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Mould heat transfer in the high speed continuous casting of steel slabs Singh, Himanshu 1998

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M O U L D H E A T T R A N S F E R IN T H E HIGH SPEED CONTINUOUS CASTING OF STEEL SLABS by H I M A N S H U S I N G H B.Tech. (Materials and Metallurgical Engineering), Indian Institute of Technology, Kanpur, India, 1996 A T H E S I S S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F A P P L I E D S C I E N C E in T H E F A C U L T Y O F G R A D U A T E S T U D I E S (Department of Metals and Materials Engineering) We accept thisthesis as conforming to^febe^re^uireci standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A June 1998 © Himanshu Singh, 1998 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada Date II DE-6 (2/88) A b s t r a c t This investigation studies mould heat removal in operational slab casters. These i n -clude both the conventional (or thick slab) as well as th in slab (of the C S P type) casters. M o u l d wall temperatures and other data measured in-plant were analysed us-ing mathematical models developed by other researchers, in addition to new models and commercial finite element software. The primary objective was the calculation of mould heat fluxes, and how this related to aspects of caster operation and slab surface quality. First ly, the mechanism of heat transfer in slab caster moulds postulated by previous researchers was validated. Heat fluxes calculated for a billet caster using powder l u -brication showed that reducing cooling water velocities resulted in an increase in heat transfer. This is due to higher mould hot face temperatures causing the formation of a smaller slag r i m , and a hotter, more fluid l iquid flux. This mechanism of mould heat transfer was used to resolve transverse corner cracking in a newly commissioned conventional slab caster which had commenced high speed casting. The problem was traced to inadequate mould lubrication and heat transfer, caused by inordinately high water velocities. The incidences of cracking fell drastically i i I l l after a reduction in cooling water velocities. Secondly, heat fluxes were calculated for the C S P caster. A big dip i n heat fluxes was seen i n the central portion of the fixed broad face. It was postulated that this could be due to a combination of water flow differential between the two broad faces, and a squeezing in of the mould pocket bulge i n the strand. Addit ional ly , the two broad faces, as well the narrow faces, were found to have unequal heat extraction rates. Final ly , the effect of the mould hot face temperature on the mould heat transfer was used to develop a procedure of water velocity variation into the working life of C S P caster moulds. Models were used to calculate water velocities which maintained a constant hot face temperature, while the wall thickness reduced. It was found that the current operational practice grossly over-estimated the water flows required in the latter stages of the mould life. C o n t e n t s A b s t r a c t i i C o n t e n t s iv L i s t of T a b l e s v i i i L i s t of F i g u r e s x 1 I n t r o d u c t i o n 1 2 L i t e r a t u r e R e v i e w 4 2.1 Heat Transfer Mechanism in Slab Casting 4 2.1.1 The M o u l d Wal l - Steel Shell Gap 6 2.1.2 The M o u l d Hot Face Temperature 8 2.1.2.1 Water Velocity 9 2.1.2.2 M o u l d W a l l Thickness . 9 2.2 Quantification of Heat Transfer 10 2.2.1 Use of Water A T s 11 iv CONTENTS v 2.2.2 Use of Embedded Thermocouples 12 2.2.2.1 Integrated form of Fourier's Law 13 2.2.2.2 Inverse Boundary Solution 15 2.2.3 Use of Heat F l u x Functions 17 2.3 Higher Casting Speeds in Conventional Casters 21 2.4 Heat Removal in T h i n Slab Casting 24 3 S c o p e a n d O b j e c t i v e s 31 4 M a t h e m a t i c a l M o d e l l i n g 33 4.1 Model l ing of the M o u l d Longitudinal Section 33 4.1.1 The Forward Problem 34 4.1.2 The Inverse Heat Conduction Problem 36 4.2 One Dimensional Model l ing 37 4.2.1 Assumptions 39 4.2.2 Model Derivation 40 4.3 F E M Model l ing 42 4.4 Model l ing of Strand Solidification 44 5 I n d u s t r i a l M e a s u r e m e n t s of H e a t T r a n s f e r 45 5.1 Conventional Casters 45 5.1.1 The Company A #1 Caster 47 5.1.2 The Company A #2 Caster 51 5.2 The C S P Caster 51 CONTENTS v i 5.2.1 M o u l d Pocket 52 5.2.2 Broad Face Cooling 53 5.2.3 Narrow Face Cooling 54 5.2.4 M o u l d Instrumentation 58 5.2.5 Data for Heat Flow Analysis 58 5.2.5.1 M o u l d W a l l Temperature 59 5.2.5.2 Water Heat Transfer Coefficient 63 5.2.5.3 Water Temperatures 64 5.3 The Bil let Caster 64 6 H e a t T r a n s f e r i n H i g h S p e e d C o n v e n t i o n a l S lab C a s t i n g 67 6.1 Role of Water Velocity 67 6.2 M o u l d Heat Transfer in the Company A Casters 68 6.2.1 Original Operational Practice 70 6.2.2 Water Velocity Changes 72 6.3 Effects of Changes 74 6.4 Mechanism of Crack Formation 78 7 H e a t T r a n s f e r i n T h i n S lab C o n t i n u o u s C a s t i n g 81 7.1 Calculation of Heat Fluxes 82 7.1.1 Assumptions for the F E M Models 82 7.1.2 Results from the F E M Models 85 7.2 Average and Specific M o u l d Heat Removal 98 CONTENTS v i i 7.3 Heat Flow Trends in the Cast 100 7.3.1 Broad Face Heat Flow 103 7.3.2 Narrow Face Heat Flow 105 7.4 Water Flow Differentials 106 7.5 F i t t i n g of Heat F l u x Profiles 108 7.5.1 Meniscus Heat Fluxes I l l 7.5.2 F i t ted q0 Values 112 7.6 Strand Shell Thickness/Surface Temperature 113 7.7 Compensating for M o u l d W a l l Thickness 118 7.7.1 The Constant Thermal Resistance Approach 118 8 C o m p a r i s o n between C o n v e n t i o n a l a n d T h i n S lab C a s t i n g 123 8.1 M o u l d Solidification Parameters 123 8.2 M o u l d Design 125 8.2.1 Broad Face Cooling Holes 125 8.2.2 Hot Face Coatings 125 8.3 Hot Face Heat Fluxes and Temperatures 126 8.4 Average M o u l d Heat Fluxes 129 9 C o n c l u s i o n s a n d R e c o m m e n d a t i o n s 132 B i b l i o g r a p h y ' 135 List of Tables 2.1 M a x i m u m casting speeds for 200 m m thick slabs 22 4.1 List of symbols used in the 1-D model 41 5.1 Design details of the Company A and Company B slab casters 46 5.2 Steel composition (in wt.%) for the Company A heats 46 5.3 Summary of data used for calculating heat transfer conditions for the Company A $ 1 caster 50 5.4 Summary of data used for calculating ini t ia l heat transfer conditions for the Company A #2 caster 50 5.5 Summary of data used for calculating heat transfer conditions after water velocity reduction for the Company A #2 caster 50 5.6 Details of the C S P caster at Company C 52 5.7 Thermocouple locations on the C S P caster at Company C 55 5.8 Slab numbers and the times between which they were cast 59 5.9 Steel composition (in wt.%) for the five slabs analysed 59 vm LIST OF TABLES ix 5.10 Water velocities and heat transfer coefficients for the C S P caster broad faces 63 5.11 Water inlet temperature and A T s for the C S P caster 64 5.12 Bi l let caster design details and casting conditions 65 L i s t of F igures 2.1 Schematic of temperature profile and resistance to heat flow across steel shell to cooling water, and longitudinal section through steel slab and casting mould 5 2.2 Schematic of temperature across a continuous casting slab mould and steel shell 5 2.3 Resistances to heat flow between the shell surface and the mould cooling water 6 2.4 A x i a l profiles of gap and shell resistances i n the mould 6 2.5 Schematic representation of the various factors affecting the heat transfer between the strand and the mould 7 2.6 Comparison of the m a x i m u m slag r i m thickness at the two broad faces. . 10 2.7 Comparison of the model-calculated meniscus heat flux at the inside- and outside-radius faces 10 2.8 Variat ion of mold heat removal rate with casting speed 12 2.9 M o l d wide face heat removal 12 LIST OF FIGURES x i 2.10 Dual thermocouple installation on wide and narrow walls parallel to hot face 13 2.11 Predicted steady-state isotherms in the wall of a slab mould 14 2.12 Comparison of the axial heat-flux profiles predicted by 2-D and 3-D mod-els of the mold wall with the same mold temperature data 15 2.13 Heat flux plotted against t ime-in-the-mould for a billet mould and slab moulds 18 2.14 Heat flux in the meniscus region as a function of transit time 18 2.15 Influence of casting speed on axial heat-flux profiles at centre-plane of narrow face 20 2.16 Normalized local mold beat flux for low carbon strip grade 20 2.17 Change in the average m a x i m u m casting speed 23 2.18 Layout of the Nucor C S P continuous thin slab casters 24 2.19 Schematic drawing of the convex mold 25 2.20 Longitudinal profiles of the temperature in the broad mold plate of a funnel-shaped mold 26 2.21 Transverse profiles of the temperature in a broad mold plate of a funnel-shaped mold. 26 2.22 Transverse profiles of the temperature in a narrow mold plate of a funnel-shaped mold 26 2.23 Temperature contours on inside face of a 20-mm-thick mold 27 LIST OF FIGURES x i i 2.24 Calculated mold temperatures (along outboard edge of funnel) 5 m m from the hot face for three mold thicknesses, compared with values mea-sured at Nucor Steel for a 20-mm-thick mold 28 2.25 Computed variation of mold heat flux with position for the 20-mm-thick mold 28 2.26 Integral mold heat flux versus casting speed for two cases of thin slab casting with two different mold powders (i.e. , low and high viscosity), in comparison with conventional slab casting 29 4.1 Schematic diagram of longitudinal mid-plane through a mould 34 4.2 Schematic diagram of the transverse section through the mould wall em-ployed in the 2-D (transverse) model 35 4.3 M o d e l predicted isotherms on the transverse section of the copper plate. 35 4.4 Schematic diagram showing the domain for the Inverse Heat Conduction analysis 37 4.5 Conceptual flow-chart of the F O R T R A N program developed to compute the solution for the I H C P associated to estimation of mould heat flux profile 38 4.6 Schematic of 1-D heat conduction in the mould wall 39 5.1 Thermocouple layout for the Company A #1 caster 47 5.2 Typica l thermocouple traces for the Company A #1 caster 48 5.3 Company A #1 caster wall temperatures averaged for each casting speed. 49 LIST OF FIGURES xiii 5.4 Schematic of side view of a C S P caster broad face 53 5.5 Schematic of top view of a C S P caster broad face 54 5.6 Transverse section of the C S P caster broad face 55 5.7 Transverse section of the C S P caster narrow face 56 5.8 Thermocouple and mould pocket locations on the C S P caster broad face. 57 5.9 Top row thermocouple readings for the C S P caster narrow faces 60 5.10 Top row thermocouple readings for the left half of the C S P caster fixed broad face 61 5.11 Top row thermocouple readings for the right half of the C S P caster fixed broad face 62 6.1 Effect of changing water velocity on heat fluxes and temperatures on the mould hot face during billet casting with powder 69 6.2 Hot face heat flux and temperature profiles down the mould wall for the Company A and #1, #2 (before water velocity reduction) Company B casters 71 6.3 Calculated hot face temperature profiles for the Company A #2 caster after water velocity reduction 73 6.4 Hot face heat flux and temperature profiles down the mould wall for the Company A #2 (before and after water velocity reduction) Company B casters 76 6.5 Specific heat extraction by the mould with casting speed for the C o m -pany A and Company B casters 77 LIST OF FIGURES x i v 6.6 Mechanism of transverse corner crack formation in the Company A #2 caster 79 7.1 Transverse section of the C S P caster broad face 83 7.2 Transverse section of the C S P caster narrow face 84 7.3 Calculated isotherms (in °C) at a top row thermocouple on the C S P caster narrow face 86 7.4 Calculated isotherms (in °C) at a bottom row thermocouple on the C S P caster narrow face 86 7.5 Calculated isotherms at a top row thermocouple on the C S P caster broad face 87 7.6 Calculated isotherms at a bottom row thermocouple on the C S P caster broad face 87 7.7 Heat flux and hot face temperatures on the mould broad faces for slab 10851-01-06 88 7.8 Heat flux and hot face temperatures on the mould broad faces for slab 10851-02-02 89 7.9 Heat flux and hot face temperatures on the mould broad faces for slab 10851-03-06 90 7.10 Heat flux and hot face temperatures on the mould broad faces for slab 10851-04-04 91 7.11 Heat flux and hot face temperatures on the mould broad faces for slab 10851-05-01 92 LIST OF FIGURES x v 7.12 Heat flux and hot face temperatures on the mould narrow faces for slab 10851-01-06 93 7.13 Heat flux and hot face temperatures on the mould narrow faces for slab 10851-02-02 94 7.14 Heat flux and hot face temperatures on the mould narrow faces for slab 10851-03-06 95 7.15 Heat flux and hot face temperatures on the mould narrow faces for slab 10851-04-04 96 7.16 Heat flux and hot face temperatures on the mould narrow faces for slab 10851-05-01 97 7.17 Average heat flux on each face and specific mould heat removal in cast #10851 99 7.18 Average F E M calculated broad face heat fluxes into cast #10851 101 7.19 Average F E M calculated narrow face heat fluxes into cast #10851 102 7.20 F i t t i n g of heat flux profiles at the thermocouple column locations 108 7.21 q0 values calculated for the broad faces of the two slabs 109 7.22 q0 values calculated for the narrow faces of the two slabs 110 7.23 Solidified shell thickness and strand surface temperature at the mould exit for the broad faces of slab 10851-01-06 114 7.24 Solidified shell thickness and strand surface temperature at the mould exit for the narrow faces of slab 10851-01-06 115 LIST OF FIGURES x v i 7.25 S o l i d i f i e d shel l th ickness a n d s t r a n d surface t e m p e r a t u r e at the m o u l d e x i t for the b r o a d faces of slab 10851-05-01 116 7.26 S o l i d i f i e d shel l th ickness a n d s t r a n d surface t e m p e r a t u r e at the m o u l d ex i t for the n a r r o w faces of slab 10851-05-01 117 7.27 C a l c u l a t e d v a r i a t i o n of water v e l o c i t y w i t h w a l l th ickness at C o m p a n y D to m a i n t a i n constant hot face t e m p e r a t u r e 120 7.28 C a l c u l a t e d a n d a c t u a l water f low rate v a r i a t i o n w i t h w a l l th ickness at C o m p a n y D 121 8.1 Spec i f i c m o u l d heat e x t r a c t i o n ( in k J / k g ) for t h i c k s lab , b i l l e t a n d C S P casters 124 8.2 H o t face heat f luxes vs. hot face t e m p e r a t u r e s for b i l l e t , c o n v e n t i o n a l slab a n d C S P casters 127 8.3 A v e r a g e m o u l d heat f luxes for t h i c k s lab, b i l l e t a n d C S P casters 129 Chapter 1 Introduct ion Over the last couple of decades, continuous casting technology has revolutionized the economics of steelmaking, and continues to do so. Continuous casting offers the steel-maker the potential for improved productivity, quality and uniformity at reduced in-vestment and operating costs. Whi le the world crude steel output is more or less static at around 750 M T P A , the share of continuously cast steel in total output has been steadily rising, being 77.6% in 1996 [1]. In the same year, 97% of Canada's steel was continuously cast. Beginning in the 1960s, continuous casting of slabs has virtual ly replaced the ingot casting route, since it eliminates the need for the capital and energy intensive roughing mil ls . This move to cast a product closer to its final shape took a leap forward when Nucor Steel commercialised the S M S thin slab casting technology in 1989. This process casts 50 m m thick slabs, instead of the traditional 250 m m or so in the conventional casters. Since 1922, when wide coilable hot rolled strip production was first implemented by 1 Ch.l Introduction 2 J . B . Tytus at the American Rol l ing M i l l Company [2], the market for flat products had been the sole domain of the integrated steel mil ls . The main reason for this was the heavy capital investment required - both i n the upstream ironmaking facilities, as well as the downstream rolling of a 250 m m section down to a final product thickness of 2.5 to 25 m m . However, the advent of thin slab casters now puts the flats market within the reach of mini-mil ls , since the capital cost of building a m i n i - m i l l is a third of that for an integrated m i l l of the same production capacity. Whether conventional or thin slab, the continuous casting process is essentially one of heat extraction. The highest h e c i t flux densities encountered in an industrial environ-ment is seen in the mould. The mould, which is rightly called the "heart" of the casting machine, is responsible for taking l iquid steel at ~ 1 5 5 0 ° C and continuously producing a section with a solidified shell generally able to withstand the ferro-static pressure of the l iquid core. Heat removal by the mould is a key factor i n the operation of both the conventional and thin slab casters. There has been a recent trend to boost conventional caster product ivi ty by raising the operating casting speeds. However, this has not been without attendant problems, some of which have been linked to inadequate mould heat removal. T h i n slab casters, which can operate at more than thrice the speeds of conventional casters, have been plagued by a high incidence of mould cracking, and thus drastically reduced mould life. They have also been handicapped in penetrating the flat products market by their inabil i ty to cast good quality slabs of the crack sensitive peritectic Ch.l Introduction 3 steels. Both these factors can be traced to the high level of heat flux extraction in the mould of a thin slab caster. The present study focuses on heat removal in operating conventional and thin slab casters. Analysis was carried out based on measurements made by plant personnel. Chapter 2 Li terature Review In this chapter, aspects of heat flow in slab casting moulds are first reviewed. After this, the trend for higher casting speeds in conventional slab moulds, and the new thin slab casting technology are discussed. 2.1 Heat Transfer Mechanism i n Slab Cast ing Viewed from a heat removal perspective, the continuous casting mould is merely a mechanism for the controlled cooling of molten steel by water. Fig.2.1 illustrates a longitudinal section through a typical slab caster, where we see that water cools the l iquid steel through intervening layers of copper, mould flux (both l iquid and solid), possibly air gaps and finally a shell of solidified steel. The temperature profile across these different layers is also depicted here (as well as in Fig.2.2). From both Figs.2.1 and 2.2 it can be clearly seen that the biggest temperature drop is across the mould wall - steel shell gap. In fact, Samarasekera and Brimacombe [8] had estimated that that this gap accounts for more than 80% of the thermal resistance 4 Ch.2 Literature Review 5 Figure 2.1: Schematic diagram of: (A) temperature profile across steel shell to cooling water, (B) resistance to heat flow across steel shell to cooling water, and (C) longitudinal section through steel slab and casting mould (after [3]). Figure 2.2: Schematic of temperature across a continuous casting slab mould and steel shell [4j. Ch.2 Literature Review 6 to heat flow between the steel surface and the cooling water (see Fig.2.3). In a later study, Mahapatra et al. [7] had also calculated the gap resistance (Fig.2.4), which is comparable to those of Samarasekera and Brimacombe [8]. Since this gap is obviously I oo. 2 80 : 6 0 V-. 