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Thermal characteristics of the electroslag remelting process 1971

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THE THERMAL CHARACTERISTICS OF THE ELECTROSLAG REMELTING PROCESS BY SATISH V. JOSHI B.Tech.(Hons), Indian I n s t i t u t e of Technology, Bombay, 1967 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of METALLURGY We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA July, 1971 In present ing t h i s thes is in p a r t i a l f u l f i l m e n t o f the requirements fo r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I fu r ther agree that permission for extensive copying of th is thes is fo r s c h o l a r l y purposes may be granted by the Head of my Department or by h is representa t i ves . It is understood that copying or p u b l i c a t i o n o f th is thes is f o r f i n a n c i a l gain sha l l not be allowed without my wr i t ten permiss ion . Department of M e.tg*. 11 ^TfpJ The Un ivers i ty of B r i t i s h Columbia Vancouver 8, Canada Date i i ABSTRACT The thermal c h a r a c t e r i s t i c s of the e l e c t r o s l a g remelting process have been investigated on a laboratory scale unit. The heat generation and d i s t r i b u t i o n i n the slag bed i s discussed. The voltage gradients i n the slag bed are predicted using a resistance network analogue and tested against experimental r e s u l t s . A s e l f - c o n s i s t e n t model for electrode temperature gradients i n the e l e c t r o s l a g remelting process has been tested against experimental r e s u l t s . An unsteady-state method has been used to determine the e l e c t r i c a l resistance and the o v e r a l l heat transfer c o e f f i c i e n t of the i n t e r f a c e region, l i q u i d slag/slag skin/copper wall i n the e l e c t r o s l a g furnace. An accurate heat balance of the process i s c a r r i e d out on labora- tory scale ingots. Attention has been devoted to the influence.of various melt parameters i . e . p o l a r i t y , power input, geometry, atmosphere etc. on the melt rate. The power requirements and the melt rate for i n d u s t r i a l ingots are predicted and compared with the data c o l l e c t e d from the l i t e r a t u r e . The l i q u i d metal pool volumes i n ESR ingots are predicted from the operational data. The pool p r o f i l e s are computed using a f i n i t e d ifference technique and compared with the experimentally obtained p r o f i l e s . i i i TABLE OF CONTENTS Page TITLE PAGE . i ABSTRACT i i TABLE OF CONTENTS i i i LIST OF FIGURES x LIST OF TABLES x v i LIST OF SYMBOLS . ..; x v i i ACKNOWLEDGEMENTS xxiv CHAPTER I. INTRODUCTION 1 1.1 . The E l e c t r o s l a g Remelting Process 1 1.2 Statement of the Problem 4 1.3 The U.B.C. E l e c t r o s l a g Unit 6 1.4 Choice of Materials 7 CHAPTER I I . DETERMINATION OF VOLTAGE GRADIENTS IN THE SLAG BED OF THE ESR PROCESS 10 11.1 Mechanism of Heat Generation .. 10 11.2 Measurement of Temperature i n the Slag Bed 12 11.3 Determination of Is o p o t e n t i a l Contours i n the Molten Slag Bed 13 II . 3.1 Introduction .13 11.3.2 Solution by E l e c t r i c - R e s i s t a n c e Network .... 14 11.3.3 Discussion 16 11.4 Electrochemical p o l a r i z a t i o n i n ESR .18 11.5 E f f e c t of Ca and A l Dissolved i n the Slag 18 11.6 Measurement of Voltage Gradients i n the Slag Bed.... 19 i v Page CHAPTER I I I . ELECTRODE TEMPERATURE GRADIENTS IN THE ELECTRO- SLAG PROCESS 20 I I I . l Introduction 20 I I I . 2 Experimental 22 111.2.1 Temperature Measurement 22 111.2.2 ESR Operating Conditions 22 I I I . 3 Discussion 23 111.3.1 Formulation of the Problem 23 111.3.2 Calculated Temperature P r o f i l e s 32 111.3.3 Correlation with Experiment 32 CHAPTER IV. MEASUREMENT OF ELECTRICAL AND THERMAL PROPERTIES OF THE SLAG SKIN REGION 37 IV. 1 Introduction 37 IV. 2 Experimental 38 IV.2.1 E l e c t r i c a l and Thermal Measurements 38 IV. 2.2 ESR E l e c t r i c a l Data 41 IV. 3 Discussion 44 IV.3.1 The Thermal Resistance of the Slag Skin.. 44 IV. 3.2 The E l e c t r i c a l Resistance of the Slag Skin 48 CHAPTER V. HEAT BALANCE OF THE PROCESS 50 V. l Introduction 50 V.2 Experimental 54 V. 2.1 ESR Ingot Schedule 54 V.2.1.1 Melt Record 54 V.2.1.2 Molds 54 V.2.1.3 Electrodes '54 V Page V.2.1.4 Slag Composition 55 V.2.1.5 P o l a r i t y 55 V.2.1.6 Continuous Slag Addition 55 V.2.1.7 Atmosphere Control . 55 V.2.1.8 Experimental Data 56 V.2.2 Measurement of Temperature P r p f i l e s i n the Mold 56 V.2.3 Measurement of the Heat Leaving Through the Bottom of the Mold 65 V.3 D i s t r i b u t i o n of Heat Input i n the Slag Bed 65 V.3.1 Power Input 65 V.3.2 Resistance Heating of the Slag 66 V.3.3 E f f e c t of Dissolved Ca and A l on the Conductivity of the Slag 68 V.3.4 Heat Generation Due to P o l a r i z a t i o n 71 V.4 An Analysis of the Heat Transferred to Mold Cooling Water 71 V.4.1 Introduction 71 V.4.2 Non-boiling Region 72 V.4.2.1 Introduction 72 V.4.2.2 C a l c u l a t i o n of Reynolds Number.. 73 V.4.2.3 C a l c u l a t i o n of the Heat Transfer C o e f f i c i e n t i n the Non-boiling Region 75 V.4.3 Surface B o i l i n g Region 77 V.4.3.1 Introduction 77 V.4.3.2 E f f e c t of Dissolved A i r 80 V. 4.4 Calculations 80 V.4.4.1 Introduction 80 V. 4.4. 2 Region A 81 v i Page V.4.4.3 Region C 82 V.4.4.4 Region B 82 V.5 A D e t a i l Analysis of the Heat D i s t r i b u t i o n i n the Laboratory ESR Unit 85 V.5.1 Introduction 85 V.5.2 Heat Balance of the Slag Bed Region 85 V.5.2.1 Heat Input 85 V.5.2.2 Heat Output 85 V.5.2.2.1 Heat Required to Melt the Electrode 85 V.5.2.2.2 Heat Lost by Radiation from the Slag Surface 86 V.5.2.2.3 Heat Lost to Cooling Water Across the Slag Bed 87 V.5.2.2.4 Heat Picked up by the F a l l i n g L i q u i d Metal Droplets 87 V.5.2.3 Heat D i s t r i b u t i o n i n the Slag Bed 88 V.5.2.3.1 Introduction 88 V.5.2.3.2 Heat Balance of the Region Above the Electrode Tip 89 V.5.2.3.3 Heat Balance of the Region Below the Electrode Tip 89 V.5.3 Approximate C a l c u l a t i o n of the Heat Transfer C o e f f i c i e n t Across the Liq u i d Slag-Liquid Metal Interface 90 V.5.4 Heat Balance of the L i q u i d Metal Region.. 91 V.5.5 Heat Balance of the S o l i d i f i e d Ingot Region 91 V.5.5.1 Heat Input 91 V.5.5.2 Heat Output 91 v i i Page V.5.5.2.1 Heat Going to Mold Cooling Water 91 V.5.5.2.2. Heat Going to Base Plate Cooling Water.. 92 V.5.5.2.3 Sensible Heat Retained by the Ingot 92 V.5.5.2.4 T o t a l Heat Output ... 93 V.5.6 Heat Balance for Ingot Nos. 1, 10 and 16 93 V.6 Discussion 93 V.6.1 Comparison of the D i f f e r e n t E l e c t r i c a l Configurations 93 V.6.2 E f f e c t of Electrochemical and Chemical Reactions .. 102 V.6.3 E f f e c t of P o l a r i t y on the Slag Skin Thickness 104 V. 6.4 Correlation and P r e d i c i t i o n of Operating • Parameters for E l e c t r o s l a g Processing.... 105 CHAPTER VI. PREDICTION OF POOL VOLUMES IN ESR INGOTS 116 VI.1 Introduction 116 VI.2 P r e d i c t i o n of the Height of the C y l i n d r i c a l Portion of the Pool Volume 118 VI.3 P r e d i c t i o n of Pool P r o f i l e s Using E x p l i c i t F i n i t e Difference Method 119 VI. 3.1 Introduction 1.19 VI.3.2 Derivation of the Formulae For the E x p l i c i t F i n i t e Difference Method 120 VI.3.3 Saliant Features of the Computer Programme 121 VI.3.4 Results 129 CHAPTER VII. CONCLUSIONS 131 v i i i Page APPENDIX I. THE PHYSICAL PROPERTIES OF ESR SLAGS 134 A.I.I Introduction 134 A.I.2 Measurement of Density of CaF^ Based Slags 136 A. 1.2.1 Introduction ' 136 A.I.2.2 Experimental 139 A. I.2.2.1 Apparatus 139 A.I.2.2.2 C a l i b r a t i o n and Measurement 140 A.I.2.3 Results 141 A.I.3 Measurement of V i s c o s i t y of the CaF^ Based Slags. 