in the cooling water velocity or the volume flow rate is
not as effective as increasing the refractory conductivity nor the cooling system area
CHAPTERS - 97
for the purpose of promoting skull formation. As the refractory conductivity and
cooling system area have the greatest influence on the heat transfer through the
lining/cooling system, it is useful to illustrate the results from these cases together. Figure 5.30 graphically illustrates the change in T2 max relative to both kr and A,
while the change in q is illustrated in Figure 5.31.
1800...-.- :
1700 ..-- - -Ac 25%
1600 -- _ . .- -Ac = 40% Ac =50%
1500 - -Ac1400 -- ---... -Ac = 75% .... --• ____ 1300-- -. 1200-- . -H ---ii00
2040 60 80 100 120 140 kr(WImK
Figure 5.30 Comparison of influences on hot face temperature by refractory
conductivity and cooling system area.
Figure 5.31 Comparison of influences on heat flow by refractory conductivi-
ty and cooling system area.
CHAPTER 5
From these illustrations it follows that a change in the refractory conductivity is the
dominant factor influencing q, T2,,,, and x, the skull thickness. A change in the cooling system area does not influence T2m greatly, although the heat flow will increase to some extent, especially at lower refractory conductivities. In Chapter 6
similar results will be obtained via more realistic three-dimensional models. These
will then be compared with the two-dimensional solutions as to verify the extent of the different influences.
5.8 Three-dimensional numerical models of lining/cooling systems
In the previous sections of this chapter, two-dimensional models have been
investigated with regard to accuracy of solving two-dimensional flow, differences
between numerical and analytical two-dimensional conduction solutions, and
influences of different variables on possible skull formation.
The next step in the numerical investigation of the blast furnace lining/cooling
system, is to create three-dimensional models of different lining/cooling system
combinations in order to evaluate them regarding magnitude and not only
percentage change. These models must be as far as possible a true approximation
of the actual layout. All boundary values and material properties as discussed in sections 5.5 and 5.6, and listed in Table 5.4, are incorporated in the models and any changes to these will be noted further on.
Basically three types of cooling systems are investigated which include copper flat
plate coolers, cast iron staves and copper staves. Each of these are investigated
with regard to four different refractory materials namely high alumina, silicon
carbide, semi-graphite and graphite. The influence of the convection heat transfer
coefficient, the cooling system area, and the refractory conductivity on skull
formation, are investigated using the models for the copper flat plate coolers.
Six different three-dimensional models will be created, including three for the flat
plates, one for the cast iron staves, and two for the copper staves. For further
comparisons only boundary values and material properties will be changed. As
stated previously, all models are created and all simulations are done using the
computational fluid dynamics program, FIo++ [38].
CHAPTER 5 99
Tf
hf
Refractory Flat plate Mortar type brickwork Mouldable cooler refractories
tm tpt JL
Furnace shell plate
td
5.8.1 Copper flat plate coolers
The flat plate coolers investigated are assumed to be manufactured from 99.5%
copper and consist of a shell and a series of divided channels through which the cooling water flows as shown in Figure 5.32(a). The cooling water first travels through the channel nearest to the inside of the furnace to ensure the greatest
temperature difference at the hot face for maximum heat transfer. During - - --installation-thecoolersare
built around the coolers.
To ensure that no air gaps exist between the coolers and the refractories, mortar
type refractories and a mouldable material are used around the coolers (Figure
5.32(a)). The mortar type refractory material is pumped into the open spaces after installation of the refractory lining.
After installation the refractory lining covers the noses of the flat plate coolers (part
of coolers nearest to inside of furnace) with an approximate depth of 250 mm. This
is worn away during the first few months of operation and can not be regained with
gunniting. In accordance with Van Laar et al [6], Kramer et al [39] and Tijhuis [2],
the assumption is made, for calculation purposes, that the frontal face of the
refractory lining is already worn away to the same depth as the cooler nose ends (Figure 5.32 (b)).
a) Top view b) Side view
Figure 5.32 Flat plate cooler layout and positioning in furnace shell
CHAPTERS
For the first case or arrangement investigated, the flat plate coolers are spaced with a horizontal pitch, Ph, of 500 mm and a vertical pitch, P, of 300 mm (Figure 5.33).
The flat plate coolers have a depth, 4,, of 670 mm and a width, 1,,, of 450 mm, while the shell thickness, 6, is equal to 55 mm. The thickness of the mortar type refractories, 'm, differs from plate cooler to plate cooler, but on average equals 50 mm. The last parameter shown in Figure 5.32 is the flat plate cooler thickness, th,
that equals 65 mm.
Horizontal pitch Ph
II
Simulated area
Vertical
pitch P,,
-
-E------•- - - • - - - - - - - - - - - -
Figure 5.33 Cooler arrangement on outside view of furnace shell
Figure 5.33 also shows the area of the lining/cooling system to be modelled or
simulated from the outside of the furnace shell and represents a symmetrical portion
of the system. In Figure 5.34 the three dimensional model is illustrated with the
furnace shell to the bottom, the hot face on top and a vertical pitch equal to 300
mm. The grid constructed for the simulation consists of 42 048 cells without any
extreme mesh refinement. The input file, as created for this model in Flo++[38], is included in Appendix D.
As shown in Figure 5.33, only one quarter of each of the two simulated flat plate coolers are included in the model. The water flows in the channels are connected
via cyclic boundaries to form a closed system with the inlet in one flat plate cooler
and the outlet in the other. Thus, water flow leaving for instance the outer cooling
channel of the bottom flat plate in the model, enters the outer channel of the top flat plate. This is indicated by the arrows in Figure 5.34. For the next channel, for instance, water flow leaves the top flat plate and enters the bottom flat plate.
CHAPTERS 101
Version 2.10
DATE: 03 Nov 1997 CASE: d:\work\flatplates
e11 z x
Figure 5.34 Three-dimensional model for flat plate cooler case with vertical pitch of 300 mm.
Symmetry is assumed for the top, bottom and side boundaries, while the boundary
values for the hot face inside the furnace and the frontal face on the outside of the furnace are applied as previously discussed and listed in Table 5.4. Mass flow rate at the outlet is specified equal to the inlet mass flow rate as determined by the inlet
velocity chosen and the inlet area. Also indicated in Figure 5.34 are the different materials forming part of the model as set out in Figure 5.32.
The arrangement illustrated in Figure 5.34 is a common and also modem arrangement of flat plate coolers and will be used for the comparison with cast iron
and copper staves. In practise the vertical pitch, P, is sometimes extended up to 600 mm. This is not as common neither as modem arrangement as discussed in Chapters 2 and 3. Figure 5.35 shows the three dimensional model to be used for this arrangement. The same amount of cells is used as for the model in Figure 5.34.
As discussed in Chapter 2, cigar coolers are sometimes used to increase the cooling
capacity during a campaign if the original cooling system design is not adequate or
if the campaign is to be extended beyond the original planned period. In Figure 2.6
the position of such a cigar cooler in the furnace shell with regard to the flat plate
coolers was illustrated. Only one quarter of each of the cigar coolers will form part
CHAPTER 5 102
of the simulation model. The three-dimensional model incorporating the cigar coolers is shown in Figure 5.36.
Figure 5.35 Three-dimensional model for flat plate cooler case with vertical
pitch of 600 mm.
Figure 5.36 Three-dimensional model of the flat plate cooler case
incorporating the cigar coolers.
CHAPTER 5 103
All three cases or arrangements discussed up to now represent the three different
cooling system areas evaluated regarding their influence on possible skull formation.
The other two variables investigated require only changes to the boundary values or
material properties. The first of these is the convection heat transfer coefficient of
the cooling water which is varied by varying the inlet velocity. Two inlet velocities,
namely 3m/s and 6m/s are investigated. The inlet and outlet have the same cross - -- ---------------------------- --
The other variable is the refractory lining or refractory material conductivity. This
is investigated for the four different materials as set out in Section 5.6, Table 5.1. The different refractory materials are also combined with cast iron and copper
staves in order to determine the best combinations of refractory materials and cooling systems.
5.8.2 Cast iron staves
The cast iron staves investigated consist of a cast iron body and cast-in pipes
through which the cooling water flows as shown in Figure 5.37. The staves are cast
with cast iron ribs on the hot face side which is filled with cast-in bricks or
refractory material. The actual refractory lining is built like a wall in front of the
staves. This is usually worn away early in the campaign leaving only the ribs with
refractory inserts. The same assumption is made as with the flat plate coolers in
that the refractory is already worn away to the same depth as the rib noses.
Figure 5.37 (a) shows a side view of the stave assembly inside the furnace. From
the hot face side the assembly consists of the cast iron ribs, the refractory inserts,
the stave cast iron block including the steel pipe with cooling water, the filling mass
between the stave cooler and the shell, as well as the shell. Also shown is the
separation layer between the cast iron stave and the cast-in cooling pipe. According
to Helenbrook et al [24], this separation layer represents a thermal resistance of between 0.0035 and 0.0045 m2K/W.
Figure 5.37 also shows the main dimensions of the cast iron stave layout. The
cooling pipes have a diameter of 80NB and the distance between the pipes (Figure 5.37(b)) is 220 mm. The stave body thickness is 190 mm, and the rib thickness and
rib height are both 75 mm. This is all in accordance to an assembly in a similar
CHAPTER5 - 104
flfl
MI .)11 iMP -
a) Side view b) Top view
study published by Tijhuis [2]. The height of the refractory inserts is 150 mm or twice that of the cast iron ribs.
Furnace steel Cast iron Separation Mortar type Refractory shell stave body layer filling material insert
Iir Hot face Hot face
Figure 5.37 Cast iron stave layout and positioning in furnace.
Also shown in Figures 5.37 (a) and (b), is the section to be simulated as indicated by the dotted lines. The three-dimensional model is shown in Figure 5.38. The grid consists of 31 200 cells which include mesh refinement to some extent for the pipe
flow. This, together with the separation layer between the cast-in cooling water
pipe and the cast iron, are illustrated more clearly in Figure 5.39. The separation
layer has a 2 mm thickness and a conductivity of 0.5 W/mK, which gives it a one-dimensional thermal resistance of 0.004 m 2KJW in accordance to the values suggested by Helenbrook et al [24].
An inlet velocity for the cooling water of 3m/s is assumed, while the cross sectional
area for both the inlet and outlet are the same as for a 80NB pipe. Symmetry
boundaries are assumed for the top, bottom and side boundaries, except for the inlet
and outlet boundaries on the top and bottom. The boundary values for the hot face
inside the furnace and the frontal face on the outside of the furnace, as well as all
material properties and other values, are applied as discussed in Sections 5.5 and
CHAPTER 5
5.6 and listed in Table 5.4. The input file as created in and for FIo±+ [38] for this model, is included under Appendix E.
Flo++ r..¼Version 2.10
DATE: 20 Jun 1997 CASE: d:\worlc\staves
Side view
Top view Hot face [
Figure 5.38 Three-dimensional model of cast iron stave.
ciiiiLtaI
DATE: 20 Jun 1997 CASE: d:kwork%st2ves
Separation layer L
Figure 5.39 Detail of mesh refinement and separation layer in three-
dimensional model for cast iron stave.
CHAPTERS 106
5.8.3 Copper staves
The same model used for the cast iron staves is used for the copper staves. Only
the cast iron material properties are changed to copper material properties, and the
separation layer is omitted as the cooling channels or pipes are drilled directly into
the copper block. The copper staves investigated are also not casted but rolled —copper blocks^-asdescribed^by-Helenbrook^et- 01244]—.The-three-di ffiensibhal^rffo—del^
to be used is the same as illustrated in Figure 5.27 excluding the separation layer.
Another model for the copper staves includes an accretion layer or skull attached to
the hot face boundary. The skull thickness will be varied between 10 mm and 50
mm to determine the obtainable skull thickness for combinations with different refractory materials. Skull conductivity is applied as discussed in Section 5.5 and listed in Table 5.4. The three-dimensional model is shown in Figure 5.29 and the
input file as created in and for Flo++ is included under Appendix F.
Figure 5.29 Three-dimensional model of copper stave incorporating an
accretion layer.
CHAPTER 5 - 107
5.9 Conclusion
It was confirmed that the computational fluid dynamics program, Flo+±, is capable
of obtaining true and realistic solutions for the purpose of comparing the
effectiveness of different combinations of lining/cooling systems. The different
parameters to be compared have been identified as well as the variables influencing them.
A two-dimensional comparison revealed that the refractory conductivity has the
greatest influence on the hot face temperature, heat flow and indirectly skull
formation, while the cooling system area is close behind. It was also determined
that a realistic change in the convection heat transfer coefficient of the cooling
water does not seem to have a significant influence. This was investigated by varying the inlet velocity of the cooling water.
Six different three-dimensional numerical models have been created for the purpose
of approximating different lining/cooling systems. The results from these will be
discussed in the next chapter. Where applicable, results will be compared also with
results obtained from the two-dimensional models in this chapter. These
comparisons will only be with regard to the degree of influences and not actual
values, as the two-dimensional models are not approximations of actual
lining/cooling systems. As the three-dimensional models are approximations, the
results will also be discussed with regard to values and the effect thereof on
mechanical and chemical wear as well as possible skull formation.
CHAPTER 5 108
CHAPTER 6 RESULTS, DISCUSSIONS AND SOME CONCLUSIONS
6.1 Introduction
In Chapter 5 the different three-dimensional models to be used in this study have been developed and discussed. These models are now utilised to obtain comparative - results^between a sèriës of differenfiining/oling system configurations subjected to a range of different blast furnace operating conditions.
These results will be compared and discussed while some conclusions will be made.
First of all the fluid dynamic solution must be verified as discussed in Section 5.4.
This is also to verify the grid sizing and configuration. Secondly the influence of
the cooling system convection heat transfer coefficient, the cooling system area and
the refractory conductivity on skull formation will be discussed. This will be
followed by a comparison between heat transfer results for different lining/cooling
system combinations, including possible steam layer formation in the cooling
elements as well as skull formation on the lining hot faces.
Next is a section with final conclusions regarding the comparison between the
different lining/cooling system combinations. Finally possible future work on the
subject of blast furnace lining/cooling systems will be discussed.
6.2 Verification of fluid dynamics results
As stated previously, three-dimensional steady water flow is solved with water
properties as listed in Table 5.3 [40]. The results are to be verified with regard to
f for the cases with a 3 m/s inlet velocity. All velocity and pressure profiles for the
different three-dimensional models will be discussed, including the flat plate cooler case with an inlet velocity of 6 m/s. The results will be discussed separately for the
different cooling systems, starting with the flat plate coolers.
All boundary values, material properties and other values are applied and used as discussed in Sections 5.5 and 5.6 and listed in Table 5.4. Examples of the input
files as created in Flo++ for the different three-dimensional models are included in
Appendices D, E and F as referred to in Section 5.8.
CHAPTER 6 1
6.21 Copper flat plate coolers
Figure 6.1 shows the solution to the velocity field on a plane through the centre of
the water channels. The flat plate cooler is viewed from above as positioned in the
furnace shell. An inlet velocity of 3 m/s is utilised which represents a volume flow rate of 8.6 M3 /h. The variation in velocity is indicated by use of three-dimensional
vectors which are sized and colour coded according to the different velocities.
Version 2.10
H
I
I
I
•
I
I
300mm
t / I
Ii
• I
Il J 1111 N
GMAX 30922e+000 GMIN 0.0000e+000
2.7486e+000
2.0615e+000 1.7179e+000 1.3743e+000
______ 1.0307e+000 6.8716e-001 3.4358e-001 0.0000e+000
IlIl
• ' I IN
i.\ i, \\\.._/
. . •.
Il _.'/,'11 ;:. ç\\\'_'ñI
Z X
Figure 6.1 Velocity vector profile for flat plate cooler with 3 m/s inlet velocity.
As discussed in Section 5.8, cyclic boundaries are utilised to connect the water
channels forming part of the two separate flat plate coolers. Together these
channels form a complete flow circuit found in a single flat plate cooler. As can be
seen in Figure 6. 1, the velocity decreases after the inlet due to an increase in the cross sectional area in the channel.
Through the critical outer channel the velocity stays reasonably constant, with a
uniform high velocity profile being forced onto the flow boundary in the cooler nose
region. This is important for the prevention of nucleate boiling as well as the stable
formation of a steam layer as will be discussed later on in this chapter. In the larger
inner channels the velocity reduces while sharp corners cause vortices to be formed.
CHAPTER 6 110
Velocity increases again at the outlet where the cross sectional area is reduced back to almost the same area as the inlet.
In order to determine whether or not turbulent flow is experienced, the Reynolds
number, Rex, is used as an indication. Equation (5.18) gives the formulation of the
dimensionless Reynolds number for flow over a total length L. From visual inspection of Figure 6.1 it follows that a approximate average free-stream velocity,
--u,-of-2:4- m/s-is achieved ava distance-of-approximately 300 --myn-&orrrthe inlet—.-B-y---- -
substituting the velocity and length, as well as the water density and viscosity as
listed in Table 5.3, into Equation (5.18), a Reynolds number equal to 1.23 x 106 is obtained. This indicates turbulent flow as the Reynolds number is above 5 x 105,
the value where the transition between laminar and turbulent flow occurs [40].
Next the pressure distribution or pressure changes through the channels can be
discussed according to Figure 6.2. The same plane is viewed as with the velocity
profile in Figure 6.1. The resulting pressure distribution is illustrated relative to a
reference pressure specified at the inlet. As incompressible water flow is studied
with a fixed density, the value of the reference pressure is unimportant. Only the relative pressure changes through the system are important.
-....-:-.. __Version 2.10
\ \ . //____ DATE: 07 Jul 1997 CASE: d:\work\flatplates PRESSURE
rER 205 GMAX 3.4008e+003 GMIN -1.2798e+004
1.7809e+003 L... 1.6100e+002 I---
I .3.0788e+003 -4.6987e+003 -6.3186e+003 -7.9385e+003 -9.5584e+003 -1.1178e+004 -1.2798e+004
Figure 6.2 Pressure distribution through flat plate cooler channels - 3 m/s
inlet velocity.
CHAPTER 111
Immediately after the inlet the pressure increases due to the increase in the cross
sectional area. As with the velocity, the pressure remains fairly stable through the
critical nose channel. Relative sharp pressure drops occur through the inner
channels, especially around the sharp corners. A final pressure drop takes place in
the smaller outlet cross sectional area before the water leaves the system.
-- --=InFigure -
From this it can be concluded that a total cooling water pressure drop over a single
flat plate cooler is lower than 15 kPa. This is for an inlet velocity of 3m/s or a volume flow rate of 8.6 m3/h.