40 j 2.4 20, S lob-(High heal flux practice) S lob-(Low heat flux practice) Billet Gop-lLow heot flux proctice) Gap-(Htgh heal f l jx practice) Gop-lBillet) Slab mould wall Billet mould wall Cooling water interface 100 2 0 0 3O0 4 0 0 5 0 0 6 0 0 'Meniscus Distance down the mould ( m m ) Figure 2.3: Resistances to heat flow be-tween the shell surface and the mould cooling water for the billet mould and slab moulds with low and high heat-flux prac-tices [8]. ca 0.3 0.6 0.9 1.2 Resistance to Heat Flow (°C m2/kW) Figure 2.4: Axial profiles of gap and shell resistances in the mould; C=0.04%; cast-ing speed — 0.75 m/min; Pemco 389 flux the rate controlling step in heat transfer from the steel to water, it merits more attention. 2.1.1 The Mould Wall - Steel Shell Gap A n electrical resistance analogy of the various resistances to heat removal from the solidifying strand is presented in Fig.2.1. We see that heat transfer across the gap is controlled by the thickness and thermal properties of the materials f i l l ing the gap, viz. Ch.2 Literature Review 7 air and mould flux. Over most of the mould faces, the flux exists as thin layers of solid and l iquid mould powder of varying thickness [4]. In addition, solid mould flux can exist either in the glassy or crystalline states. Branion [10] has pointed out that the different states of the mould flux in the gap, and their proportions w i l l , among other factors, depend on the temperatures of the mould hot face, strand surface and the solidification characteristics of the flux. Since these three different layers have different thermal and radiative conductivity (heat being transferred by both the conductive and radiative modes [11]), it follows that the Mould level C a s t i n g Steel C contro l speed content Figure 2.5: Schematic representation of the various factors affecting the heat transfer between the strand and the mould [llj. above mentioned factors w i l l affect heat transfer through the gap. However, the overall heat transfer mechanism is quite complex [11], as can be gauged from Fig.2.5. Ch.2 Literature Review 8 2.1.2 T h e M o u l d Hot Face Temperature Based on extensive industrial trials on an operational slab caster at the Stelco Lake Erie Works, Mahapatra et al. [7] clarified the strong influence of mould hot face temperature on heat removal, through the formation of oscillation marks. Takeuchi and Brimacombe [12] had proposed a mechanism for oscillation mark for-mation based on the response of the partially solidified shell at the meniscus to fluid pressure development in the mould-strand gap. Kawakami et al. [13] had also postu-lated a similar mechanism, which also takes into account the solid slag r i m attached to the mould wall at the meniscus. This r i m aids in oscillation mark formation by inter-acting mechanically with the solidifying shell, as well as by increasing the fluid pressure in the mould-strand gap [13]. Oscil lation marks decrease heat transfer by increasing the gap between the mould and strand. A reduction in mould hot face temperature w i l l lead to the formation of a thicker slag r i m and a colder, more viscous flux. The combined effect of these two results in deeper oscillation marks, and lower heat transfer [7]. Hence, any parameter that affects the hot face temperature influences heat removal by the continuous slab casting mould. From the thermal resistance circuit in Fig.2.1, it is apparent that for a given slab mould, the hot face temperature depends on the forced convective heat transfer coefficient at the cold face of the mould, and the thickness of the mould wall . Generally speaking, the copper conductivity, types and thickness of coatings applied to the hot face, the Ch.2 Literature Review 9 configuration of the cooling channels, and the inlet temperature of the water would also play a part [9]. 2.1.2.1 W a t e r V e l o c i t y If there is no scale deposition on the mould cold face, and cooling is in the convective regime, the heat transfer coefficient varies almost linearly wi th water velocity (in fact, to the power 0.8 [14]). A reduction in water velocity lowers the heat transfer coefficient, and raises the copper temperature, resulting in a thinner slag r i m , a hotter, less viscous flux, shallower oscillation marks and enhanced heat extraction [7]. Fogleman and Orie had reported that for the continuous casting of carbon steel slabs, a reduction in water flow rate from 110 to 98 litre/s resulted in the specific heat removal (i.e. heat extracted per unit mass of steel cast) increasing from 62.8 to 81.4 k J / k g [15]. A study of breakout shells also revealed an increase of ~6.4 m m (to ~28.6 mm) in the solidified shell thickness at the mould exit [15]. In billet casting of peritectic steels (0.11 < % C <0.14) with mould powder, Pinheiro [16] reports an increase in the meniscus heat flux of 10% when the cooling water velocity was reduced from 9.9 to 7.6 m/s . 2.1.2.2 M o u l d W a l l T h i c k n e s s A n increase in the copper thickness has the same effect as reducing water velocity, since it increases the thermal resistance between the copper hot face and the cooling water Fig.2.1. Mahapatra et al. [7] conducted trials on a curved slab caster, where the outside Ch.2 Literature Review 10 radius copper plate was 6 m m thicker at the meniscus than the inner radius plate. Whi le Outside Radius 0.04 %C 0.09 %C 0.18 %C Figure 2.6: Comparison of the maximum slag rim thickness at the two broad faces for three different grades of steel; casting speed = 0.75 m/min [7]. 0.04 %C 0.09 %C 0.1 B%C Figure 2.7: Comparison of the model-calculated meniscus heat flux at the inside- and outside-radius faces for three different steel grades; casting speed = 0.75 m/min [7J. this additional thickness contributes only a small amount to the total thermal resistance, it does significantly affect the mould hot face temperatures. It was found that at the meniscus, the outer radius copper working face was 40°C hotter than its inner radius partner. This resulted in a smaller slag r i m (Fig.2.6) and enhanced heat extraction for the outer radius wal l , with the meniscus heat flux being ~10% greater (Fig.2.7). 2.2 Quantification of Heat Transfer Since the mould is a heat extraction device, monitoring its heat transfer characteristics is essential to gauging its performance. This is usually accomplished by using the rise in temperature of the cooling water and/or readings from thermocouples embedded in the mould walls. In addition, functions specifying the heat flux profile down the mould wall are also in use. These methods are discussed below. Ch.2 Literature Review 11 2.2.1 Use of Water A T s Cooling water for the mould flows counter-current to the casting direction, i.e. the water enters the mould at the bottom, flows up and exits near the top (see Fig.2.1). During this process of cooling the mould, the water itself heats up, and this temperature differential ( A T ) between the inlet and outlet can be used to monitor heat removal by the mould. M u l t i p l y i n g the temperature rise for each face with the corresponding water flow rate gives us the total rate of heat removal from that face. D i v i d i n g this by the exposed mould face area gives an "average" figure for the heat extracted by that face. This is expressed in the following equation [17]: Qa = C * ^ A T (2.1) where, Qa = average heat flux extracted by a mould face ( W / m 2 ) Cp = specific heat of water ( J /kg°C) pw = density of weiter (kg/m 3 ) w = water flow rate (m 3 /s ) A T = cooling water temperature rise from inlet to outlet (°C) A = exposed mould face area (m 2 ) . E m l i n g and Dawson [17] describe the use of a breakout detection and control system at L T V Steel that uses these heat flux values for each mould face. They also caution against merely monitoring A T values, since this is inversely proportional to the water flow rate, and random variations in flow rate could lead to false alarms. Ozgu and K o c a t u l u m [21] have plotted these heat flux values against casting speed (Fig.2.8) for Ch.2 Literature Review 12 1 3 0 0 6 1 « 0 0 f-i j 1 3 0 0 < > § 1 2 0 0 uj oe y- 1 1 0 0 u i X o 1 0 0 0 o a 9 0 0 8 0 0 S L A B P E R I M E T E R °8 o o o o O L O W C A R B O N S T R I P • M E D I U M C A R B O N P L A T S C A S T I N G S P E E D , m / m l n Figure 2.8: Variation of mold heat re-moval rate with casting speed [21 J. 175 180 T s x k so M O L D 6 H A 3 C * X 1B» • A L O W c *-<J I 1 0 * 0 t-« o C UM r t n • - 1 0 0 PLATE 11-11 • D L O W C »•» I L O W 0 4-» a p L O W C •-• • T L I N E P I M ••a r P L A T E I I - I I 2 . 0 2 SPEED, m/mln Figure 2.9: Mold wide face heat removal [30]. the No.2 caster at Bethlehem Steel, Burns Harbor. Gilles et al. [30] have done the same for Bethlehem Steel, Sparrows Point (Fig.2.9). It is clearly seen that the heat extraction rate increases almost linearly with casting speed. 2.2.2 Use of Embedded Thermocouples The use of thermocouples in moulds is popular because they are inexpensive, easy to install , and their signals are easily interpreted [22]. This k ind of thermal monitoring is most commonly used for breakout detection [18, 23, 24, 25, 26, 27]. Here we shall discuss their use in calculating heat extraction by the mould. This is most commonly accomplished by either of the two methods described below. Ch.2 Literature Review 13 2.2.2.1 Integrated form of Fourier's Law In this procedure, two thermocouples are placed at different horizontal distances from 615 + 485 »l« 635 »|« 615-NARROW WALL II I I I I BOTTOM WATER CHANNEL 102 152 — 5 229 11 t • 11 11 4-1 I 4 5 7 711 II I I 900 WIDE WALL 21.6 i T o o 11.5 r HOT FACE 259 NARROW WALL O o SECTION OF TOP VIEW DIMENSIONS: mm Figure 2.10: Dual thermocouple installation on wide and narrow walls parallel to hot face [21]. the hot face [20, 21, 24, 29, 31]. Fig.2.10 depicts such an installation, where the ther-mocouples are placed through holes drilled i n through the top. The heat flux and the temperature distribution between the hot face and the water channels are then simply calculated from the gradient of the temperatures measured at these two points, i.e. the integrated form of Fourier's Law for heat conduction [24]: kcu (T2 - Ti) (2.2) where, q ( W / m 2 ) is the local heat flux, kcu ( W / m K ) is the thermal conductivity of the mould wall , s (m) is the distance between the two thermocouples, and T\ and T2 (°C) Ch.2 Literature Review 14 are the temperatures measured by the two thermocouples. Whi le this method is computationally quite simple, Samarasekera and Brimacombe [8] have pointed out the pitfalls of using this method, especially near the meniscus Figure 2.11: Predicted steady-state isotherms in the wall of a slab mould with high heat-flux practice under standard conditions [8]. region. This procedure assumes that heat flow through the mould wall is essentially one dimensional (i.e. there is no axial component), and this is only true 50-60 m m below the meniscus [8], as can be seen from the temperature contours in Fig.2.11. Near the meniscus there is strong axial heat flow, and just using Eq.2.2 can lead to under-estimation of the heat fluxes by 25-90% [8]. In an interesting variation of this method, E m l i n g and Dawson [17] have reported the development of a heat flux sensor by Kawasaki Steel. This is mounted flush with the 10mm 5 2 0 H 425H Ch.2 Literature Review 15 mould cold face, and measures the local heat flux from Eq.2.2. Besides greatly enhanced ease of usage, this sensor removes uncertainty in the value of the distance dimension ( ' 5 ' in Eq.2.2). Of course, it too suffers from the same drawbacks discussed above. 2.2.2.2 Inverse B o u n d a r y S o l u t i o n Here, the differential form of Fourier's Law is solved to back calculate the heat fluxes (and temperature profile in the mould wall) from a single column of thermocouple mea-surements. This is accomplished by manually adjusting the boundary condition (hot face heat flux) so that there is the smallest possible difference between the temperatures predicted from the model and the time-averaged values measured by the thermocou-ples [6, 28]. Various researchers have reported modelling of a two dimensional longitudinal section [3, 6, 8, 28], two dimensional transverse section [4, 6, 30, 32], or even a ful l three d i -2400 400 - / I 0 ^ — 1 1 1 I 1 r — 1 1 0 200 400 600 800 Dislance Below Top of Mold (mm) Figure 2.12: Comparison of the axial heat-flux profiles predicted by 2-D and 3-D models of the mold wall with the same m.old temperature data [6J. mensional section [6] of the mould wall . Ch.2 Literature Review 16 Mahapatra et al. [6] compared the performance of 2-D mathematical heat transfer models with that of a 3-D one. The predicted heat flux profiles for the same conditions are shown in Fig.2.12. The 2-D transverse heat flow model is found to predict a lower meniscus heat flux, due to neglect of the axial component of heat conduction. However, lower down in the mould, where the heat transfer is basically 1-D [4], the predictions compare very well with the 3-D model. The 2-D axial model, on the other hand, accu-rately predicts the meniscus heat flux, while under-estimating the flux lower down by a constant amount. Mahapatra et al. [6] have pointed out that this is due to the neglect of the cooling water slots and thermocouple leads. However, a high degree of computational intensity is associated wi th the accuracy of the 3-D model. Moreover, the 2-D axial model correctly calculates the peak heat flux, and error in heat flux estimation below the meniscus is fairly uniform. Mahapatra et al. [6] suggest that reliable heat flux profiles can be back calculated by first applying the 2-D axial model, and then bumping up its heat flux predictions by a factor. Recently, Pinheiro [16] has developed a model that automates the solution of the in -verse boundary problem. This is a 2-D axial model, and is discussed further in the next chapter. Ch.2 Literature Review 17 2.2.3 Use of Heat Flux Functions In 1956, Savage and Pri tchard had reported the following relation for heat transfer in billet casting: q = 2680 - 335\/t (2.3) where, q = instantaneous mould heat flux ( k W / m 2 ) t — residence time below the meniscus (s). The residence time is calculated by dividing distance down the meniscus with the casting speed. Though this was originally developed for billet casting with o i l , this relation matches quite well with profiles calculated by Samarasekera and Brimacombe [8] in 1979 for slab casters (Fig.2.13). Other researchers have reported exponential forms of empirical functions [35, 36, 37]: q = ae-bt + c (2.4) q = ae'' + be~t/n + c (2.5) where a, b, c and n are empirical coefficients. However, Konishi [34] had found that there is no significant difference in the heat fluxes derived from the above two equations, and thus used the simpler exponential form (Eq.2.4). Konishi [34] also performed regression analysis on the data of Hirak i et al. [38] using three different equations: a square root function of the form in Eq.2.3, the exponential function i n Eq.2.4 and a third Ch.2 Literature Review 18 <»ooo|j-I 3 6 0 0 [ t -I ocfL I n Casung operation Billet (Savage 8 Pritchord) Slab ; high beat f lu i practice Stab ; low heat flux practice J L 10 2 0 3 0 4 0 5 0 6 0 Time ( s ) Figure 2.13: Heat flux plotted against time-in-the-mould for a billet mould (Savage and Pritchard [5]) and slab moulds with low and high heat-flux practices [8]. 8000 7000 6000 CM | 5000 J 4000 L L I 3000 x 2000 1000 0 o Hiraki et al. — Square Root Function Exrjonential Function ~* \ — * \ \ \ » \ > \ \ - \ — F 'olynomial F unction \ \ y — \ \ ' - m I I . . . . r 0.5 1 1.5 Transit Time, s 2.5 Figure 2.14: Heat flux in the meniscus region as a function of transit time derived from the data of Hiraki et al. [38] (after [34]). Ch.2 Literature Review 19 order polynomial . The regression equations for the mould heat fluxes (in k W / m 2 ) are expressed as [34]: 4510 - 1 6 0 ^ (2.6) 5960e -2.3t + 1490 (2.7) - 8 3 7 t3 + 4348 t2 - 7644 t + 6214 (2.8) The curves are also depicted in Fig.2.14. ft is interesting to see that all of these three very different equations fit the data of Hirak i et al. [38] very well , but predict widely varying meniscus heat fluxes (at t — 0) - from ~4500 to 7500 k W / m 2 . In other words, there is hardly any difference between these equations lower down in the mould, but significant variation in the meniscus region. Fig.2.14 underlines the problem of trying to extrapolate heat fluxes to the meniscus, from those calculated lower down in the mould. Even if a single equation is used to evaluate the meniscus heat flux, there is another serious drawback - the effect of casting speed is not accounted for. It is a well known fact [7, 39] that the meniscus heat flux increases with casting speed, as can be seen in Fig.2.15. However, in these equations, since the meniscus heat flux is assessed at t = 0, peak heat flux is invariant with casting speed. Another popular form of empirical equation in use is the power function: q = at -b Ch.2 Literature Review 20 Speed - 0 . 5 0 rn/min Speed - 0 . B 0 m/mln 200 400 600 Distance Below Top of Mold (mm) Figure 2.15: Influence of casting speed on axial heat-flux profiles at centre-plane of narrow face; Stg 179 mold flux; C = 0.21%; tundish temperature = 1545°C [V-Figure 2.16: Normalized local mold heat flux for low carbon strip grade [29]. Wolf [39] reports values of 3.55 M W / m 2 and -0.5 for a and b respectively. Using the thicknesses of breakout shells, Chiang [3] has also used a similar function to evaluate heat flux profiles. Working on results from an experimental caster, Gilles [29] has reported the following function for casting low carbon steels: (2.10) 7.886 - 0.663 t 0 < t < 1 7.222 r 0 - 5 5 8 t>l where q is evaluated in M W / m 2 . Fig.2.16 shows the good fit of this equation with experimental data, for a range of casting speeds from 0.8 to 2.0 m / m i n . The power function in Eq.2.9 presents even more difficulty i n evaluating meniscus heat fluxes, since it is singular at t = 0. One might use a different function for low residence Ch.2 Literature Review 21 times, as in Eq.2.10. Alternately, Wolf [39] has recommended evaluating Eq.2.9 at meniscus dwell times (corresponding to distances of ~ 5 m m below the meniscus) for obtaining peak heat fluxes. This has the added advantage of accounting for the effect of casting speed. 