142 A.I.3.1 Introduction 142 A.I.3.2 Experimental 142 A. 1.3.2.1 Apparatus 142 A. I.3.2.2 Procedure 143 A. I.3.2.3 C a l i b r a t i o n 144 A.I.3.2.4 Errors Involved 14,5 A.I.3.3 Results 146 APPENDIX I I . CALCULATION OF THE RESISTANCE OF THE VOLUME ELEMENTS IN THE VOLTAGE GRADIENT ANALYSIS 147 A . I I . l Introduction 147 A. I I . 2 C a l c u l a t i o n of R 147 z A. I I . 3 C a l c u l a t i o n of R 148 r A. I I . 4 C a l c u l a t i o n of R g and R 1 3 148 APPENDIX I I I . COMPUTER PROGRAMME TO DETERMINE THE TEMPERATURE GRADIENTS ON THE MOLD 150 i x Page APPENDIX IV. CALCULATION OF POWER REQUIREMENT FOR MAKING AN INDUSTRIAL SCALE INGOT 154 APPENDIX V. DERIVATION OF FORMULAE FOR THE EXPLICIT FINITE DIFFERENCE METHOD 157 APPENDIX VI. COMPUTER PROGRAMME TO DETERMINE THE POOL PROFILES IN ESR INGOTS 163 BIBLIOGRAPHY •/ 173 FIGURES 178 6 X LIST OF FIGURES Figure Page 1 Schematic diagram of the e l e c t r o s l a g remelting unit 178 2 Voltage gradient i n an arc . 179 3 ESR experimental set up for temperature measurement under an argon atmosphere 180 4 D e t a i l s of the thermocouple arrangement 181 5 Temperature d i s t r i b u t i o n i n the slag bed for d.c. negative (air) 182 6 Temperature d i s t r i b u t i o n i n the slag bed for d.c. negative (argon) 183 7 Temperature d i s t r i b u t i o n i n the slag bed for a.c. (air) 184 8 Temperature d i s t r i b u t i o n i n the slag bed for a.c. (argon) 185 9 Temperature d i s t r i b u t i o n i n the slag bed for d.c. p o s i t i v e (argon) 186 10 Temperature d i s t r i b u t i o n i n the slag bed for d.c. p o s i t i v e - ' l i v e ' mold (argon) 187 11 Assumed temperature d i s t r i b u t i o n i n the slag bed (ingot no. 1) 188 12 Subdivision of the slag bed 189 13 Resistance of a volume element 189 14 Resistance network 190 15 Network resistance f o r a single j u n c t i o n 191 16 Iso p o t e n t i a l contours i n the ESR slag bed 192 • 17 E f f e c t of f i n i t e mold wal l - s l a g skin resistance on the i s o p o t e n t i a l contours Cslag skin r e s i s t i v i t y = 250 ohm cm) 193 18 E f f e c t of f i n i t e electrode-slag skin resistance on the i s o p o t e n t i a l contours (slag skin r e s i s t i v i t y = 0.2 ohm cm) 194 x i Figure Page 19 E f f e c t of f i n i t e electrode-slag skin resistance on the i s o p o t e n t i a l contours (slag skin r e s i s t i v i t y = 20 ohm cm) 195 20 (a) Anodic p o l a r i z a t i o n curves f o r CaF2-Al20"3 slags determined by galvanostatic experiments 1 2! 196 (b) Cathodic p o l a r i z a t i o n curves for CaF2~Al203 slags determined by galvanostatic experiments-^7 196 21 (a) Anodic p o l a r i z a t i o n curves on ESR electrodes i n C a F 2 - A l 2 0 3 s l a g s 1 2 197 (b) Cathodic p o l a r i z a t i o n curves on ESR electrodes i n C a F 2 - A l 2 0 3 s l a g s 1 2 197 22 Experimentally obtained voltage gradient i n the slag bath 198 23 Schematic outline of the experimental set up for electrode temperature measurement 199 24 Electrode temperature gradient for 2.54 cm diameter electrode of AISI 1018 s t e e l i n electrode negative p o l a r i t y 200 25 Electrode temperature gradient for 3.81 cm dimater electrode of AISI 1018 s t e e l i n electrode negative p o l a r i t y 201 26 Electrode temperature gradient f or 2.54 cm diameter electrode of AISI 321 s t e e l i n electrode negative p o l a r i t y 202 27 Electrode temperature gradient for 2.54 cm diameter electrode of AISI 1018 s t e e l i n electrode p o s i t i v e p o l a r i t y 203 28 Electrode temperature gradient for 3.81 cm diameter electrode of AISI 1018 s t e e l i n electrode p o s i t i v e p o l a r i t y 204 29 Electrode temperature gradient for 2.54 cm diameter electrode of AISI 321 s t e e l i n electrode p o s i t i v e p o l a r i t y 205 30 Outline diagram to i l l u s t r a t e the parameters used i n the computation of the electrode temperature gradient 206 31 V a r i a t i o n of configuration factor with a x i a l length and 3 207 x i i Figure Page 32 Electrode temperature gradients f or 3.81 cm diameter electrode of AISI 1018 s t e e l i n electrode negative p o l a r i t y i n VAR and ESR processes 208 33 Current paths i n an ESR mold (a) mold insulated (b) mold grounded 209 34 Experimental apparatus f o r measuring the e l e c t r i c a l and thermal resistance of the slag skin 210 35 Slag s k i n e l e c t r i c a l resistance as a function of temperature (slag temperature constant at 1600°C)... 211 36 Slag skin e l e c t r i c a l resistance as a function of temperature for CaF£ slag at d i f f e r e n t slag bath temperatures 212 37 Time dependence of cylinder thermal parameter; s l a g temperature constant at 1650°C 213 38 Time dependence of cylinder thermal parameter; slag composition constant at CaF^ + 25 wt.% A^O^ 214 39 Radial dimensions of the mold-slag skin system 215 40 Mold region temperature p r o f i l e derived from eq. (4.8) by assuming that k = 0.8 x 10~2 C a l cm-l°C-lsec-l f t ? ? 215 41 (a) view of the laboratory ESR unit (b) powder feeder 216' 42 Mold connection i n ESR p r a c t i c e (a) l i v e (b) f l o a t i n g Cc) insulated 217 43 Atmospheric s h i e l d (type (I)) 218 44 Atmospheric s h i e l d (type (II)) 219 45 Atmospheric s h i e l d (type (III)) 220 46 Mold current i n d.c. +ve ' l i v e ' operation 221 47 Thermocouple arrangement on the mold 222 48 Thermocouples clad copper molds 223 49 Temperature p r o f i l e on the mold for ingot no. 1 .... 224 50 Temperature p r o f i l e on the mold for ingot no. 3 .... 225 x i i i F i g u r e Page 51 Temperature p r o f i l e on t h e mold f o r i n g o t no. 8 .... 226 52 Temperature p r o f i l e on the mold f o r i n g o t no. 9 .... 227 53 Temperature p r o f i l e on the mold f o r i n g o t no. 10 ... 228 54 Temperature p r o f i l e on the mold f o r i n g o t no. 13 ... 229 55 Temperature p r o f i l e on the mold f o r i n g o t no. 16 ... 230 56 Temperature p r o f i l e on the mold f o r i n g o t , no. 19 ... 231 57 Temperature d i s t r i b u t i o n i n the mold c o o l i n g water f o r i n g o t no. 1 232 58 P l o t of temperature v s . d i s t a n c e from the s l a g / m e t a l i n t e r f a c e f o r base p l a t e thermocouples 233 59 V o l t a g e g r a d i e n t s i n the s l a g bed f o r i n g o t no. 1 .. 234 45 47 60 P l o t of heat f l u x v s . excess temperature .'. 