For the case with an inlet velocity of 6 m/s, the relative velocity distribution does
not look much different from that for the case with an inlet velocity of 3 m/s. This
can be observed by comparing Figures 6.1 and 6.4, where Figure 6.4 is for the case
with an inlet velocity of 6 m/s. In the latter each velocity range, as represented by a
different colour, is almost double in value compared to the case with a 3 m/s inlet velocity.
r9HO++ Version 2.10
DATE: 07 Jul 1997 CASE: d:worIc\flatpIates PRESSURE Relative N/m2 ITER 205 GMAX 3.4008e+003 GMIN -1.2798e+004
i 3.4008e+003 1 1.7809e+003
F--1 1.6100e+002 -1.4589e+003
.J -3.0788e+003 -4.6987e+003 -6.3186e+003 -7.9385e+003 -9.5584e+003 -1.1178e+004 -1.2798e+004
x
Figure 6.3 Pressure difference at inlet and outlet boundaries for the case
with inlet velocity of 3 m/s.
CHAPTER 112
Version 2.10
T:E :ZteS
VELOCITY Magnitude MIS
ITER 203 Ai GMAX 6.2032e+000
S
t :
GMIN 0.0000e+000
6.2032e+000 5.5139e±000-=-4.8247e+000
I :sit
4.1355e+000 3.4462e+000
H . I 2.7570e+000 I I' . Il' it I 2.0677e+000 Ill lil t 1.3785e+000
'II Ii 6.8924e.001 Hill 0.00 00e+000
: I •LJ
\//
Figure 6.4 Velocity vector profile for flat plate cooler with a 6 m/s inlet
velocity.
The same is true for the pressure distribution as illustrated for the 6 m/s inlet velocity case in Figure 6.5. Only small differences are noticeable in the colour
display. This is misleading as the total pressure loss over the complete flat plate cooler reaches 50 kPa, which is substantially higher than for the previous case. The
high increase in the pressure drop is directly related to the high increase in the
kinetic energy spent due to the quadratic relationship with the velocity [50]. It is
concluded therefore that for this flat plate cooler design, the increase in pressure
drop is higher than the corresponding increase and gain in velocity for velocities above 3 m/s.
For the case incorporating the cigar cooler, Figure 6.6 illustrates the same plane
view as previously for the velocity profile. All boundary values, material properties
and other values, regarding the flow solution, are used as listed in Table 5.4. An
inlet velocity of 3 m/s is used and the velocity profile for the flat plate cooler is the
same as for the case without the cigar cooler. For the cigar cooler the velocity also
decreases directly after the inlet due to the cross sectional area increase. In the nose
region some vortices are formed due to the sharper corners in the cigar cooler
compared to the flat plate cooler nose channel.
CHAPTER 6 113
Flo++ IL Version 2.10
DATE: 07 Jul 1997 CASE: d:\work'flatplates PRESSURE Relative N1m2
hER 203 GMAX 1.3225e+004
GMIN -5.0296e+004
I 1.3225e+004 6.8729e+003 5.2081e+002 -5.8312e+003 -1.2183e+004
I -1.8535e+004
_- -2.4887e+004 -3.1239e+004 -3.7592e+004 -4.3944e+004 -5.0296e+004
Y
z x
Figure 6.5 Pressure distribution through flat plate cooler channels - 6 m/s inlet velocity.
When the refractory lining is worn away up to the cigar cooler, this flow pattern
could cause steam formation to take place due to the trapping of water in the
vortices next to the hot face. This will be discussed later on in Chapter 6 with
regard to water pressure and temperature. At the outlet velocities as high as 3.3
m/s are reached which is higher than that for the flat plate cooler. This is due to a
more aggressive velocity profile in the channel before reaching the outlet.
The pressure distribution is illustrated in Figure 6.7. As can be expected due to the
shorter path, the pressure drop through the cigar cooler is much lower than the
pressure drop through the flat plate cooler. A total pressure drop of ± 6 kPa was
obtained.
CHAPTER6 114
('Version 2.1O
DATE: 14 Jul 1997 CASE: d:kworMflatplates VELOCITY Magnftude
ITER 187 GMAX 33188e+000 GMIN 0.0000e+000
:;' If 33188e+000 J.l. Lt 2.9501e+000 - I 25813e+000
: 111 2.2125e+000
III1.8438e+000
'II 1.4750e+000 I 1.1063e+000
0
7.3751e-001 1 1 3.6876e-001 I I d 0.0000e+000
'
a)L
Version 2.10
Jul 1997 Arkates
VELOCITY Magnitude
I I ' ITER 187 - GMAX 33188e+000
GMIN 0.0000e+000
2.9501e+000 I 11 2.5813o+000
2.2125e+000 I. 1 1.8438e+000 I - 1 I I I I 1.4750e+000
- 1 I 1.1063e+000 H . - U 7.3751e-001 1i. fi I' 3.6876e-001
I 00000e+000
1 1 1110 it Y
b) IJ)) i ______
z x
Figure 6.6 Velocity vector profile for flat plate cooler arrangement
incorporating a cigar cooler.
CHAPTER 6 its
JVersion 2.10
DATE: 14 Jul 1997 CASE: d:\work\flatplates PRESSURE Relative N/m2
I ITER 187 GMAX 3.4008e+003 GMIN -12798e+004
r 3.4008e+003 F--- 1.7809e+003
I -
- 1.6100e+002=-= -1.4589e+003
I------I -3.0788e+003 I -4.6988e+003 I - I -63187e+003 I t•i -7.9386e+003 I -9.5585e+003
-11178e+004 1.2798e+004
V
a)I F
c DATE: 14 Jul 1997 CASE d\work\fiatplates PRESSURE Relative N1m2
ITER 187 GMAX 3.4008e+003 GMIN -1.2798e+004
3.4008e+003 I-I 1.7809e+003
LGlOOe+002 -14589e+003
j------ -3.0788e+003 F -4.6988e+003
-6.3187e+003
-9.5585e+003 -11178e+004 -1.2798e+004
b) --- -il-
V
z x
Figure 6.7 Pressure distribution through flat plate cooler arrangement
incorporating a cigar cooler.
As discussed in Chapter 5, Section 5.4, the non-dimensional distance y must fall within certain limits. This is to ensure the correct calculation of the velocity, and
eventually, temperature profiles in the boundary layer. According to Holman [40], these limits for y are between 30 and 400 for turbulent flow. In Figure 6.8 the
CHAPTER 116
boundary values for y are illustrated for the case with an inlet velocity of 3 m/s. A
maximum of approximately 2000 was achieved although it is not visible in Figure
6.8. If the model is slightly tilted to the back as shown in Figure 6.9, the regions
with the higher y' values become visible.
I
17o++ Version 2.10
- -- -= - DATE: 07 Jul1997--CASE: d:\work\flatplates YPLUS
ITER 205 GMAX 2.0333e+003 GMIN 0.0000e+000
2.0333e+003
1.8300e+003 1.6267e+003 1.4233e+003 1.2200e+003
• 1.0167e+003 8.1334e+002 6.1 000e+002 4.0667e+002 2.0333e+002 0.0000e+000
V
X z
Figure 6.8 values for 3 m/s inlet velocity.
Flo++
..
Version 2.10
DATE: 07 Jul 1997 CASE: d:\work\flatplates
YPLUS
ITER 205 GMAX 2.0333e+003 GMIN 0.0000e+000
i 2.0333e+003 F I 1.8300e+003
I 1.6267e+003 1.4233e+003 1.2200e+003
F I 1.0167e+003 8.1334e+002 6.1000e+002 4.0667e+002 2.0333e+002 0.0000e+000
V
x
z
Figure 6.9 y values as seen on tilted view.
CHAPTER 117
These high values are only present on the sharp corners in the inner channels of the
flat plate cooler. For the rest of the model they' values are within the limits except
for small areas in front of the inlet and outlet where values vary between 400 and
600. Overall the y values are acceptable and an adequate flow solution of the boundary layer has been obtained.
-- - For the-above=case with an--inlet velocity of 3=m/sthis flow solUtion resulted in i • convection heat transfer coefficient solution as illustrated in Figure 6.10. Water
properties are used as listed in Table 5.3 for a bulk temperature equal to 320 K.
The bulk temperature was assumed by considering the inlet temperature and the
expected maximum temperature for the cooling water. The heat transfer coefficient reaches a maximum value of 7877 W/m2K at the inlet, while a value of approximately 6000 W/m2K is maintained through the critical nose channel as
determined from visual inspection. These values or results are realistic if compared to the results obtained and verified in Section 5.4.
no+ + Version 2.10
•DATE: 07 Jul 1997 CASE: d:\work\flatplates HEAT COEFFICIENT
ITER 205 GMAX 7.8767e+003 GMIN 0.0000e+000
7.8767e+003 7.0890e+003
---. 6.3014e+003 I------ 5.5137e+003 -.------i 4.7260e+003 r- -] 3.9383e+003
I 3.1507e+003 2.3630e+003 1.5753e+003 7.8767e+002 0.0000e+000
ly
Figure 6.10 Convection heat transfer coefficient for 3 m/s inlet velocity.
In Figure 6.11 the convection heat transfer coefficient results are illustrated as
obtained for the case with an inlet velocity of 6 m/s. A maximum value of 13650 W/m2K occur at the inlet and an average value of approximately 10000 W/m2K is
CHAPTER •-•• - 118
maintained through the critical nose channel. Again these results are realistic if
compared to previous results as obtained in Section 5.7. The convection heat
transfer coefficient is almost doubled due to a 100% increase in inlet velocity.
Figure 6.11 Convection heat transfer coefficient for 6 m/s inlet velocity.
6.2.2 Cast iron and copper staves
The same model with regard to geometry and the fluid dynamics solution is used for
the cast iron and copper staves. Thus, the same flow solution results were obtained
for both cases. Figure 6.12 illustrates the velocity distribution on a plane through
the middle of the cast in steel tubing in the cast iron stave, or the cylindrical drilled
channel in the copper stave. The plane is viewed from the side of the stave as
installed in the furnace shell with the hot face or furnace inside on the right.
An inlet velocity of 3 m/s is specified. All boundary values and material properties are used as listed in Table 5.4. A boundary layer can be seen to form as the flow progresses from the inlet to the outlet. Due to the blunt velocity profile, the flow is
expected to be turbulent. For the diameter of 80 mm, a Reynolds number equal to 4.1 x 105, indicating turbulent flow [40], is calculated using the version of Equation
(5.18) suitable for tube flow [40] and a mean velocity of 3 m/s. A slightly higher
maximum velocity than the inlet velocity is also visible in the centre of the stream.
CHAPTER 119
. -
2.10
DATE: 12 Jun 1997 CASE: d:\work\staves VELOCITY Magnitude rn/s ITER 44 GMAX 3.1639e+000 GMIN 0.0000e+000
3.1632e+000 2.81 18e+000 2.4603 e+000 2.1088e+000 1.7573e+000 1.4059e+000 1 .0544e+000 7.0294e-001 3.5147e-001 0.0000e+000
L.
..,.
,......
i4
Figure 6.12 Velocity profile through cast iron and copper staves.
Flo++ ,Version 2.10 ________
DATE: 12 Jun 1997 CASE: d:\work\staves PRESSURE Relative N/m2 ITER 44 GMAX 6.2064e+001 GMIN -5.1550e+002
L.I-5.3449e+001 -1.1121e+002
I .22672e+002 .3447oo .34223e+002 -3.9999e+002 .45774e+002 5.1550e+002
LX
Figure 6.13 Pressure distribution through cast iron and copper staves
In Figure 6.13 the pressure distribution results are illustrated. As is expected from
turbulent tube flow, there is a steady drop in pressure from the inlet to the outlet,
CHAFFER 6 120
with evidence of the progressive forming of the turbulent boundary layer. A total
pressure drop of approximately 550 Pa through the tube section used in the model
is indicated.
The pressure drop can also be calculated using the following equation [50]:
-- (J)
where represents the friction coefficient to be determined from the Moody chart
[50], p = 989 kg/rn3, the water density, g 9.81 m/s2, gravity force, L = 450 mm, the tube length,, V = 3 m/s, the water velocity, and d = 80 mm, the tube diameter..
Using a roughness of 0.046 for commercial steel or wrought iron [50], and the Reynolds number, Red = 4.1 x 10 5 , previously determined, a friction coefficient off
= 0.019, is determined from the Moody chart [50]. Substituting into Equation
(6. 1), it results in a calculated pressure loss of 476 Pa. This is adequately close to
the pressure loss of 550 Pa read from Figure 6.13.
The boundary values calculated for/ are shown in Figure 6.14. These values are
comfortably within the limits as set out in Section 5.4 [40]. A maximum y' value of
265.16 is reached a small distance from the inlet after which it decreases with a
minimum of2l 1.26 at the outlet.
This flow solution as obtained for both the cast iron and copper staves resulted in a
convection heat transfer coefficient distribution as shown in Figure 6.15. The distribution on the tube boundary is almost a footprint of the distribution pattern
obtained for y shown in Figure 6.14. A maximum value of 2235 W/m 2K is obtained with an average value of approximately 2000 W/m 2K as visually determined from Figure 6.15.
This is of the same magnitude and in accordance with the results obtained in Section 5.4 and Section 5.7. T Ik = 320 K is used for determining the cooling water
properties used.
CHAPTER6 121
IIJMass •u••iiii •.u.uIi_____________________
•u.uuuui •.uuuuui ..uuuuIl: II.u.uIII
- II.uuuII: •••uIIuI:
U y - • N fi •.uiuIIr
•luuIlr Ii Ik U U
•UUIuIII
- ii[ =: •
- - . - . .
:1 •UUIUflp ::: .
::i..I1uuiiiiii. .Itiiuu•UIIIiui•
. . HIIUNU•UiiIuII •i,.uu..iiiuii
I I
:IIi.....uIuhii ,,i.....uuuuuii
II, MOORE
iIiiIIII•UUUUI1L IIIIEI•UUIUIIIII: IiHaiuuuiiiui•
!iii•iIU••iuuuii Iiuuii.uuiuuii
iuui.U..uuIiII uI.uu ...lUuuluI
u..u...iuu,i
u uI ;IIIUIU.0 • .I.u.UUuuII•
Figure 6.14 y values for cooling water flow through cast iron and copper
staves.
•..uiiii
iHhi •uI.Iuui; ::
OHill .II
UUUU11II! •uI.iuIr •..i.iii •..u.iit •.uiiIiii -
UlUlilil fi mallailli • . . . .
:00WI
.•.•a..u.uhI - , - It:
1IIUllIfl
..uiuiuI. - I I
Ii •uuuiin NINKIIIIIIIIII low • • - ;UuIIlJ...uu,Il: ufl'i'i..uU..II.
- • !:I,!(IIIUIIUUIII . :uluIii.u.nuui:
- I I
:iIu..u.iuuiw. IIIIUUII•uuuuuIi;
- 1
IIIIiU.I•UuuuuIii NIIIUUUUUI11IIIi IJIIMUU.lIiiiII: IIIuU.uI...,iiw •,Ii,iiU..i.ii,i 1 ,iuiU•uuuiifl I IIiiuU••uuiiII• IIISII...uuuu,ui .UIIIUUUUUIIUIIII
________________
..monsoons uIIloilo uui
Figure 6.15 Convection heat transfer coefficient for cast iron and copper
stave models.
CHAPTER 6 122
6.3 Variables influencing skull formation
For the purpose of investigating the variables influencing skull formation, the three-
dimensional models for the flat plate coolers are utilised. These models are useful
as the complete flow system is included for a comparison between different inlet velocities, as well as a comparison between different cooling system areas. As with
the two-dimensional analysis in Section 5.7, the three variables to be investigated include the-convection heat-transfer-coefficient by-varying-the in1etvelocitythe
cooling system area and the refractory conductivity.
The influence of the convection heat transfer coefficient on skull formation is
investigated by comparing the results for two different inlet velocities, namely 3 m/s
and 6 m/s. Thus, there is a difference of 100% between the two inlet velocities.
For this investigation, the model with a vertical pitch or spacing between flat plate
coolers of 300 mm is selected, while semi-graphite with a heat conductivity of 55
W/mK [2] is used as the refractory material.
From the previous section it follows that an inlet velocity of 3 m/s resulted in an
average convection heat transfer coefficient of approximately 6000 W/m2K, while an inlet velocity of 6 m/s resulted in an average, determined by visual inspection of approximately 10000 W/m2K. This difference of approximately 70% was illustrated
in Figures 6.10 and 6.11. The respective temperature solutions for the two cases
are illustrated in Figures 6.16 and 6.17. All boundary values and material properties
are applied as presented in Section 5.5 and 5.6, and listed in Table 5.4. The temperature distributions are plotted for the boundaries covering the model with the hot faces on top.
For an inlet velocity of 3 m/s, a maximum hot face temperature of T2 1041 K 768 °C and a heat flow of 197 kW/m2 are obtained. For an inlet velocity of 6 m/s, the maximum hot face temperature decreased to T2 = 1030 K = 757 °C and the heat flow increased to 200 kW/m2. The results for the varying convection heat transfer coefficients are summarised in Table 6.1.
FromTable 6.1 it can be concluded that an increase as high as 100% in the inlet velocity has only a small influence on T2,,, and q ", both positive indicators of skull formation. These results compare well with the results obtained for the two-
dimensional model in Section 5.7.
CHAPTER 6 123
Table 6.1 Comparison of results for different convection heat transfer
coefficients.
Inlet velocity Convection Maximum Heat flux heat transfer hot face
coefficient
temperature
Ut (m/s) - h (W/m2K) T2,, (K) q" (kW/m2)
appt6x6000 -- - T04l 1-97—--
Case 2 6 approx. 10000 1030 200
% Difference 100% 67% 1.1% 1.5%
The influence of the cooling system area on skull formation is investigated using the
three different models for the flat plate coolers as described in Section 5.8. This include the two models with vertical pitches of respectively 300 mm and 600 mm,
as well as the 300 mm vertical pitch model incorporating a cigar cooler. Boundary
values and material properties are kept constant for all three cases with an inlet velocity of 3 m/s and furnace inside parameters as discussed in Sections 5.5 and 5.6, and listed in Table 5.4. The results are shown in Table 6.2 for a constant refractory conductivity of 55 W/mK.
Table 6.2 Comparison of results for the different cooling system areas.
Maximum hot face Heat flux temperature q" (kW/m2)
T2 (K)
Value Difference Value Difference
P = 60Omni 1204 161
P = 300mm 1041 163 197 36 = 300 mm 933 108 211 14
& cigar cooler -
From Table 6.2 it can firstly be concluded that a realistic increase in the cooling
system area has a much higher positive influence T2, and q", both positive indicators of skull formation, than a realistic increase in the convection heat transfer
coefficient. Secondly it can be concluded that the change in vertical pitch from 600
mm to 300 mm has a greater influence on skull formation than the installation of a
cigar cooler. This can directly be related with the actual increase in cooling system
area which is lower for the case incorporating the cigar cooler.