2.3 Higher Casting Speeds in Conventional Casters A straightforward way to improve caster productivity without increased capital costs is to ramp up the casting speed. For example, at the Sparrows Point works of Bethlehem Steel, there was a high frequency of single strand and narrow width casting [30]. Simu-lation studies had shown that only higher casting speeds could enable annual tonnage targets to be met. This allowed for the development of a surge capacity, that would ensure adequate machine tonnage throughput when casting conditions were otherwise unfavourable [30]. Table 2.1 shows the product mix at Sparrows Point , and the cast-ing speed targets established. A successful implementation of this program resulted in an increase in the average casting speed from 1.24 m / m i n i n 1987 to 1.36 m / m i n in 1989, and a corresponding jump in caster uti l ization from 69.2 to 83.8% in the same period [30]. For the new casting regime, slab surface quality was reported to be at least as good as that for the lower casting speeds. However, a higher incidence of transverse corner cracking for the crack sensitive grades was encountered. This was remedied by employ-ing a different mould flux. In addition, high mould hot face temperatures were reduced Ch.2 Literature Review 22 Speed, m/mln Grade (Carbon) Low Carbon (<.08) C r i t i c a l (.08-.14) Medium Carbon (.17-.21) Line Pipe (.08-.17) Plate (.15-.16) High Carbon (.22-.80) Production 70 13 Original Maximum 1.7 1.4 1.1 1.4 1.3 1.4 Potential Maximum 2.5 1.7 2.0 1.7 1.5 1.5 Operating Constraints Metallurgical Length Surface Quality Breakouts Surface Quality Surface Quality Breakouts * Start of Program Table 2.1: Maximum casting speeds for 200 mm thick slabs [30]. Ch.2 Literature Review 23 by decreasing the copper wall thickness, and increasing both the number of water cool-ing channels as well as the water velocity [30]. A similar program for higher casting speeds was implemented at Dofasco Inc. [40]. There, the ingot stream for casting was shut down, resulting in a reduction of plant steelmaking capacity by 2 M T P A . This made it necessary to maximise the output of the caster, to reduce the need for purchased slabs. The average m a x i m u m casting speed 1-8 | • — I c Figure 2.17: Change in the average maximum casting speed [40]. was increased from 1.35 to 1.49 m / m i n , without any deterioration of slab quality. This met the targets set for the project, as can be seen in Fig.2.17. In 1987, Wada et al, [19] had reported average casting speeds of 2.2 m / m i n at the No.5 caster (with a slab thickness of 220 mm) in the Fukuyama works of Nippon Kokan. In addition, casting speeds of upto 3.0 m / m i n had been reached in casting trials, without problems in operations or slab quality [19]. Ch.2 Literature Review 24 2.4 Heat Removal i n T h i n Slab Cast ing Less than a decade ago, Nucor Steel revolutionized continuous casting when it com-mercialised the thin slab caster of SMS Schloeman Siemag in its green-field plant at Crawfordsville, Indiana. In spite of tremendous odds [43, 44], the C S P (Compact Strip Production) process proved to be successful. Besides Crawfordsville, C S P machines Figure 2.18: Layout of the Nucor CSP continuous thin slab casters [47]. have also been installed at Nucor Hickman (in 1992 and 1994), Nucor Berkeley County (1996) and at Gal lat in Steel (1995) [42]. Fig.2.18 shows the layout of the Nucor Steel C S P line. In an interesting development, Acme Steel was the first to feed its C S P from a B O F (1996), having leapfrogged directly from an ingot shop to thin slab casting [45]. The C S P process produces slabs of 50-60 m m thickness [46]. One of the problems that immediately becomes apparent is the placement of an S E N (Submerged Entry Nozzle) in a such a confined space. The SMS caster tackles this via. a funnel shaped mould. Fig.2.19 depicts this mould, where, to accommodate the S E N , there is a funnel shaped bulge in the meniscus region. This funnel (or pocket) gradually tapers away, so that Ch.2 Literature Review 25 Figure 2.19: Schematic drawing of the convex mold [46]. the broad face walls are parallel lower down the mould. Wiinnenberg and Schwerdtfeger [47] had measured mould wall temperatures in a C S P machine over a cast. Fig.2.20 shows longitudinal profiles of broad face temperatures, while Figs.2.21 and 2.22 depict transverse profiles of broad and narrow face tempera-tures respectively. It is apparent that in the upper part of the mould the heat removal is more or less steady state, and decreases with distance below the meniscus (Fig.2.20). However, there is strong time dependence in the lower part of the mould (Figs.2.20 and 2.21). Wiinnenberg and Schwerdtfeger [47] postulate that the unsteady state heat transfer reflects the varying contact between mould and strand, because of the mechan-ics involved in squeezing in the bulge in the strand. There is also variation in heat removal from the two broad faces. Fig.2.22 shows that Ch.2 Literature Review 26 250 200 U o 2 100 E 50 AISI grade 1024 -2.4 m/min 954 mm x 60 mm 8 mm concave shape Different times Meniscus I I 0 100 200 300 400 500 600 Distance From Top ol Mold (mm) 700 Figure 2.20: Longitudinal profiles of the temperature in the broad mold plate of a funnel-shaped mold at a distance of 5 mm from the hot face [47]. o 2 9 0 k 0 o. £ 300 260 .220 180 300 260 220 180 (a) AISI grade 1024 4 m/min 1,030 mm x 60 mm 10 mm concave shape - min - a — - f — — - a a 2 5 ' 4 0 x" o 42-53 i > . . i-•85-100 i i i i i 200 400 600 800 1,000 - - * * — i i i i i i i * i 200 400 600 Distance From Narrow Face (mm) 800 1,000 Figure 2.21: Transverse profiles of the temperature in a broad mold plate of a funnel-shaped mold at a distance of 5 mm from the hot face at (a) 245 mm and (b) 755 mm from the top of the mold [47]. o Distance from top of mold: 300h a i60 mm 500 mm 250 h o 850 mm 200h • 150 9 B 100 h 0 ft, E 50 0. AISI grade 1015 4 m/min 1,030 mm x 60 mm 10 mm concave shape J_ "0 10 20 30 40 50 Distance From Loose Side (mm) 60 Figure 2.22: Transverse profiles of the temperature in a narrow mold plate of a funnel-shaped mold at a distance of 5 mm from the hot face [47]. Ch.2 Literature Review 27 temperature profiles are non-symmetrical in the lower part of the narrow face walls. Wiinnenberg and Schwerdtfeger [47] trace this to differing intensities of shell deforma-tion on the outer and inner mould sides. O'Connor and Dantzig [46] had conducted detailed finite element analysis of heat trans-fer in the moulds at Nucor Steel, and Fig.2.23 shows the predicted temperature contours Figure 2.23: Temperature contours on inside face of a 20-mm-thick mold [46]. on the hot face of a mould with a wall thickness of 20 m m . These contours match well wi th patterns of zinc pickup by the mould [46]. ft is seen that the peak hot face temperatures are ~ 4 5 0 ° C , which is substantially higher than the maxi mu m of 350°C recommended by Wada et al. [19]. Fig.2.24 shows the computed and measured temper-ature profiles down the mould, along the outboard edge of the funnel (vertically through the highest temperatures in the mould). Like in Fig.2.20, these too were at a distance Temperature (C) A - 225 B - 2S0 C - 275 D - 300 I - 325 F - 350 C - 375 • - 400 I - 425 J - 450 X - 475 Ch.2 Literature Review 28 600 100 200 300 Temperature (°C) 400 500 Figure 2.24: Calculated mold temperatures (along outboard edge of funnel) 5 mm from the hot face for three mold thicknesses, compared with values measured at Nucor Steel for a 20-mm-thick mold [46]. Figure 2.25: Computed variation of mold heat flux with position for the 20-mm-thick mold [46]. Ch.2 Literature Review 29 of 5 m m from the hot face. However, temperatures at Nucor Steel are much higher than those reported by Wiinnenberg and Schwerdtfeger [47]. The repercussions of running the mould so hot are seen in the high incidence of mould cracking and reduced working life reported by Nucor Steel [41, 46]. O'Connor and Dantzig [46] had also calculated the peak and average hot face heat fluxes to be ~5.1 and 3.1 M W / m 2 respectively. Fig.2.25 shows the heat flux pattern on the mould cold face. Wolf [51] had compared overall mould heat removal for thin and thick slab casters. «1 B 0 0 2 Slab thickness (mm) Mold powder • B © 50 70 A (low viscosity) B (high viscosity) 3.5 • 3.0 2.5 -2.0 It 1.5 1.0 - Conventional slab casting % 1 2 3 4 5 6 Cast ing S p e e d ( m / m i n . ) Figure 2.26: Integral mold heat flux versus casting speed for two cases of thin slab casting with two different mold powders (i.e. , low and high viscosity), in comparison with conventional slab casting [51]. These is presented in Fig.2.26 as plots of integral mould heat fluxes (i.e. those obtained by the water A T method described in Section 2.2.1) vs. casting speed. The 50 m m thick slabs were cast from a C S P caster, and the 70 m m slabs from the C O N R O L L process Ch.2 Literature Review 30 of Voest-Alpine Stahl Linz G m b H [51]. W h i l e the casting speeds and heat fluxes of the C S P casters are much beyond the ranges of conventional slab casters, it is instructive to see that, when extrapolated back, the regression lines for th in slab casters lie in the conventional caster range. Chapter 3 Scope and Objectives The continuous casting of steel slabs has been the subject of extensive research, although this has been mainly focussed on the conventional (or thick slab) casters. Among other significant work, previous investigators had postulated a mechanism for heat transfer in the slab caster mould. The goal of this investigation was to study heat transfer in both conventional and thin slab casters, as well its effect on some aspects of mould operation and slab quality. This was achieved with the help of previously developed models, used i n conjunction with new models and commercial finite element method software. To accomplish this the following specific tasks were carried out: 1. A n inverse heat conduction model was uti l ized to analyse data from a billet caster which used mould powder as lubricant. 2. M o u l d temperature data for conventional slab casters were examined. Mathe-matical models were employed to calculate heat fluxes and hot face temperatures, which were linked with slab surface quality. 31 Ch.3 Scope and Objectives 32 3. F ini te element method models were developed to back-calculate mould heat fluxes from measured mould wall temperatures for an operational C S P caster. 4. A simple prescription was developed for the accurate variation of water velocity into the working life of a C S P mould. Chapter 4 M a t h e m a t i c a l M o d e l l i n g This chapter discusses the mathematical models that have been used in the present study to analyze the heat flow conditions in continuous casting moulds. In addition, a model that predicts the solidified shell thickness at the mould exit is also introduced. Reasons for the applicability of these models in the present study are presented. 4.1 Modelling of the Mould Longitudinal Section In this section two complementary models are described. The first gives a solution to the "forward" problem i.e. given the boundary conditions (primarily the hot face heat flux), the model calculates the thermal field in the mould wall . The second model solves the "inverse" problem - finding the heat flux based on temperatures measured within the mould wall . 33 Ch.4 Mathematical Modelling 34 4.1.1 The Forward Problem This model was developed by Samarasekera [48] at the University of Br i t i sh Columbia , and has been described in detail elsewhere [8, 48]. It has been used extensively to calculate the thermal field in both billet and slab casting moulds [8]. Fig.4.1 shows Backing mould ii ! Cooling water Figure 4.1: Schematic diagram of longitudinal mid-plane through a mould [8]. the domain of calculation - a vertical plane through the mould wal l , cooling water channel and water jacket/backing plate. The model assumes steady state conditions, and solves Fourier's Law of heat conduction to calculate the temperature field in the two dimensional longitudinal section, based on a user imposed heat flux on the mould hot face. Since a longitudinal section of the mould is modelled, it is assumed there is no heat conduction in the transverse direction - that of the mould width . W h i l e this assumption is reasonably valid for the mid-plane of a billet mould, it is not so apparent for slab Ch.4 Mathematical Modelling 35 casters. There, the mold wall is cooled by water flowing through a large number of vertical cooling channels machined into the copper walls. This is shown schematically mm Width Backing Plate Thickness Copper Plate Cooling Channel Slot c Cooling Channel B Thermocouple Location • Hot Face Figure 4.2: Schematic diagram of the transverse section through the mould wall employed in the 2-D (transverse) model [6]. Hot face O O U o C C3 D Figure 4.3: Model predicted isotherms on the trans-verse section of the copper plate [49]. in Fig.4.2, which depicts a transverse section of a wall . The cooling channels are located at fixed intervals, and can thus result in heat conduction along the width of the copper plate. Mahapatra [49] had modelled a transverse slice of the wall (area A B C D in Fig.4.2) and the results are shown in Fig.4.3. It is interesting to see that any two dimensional effects Ch.4 Mathematical Modelling 3 6 are confined to the area between the channels. In front of the channels, the isotherms are more or less parallel to each other, especially near the hot face. Similar temperature contours have been reported by other researchers [4, 30, 32]. Fig.4.3 validates the assumption that the cooling channels do not cause significant transverse heat conduction in the region between the water channels and the hot face. This implies that as long as thermocouples are located i n this region of the mould wall , there are no serious errors introduced by use of a 2-D longitudinal model (except those pointed out by Mahapatra et al. [6] in Fig.2.12). 4.1.2 The Inverse Heat Conduction Problem As had been discussed in Section 2.2.2.2, a model that solves the forward problem can also be used for the inverse problem, by manually adjusting the boundary heat flux. A mathematically more rigorous approach consists in an analytical or numerical solution to the Inverse Heat Conduction Problem ( I H C P ) . Pinheiro [16] has recently developed such a model, which calculates the heat flux profile down the mould wall . The I H C P can be succinctly stated as follows: given M measured temperatures Tj (j = l , 2 , . . . , M ) , estimate the heat flux profile components ( i = l , 2 , . . . , M ) that give rise to these temperatures. Fig.4.4 shows a schematic of the stated problem. The solution of the I H C P is effected by minimizing the least square error between the measured temperatures and those computed by the direct solution, using the estimated values of the heat flux components. The minimizat ion is done wi th respect to each of Ch.4 Mathematical Modelling 37 x=o x=x, z=o • T , • T , Meniscus cooling water Heat Flux Profile ? •T, M Mould Figure 4.4: Schematic diagram showing the domain for the Inverse Heat Conduction analysis [16]. the unknown heat flux components [16]. Of course, there are problems of uniqueness and stability, inherent in the solution of such an ill-posed problem. Pinheiro [16] has addressed this by the use of a "regularization" technique, which reduces the magnitude of oscillations in the solution. A flowchart of the solution technique is presented in Fig.4.5 (the sensitivity matrix X represents changes in the computed temperatures with respect to changes in the heat flux components). Pinheiro [16] reports the inverse procedure to be not only reliable, but much easier and faster to perform compared to the trial-and-error approach. In addition to the 2-D I H C P modelling described, a one dimensional, steady state model was developed and used to back-calculate heat fluxes i n conventional slab casters. 4.2 One Dimensional Modelling Ch.4 Mathematical Modelling 38 Read: m Measured temperatures T j Regularization coefficient a Heat flux components q°i , I Solve direct problem for q'i 1 Compute q'i by sequentially perturbing q"i by 10% Solve direct problem for each q'i Compute sensitivity matrix X Compute transpose of X, X T I Compute [A] = (XTX+a*I) Compute {f}=XT(T-T°) Direct Problem subroutine 1 ' Matrix Inversion Compute [A]"1 w subroutine 1 Compute Solution: q = q°+[A]-1 {f} Figure 4.5: Conceptual flow-chart of the FORTRAN program developed to compute the solution for the IHCP associated to estimation of mould heat flux profile [16]. Ch.4 Mathematical Modelling 39 Thomas [4] had mentioned that below the meniscus region, heat conduction in the mould wall is basically one dimensional. This is also apparent from an inspection of Figs.2.11 x=0 x=l x=L T(0) Cold face MOULD W A L L TMC Hot location face Figure 4.6: Schematic of 1-D heat conduction in the mould wall. and 4.3. In Fig.2.11 it is seen that 50-60 m m below the meniscus, the axial isotherms are parallel. The same is seen in Fig.4.3, where the transverse temperature contours are parallel. It can thus be concluded that a one dimensional model can be safely used to describe heat conduction below the meniscus. Fig.4.6 shows a schematic of this one dimensional system. 4.2.1 Assumptions 1. Heat conduction is one dimensional (into the mould wall thickness) and steady state. 2. Thermal conductivity of the mould wall is temperature independent [6]. 3. The water cools the mould in the convective cooling regime [6, 8, 16]. 4. There is a linear rise in the temperature of the cooling water between the inlet and outlet. Ch.4 Mathematical Modelling 40 4.2.2 M o d e l Derivation For the 1-D steady state system shown in Fig.4.6, the Laplacian reduces to: d2T = 0 dx2 (4 . i ; The solution of this wi l l lead to a linear temperature profile of the form T = a + b x (4.2) where a and b are constants to be evaluated from the boundary conditions. Now, at the mould hot face, k dT_ dx =>. kb = q b (4.3) A t the mould cold face there is convective cooling by the water, hence k — dx = h (T(0) - Tw) x=0 kb — h(a — T u a = Tw + h (4.4) Substituting Eq.4.3 and Eq.4.4 i n Eq.4.2, we get: (4.5) If there is a thermocouple at a distance / from the cold face, then: T(l) = T, known (4.6) Ch.4 Mathematical Modelling 41 specific heat of water (4182 J / k g ° C ) dhyd hydraulic diameter of cooling channel (m) h heat transfer coefficient at the mould wall cold face ( W / m 2 o C ) k thermal conductivity of the mould wall ( W / m ° C ) h njyj thermal conductivity of water (0.597 W / m ° C ) q heat flux into the mould hot face at the thermocouple location ( W / m 2 ) I horizontal distance of the thermocouple from the mould cold face (m) L effective thickness of the mould wall (m) ^channel vertical length of the cooling channel (m) T mould wall temperature (°C) T-inlet inlet water temperature (°C) Tknown temperature measured by the thermocouple (°C) T 1 outlet outlet water temperature (°C) T water temperature at the thermocouple location (°C) Uw flow velocity of water (m/s) X distance into the mould wall thickness (m) z vertical distance between the thermocouple and water inlet (m) viscosity of water (993 x l O - 6 N s / m 3 ) Pw density of water (998.2 k g / m 3 ) Table 4.1: List of symbols used in the 1-D model. Ch.4 Mathematical Modelling 42 Substituting this in Eq.4.5 leads to: Fknown — Tw ~\~ ~T ~\~ ~T I (4*7) h k Eq.4.7 can then be re-arranged to yield an expression for the hot face heat flux: " = l/h + l/k ( 4 " 8 ) Since a linear variation of the cooling water temperature is assumed, rr n-i , (^outlet ~ 7in/ e i \ f A n\ Tw = Tiniet + [ j ) Z (4-9) V ''channel ' The heat transfer coefficient at the cold face is evaluated from the expression of Szekely and Themelis [14]: h = 0.023 — (pwUwdhyA (9i^A°A ( 4 . i o ) dhyd \ fJ-w j \ k"w ' The physical properties of water were evaluated at the bulk water temperature [6, 16] and their values are given in Table 4.1. The hydraulic diameter of the cooling channel (dhyd) is defined as: /crossectional area of coolinq channel\ , , _ . dhyd = 4 : '- f (4.11) y perimeter oj cooling channel J 4.3 F E M M o d e l l i n g Fini te element method modelling using commercial software- was also carried out in the present study. The F E M models were used to back-calculate heat fluxes for th in slab casters. This was accomplished by analyzing transverse sections of the mould wall , Ch.4 Mathematical Modelling 43 similar to that in Fig.4.3. The finite element models (i.e. system geometry, material properties, boundary condi-tions and meshing) were defined in M S C / P A T R A N 1 (Version 6.0), since it provided a convenient graphical user interface. From M S C / P A T R A N , the models were exported as an A B A Q U S 2 file and solved using A B A Q U S (Version 5.6) on the Silicon Graphics 3 workstations at the Centre for Metallurgical Process Engineering, University of Br i t i sh Columbia . Commercial F E M packages were used since the thin slab casters had a different cooling geometry, incorporating cooling holes on the narrow faces, and both slots and holes on the broad faces. It was thought that the more complicated cooling arrangements would preclude the use of the 1-D model described above. Transverse sections of the mould wall adjacent to thermocouple locations were modelled. Hot face heat fluxes were obtained by a trial-and-error method, i.e. manually adjusting the heat flux boundary condition in the model unt i l the calculated and thermocouple measured temperatures matched. For the cold face boundary conditions, a procedure similar to the 1-D model was adopted. The heat transfer coefficient was evaluated using Eq.4.10, while the water temperature was obtained by linearly interpolating between the inlet and outlet temperatures (Eq.4.9). •"•Registered trademark of The MacNeal-Schwendler Corporation. 