235 47 61 C o r r e l a t i o n of p o o l - b o i l i n g h e a t t r a n s f e r d a t a 236 48 62 E f f e c t of d i s s o l v e d a i r on the heat f l u x 237 63 P l o t of (q/A) v s . AT f o r (a) n o n - b o i l i n g and (b) s u r f a c e b o i l i n g c o n d i t i o n s 238 64 Heat d i s t r i b u t i o n i n an ESR u n i t 239 65 Heat g e n e r a t i o n d i s t r i b u t i o n i n the s l a g bed ( f o r i n g o t no. 1) 240 66 Heat l o s t by r a d i a t i o n from the s l a g s u r f a c e 241 67 B l o c k diagram f o r the heat b a l a n c e of the s l a g r e g i o n 241 68 B l o c k diagram f o r the heat b a l a n c e of the l i q u i d m e t a l r e g i o n 242 69 B l o c k diagram f o r the heat b a l a n c e o f the s o l i d i f i e d i n g o t 242 70 ESR u n i t ' s a n a l o g c i r c u i t 243 71 P i c t u r e s of s l a g cap and s l a g s k i n of some of the ESR m e l t s 244 x i v F i g u r e Page 72 P i c t u r e s o f the s l a g cap and s l a g s k i n of some of the ESR m e l t s 246 73 B o e h l e r s i n g l e phase a.c. ESR melt r a t e v s . i n g o t diameter6 247 74 E f f e c t o f melt r a t e on the shape of t h e l i q u i d m e t a l p o o l 248 75 S u b d i v i s i o n of the molten m e t a l p o o l 249 76 Macrographs of ESR i n g o t s 250 77 S u b d i v i s i o n : of the i n g o t 251 78 Average temperature d i s t r i b u t i o n on t h e mold a c r o s s the s o l i d i f i e d i n g o t 252 79 Nodal p o i n t s c o n f i g u r a t i o n 126 80 P r e d i c t e d p o o l p r o f i l e f o r i n g o t no. (1) 253 81 P r e d i c t e d p o o l p r o f i l e f o r i n g o t no. (10) 253 82 P r e d i c t e d p o o l p r o f i l e f o r i n g o t no. (16) 254 83 P r e d i c t e d p o o l p r o f i l e f o r i n g o t no. (21) 254 84 P r e d i c t e d p o o l p r o f i l e f o r i n g o t no. (26) 255 85 P r e d i c t e d p o o l p r o f i l e f o r i n g o t no. (28) 255 21 86 E l e c t r i c a l c o n d u c t i v i t y of C a F 2 ~ A l 2 0 3 s l a g s 256 87 A s c h e m a t i c diagram of the a p p a r a t u s f o r the measure- ment of d e n s i t y o f CaF^ based s l a g s 257 88 E x t e r n a l c i r c u i t r y r e q u i r e d t o o p e r a t e the t r a n s d u c e r 258 . 89 The d e n s i t y measurement a p p a r a t u s 259 90 E f f e c t o f o x i d e s on the s u r f a c e t e n s i o n of CaF^^^'''^ 260 91 D e n s i t y v s . temperature f o r C a F 2 ~ A l 2 0 3 system 261 92 D e n s i t y v s . temperature f o r CaF2~Ca0 system 262 93 A s c h e m a t i c diagram of t h e apparatus f o r the measure- ment of v i s c o s i t y of CaF2 based s l a g s 263 94 A c l o s e up view of the v i s c o s i t y measurement apparatus 264 X V Figure Page 95 The v i s c o s i t y measurement apparatus 264 96 V a r i a t i o n of c o e f f i c i e n t of v i s c o s i t y with % A1„0„ at 1600°C 7.... 265 97 V a r i a t i o n of c o e f f i c i e n t fo v i s c o s i t y with tempera- ture for CaF2-Al20.j system 266 98 Schematic diagram of the section of the slag bath .. 267 99 Schematic diagram of the section of the slag bath .. 267 100 General element for case 1 268 101 General element f o r case 2 269 102 General element for case 3 269 103 General element for case 5 270 104 General element for case 6 270 105 General element for case 8 270 x v i LIST OF TABLES T a b l e Page I C o m p o s i t i o n of the a l l o y s s t u d i e d 7 I I Parameters used i n the computation of c u r v e s shown i n F i g . (24) to F i g . (29) 33 I I I V a l u e s of the o v e r a l l h e a t t r a n s f e r c o e f f i c i e n t , U, c a l c u l a t e d from the d a t a of F i g . (37) and F i g . (38). 42 3 6 IV O p e r a t i n g r e s i s t a n c e s i n the ESR p r o c e s s 43 V ESR m e l t r e c o r d 57 VI Chemical a n a l y s i s of the EN 25 s t e e l i n g o t s 62 V I I C a l c u l a t i o n of heat i n p u t d i s t r i b u t i o n i n the s l a g bed u s i n g a.c. e l e c t r i c a l c o n d u c t i v i t y 67 V I I I C a l c u l a t i o n of heat i n p u t d i s t r i b u t i o n i n the s l a g bed u s i n g d.c. e l e c t r i c a l c o n d u c t i v i t y 70 IX E x p e r i m e n t a l d a t a f o r i n g o t no. 1 ( T a b l e V) 74 X P h y s i c a l p r o p e r t i e s of water at 40-50°C 74 XI Heat b a l a n c e f o r i n g o t no. 1, 10 and 16 94 XII E x p e r i m e n t a l r e s u l t s f o r t h e i n s u l a t e d mold unshunted and shunted to ground t h r o u g h 0.5 ohm r e s i s t o r 3 6 99 X I I I C a l c u l a t e d v a l u e s of Z f o r the l a b o r a t o r y made i n g o t s 110 XIV C a l c u l a t e d v a l u e s of Z f o r i n d u s t r i a l i n g o t s 112 51 XV O p e r a t i n g c o n d i t i o n s f o r an i n d u s t r i a l s c a l e i n g o t 119 XVI P h y s i c a l p r o p e r t i e s of pure i r o n used i n the a n a l y s i s ' ^ 126 XVII Parameters used i n the p r e d i c t i o n of p o o l p r o f i l e s i n EN 25 and FVE i n g o t s 130 X V III P h y s i c a l p r o p e r t i e s of ESR s l a g s 137 x v i i LIST OF SYMBOLS CHAPTER I I c r o s s s e c t i o n a l a r e a , cm^ c o n d u c t i v i t y , ohm ''"cm ^ ( r r e s i s t i v i t y p o t e n t i a l , v o l t s l e n g t h , cm r a d i a l c o o r d i n a t e ^ _ r ^ • = r e s i s t a n c e , ohms A c A t + , t _ : t r a n s f e r e n c e numbers, d i m e n s i o n l e s s Z : v e r t i c a l c o o r d i n a t e CHAPTER I I I a : r a d i u s o f the e l e c t r o d e , cm A 2 A : a r e a , cm C : c o n s t a n t s n 3 ae±a T D : , r a d i a t i o n - c o n d u c t i o n parameter, d i m e n s i o n l e s s F : c o n f i g u r a t i o n f a c t o r , d i m e n s i o n l e s s i7 2 s l a g j . 1 E : T — ° — , d i m e n s i o n l e s s T o -2 -1 -1 h : heat t r a n s f e r c o e f f i c i e n t , c a l cm sec °K c -1 -1 -1 K : th e r m a l c o n d u c t i v i t y of the e l e c t r o d e , c a l cm s e c °K I : l e n g t h of the e l e c t r o d e , cm I L : — , d i m e n s i o n l e s s e l e c t r o d e l e n g t h X V I 1 1 h a . —rf— , convection parameter, dimensionless r,tj),z: c y l i n d r i c a l polar coordinates r,z : length along r,z d i r e c t i o n s , cm r z R,Z : — , — , dimensionless a a r2 T T o T oo E a mold radius, cm temperature at any point i n the electrode, °K electrode surface temperature at the slag/gas i n t e r f a c e , °K average temperature of argon, °K average temperature of the ins i d e surface of the copper mold, °K c o e f f i c i e n t of a b s o r p t i v i t y , dimensionless c o e f f i c i e n t of e m i s s i v i t y , dimensionless -1 -2 -4 Stefan-Boltzmann constant, c a l sec cm °K r 2 B : — , dimensionless Si T - T X : — ^ , dimensionless temperature at any point i n the electrode o T oo X^ : — , dimensionless average temperature of argon o X : Y~ , dimensionless average temperature of ins i d e surface of ° the copper mold. Subscripts electrode surface slag surface at slag/gas i n t e r f a c e mold surface argon bulk x i x Superscripts * : e f f e c t i v e r a d i a t i o n environment (water cooled copper mold) CHAPTER IV 2 A : heat t r a n s f e r area, cm ty c : conductivity ( = r^—.—r—-) , ohm ^cm "*" J r e s i s t i v i t y Cp : s p e c i f i c heat of the copper c y l i n d e r , c a l g ^°C "*" h. : heat trans f e r c o e f f i c i e n t of the discontinuous i n t e r f a c e between l n t ' -2 - l o -1 the slag skin and the inner face of the mold w a l l , c a l cm sec °C h .. : heat transfer c o e f f i c i e n t , describing the t r a n s f e r of heat from 8 -2 -1 -1 the bulk slag to the slag skin, c a l cm sec °C ^ s l a g 1 a v e r a S e thermal conductivity of the slag s k i n , c a l cm ''"sec ^°C "*" -1 -1 -1 K : thermal conductivity of copper, c a l cm sec °C H : c h a r a c t e r i s t i c a x i a l length, cm T • c • J • • r ^v. - I - J volume L : s i g n i f i c a n t dimension of the copper cy l i n d e r = -z , cm r surface area m : mass of the copper c y l i n d e r , g q : heat transferred per second, c a l sec ^ r.. „ „: r a d i a l dimensions of the copper mold slag-skin system as shown i n F i g . (39), cm R : resistance, ohm t : time, sec T : temperatures at locations as shown i n F i g . (40), °C C, D, E T ^ : temperature of the inner surface of the copper mold w a l l , °C T^ : copper cy