CHAPTER 6
F70++ Version 2.10
DATE: 07 Jul 1997 CASE: d:\work\flatplates TEMPERATURE Kelvin
ITER 205 GMAX 10410e+003 GMIN 3.0000e+002
- 1.7550e+003 j 1.6095e+003 1.4640e+003
1.3185e+003 ------ 1.1730e+003
1.0275e+003 I!!.. U 8.8200e-i-002 Ii 7.3650e+002
5.91 00e+002 4.4550e+002 3.0000e+002
Y
z x
Figure 6.16 Isotherms on external faces of model for the case with 3 m/s inlet velocity.
F9 6+1
Version 2.10
DATE: O7 Jul 1997 CASE: d:\work\flatplates TEMPERATURE Kelvin
ITER 203 GMAX 1.0299e+003 GMIN 3.0000e+002
r-i 1.7550e+003 F I 16095e+003 I I 1.4640e+003 I—1 1.3185e+003
1.1730e+003 I 1.0275e+003 !4 8.8200e+002
7.3650e+002 59100e+002 4.4550e+002
- 3.0000e+002
Figure 6.17 Isotherms on external faces of model for the case with a 6 m/s inlet velocity.
CHAPTER 6 125
A further conclusion to be made involves the possible improvement of an existing
lining/cooling system. As discussed in Chapter 2, cigar coolers can be installed
during a campaign. Thus, if the lining/cooling system is not performing as it should,
or if the campaign is extended beyond the planned period, cigar coolers can be used to improve the cooling of the furnace shell.
By positioning the cigar cooler between the flat plate coolers as shown in Figure- -
temperatures usually occur. This accurate positioning is reflected in Table 6.2
where the percentage decrease in the maximum hot face temperature is higher than
the percentage increase in heat flux. With the decrease in vertical pitch the result
was the opposite. Although both cases have a positive influence on skull formation, a greater decrease in hot face temperature is more desirable due to the possible
influence on mechanical and chemical wear mechanisms as discussed in Chapters 2 and 3.
As discussed in Section 2.2, CO-disintegration and Oxidation are two chemical
attack mechanisms that could occur at temperatures as low as 400 to 500 °C. In
Figure 6.18 a boundary isotherm plot for the flat plate cooler arrangement with a
vertical pitch of 300 mm is shown. The colours are compressed between 673 and
773 K (400 and 500 °C). This can be compared with the case with the cigar cooler
as shown in Figure 6.19. Both cases are for a refractory lining with a conductivity
of 2 W/mK. From this it is evident that a greater part of refractory lining is
subjected to these chemical attack mechanisms if a cigar cooler is not present.
The model incorporating a vertical pitch of 300 mm is used to investigate the influence of refractory conductivity on skull formation. Boundary values and material properties, as listed in Table 5.4, are kept constant as previously which include an inlet velocity of 3 m/s. Four different refractory conductivities are investigated namely 2 W/mK, 25 W/mK, 55 W/mK and 135 W/mK. These values can respectively be linked to high alumina, silicon carbide, semi-graphite and
graphite as discussed in Section 5.6 [2]. The results obtained for the maximum hot
face temperature and the heat flux are summarised in Table 6.3.
CHAPTER 6 126
pFLQ- HO++ Version 2.10
DATE: 08 Jul 1997 CASE: d :\work\flatplates TEMPERATURE Kelvin
ITER 205 GMAX 1.7248e+003 GMIN
7.7300e+002 7.6300e+002
7.4300e+002 7.3300e+002 7.2300e+002 7.1300e+002 7.0300e+002 6.9300e+002 6.8300e+002 6.7300e+002
z x
Figure 6.18 Isotherms between 673 and 773 K for P = 300 mm.
pr
7.7300e+002 7.6300e+00 75300e4002 7.4300e+002 7.3300e+002 7.2300e+002 7.1300e+002
j 7.0300e+002 6.9300e+002 6.8300e+002 6.7300e+002
Figure 6.19 Isotherms between 667 and 773 K for P = 300 mm including a cigar cooler.
CHAPTER 6 12
Table 6.3 Comparison of results for the different refractory material
conductivities.
Refractory conductivity Maximum hot face Heat flux temperature
k, (W/mK) T21 (K) g" (kW/m2) Value Difference Value Difference Value Difference
2 1725 38.5
25 23 =1337 -388 -- 133.8--=-- -953
55 30 1041 296 196.6 62.8
135 80 873 168 235.8 39.2
From these results it follows that the refractory conductivity is the variable with
greatest practically achievable influence on skull formation. Again these results
correspond well with the results obtained in Section 5.7 for the two-dimensional
model. It can also be concluded that although the difference between the successive
conductivity values progressively increases, the corresponding differences between successive values for both T21,,,,. and q" decreases. As was the case with the two-
dimensional analysis, this is attributed to the decrease in the conductivity difference
between the refractory material and the cooling system material, in this case copper.
As was the case with the results for the two-dimensional analysis, the cooling
system area and refractory conductivity are the two variables that have the greatest
influence on skull formation. The temperature solutions for these two variables can
be compared as shown in Figure 6.20. On the left the temperature solutions for a
refractory conductivity of 2 W/mK are shown for an increasing cooling system area
from top to bottom, while the same is done for a refractory conductivity of 135
W/mK on the right. All temperature distributions are compared for the same temperature range between 300 K and 1755 K.
The decrease in lining temperature due to the increase in refractory conductivity is
clearly visible in Figure 6.20, while the influence of the change in cooling system area is less obvious.
CHAPTER 6 128
D = 609 mm; kr = 2 W/mK P = 600 mm; kr = 135 W/mK
. '%1V.. 210 Lii DATE, oa.Ml ggl DATE OA.kAt7 CAM dV^MJW^n CASE d bAWA1pI
TBERATLA KOAIfl
ifTE 2W JTM 2C5 CMIII 1 7348g. CMIX 8T33le.02 Gl.CN
1 35C0..103CMII 3e.DA2
1 1 = 146401.E13
1 14&10e.G33
1 3I85e.3 13185IIII33 1 ll3OA.3 1 O275e.3
1 1730e.003 1 02T5o.DA3
883II1.M2 88XCA.TE2 7 366O..2 591CM.032
7 3MI..002 59103..TE2
44550.0323 fDA.TI2
41OI.IX2 3
P., = 300 mm: k..=2 W/mK P..=300 mm k.= 135W/ink
DATE 14M 1997 DATE 21JU1997
FTER 187 [TER 197
3 +002
= 3(H) mm & cigar cooler; k, = 2 W/mK P = 300 mm & cigar cooler; k = 135 W/mK
Figure 6.20 Isotherms for different combinations of refractory conductivities and cooling system areas.
The influence of these two variables on skull formation can finally and most
effectively be compared graphically. Figure 6.21 is a graphical presentation of the
maximum hot face temperature for the three different cooling system areas due to
the change in the refractory conductivity. It is observed that the rate of decrease in
the maximum hot face temperature slows down as the refractory conductivity
increases. As discussed previously, this is due to the decrease in the difference
between the refractory and cooling element conductivities.
CHAPTER 6 129
1800 ___
1700 L = 300 + cigar 1600
1500 -
__ 1111 ____ __
900• ____••__ ______
800 11 0 20 40 60 80 100 120 140
Refractory conductivity, k,. (WImK)
Figure 6.21 Graphical representation of T211, for the different refractory
conductivities and cooling system areas.
A second observation is with regard to the influence of the two variables on each
other. According to Figure 6.21 the greatest difference in maximum hot face
temperature between the three cooling system areas occur at a refractory conductivity of 55 WImK. The difference decreases for lower and higher refractory
conductivities. Again this can be attributed to the difference in conductivity
between the cooling elements and the refractory material.
Figure 6.22 is a graphical representation of the change in heat flux for the three different cooling system areas relative to the change in the refractory conductivity.
The same observation as for the maximum hot face temperature, regarding the
decrease in differences for lower and higher conductivities, can be made. Again the
influence of the refractory conductivity on the heat flux and skull formation is
dominating the influence of the cooling system area.
It can be concluded that, as was the case for the two-dimensional analysis in Section 5.7, an increase in refractory conductivity has the greatest positive influence on
skull formation. A change in cooling water flow rate, and thus the convection heat
transfer coefficient, has an insignificant influence on skull formation. The cooling
system area has a more significant influence on skull formation, although not as high
as the refractory conductivity. It was also shown that cigar coolers can be used to
improve existing blast furnace lining/cooling systems.
ChAPTER 6 130
1s,IsIs1.I
-'iIiIiS1
IIISiSISI
D:sI.IsI.I
0
0 20 40 60 80 100 120 140 Refractory conductivity, k, (WImK)
Figure 6.22 Graphical representation of q" for the different refractory conductivities and cooling system areas.
6.4 Heat transfer results for the three different cooling systems
Before a comparison can be made between the cooling systems, it is necessary to
determine the best refractory combination for each of the cooling systems. This will
be done by comparing the maximum hot face temperature and the heat flux for each
of the cooling systems combined with the four refractory conductivities. The
isotherm distributions will also be discussed and compared. First the heat transfer
results as obtained for the copper flat plate coolers will be discussed, then the results for the cast iron staves, and finally the copper staves.
6.4.1 Copper flat plate coolers
In Section 6.3 two different copper flat plate cooler arrangements have been
discussed. The only difference between these arrangements is the vertical pitch,
where one is 300 mm and the other one 600 mm. From the results and discussions
it followed that the increase in cooling area coverage by decreasing the vertical
pitch from 600 mm to 300 mm, has a significant positive influence on the heat
transfer results. It is in accordance with the European and world trends to use a
300 mm vertical pitch arrangement [8]. The model with a vertical pitch of 300 mm
is therefore used in this study to investigate the heat transfer results for copper flat plate coolers.
CHAPTER 6 131
As stated in Table 2.7 [20], an average velocity of 2.5 m/s currently forms the
upper limit for copper flat plate cooler channel flows. According to the velocity vectors for a 3 m/s inlet velocity as illustrated in Figure 6.1, a velocity of approximately 2.5 m/s is maintained in the critical outer channel. An inlet velocity of 3 m/s is therefore used to obtain the heat transfer results for the copper flat plate coolers.
Figure 6.23 illustrates the temperature distribution or isotherms for the four
different refractory conductivities, as listed in Table 5.1, combined with the flat
plate cooler model. All boundary values and material properties are applied according to Sections 5.5 and 5.6 of the previous chapter.
'4WAT1 — I ;42I4T1 s' •,
DATE DOMIM7 DATE 27^glM
6— 172401-063
59 10 ^02 4, 550-002
- k = 135 W/mK 17 ' k = 55 W/mK — Wr.hm 2.10 OPL 4MOMLM 2.10
d7 g 6
0 003 I 7550 333 0095 003___________
I
0095 323 640 *003 7 31450.002
540 *553
I 37053,323 I I730.003 177304.553 I 0275e.003 882500.002 302705.553
082508*322 730500*003 557000*002
736505.642 597065.552 445500*002
303200*002 445505*322 305965.052
I-c I-c
Figure 6.23 Comparison of isotherms for flat plate cooler model combined
with four different refractory conductivities.
In Figure 6.23, the refractory conductivity is increased in a clockwise manner, starting with 2 W/mK for high alumina, and ending with 135 W/mK for graphite. All four illustrations are for a temperature range between 300 and 1755 K (27 and
1482°C) in order to be able to compare them according to the isotherm colour coding.
CHAPTER - 132
From Figure 6.23 it is clear that an increase in the refractory conductivity causes the
overall lining temperature to decrease significantly. Furthermore, only the hot face
temperature for the illustration associated with high alumina is not below the
expected skull formation initiation temperature of 7'3 = 1423 K. Graphite with a conductivity of 135 W/mK gives the most positive results according to Figure 6.23
with a maximum hot face temperature of only 873 K (600°C).
From Figure 6.23 the-maximum-hot face temperatures can be seen to bepositioned-
on the two corners of the model where the vertical and horizontal centre lines
through the flat plates intersect. It is to be expected as these are the most distant
positions from the cooling elements in all directions. For graphite with a
conductivity of 135 WImK this is not true as illustrated in Figure 6.24, a plane view
of the model hot face isotherm distribution.
no++ Version 2.10
DATE: 30 Aug 1997 CASE: d:\work\flatplates
- TEMPERATURE L Kelvin
ITER 205 GMAX 8.7331e+002 GMIN 3.0000e+002
8.7331e+002 8.1599e+002 7.5867e+002 7.0134e+002 6.4402e+002
- 5.8670e+002 - 5.2937e+002
4.7205e*002 4.1473e+002 3.5741e+002 3.0008e+002
x
Z
Figure 6.24 Plane view of isotherms on hot face for refractory conductivity
equal to 135 W/mK.
According to the colour coding, the maximum hot face temperature can be seen to
be positioned on the ramming material between the graphite and copper cooler.
This is due to the relatively low ramming conductivity of 15 W/mK compared to the
graphite and copper conductivities. Even the resistance due to a longer heat
CHAPTER 133
1800
1700
1600
1500
1400
1300
1200
1100
1000
900
800
conduction route from the expected maximum hot face temperature position to the
copper coolers is overshadowed by this difference in conductivity.
The results can be discussed even better if viewed graphically as shown in Figure
6.25. Both the maximum hot face temperature and the heat flux are illustrated against an increasing refractory conductivity. The rate of decrease in the maximum
hot face temperature slows down as the refractory conductivity increases. This is - - _-
and the cooling element. The same applies to the increase in heat flux.
eIeIsi.]
IIsI.Isisr
'C
100000Cu 0 =
0 0 20 40 60 80 100 120 140
Refractory conductivity, It r (Wim K)
Figure 6.25 Graphical presentation of heat flux and maximum hot face
temperature for the copper flat plate cooler model combined
with different refractory conductivities.
From Figures 6.23 and 6.25, the conclusion can be made, from a thermal point of view, that graphite is the best choice for a refractory material to combine with
copper flat plate coolers. Unfortunately, according to Hebel et al [7], microporous
semi-graphite should be a better choice due to a higher cold crushing strength as
well as a better pig iron and slag resistance (See Table 2.6). Tijhuis et al [3] from
Hoogovens differ from this as shown in Table 2.3, where the cold crushing strain for both graphite and semi-graphite are stated equal to unity.
Despite this disagreement, it is interesting to note that, according to Burteaux et al
[8], Hoogovens opted for a combination graphite and semi-graphite in the bosh, as
well as a sialon bonded silicon carbide bricking layer in front of the graphite layer in
CHAPTER 6 134
the bosh, belly and lower stack areas of Blast furnace 6, Ijmuiden (See Figure 3.4).
Therefore, it is concluded that semi-graphite is a best option if skull formation as
well as the mechanical and chemical wear phenomena are considered. Semi-
graphite will thus be used in combination with copper flat plate coolers for the
comparison with the other cooling systems.
6.4.2 Cast iron staves
Only one model as specified in Section 5.8 is used for cast iron staves in this study.
An inlet velocity of 3 m/s is used which is sustained for most of the length of the
simulated tube section as was previously shown in Figure 6.12. Again this is in
agreement with the maximum value as specified in Table 2.7 [20] for cast iron
staves. All material properties and boundary values are also applied as specified in
Section 5.5 and 5.6, and listed in Table 5.4.
Figure 6.26 shows the temperature distributions for the cast iron stave model
combined with the four refractory conductivities. The illustrations are arranged
clockwise from the lowest to the highest refractory conductivity. A temperature
range of 300 to 1700 K (27 to 1427°C) is selected for all four conductivities in
order to compare results on an equal basis.
From Figure 6.26 it is clear that the increase in refractory conductivity has a great
influence on the maximum hot face temperature only up to 25 W/mK, which
represents silicon carbide. This is due to the lower conductivity of cast iron
compared to copper used for the cooling elements. As the refractory conductivity
approaches and exceeds 40 W/mK, the conductivity of cast iron [40], the cooling
elements start dominating the heat transfer solution of the model.
For the two cases with refractory conductivities higher than that for cast iron, the
maximum hot face temperatures can be seen in Figure 6.26 to be present in the cast
iron ribs. Furthermore, it is evident that although the maximum hot face
temperature decreases with the increase in refractory conductivity, the average
stave temperature is increasing as the isotherms are pushed deeper into the model.
It is also due to the fact that the cast iron stave starts to form the main heat barrier
or resistance at refractory conductivities higher than 40 W/mK.
CHAPTER 6
k = 2 W/mK NRo++ k = 25 W/mK 1F70++ .)Vfl1on 219 ..S')VI.nS9O 2.10
D.81E 12J99 997 CASE- d'b.eS.S
DATE, 2.55 1997 CASE d'bcnsa
TDAPE TUM TE9AATUSE SaSS - ASIAn
aER
I 7TEOe.C93 CM
12 3
ACM:-C34
k = 135 W/mK k = 55 WImK DA 12J-997 MM 12—IM7
1414
40 "03
Figure 6.26 Comparison of isotherms for cast iron stave model combined with four different refractory conductivities.
In Figure 6.27 a graphical representation of the maximum hot face temperature as
well as the heat flux is shown relative to the increasing refractory conductivity.
Here it is evident that the influence of the refractory conductivity is limited for
values above 40 W/mK. Graphite is the only refractory material that will cause
possible skull formation, and then only just. Thus, for the chosen furnace inside
conditions, skull formation is highly unlikely for the cast iron stave model.
For cast iron staves it can thus be concluded that the greatest positive change in hot
face temperatures and heat flow is obtained by changing the refractory conductivity
from 2 to 25 W/mK, or from high alumina to silicon carbide. For higher refractory
conductivities the average stave temperatures are increased as well as the
temperature gradient within the stave without any significant influence on possible
skull formation or wear resistance. Sialon bonded silicon carbide with a
conductivity of approximately 25 W/mK is thus chosen as the refractory material to
combine with cast iron staves. This is also in accordance with actual results
obtained by Nippon Steel Corporation [21] and British Steel [23] as discussed in
Chapter 3.
CHAPTER 6 136
1700
1650
.1600
1500
1450
LL UI-Ij
ILes1s1e1s]
I1:sisisJ
l80000ç
175000
170000=
160000 0 20 40 60 80 100 120 140
Refractory conductivity, k,. (WImK)
Figure 6.27 Graphical presentation of heat flux and maximum hot face
temperature for the cast iron stave model combined with
different refractory conductivities.
6.4.3 Copper staves
A similar three-dimensional model is used for the copper staves as was previously
used for the cast iron staves, with the only difference the absence of the separation
layer on the cast in tubing. As discussed in Section 6.2, the fluid dynamic solution
is equal to that obtained for cast iron staves. Except for the higher copper
conductivity, the same material properties and boundary values are applied as for the cast iron staves, as listed in Table 5.4.
Figure 6.28 shows the temperature distribution for the copper stave model
combined with the four refractory conductivities. The illustrations are arranged
clockwise from the lowest to the highest refractory conductivity. A temperature
range of 300 to 1610 K (27 to 1337°C) is selected for all four conductivities in order to compare results on an equal basis.