2Registered trademark of Hibbitt, Karlsson & Sorensen, Inc. 3Registered trademark of Silicon Graphics, Inc. Ch.4 Mathematical Modelling 44 Mesh refinement was carried out, by reducing the element edge length from 3 to 1 m m . After 1.5 m m , no effect of further refinement could be discerned on the calculated ther-mal field and this mesh size was used for all the F E M analysis in this study. A more detailed description of the F E M models and results are presented i n a later chapter. 4.4 Modelling of Strand Solidification Chandra [50] had developed a model for calculating solidification in a continuously cast strand. This was part of a more intricate model encompassing the mechanical interaction between the strand and mould in a billet caster, and has been described in detail elsewhere [50]. The model needs a user specified mould hot face heat flux. The effects of tundish superheat and the steel composition on solidification are also accounted for. The model was used to estimate the shell thickness at the mould exit for the thin slab caster strands. Chapter 5 Industr ia l Measurements of Heat Transfer This chapter presents design and instrumentation details of the casters studied in the present investigation. These include conventional and thin slab casters, as well as a billet caster. Where appropriate, samples or summary of data used for mathematical modelling have also been furnished. 5.1 Conventional Casters Heat transfer in the two conventional (or thick slab) casters at Company A was analysed. Table 5.1 summarizes the caster designs for the two Company A casters, as well as a similar caster from Company B . A l l the heats studied were the the same Company A grade EA061 (composition in Table 5.2), which is an L C A K steel. Details about the two Company A casters vis. a vis. instrumentation and the data received are given below. 45 Ch.5 Industrial Measurements of Heat Transfer 4 6 C o m p a n y A #1 C o m p a n y A # 2 C o m p a n y B M o u l d length (mm) 904 900 900 M o u l d coppers C r - Z r alloyed C r - Z r alloyed A g bearing Slab thickness (mm) 265.8 223 254 Hot face coating 3 m m of N i 1 2 m m of N i None Effective wall thickness (mm) 24 18.65 30 Meniscus level (mm from mould top) 100 100 100 Cooling channel section ( m m x m m ) 21x5 12x5 25x9 No. of channels: — on broad faces 57 102 78 — on narrow faces 9 11 8 Cooling water velocity (m/s) ~ 9 - l l - 7 - 1 1 - 5 Casting speeds (m/min) -0 .5-1 .9 -0 .8-1 .6 -0 .8-1 .6 Table 5.1: Design details of the Company A and Company B slab casters. 1 Only on the bottom 500 mm of the mould. c M n S P Si Cr N i Sn T i V A l 0.050 0.200 0.015 0.018 0.050 0.100 0:080 0.020 0.025 0.008 0.065 Table 5.2: Steel composition (in wt.%) for the Company A heats. Ch.5 Industrial Measurements of Heat Transfer 47 5.1.1 T h e Company A #1 Caster B F 1 1 3 2 4 - 1 2 23-11 1 4 C E N T R E 1 6 ! L i f e I 2 i 3 1 6 4 C E N T R E " " " L I N E 229.5mm J^p J_ _ 1 535^ 5mrrl 83mm _ l J o o B E 2 ± 5 - 1 7 -6-m i 1880mm tf. %\ * " " T 2 ] o i*> ! Figure 5.1: Thermocouple layout for the Company A #1 caster. This caster is instrumented with two rows of thermocouples, 200 and 300 m m below the mould top. There are four columns of thermocouples on each broad face, and two on each narrow face. Fig.5.1 shows the thermocouple layout in a top view of the caster, with the inner and outer rings of numbers denoting the top and bottom row of thermo-couples respectively. As is the usual practice, the thermocouples are placed in through the bolts holding the copper walls to the steel backing plates. They were located 6.5 m m from the mould hot face (i.e. 17.5 m m from the cold face). Readings from all the 24 thermocouples were received, together wi th the corresponding water flows, A T s and casting speeds. Each variable was logged at a 2 H z frequency. The data consisted of non-contiguous sets of 300 continuous samples, i.e. 150 s sections of mould operation. Fig.5.2 shows the wall temperatures measured by two thermocouples, one each from a broad and narrow face. The raw data received from Company A was then averaged with respect to the casting speed, i.e. values of each variable were collected for the same casting speed, and av-eraged so that a unique number was obtained for a single casting speed. Average wall Ch.5 Industrial Measurements of Heat Transfer 48 CD ro i CD CL. E CD 0 300 600 900 1200 1500 1800 2100 2400 2700 3000 Time (s) Figure 5.2: Typical thermocouple traces for the Company A.#l caster. temperatures from each mould fa,ce have been plotted in Fig.5.3. Table 5.3 summarizes the data used for calculating heat fluxes for the #1 caster. To enable comparison with the #2 caster, heat fluxes were calculated at a casting speed of 1.7 m / m i n , and the values in Table 5.3 correspond to this speed. Only two wall temperatures (for the two middle thermocouple columns) have been reported for each broad face, since the narrow width of the slabs being cast placed the outer two columns of thermocouples outside the casting zone. Ch.5 Industrial Measurements of Heat Transfer 49 300 T 290 -280 -270 -260 -250 -240 -230 -220 -o o 210 -i_ Z3 200 -E CD Q. 190 -E tu 1-180 -Wall 170 -160 -150 -140 -130 -120 -110 -100 -90 -80 -• T M C 2 (on BF 1) o T M C 8 (on BF 2) T T M C 5 (on NF 1) v T M C 1 1 ( o n N F 2 ) o Q> p o. o o o o O O ! o .5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 Casting speed (m/min) Figure 5.3: Company A #1 caster wall temperatures averaged for each casting speed. Ch.5 Industrial Measurements of Heat Transfer 50 B F 1 B F 2 N F 1 N F 2 Water velocity (m/s) 9.88 9.91 9.06 9.05 Water inlet temperature (°C) 40.00 40.00 40.00 40.00 Water A T (°C) 5.13 4.90 6.71 6.36 Copper temperatures (°C): — @ 200 m m from mould top 242, 243 228, 238 137, 135 133, 131 — @ 300 m m from mould top 173, 172 175, 178 114, 112 111, 111 Table 5.3: Summary of data used for calculating heat transfer conditions for the Com-pany A #1 caster (steel grade EA.061 cast at 1.7 m/min). B r o a d faces N a r r o w faces Water velocity (m/s) 8.7 11.0 Water inlet temperature (°C) 40.03 40.03 Water A T (°C) 5.94 9.52 Copper temperatures (°C): — @ 200 m m from mould top 130 110 — @ 300 m m from mould top 118 99 Table 5.4: Summary of data used for calculating initial heat transfer conditions for the Company A #2 caster (steel grade EA061 cast at 1.7 m/min). B r o a d faces N a r r o w faces Water velocity (m/s) 7.08 7.33 Water inlet temperature (°C) 40.00 40.00 Water A T 1 (°C) 9.50 15.00 Copper temperatures (°C): — @ 200 m m from mould top 150 130 — @ 300 m m from mould top 125 110 Table 5.5: Summary of data used for calculating heat transfer conditions after water velocity reduction for the Company A #2 caster (steel grade EA061 cast at 1.7 m/min). Extrapolated from values available from lower casting speeds. Ch.5 Industrial Measurements of Heat Transfer 51 5.1.2 T h e Company A #2 Caster Heat transfer at Company A #2 was studied from the perspective of cooling water velocity changes. Unfortunately, operational data supplied by Company A was quite scarce, wi th only a single time-averaged copper temperature for the broad and narrow faces being given. This was was for a casting speed of 1.7 m / m i n . As before, thermo-couples are located 200 and 300 m m below the mould top, and for the #2 caster, are placed 3 m m from the mould cold face. Table 5.4 summarizes the data used for calculating the ini t ia l thermal conditions in the caster. Water velocities were then turned down at the Company A #2 caster, and the data used for heat flux calculations made after the change are i n Table 5.5. Correspond-ing water A T s for the wall temperatures were not available, and hence the values given in Table 5.5 have been linearly extrapolated up from those for available lower casting speeds. 5.2 The C S P Caster Some relevant design details of the S M S thin slab (or C S P ) caster studied in this investigation are summarised in Table 5.6. A schematic of this type of mould has also been presented in Fig.2.19. Because of the unique characteristics of the C S P mould, there are some very interesting aspects of the design, and these are discussed below. Ch.5 Industrial Measurements of Heat Transfer 52 M o u l d length (mm) 1100 M o u l d coppers C r - Z r alloyed Slab thickness (mm) 50 Hot face coating None Effective wall thickness (mm): — on broad faces 15 - 25 — on narrow faces 19 Meniscus level (mm from mould top) 70 Nominal cooling channel section ( m m x m m ) 20x25 No. of channels on broad faces 38 Cooling hole diameter (mm): — on broad faces 9 — on narrow faces 14 No. of cooling holes: — on broad faces 22 — on narrow faces 2 Cooling water velocity (m/s) ~8.4-13 Casting speeds (m/min) ~ 4 Table 5.6: Details of the CSP caster at Company C. 5.2.1 Mould Pocket As is shown in Fig.2.19, the C S P caster accommodates the S E N by a funnel shaped bulge, or pocket, in the meniscus region. This pocket extends a m a x i m u m of 60 m m into each broad face, so that the distance between the broad faces is 170 m m at the centre of the mould top. The m a x i m u m width of the pocket is 1150 m m , at the mould top. B o t h the pocket width and depth taper away, and at 850 m m down from the mould top the broad faces become parallel. A frontal projection of the pocket on the mould broad face is shown in Fig.5.8. Ch.5 Industrial Measurements of Heat Transfer 53 5.2.2 Broad Face Cooling As can be seen from Table 5.6, the broad faces are cooled by water flowing through both rectangular channels and circular holes. The ends of the cooling slots and holes are machined parallel to the mould hot face (as shown in Figs.5.4 and 5.5), so that in spite of the slant introduced by the mould pocket, effective wall thickness is constant. However, this implies a varying depth for the cooling channel. A constant cross-section is maintained for the water flow by using metal inserts that vary in depth down the mould, such that a rectangular annulus of constant dimensions is left for the cooling water. The cooling slot extends from 32 m m down from the mould top to 32 m m up Figure 5.4: Schematic of side view of a CSP caster broad face. from the mould bottom. Cooling holes are present in the C S P caster broad faces too, but are only located Ch.5 Industrial Measurements of Heat Transfer 54 Copper mould wall Centre Line Figure 5.5: Schematic of top view of a CSP caster broad face. adjacent to the bolt holes, and extend from 32 m m to 360 m m down the mould top. Fig.5.6 shows the detail on a transverse section of the broad face near a bolt hole, located at the left centre line. The right centre line bisects a cooling slot. The effective wall thickness (23.2 mm) shown here is that reported by Company C for the cast being studied. In practice, the coppers are machined down to 15 m m from an ini t ia l thickness of 25 m m , and then scrapped. 5.2.3 Narrow Face Cooling The narrow faces have a width of 50 m m , and only incorporate two cooling holes each. These are of 14 m m diameter, and like the broad face slots, extend down the ful l mould length, except for 32 m m at each end. The transverse section shown in Fig.5.7 gives dimensional details of the narrow face. The wall thickness given here (19 mm) is for new coppers, since Company C did not supply any measurements for wall thickness after wear. Ch.5 Industrial Measurements of Heat Transfer 55 HOT F A C E Copper-mould wall Thermocouple location Cooling hole (for water) Cooling slot (for water); Symrrietry line Symmetry line Figure 5.6: Transverse section of the CSP caster broad face. B r o a d Faces N a r r o w Faces Distance of top row from mould top (mm) 227 170 Distance of bottom row from mould top (mm) 389 365 Distance from cold face (mm) 9 3 Table 5.7: Thermocouple locations on the CSP caster at Company C. Ch.5 Industrial Measurements of Heat Transfer 56 H O T F A C E Figure 5.7: Transverse section of the CSP caster narrow face. Ch.5 Industrial Measurements of Heat Transfer 57 575 mm 744 mm C E N T R E ! 780 mm i Figure 5.8: Thermocouple and mould pocket locations on the CSP caster broad face. Ch.5 Industrial Measurements of Heat Transfer 58 5.2.4 Mould Instrumentation The mould is instrumented with two rows of thermocouples for breakout detection and control. Each broad face has eight columns of thermocouples, which are placed through holes drilled in through the bolts, with the columns being symmetrical around the mould centre. The narrow faces have only a single column of thermocouples. Details of the thermocouple locations are given in Table 5.7, as well as in Figs.5.6 and 5.7. Thermocouple numbering for the broad faces is shown in Fig.5.8. A l l the thermocouples were operational, except #4 on the loose face. This was turned off because of excessive interference from the electro-magnetic brake. 5.2.5 Data for Heat Flow Analysis M o u l d wall temperature readings were supplied by Company C as screen printouts from the control software. Cast # 10851, consisting of 5 heats, was selected for analysis. After inspecting the data, it was decided that a representative slab from each heat would be analysed in detail . The slabs were chosen so that they corresponded to periods of fairly steady-state mould operation, as well as being all cast at the same speed of 3.96 m / m i n . Table 5.8 gives the identification numbers of the five slabs selected, and also the start and end times (in terms of minutes into the cast), between which they were produced. The total length of the cast was about 195 minutes. Steel compositions of the five slabs are given in Table 5.9. Now, for the back-calculation of the heat fluxes, three main sets of data are required Ch.5 Industrial Measurements of Heat Transfer 59 Slab # Start time (min) E n d time (min) 10851-01-06 35.5 40.4 10851-02-02 45.3 51.4 10851-03-06 115.7 124.3 10851-04-04 141.8 148.6 10851-05-01 164.1 167.9 Table 5.8: Slab numbers and the times between which they were cast. Slab C M n S P Si Cr Ni Cu Mo Sn T i V 01-06 0.501 0.627 0.001 0.014 0.174 0.034 0.011 0.017 0.006 0.002 0.038 0.008 02-02 0.824 0.880 0.002 0.010 0.155 0.033 0.016 0.017 0.006 0.004 0.04 0.006 03-06 0.824 0.847 0.002 0.011 0.170 0.042 0.015 0.024 0.008 0.003 0.04 0.007 04-04 0.826 0.869 0.001 0.014 0.179 0.031 0.012 0.018 0.006 0.004 0.03 0.007 05-01 0.861 0.851 0.007 0.011 0.211 0.036 0.013 0.014 0.007 0.002 0.047 0.005 Table 5.9: Steel composition (in wt.%) for the five slabs analysed. in the F E M models - mould wall temperature, the water heat transfer coefficient, and the water temperature at the thermocouple location. 5.2.5.1 M o u l d W a l l T e m p e r a t u r e Fig.5.9 shows the temperatures measured for the entire cast by the upper thermocouples on the narrow faces. Figs.5.10 and 5.11 plot the same for the upper row of thermocouples on the fixed broad face (locations of the thermocouple numbers are detailed in Fig.5.8). The width (1422 mm) of the slabs selected placed the broad face thermocouples 1,2,15 and 16 outside the casting zone. Thermocouple readings corresponding to the time intervals for the slabs were averaged to obtain a unique wall temperature for each thermocouple location in each slab. Ch.5 Industrial Measurements of Heat Transfer 60 210 205 200 195 190 185 o ° , 180 175 170 165 i — | 160 155 150 145 140 135 130 CD i_ -*—< ro CD Q. E CD [ South NF No rtn Nr I -| I » . • . * J . . . ^ . -s . -f | _ «' < - •• — 1 1 I 20 40 60 80 100 120 140 Time into cast (min) 160 180 200 Figure 5.9: Top row thermocouple readings for the CSP caster narrow faces. Ch.5 Industrial Measurements of Heat Transfer 61 O CD CO CU CL E cu .co 130 0 20 40 60 80 100 120 140 160 180 200 Time into cast (min) Figure 5.10: Top row thermocouple readings for the left half of the CSP caster fixed broad face. Ch.5 Industrial Measurements of Heat Transfer 62 140 -\ 130 -I ! I ! 1 1 1 I 1 1 1 0 20 40 60 80 100 120 140 160 180 200 Time into cast (min) Figure 5.11: Top row thermocouple readings for the right half of the CSP caster fixed broad face. Ch.5 Industrial Measurements of Heat Transfer 6 3 5.2.5.2 W a t e r H e a t T r a n s f e r Coeff ic ient Eq.4.10 was used to evaluate the coefficient, wi th the values for the water constants substituted from Table 4.1. The total water flow rate to the mould was given in the log sheets. Flow to each of the narrow faces was maintained at a constant 41 G P M , and subtracting this from the total flow gave the flow rate for the broad faces. It was assumed that flow was equally divided between each of the two sets of narrow and broad faces. Water velocities were then obtained by simply dividing the flow rate for each mould face by the total cross-sectional area of slots and/or holes. Since flow for each narrow face was 41 G P M , this implied a water velocity of 8.4 m/s , Slab # 01-06 02-02 03-06 04-04 05-01 Water velocity (m/s) 12.3 10.8 10.8 10.7 10.8 Heat transfer coefficient ( k W / m 2 o C ) : — cooling holes 36.0 32.5 32.5 32.4 32.5 — cooling slots 37.9 34.2 34.2 34.0 34.1 Table 5.10: Water velocities and heat transfer coefficients for the CSP caster broad faces. and a corresponding heat transfer coefficient of 24.4 k W / m 2 o C . The total water flow to the mould was different for each slab, and the resulting broad face water velocities and heat transfer coefficients are summarised in Table 5.10. Even though the same water velocities have been assumed for the cooling slots and holes, they have different heat transfer coefficients because of dissimilar hydraulic diameters. Ch.5 Industrial Measurements of Heat Transfer 6 4 Slab # 01-06 02-02 03-06 04-04 05-01 Water inlet temperature (°C) 42.1 42.1 42.2 42.1 42.2 F ixed broad face A T (°C) 6.8 7.6 7.6 7.4 7.4 Loose broad face A T (°C) 6.8 7.8 7.5 7.3 7.3 South narrow face A T (°C) 8.0 6.9 7.0 6.7 7.1 Nor th narrow face A T (°C) 7.1 6.0 8.0 7.9 7.3 Table 5.11: Water inlet temperature and A T s for the CSP caster. 