l i n d e r temperature at t = 0, °C ''"slag1 b u l k slag temperature,°C T : copper cylinder temperature at t = t, °C XX -2 -1 -1 U : o v e r a l l heat transfer c o e f f i c i e n t , c a l cm sec °C CHAPTER V 2 A : area, cm c : conductivity, ohm "*"cm 0^ : s p e c i f i c heat, c a l g "*"°C d : electrode diameter, cm D : ingot diameter, cm D^,D2: dimensions of the annulus, cm : average bubble diameter, cm D : hydraulic diameter, cm -2 -1 G : mass v e l o c i t y of f l u i d flowing through the annulus, g cm sec -2 -1 G^ : mass v e l o c i t y of the bubbles per unit area, g cm sec -2 -1 -1 h : heat transfer c o e f f i c i e n t , c a l cm sec °C -2 -1 h^k : heat trans f e r c o e f f i c i e n t for non-boiling region, c a l cm sec °C h ^ heat trans f e r c o e f f i c i e n t f o r the surface b o i l i n g region, -2 -1 -1 c a l cm sec °C I : current, amperes -1 -1 -1 k : thermal conductivity, c a l cm sec °C I : length, cm L : la t e n t heat, c a l g ^ m : mass, g MR : melt rate, g sec Nu : Nusselt number, dimensionless P : power, Kcal sec ̂ Pr : Prandtl number, dimensionless q : heat transferred per unit time, c a l sec ^ X X I q.,q ,q : t o t a l heat transferred across the regions shown i n F i g . (49), A 15 L* ^ Kcal sec Q i ^ ' as defined i n F i g . (64), c a l sec r : r e s i s t i v i t y , ohm cm R : ^ir- > resistance, ohms A Re: Reynolds number, dimensionless St: Stanton number, dimensionless T : temperature, °C V : voltage, v o l t s W : water rate through the annulus, g sec V I ' d 2 „ 1 -1 , Kcal g D 2(|) MR p : density, g cm 3 u ' v i s c o s i t y , poise AT : temperature d i f f e r e n c e , °C CHAPTER VI 2 A C P h area, cm s p e c i f i c heat, c a l g ^°K ^ -2 -1 heat transfer c o e f f i c i e n t , c a l cm sec °K h. ^ : heat transfer c o e f f i c i e n t f o r the bottom surface, bottom c a l cm sec K h ., : heat transfer c o e f f i c i e n t f o r the flow of heat from the mold S l d e -2 -1 -1 wal l to the mold cooling water, c a l cm sec °K h : heat transfer c o e f f i c i e n t for the top surface, top -i -2 - l o ^ - l c a l cm sec K -1 -1 -1 thermal conductivity, c a l cm sec °K x x i i k ^.j. : e f f e c t i v e thermal conductivity, c a l cm sec °K e f f J ' £ : length, cm L : length of the mold, cm : la t e n t heat, c a l g ^ C p. V MR : —TI— , dimensionless K AT ' 2 . C p Az MZ : — £ — dimensionless K AJ- q : heat transferred per unit time, c a l sec ^ r,(j),z : c y l i n d r i c a l polar coordinates T : temperature, °K t : time, sec k 2 - 1 a : — T T - , thermal d i f f u s i v i t y , cm sec y P -3 p : density, g cm Ar : length of the element along the r axis, cm At : time element, sec AT : temperature d i f f e r e n c e , °K Az : length of the element along the z axis, cm APPENDIX I d : diameter of the suspension wire, cm L t " L o E : 1 + 3 {— } , dimensionless o -2 g : acceleration due to g r a v i t y , cm sec : constant L : length of the inner c y l i n d e r immersed i n the s l a g , cm x x i i i L Q : length of the cylinder at room temperature, cm L : length of the cylinder at t °C, cm r^ : radius of the inner c y l i n d e r , cm r^ : radius of the outer c y l i n d e r , cm T : temperature, °C : torque, dynes cm t : time of r o t a t i o n , sec 3 V Q : volume of the bob at room temperature, cm W : weight of the bob, g p : density, g cm 3 y : surface tension, dynes cm ^ a : c o e f f i c i e n t of l i n e a r expansion, °C ^ n : c o e f f i c i e n t of v i s c o s i t y , poise to : --— , angular v e l o c i t y of the outer c y l i n d e r , sec Subscripts a : a i r m : melt w : water xxiv ACKNOWLEDGEMENTS The author would l i k e to express his gratitude to hi s research advisor, Dr. A. M i t c h e l l , for his keen interest[and valuable advice during the course of t h i s research project. Thanks are also due to Dr. J . Cameron and my fellow graduate students of the ESR group, for t e c h n i c a l help and innumerable h e l p f u l discussions. The assistance of the departmental t e c h n i c a l s t a f f , i n p a r t i c u l a r Mr. A. Thomas, throughout the experimental programme i s greatly appreciated. The f i n a n c i a l assistance by the National Research Council of Canada and the American Iron and Steel I n s t i t u t e i s g r a t e f u l l y acknowledged.. 1 CHAPTER I INTRODUCTION 1.1 The E l e c t r o s l a g process The e l e c t r o s l a g remelting process (ESR) has i n the past decade 12 3 received increasing i n d u s t r i a l attention. ' ' The demand for superior q u a l i t y , high performance s p e c i a l a l l o y s has been s t e a d i l y r i s i n g . The chief competitors of the e l e c t r o s l a g process are the vacuum arc remelting (VAR) and to a lesser degree, the electron-beam melting and the vacuum induction melting processes. The struggle to improve the q u a l i t y of a l l o y s t e e l s and other high melting s p e c i a l a l l o y s and reactive metals i s aimed at Cl) reducing the i n c l u s i o n content C2) reducing the gas content (3) reducing the segregation (4) r e t a i n i n g the reactive elements present. 4 This i s achieved using two methods of approach : (1) increasing the p u r i t y of the l i q u i d metal. (2) improving the structure of the ingot. Two groups of methods have found use i n the m e t a l l u r g i c a l industry for increasing the q u a l i t y of the metal i n the fused state: (1) processing the metal under vacuum, 2 (2) treatment of the metal with s p e c i a l slags outside the furnace. The vacuum processing i s ca r r i e d out ei t h e r during the smelting or outside the furnace. Although t h i s treatment removes s u b s t a n t i a l amounts of 0, N, H and other impurities present, most of these methods have some serious shortcomings. In vacuum induction melting, the contamination from the re f r a c t o r y l i n i n g as w e l l as the evaporation of Mn, S i and other'elements of high vapor pressure occurs frequently. The out-of-furnace treatment of the metal with various o x i d i z i n g slags of the system CaF2-CaO-Al203, on the other hand, i s quite e f f e c t i v e i n reducing the s u l f u r , phosphorus and the non-metallic i n c l u s i o n content of the metal. i However, these methods do not provide the p o s s i b i l i t y of any s i g n i f i c a n t improvement of the ingot structure which i s e s s e n t i a l f o r the production of high q u a l i t y metal. Various methods are suggested f o r improving the structure of the ingot. These involve the heating of the ingot top, teeming, r a t i o n a l construction of the casting mold etc. To improve the ingot structure, d i r e c t i o n a l s o l i d i f i c a t i o n i s generally attempted. The c o l d - c r u c i b l e processes i . e . the vacuum arc remelting, e l e c t r o - slag and the electron beam remelting, combine both the objectives of increasing the general p u r i t y of the metal and improving the structure of the ingot and as such have found increasing i n d u s t r i a l a p p l i c a t i o n s . The electron-beam melting process uses a concentrated f l u x of . electrons as the source of heat. The presence of high vacuum together with the u n i d i r e c t i o n a l s o l i d i f i c a t i o n of the l i q u i d metal i n a 3 water-cooled copper mold guarantees an e f f e c t i v e p u r i f i c a t i o n of the metal from the gases and the non-metallic i n c l u s i o n s . Although possess- ing the p o t e n t i a l f o r large scale i n d u s t r i a l usage, at the present, th i s process i s used only f o r r e f i n i n g some very high melting metals and a l l o y s . This i s due to the complexity of the equipment and the high c a p i t a l and operating costs. In the e l e c t r o s l a g remelting process (ESR), a metal electrode i s melted i n a molten superheated slag pool. The slag i s rendered molten by resistance heating. High current at low voltages i s delivered to the slag through the electrode and the r e f i n e d molten metal i s immediately s o l i d i f i e d i n a water cooled copper mold ( F i g . 