From Figure 6.28 it is clear that an increase in the refractory conductivity causes the
maximum hot face temperature to decrease significantly. As was the case with the
copper flat plate coolers, only the maximum hot face temperature for the illustration
associated with high alumina, is not below the expected skull formation initiation
temperature. Graphite with a conductivity of 135 W/mK gives the most positive
CHAPTER 6 137
results according to Figure 6.28 with a maximum hot face temperature of only 742 K (469°C).
VWOM, 2.10
CASE W^ TEMPERATURE TEWPE^TURE
I 01W.-M 4^-=
j
.9300 02
CATE: 12 ^ 1997 DATE 12,bn 1997
G.M 74211-032 G^ .002
;4T9 I-W3
02170 ^3 -OW
I 24004+W2
Figure 6.28 Comparison of isotherms for the copper stave model combined
with four different refractory conductivities.
The results can be represented graphically for discussion as shown in Figure 6.29. Both the maximum hot face temperature and the heat flux are illustrated against an increasing conductivity. The rate of decrease in the maximum hot face temperature
slows down as the refractory conductivity approaches the value of the copper stave conductivity.
Similar to cast iron staves, but not to the same extent, the highest positive influence on hot face temperature and heat flow, and thus skull formation, is due to the change from high alumina to silicon carbide. The change from silicon carbide to
semi-graphite has a further significant influence on these parameters. The maximum
hot face temperature is, for instance, lowered with a further 150 degrees.
As for copper flat plate coolers, it is concluded that semi-graphite is the best
refractory material to combine with copper staves. Again this is true if skull
formation as well as mechanical and chemical wear mechanisms are considered.
CHAPTER 6 - 138
Semi-graphite will thus be used in the next section in combination with copper
staves for the comparison with the other cooling systems.
0 20 40 60 80 100 120 Refractory conductivity, kr (WImK)
P4iiSIIi
jiCIIjIjOII
0
410000
w 390000 =
c)L.i.IiIo1
CSjSjIjS]
Figure 6.29 Graphical representation of heat flux and maximum hot face
temperature for the copper stave model combined with different
refractory conductivities.
6.5 Comparison of results for different lining/cooling system combinations
As a best refractory material or refractory conductivity, among those currently
available, has been chosen for the different cooling systems, these lining/cooling
system combinations can now be compared. It is done in relation with possible
skull formation, resistance to chemical and mechanical wear mechanisms, as well as
possible undesirable steam layer formation inside the cooling water channels.
6.5.1 Possible skull form au on
In the previous section the three different cooling systems under investigation were
discussed in relation to four different refractory conductivities. For each of the
cooling systems a most suitable refractory combination has been chosen. Before
these combinations are compared regarding possible skull formation, it is necessary
to discuss the heat transfer results for the different cooling systems in perspective to each other.
CHAPTER 6
This is done graphically by illustrating the differences between the maximum hot
face temperatures as well as the heat fluxes for the three cooling systems relative to
the refractory conductivities. Figure 6.31 is a graphical representation of the
maximum hot face temperatures while Figure 6.32 illustrates the heat fluxes.
1800
1700
1600
1500
1400
1300
1200 CL
1100
1000
900
800
7000 20 40 60 80 100 120 140
Refractory conductivity, k, (Wim K)
Figure 6.31 Comparison of maximum hot face temperatures between the
three chosen cooling system and refractory lining combinations.
Figure 6.32 Comparison of heat flux values between the three chosen cooling
system and refractory lining combinations.
CHAPTER 6 - 140
In Figure 6.31 the maximum hot face temperatures can be seen to be relatively close
at the lowest refractory conductivity of 2 W/mK. Thereafter the differences
increase, with the values for the cast iron stave model levelling out much sooner
due to the lower conductivity of cast iron as discussed earlier. The values for the
copper flat plate cooler model and the copper stave model follow very much the
same pattern, although the values for the copper stave model is overall visibly
lower. Also indicated in Figure 6.31 are the points on the three graphs
corresponding to- the- respectively selected refractory conductivities.
In Figure 6.32 the great difference between the heat flux values for the copper stave
model and the values for the other two models is clearly evident. The heat flux
values for the copper flat plate cooler model and the cast iron stave model are
relatively close with the values for the cast iron stave model again levelling out after
a refractory conductivity of 25 W/mK. Again the values corresponding to the
chosen refractory conductivities are marked on the three graphs.
From the above results it is clear that the copper stave model is most likely to
enhance skull formation. This is according to both the maximum hot face
temperatures and the heat flux values obtained and illustrated. A close second
place, although not as close with the heat flux as with the maximum hot face temperature, is the copper flat plate cooler model.
The heat loss to be expected for the copper stave model according to Figure 6.32
could be a disadvantage, although actual skull formation may reduce this to
acceptable levels. This will be discussed in more detail in Section 6.6. The
relatively high heat flux experienced by the copper stave model is also a strong
indication of its ability to cope with sudden and extreme temperature fluctuations in
front of the hot face. This is in accordance with transient predictions published by
Helenbrook [24] for the temperature rise in copper staves after loss of the skull or accretion layer.
Figure 6.33 illustrates the temperature or isotherm distribution for the three models
as combined with the previously selected refractory conductivities. All three
illustrations are for a temperature range between 300 and 1473 K (27 and 1200°C).
From this comparative illustration it is evident that the copper stave model
combined with a refractory conductivity of 55 W/mK, representing semi-graphite, is
likely to promote skull formation best.
CHAPTER 6 141
=55 W/mK k. =25 W/mK -OATE
22 ^ 1927
t : 3473
, , 2^1^
!
— j
flat ate cooler model. lç=55W/mK
OATh. 22.. 1M7 CASE d;Ane
TEMP8S*TURE KZMn
rrER 44 084*5 B 48*54.002 08418 32*50r002
473Q.503 2 55 7 4-. 003 .2Z34003
I12114.003 I C00Be.003 868508.002 76620e.002 B 51804.002 524604+002 4 1730e.002 3=020 2
b) Cast iron stave model.
c) Copper stave model.
Figure 6.33 Comparison of the isotherm distribution for the three chosen
lining/cooling system combinations.
The copper flat plate cooler model is again in close second place as combined with
the same refractory material chosen for the copper stave model. From Figure 6.33
b) it is evident that the cast iron stave model as combined with a refractory material
representing sialon bonded silicon carbide is not likely to enhance any skull formation.
It is confirmed by the illustration of the isotherms ranged between 1373 and 1473 K
(1100 and 1200°C) for the cast iron stave model as shown in Figure 6.34. As
discussed in Section 5.7 of the previous chapter, skull formation is likely to
commence at temperatures below 1150°C (1423 K). In Figure 6.34, temperatures
in the refractory lining as well as the cast iron ribs are still equal to or above this value.
CHAPTER 6 142
Version 2.10
DATE: 22 Jun 1997 CASE: d:work\staves TEMPERATURE Kelvin
[TER 44 GMAX 1.4665e+003 GMIN 3.0000e+002
I I 1.4730e+003 I 1.4630e+003
= -
—1.4530e+003 - I 1.4430e+003 I 1 1.4330e+003
I 1.4230e+003 LUFI=I 1.4130e+003
1.4030e+003 1.3930e+003 1.3830e+003 1.3730e+003
z X
Figure 6.34 1100 to 1200°C isotherm in cast iron stave model illustrating
small likelihood of skull formation.
It is concluded that a copper stave arrangement combined with semi-graphite will
definitely enhance skull formation more than any of the two other cooling system
arrangements investigated. Copper staves will also cope better with extreme
temperature fluctuations as can be expected in the bosh, belly and lower stack areas
of the blast furnace. The only reservation is the expected higher heat loss through
the copper staves of which the magnitude will be determined in Section 6.6.
6.5.2 Chemical and mechanical wear mechanisms.
As discussed in Section 2.2, high temperatures and heavy temperature fluctuations,
together with chemical attack mechanisms, are responsible for most of the lining
wear experienced in the bosh, belly and lower stack areas of a blast furnace. The
main chemical attack mechanisms are alkali attack, CO disintegration and oxidation. These are also important for wear in the long term.
The reactive kinetics involved depends on the temperature of the lining and on the
presence of catalysts in the refractory, which are found as impurities in the
materials, such as the ash of carbonaceous products. As for the impurities, both the
modern refractory materials selected in this study, namely sialon bonded silicon
CHAPTER 143
carbide and microporous semi-graphite, have high densities and very low levels of
impurities. For example, the density and purity of microporous semi-graphite is
increased by multiple pitch impregnations and rebaking as discussed in Section 2.3.
Lining temperatures on the other hand are important for the initiation and rate of
chemical reactions causing wear. According to Table 2.2 [6], oxidation by 02 is the
first to commence at temperatures above 400°C, followed by CO disintegration at temperatures between 450 and 850°C. -Alkali -and zinc attack ours at temperatures between 800 and 950°C, while oxidation by CO2 and H20 is promoted by temperatures above 700°C.
Chemical attack on the refractory lining is therefore likely to commence at
temperatures between 400 and 500°C. It is thus necessary to keep lining
temperatures close to or below these levels in order to minimise chemical wear and
improve lining life. Figure 6.35 is a comparison of the 400 to 500°C (673 to 773
K) isotherm between the three lining/cooling system combinations.
k = 55 W/mK R04-F lç = 25 W/mK
7 3`20'312 7 D002
77.73001-002
7 a 3D e-002 7 3300 002
7 0=1170300 -OD2
M U-002 00 8733 OD.-002
nat ate cower moaei. lç 55 W/mK
V^dm 2.10
DOSS 22Jo,1897 CASE d.bc$7s20000 IE8PSRArURE KtMfl
7025 .0
2505 84638 -072
0910 30030.02 773200.02 782000.07 753000.02 7 3305.33
00 7320.02 723030252 773030.092 70333.252 89300..02 83230.252
. i 873200.02
b) Cast iron stave model.
c) Copper stave model.
Figure 6.35 Comparison of chemical attack initiation isotherm between the
three chosen lining/cooling system combinations.
CHAPTER 6 144
From Figure 6.35 it is clearly evident that both the copper flat plate cooler model
and the copper stave model will experience much less chemical attack than the cast
iron stave model. Besides the silicon carbide lining, the whole cast iron stave is at
temperatures above the chemical attack initiation isotherm as illustrated. Only a
small section of the copper stave ribs are within the 400 to 500T isotherm, while the rest of the copper stave as well as the whole copper flat plate cooler are below the-criticaF= temperatures. - - -----------
In the flat plate cooler model, the chemical wear initiation isotherm can be seen to
reach the deepest into the semi-graphite lining underneath the same hot face area
where the maximum hot face temperature occurred. For the copper stave model
the penetration of the isotherm is not so deep and more evenly spread. If the
isotherm is assumed to indicate the level of future wear, the copper flat plate model
can be seen to form deeper although less cavities in the lining than the copper stave
model. The copper stave model will form ring cavities in the circumference, vertically separated by the copper ribs.
It is concluded from above results that copper staves in combination with semi-
graphite will resist chemical wear best. This is the result of overall lower and more
uniform lining temperatures. Copper flat plate coolers combined with semi-graphite
will also resist chemical wear well, due to low lining temperatures, although there
are higher differences in lining temperatures. Cast iron staves together with silicon
carbide is not suitable for these high temperature areas of the blast furnace, as high
lining and stave temperatures will definitely enhance chemical wear.
As discussed in Section 2.2, apart from the fact that temperature plays an important
role in chemical attack mechanisms, it also influences mechanical attack
mechanisms. For instance, there is the relation with the thermal expansion of the
lining materials. If the lining material has a high thermal expansion, the thermal
stresses in the bricks may exceed the critical crushing values, or more specific, the
material's cold crushing strain value. Bricks will then start to crack.
Table 2.3 is a comparison of crushing resistance for blast furnace refractory
materials as published by Hoogovens Technical Services [3]. Included in the
comparison is the so-called and previously discussed critical crushing temperature
for different refractory materials. As devised by Hoogovens, this value should
CHAPTER . 145
indicate the temperature above which the refractory bricks are likely to crack if
constrained as in the furnace lining. In Table 6.4 these values are compared with
the maximum hot face temperatures obtained for the three different lining/cooling
system combinations.
Table 6.4 Comparison of critical crushing temperatures with the obtained
maximum hot face temperatures.
Lining/cooling system Critical Max. hot Difference Remarks crushing face temp.
temp.
Copper flat plate 2500°C 768°C 1732°C No brick cracking to coolers combined with (1041K) be expected due to semi-graphite. thermal expansion.
Cast iron staves 170°C 1194°C -1024°C Cracking of bricks to combined with silicon (1467K) be expected due to carbide. thermal expansion
Copper staves 2500°C 5740C 1926°C No brick cracking to combined with semi- (847K) be expected due to graphite. thermal expansion.
From Table 6.4 it is evident that the semi-graphite bricks in both the copper flat
plate cooler model and copper stave model are not likely to experience any
cracking, while the silicon carbide bricks in the cast iron stave model most likely
will. Although it was mentioned in Section 2.3 that different companies or
manufacturers may have different material property data sets, the trend and
magnitude of values rarely differ too much. Therefore it is concluded that, from a
mechanical wear point of view, cast iron staves combined with silicon carbide is not
a suitable lining/cooling system for the high temperature bosh, belly and lower stack
regions of the blast furnace.
Figures 6.36 and 6.37 illustrate plane views of the hot face temperatures for
respectively the copper flat plate cooler model and the copper stave model. The hot
face planes are viewed from the inside of the furnace. Isotherm colours are scaled
separately for each model between the maximum and minimum hot face
temperatures. Indicated in both figures are the actual distance between the
minimum and maximum hot face temperature positions.
CHAPTER 6 146
To furnace top
Semi-graphite Semi-graphite Semi-graphite
A Graphitic ['P11o++ I ramming Nose of copperVersion 2.10 To furnace top material flat plate cooler
DATE: 07 Jul 1997 I CASE: d:\work\flatplates w
TEMPERATURE I k Kelvin
- [TER 205 ------------- GMAX 1.0410e+003
GMIN 3.0000e+002 - 1.0410e+003
9.7857e+002 Serni-graphite L_--J 9.1618e+002
8.5379e+002 7.9140e+002
6 7.2900e+002
.6661e+002 6.0422e+002 5.4183e+002 4.7944e+002 4.1705e+002
x 50(1 mm I
P1
100 mm
Figure 6.36 Plane view of hot face temperatures for the copper flat plate
cooler model.
Cooling water flow direction: lower hot face temperatures due to increasing heat transfer due to
increasing turbulent flow/boundary layer
FFlo++ Version 2.10
DATE: 22 Jun 1997 CASE: d:\work\staves TEMPERATURE Kelvin
hER 44 GMAX 8.4668e+002 GMIN 3.0000e+002
8.4668e+002 8.2999e+002 8.1329e+002 7.9659e+002 7.7989e+002 7.6320e+002
- 7.4650e+002 7.2980e+002 7.1311e+002 6.9641e+002 6.7971e+002
100 mm
ly z x
Figure 6.37 Plane view of hot face temperatures for the copper stave model.
Apart from the fact that the maximum hot face temperature for the copper stave
model is lower than for the copper flat plate cooler model, the difference between
the maximum and minimum hot face temperatures is much lower for the copper
CHAPTER6 147
stave model. While the difference is 167 degrees for the copper stave model, it is
624 degrees for the copper flat plate cooler model. The most important reason for
this is the greater distance between the positions of the maximum and minimum hot
face temperatures for the copper flat plate cooler model.
The result of a high difference in temperatures on the hot face is twofold. Firstly it
will result in greater stress differences and concentrations in the refractory
brickworkk-due4o the greater difference in-expansion from-one spot to another. This
will result in a higher mechanical wear rate for the copper flat plate cooler model.
Secondly, this is an example of the previously mentioned "point cooling effect" of
flat plate cooler arrangements in contrast with the "blanket cooling effect" of stave
cooler arrangements. Due to this the accretion layer or skull is unlikely to have a
uniform thickness and will dislodge easier from the hot face.
It is concluded that the copper stave lining/cooling system investigated will
experience less stress concentrations in the refractory brickwork than for the copper
flat plate cooler system due to smaller differences in the hot face temperatures.
Skull formation and the thickness thereof will also be more uniform and stable.
6.5.3 Possible steam layer formation.
Although boiling heat transfer can be a very powerful heat transfer tool, it is a very
sensitive method which could easily lead to a sudden rise in temperature if not
controlled properly [41]. As the cooling systems under investigation in this study
are not designed for boiling heat transfer to take place, steam formation in the
cooling water channels, especially the formation of a stable steam layer, must be
avoided as far as possible.
Figure 6.38 shows a plane view through the flat plate cooler model nose end nearest
to the hot face. A temperature range between 370 and 400 K (97 and 127°C) is
plotted showing temperatures above 400 K in red and below 370 K in blue.
Cooling water temperatures can be seen to be below 370 K (97°C). The cooling
water pressure inside the cooling channels is usually 200 kPa or higher [8].
According to the international steam tables [42], steam formation should start
taking place at temperatures above ± 120°C (393 K) for water with a 200 kPa
CHAPTER 6 148
pressure. The copper flat plate cooler model is therefore unlikely to experience any
steam formation in the cooling water channels.
Figure 6.38 Steam formation initiation isotherm in copper flat plate cooler
model nose end nearest to hot face.
Figure 6.39 shows a zoomed plane view through the cooling channel in the cast iron
stave model. Colour coding of the temperatures are ranged between 370 and 390 K
(97 and 117°C). Red indicates temperatures above 390 K (117°C) while blue
indicates temperatures below 370 K (97°C).
Temperatures in the boundary layer area can be seen to exceed 390 K (117°C). If
the thickness of the 20 degree illustrated isotherm is compared with the thickness of
the red band between the isotherm and the cooling channel side, a much higher
maximum cooling water temperature can be expected than 120°C. This will lead to
steam formation, as well as a possible stable steam layer. Also interesting is the
higher thickness of the mentioned red band on the hot face side than on the other
side of the cooling channel.
CHAPTER 6 149
Figure 6.39 Steam formation initiation isotherm in cast iron stave model cooling water channel.
For the copper stave model the same isotherm and plane view are plotted as for the
cast iron stave model. Again cooling water temperatures are high enough to
enhance the possibility of steam formation as can be seen in Figure 6.40. The
reason why steam formation is more likely to take place in the staves than in the flat
plate coolers is twofold. Firstly the ratio of cooling water volume to the cooling
element material volume is much higher for the flat plate coolers. Thus, heat is
removed more effectively from the cooling element body which reduces heat build
up and higher temperatures next to the cooling channels.
Secondly, the shape of the cooling channels in the flat plate coolers enhance
turbulent flow to and through the critical outer channel. Water is virtually forced
up against or into the nose channel wall next to the hot face. A stable steam layer is
thus unlikely to form. It can be concluded that copper flat plate coolers are highly
effective in the removal of heat and that steam formation is unlikely to take place.