5.2.5.3 Water Temperatures Water inlet temperatures and A T s were noted in the log sheets. The linear interpo-lation technique described in Section 4.2 was used to calculate the water temperature corresponding to the location of a thermocouple row. Table 5.11 summarises the water temperature information supplied by Company C . 5.3 The Billet Caster In 1995, an instrumented mould tr ial was carried out by Pinheiro [16] and other re-searchers from the University of Br i t i sh Columbia at a Canadian billet casting m i n i -m i l l . Instead of oi l (the usual lubricant for billet casting) powder was used at this t r ia l , which enables comparison with slab casters. Details of the plant t r ia l , instrumentation, data acquisition etc. have been reported by Pinheiro [16]. The casting conditions and the mould design details are summarised in Table 5.12. The mould was instrumented with thermocouples installed through holes dril led half-way into the wall thickness. Hence they were 7.8 m m from the mould hot face. O n the Ch.5 Industrial Measurements of Heat Transfer 65 Machine type curved M o u l d material D H P copper M o u l d section ( m m x m m ) 209x209 M o u l d length (mm) 812.8 M o u l d wall thickness (mm) 15.6 Corner radius (mm) 3.175 M o u l d taper parabolic Init ial taper (100 m m below the mould top, pc t . /m) 4.9 M o u l d constraint 4 sided Water channel gap (mm) 4.99 Metallurgical length (mm) 19787 Steel carbon content (%) 0.11 M o u l d oscillation frequency (cpm) 150 Casting speed (m/min) 1.22 Negative strip t ime (s) 0.14 Cooling water flow rate ( G P M ) 500 650 Table 5.12: Billet caster design details and casting conditions (after [16]). Ch.5 Industrial Measurements of Heat Transfer 66 mould east face (for which the calculations were performed) there were a total of 15 working thermocouples down the mould length. During the heat the water flow rate was increased from 500 to 650 G P M , which trans-lates to an increase in water velocity from 7.7 to 9.9 m/s . For each period of constant water velocity, sections of thermocouple readings which represented steady state condi-tions were selected and time-averaged to eliminate noise. Chapter 6 Heat Transfer i n H i g h Speed Conventional Slab Cast ing In late 1996, Company A commissioned a second conventional slab caster, of which some aspects of the mould design are presented in Table 5.1. High speed casting was com-menced at this caster, but the cast slabs were plagued by a high incidence of transverse corner cracking - which led to upto a third of the production being scrapped. Cracks were found on all four corners, and for all the grades being cast. In this chapter we shall look at how this problem was tackled by changing the cooling water velocity to modify heat transfer conditions in the mould. 6.1 Role of Water Velocity Mahapatra et al. [7] had postulated a mechanism for mould heat transfer with powder casting which has been reviewed in Section 2.1. Whi le they had found evidence of the effect of wall thickness on heat transfer, they only postulated effects of water velocity. Here we shall investigate the effects of water velocity on mould heat transfer. 67 Ch.6 Heat Transfer in High Speed Conventional Slab Casting 68 As has been described in Section 5.3, data for validating water velocity effects on mould heat transfer had been obtained from a billet caster using powder lubrication. Design details for the billet caster mould are in Table 5.12. The measured mould wall temper-atures were input to the I H C P model described in Section 4.1.2 to obtain the mould heat fluxes and hot face temperatures. The calculated axial profiles of the mould hot face heat flux and temperature are shown in Fig.6.1. It is clearly seen that the peak heat flux (at the meniscus) is higher by ~0.45 M W / m 2 for the lower water velocity, which implies a more than 18% increase. The peak hot face temperature also reflects a similar difference of 15%, with that for the lower water velocity being more than 20°C hotter. W h i l e the heat flux profile for the lower water velocity is definitely higher in the upper part of the mould (upto ~350 m m from the mould top), the difference is not so strong in the lower half of the mould. Fig.6.1 clearly demonstrates the validity of the heat transfer mechanism proposed by Mahapatra et al. [7]. Everything else being the same, a reduction in water velocity raises mould hot face temperatures, resulting in the formation of a smaller slag r i m at the meniscus, and a hotter, more fluid, mould flux. The end effect, as explained in Section 2.1, is a higher mould heat flux, especially in the meniscus region. 6.2 Mould Heat Transfer in the Company A Casters A s was mentioned earlier, the Company A #2 caster produced slabs with a high inci-dence of transverse corner cracks. In the previous section the effect of water velocity on Ch.6 Heat Transfer in High Speed Conventional Slab Casting 6 9 0 100 200 300 400 500 600 700 800 220 n 1 1 1 , 1 1 40 "I 1 1 1 1 1 1 i 1 0 100 200 300 400 500 600 700 800 Distance from mould top (mm) Figure 6.1: Effect of changing water velocity on heat fluxes and temperatures on the mould hot face during billet casting with powder. Ch.6 Heat Transfer in High Speed Conventional Slab Casting 70 mould heat transfer was elucidated viz. lower water velocities result in higher mould hot face heat fluxes and temperatures. This section deals with how the cracking problem was resolved by changing the cooling water velocities i n the #2 caster. 6.2.1 Original Operational Practice Data supplied by Company A has been summarised in Section 5.1. The 1-D heat trans-fer model developed in Section 4.2 was used to back-calculate heat fluxes and hot face temperatures for both the Company A #1 (data i n Table 5.3) and #2 (data in Ta-ble 5.4) casters, and the results are presented in Fig.6.2. Also shown i n the figure are corresponding profiles for another caster very similar to Company A #2 (Company B i n Table 5.1). The heat flux and the hot face temperatures reported by Company B were for the same steel grade and casting speed. It is interesting to compare the thermal states of the three different casters in Fig.6.2. A t least below the meniscus, the broad face heat flux for Company A #2 agrees quite well wi th that for Company B , while that for the Company A #1 caster is higher. However, the heat flux on the narrow faces is quite different. Normally , narrow face heat flux is higher than that for the broad faces, since the l iquid steel stream from the S E N impinges on the narrow faces of the strand. This is indeed seen to be the case for Company B . However, for both the Company A casters, narrow face heat fluxes are lower than those on the broad faces. There is an especially big discrepancy for the Company A #1 caster - here the narrow face heat flux is even lower than for the #2 caster. This is also seen in Fig.5.3, where Ch.6 Heat Transfer in High Speed Conventional Slab Casting 71 3.0 2.5 CM E g 2.0 x i 1.5 co CD X 1.0 i 0.5 A C o m p a n y B (broad face) — A - C o m p a n y B (nar rowface) • C o m p a n y A #1 (broad face) — D - C o m p a n y A #1 (narrow face) • C o m p a n y A #2 initial (broad face) — O - C o m p a n y A #2 initial (narrow face) 0 100 200 300 400 500 600 700 800 400 350 O cu 2 300 ro i_ CD Q. £ r— CD O CO O X 250 200 150 100 0 100 200 300 400 500 600 Distance from meniscus (mm) 700 800 Figure 6.2: Hot face heat flux and temperature profiles down the mould wall for the Company A #1, #2 (before water velocity reduction) and Company B casters. Ch.6 Heat Transfer in High Speed Conventional Slab Casting 72 the narrow face wall temperatures are substantially lower than the broad face tempera-tures. This difference exists for the #1 caster in spite of the both the broad and narrow faces having the same wall thickness and water velocities. Calculated hot face temperature profiles are also plotted i n Fig.6.2. Hot face tempera-tures for Company A are well below those reported by Company B . For the broad faces, even though the heat fluxes are calculated to be the same, water velocities are signifi-cantly higher for Company A (see Table 5.1), leading to lower hot face temperatures. Water velocities are even greater on the Company A #2 narrow faces (Table 5.4). However, it must be cautioned that the 1-D model might be under-estimating heat fluxes for the narrow faces, since significant transverse heat flows could be present here. Also , lower narrow face heat fluxes (and hot face temperatures) may be a result of inadequate contact between the strand and the narrow faces. 6.2.2 Water Velocity Changes From the above calculations it is clear that the very high cooling water velocities used at the Company A #2 caster have a role to play in the transverse edge cracking problem. Fig.6.2 shows that though broad face heat fluxes for the Company A #2 caster match those of Company B , the high water velocities in use at the #2 caster result in very low hot face temperatures. This has a strong negative effect on mould-strand lubrication, due to the formation of a colder, more viscous l iquid slag. The biggest problem in gauging the thermal state of the caster was a lack of ther-Ch.6 Heat Transfer in High Speed Conventional Slab Casting 73 mocouples near the meniscus. Heat flux conditions at the meniscus are of the utmost importance, since this decides the ini t ia l strand solidification and shrinkage. However, it was found that the broad face copper temperatures supplied by Company A for the #2 caster (see Table 5.4) matched some temperature profiles reported by Mahapatra [49]. These were then used to extrapolate wall temperatures to the meniscus region, and also lower down the mould. This temperature profile was then input to the I H C P model of Pinheiro [16] (Section 4.1.2) to obtain a heat flux profile down the mould wall . The hot face heat flux so obtained was used in the 2-D heat conduction model of Samarasek-era [48] (Section 4.1.1) to evaluate the effect of reduced cooling water velocities on the mould hot face temperature. The in i t ia l water velocity was about 8.7 m/s on the broad faces, and as can be seen 400 -[ 350 -300 -o 250 -CD -*—• TO 200 -CD (~\ E 150 -CD 1-100 -50 < 0 -j j Water velocity 5 m/s —• — Water velocity 7 m/s —•— Water velocity 8.7 m/s > • A . • • . , \ ; \ \ ' / \ 1 | w ^ \ - ! ! ^ 1 I i 100 200 300 400 500 600 700 Distance down mould (mm) 800 900 Figure 6.3: Calculated hot face temperature profiles for the Company A #2 caster after water velocity reduction. Ch.6 Heat Transfer in High Speed Conventional Slab Casting 74 from Table 5.1 this seems higher than desirable. The 2-D model was run with both this water velocity, and after it had been first reduced to 7 and then 5 m/s . The calculated hot face temperatures are shown in Fig.6.3. It is seen that the peak calculated hot face temperature increases from ~ 3 0 0 ° C to ~ 3 4 0 ° C as the velocity reduces from 8.7 to 5 m/s . Of course, the magnitude of these changes would be greater in actuality, as the hot face heat flux would also increase on reducing water flow rates. For the present heat flux conditions, 5 m/s was established as a safe lower bound for water velocity, since it maintained the mould cold face below the boiling temperature for water at the operational pressure. From the above, it was felt that a velocity drop to 7 m/s would be effective in achieving the opt imum peak hot face temperature of 350° C , while simultaneously preventing the advent of boiling on the mould cold faces. Subsequently, water velocities were turned down to 7 m/s for both the broad and narrow faces at the Company A #2 caster. 6.3 Effects of Changes The incidence of transverse corner cracks fell drastically after the reduction in water velocities. In addition, Company A also reported the following changes: 1. A n immediate, dramatic increase in wall temperatures, especially for the narrow faces (due to the larger decrease in water velocity)-. 2. Hotter slab surface temperatures. Ch.6 Heat Transfer in High Speed Conventional Slab Casting 75 3. A marked reduction in the off-corner "black stripes" seen on the strand surface at machine exit. 4. Uni form and shallower oscillation marks. These changes indicate improved heat extraction in the mould , as well as reduced me-chanical interaction between the mould and strand. Unfortunately, complete data was not reported by Company A for the same casting speeds (~1.7 m / m i n ) for which the earlier heat flux calculations were made. Hence, a direct comparison of mould heat flux for before and after the water velocity change re-quired extrapolation of water A T values from other casting speeds. This and other data used for the 1-D heat flux model calculations are summarised in Table 5.5. Company A #2 caster heat flux and hot face temperatures for after the water velocity reduction are presented in Fig.6.4. For the sake of comparison, results from before the change for the #2 caster (previously shown in Fig.6.2) are also given in the same figure. The heat fluxes for after the water velocity change reveal that, for the broad faces, there is a slight increase at 100 m m below the meniscus, which would be higher at the meniscus. Heat fluxes seem to decrease for the narrow faces, which might be due to the increased heat removal on the broad faces causing enhanced strand shrinkage along the mould width . Besides increasing the mould-strand gap at the narrow faces, heightened shrinkage has the more important effect of reducing mechanical interaction between the mould and strand. A t 100 m m below the meniscus, there are large increases i n the hot face temperatures, Ch.6 Heat Transfer in High Speed Conventional Slab Casting 76 3.0 2.5 -CM E g 2.0 x 1.5 ro CU X 1.0 0.5 0 400 350 O £ 300 CO I cu C L E cu I -CD 200 o X 250 150 4 100 —•— Company A #2 final (broad face) — O - Company A #2 final (narrow face) • Company A #2 initial (broad face) —0-- Company A #2 initial (narrow face) 100 200 300 400 500 600 700 800 I I I \ I I ' — c < 0 100 200 300 400 500 600 Distance from meniscus (mm) 700 800 Figure 6.4: Hot face heat flux and temperature profiles down the mould wall for the Company A #2 (before and after water velocity reduction) and Company B casters. Ch.6 Heat Transfer in High Speed Conventional Slab Casting 77 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Casting speed (m/min) 2.0 2.2 2.4 Figure 6.5: Specific heat extraction by the mould with casting speed for the Company A and Company B casters. Ch.6 Heat Transfer in High Speed Conventional Slab Casting 78 for both the broad and narrow faces. As with the broad face heat fluxes, the increase in hot face temperature would be much higher i n the meniscus region. This rise in mould hot face temperatures results in a hotter, more f luid l iquid slag in the mould-strand gap, which in turn implies reduced mould-strand friction. Specific heat removal for the three moulds studied here (Company A #1, Company A #2 and Company B) was also calculated by using water A T s . Eq.2.1 was used to eval-uate the total rate of heat removal from each mould face, which were then totalled up to yield the total rate of heat removal by the mould. D i v i d i n g this by the mass rate of steel output from the mould gives the specific mould heat extraction (i.e. amount of heat removed by the mould per unit mass of steel cast). Specific mould heat removal is plotted in Fig.6.5, where, as is the usual trend, it is seen to decrease wi th casting speed. Compared to the other two casters, specific mould heat removal seems to be slightly higher for Company A #2, especially after the water velocity reduction. 6.4 Mechanism of Crack Formation From the calculations and observations in the previous sections, we can postulate a mechanism for transverse cracking at the #2 caster of Company A . The problem could have been related to inadequate strand shrinkage (in the thickness direction), and a consequent rise in mould-strand frict ion, just below the meniscus. The slab caster mechanics are such that the mould walls bulge i n due to thermal strain during casting. If there is insufficient strand shrinkage, mechanical interaction and Ch.6 Heat Transfer in High Speed Conventional Slab Casting 79 Deformed mould shape (exaggerated) Inadequate strand shrinkage Figure 6.6: Mechanism of transverse corner crack formation in the Company A #2 caster. friction between the strand and mould takes place near the corners. The resulting longitudinal strains imposed on the strand can thus lead to transverse cracks opening up. This mechanism of cracking (depicted in the strand cross-section shown in Fig.6.6) is buttressed by the fact that off-corner longitudinal "black stripes" were found on the strand surface at the machine exit. Darker areas on the strand are, of course, indications of close contact between the strand and mould. Thus, the remedy would be to increase both heat transfer (which results in enhanced strand shrinkage) as well as lubrication (to reduce frictional forces on the strand). Both of these changes were effected by reducing the cooling water velocities, which resulted in increased hot face heat fluxes and temperatures. Interestingly, Gilles [30] had also reported an increased incidence of transverse corner cracks (though only for crack sensitive grades) while conducting high speed trials at Bethlehem Steel, Sparrows Point. However, no significant relationship between cracking Ch.6 Heat Transfer in High Speed Conventional Slab Casting 80 and friction signals (measured by load cells) was found. A t Sparrows Point, cracking incidences were remedied by switching to a different mould powder [30]. Chapter 7 Heat Transfer in T h i n Slab Continuous Cast ing This chapter studies heat removal in thin slab casters (described in Section 2.4). As was mentioned in Section 4.3, finite element modelling was used for the C S P caster at Company C to obtain the heat fluxes on the hot face in front of each thermocouple location. The heat fluxes were calculated by a trial-and-error method, by manually ad-justing the heat flux imposed as a boundary condition in the model unti l the measured wall temperature at the thermocouple location matched the model prediction. Heat flux and hot face temperatures were thus obtained for al l the thermocouple locations on the broad and narrow faces. After this, a heat flux profile was fitted to the two heat flux values calculated at each thermocouple column. The heat flux profile gives the heat flux down the mould wall , and this was then used in a strand solidification model to calculate the shell thickness and strand surface temperature at the mould exit. Finally, a simple method was developed for varying cooling water velocity with the mould wall thickness, as it is re-machined during its working life. 81 Ch.7 Heat Transfer in Thin Slab Continuous Casting 82 7.1 Calculation of Heat Fluxes Three different finite element method models were used to back-calculate heat fluxes for the Company C caster. One model was used for the mould narrow faces, while one each was used for the upper and lower thermocouple rows on the broad faces. A single model could not be used for the broad faces because of the presence of cooling holes adjacent to the thermocouples in the top row. Transverse sections of the mould wall adjacent to each thermocouple location (shown in Fig.7.1 for the broad faces and Fig.7.2 for the narrow faces) were modelled. As previ-ously mentioned in Section 5.2, heat flow conditions for five slabs from the cast #10851 were analysed, with a representative slab from each of the five heats making up the cast. Input data used for the finite element models has been summarised in Section 5.2. 