1). The vacuum arc remelting (VAR) process consists of melting a consumable electrode i n vacuum or i n an atmosphere of i n e r t gas, by means of a high current e l e c t r i c arc maintained between the lower end of the electrode and a pool of molten metal contained i n a water cooled copper mold. Except for the fa c t that a consumable electrode i s remelted and that the metal i s s o l i d i f i e d i n a water cooled metal mold, the e l e c t r o - slag process i s d i s t i n c t l y d i f f e r e n t from the vacuum arc remelting process. The main advantages of the ESR process over the VAR may be summarized as follows: Cl) good surface q u a l i t y of the ingot, r e a d i l y useable for forging C2) a c e r t a i n degree of r e f i n i n g (mainly of sulfu r ) i s possible (3) possible to use e i t h e r a.c. or d.c. power C4) lower c a p i t a l cost 4 (5) safer i n operation than VAR (6) can tol e r a t e r e l a t i v e l y complicated mold shapes. While i t i s usually accepted that the e l e c t r o s l a g remelting complements VAR by i t s a b i l i t y to change the ingot chemistry as w e l l as i t s structure, the cost f a c t o r does not allow one to make a clear choice f o r i n d u s t r i a l operation.^ The lower c a p i t a l cost and the s l i g h t l y higher production rate of the ESR equipment i s o f f s e t by the higher s p e c i f i c power required and the cost of the slag i t s e l f . The t y p i c a l power consumption for ESR process i s 1200 to 2000 KWH 5 6 per ton of the metal while f o r VAR, i t i s s l i g h t l y l e s s . ' ESR ingots have already exceeded the maximum s i z e of VAR ingots, 7 as a producer reports having produced ingots of 23 tons. Except for Russia, which does not have many VAR i n s t a l l a t i o n s , ; i n the rest of the world, the ESR process today i s , at the best, a comple- mentary process to VAR, f o r r e f i n i n g high q u a l i t y a l l o y s . This i s mainly due to the i n s t a l l a t i o n of large VAR furnaces i n the a l l o y s t e e l industry i n the early s i x t i e s , p r i o r to the advent of the ESR process. 1.2 Statement of the Problem The e l e c t r o s l a g remelting process i s su i t a b l e as a modern secondary r e f i n i n g process l a r g e l y because of i t s v e r s a t i l i t y . This i s due to the large number of av a i l a b l e combinations of slag chemistry, the more f l e x i b l e power requirements and the greater freedom of choice of electrode c h a r a c t e r i s t i c s . Despite rapid advances i n the design and a p p l i c a t i o n of the 5 e l e c t r o s l a g equipment, much work of a fundamental nature i s required before the phys i c a l and chemical processes inherent to the e l e c t r o s l a g system are understood. The purpose of the present work i s to study the thermal c h a r a c t e r i s - t i c s of the e l e c t r o s l a g process. I t i s necessary to understand the mode of heat generation and d i s t r i b u t i o n i n the ESR process to achieve e f f e c t i v e control during i t s operation. It i s convenient to divide the study into s i x sections. Cl) Heat generation i n the slag bath: The slag bath i s the most important part of the process. I t i s the r e s i s t i v e and the r e f i n i n g element. I t i s therefore necessary to examine the form of heat generation i n the slag bath. (2) Temperature gradients on the electrode: I t i s necessary to know the temperature gradients on the electrode as i t controls the extent of electrode oxidation, structure of the ingot, as w e l l as the degree of thermal i n s t a b i l i t y during electrode changes i n large i n d u s t r i a l u n i t s . C 3 ) Thermal and e l e c t r i c a l c h a r a c t e r i s t i c s of the slag skin region: As a s i g n i f i c a n t portion of the heat leaves the system across the l i q u i d slag region, the study of heat transfer i n the system sl a g / s l a g skin/mold i s v i t a l to the understanding of the ESR operation. The study of the e l e c t r i c a l c h a r a c t e r i s t i c s of th i s region i s necessary to c o r r e l a t e the observed r e l a t i v e s t a b i l i t i e s of the d i f f e r e n t e l e c t r i c a l configurations. g (4) Heat balance of the process: e l i t e s and B e a l l studied the heat transfer to the water-cooled copper mold during vacuum arc remelting 6 of zirconium and titanium. No such study i s reported on the ESR process. I t i s e s s e n t i a l to carry out an accurate heat balance of the process to understand the mode of heat d i s t r i b u t i o n . This should enable the p r e d i c t i o n and c o r r e l a t i o n of the various operating para- meters of the process for i n d u s t r i a l scale ingots. (5) P r e d i c t i o n of pool volumes i n ESR ingots: For an e f f e c t i v e c o n t r o l , i t i s necessary to be able to predict the pool volumes i n the ESR ingots. The pool volume and i t s shape, control the surface q u a l i t y and the structure of the ingot. (6) Measurement of the p h y s i c a l properties of the slag : The slag serves many purposes, not a l l of them being compatible. The slag should have the appropriate melting point, vapor pressure, e l e c t r i c a l r e s i s t i v i t y , v i s c o s i t y , density, surface tension and thermal capacity or a best possible combination of these properties. Attempt i s made here to measure (1) the density and (2) the v i s c o s i t y of the CaF^ based slags. 1.3 The U.B.C. E l e c t r o s l a g Unit For the purpose of i n v e s t i g a t i n g the influence of various para- meters on the thermal c h a r a c t e r i s t i c s of the process, experiments have been c a r r i e d out with the U.B.C. e l e c t r o s l a g u n i t . The design of t h i s unit i s s p e c i f i c a l l y adapted to the requirements of a range of research 9 projects and has been described i n d e t a i l by Etienne. E l e c t r o s l a g remelting i s one of the few m e t a l l u r g i c a l processes which can be i scaled down without loosing i t s i n t r i n s i c properties. Thus i t i s possible to predict the operation c h a r a c t e r i s t i c s of large i n d u s t r i c a l scale units by c o r r e l a t i n g the data obtained on the small laboratory u n i t . 