Furthermore, if steam formation is to be prevented in cast iron as well as copper
staves, much higher pressures and better designs are to be used.
CHAPTER 6 150
7T) .I1o++ Version 2.10
CMW DATE: 12 Jun 1997 CASE: d:\workstaves TEMPERATURE Kelvin
ITER 44 GMAX 8.4668e+002 GMIN 3.G000e+002
3.9000e+002 3.8800e+002
=3.8600e+002= 3.8400e+002 3.8200e±002 3.8000e+002 3.7800e+002
77 3.7600e+002 3.7400e+002
/ 3.7200e+002 3.7000e+002
Cooling water
Y
z x
Figure 6.40 Steam formation initiation isotherm in copper stave model
cooling water channel.
6.6 The influence of skull formation on heat losses and hot face temperatures.
Up to this point in the study skull formation was investigated as determined by the
heat flux and maximum hot face temperature levels. As discussed in Section 5.2, all
three of these parameters are dependent on each other. One of the main advantages
of skull formation, as discussed in Section 5.2, is the decreasing effect on the lining
temperature together with a simultaneous decrease in heat flux. Thus, the
viewpoint of the investigation will now be reversed. The heat flux and lining
temperature are to be investigated as determined by the skull or accretion layer
formation.
The heat flux and lining temperature values are to be compared for the three
different lining/cooling system combinations. Results will be checked against
results as obtained in literature. Finally, the copper stave model incorporating a
skull, as described in Section 5.8, will be investigated.
As discussed in Section 5.5, if a 50 mm skull or accretion layer is assumed to have
formed on the hot face of the lining/cooling system, the heat transfer resistance
from the furnace inside changes from the value obtained in Equation (5.24) to the
CHAPTER 6 151
value obtained in Equation (5.25). The new resistance value obtained in Equation
(5.25), now includes for the resistance due to the accretion layer, and is almost a
seven fold increase from the value obtained in Equation (5.24). The heat
conductivity of the skull or accretion layer is used as discussed in Section 5.5 and listed in Table 5.4.
The results discussed up to now, indicated that a skull or accretion layer is unlikely to form on the cast iron stave model. Furthermore, a 50 mm-thick skull is unlikely - to form on any of the three lining/cooling system models. The main reason for this
is the high furnace inside temperature of Tf= 1500°C used. As discussed in Chapter
1, this was done to evaluate the lining/cooling systems against the extreme operating conditions and fluctuations expected.
According to Helenbrook et al [24], a furnace inside temperature as low as 8710C
(1600°F) was used in a similar study to predict heat flux and lining temperature
values close to actual measured values. Thus, in order to evaluate and compare the
three lining/cooling systems if a 50 mm skull is assumed to have formed, the furnace
inside temperature is lowered to the lower limit of 1200°C as stated in Section 5.5.
Figure 6.41 is a graphical illustration of the maximum lining hot face temperature, T2, for the three chosen lining/cooling system combinations with respect to different
furnace inside scenarios. Three different furnace inside scenarios are investigated.
The values as used up to this point in the study forms the first scenario. Secondly,
the furnace inside temperature is lowered to 1200°C (1473 K). In the final scenario
a 50 mm skull or accretion layer is added to the lower furnace inside temperature.
A sharp drop in the maximum lining hot face temperatures for all three
lining/cooling systems are evident after the 50 mm skull is added. This is due to the
high increase in the overall heat transfer resistance between the furnace inside and
the lining/cooling system. Copper staves remain the cooling elements with, the
lowest maximum lining hot face temperature with a val9e equal to 388 K (1550C).
Copper flat plate coolers stay in a close second place followed by cast iron staves.
It is important to note that the values for the three lining/cooling system
combinations are converging upon each other relative to the change in the furnace inside parameters.
CHAPTER 6 152
I-
300-. T f = 1500CC
(1773T = 1200C (1473 K) T, = 1200°
Furnace inside parameters(1473 K) & 50mm skull
a
1300
a 1100 E C,
C)
900 0
CCD
C
Figure 6.41 Maximum lining hot face temperatures relative to changing furnace inside parameters.
Isotherm distributions for the three chosen lining/cooling system combinations are
shown in Figure 6.42. These results are for the furnace inside scenario
incorporating the lower furnace temperature of 1200°C and a 50 mm skull or
accretion layer. A big difference is observed in the lining temperature between the
higher conductivity copper and semi-graphite combinations and the lower
conductivity cast iron staves and silicon carbide combination.
Figure 6.43 is a graphical illustration of the heat fluxes to be expected for the three
lining/cooling system combinations. The results are again illustrated with respect to
the same furnace inside scenarios used for the maximum lining hot face
temperatures.
As with the maximum hot face temperature, there is a sharp drop in the heat flux
after the 50 mm skull is added for all three models or cases. Especially for copper
staves the drop in the heat flux values is very high. Important though is the fact that
the drop in heat flux values for copper flat plate coolers is higher than the drop for
cast iron staves. As the values for these two lining/cooling systems were relatively
close together before the 50 mm skull was added, the difference in the amount of
change resulted in the copper flat plate coolers having the lowest heat flux value.
CHAPTER 6 153
CRAPTER6 154
flat ate -cooler model. 55 W/mK V-1on 2.10
DATE 30444 1997 CASE dEes TEMPERATURE Aetna
tIER 44 DM95 30810..002 GUN 30530e.002
701E0 2 B B0t.O02
2'E0t-.002 5 BTOe.002 541503.002 501503.002 4 RrOe.002 421503.002 3.91503.002 3 4150e002 3 01003.002
lc=55W/mKL&21O k, 25 [tZcza0Ted FTER M FTER GUN 3 mzv^EMM 0 5 4 BE3 2=0 3 4=e*Mz X _
o) Cast iron stave model.
c) Copper stave model.
Figure 6.42 Isotherm distributions for furnace inside temperature 1200°C
and a 50 mm skull or accretion layer.
WII'I'Is
I.:.I.I.I.1
I;IiIiSjSI
isssIsIsi
0T ,= 12 00°CJ -, r= 1200°C(1473K)(1473& I (1773
Furnace Inside parameters 50a siwU
Figure 6.43 Heat fluxes relative to changing furnace inside parameters.
If Figure 6.41 is viewed together with the results in previous sections, it is evident
that the actual final skull thicknesses will not be the same for all three lining/cooling
system combinations. The skull thickness will be the greatest for the copper staves
followed by the copper flat plate coolers and finally the cast iron staves. Thus, from
Figure 6.42, it follows that the actual final copper staves heat flux value will be
lower relative to the actual final copper flat plate coolers and cast iron staves heat
flux values. The actual final heat flux value for the copper flat plate coolers on the
other hand will be lower relative to the values for the cast iron staves.
From the above it is concluded that the heat flux and maximum lining hot face
= - temperature-values-for-the-copper -flat plate-coolers- are lower than for the castlrdh
staves if a 50 mm skull is added to both models. It is also concluded that the same
is expected for the copper staves if final skull thicknesses were to be observed. As
stated in Table 3.5, MAN GHH observed this lower actual heat flux for copper
staves than for cast iron staves in Blast furnace B, Preussag, Salzgitter [24].
These actual measurements compare well with temperature and heat flux
predictions also done by MAN GHH [24]. It is important to note that these
predictions were made, using a furnace inside temperature of only 871'C (1600°F)
[24] compared to 1200°C, the lower temperature used in this study. The same
furnace inside heat transfer resistance was used as in this study. Thus, much lower
heat flux and hot face temperature values could be expected for copper staves than
predicted.
Another conclusion to be made from the above results is that high conductivity
materials do not necessarily enhance heat losses as was indicated by previous
results. This is due to the lowering of the lining hot face temperatures which in turn
enhances skull or accretion layer formation. The high increase in heat transfer
resistance caused by the accretion layer prevents high heat losses. Lining/cooling
systems consisting of high conductivity materials such as copper and semi-graphite
thus do not necessarily experience higher heat losses than lower conductivity
lining/cooling system combinations such as cast iron staves and silicon carbide.
The copper stave model incorporating a skull or accretion layer, as introduced in
Section 5.8 of the previous chapter, can be used to further prove the statement that
higher conductivities do not necessarily result in higher heat losses. The original
furnace inside scenario with a temperature of 1500°C (1773 K) is used. For the
purpose of comparing the actual heat losses relative to the material conductivities
used, the refractory conductivity in the model is varied between 25 and 135 W/mK.
CHAPTER 1
All other material properties and boundary values are used as discussed in Sections
5.5 and 5.6, and listed in Table 5.4.
Figure 6.44 illustrates a plane view through the copper stave model with a
refractory conductivity of 55 W/mK. As indicated a skull or accretion layer with a
20 mm thickness is included in the model. The difference between T3, the hot face
temperature on the skull, and T2, the lining hot face temperature, is in the region of
700°C. -This=is-extremely -high relative to the temperature difference in-the rest of
the model. Thus, the skull or accretion layer is seen to completely dominate the
heat transfer solution by insulating the lining/cooling system from the furnace inside.
k =55 W/mK J1J7Ij+.4. Version 2.10
DATE: 22 Jun 1997 Furnace shell 7'3 = 1145°C CASE: d:\work\staves
T2 = ±400°C TEMPERATUREKelvin
/ITER 44 GMAX GMIN 3.0000e+002
F .- 1.4165e+003
1.1932e+003 .J 1.0816e+003
I 9.6992e+002 8.5826e+002
.,..., 7.4661e+002 4 6.3496e+002 / 5.2331e+002 / 4.1165e+002
I ,,
Cooling water channel Skull = 20 mm y
z x
Figure 6.44 Plain view of temperature distribution through the copper stave
model with a 20 mm accretion layer.
Graphically, both the skull hot face temperature and the heat flux results for the
different refractory conductivities can be illustrated relative to the skull thickness as
shown in Figure 6.45. The x-axis, representing the skull thickness, crosses the y-
axis, representing T3, at the skull formation initiation temperature of 1423 K
(1150°C). For all three refractory conductivities the skull hot face temperature, T3,
crosses the skull initiation temperature between a skull thickness of 0.01 and 0.03 m
as indicated. Thus, for all three cases a skull of approximately 20 mm is likely to
form.
CHAPTER 6 156
1600
1500
:... -500000
14M 1 -I-__________
1300-
1200
1100 E
1000
900
800.
O01 .02 0iO3 0.04 .0 6
400000 .
350000
=
Temp. - icr =25 W/mK Temp. - = 55 W/mK
- Temp. - icr =135 wImK
Heat- kr = 25 WIm)( Heat - Icr =55 W/mK Heat - Icr = 135 W/mK
: • .;
. .
•. •••.••••.••-.•---- ._ _- . . .
.
700 •: •:: : 250000Skull thickness (m)
Figure 6.45 Maximum skull hot face temperature and heat flux values for
different refractory conductivities relative to skull thicknesses.
In order to evaluate the respective skull thicknesses and associated heat fluxes for
the different refractory conductivities, it is necessary to scale up that area of the graph in Figure 6.45. Figure 6.46 shows the skull hot face temperature and heat
flux results for the skull thicknesses between 0.01 and 0.03 m. The heat flux scale
on the right hand side is reduced to only show values between 300 and 380 kW/m2.
The temperature scale on the left hand side is zoomed in around the skull formation initiation temperature of 1423 K (1150°C).
As indicated in Figure 6.46, the skull thickness is the highest for the highest
refractory conductivity of 135 W/niK and thinner for lower conductivities. Relative
to the different skull thicknesses obtained, the highest refractory conductivity of 135
W/mK has the lowest heat flux or heat loss value. Lower refractory conductivities
have an increasingly higher heat flux or heat loss value. These results are summarised in Table 6.5.
CHAPTER 6 157
1550 ------.. ... 380000 ........ -Temp.-)g= 25W/mK Temp.-io=55W/mK -Terr.-kr135W/mK -Heat -kr=25W/mK
1500 -Heat.- kr=55 WImK -Heat -kr135W/mK
1450. __________ 360000
0.0187 0.02070.022!
350000 E 140(1) * 0,( D3
340000 1350_
- E . ,.- 331000....-.- 330000
Skull thickness (m)
Figure 6.46 Maximum skull hot face temperature and heat flux values for different refractory conductivities relative to different skull thicknesses obtained.
These results obtained for the copper stave model, incorporating an accretion layer
or skull, prove that high conductivity materials in the lining/cooling system does not
increase heat losses. In fact, due to a higher accretion layer thickness, heat losses as
well as lining temperatures are lower than for lower conductivity materials. Thus,
copper for cooling elements and semi-graphite as refractory material are superior
regarding heat losses to lower conductivity materials such as cast iron and high
alumina or silicon carbide.
Table 6.5 Comparison of heat flux values relative to the skull thicknesses obtained for the different refractory conductivities.
Refractory conductivity Skull thickness Heat flux (W/mK) (mm) (kW/m2)
25 18.7 334
55 20.7 331
135 22.1 329
6.7 Conclusion
First of all in this chapter the fluid dynamics solutions for the three-dimensional
models were evaluated according to the method discussed in Section 5.4. All y
values for the different models were inside the acceptable limits as shown in Figures
CHAPTER 6 158
6.8, 6.9 and 6.14. The velocity and pressure profiles for the different three-
dimensional models were discussed separately, including the flat plate cooler case with an inlet velocity of 6 mIs. The predicted pressure drops, especially for the flat
plate cooler models, were close to actual measured results found in literature [18] and known from practical experience.
For all the three-dimensional models the convection heat transfer coefficients
obtained were realistic-and compared well with -the resultsobtainedand verified in Section 5.4. The convection heat transfer coefficient for the copper flat plate cooler
model, with an inlet velocity of 3 m/s, was slightly higher at approximately 6000 W/m2K due to the bends and varying cross sectional areas.
For the case with a 6 m/s inlet velocity, the average value was approximately 10000 W/m2K. The cast iron and copper stave models obtained an average value of approximately 2000 W/m 2K for a 3 m/s inlet velocity. Finally, it was concluded that
the fluid dynamics solutions for all models were satisfactory and acceptable.
For the purpose of investigating the variables influencing skull formation in Section
6.3, the three-dimensional models for the flat plate coolers were used. These
models were useful as the complete flow system is included for a comparison
between different inlet velocities, as well as a comparison between different cooling
system areas. As was the case for the two-dimensional analysis in Section 5.7, the
three variables investigated included the convection heat transfer coefficient by
varying the inlet velocity, the cooling system area and the refractory conductivity.
It was concluded that, as was the case for the two-dimensional analysis in Section
5.7, an increase in refractory conductivity had the greatest positive influence on
skull formation. Although the difference between the successive conductivity
values progressively increased, the corresponding differences between successive values for both T2max and q" decreased. As was the case with the two-dimensional analysis, this was attributed to the decrease in the conductivity difference between
the refractory material and the cooling system material, in this case copper.
A change in cooling water flow rate, and thus the convection heat transfer
coefficient, had a small influence on skull formation. The cooling system area had a
more significant influence on skull formation, although not as high as the refractory
CHAPTER6 159
conductivity. It was also shown that cigar coolers can be used to improve existing
blast furnace lining/cooling systems.
Before the different cooling systems were compared, the best refractory material to
combine with each of the cooling systems were determined. This was done in
Section 6.4 by comparing the maximum hot face temperatures and the heat flux
values for each of the cooling systems combined with the four refractory
-- conductivities--The isotherm distributions were also discussed and compared:
In order to determine the best refractory material to combine with copper flat plate
coolers, the model with a vertical pitch of 300 mm and an inlet velocity of 3 m/s
was used. This is in accordance with the world trends as discussed in Chapters 2
and 3. After considering the influence on skull formation, the chemical and
mechanical wear resistances, as well as actual performances as discussed in
Chapters 2 and 3, it was concluded that semi-graphite is the best refractory material
to combine with copper flat plate coolers.
Only one cast iron stave model as specified in Section 5.8 with a 3 m/s inlet velocity
was used to determine the best refractory material combination. It was concluded
that the greatest possible change in hot face temperatures and heat flux values are
obtained by changing the refractory material from high alumina to silicon carbide.
For higher refractory conductivities the average stave temperatures increased as
well as the temperature gradient within the stave without any significant influence
on possible skull formation or wear resistance. In accordance to current trends,
sialon bonded silicon carbide was chosen as the refractory material to combine with
cast iron staves.
The same model was used for the copper staves as for the cast iron staves, with the
only difference the absence of the separation layer on the cast in tubing. Similar to
cast iron staves, the change from high alumina to silicon carbide had the highest
positive influence, although the change from silicon carbide to semi-graphite was
also significant as it lowered the maximum hot face temperature by a further 150
degrees.
Due to this and for much the same reasons explained for copper flat plate coolers, it
was decided that semi-graphite is the better refractory material to combine with
CHAPTER 6 160
copper staves. Again this was concluded considering skull formation as well as the
mechanical and chemical wear mechanisms.
After the better refractory materials to combine with the different cooling systems
were decided on, these lining/cooling system combinations were compared in
Section 6.5. Possible skull formation, resistance to chemical and meôhanical wear
mechanisms, as well as undesirable steam layer formation inside the cooling
-- channels,-were used as parameters-for the comparison.
It was concluded that a copper stave arrangement combined with semi-graphite will
enhance skull formation more than any of the other two cooling system
arrangements investigated. The maximum hot face temperatures and heat flux
values were used as variables in the comparison as shown in Figures 6.31 and 6.32.
It was also concluded that copper staves will cope best with extreme temperature
fluctuations as can be expected in the bosh, belly and lower stack regions of the
blast furnace. The only reservation was the expected higher heat loss for the copper
staves.
From literature it was concluded that chemical attack on a refractory lining is most
likely to commence at temperatures between 400 and 5 000C. By comparing the 400 and 500'C isotherm, it was concluded that copper staves in combination with
semi-graphite will resist chemical wear best. This was the result of overall lower
and more uniform lining temperatures as visible in Figure 6.35. Copper flat plate
coolers combined with semi-graphite will also resist chemical wear well, while cast
iron staves combined with silicon carbide is not suited for these high temperature
areas of the blast furnace.
By comparing the predicted maximum hot face temperatures with the critical
crushing temperatures for the different refractory materials (Table 6.4), it was
concluded that the semi-graphite bricks in both the copper cooling systems are not
likely to experience any cracking, while the silicon carbide bricks in the cast iron
stave model most likely will. Therefore it was concluded that, also from a
mechanical point of view, cast iron staves combined with silicon carbide is not a
suitable lining/cooling system for the high temperature bosh, belly and lower stack
regions of the blast furnace.
CHAPTER6 161
A further conclusion made regarding mechanical wear mechanisms, was that the
copper staves will experience less and smaller stress concentrations in the refractory
brickwork than for the copper fiat plate coolers. It is due to the smaller difference
in hot face temperatures for copper staves than for copper flat plate coolers as
indicated in Figures 6.36 and 6.37. Skull formation and skull thickness will also be
more stable and uniform due to this.