7.1.1 Assumptions for the F E M Models The domain of calculation for the broad face is shown i n Fig.7.1. The transverse section shown there is actually for the mould wall adjacent to the top row of thermocouples only, since the cooling hole is absent for the bottom row. The metal insert placed into the cooling slot is excluded from the calculations. For the narrow faces, calculations were made on only half of the section shown in Fig.7.2, due to symmetry about the centre line. Other assumptions made for carrying out the finite element modelling are listed below: Ch. 7 Heat Transfer in Thin Slab Continuous Casting 83 HOT F A C E Copper -mould wall Thermocouple location Cooling hole (for water) Metal^ insert 17.5 mm Symmetry line Cooling slot : (for water); 12.5 mm Symmetry line Figure 7.1: Transverse section of the CSP caster broad face. Ch.7 Heat Transfer in Thin Slab Continuous Casting 84 H O T F A C E Figure 7.2: Transverse section of the CSP caster narrow face. Ch. 7 Heat Transfer in Thin Slab Continuous Casting 85 1. Since the meniscus level is 70 m m (from the mould top), al l the thermocouples are located at least 100 m m from the meniscus (see Table 5.7). Thus, there would be no significant downward heat flow at the thermocouple locations. This enables the use of a 2 dimensional model for the transverse slice of the mould walls shown in Figs.5.6 and 5.7. 2. There is a linear variation of the cooling water temperature between the inlet and outlet. This enables the use of linear interpolation between the inlet and outlet temperatures to find the water temperature at the thermocouple height. 3. Water cooling is in the convective regime, with the heat transfer coefficient at the mould-water interface evaluated from the correlation of Szekely and Themelis [14] (given in Eq.4.10). 4. Heat flux is invariant along the width of the hot face present in the calculation domain. 5. Besides the hot face and cooling holes/slots, all other boundaries are adiabatic. Because of symmetry, the centre lines are also adiabatic. O n the broad faces, there is no thermal interaction between the cooling water and the metal insert. 6. The system is at steady state. 7.1.2 Results from the F E M Models Figs.7.3 and 7.4 show typical calculated heat fluxes and isotherms on the narrow face (NF) sections at the thermocouple locations. As mentioned earlier, the hot face heat Ch.7 Heat Transfer in Thin Slab Continuous Casting 86 Figure 7.3: Calculated isotherms (in °C) at a top row thermocouple on the CSP caster narrow face. Figure 7.4: Calculated isotherms (in °C) at a bottom row thermocouple on the CSP caster narrow face. Ch.7 Heat Transfer in Thin Slab Continuous Casting 87 Figure 7.5: Calculated isotherms (in °C) at a top row thermocouple on the CSP caster broad face. Figure 7.6: Calculated isotherms (in°C) at a bottom row thermocouple on the CSP caster broad face. Ch. 7 Heat Transfer in Thin Slab Continuous Casting 88 Slab 10851-01-06 3.0 2.8 2.6 ^ 2 4 E ^ 2.2 ^ 2.0 £ 1.8 CO CD X 1.6 1.4 1.2 1.0 Loose BF (top row Loose BF (bottom row) Fixed BF (top row) Fixed BF (bottom row) - i 1 1 1 — 1 — i - i 1 1 1 1 1 1 1 1 — -700 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700 Figure 7 01-06. - i 1 1 1 1 1 1 1 r --700 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700 Distance from centre of mould width (mm) 7: Heat flux and hot face temperatures on the mould broad faces for slab 10851-Ch.7 Heat Transfer in Thin Slab Continuous Casting 89 Slab 10851-02-02 3.0 180 i — — i 1 1 i- 1 1 1 1 1 1 1 1 1 1— -700 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700 Distance from centre of mould width (mm) Figure 7.8: Heat flux and hot face temperatures on the mould broad faces for slab 10851-02-02. Ch.7 Heat Transfer in Thin Slab Continuous Casting 90 Slab 10851-03-06 - i 1 1 1 1 r -700 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700 Figure 7 03-06. -j r 1 1 i 1 1 1 1 r -700 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700 Distance from centre of mould width (mm) 9: Heat flux and hot face temperatures on the mould broad faces for slab 10851-Ch.7 Heat Transfer in Thin Slab Continuous Casting 91 Slab 10851-04-04 CN 3.0 2.8 2.6 2.4 Loose BF (top row) Loose BF (bottom row) Fixed BF (top row) Fixed BF (bottom row) -700 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700 O CD 13 03 L_ CD CL E CD I -CD O CO O 320 310 300 290 280 270 260 250 240 230 220 210 200 190 180 I A k " ^ IF — --c • o / _ y ~) / / y C j A / " A A / ' L / | -700 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700 Distance from centre of mould width (mm) Figure 7.10: Heat flux and hot face temperatures on the mould broad faces for slab 10851-04-04. Ch.7 Heat Transfer in Thin Slab Continuous Casting 92 Slab 10851-05-01 CM 3.0 2.8 2.6 2.4 E g 2.2 x 2.0 £ 1.8 co CD X 1.6 1.4 1.2 1.0 320 310 300 Q 290 ° — 280 CD 3 270 I 260 C L E CD - • — Loose BF (top row) -O— Loose BF (bottom row) -A— Fixed BF (top row) - A - Fixed BF (bottom row) -700 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700 CD o co o X 250 240 230 220 210 200 190 180 I | ...... : : I j — — . / K — / 1 o — I • A. _ —c ) — . J \ N. I ....— z_ \ l X I / X X 1 J / 1 — -L ^ J L - 1 --700 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700 Distance from centre of mould width (mm) Figure 7.11: Heat flux and hot face temperatures on the mould broad faces for slab 10851-05-01. Ch. 7 Heat Transfer in Thin Slab Continuous Casting 93 Slab 10851-01-06 3.0 2.8 2.6 2.4 Top row i i Bottom row South N F North N F 300 280 H O 260 ^ 240 -I 2 220 -] CD I " 200 CD 180 CD £ 160 4 £ 140 120 100 South N F North N F Figure 7.12: Heat flux and hot face temperatures on the mould narrow faces for slab 10851-01-06. Ch.7 Heat Transfer in Thin Slab Continuous Casting 94 Slab 10851-02-02 Figure 7.13: Heat flux and hot face temperatures on the mould narrow faces for slab 10851-02-02. Ch. 7 Heat Transfer in Thin Slab Continuous Casting 95 Slab 10851-03-06 3.0 2.8 2.6 Bgg i i i . M - ; i j o p row Bottom row South NF North NF 300 280 O 260 <L) 240 H 2 220 H CD I" 200 CD l ~ 180 H 8 ^ 160 ° 140 120 100 South NF North NF Figure 7.14: Heat flux and hot face temperatures on the mould narrow faces for slab 10851-03-06. Ch.7 Heat Transfer in Thin Slab Continuous Casting 96 Slab 10851-04-04 WE 2.4 -\ •| 2.2 2.0 -| 1.8 1.6 1.4 -1.2 -1.0 x 3 CO CD South NF North NF O 260 H o South NF North NF Figure 7.15: Heat flux and hot face temperatures on the mould narrow faces for slab 10851-04-04. Ch.7 Heat Transfer in Thin Slab Continuous Casting 97 Slab 10851-05-01 3.0 2.8 2.6 2.4 i i Bottom row o cu Z5 TO CD CL E cu I— Q) O CD O X 300 280 260 240 220 -200 -180 -160 140 120 100 South N F North N F South NF North N F Figure 7.16: Heat flux and hot face temperatures on the mould narrow faces for slab 10851-05-01. Ch.7 Heat Transfer in Thin Slab Continuous Casting 98 flux is assumed to be invariant across the width of the hot face in the calculation domain. Figs.7.5 and 7.6 depict the same for a broad face (BF) thermocouple column. In some cases the isotherms intersecting the cooling water channels/holes are higher than 100°C. However, init iat ion of boiling is not an issue, since the boil ing point of water is ~ 1 5 0 ° C at the C S P caster operational pressures. The models were run for all the thermocouples 1 , which impl ied 4 narrow face, 12 broad face top row, and 11 broad face bottom row thermocouples for each of the five slabs analysed. The incident heat flux and the temperatures of the mould hot face section facing each thermocouple were obtained from the models. These have been plotted as profiles across the mould width for the broad faces of the five slabs (in Figs.7.7 to 7.11). As marked i n these figures, the north and south narrow faces are located at the left and right edges, respectively, of the broad faces. Heat flux and hot face temperature results for the narrow faces of the five slabs are presented in Figs.7.12 to 7.16. These are plotted as bar charts since the narrow faces only have one column of thermocouples each. 7.2 Average and Specific Mould Heat Removal In addition to the heat fluxes calculated from the F E M models, the cooling water A T method (discussed in Section 2.2.1) was used to estimate average heat fluxes on each mould face, as well as the total specific heat extraction by the mould. As mentioned 1 Except for thermocouple #4 on the loose broad face, which had been turned off. Ch.7 Heat Transfer in Thin Slab Continuous Casting 99 x 3 CO CD X CD C D CO i_ CD > < C D JUL CO > o E CD or CO CD X o o o CD Q. V) 0 20 40 60 80 100 120 140 160 180 200 T i m e into c a s t (min) Figure 7.17: Average heat flux on each face and specific mould heat removal in #10851. cast Ch.7 Heat Transfer in Thin Slab Continuous Casting 100 earlier, it was assumed that water flow on each narrow face was 41 G P M , with the remainder from the total flow divided equally among the two broad faces. Since water A T s were available for each face for the entire duration of the cast, they were used to calculate an average heat flux for each mould face, and their variation into the cast #10851 is plotted in Fig.7.17. It should be noted that the heat fluxes shown in Fig.7.17 are quite different from those calculated by the F E M models - the latter are heat fluxes at specific locations on the mould hot face (in front of the thermocouples), while the former is an average for the entire face. Heat removal rates for each face were then obtained by mult iply ing the average heat flux on a mould face by the corresponding face area. These were then totaled up for the four faces, and divided by the rate of steel output from the caster. This yields the specific heat extracted by the mould (in k J / k g ) , and has also been plotted in Fig.7.17. Specific heat extraction reflects the trend in broad face heat fluxes, since a near insignificant fraction of the total heat removed by the mould is through the narrow faces. 7.3 Heat Flow Trends in the Cast For each of the five slabs studied, F E M calculated heat fluxes across the mould broad faces (at the top and bottom row thermocouple locations) are plotted in Figs.7.7 to 7.11. Similarly, Figs.7.12 to 7.16 show the F E M calculated narrow face heat fluxes for the slabs. The calculated broad face heat fluxes for each slab were then averaged across the slab width for each row of thermocouples on the fixed and loose broad faces. Thus, a Ch.7 Heat Transfer in Thin Slab Continuous Casting 101 0 3.0 2.8 4 2.6 2.4 4 2.2 2.0 1.8 -1.6 -1.4 -1.2 -1.0 0 Loose BF (top row) Loose BF (bottom row) 20 40 60 80 100 120 140 160 180 200 Fixed BF (top row) - A - - Fixed BF (bottom row) 20 40 60 80 100 120 140 160 180 200 Time into cast (min) Figure 7.18: Average FEM calculated broad face heat fluxes into cast #10851. Ch.7 Heat Transfer in Thin Slab Continuous Casting 102 CO CD X CD CD O CD o 0 20 40 60 80 100 120 140 160 180 200 Time into cast (min) Figure 7.19: Average FEM calculated narrow face heat fluxes into cast #10851. single, mean value of heat flux was obtained for each thermocouple row on each slab, and these have been plotted against time into the cast in Fig.7.18. Table 5.8 gives the times between which each slab was produced, and the mid-point of the start and end times was used to plot the mean, F E M calculated heat fluxes against the time-line. The Fig.7.18 shows the trend of average F E M calculated broad face heat fluxes into the cast, wi th the size of the error bars indicating the magnitude of the heat flux variation (at each thermocouple row location) across the width of the broad faces. Similar to the broad faces, Fig.7.19 plots the pattern of narrow face heat fluxes into the cast. Here, since only one column of thermocouples was present on each narrow face, averaging across the face to obtain a unique value for each thermocouple row was not required. -A- -South NF (top row) South NF (bottom row) North NF (top row) North NF (bottom row) Ch. 7 Heat Transfer in Thin Slab Continuous Casting 103 Figs.7.7 to 7.19 give a good idea of mould heat flow for cast #10851, and these trends are discussed below. 7.3.1 Broad Face Heat Flow As can be seen from Figs.7.7 to 7.11, the pattern of B F heat flux variation across the mould width is preserved throughout the cast, wi th very similar heat flux profiles for all the five slabs. Heat fluxes are quite steady across the mould width for the loose B F . However, for the fixed B F , there is a very high variation across the mould width , especially for the top row of thermocouples. The most striking feature of the fixed B F heat flux profile is the deep valley in the middle of the face. This depression in heat flow is present at the locations of both the upper and lower rows of thermocouples, from about -600 to 600 m m . It is interesting to note that this coincides approximately with the location of the mould pocket, which extends a m a x i m u m of 575 m m on each side of the mould centre. Thus, it is quite probable that the valley i n the fixed B F heat flux profile is due to the squeezing of the strand as the pocket depth decreases down the mould wall . Wiinnenberg and Schwerdtfeger [47] had also pointed out a difference in heat flow be-tween the two B F s of a C S P caster (Section 2.4). They had linked this to differing intensities of shell deformation on the two B F s . Besides lowered fixed B F heat extrac-t ion, surface cracks in the slabs can be another detrimental result from the squeezing of the strand. Transverse mechanical strains are directly introduced in the strand due to squeezing. In addition, the transverse variation in the heat flux profile results in Ch.7 Heat Transfer in Thin Slab Continuous Casting 1 0 4 transverse thermal gradients, and thus thermal strains, i n the strand. The combination of these two transverse strains would favour the formation of longitudinal facial cracks. However, this difference between the two B F s vis. a vis. heat flow does not seem to be reflected in the average heat fluxes calculated from water A T s . Fig.7.17 shows that throughout the cast, loose and fixed B F heat extraction are almost the same. It has to be remembered, though, that the fluxes in Fig.7.17 were calculated with the assumption of equal water flows on the two BFs . This may not be accurate, as blockages in the cooling channels can result in different flows for the two B F s . Scale deposition in the loose B F cooling channels is another possibility. These would raise wall temperatures without much effect on the water A T s . Looking at heat removal trends into the cast, both Figs.7.17 and 7.18 show that broad face heat fluxes decrease into the cast. As shown in Figs.5.10 and 5.11, broad face mould wall temperatures also decrease, since they are proportional to the heat fluxes. Fig.7.18 also reveals that though the heat flux variability of the fixed B F is much higher than that for the loose B F , it does seem to decrease a bit for the fixed B F , and increase slightly for the loose B F , as the cast progresses. Again , for the fixed B F , it is seen that though the heat flux at the top row of thermo-couples is always higher than at the bottom row, on some occasions the top row hot face temperatures are lower than for the bottom row (Figs.7.8 and 7.9). This is due to the higher cooling intensity at the top row of thermocouples, which have a cooling hole in addition to the cooling slot. Thus, hot face temperature profiles (down the mould Ch.7 Heat Transfer in Thin Slab Continuous Casting 1 0 5 wall) for the C S P caster B F s would be quite different than for conventional casters. There, water cooling is uniform down the entire mould wal l , resulting in a steep drop in hot face temperatures below the meniscus. However, since the C S P casters have additional cooling at the meniscus, the drop in hot face temperatures would not be so sharp. Indeed, as is sometimes seen, they may even rise if the hot face heat flux is low enough. 