7 1.4 Choice of Materials An important problem has been the s e l e c t i o n of s u i t a b l e a l l o y and slag compositions f o r the present study. A l l o y compositions: Vibrac EN 25, 321 s t a i n l e s s s t e e l , Ferrovac E, Armco i r o n , AISI 1018 s t e e l and AISI 630 s t e e l have been used i n the present i n v e s t i g a t i o n s . Table I gives the composition of the a l l o y s studied. Table I. Composition of a l l o y s studied (1) Vibrac EN 25 (supplied by B r i t i s h S t eel Corporation) Fe C Mn S i S P Ni Cr Bal 0.28 0.67 0.22 0.058 0.012 2.5 0.72 Mo. _ Sn Cu A l 0.6 0.028 0.27 0.01 (2) A u s t e n i t i c Stainless S t e e l : 321 grade. A i r melted (supplied by Atla s Steels Company, Welland, Ontario). Fe Cr Ni T i S i Mn C P Bal 17.78 10.60 0.58 0.56 1.86 0.05 0.031 S 0 0.018 0.0009 8 (3) Ferrovac E: vacuum melted (supplied by Crucible Steel Company, Sorel, Quebec) Fe C Mn P S Si Ni Cr Bal 0.01 0.001 0.002 0.004 0.006 0.01 <0.01 Mo N 0 H Co Cu V W 0.001 0.0002 0.00092 0.000018 0.006 0.006 <0.002 0.02 (4) 1018 Stee l : (supplied by Atlas Steel Company) Fe C Mn P S max max Bal 0.15-0.20 0.6-0.9 0.04 0.05 (5) AISI 630 (supplied by Armco) Fe C Mn S i P S Cr Ni Bal 0.07 1.0 1.0 0.025 0.025 16.5 4.0 Co + Ta Cu Mo 0.3 4.00 0.5 (6) Armco Iron (supplied by Armco) Fe C Mn P S S i 0 Bal 0.012 0.017 0.005 0.025 trace 0.065 9 Slags: Calcium f l u o r i d e i s the basic constituent. Part of t h i s material ( f l o t a t i o n concentrate) i s used as a dry powder to make up for the required proportion of powder and granules. Most of the calcium f l u o r i d e used i s prefused i n a graphite c r u c i b l e . Induction heating and argon blanket are used. The main impurities of CaF 2 are calcium oxide, s i l i c a and i r o n oxide. For the measurement of density and v i s c o s i t y of CaF 2 base slags, extra pure CaF^ ( B r i t i s h Drug House) was used. Alumina i s used ei t h e r as powder (Alcan, 99.9% purity) or granules of electrofused alumina (Norton Co.) of equivalent p u r i t y . Calcium oxide i s prepared from calcium carbonate (technical grade). Calcium t i t a n a t e i s commercially a v a i l a b l e as powder (Cerac Corp.) normally used for spray coating. I t i s cold pressed and sintered before use. 10 CHAPTER II DETERMINATION OF VOLTAGE GRADIENTS IN THE SLAG BED OF THE ESR PROCESS II.1 Mechanism of Heat Generation Descriptions'^'"'"^'"''''" of the e l e c t r o s l a g remelting process have at t r i b u t e d the heat generation mechanism v a r i o u s l y to 'soft' arcs and to r e s i s t i v e heating, but are not s p e c i f i c as to how the resistance i s constituted. In order to understand the mechanism of heat generation i n ESR, i t i s l o g i c a l to compare ESR and vacuum arc remelting (VAR) processes since they are apparently s i m i l a r , i n both t h e i r m e t a l l u r g i c a l aims and operations. The major difference between the two processes i s the method by which the heat i s generated. In the high i n t e n s i t y arc present i n VAR, there are three points of heat generation (1) cathode f a l l (2) anode f a l l (3) the transfer resistance of the plasma The heat generation mechanism i n an arc i s a mixture of joule heating, due to the transfer resistance of the plasma, and the p a r t i c l e emission and bombardment which gives r i s e to the observed steep voltage gradients i n the terminal regions, c a l l e d the anode and cathode 11 f a l l (Fig. (2)). It i s i n t e r e s t i n g to consider what e f f e c t ? , i f any, w i l l r e s u l t from the i n t e r p o s i t i o n of a l i q u i d slag between the two electrodes which are at a p o t e n t i a l difference high enough to cause a sustained arc i n the absence of the slag, whether or not the arc w i l l be extinguished depends upon the r e l a t i o n between the e l e c t r i c a l transport e f f e c t s and the heating e f f e c t s i n the slag. If the heat generated by the various resistances involved i s great enough to b o i l the s l a g , then the i o n i z a b l e vapor w i l l provide a very stable arc path. I f , on the other hand, the heat can be d i s s i p a t e d at a temperature w e l l , below the b o i l i n g point, e l e c t r i c a l transport i s by i o n i c movement i n the slag. 12 M i t c h e l l and Beynon have shown that a current density of the 4 5 -2 order of 10 -10 Amp. cm i s necessary for the sustained existence 13 of an arc i n the e l e c t r o s l a g process. Mironov et a l . have also reported s i m i l a r findings i n t h e i r study of the c h a r a c t e r i s t i c s of the ESR process. As the maximum current density r a r e l y exceeds 150 -2 Amp. cm i n laboratory scale units (much lower for i n d u s t r i a l scale u n i t s ) , one can conclude that the bulk of the heat i s generated i n the slag bed by the f r i c t i o n a l d i s s i p a t i o n i n i o n i c movement. Joule heating i s generated by the opposing f l u x of 14-17 cations and anions. There i s every reason to suppose that the slags used are e n t i r e l y i o n i c with t - t_ - 0.5 and that the current i s c a r r i e d by i o n i c d i f f u s i o n i n the impressed p o t e n t i a l gradient. There should be no asymmetry of heat generation i n the slag beyond that accounted for by the geometry of the system. This p r o v i s i o n 12 would i n c l u d e s k i n e f f e c t s a t a l a r g e enough c r u c i b l e s i z e , but i t i s c a l c u l a t e d t h a t the 60 Hz s k i n depth i n l i q u i d c a l c i u m f l u o r i d e i s a p p r o x i m a t e l y 40 cm, and thus a c r u c i b l e d i a m e t e r l a r g e r than 100 cm would be r e q u i r e d b e f o r e the heat g e n e r a t i o n showed s i g n i f i c a n t r a d i a l asymmetry. As the e l e c t r o d e and the i n g o t do not c o n s t i t u t e a s y m m e t r i c a l arrangement i n the s l a g b a t h , i t i s n e c e s s a r y t o examine the form o f r e s i s t i v e heat g e n e r a t i o n i n the s l a g b u l k . In o r d e r to be a b l e t o do so, i t i s f i r s t n e c e s s a r y to c a l c u l a t e the i s o p o t e n t i a l c o n t o u r s i n the s l a g bed. T h i s may be m o d e l l e d f o r an a x i a l l y s y m m e t r i c a l system by the use of a r e s i s t a n c e network analogue which w i l l accommodate the temperature dependent r e s i s t i v i t y o f the s l a g . As the temperature d i s t r i b u t i o n i n the s l a g bed was unknown, i t was f i r s t e x p e r i m e n t a l l y determined f o r v a r i o u s e l e c t r i c a l c o n f i g u r a t i o n s . I I . 2 Measurement o f Temperature i n the S l a g Bed The problem of temperature measurement i n an o p e r a t i n g ESR u n i t has been s t u d i e d i n s e v e r a l c o n t e x t s . There e x i s t s s u b s t a n t i a l e x p e r i m e n t a l d i f f i c u l t y i n measuring m i l l i v o l t thermocouple p o t e n t i a l s i n a system c o n t a i n i n g i n t e n s e magnetic f i e l d s , at a h i g h temperature i n a c o r r o s i v e s l a g and a t a.c. o r d.c. p o t e n t i a l s s i g n i f i c a n t l y above ground. I f a b a r e thermocouple i s immersed i n the s l a g (which r a p i d l y d i s s o l v e s even cermet r e f r a c t o r i e s ) i t w i l l t r a n s i e n t l y r e c o r d the s u r f a c e temperature b e f o r e b e i n g d e s t r o y e d by the m e t a l l i c c o n t e n t 20 of the s l a g . S i n c e the s l a g i s a t a p o t e n t i a l above ground, the . temperature measuring i n s t r u m e n t s must be f l o a t i n g and have adequate 13 common mode rejection. T r i a l s established that boron n i t r i d e i s an excellent material for thermocouple protection tubes i n this context as i t i s compatible with the W-3Re/W-25Re thermocouple.used, i s an e l e c t r i c a l insulator at the temperatures experienced, and w i l l r e s i s t attack by the ESR slag for a considerable time. Measurements of the slag temperature were made with the above combination