- --= Steam formation in the-cooling water channels-was-found likely to-take place in the =
stave cooling systems. The reason for this was found to be two-fold. Firstly, the
ratio of cooling water volume to the cooling element material volume is much
higher for the flat plate coolers.
Secondly, the shape and design of the flat plate cooler cooling channels enhance
heat removal especially in the critical nose channel. Copper flat plate coolers are
therefore more effective in the removal of heat and steam formation is unlikely to
take place. Furthermore, it was concluded that if steam formation is to be
prevented in cast iron as well as copper staves, higher pressures and better designs
are to be used.
The influence of skull formation and actual skull thicknesses on hot face
temperatures and heat flux values were investigated via two different routes. First
of all the three chosen lining/cooling system combinations were used incorporating
a 50 mm skull or accretion layer. From this it was concluded that the heat flux is
the lowest for copper flat plate coolers when both a lower furnace temperature of
1200°C and a 50 mm skull were present for all three systems.
Although copper staves had the highest heat flux value, actual skull formation
should be greater due to the lower maximum hot face temperature. This would
reduce the actual heat loss considerably without increasing lining temperatures.
According to similar results and actual measurements found in literature [24],
copper stave cooling systems have lower heat losses and lining temperatures than
cast iron stave cooling systems.
Secondly, in order to prove that higher thermal conductivity materials do not
necessarily enhance heat losses, the copper stave model incorporating the skull or
accretion layer, as discussed in Section 5.8, was used. Three different refractory
conductivities were used. For each of these the actual skull thickness was
CHAPTER 6 162
determined by comparing the maximum hot face temperature with the skull
initiation temperature equal to 1423 K (1150°C).
It was proved that high conductivity materials in the lining/cooling system does not
increase heat losses (Figure 6.46). Due to a higher accretion layer thickness, heat losses as well as lining temperatures were lower for the higher conductivity
materials. Thus, copper for cooling elements and semi-graphite as refractory
- - -=- material -were found- to -=- be-- superior -regarding both heat losses and—lining temperatures.
From all these results discussed and conclusions made in this chapter, it is
concluded that high conductivity materials and an intensive cooling system are
required in the bosh, belly and lower stack regions of the blast furnace. Low hot
face and lining temperatures are hereby ensured, together with thicker and more
stable skull formation to prevent initiation of chemical and mechanical wear of the
refractory lining. The higher conductivities and intensive cooling also removes heat
more effectively during high temperature fluctuations.
Finally it is concluded that cast iron staves combined with silicon carbide is less
suited for the bosh, belly and lower stack regions of the blast furnace. Copper flat
plate coolers or copper staves combined with semi-graphite are better suited for these regions of the blast furnace.
From this temperature and heat transfer centred study it is also concluded that
copper staves are overall better suited than copper flat plate coolers. It is though necessary to consider the better support function offered by the flat plates to the refractory brickwork, as well as the higher risk of steam formation in the cooling channels of copper staves.
CHAPTER 6 163
CHAPTER 7
FINAL CONCLUSIONS, RECOMMENDATIONS AND POSSIBLE FUTURE
WORK
7.1 Introduction
In Chapter 6 the results obtained from the three-dimensional numerical analysis of
the differeritiining/66o1in'stethcombinatioiiwerediscusiëd. Conclusions were
also reached, as was the case for all previous chapters. In this chapter, first of all a
summary of conclusions will be compiled and discussed.
Secondly, some final conclusions and recommendations regarding the suitability of
the different lining/cooling system combinations for the bosh, belly and lower stack
areas of the blast furnace will be made. Finally, possible future work on blast
furnaces, and specifically the lining/cooling system, with the use of numerical
analysis, in this case computational fluid dynamics, will be discussed.
72 Summary of conclusions
In Chapter 1 the increased stress on blast furnaces due to higher productivity and
longer campaign life requirements was discussed. The quality of the lining/cooling
system design, together with the quality of the lining installation and the operation
of the blast furnace, were stated as Important variables influencing the campaign life
under high productivity conditions. It was concluded that the extreme operating
conditions of a blast furnace must therefore be used as boundary values in the
design and evaluation of the lining/cooling system.
Chapter 2 was an investigation and summarisation of the latest developments
regarding refractory linings and cooling systems for blast furnaces. Included in
Chapter 2 was a discussion on both the mechanical and chemical wear mechanisms
active inside the blast furnace. Table 2.8 was compiled as a conclusion on current
combinations of refractory linings and cooling systems used. From Chapter 2
onwards more attention was given to the bosh, belly and lower stack areas as these
areas are subjected to the highest temperature fluctuations and subsequent wear
mechanisms at extreme operating conditions.
CHAPTER 7 164
A comparison between actual performances by different refractory lining and
cooling system combinations was conducted in Chapter 3. Methods of measuring
and predicting these performances were also discussed. From these comparisons it
was already possible to make some conclusions. It was evident that silicon carbide,
graphite and semi-graphite are the superior refractory materials to be used in the
bosh, belly and lower stack regions. Most of the development on refractory linings
are also aimed at these materials.
According to the performance results taken from literature, there was still no clear
advantage for either cast iron staves nor copper flat plate coolers. Copper staves
was identified as a promising new development, specifically with regard to the high
thermal loads experienced in the bosh, belly and lower stack regions. It was
concluded that more attention and development are necessary on copper staves, as
well as practical evidence to confirm the already published results.
From the discussion on the prediction of the performance of lining/cooling systems
in Chapter 3, it was decided to use computational fluid dynamics for this purpose.
This computer intensive numerical method to solve the governing equation of the
process at hand was discussed in Chapter 4. The conclusion was reached that it
was still important to have a sound knowledge and understanding of the governing
flow and heat transfer equations as well as how the numerical solution was
obtained. This was to ensure that the results obtained are still evaluated against all
physical and technical limitations as well as computational errors. For the purpose
of this study, it was decided to use the general purpose CFD-code Flo+± [38].
In Chapter 5 it was confirmed that the CFD-code Flo±+ [38] is capable of obtaining
true and realistic solutions and the numerical models were compiled. First of all the
parameters to be used for the comparison of the different lining/cooling systems
were discussed. This included possible skull formation, hot face and lining
temperatures as well as heat fluxes.
For these parameters, it was confirmed that Flo++ [38] is capable of obtaining
realistic solutions for the purpose of comparing the effectiveness of different
combinations of lining/cooling systems. The different parameters to be compared
were clearly identified as well as the variables influencing them.
CHAPTER 7 165
A two-dimensional comparison revealed that the refractory conductivity had the
greatest influence on the hot face temperature, heat flow and indirectly skull
formation, while the cooling system area was a close second. It was also
determined that a realistic change in the convection heat transfer coefficient of the
cooling water did not have a significant influence. This was investigated by varying
the inlet velocity of the cooling water.
Finally-in Chapter 5-,-six different-threedimensional-numerical models-were created
for the purpose of approximating different lining/cooling systems. These included
three models for copper flat plate cooler arrangements, one for cast iron staves, and
two for copper staves. Unlike the two-dimensional models, these models were
approximations of actual lining/cooling systems. Thus, results from these models
were and can be discussed with regard to values and the effect thereof on the
various parameters.
First of all in Chapter 6 the fluid dynamics solutions for the three-dimensional
models were verified according to the method discussed in Section 5.4. The grid
sizing and configuration were also verified. All/ values for the different models
were inside the acceptable limits. The velocity and pressure profiles for the
different three-dimensional models were discussed separately, including the flat
plate cooler case with an inlet velocity of 6 m/s. The predicted pressure drops,
especially for the flat plate cooler models, were close to actual measured results
found in literature [18] and known from practical experience.
For all the three-dimensional models the convection heat transfer coefficients
obtained were realistic and compared well with the results obtained and verified in
Section 5.4. The convection heat transfer coefficient for the copper flat plate cooler
model, with an inlet velocity of 3 mIs, was slightly higher at approximately 6000
W/m2K due to the bends and varying cross sectional areas.
For the case with a 6 m/s inlet velocity, the average value was approximately 10000
W/m2K. The cast iron and copper stave models obtained an average value of
approximately 2000 W/m2K for a 3 m/s inlet velocity. Finally, it was concluded that
the fluid dynamics solutions for all models were satisfactory and acceptable.
For the purpose of investigating the variables influencing skull formation, the three-
dimensional models for the flat plate coolers were used. These models were useful
CHAPTER 7 166
as the complete flow system is included for a comparison between different inlet
velocities, as well as a comparison between different cooling system areas. As was
the case for the two-dimensional analysis in Section 5.7, the three variables
investigated included the convection heat transfer coefficient by varying the inlet
velocity, the cooling system area and the refractory conductivity.
It was concluded that, as was the case for the two-dimensional analysis in Section -- -
_57 imt e1 frat pitiViriflUënde on
skull formation. Although the difference between the successive conductivity
values progressively increased, the corresponding differences between successive values for both T2m and q" decreased. As was the case with the two-dimensional
analysis, this was attributed to the decrease in the conductivity difference between
the refractory material and the cooling system material, in this case copper.
A change in cooling water flow rate, and thus the convection heat transfer
coefficient, had a small influence on skull formation. The cooling system area had a
more significant influence on skull formation, although not as high as the refractory
conductivity. It was also shown that cigar coolers can be used to improve existing
blast furnace lining/cooling systems.
Before the different cooling systems were compared, the best refractory material to
combine with each of the cooling systems were determined. This was done by
comparing the maximum hot face temperatures and the heat flux values for each of
the cooling systems combined with the four refractory conductivities. The isotherm
distributions were also discussed and compared.
In order to determine the best refractory material to combine with copper flat plate
coolers, the model with a vertical pitch of 300 mm and an inlet velocity of 3 mIs
was used. This is in accordance with the world trends as discussed in Chapters 2
and 3. After considering the influence on skull formation, the chemical and
mechanical wear resistances, as well as actual performances as discussed in
Chapters 2 and 3, it was concluded that semi-graphite is the best refractory material
to combine with copper flat plate coolers.
Only one cast iron stave model as specified in Section 5.8 with a 3 m/s inlet velocity
was used to determine the best refractory material combination. It was concluded
CHAPTER 7 167
that the greatest possible change in hot face temperatures and heat flux values are
obtained by changing the refractory material from high alumina to silicon carbide.
For higher refractory conductivities the average stave temperatures increased as
well as the temperature gradient within the stave without any significant influence
on possible skull formation or wear resistance. In accordance to current trends,
sialon bonded silicon carbide was chosen as the refractory material to combine with
cast-iron staves. -= --
The same model was used for the copper staves as for the cast iron staves, with the
only difference the absence of the separation layer on the cast in tubing. Similar to
cast iron staves, the change from high alumina to silicon carbide had the highest
positive influence, although the change from silicon carbide to semi-graphite was
also significant as it lowered the maximum hot face temperature by a further 150
degrees.
Due to this and for much the same reasons explained for copper flat plate coolers, it
was decided that semi-graphite is the better refractory material to combine with
copper staves. Again this was concluded considering skull formation as well as the
mechanical and chemical wear mechanisms.
After the better refractory materials to combine with the different cooling systems
were decided on, these lining/cooling system combinations were compared.
Possible skull formation, resistance to chemical and mechanical wear mechanisms,
as well as undesirable steam layer formation inside the cooling channels, were used
as parameters for the comparison.
It was concluded that a copper stave arrangement combined with semi-graphite will
enhance skull formation more than any of the other two cooling system
arrangements investigated. The maximum hot face temperatures and heat flux
values were used as variables in the comparison. It was also concluded that copper
staves will cope best with extreme temperature fluctuations as can be expected in
the bosh, belly and lower stack regions of the blast furnace. The only reservation
was the expected higher heat loss for the copper staves.
From literature it was concluded that chemical attack on a refractory lining is most
likely to commence at temperatures between 400 and 500'C. By comparing the
CJIAPTER7 168
400 and 500°C isotherm, it was concluded that copper staves in combination with
semi-graphite will resist chemical wear best. This was the result of overall lower
and more uniform lining temperatures. Copper flat plate coolers combined with
semi-graphite will also resist chemical wear well, while cast iron staves combined
with silicon carbide is not suited for these high temperature areas of the blast
furnace.
By comparing- the predicted—maximum --hot -=face temperatures- with the critical
crushing temperatures for the different refractory materials, it was concluded that
the semi-graphite bricks in both the copper cooling systems are not likely to
experience any cracking, while the silicon carbide bricks in the cast iron stave model
most likely will. Therefore it was concluded that, also from a mechanical point of
view, cast iron staves combined with silicon carbide is not a suitable lining/cooling
system for the high temperature bosh, belly and lower stack regions of the blast
furnace.
A further conclusion made regarding mechanical wear mechanisms, was that the
copper staves will experience less and smaller stress concentrations in the refractory
brickwork than for the copper flat plate coolers. It is due to the smaller difference
in hot face temperatures for copper staves than for copper flat plate coolers. Skull
formation and skull thickness will also be more stable and uniform due to this.
Steam formation in the cooling water channels was found likely to take place in the
stave cooling systems. The reason for this was found to be two-fold. Firstly, the
ratio of cooling water volume to the cooling element material volume is much
higher for the flat plate coolers.
Secondly, the shape and design of the flat plate cooler cooling channels enhance
heat removal especially in the critical nose channel. Copper flat plate coolers are
therefore more effective in the removal of heat and steam formation is unlikely to
take place. Furthermore, it was concluded that if steam formation is to be
prevented in cast iron as well as copper staves, higher pressures and better designs
are to be used.
The influence of skull formation and actual skull thicknesses on hot face
temperatures and heat flux values were investigated via two different routes. First
of all the three chosen lining/cooling system combinations were used incorporating
-=
CHAPTER 7 169
a 50 mm skull or accretion layer. From this it was concluded that the heat flux is the lowest for copper flat plate coolers when both a lower furnace temperature of
1200°C and a 50 mm skull were present for all three systems.
Although copper staves had the highest heat flux value, actual skull formation
should be greater due to the lower maximum hot face temperature. This would
reduce the actual heat loss considerably without increasing lining temperatures.
----=--Accordingto similar -results -and actual-measurements found in literature [24]
copper stave cooling systems have lower heat losses and lining temperatures than
cast iron stave cooling systems.
Secondly, in order to prove that higher thermal conductivity materials do not
necessarily enhance heat losses, the copper stave model incorporating the skull or
accretion layer, as discussed in Section 5.8, was used. Three different refractory conductivities were used. For each of these the actual skull thickness was
determined by comparing the maximum hot face temperature with the skull
initiation temperature equal to 1423 K (1150°C).
It was proved that high conductivity materials in the lining/cooling system does not
increase heat losses. In fact, due to a higher accretion layer thickness, heat losses as
well as lining temperatures were lower for the higher conductivity materials. Thus,
copper for cooling elements and semi-graphite as refractory material were found to
be superior regarding both heat losses and lining temperatures.
7.3 Final conclusions
From all of the above conclusions, some final conclusions can be made. First of all,
in the bosh, belly and lower stack regions of the blast furnace, the cooling system is
of utmost importance since the wear reactions depend strongly on the lining
temperatures. Secondly, higher heat conductivity is a superior property in these
regions of the blast furnace for three basic reasons:
. the lowering of the refractory lining hot face temperature to minimise chemical
as well as mechanical wear,
• the resistance to temperature shocks is increased, and
• the probability of forming a stable skull on the hot face is higher.
CHAPTER 7 170
According to the "black" or "thermal" solution as discussed in Chapter 2, semi-
graphite is a suitable refractory material for use in the bosh, belly and lower stack
regions, together with a high conductivity and intensive cooling system, because:
Lining temperatures as well as the iron and ash content are very low. Hence,
chemical wear mechanisms as well as the kinetics of the reactions are limited and
slow in their occurrence. Mechanical wear is reduced due to lower thermal expansion.
• —Hot face temperatures-are lowiieceptomotingthe ftmationOfá stable skülFör
accretion layer. Cooling losses are kept low while erosion of the lining is limited.
. If temperature fluctuations occur in periods of irregularity, the lining/cooling
system can deal with this. Lining wear in these periods is minimised.
Thus, cast iron staves combined with silicon carbide is less suitable for these regions
of the blast furnace. Copper flat plate coolers and copper staves combined with
semi-graphite are better suited for these regions. Copper flat plate coolers have the
following advantages over copper staves:
• Steam formation in the cooling water channels is less likely to occur.
• Better physical support is given to the refractory brickwork.
Copper staves have the following advantages over flat plate coolers:
• Hot face and lining temperatures are lower and thus skull formation should be better.
• High heat fluxes and temperature fluctuations can better be dealt with.
• Temperature differences on the hot face are lower. This will result in less
tension in the brickwork as well as a more uniform skull or accretion layer.
Consideration of the strengths and weaknesses of both copper flat plate coolers and
copper staves lead to the conclusion and recommendation that a combined solution
should give better results than the optimum of the respective systems. This was
also proposed, although between copper flat plate coolers and cast iron staves, by
Kramer et al [43]. Figure 7.1 is a illustration of such a possible combination.
Future work on this together with other possible future work are discussed in
Section 7.4.
CHAPTER 7 171
Figure 7.1 Combined flat plate cooler and stave cooler system for blast furnace cooling 1431.
7,4 Possible future work
If the complete blast furnace is considered, the possibilities for future work using
numerical analysis are numerous. These include, but are not limited to, the gas flow
through and combustion inside the furnace shaft [44], the analysis of combustion
and heat transfer inside the hot blast stoves [45], and the flow patterns of hot metal
in the hearth [46], as well as the erosion thereof [47].
Regarding the cooling system and refractory lining, analysis of hearth cooling with
the use of spray cooling on the sides as well as underhearth cooling can also be
considered [48]. Further to this study, the possibilities of transient solutions, the
simulation of skull formation, as well as the combination of flat plate coolers and
staves can be investigated.
74.1 Transient solutions
CHAPTER 7 172
In this study only steady state solutions were considered. If the effect of high
temperature fluctuations in front of the lining hot face is to be considered, transient
solutions are very useful and appropriate. With a transient solution or investigation,
the rate of increase in hot face temperatures after the loss of a skull or accretion
layer can be compared with the critical temperature fluctuations for spalling as were
summarised in Table 2.4 [3].
This comparison will indicate-whether or -not the chosen refractory lining —can cope -
with these temperature fluctuations. Similar transient studies were conducted by
Tijhuis [2] and Helenbrook et a! [24], although not for the purpose of comparing
copper flat plate coolers and copper staves.
7.4.2 Simulation of skull formation
It is possible by use of user coding to numerically analyse or simulate skull
formation. If the skull is given a constant conductivity value, the thickness thereof
can be varied depending on the skull initiation temperature by using flexible or
sizeable grid cells. Thus, the grid cells forming the skull are stretched to increase
skull thickness or crimped to reduce skull thickness. The skull initiation isotherm
forms the boundary of these cells and determines whether stretching or crimping are
to take place. In this the latent heat of phase transformation should also be
included.