7.3.2 Narrow Face Heat Flow F E M analysis reveals that the south N F heat fluxes are consistently higher than those for the north N F . For example, as shown in Fig.7.19, heat fluxes at the top thermocouple locations on the south N F are higher than those on the north N F by a factor of at least 20%. The narrow face mould wall temperatures plotted in Fig.5.9 also show the same trend, wi th the upper thermocouple location on the south N F always being ~ 1 5 ° C hotter than for the north N F . However, heat extraction calculated from water A T s (Fig.7.19) does not show this strong, consistent difference. Average heat fluxes are higher for the south N F in the first half, and for the north N F in the second half of the cast. Possible reasons for this discrepancy might be higher water velocities (than assumed for the calculations in Fig.7.19) on the north N F . Unl ike for the broad faces, this water flow differential would probably not be caused by blockages in the cooling holes, but possibly due to the water inlet being closer to the north N F . Also , in marked contrast to the broad faces, heat fluxes and wall temperatures for the narrow faces increase into the cast. This could be explained by the increased strand Ch.7 Heat Transfer in Thin Slab Continuous Casting 106 interaction with the narrow faces, caused by reduced thermal shrinkage along its width as B F heat fluxes diminish into the cast. From the average heat flux calculations (Fig.7.17), N F heat extraction seems to be substantially lesser than for the B F s . The same is seen for the F E M calculated heat fluxes. Even though the upper row of thermocouples on the N F s is 57 m m closer to the meniscus than the upper row on the B F s (from Table 5.7), Figs.7.18 and 7.19 show that heat fluxes at the N F upper row are smaller than for the B F s . Reduced heat fluxes on the N F s may result from the N F walls being thinner than for the B F s (19 and 23.2 m m respectively). Even the lower water velocities for the N F s (8.4 m/s vs. ~10.7 m/s for the BFs) may not be adequate to compensate for the thinner effective wall thickness in the N F s . As is shown in Fig.2.7, Mahapatra et al. [7] had also discovered the same effect of thinner mould coppers resulting in lower heat fluxes. If other operational factors are constant, a thinner mould wall causes a drop in the hot face temperature. As the mould heat transfer mechanism discussed in Section 2.1 explains, a direct consequence of this is a decrease in mould heat flux. 7.4 Water F low Differentials F E M calculations had shown that the fixed broad face extracted lesser heat than the loose face. However, this trend was not seen in the average heat flux calculations (Fig.7.17), where the two broad fa,ces had equal heat removal. As mentioned previously, Ch.7 Heat Transfer in Thin Slab Continuous Casting 107 this anomaly might indicate blockages in the cooling channels, leading to a reduction in the water flow rate for the loose B F . The result of this imbalance would not show up in the average heat fluxes calculated by the water A T method, since equal water flows on the two B F s are assumed. But in the F E M models, higher heat fluxes were back calculated for the loose B F via. the hotter mould wall temperatures, possibly a result of reduced cooling water flow. Sobolewski et al. [20] had traced variations in mould wall temperatures across the broad faces of a conventional caster to restrictions in water flow caused by rust deposition in the water inlet and outlet chambers. They also reported low flows due to extensive salt deposition in the cooling slot inlet ports. O n actually measuring flows across the broad faces, they found variations of upto 8% in water flow rates across the face width. Similar restrictions to water flow, and a consequential diversion of water flows, can thus be expected for the C S P caster too. Higher water velocities (and thus reduced heat extraction) on the fixed B F might also explain why only this B F has the dip in heat fluxes in the central section of the face. In the previous chapter (in Section 6.1), the effect of water velocity on mould heat transfer had been elucidated, viz. higher water velocities cause lower hot face temperatures, which in turn results in a bigger slag r i m at the meniscus and a colder, more viscous mould slag. The net result, as Mahapatra et al. [7] have also pointed out, is a reduction in mould heat removal. Lower heat extraction results in lower strand shrinkage, and an intensification of the Ch.7 Heat Transfer in Thin Slab Continuous Casting 1 0 8 squeezing action of the mould at the pocket. This increased squeezing might cause the strand to buckle i n , increasing the strand-mould gap and thus further reducing heat transfer. As mentioned before, the combination of these two factors - thermal strain imposed on the strand due to the high heat flux variability seen across the mould face, and the mechanical strain of squeezing - can result i n the formation of longitudinal cracks. 7.5 Fitting of Heat Flux Profiles 14 12 10 8 x & 6 CD CD 4 2 0 I ! _ • FEM calculated for Narrow Face Fitted for Narrow Face (q = 3.26 t"°55) A FEM calculated for Broad Face Fitted for Broad Face (q = 3.66 t"°55) 1 | } \ \ i l \\ i i ; I I I ^ ; j j I I 1 i — — I 1 I I j i 1 I ^ i i i 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Residence Time in Mould (s) Figure 7.20: Fitting of heat flux profiles (Eq.7.1) at the thermocouple column locations. Previously, heat fluxes had been calculated in front of the thermocouple locations, for both the broad and narrow faces. A n attempt has been made to fit a heat flux profile Ch.7 Heat Transfer in Thin Slab Continuous Casting 109 CM O c r CM O cr 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 - — ± ^ = = 4 / 1 L / j r j V v _ r ^ J C -------T • i [ ; 1 i J | i L 6 r s ab 1 0851-01-0 • Loose BF — O - Fixed BF Loose and Fixed BF (average) -700 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700 -700 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700 Distance from centre of mould width (mm) Figure 7.21: qo values calculated for the broad faces of the two slabs. Ch.7 Heat Transfer in Thin Slab Continuous Casting 110 CM O c r CN 5.0 4.5 4.0 3.5 4 3.0 2.5 H 2.0 1.5 1.0 0.5 0.0 Slab 10851-01-06 5.0 o c r 4.5 4.0 3.5 -3.0 -2.5 2.0 1.5 1.0 0.5 0.0 South N F North N F Slab 10851-05-01 South N F North N F Figure 7.22: qo values calculated for the narrow faces of the two slabs. Ch.7 Heat Transfer in Thin Slab Continuous Casting 111 as a function of the residence time of the strand in the mould. From literature (Section 2.2.3), a function of the following type was selected for fitting the profile: q = qot'°-55 (7-1) Here, q is the heat flux ( M W / m 2 ) down the mould length, t (s) is the residence time of the strand below the meniscus, and qo ( M W / m 2 ) is the controlling parameter for the equation. The parameter qo was evaluated in two different ways: 1. For each column of thermocouples, the equation was fitted to the two values of heat fluxes (obtained from the F E M models) to calculate q0. Fig.7.20 plots the fitted equation (together with the two heat flux values used for fitting) at two thermocouple column locations, one each on a narrow and broad face. The meniscus heat fluxes (at t = 0) shown in Fig.7.20 were calculated by evaluating Eq.7.1 for 7 m m below the meniscus. 2. For each face of the mould an "average" heat flux has been calculated from the water A T method. This should be equal to the heat flux obtained when Eq.7.1 is integrated over the residence time of the strand i n the mould , and hence q0 can be obtained from this equality. 7.5.1 Meniscus Heat Fluxes In Fig.7.20, it is seen that the meniscus heat fluxes are estimated as ~12 M W / m 2 . Whi le these may seem quite high, Wolf [39] had also obtained values of 6-11 M W / m 2 Ch.7 Heat Transfer in Thin Slab Continuous Casting 112 while using similar heat flux functions. Gilles [29] has also used a total average of 5.6 M W / m 2 for the entire first second of casting (see Eq.2.10), i n the modelling of an experimental slab caster. In any case, there is always uncertainty in estimating meniscus heat fluxes by extrap-olating up from values calculated/measured lower down the mould. This has been discussed in Section 2.2.3, where Konishi [34] was able to fit three entirely different heat flux functions to the same data (Fig.2.14), and thus estimated a meniscus heat flux variation of ~4.5-7.5 M W / m 2 . This uncertainty was present Konishi 's [34] analysis in spite of the closest heat flux value being only 0.5 s from the meniscus. In this study, the top row thermocouples are much lower down the mould (1.5 and 2.3 s from the meniscus, for the narrow and broad faces, respectively). 7.5.2 Fitted q0 Values Calculated q0 values are shown in Figs.7.21 and 7.22 for the broad and narrow faces, respectively, of the first (#10851-01-06) and last (#10851-05-01) slabs analysed in the cast. For many of the thermocouple columns on the broad faces, the error bars (due to fitting) for q0 are quite small , showing that the selected function is a good approxi-mation of the heat flux variation down the mould length. However, at some columns, and especially for the narrow faces, the error bars are quite large, indicating that a different k ind of heat flux profile exists at those locations. This is in agreement with the findings of Wiinnenberg and Schwerdtfeger [47], who reported that heat flux may not monotonically decrease below the meniscus (Fig.2.20). Ch.7 Heat Transfer in Thin Slab Continuous Casting 113 g 0 values obtained from the "average" heat fluxes are also shown i n the same figures. For the B F s , the q0 values predicted from fitting are consistently lower, except for one case. This is the loose B F of slab #10851-01-05, which has a very close match. For the N F s , though the error bars for fitt ing are quite large, there is generally good agreement between the two values of qo. • 7.6 Strand Shell Thickness/Surface Temperature The heat flux profiles calculated in the previous section were used in the strand solid-ification model described in Section 4.4 to estimate the solidified shell thickness and strand surface temperature at the mould exit. Results are shown i n Figs.7.23, 7.24, 7.25 and 7.26 for the broad and narrow faces of the two slabs. Company C had estimated their shell thickness at ~8-10 m m , while O'Connor and Dantzig [46] report a figure of ~7-10 m m for Nucor. Shell thicknesses for slab 10851-01-6 agree well wi th this data, while those for slab 10851-05-01 seem to be on the lower side. However, it has to be remembered that slab 10851-05-01 has a significantly higher carbon content (Table 5.9), which results in a larger mushy zone. The model, which calculates shell thickness based on the solidus, would thus tend to under-estimate the effective shell thickness for these very high carbon grades. Ch.7 Heat Transfer in Thin Slab Continuous Casting 1 1 4 Slab 10851-01-06 13 12 UJ 10 O CD CO to CD c o CD 9 8 7 6 4 3 1200 | ^ ) Loos e BF 5--—< 5X \ \ J L-\ " \ r Fixe< 3 BF -700 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700 - i 1 1 1 1 1 1 1 1 1 1 1 1 r -700 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700 Distance from centre of mould width (mm) Figure 7.23: Solidified shell thickness and strand surface temperature at the mould exit for the broad faces of slab 10851-01-06. Ch.7 Heat Transfer in Thin Slab Continuous Casting 115 Slab 10851-01-06 o ° 1200 x LU o co CD CO l _ CD CL E CD \-CD O 03 t CO c: CO i — -f-< CO 1100 1000 H 900 800 -f 700 600 500 South N F North N F IlIBiil """" South N F North N F Figure 7.24: .Solidified shell thickness and strand surface temperature at the mould exit for the narrow faces of slab 10851-01-06 Ch.7 Heat Transfer in Thin Slab Continuous Casting 116 Slab 10851-05-01 -700 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700 to 500 J 1 1 1 i 1 — — I ! 1 1 1 i- 1 1 1 1 1 -700 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700 Distance from centre of mould width (mm) Figure 7.25: Solidified shell thickness and strand surface temperature at the mould exit for the broad faces of slab 10851-05-01. Ch.7 Heat Transfer in Thin Slab Continuous Casting 117 Slab 10851-05-01 ro CO CO cu c O SZ \— SZ co 8 7 6 5 4 O ° 1200 x LU 1100 -1000 \ co cu i _ =3 ro CD CL E <D h-(D o co t CO "O £Z CO CO 500 South N F North N F South N F North N F Figure 7.26: Solidified shell thickness and strand surface temperature at the mould exit for the narrow faces of slab 10851-05-01. Ch.7 Heat Transfer in Thin Slab Continuous Casting 118 7.7 Compensating for Mould Wall Thickness The C S P caster mould wall thickness reduces over its working life since the coppers are often machined to eliminate surface cracks and maintain taper. If the cooling water velocity is not correspondingly reduced, the thinner walls w i l l result in lowered hot face temperatures and hence lesser mould heat removal. W h i l e water velocities are indeed reduced in practice, the regime followed for adjusting water flows with wall thickness may not be accurate. For example, private communication with two m i n i -mills operating the C S P caster reveals that they follow different formulations - one varying water flow rate as the square of the wall thickness (Company D) and the other adopting a linear decrease (Company C ) . In this section we shall derive a procedure for the accurate reduction of water velocity with the wall thickness, so that the same heat transfer conditions are faced by the strand over the mould life. From the mechanism for mould heat transfer elucidated previously, it follows that to achieve this objective, hot face temperatures should be maintained constant. 7.7.1 The Constant Thermal Resistance Approach The thermal resistance diagram in Fig.2.1 shows that for a given heat flux, the mould hot face temperature depends on the sum of the resistances due to the wall thickness and water heat transfer coefficient at the mould cold face. Hence, a constant hot face temperature requires that the sum total of these resistances (i.e. 1/h + dcujkcu) be invariant. Ch.7 Heat Transfer in Thin Slab Continuous Casting 119 If we use the correlation of Szekely and Themelis [14] given in Eq.4.10 for evaluating the water heat transfer coefficient, and substitute the constants for water from Table 4.1, the following expression is obtained for the heat transfer coefficient: h = 5296.63 < 8 (7.2) The value for the hydraulic diameter, dhyd, is calculated for the C S P caster at C o m -pany D , and the derivation below is with reference to this caster. Now, this caster starts off with an ini t ia l effective wall thickness of 23 m m . The broad face water velocity, uw, is 11.59 m/s at this wall thickness and the C r - Z r alloyed coppers have a thermal conductivity, kcu, of 315 W / m K . The thermal resistance seen by the mould hot face is therefore: 0 - I -u d c u 1 "thermal — , T h k Cu 1 0.023 + 5296.63 (11.59)0-8 ' 315 = 9.961 x 10~ 5 m 2 K / W (7.3) As the coppers are machined the water velocities should be lowered such that ^.thermal is kept constant, i.e. 1 , dcu ^ A n ( ? 1 , . 1 n _ 5 + ^ = ^thermal = 9.961 X 10" 5296.63 u°ws 315 1.25 (7.4) 5296.63 | 9.961 x 1 0 - 5 - d c u 315 A t Company D , the coppers are machined down to a 15 m m thickness before being scrapped. Fig.7.27 shows the water velocity regime calculated from Eq.7.4, for the 15-23 m m wall thickness range. Ch.7 Heat Transfer in Thin Slab Continuous Casting 120 Figure 7.27: Calculated variation of water velocity with wall thickness at Company D to maintain constant hot face temperature. Ch.7 Heat Transfer in Thin Slab Continuous Casting 121 1600 1500 1400 1300 co O c/> S 1200 co rz 1100 H -*-» .co § 1000 4 f CO CD ro 900 T3 CO o 800 CQ 700 600 Calculated Operational practice 15 16 17 18 19 20 21 Copper Thickness (mm) 22 23 Figure 7.28: Calculated and actual water flow rate variation with wall thickness at Company D. Also shown (by the broken line) is the water velocity variation calculated from a different method. This uses the 2-D mathematical model of Samarasekera [48] described in Section 4.1.1. For the ini t ia l wall thickness and water velocity of 23 m m and 11.59 m/s respectively, a heat flux profile was imposed such that the peak hot face temperature was 350°C. The wall thickness was then successively reduced i n the model, and the water velocity turned down such that the peak hot face temperature was maintained at 350°C. It is seen that the water regimes calculated from these two entirely different procedures Ch. 7 Heat Transfer in Thin Slab Continuous Casting 1 2 2 agree remarkably well , especially at thicker wall sections. However, it is interesting to note the divergence for the last case (15 m m thickness). From the 2-D model it was found that trying to maintain a m a x i m u m hot face temperature of 350°C resulted in the init iat ion of nucleate boiling on the mould cold face. Hence, water velocity had to be raised - the value shown in Fig.7.27 just suppresses the onset of boil ing. Of course, the simple Eq.7.4 does not take these effects into account and thus calculates a lower water velocity than is safe. The water velocities calculated in Fig.7.27 were converted to flow rates and compared to those actually used in the caster, as shown in Fig.7.28. The difference in the two regimes is quite startling, and indicates that the caster should be operating at much lower water flow rates than is the current practice. C h a p t e r 8 C o m p a r i s o n between C o n v e n t i o n a l a n d T h i n Slab C a s t i n g In the previous chapters three entirely different types of casting machines have been looked at - billet, thick slab and thin slab casters. In this chapter we shall directly compare some aspects of the thermal performance of these casters. 8.1 Mould Solidification Parameters In Fig.6.5 we saw that the specific heat extraction by the mould decreases with casting speed. This is expected, since higher speeds imply lower residence times for the strand in the mould. For the conventional casters depicted in Fig.6.5, specific heat removal decreases to ~60 k J / k g for a casting speed of ~1.7-1.9 m/s . However, Fig.7.17 shows that for the C S P caster of Company C , specific heat removal is triple (~180 kJ /kg) at more than twice the casting speed (~4 m / m i n ) . Specific heat extraction for the three different thick slab casters (Company A #1 and #2, and Company B ) , the billet caster, and for the thin slab caster at Company C have been compared in Fig.8.1, where the 123 Ch.8 Comparison between Conventional and Thin Slab Casting 1 2 4 cn co > o E CD OH "co CD X T 3 Z3 o o 250 225 200 175 150 125 100 75 o CD w 50 • Thick slab casters - o CSP caster * Billet caster I | j | ! o I I i j TO ML L A | | i | | •^•^ I • I i i 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Casting Speed (m/min) 5.0 Figure 8.1: Specific mould heat extraction (in kJ/kg) for thick slab (Company A#l and #£, and Company B), billet and CSP (Company C) casters. much higher specific heat removal for the C S P caster is quite apparent. This is of course due to the fact that the slabs from a C S P caster are 4-5 times thinner than from a conventional caster. Thus, a much larger fraction of the strand section is solid at the mould exit in the C S P caster. For example, Company C had reported that shell thicknesses at mould exit for their C S P caster were ~8-10 m m . In a strand thickness of 50 m m , this corresponds to 32-40% solidification due to heat extracted by the mould. For conventional casters, a shell thickness of ~10-20 m m is expected in the casting speed range of 0.5-2.0 m / m i n . 1 The Company A #2 caster has a slab thickness of 223 m m , and thus these shell thicknesses are equivalent to only a 9-18% solidification of the strand in the mould. l TJsing the solidification constant of 15 m m / m i n 0 5 recommended by Wolf [39]. Ch.8 Comparison between Conventional and Thin Slab Casting 125 8.2 Mould Design Section 5.2 had summarised the design details of the C S P caster, and how this was substantially different from conventional casters. The mould pocket, required to ac-commodate the S E N , is of course the distinguishing feature of the C S P caster. Here, we shall discuss two aspects of mould design which offer commonality between C S P and conventional casters. 8.2.1 Broad Face Cooling Holes A n innovative aspect of the C S P caster design are the cooling holes present on the broad faces. As mentioned in the previous chapter, these are adjacent to the bolt locations, and extend about a third of the way down the mould. The holes provide needed cooling, since the normal cooling slot spacing cannot be maintained at the bolts. The same problem of reduced cooling due to irregular slot spacing is encountered for the conventional slab casters too, though this solution has not been applied there. 