attached to the electrode surface and reading out to a Sargent Model SR4 recorder. Fig. (3) and Fig. (4) give a schematic diagram of the experimental assembly. Temperature measurement was carried out i n both argon atmosphere and a i r for various e l e c t r i c a l configurations using CaF2~ 25 wt. % A^O^ slag. In a l l the cases, 3.81 cm (1.5 inches) diameter EN 25 stee l electrode was melted i n 8 cm x 45 cm mold. Fig. (5) to Fig. (10) give the observed temperature gradients i n the slag bed for the one v e r t i c a l section investigated. II.3 Determination of Isopotential Contours i n the Molten Slag Bed II.3.1 Introduction ; The isopotential l i n e s are determined here for an experimentally obtained geometrical configuration (I.N. 1, Table V). The extent of electrode immersion and the depth of the slag bed are as shown i n Fig. (11). The r e s i s t i v i t y of the slag depends upon the temperature. , Appendix I (Fig. (86)) gives the va r i a t i o n of e l e c t r i c a l conductivity with temperature for CaF2~25 wt. % A^O^ slag as obtained by M i t c h e l l and Cameron?"'" In order to calculate the isopotential contours i n the slag bed, 14 i t i s necessary to assume a temperature d i s t r i b u t i o n i n the slag bed. Fi g . (11) gives the assumed temperature d i s t r i b u t i o n based on the experimentally obtained data. Assuming r a d i a l symmetry, i t i s s u f f i c i e n t to consider the voltage d i s t r i b u t i o n i n a segment of the c y l i n d r i c a l slag bath. For convenience, a segment of one radian i s chosen. I t i s subdivided i n t o volume elements as shown i n F i g . (12). The v e r t i c a l height of the volume elements i s 0.5 cm while along the radius i t i s 1.0 cm. The volume of the elements increases away from the centre. 22 II.3.2 Solution by E l e c t r i c - R e s i s t a n c e Network. The e f f e c t of each volume element i s considered to be concentrated at the ce n t r a l point. In accordance with the e l e c t r i c a l resistance concept, the resistance of the volume of the slag may be set up approximately as shown i n F i g . (13). Here, the resistances R and R represent the resistances i n the r z c r and z d i r e c t i o n s r e s p e c t i v e l y . The composite resistance e f f e c t i s R R r z likewise shown, with separate h a l f elements and — j representing r and z d i r e c t i o n s r e s p e c t i v e l y and t o t a l l i n g R and R for the e n t i r e r J r z volume element. Consider F i g . (12). In d.c. negative (I.N.I), the surface AB i s at 23.75 v o l t s while the surface CD i s at 0 v o l t s . The resistance at the surface EF (slag/gas interface) i s assumed to be i n f i n i t e . Due to the assumed r a d i a l symmetry, surface BC has i n f i n i t e resistance. In the ESR un i t , there i s always a s o l i d slag skin against the water cooled mold. As s o l i d slag skin has very high e l e c t r i c a l resistance, 15 i t i s n o t u n r e a s o n a b l e t o assume t h a t t h e r e i s i n f i n i t e r e s i s t a n c e a t the s u r f a c e A'F'. The e f f e c t of f i n i t e s l a g s k i n r e s i s t a n c e on the p o t e n t i a l c o n t o u r s w i l l be c o n s i d e r e d l a t e r . As the s o l i d e l e c t r o d e e x i s t s i n the, s l a g bed which i s a t a temperature h i g h e r than the m e l t i n g p o i n t of the m e t a l , t h e r e e x i s t s on the s u r f a c e ED a v e r y t h i n l a y e r of s o l i d s l a g s k i n . The e l e c t r i c a l r e s i s t i v i t y of t h i s s k i n i s not known. I n i t i a l l y i t w i l l be assumed t h a t t h i s s l a g s k i n has z e r o r e s i s t a n c e . The e f f e c t of f i n i t e r e s i s t tance of t h i s t h i n s l a g s k i n w i l l be s u b s e q u e n t l y t r e a t e d . F i g . (14) g i v e s the e q u i v a l e n t r e s i s t a n c e network f o r the case where i t i s assumed t h a t th e r e s i s t a n c e a t A'F' = 0 0 and a t ED - 0 ohms. I t i s n e c e s s a r y to c a l c u l a t e the a r e a 'A' and l e n g t h f o r the v a r i o u s volume elements under s t u d y (R = ) , Appendix I I g i v e s the method o f c a l c u l a t i n g the '&' and 'A' f o r a l l t h e volume elements under c o n s i d e r a t i o n . The n u m e r i c a l s o l u t i o n o f the r e s i s t a n c e network of F i g . (14) , w i t h o u t r e c o u r s e to the e x p e r i m e n t a l e l e c t r i c a l d e t e r m i n a t i o n i s o f s p e c i f i c i n t e r e s t , p a r t i c u l a r l y i n view of the many network branches i n v o l v e d . A t any j u n c t i o n p o i n t , under s t e a d y s t a t e e l e c t r i c a l f l o w c o n d i t i o n s , the sum o f the c u r r e n t s f l o w i n g ' i n ' must be z e r o i . e . , t h e r e i s no a c c u m u l a t i o n . A c c o r d i n g l y , c o n s i d e r i n g F i g . ( 1 5 ) , the p o i n t 0 i s surrounded by p o i n t s M, N, P and Q. The r e s i s t a n c e of the f o u r c o r r e s p o n d i n g branches i s R , R , R , R r e s p e c t i v e l y . m' n p q r The c u r r e n t s i n the f o u r d i f f e r e n t b r a n c h e s , dependent on the d i f f e r e n c e i n p o t e n t i a l 'e' between the o u t l y i n g p o i n t and the c e n t e r 16 j u n c t i o n are next considered. The f o l l o w i n g r e l a t i o n s h i p s may be set up m n p q Thus, to s a t i s f y the steady s t a t e c o n d i t i o n s , ( i h e M + ^ + ( i r ) e r + ( i r ) e Q = ^ - J L f (2.2) m n p q In the present case, i t i s assumed that a v o l t a g e of 23.75 v o l t s i s impressed between the e l e c t r o d e (0 v o l t s ) and the molten metal bath (23.75 v o l t s ) . Equations s i m i l a r to (2.2) can be w r i t t e n f o r a l l the 29 j u n c t i o n p o i n t s . This leads to 29 l i n e a r simultaneous equations i n 29 unknowns. These can be e a s i l y solved w i t h the a i d of the computer. F i g . (16) gives the voltage d i s t r i b u t i o n obtained. II.3.3 D i s c u s s i o n t F i g . (16) i l l u s t r a t e s the manner by which the s l a g volume, the geometry, a p p l i e d voltage and r e s i s t i v i t y combine to determine the voltage gradients and hence the heat input i n the s l a g bath. The region of steep voltage gradient l i e s below the e l e c t r o d e t i p and most of the heat generation takes place below t h i s l e v e l . The s l a g above the e l e c t r o d e t i p , due to low v o l t a g e g r a d i e n t s , does not 17 get heated to the same extent and performs a coolant function i n the system. The curvature i n the current l i n e s i s l a r g e l y above the electrode t i p , and there i s n e g l i g i b l e h o r i z o n t a l current vector near the ingot surface. This comment, of course, neglects the a.c. skin e f f e c t which would lead to intense curvature i n t h i s l a t t e r region i n a larger ESR unit. The s i g n i f i c a n c e of such a current pattern l i e s i n the form of s t i r r i n g pattern which might be established by a configuration of electromechanical forces imposed on the ESR melt. In the present analysis i t was assumed that the slag s k i n on. the mold has i n f i n i t e e l e c t r i c a l resistance. F i g . (17) shows the e f f e c t of considering a f i n i t e slag skin resistance (r - 2 0 0 - 3 0 0 ohm. cm). It i s clear from F i g . (17) that t h i s consideration does not s i g n i f i - cantly d i s t o r t the voltage gradients. F i g . (18) and F i g . (19) consider the e f f e c t of f i n i t e resistance of the slag skin on immersed electrode. It i s clear that except for an unreasonably high value of skin resistance, the e f f e c t of f i n i t e slag skin resistance on electrode i s not s i g n i f i c a n t . I t w i l l be shown i n Chapter IV that at a high electrode temperature (> 1 0 0 0 ° C ) , the slag skin has a r e l a t i v e l y low e f f e c t i v e resistance due to good contact with the electrode. Hence F i g . (16) i s adequate i n describing the voltage p r o f i l e s i n the ESR slag bed. In the present model, the applied voltage was d e l i b e r a t e l y equated to the p o t e n t i a l seen by the slag bulk at the electrode-slag i n t e r f a c e s . However, by doing so, the electrochemical p o l a r i z a t i o n present i n ESR was neglected. 