For steady state solutions this will result in a skull with a varying thickness along
the hot face. Thus, for comparative studies between flat plate coolers and staves,
the influence of both "blanket" and "point" cooling on uniform skull formation can
be determined.
Z4.3 Combination offlat plate coolers and staves
In Figure 7.1 a possible combination of flat plate coolers and staves in the same
cooling system was illustrated as suggested by Kramer et al [43]. The suggestion
was for copper flat plate coolers to be combined with cast iron staves. As stated in
Section 7.3 as a final recommendation, consideration of the strengths and
weaknesses of both copper flat plate coolers and copper staves lead to the
conclusion that a combination should give better results.
CHAPTER 1
In order to accommodate both flat plate coolers and staves as illustrated in Figure
7. 1, it will probably be necessary to increase the vertical pitch between flat plates to
at least 600 mm. It is interesting to note that this will reduce the number of flat
plate coolers required by the same number of copper staves required. Thus, costs
are not necessarily higher and no extra cooling water will be required.
Furthermore, the width of the refractory lining and the depth of the flat plates can also be reduced to some extent.
To conclude, numerical analysis, and more specifically computational fluid
dynamics, can be used, as done in this study, to investigate, compare, predict and
design lining/cooling systems for blast furnaces in order to ensure longer campaign lifes and better performances.
CHAPTER 7 174
REFERENCES
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stack. Iron and Steel Engineer, August 1996, pp 43-48.
3. Tijhuis, G;J., Bleijendaa1 NG.J-; BF cooling--and- refractory -technology:
Steel Times International, March 1995, pp 26 - 27.
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10 Bauer, J.M., Schmidt-Whitely, R.D., Dumas, D., Du Mesnildot, D., Kiehl,
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11 Konig, G.; Grundsatzliche Uberlegungen zur if-Zustellung von Hochofen.
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12 Hirota, T.; Silicon carbide refractories for blast furnaces. Taikabutsu
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13 Fickel, A.; Detrimental effects to specially banded SiC-refractories. Spre WG
IV April 1985.
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14 Vogel, R., Koen, W., Van Rijn, P.; Gro3reparatur und modernisierung -
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15 Lamont, P.H.; Synthetic carbon and graphite - a modern material for the
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von HochOfen im- Hinblick auf Kohienstoff- und Graphitprodukte. XkTV
Inlerntionales Feuerfest-Kolloquium, October 1982.
17 Hardy, C.W.; Future refractory requirements for the steel industry. Sepc.
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18 SeligmUller, HT.; Aspects of improving blast furnace cooling. Consistent
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19 Heinrich, P., Hille, H., Kraft, W., Reichenstein, E.; HochOfenkuhlung mit
unterschiedlichen systemen - Entwicklung, stand, betriebsergebnisse und
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20 Heinrich, P., Hille, H., Richert, K.; Hochofenpanzerkuhlung - Bauliche
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21 Nippon Steel Corporation; Stave cooling for prolonged blast furnace
campaigns. Steel Times International, March 1995, p 30.
22 Kobayashi, K., Matsumoto, T., Yanagisawa, K.; Technology for prolonging
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23 Carmichael, I.F.; New concepts and designs for blast furnace linings and
cooling systems. Iron and Steel Engineer, August 1996, pp 3 5-42.
24 Helenbrook, R.G., Kowalski, W., Grosspietsch, K., Hille, H.; Copper staves
in the blast furnace. Iron and Steel Engineer, August 1996, pp 30-34.
25 Hebel, R., Steiger, R., Jeschar, R., Streuber, C.; Temperatures in the blast
furnace refractory lining - Theoretical calculations, measurements and
determination of the wear profile. Ironmaking Conference Proceedings,
1995, pp 101-111.
26 Van Vlack, L.H.; Materials for Engineering - concepts and applications.
World student series, Addison-Wesley Publishing Co., 1982.
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27 Anderson, D.A., Tannehill, J.C., Pletcher, R.H.; Computational fluid
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Corporation, 1984.
28 Troscinski, M.A.; How fluid software provides solid results. Machine
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-- 29Dvorak,= P; Better than ==the biggest wind tunnel.- Machine Design,
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30 Ilegbusi, O.J.; Application of the two-fluid model of turbulence to tundish
problems. ISJflnternasional, Vol. 34, No. 9, 1994, pp 732-738.
31 Chatterjee, A., Ajmani, S.K.; Optimising fluid flow in the tundish. Steel
Technology International, 1994, pp 155-1160.
32 Chen, H.S., Pehlke, R.D.; Mathematical modeling of tundish operation and
flow control to reduce transition slabs. Metallurgical and Materials
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34 Zhu, M., Inomoto, T., Sawada, I., Hsiao, T.; Fluid flow and mixing
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35 Lea, C.J.; Computational modelling of mine fires. The Mining Engineer,
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36 Rhodes, N., Bell, R.J.; CFD analysis uncovers ways to lower condenser
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37 Patankar, S.V.; Numerical heat transfer and fluid flow. Series in
computational methods in mechanical and thermal sciences, McGraw-Hill
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38 Softflo; Flo++ User's Manual. Softflo cc, 1995.
39 Kramer, H.D., Seligmuller, H.T.; Physical-theoretical principles of blast
furnace cooling. Stahl undEisen, 1976, pp 145-153.
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40 Holman, J.P.; Heat Transfer. Mechanical Engineering Series, McGraw-Hill
Book Co., 1989.
41 Rohsenow, W.M., Hartnett, J.P., Ganic, E.N.; Handbook of heat transfer
fundamentals. McGraw-Hill Book Co., 1985.
42 Van Wylen, G.J., Sonntag, R.E.; Fundamentals of classical thermodynamics,
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43 Kramer, H., Streuber, C.; HochofenpanzerkUhlung - theoretiche grundlagen.
Stahl und Eisen, Vol. 106, No. 5, 1986, pp 197-203.
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45 Shklyar, F.R., Solomentsev, S.L., Korshikov, V.D.; Calculation of
temperature fields in hot blast stoves with internal off centre combustion
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model of steady state heat transfer in blast furnace hearth and bottom.
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REFERENCES 178
APPENDIX A INPUT FILE FOR TWO-DIMENSIONAL CONDUCTION MODEL WITH
HIGH CONDUCTIVITY DIFFERENCES
II 2Dana: Flo++ input file
reset
cgro 0 -= --mcre050100-i000500-i0001
cgro 1 mere 50 450 20 0 500 25 0 1000 1 cgro 2 mere 50 450 20 500 1000 25 0 1000 1 mere 450 50050100050010001
vmer all vcom all energy on
bzone 1 west bzone 2 east
cgdef 0 0 cgdef 1 1 cgdef 2 2 mdef 0 solid mdef I solid mdef 2 solid
material 0 init0000 130000 cond const 10
material I init0000 100000 cond const 25
material 2 mit 0 0 0 0 800 0 0 cond const 350
energy on
bgdef I wall
fixed 1423
bgdef 2 wall
APPENDIX A 179
fixed 303 .00033
vmerge all vcom all
cony .000 1 rela .7 .7 .7 .2 1 .7 .7 iter 200 10
wmesh 0.001 wall y wdef save 1 pity hidd cp
APPENDIX A 180
APPENDIX B INPUT FILE FOR TWO-DIMENSIONAL MODEL OF CONVECTION
HEAT TRANSFER ON A FLAT PLATE
II skull : Flo++ input file
reset cgro 2 mcre 0 450 18 0 1000 50 0 1000 1 cgro-3 - mere 450 500 15 0 1000 500 1000 1
cset none cset cgroup 3 view 0 -1 pity hidd cp bview 3 view 0 1 cp bview 4
vmer all vcom all energy on
bzone 1 west bzone 2 east bzone 2 front bzone 2 back
cgdef 2 2 cgdef 3 3 mdef 2 solid mdef 3 fluid
material 2 mit 0 0 0 0 800 0 0 cond const 350
material 3 mit 0 1.5 003200.001 0.001 pran 3.75 cond const 0.642 dens const 989 vise const .00058 pref 100000 cmax turb on
APPENDIX B 181
energy on
bgdef 1 wall
fixed 1773 0.00435
bgdef 2 symm
bgdef 3 inlet 0=0 1.50989300 .001 .001
bgdef 4 outlet I
cset none cset all
vmerge all vcom all
mom cmax cony .0001 rela .7 .7 .7 .2 1 .7 .7 iter 200 10
wmesh 0.001 wall y wdef save I view 0 cset none cset all pity hidd screen reverse cp
APPENDIX B 182
APPENDIX C INPUT FILE FOR TWO-DIMENSIONAL MODEL FOR ]INVESTIGATING
THE INFLUENCE OF DIFFERENT VARIABLES ON SKULL FORMATION
II skull: Fio++ input file
reset
cgro1 - mcre0400 16050025010001 cgro 2 mcre0450 18500100025010001 mcre 400 450 2 0 500 25 0 1000 1 cgro 3 mere 450 500 15 0 1000 50 0 1000 1
cset none cset cgroup 3 view 0-1 pity hidd cp bview 3 view 0 1 cp bview 4
vmer all vcom all energy on
bzone I west bzone 2 east bzone 2 front bzone 2 back
cgdef 11 cgdef 2 2 cgdef 3 3 mdef 1 solid mdef 2 solid mdef 3 fluid
material I init0000 100000 cond const 55
material 2 mit 0 0 0 0 8000 0
APPENDIX C 183
cond const 350
material 3 mit 0 3 0 0 320 0.001 0.001 pran 3.75 cond const 0.642 dens const 989 visc const .00058 pref 100000 915
-- ---=turb=on
energy on
bgdef 1 wall
fixed 1773 0.00435
bgdef 2 symm
bgdef 3 inlet 0 0 3 0 989 300.001 .001
bgdef 4 outlet 1
cset none cset all
vmerge all vcom all
moni 915 cony .0001 rela .7 .7 .7 .2 1 .7 .7 iter 200 10
wmesh 0.001 wall y wdef save 1 pity hidd cp
APPENDIX 184
APPENDIX D INPUT FILE FOR THREE-DIMENSIONAL MODEL OF COPPER FLAT
PLATE COOLER ARRANGEMENT WITH A 300 mm VERTICAL PITCH
reset
//***** Define values for specific nodal points of the copper shell outside
-- --#def v2 2 Drawing 1 #defvbb 24 Drawing 1 #defvbe 32 Drawingi
defvtop 40 Drawingi
/1* * * * * *Create nodes for copper shell of outside water channel as shown in drawing
vi v v2 0 22 vvini 0277 vint v2 vin vcop 3 vtop vran 1 vin 1 8.5
#defvm vmax vvbbO 577
vvm+vini +225 577
vint vbb vmax 1 vbb + vtop 40 vintvini vbb 12 vini + ii 340
csys 0 local 2 cyli 100 577 0
vcop9 1 vranvbbvmaxvtopo-1i.25
csys 0
• vtop 226.5 677
• vtop * 3 226.5 652
vint vtop vmax 1 2 * vtop 40 vint vbe vtop 7 vbe + 1 1 3 40
/1* * * * * * *Drawing 1: Nodes created for copper shell of outside water channel********* VP
//*******Create nodes for copper rib between outside and first inside water channel as shown in drawing 2********
APPENDIX D 185
#defvl vtop * 9 + 1 vvl 57 vvmax+1 5722 #def vm vmax vvl +v[fll 57277 vint vm vmax #defvm vmax vcop 3 vtop vran vi vmax 1 5
—esysC- - - local cart 57277000-1.528
vvl +25 0285.1 vint vm vi +25 vcop 3 vtop vran vm + 1 vi + 25 1 5
csys 0 local 4cyli 115 562
vcop 8 1 vran vi + 25 vmax 40 0 -12.857143
csys 0
#defvt vtop * 10 vvt 226.5 612 • vtop * 12 226.5 602 vint Vt vmax 1 Vt +40 40 vintvt-7vt6vt-6 1340
/1* * * * * * *Drawing2: Copper rib between outside and first inside water channel*********** VP
//*******Create nodes for outer water channel as shown on drawing 3********
#defvt vtop * 2 #defvtl Vtop * 3 vintvt+i vi 6vtl + 140 40 1
#defvl vtop * 18 + 1 vvl 139 vvl + 1 139 22 vvl + 29 139 522 vvl+5 139102 vcop 3 40 vran vi vi + 29 1 5 vintvl + lvi +53 vi +21340 vintvl +5 vi +29 23 vi +61 3 40 0.95
csys 0
APPENDIX D 186
local 5 cyli 169 522 0
vcop5 I vranvi + 29 vmax 40 0 -22.5
csys 0
vvi +39 226.5 552
vcop340vranvl+39v1 +3910-5 vintvi +33 vi +395v1 +341340
/1* * * * *Drawing3: Outer water channel included between copper* * * * * * * * * * * * VP
//*******Create nodes for second cooling water channel, as well as part of inner water channel, and for mouldable refractory material as shown on drawing 4************
#defvtvtop* 11 #defvti vtop * 12 vintvt+ lvi 6vtl + 140 40 1
#defvnvtop * 22+1 #defvnl vtop * 22 + 2 #defvn2 vtop * 22 + 27 #defvn3 vtop * 22 + 32 #defvn4 vtop * 22 + 40 #defvn5 vtop * 22 + 17 vvn 167 vvni 16722 vvn2 167486 • vn3 167 525 • vn4 226.5 525 vvn5 167350 vint vni vn5 14 vnl + 1 1 vint vn5 vn2 9 vn5 + II vint vn2 vn3 4 vn2 + I I vint vn3 vn4 7 vn3 + 1 1 vintvtop*20+lvn ivtop*21+ 140 40 1
#defvm vmax
v vm * 5 + 1 -28.5 #def vi vmax vvl+23 -28.5 577 vvi+27 -28.5 677 vvi+31 100677 vint vi vi + 23 22 vi + 11 vintvi+23v1+273v1+241 vintvl+27v1+31 3 vi+28 I
APPENDIX 1) 187
vint 1 vi I vm + 1 vm 32 1
vcom all #def vs vmax
//*******Drawing4: Second cooling water channel, part of inner channel, and mouldable refractory material** * * * * * VP
//*******Copy current node set in the z-direction to include for one quarter of the planned model as shown on drav.iing5*****
vcop 5 vs vran 1 vs 1 0 0 3.5 vcop 2 5 * vs vran 1 vs 10 0 20 vcop 2 6 * vs vran 1 vs 1 0 0 30 vcop 2 7 * vs vran 1 Vs 1 0 0 46.75
vcop 2 8 * vs vran 1 vs 1 0 0 90 vcop29*vsvranlvsl 00153.25 #defv3 vmax cgroup 0
//*******Drawjng5: Node set for one quarter of final planned model, excluding part of inner channel************* view 10 0 VP
/1* * * * * *Create first layer of cells in the z-direction, as well as all cell layers for part of the inner channel as shown in drawing 7*****
cvs -31 Vs -63 vs -62 vs -302 * vs -312 * vs -632 * vs - 62 2 * Vs -30 ccop 311 cran 111 #def cm cmax cvm+1 12 vm + 2 vs + vrn + 1 vs+ 1 vs+2vs+vm+2 ccop 31 1 cran cmax cmax 1 #def cr cmax c14142 2 vs + 1 vs+41 vs+42vs+2 #def ci cmax ccop 39 1 cran cmax cmax 1 ccop 22 40 cran ci cmax I #def cp emax cgroup 3 mcreate 167 226.5 8 022 1 0 3.5 1 cgroup 0 mcreate 167 226.5 8 22 350 15 0 3.5 1 mcreate 167 226.5 8 350 486 10 0 3.5 1 mcreate 167 226.5 8 486 525 5 0 3.5 1 4defbce cmax cgroup 3 mcreate 167 226.5 8 0 22 1 3.5 7 1
APPENDIX D 188
cgroup 0 mcreate 167 226.5 8 22 350 15 3.5 7 1 mcreate 167 226.5 8 350 486 10 3.5 7 1 mcreate 167 226.5 8 486 525 5 3.5 7 1 cgroup 3 mcreate 167 226.5 8 0 22 1 7 10.5 1 cgroup 0 mcreate 167 226.5 8 22 350 15 7 10.5 1 mcreate167226.58350486 10710.51
=mcreate467-226=5-8486=52-5=5-7=10-5=1-=--==-=-= cgroup 3 mcreate 167 226.5 8 0 22 110.5 14 1 cgroup 0 mcreate 167 226.5 8 22 350 15 10.5 14 1 mcreate 167 226.5 8 350 486 10 10.5 14 1 mcreate 167 226.5 8 486 525 5 10.5 14 1 #defbcec cmax cgroup 3 mcreate 167 226.5 8 0 22 114 20 1 cgroup 0 mcreate 167 226.5 8 22 350 15 14 20 1 mcreate 167 226.5 8 350 486 10 14 20 1 mcreate 167 226.5 8 486 525 5 14 20 1 cgroup 3 mcreate 167 226.5 8 0 22 1 20 30 1 cgroup 0 mcreate 167 226.5 8 22 350 15 2030 1 mcreate 167 226.5 8 350 486 10 20 30 1 mcreate 167 226.5 8 486 525 5 20 30 1 #defbcel emax cgroup 3 mcreate 167 226.5 8 0 22 1 30 46.75 1 egroup 0 mcreate 167 226.5 8 22 350 15 30 46.75 1 mcreate 167 226.5 8 350 486 10 30 46.75 1 mcreate 167 226.5 8 486 525 5 30 46.75 1