8.2.2 Hot Face Coatings One of the biggest problems in C S P caster operation is the short working life of the moulds. As mentioned in the previous chapter, coppers are taken off-line and machined to eliminate surface cracks, and are then scrapped after the effective wall thickness reduces to a certain amount (down to 15 m m from 25 m m for Company C ) . For con-ventional casters, it has become standard operating practice to use a coating of a more refractory metal (usually N i and/or Cr) on the mould hot face. For example, at the Ch.8 Comparison between Conventional and Thin Slab Casting 126 Company A #1 caster, a 2 m m N i step is used on the mould hot face. The coatings have the dual advantage of extending the mould working life, as well as eliminating the uptake of copper from the mould by the strand. Unl ike conventional casters, C S P casters do not use hot face coatings. Their adoption would, as for thick slab casters, increase both the mould life and the strand surface quality. Of course, to offset the ef-fect on hot face temperatures, water velocities would have to be increased accordingly, since the hot face coatings add to the thermal resistance offered by the mould wall . 8.3 H o t Face Heat Fluxes and Temperatures Fig.8.2 plots hot face heat fluxes vs. hot face temperatures for the billet caster, the conventional slab caster of Compiany B , and the C S P caster of Company C . For the billet and thick slab casters, the heat fluxes and temperatures are at the meniscus, while for the C S P caster they are at the locations of the thermocouples, and are thus well below the meniscus. Ffeat fluxes and hot face temperatures for the slab caster had been gathered by Company B for a wide variety of casting speeds and steel grades. For the billet caster, data was obtained for different water velocities and mould flux grades, and thus has a smaller range than for Company B . As mentioned earlier, wall temperatures and other operational data for the billet caster were collected by Pinheiro [16]. These were input to the I H C P model described in Section 4.1.2 to calculate the heat fluxes and hot face temperatures. Results for the C S P caster are from the F E M analysis of heat flow presented in the previous chapter. Ch.8 Comparison between Conventional and Thin Slab Casting 127 • Billet caster @ meniscus Billet regression line A Thick slab caster @ meniscus Slab regression line • CSP caster @ BFs top row BF top row regression line • CSP caster @ BFs bottom row BF bottom row regression line • CSP caster @ NFs - - - NF regression line 150 175 200 225 250 275 300 325 350 375 400 Hot Face Temperature (°C) Figure 8.2: Hot face heat fluxes vs. hot face temperatures for billet, conventional slab and CSP casters. Ch.8 Comparison between Conventional and Thin Slab Casting 128 In spite of the variation in casting conditions (especially for the billet and conventional casters), data for each caster seems to follow a linear pattern, and the regression lines are also shown in Fig.8.2. The difference in the regression lines is a clear reflection of the different wall thicknesses and cooling water velocities for the casters. The billet caster has much thinner coppers (15.6 m m thick) than the thick slab (30 mm) or the C S P caster (19 and 23.2 m m for the narrow and broad faces respectively). This means, as can be seen i n Fig.8.2, that for the same heat flux the billet caster has lower hot face temperatures. Heat fluxes and temperatures have a very linear relation for the C S P caster, since they were calculated with almost the same casting conditions throughout. For the broad faces, data points for the top and bottom row thermocouples lie on different lines since the top row has a higher cooling intensity due to the additional presence of cooling holes. In fact, regression lines for the narrow faces and the top row broad face thermocouples are very close, since the thinner mould walls in the former are matched by more intense water cooling for the latter. Data for both the upper and lower thermocouples on the narrow faces fall on one line as there is no difference in cooling at the two locations. The regression line for the Company B thick slab caster is the left-most, since it has the thickest mould walls and lowest water velocities of the three different casters. Even though the billet caster has a lower range of peak hot face temperatures, meniscus heat fluxes for the billet caster seem to be higher than for the Company B slab caster. Different operational parameters (e.g. mould powder properties or casting speed) can be a possible reason for this discrepancy. It also has to be remembered that Company B Ch.8 Comparison between Conventional and Thin Slab Casting 129 uses the integrated form of Fourier's Law (Eq.2.2) to calculate heat fluxes for the slab caster. As has been described in Section 2.2.2.1, this method can lead to a significant degree of under-estimation of heat fluxes at the meniscus, where a strong 2-D thermal field is present. 8.4 Average Mould Heat Fluxes 3.5 3.0 2.5 x "co CD X 2 1.5 o 1.0 0.5 • Thick slab casters Regression line ° CSP caster A Billet caster 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Casting Speed (m/min) Figure 8.3: Average mould heat fluxes for thick slab (Company A#l and #2, and Company B), billet and CSP (Company C) casters. In Fig.8.1, specific mould heat extraction had been plotted against casting speed, for conventional and C S P casters. It was seen that specific heat extraction for the thin slab casters was much higher than for thick slab casters. B y using the same water A T method, average mould heat fluxes were also estimated for these casters, and have been Ch.8 Comparison between Conventional and Thin Slab Casting 130 plotted vs. casting speed in Fig.8.3. As is the usual trend, mould heat fluxes are seen to increase almost linearly with casting speed. As Mahapatra [49] has pointed out, this is because higher casting speeds result in a reduced thickness of the solidified steel shell. The thinner shell is thus more susceptible to ferrostatic pressure, which pushes it closer to the mould wall , reducing the mould wall -strand gap, and thus decreasing the resistance to heat transfer. A t the same time, a higher rate of heat input to the mould flux diminishes the fraction of solid mould slag in the mould wall-strand gap, which again lowers the thermal resistance of the gap. A t the meniscus region, a smaller slag r i m is formed, which has lesser mechanical interaction wi th the solidifying steel shell, resulting in shallower oscillation marks. This again reduces the wall-strand gap. Also , a hotter, more fluid l iquid flux is formed at the meniscus, which ensures better infiltration into the gap. Thus, higher casting speeds result in an overall increase in mould heat removal, especially in the meniscus region (Fig.2.15). This is especially true for the C S P casters. As has been seen from the results of the F E M modelling in this investigation, as well as reported by O'Connor and Dantzig [46], C S P caster moulds run much hotter than conventional casters. The discussions in Sec-tion 2.4 had shown that the peak hot face temperatures for C S P casters are ~ 4 5 0 ° C , which is much in excess of the recommended m a x i m u m of 350°C [19] for conventional casters. The extremely high hot face temperatures cannot but lead to a high rate of mould heat removal. In Fig.8.1, it was seen that specific heat removal for billet casters was higher than for thick slab casters, which, as explained for C S P casters, is due to a smaller section size Ch.8 Comparison between Conventional and Thin Slab Casting 131 of the strand. However, as Fig.8.3 shows, average mould heat fluxes for billet casters (using mould powder as lubricant) are indistinguishable from those for conventional slab casting. Fig.8.3 is quite similar to Fig.2.26 (from Wolf [51]), which also depicts average mould heat fluxes for thick and thin slab casters. The data presented by Wolf [51] estimates average mould heat fluxes of ~2.5 M W / m 2 for a C S P caster, at a casting speed of ~ 4 m / m i n . This is slightly higher than the heat fluxes calculated here for the C o m -pany C C S P caster, which are between ~2-2 .5 M W / m 2 at the same casting speed. Unlike for specific mould heat extraction, average heat fluxes seem to follow the same trend as for thick slab casters. Wolf [51] had presented heat flux data in Fig.2.26 for a wide range of casting speeds, and when extrapolated back to thick slab speeds, C S P and conventional slab average heat fluxes are quite similar. The same is seen in the present investigation, where heat fluxes for the C S P caster are close to the line extrapolated up from the conventional caster data. Fig.8.3 shows that average mould heat removal for three different types of casters (billet, thick and thin slab) have almost the same variation wi th casting speed. This supports the findings of Mahapatra et al. [7], who had noticed that, i n slab casters, casting speed is by far the most influential operational parameter vis. a vis. mould heat fluxes. The same is seen in Fig.8.3, where three distinct caster designs, using different types of mould powder, and casting dissimilar steel grades, can use almost the same function to describe average mould heat flux variation with casting speed. C h a p t e r 9 C o n c l u s i o n s a n d R e c o m m e n d a t i o n s The following is a brief summary of the work accomplished during this investigation: 1. The mechanism of heat transfer in slab caster moulds postulated by Mahapa-tra et al. [7] was validated. Heat fluxes back-calculated from data collected by Pinheiro [16] for a billet caster using powder lubrication showed that, everything else being the same, a lowering of cooling water velocities resulted in an increase in heat transfer. This is due to higher mould hot face temperatures resulting in the formation of a smaller slag r i m , and a hotter, more fluid l iquid flux. 2. The Company A #2 caster had been plagued by a high incidence of transverse corner cracking. Excessively high water velocities, leading to inadequate mould lubrication and heat transfer, were identified as the root cause of the problem. The incidences of cracking fell drastically after a reduction in water flow rates. 3. Heat fluxes were calculated for an operational C S P caster (at Company C) . A big dip in heat fluxes was seen in the central portion of the fixed broad face. It was postulated that this could be due to a combination of water flow differential 132 Ch.9 Conclusions and Recommendations 133 between the two broad faces, and a squeezing i n of the mould pocket bulge in the strand. In addition, the two broad faces, as well the narrow faces, were found to have unequal heat extraction rates. 4. Heat flux profiles were fitted to the calculated heat flux values. The profiles were input to a solidification model to estimate the solidified shell thickness of the strand at the mould exit. The calculated values of shell thickness agreed well wi th those reported by Company C . 5. The effect of the mould hot face temperature on mould heat transfer was used to introduce a procedure of water velocity variation into the working life of C S P caster moulds. Models were used to calculate water velocities which maintained a constant hot face temperature, while the wall thickness reduced. It was found that the current operational practice grossly over-estimated the water flows required in the latter stages of the mould life. 6. O n comparing mould heat extraction between conventional and C S P casters, it was found that the latter had a much higher specific heat removal. O n the other hand, average mould heat fluxes for C S P casters are similar to values obtained by extrapolating up from the conventional casting speeds. A m o n g the highlights of this investigation has been the calculation of heat flux profiles for an operational C S P caster. These had graphically shown the effect on mould heat transfer of the squeezing in of the bulge in the strand, as well as possible discrepancies in water flow. W h i l e the present analysis has revealed much information on the thermal Ch.9 Conclusions and Recommendations 134 state of a C S P caster mould, significant work st i l l needs to be carried out to gain a fuller understanding. The chief handicap for the thermal analysis carried out in this study had been the use of a C S P caster not specifically instrumented for such a study. Thus, thermocouples meant for breakout detection, which are of necessity placed well below the meniscus, were used. Monitoring the thermal field at the meniscus region is of prime importance, and in this investigation heat transfer in this v i ta l area could only be guessed at. A C S P caster has never been fully instrumented for a detailed analysis of mould heat flow. Readings from such an instrumented mould, if fed into a ful l three dimensional model of the mould, would definitely lead to significant insights into the dynamics of a C S P caster mould. B i b l i o g r a p h y [1] "Statistical Information", Iron & Steelmaker, V o l . 24, No. 13, 1997, pg. 10. [2] M . M . Wolf, "Historical perspectives on continuous casting in the m i n i m i l l s " , Near-Net-Shape Casting in the Minimills (Proceedings of the International Symposium), Vancouver, Canada, 1995, pp. 3-22. [3] L . K . Chiang, " M o u l d Heat Transfer and Solidification Phenomena in the Con-tinuous Casting of Steel Slabs", 13th Process Technology Conference Proceedings, I S S - A I M E , 1995, pp. 293-315. [4] B . G . Thomas,"Mathematical Modeling of the Continuous Slab Casting M o l d : a State of the A r t Review", Mold Operation for Quality and Productivity, 1991, ISS-A I M E , Warrendale, P A , pp. 69-82. [5] J . Savage and W . H . Pr i tchard, "The problem of rupture of the billet in the con-tinuous casting of steel", Journal of the Iron and Steel Institute, 1954, V o l . 178, pp. 269-277. [6] R . B . Mahapatra , J . K . Brimacombe, I .V . Samarasekera, N . Walker, E . A . Paterson and J . D . Young, " M o u l d Behaviour and Its Influence on Quali ty in the Contin-uous Casting of Steel Slabs: Part I. Industrial Trials, M o l d Temperature Mea-surements, and Mathematical Model l ing" , Metallurgical Transactions B, V o l . 22B, 1991, pp. 861-874. [7] R . B . Mahapatra , J . K . Brimacombe and I .V. Samarasekera, " M o u l d Behaviour and Its Influence on Quali ty in the Continuous Casting of Steel Slabs: Part II. M o u l d Heat Transfer, M o u l d F l u x Behaviour, Formation of Oscil lation Marks , Longitu-dinal Off-Corner Depressions, and Subsurface Cracks" , Metallurgical Transactions B, V o l . 22B, 1991, pp. 875-888. [8] I .V. Samarasekera and J . K . 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Lee, " O p t i -mization of Casting Conditions by the Measurement of M o u l d W a l l Temperature at Pohang Works" , 77th Steelmaking Conference Proceedings, I S S - A I M E , 1994, pp. 347-356. [19] T . Wada, M . Suzuki and T . M o r i , " H i g h Speed Casting of 3 .0m/min at N K K Fukuyama No.5 Slab Caster", 70th Steelmaking Conference Proceedings, ISS-A I M E , 1987, pp. 197-204. [20] R . Sobolewski, S .C. Sander, J . G . K u c z m a and A . J . Rumler , " A n Experimental , In-strumented M o l d for Heat Transfer and Operating Conditions Study" , 73rd Steel-making Conference Proceedings, I S S - A I M E , 1990, pp. 275-280. [21] M . R . Ozgu and B . K o c a t u l u m , "Thermal Analysis of the Burns Harbor No.2 Slab Caster M o l d " , 76th Steelmaking Conference Proceedings, I S S - A I M E , 1993, pp. 301-308. [22] M . R . Ozgu, "Continuous Caster Instrumentation: State-of-the-Art Review" , Cana-dian Metallurgical Quarterly, V o l . 35, 1996, pp. 199-223. BIBLIOGRAPHY 137 [23] D . E . Humphreys, J . D . M a d i l l , V . Ludlow, D . Stewart, S .G . Thornton, and A . S . Normanton, "Appl ica t ion of M o u l d Thermal Monitor ing i n the Study of Slab Sur-face Quali ty for Heavy Plate Grades at Scunthorpe Works, Br i t i sh Steel", 1st Eu-ropean Conference on Continuous Casting, Florence, Italy, 1991, pp. 1.529-1.540. [24] S. Petry, "Advanced Thermal M o u l d M o n i t o r i n g " , 13th Process Technology Divi-sion Conference Proceedings, I S S - A I M E , 1995, pp. 209-215. [25] M . W . Nichols, W . C . B i l s k i , R . D . M c G i n n i s and J . W . Weyant, "Development and Implementation of a Thermocouple Based Breakout Detection System for the Slab Caster at Lukens Steel", 75th Steelmaking Conference Proceedings, I S S - A I M E , 1992, pp. 789-794. [26] F . Haers, S .G . Thornton, "The Appl icat ion of M o u l d Thermal Monitor ing on the Two Strand Slab Caster at Sidmar, B e l g i u m " , 76th Steelmaking Conference Pro-ceedings, I S S - A I M E , 1993, pp. 425-436. [27] P. Bellomo, G . Salvemini, E . Santa M a r i a and F . V i c i n o , " O n Line Detection of M o l d Thermal Transfer Characteristics", 77th Steelmaking Conference Proceedings, I S S - A I M E , 1994, pp. 319-327. [28] M . M . Col lur , D . R . Borrebach and R . A . K a r d i b i n , " M o l d Heat Transfer Character-istics", 13th Process Technology Division Conference Proceedings, I S S - A I M E , 1995, pp. 163-173. [29] H . L . Gilles, "Development of Thermal Solidification Models for Bethlehem's Slab Casters", 76th Steelmaking Conference Proceedings, I S S - A I M E , 1993, pp. 315-329. [30] H . L . Gilles, M . Byrne, T . J . Russo and G . A . 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Kanazawa, "Influence of M o u l d Heat Fluxes on Longitudinal Surface Cracks during High Speed Continuous Casting of Steel Slab" 77th Steelmaking Conference Proceedings, I S S - A I M E , 1994, pp. 397-403. [39] M . M . Wolf, " M o u l d Heat Transfer and Lubrication Control - Two Major Functions of Caster Product ivi ty and Quali ty Assurance" 13th Process Technology Division Conference Proceedings, I S S - A I M E , 1995, pp. 99-117. [40] D . Currey, "Opt imizat ion of Casting Speed for Higher Product iv i ty on Dofasco's N o . l Continuous Caster", 78th Steelmaking Conference Proceedings, I S S - A I M E , 1995, pp. 287-294. [41] J . K . Brimacombe and I .V. Samarasekera, "The challenges of thin slab casting", Near-Net-Shape Casting in the Minimills (Proceedings of the International Sympo-sium), Vancouver, Canada, 1995, pp. 33-53. [42] " I & S M 1997 Continuous Caster Roundup" , Iron & Steelmaker, V o l . 24, No. 11, 1997, pp. 20-32. [43] R. Preston, "Annals of Enterprise (Hot Metal - I ) " , The New Yorker, Feb. 25, 1991, pp. 43-71. [44] R. Preston, "Annals of Enterprise (Hot Metal - I I ) " , The New Yorker, M a r . 4, 1991, pp. 41-79. [45] R . F . Davis, " A c m e Steel: The Minigrated™ M i l l " , Near-Net-Shape Casting in the Minimills (Proceedings of the International Symposium), Vancouver, Canada, 1995, pg. 327. [46] T . G . O'Connor and J . A . Dantzig, "Model ing the Thin-Slab Continuous-Casting M o l d " , Metallurgical and Materials Transactions B, V o l . 25B, 1994, pp.443-457. [47] K . Wiinnenberg and K . Schwerdtfeger, "Principles in T h i n Slab Cast ing" , Iron & Steelmaker, V o l . 23, No. 4, 1995, pp. 25-31. BIBLIOGRAPHY 139 [48] I .V . Samarasekera, "Thermal Distortion of Continuous Casting M o u l d s " , Ph.D. Thesis, 1980, University of Br i t i sh Columbia , Vancouver, Canada. [49] R . B . Mahapatra , " M o u l d Behaviour and Product Qual i ty i n the Continuous Cast-ing of Slabs", Ph.D. Thesis, 1989, University of Br i t i sh Columbia , Vancouver, Canada. [50] S. Chandra, "Heat Transfer, O i l Lubrication and M o u l d Taper in Steel Bi l let Cast-ing Machines" , Ph.D. Thesis, 1992, University of Br i t i sh Columbia , Vancouver, Canada. [51] M . M . Wolf, " M o l d Length in Slab Casting - A Review" , Iron & Steelmaker, V o l . 23, No. 2, 1996, pp. 47-51. 

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