defbce2 cmax cgroup 3 mcreate 167 226.5 8 0 22 1 46.75 90 1 cgroup 0 mcreate 167 226.5 8 22 350 15 46.75 90 1 mcreate 167 226.5 8 350 486 1046.75 90 1 mcreate 167 226.5 8 486 525 5 46.75 90 1 cgroup 3 mcreate 167 226.5 8 0 22 1 90 153.25 1 cgroup 0 mcreate 167 226.5 8 22350 15 90 153.25 1 mcreate 167 226.5 8 350 486 10 90 153.25 1 mcreate 167 226.5 8 486 525 5 90 153.25 1
APPENDIX D- 189
#def cml cmax
//*******Drawjng7: First layer of cells in the z_direction******* view 0 cp
,//******modify and copy cells - shown on drawing816*******
= -in z-direction as shown in drawing 8******* cgroup 3 cgmod óran 1 cr 31 cgmod cran cr + 1 cp 39 ccop 9 vs cran 1 cp 1 exist //*copy cells to 4 levels****
/I******drawings: Show cells as copied in zdirection******* view I pltype hidden cp
vcomp all vmerge all ccomp all
//******py cells and reverse numbering sequence of cells on x-axis to include half final planned model as shown in drawing 9******** csys 0 local 6 cart -28.5 0 0 csys 6
#defvne vmax #def mcm cmax vref 1 vmax all ccop 2 vne cran I cmax 1 exist crev I cran mcm + 1 cmax 1
csys 0
//*****drawing9: Two halfs of flat plates as seen from top - mirror images******* cp
//*****py cells and reverse numbering sequence of cells on z-axis to include for flat plate at 300mm vertical pitch as shown in drawing 10
local 7 cart -28.50 153.25 csys 7
APPENDIX D 190
#def men cmax #defv4 vmax vref 3 vmax all ccop 2 v4 cran 1 cmax 1 exist crev 3 crari men + 1 cmax 1
/I** *drawing 10: 3-D view of model with final number of cells* ******** view 12 3 cp
csys 0
H** *modify cells to cell group for mouldable refractory material as shown on drawing 1l
#def ncn men + mcm cgroup 2 egmod cran 2 cm 1 cgmod cran 2 + cm cm + cml 1 cgmod cran 2 + cml + cp cm + cml + cp 1 repeat 3 0 cp cp 0 egmod cran 2 + ncn cm + ncn 1 cgmod cran 2 + cm]. + ncn cm + cml + ncn 1 cgmod cran 2 + cml + cp + ncn cm + cml + cp + nen 1 repeat 3 0 cp cp 0 cgmod cran cm + 2 cr 1 egmod cran cm + 2 + cml cr + cml I cgmod cran cm + 2 + cml + cp cr + cml + cp 1 repeat 3 0 cp cp 0 egmod cran ncn + cm +2 ncn + cr I cgmodcranncn+cm+2+cmlncn+cr+cml 1 cgmod cran cm + 2 + cml + cp + ncn cr + cml + cp + ncn 1 repeat 3 0 cp cp 0 cset none cset gxyzran 0 -29 500 -10 700 29 47 cset gxyzran 0 -500 -28 -10 700 258 278 cgmod cset
/I** *drawing 11: Mouldable material visible in light btue******* eset all view Ill cp
//****modify cells to cell group for water as shown on drawing l3**
cset none cset cran I bce 1 cset cran ncn + I ncn + bce I cgroup I
APPENDIX 191
cgmod cran 141 413 1 cgmod cran 492 764 1 cgmod cran 843 1168 1 cgmod cran 141 + cml 413 + cml I repeat 2 0 cp cp 0 cgmod cran 492 + cml 764 + cml 1 repeat 2 0 cp cp 0 cgmod cran 843 + cml cp + cml 1 repeat 2 0 cp cp 0
-cgmod-cran=bce+-=1-bcec-1=----=---= - cgmod cran 141 + ncn 413 + ncn 1 cgmod cran 492 + ncn 764 + ncn 1 cgmod cran 843 + ncn 1168 + ncn 1 cgmod cran 141 + cml + ncn 413 + cml + ncn 1 repeat 2 0 cp cp 0 cgmod cran 492 + cml + ncn 764 + cml + ncn 1 repeat 2 0 cp cp 0 cgmod cran 843 + cml + ncn cp + cml + ncn 1 repeat 2 0 cp cp 0 cgmod cran bce + 1 + ncn bcec + ncn 1
/1* * * * drawing 13: Water channels indicated by green cells* * * * * cp
//****modif,, cells to cell group for copper as shown in drawing 14****
#defbced bce - cp cgroup 4 cgmod cran 63 140 1 cgmod cran4l4 491 1 cgmod cran 765 842 1 cgmod cran 928 1120 8 repeat 3 0 bced bced 0 cgmod cran 63 + cml 140 + cml 1 repeat 2 0 cp cp 0 cgmod cran 414 + cml 491 + cml 1 repeat 2 0 cp cp 0 cgmod cran 765 + cml 842 + cml 1 repeat 2 0 cp cp 0
cgmod cran 63 + cml + cp + cp + cp cml + cp + cp + cp + cp 1 repeat 1 0 cp cp 0 cgmod cran bcec + 1 bcel 1
cgmod cran 63 + ncn 140 + ncn 1 egmod cran 414 + ncn 491 + ncn 1 cgmod cran 765 + ncn 842 + ncn 1 cgmod cran 928 + ncn 1120 + ncn 8 repeat 3 0 bced bced 0
APPENDIX D 192
cgmod cran 63 + cm + ncn 140 + cm + ncn 1 repeat 2 0 cp cp 0 cgmod cran 414 + cm + ncn 491 + cm + ncn I repeat 2 0 cp cp 0 cgmod cran 765 + cml + ncn 842 + cml + ncn I repeat 2 0 cp cp 0
cgmod cran 63 + cml + cp + cp + cp + ncn cml + cp + cp + cp + cp + ncn 1 repeat 1 0 cp cp 0
- cgmodcran bcec + 1 + ncnbcel-+ ncn-1 -
cset none cset all
/f****Drawingl4: Copper ribs between water channels shown in magenta****** view 12 3 cp
ll******modifr copper cells to water cells in order to connect water_channel*****
cgroup 1 cgmod cran 766 769 1 cgmod cran 805 808 1 cgmod cran 766 + cml 769 + cml 1 repeat 2 0 cp cp 0 cgmod cran 805 + cml 808 + cml 1 repeat 2 0 cp cp 0
cgmod cran 415 + ncn 417 + ncn 1 cgmod cran 454 + ncn 456 + ncn 1 cgmod cran 415 + ncn + cml 417 + ncn + cml 1 repeat 2 0 cp cp 0 cgmod cran 454 + ncn + cml 456 + ncn + cml 1 repeat 2 0 cp cp 0
I/**** *drawing l5: Connection of water channels in two quarter flat plates******** cset none cset cran I bce I cset cran ncn + 1 ncn + bce I view 0 cp
H* *modify water cells to copper cells in the in-and outlet as shown in drawing 16******
cgroup 4 cgmod cran 141 141 39 cgmod cran 375 375 39
APPENDIX D 193
cgmod cran 492 882 39 cgmod cran 921 927 1 repeat 3 0 bced bced 0 cgmod cran 141 + cml 141 + cml 39 repeat 2 0 cp cp 0 cgmod cran 375 + cml 375 + cml 39 repeat 2 0 cp cp 0 cgmod cran 492 + cml 882 + cml 39 repeat 2 0 cp cp 0
cgmodcran 11 + ncn 882 + ncn 39 cgmod cran 926 + ncn 927 + ncn 1 repeat 3 0 bced bced 0 cgmod cran 141 + ncn + cml 882 + ncn + cml 39 repeat 2 0 cp cp 0
//*****drawjngl6: Inlet and outlet in different flat plates**** cp view 1 2 3 cp
vmerge all 0.01
pitype hidden
//* Boundary cells for inlet************ cset none cset cran 180 336 39 cset cran 180 + cml 336 + cml 39 repeat 2 0 cp cp 0 view 0 -1 cp bview 1
//*****Boundary cells for outlet***** cset none cset cran 921 + ncn 925 + ncn I repeat 3 0 bced bced 0 view 0 -1 cp bview 2
//****drawing 17: Inlet and outlet boundaries** ** view 111 bp
//*** 3tBoundary for hot face on model inside furnace***** pitype hidden cset none
APPENDIX I)
cset xyzrange -1000 1000 600 700 -1000 1000 view 0 1 cp bview 5 I/** *drawing 19: Boundaries including inlet, outlet and hot face** view 1 2 3 bp cset none cset all
#defbcl bmax //*****Create cyclic boundary 1 cset none cset cran 179 413 39 csetcran 530 764 39 cset cran 881 92039 csetcran 1128 1168 8 repeat 3 0 bced bced 0 cset cran 179 + cml 413 + cml 39 repeat 2 0 cp cp 0 cset cran 530 + cml 764 + cml 39 repeat 2 0 cp cp 0 cset cran 881 + cml 920 + cml 39 repeat 2 0 cp cp 0 view 1 cp bview 6 //*****drawing2o: Boundary cells as seen from x-direction, including cyclic boundary 1****** bp
#defbcll bmax I/*****Create cyclic boudary 2********* cset none cset cran 179 + ncn 413 + ncn 39 cset cran 530 + ncn 764 + ncn 39 cset cran 881 + ncn 920 + ncn 39 cset cran 1128 + ncn 1168 ± ncn 8 repeat 3 0 bced bced 0 cset cran 179 + ncn + cml 413 + ncn + cml 39 repeat 2 0 cp cp 0 cset cran 530 + ncn + cml 764 + ncn + cml 39 repeat 2 0 cp cp 0 cset cran 881 + ncn + cml 920 + ncn + cml 39 repeat 2 0 cp cp 0 view -1 cp bview 7 ll**drawing21: All boundaries created, including cyclic boundary 2****
APPENDLXD 195
view -12 3 bp pitype hidden view 1 2 3 cp
idefbkl bmax
vcomp all ccomp=all ---- --
//****boudary cells on sides(x-positive and negative), symmetry**** bzone 3 north bzone 3 east bzone 3 west //****boundy cells back and front, symmetry for top and bottom of model in furnace******* bzone 3 front bzone 3 back I/boundary cells on bottom (with in- and outlet), furnace shell***** bzone 4 south
csys 0 cset none cset all
cgdefo 0 *****refractory***** cgdef 1 1 cgdef 2 2 *****mouldable***** cgdef 3 3 cgdef44 *****copper*****
mdef 0 solid *****refractory***** mdef 1 fluid ****water*** mdef 2 solid *****mouldable***** mdef3 solid *****steel***** mdef4 solid *****steel*****
on solution of energy equation****** energy on
//*****Spify material properties**** material 0 *****refractory*****
init. 0000400 cond const 135
material I mit 0 3 0 0 320 .001 .01 dens const 989
APPENDIX D 196
visc const 0.00058 cond const 0.642 pran 3.75 prefO 179 turb on
material 2 *****mouldable***** mit 0 0 0 0 400 cond const 15
material 3 mit 0 0 0 0 300 cond const 45
material 4 *****copper***** mit 0 0 0 000 cond const 350
energy on
II****inlet boundary***** bgdef 1 inlet constant 0 0 3 0 989 300 0.001 0.01
11* * * *outlet boundary* * * * * * bgdef 2 outlet 1
ll****symmetry boundary back, front and sides**** bgdef 3 symmetry
//****boundary on furnce outside - with inlet and outlet***** bgdef 4 wall
fixed 300 0.2
//****hot face boundary***** bgdef 5 wall
fixed 1773 0.00435
//*****cyclic boundaries***** bgdef 6 cyclic 0
bgdef 7 cyclic 0
//****cyclic boundary pairing*****
APPENDIX D
cycpbcl + 1 bcll + I repeat 87 11
//****cell to be monitored***** monitor 179
I/***Specify solution control*** iter 500 10 relax 0.7 0.7 0.7 0.1 10.70.7
==COflV0.00i -=
vmerge all
//***Create mesh and write definition file**** wmesh 0.001 wall y wdef save 1
//****drawing22: 3-13 view of complete final model***** view 111 cset all cp
APPENDIX D 198
APPENDIX E INPUT FILE FOR THREE-DIMENSIONAL MODEL OF CAST IRON
STAVE ARRANGEMENT
reset
csys 0 #defvl 11 * 5 + 1 idefv211 *5+6
-- #defv311_*6= vvl -15 vv2-15 15 • v3 0 15 vintvlv24vl+1 1 vint v2 v3 4 v2 + 11 #defv4 11 * 14+1 v v4 -38 csysl vcop 11 1 vran vmax vmax 10 -9 csys 0 #defv5 11 * 15 + 1 v v5 -40 csys 1 vcop 11 1 vran vmax vmax 10 -9 csys 0 vintvlv48vl+11 11111 #defvm vmax
#defv0ll*16+1 v vO -42 csys I vcop 11 1 vran vmax vmax 1 0 -9 #def vm0 vmax csys 0 #defvl 11 * 30+1 #defv2 11*30+6 #defv3 11 * 31 vvl -95 vv2-95 110 vv3 0110 vintvlv24vl+11 vintv2v34v2+1 1 vintvOvl9vm0+1 111111.2 vcomp all #defvml vmax vcop 61 vmax wan I vmax 10 0 7.5 #defvm vmax
cgroup 0
APPENDIX E 199
c 121213 12+vml 1 +vml 2+vml 13 +vml ccop 10 1 cran 111 active ccop 10 11 cran I cmax 1 active #def ci cmax cgroup 5 ccop 2 11 cran cmax - 9 cmax 1 active cgroup I ccop 11 11 cran cmax - 9 cmax I active #def co cmax ccop6Ovmlcranl cmax iexist= #def cii cmax
#def mcm cmax vref 1 vmall ccop 2 vm cran I cmax 1 exist crev 1 cran mcm + 1 cmax 1 #def cb cmax
cgroup 0 mcreate -15 15 10 0 15 5 0 450 60 #def cb 1 cmax
egroup 1 mcreate95 17050110575 150 10 mcreate95 170501105300375 10
cgroup 2 mcreate -145-95301105045060
cgroup 3 mcreate-195 -145201105045060
cgroup 4 mcreate95 170501105075 10 mcreate95 17050110515030020 mcreate 95 170501105375450 10
vmerge all
cset none cset cran 1 ci I cset cran cii + 1 cii +j cset cran cb + I cbl pitype hidden view 0 0 -1 cp bview 1 cset none cset cran cii - co + I cii - co + ci
APPENDIX E 200
cset cran cb - Co + I cb - Co + ci Cset cran Cb + 1 cbl view 0 0 1 Cp
bview 2
cset none cset all
bzone3north - ---- - ---bzone 3 south bzone 4 east bzone 5 west bzone 3 front bzone 3 back
cgdef 0 0 cgdef 1 1 cgdef 2 2 cgdef 3 3 cgdef 4 4 cgdef 5 5 mdef 0 fluid mdef 1 solid mdef 2 solid mdef 3 solid mdef 4 solid mdef 5 solid
energy on
material 0 init003O32O.0O1 .01 dens const 989 visc const 0.00058 cond const 0.642 pran 3.75
prefO 1 turb on
material I mit 0 0 0 0 400 cond const 40
material 2 mit 0 0 0 0 400 cond const .05
material 3
APPENDLX E 201
mit 0 0 0 0 300 cond const 45
material 4 mit 0 0 0 0 400 cond const 25
material 5 mit 0 0 0 0 400
- condconst0.5 - -
energy on
fl* f **inlet boundary***** bgdef 1 inlet constant 0 0 0 3 989 300 0.001 0.01
//****outlet boundary***** bgdef 2 outlet 1
H* symmetry boundary back, front and sides**** bgdef 3 symmetry
II****hot face boundary***** bgdef 4 wall
fixed 1473 0.02935
//****boundary on furnce outside - with inlet and outlet***** bgdef 5 wall
fixed 300 0.2
//****celi to be monitored***** monitor 1
iter 1000 10 relax 0.7 0.7 0.7 0.2 1.0 0.7 0.7 cony 0.00 1
vmerge all
wmesh 0.001 wally wdef save I
pity hidd
APPENDLXE 202
view 111 cp
APPENDIX E 203
APPENDIX F INPUT FILE FOR THREE-DIMENSIONAL MODEL OF COPPER STAVE
ARRANGEMENT INCORPORATING AN ACCRETION LAYER
reset
csys 0 #defvl 11 * 5+ 1 #defv2 11 * 5 + 6
vvl -15
vv2-15 15 vv3 015 vintvl v24v1 + 11 vint v2 v3 4 v2 + 11 #defv4 11 * 14 + I vv4-38 csys I vcop 11 1 vran vmax vmax 1 0 -9 csys 0 #defv5 11 * 15 + 1 vv5 -40 csys 1 vcop 11 1 vran vmax vmax 10 -9 csys 0 vintvlv48vl+11 11111 #def vm vmax
#defvO 11 * 16 + 1 V vO -42 csys 1 vcop 11 1 vran vmax vmax 10 -9 #defvmO vmax csys 0 #defvl 11 * 30 +1 #defv2 11 * 30+6 #defv3 11 * 31 vvl -95 vv2-95 110 vv3 0110 vintvlv24vl+11 vint v2 v3 4 v2 + 11 vintvOvl9vm0+1 111111.2 vcomp all #defvml vmax vcop 61 vmax vran 1 vmax 10 0 7.5 #def vm vmax
cgroup 0
APPENDIX F 204
c121 2 1 12+vml 1+vml 2+vml 13+vml ccop 10 1 cran 111 active ccop 10 11 cran I cmax I active #def ci cmax cgroup 1 ccop 12 11 cran cmax - 9 cmax I active #def co cmax ccop 60 vml cran 1 cmax I exist #def cii cmax
#def mcm cmax vref 1 vmall ccop 2 vm cran 1 cmax I exist crev 1 cran mcm + 1 cmax 1 #def cb cmax
cgroup 0 mcreate -15 15 10 0 15 5 0 450 60 #def cb 1 cmax
cgroup I mcreate 95 17050110575 15010 mcreate95 170501105300375 10
cgroup 2 mcreate -145-95301105045060
cgroup 3 mcreate -195-145201105045060
cgroup 4 mcreate 95 170 5 0 110 5 0 75 10 mcreate 95 170501105 150 300 20 mcreate 95 17050 1105375450 10
cgroup 5 mcreate 170270701105045060
vmerge all
cset none cset cran I ci 1 cset cran cii + 1 cii + ci cset cran cb + 1 cbl pltype hidden view 0 0 -1 cp bview I cset none
APPENDIX F
205
cset cran cii - Co + 1 cii - Co + C
cset cran cb - Co + 1 cb - Co + Ci
cset cran Cb + 1 cbl view 0 0 1 C
bview 2
cset none cset all
bzone 3 north bzone 3 south bzone 4 east bzone 5 west bzone 3 front bzone 3 back
cgdef 00 Cgdef 1 1 cgdef 2 2 cgdef 3 3 cgdef 4 4 cgdef 5 5
mdef 0 fluid mdef I solid mdef 2 solid mdef 3 solid mdef 4 solid mdef 5 solid
energy on
material 0 mit 0 0 3 0 320.001 .01 dens const 989 visc const 0.00058 cond const 0.642 pran 3.75 prefO I turb on
material I mit 0 0 0 0 400 cond const 350
material 2 mit 0 0 0 0 400 cond const .2
APPENDIX F 206
material 3 mit 0 0 0 0 300 cond const 45
material 4 mit 0 0 0 0 400 cond const 55
material 5
init0000 800 cond const 2
energy on
11* * * *inlet boundary* * * * bgdef 1 inlet constant 0 0 0 3 989 300 0.001 0.01
//****outlet boundary****** bgdef 2 outlet
/f****symmetry boundary back, front and sides**** bgdef 3 symmetry
//****hot face boundary***** bgdef 4 wall
fixed 1473 0.00435
//****boundary on ftirnce outside - with inlet and outlet***** bgdef 5 wall
fixed 300 0.2
to be monitored*** monitor 1
iter 1000 10 relax 0.7 0.7 0.7 0.2 1.0 0.7 0.7 cony 0.001
vmerge all
wmesh 0.001 wall y wdef save I
APPENDIX F 207
pity hidd view 111 cp
APPENDIX F 209