18 11.4 Electrochemical P o l a r i z a t i o n i n ESR With the exception of the s i t u a t i o n where the slag has a s u b s t a n t i a l electron m o b i l i t y , ions must be discharged at the electrode and ingot surfaces i f the current passes through the system. The passage of current requires both the anodic and cathodic i n t e r f a c i a l p o t e n t i a l s to be displaced from t h e i r equilibrium values, giving r i s e to over- p o t e n t i a l s on both the surfaces. The anodic process i n the d.c. e l e c t r o s l a g melting of pure i r o n 12 has been postulated by M i t c h e l l and Beynon to be the corrosion of * I | i r o n , giving an i n t e r f a c e layer of saturation of Fe . The cathodic process i s postulated to be the deposition of A l or Ca which may subsequently dissolve i n either the metal or the slag phases. F i g . (20) and F i g . (21) give the experimentally obtained p o l a r i z a t i o n 12 curves for pure i r o n . In a.c. e l e c t r o s l a g melting, i t was found j | that there i s no p o l a r i z a t i o n with Fe ——*- Fe + 2e reaction •< occurring at both the electrodes. F i g . (20 and (21) show that the maximum overpotential i s approxi- mately 1.0 v o l t . This w i l l not a l t e r the i s o p o t e n t i a l l i n e s s i g n i f i - , cantly. However, the heat generation i n the metal-slag i n t e r f a c i a l region as a r e s u l t of current passing through t h i s overpotential i s very important. This w i l l be considered i n d e t a i l i n Chapter V. 11.5 The E f f e c t of Ca and A l Dissolved i n the Slag The r e s i s t i v i t y values used i n the analysis are applicable only to a.c. e l e c t r o s l a g r e f i n i n g . As discussed e a r l i e r , the cathodic reaction product i n d.c. operation i s Ca and A l . Both these elements are 19 soluble i n the CaF^ based slags. Addition of these elements s i g n i f i c a n t l y increases the e l e c t r i c a l conductivity of CaF£ based slags. I t s e f f e c t on ESR operation w i l l be discussed i n d e t a i l i n Chapter V. The voltage gradients w i l l remain unaltered i f the temperature dependence of the e f f e c t i v e r e s i s t i v i t y of the slag i n d.c. operation i s proportion- ately the same as the slag i n a.c. operation. Although the e f f e c t i v e r e s i s t i v i t y i n d.c. operation w i l l be les s s e n s i t i v e to temperature, as the temperature dependence i s unknown, i t has been assumed here to be proportionately s i m i l a r to the a.c. operation s l a g . II.6 Measurement of Voltage Gradients i n the Slag Bed The predicted voltage gradients were experimentally v a r i f i e d r using a voltage probe. Voltage was measured i n CaF2~25 wt. % ^l^O^ slag (3.81 cm diameter EN 25 s t e e l electrode i n 8.0 cm diameter copper mold) between the electrode and a boron n i t r i d e insulated molybdenum wire probe. The probe was lowered v e r t i c a l l y down into the slag bath at constant speed by a motor and the voltage recorded on a Sargent Model SR 4 recorder. F i g . (22) gives the experimentally obtained voltage gradient across a v e r t i c a l section and compares i t with the predicted gradient. The agreement appears to be reasonably good.; Thus, i n s p i t e of the many si m p l i f y i n g assumptions made, f i g . (16) gives a f a i r estimate of the voltage gradients i n an operating ESR slag bath. 20 CHAPTER III ELECTRODE TEMPERATURE GRADIENTS IN THE ELECTROSLAG PROCESS I I I . l Introduction In the e l e c t r o s l a g remelting process, the amount of heat flowing out through the electrode plays a s i g n i f i c a n t part i n the process for a number of reasons. F i r s t l y , i t i s a d i r e c t contribution to the heat balance i n the melting electrode t i p region and therefore to the process operating temperature. I t also determines the electrode temperature above the slag/gas i n t e r f a c e and thus the amount of possible electrode oxidation i n cases where i n e r t atmosphere i s not used and the degree of thermal i n s t a b i l i t y during electrode changes i n large i n d u s t r i a l u n i t s . F i n a l l y , the time the electrode material spends whilst t r a v e l l i n g through the electrode temperature gradient determines the extent to which second phase p a r t i c l e s w i l l be dissolved before the matrix melts. This l a t t e r e f f e c t has not been investigated i n ei t h e r the vacuum arc remelting (VAR) or ESR context, but i s l i k e l y to have at le a s t three s i g n i f i c a n t m e t a l l u r g i c a l consequences described; as follows. The second phase may be oxide i n c l u s i o n s , such as s i l i c a , which should dissolve progressively i n a s t e e l as the temperature increases. 21 Thus the s i l i c a i n c l u s i o n d i s t r i b u t i o n present i n the melting electrode t i p w i l l be closer to that i n the bulk electrode than would be predicted by an equilibrium analysis of the heating process. The way i n which 23 t h i s may a f f e c t ingot i n c l u s i o n content has been b r i e f l y outlined. A l t e r n a t e l y , i f the second phase i s a more soluble material, such as a carbide (TiC i n a s t a i n l e s s s t e e l , f or example), then the major e f f e c t of r e t a i n i n g t h i s through the l i q u i d period i n both VAR and ESR (due to a low s o l u t i o n rate compared to the l i q u i d metal residence time) w i l l be that any electrode carbide p a r t i c l e s p e r s i s t i n g to the ingot stage w i l l act as n u c l e i for subsequent carbide growth. Thus, the structure of the ingot produced would depend upon the carbide d i s t r i b u t i o n i n the electrode. In the case where the second phase has a lower melting point than the matrix (as for example, an eutectic carbide) then the point at which t h i s melts r e l a t i v e to the t i p of the electrode w i l l l a r g e l y determine whether or not large pieces of electrode become p h y s i c a l l y detached and f a l l to the ingot s o l i d i f y i n g - front without melting. This l a t t e r defect i s w e l l known i n the ESR processing high-speed s t e e l s . The problem of the electrode temperature gradient i n ESR may be divided conveniently into two sections, r e l a t i n g to the heat tran s f e r regimes above and below the slag/gas i n t e r f a c e . The present study r e l a t e s to the gradients above the slag/gas i n t e r f a c e and compares the experimental r e s u l t s obtained, with the t h e o r e t i c a l computation of t h i s gradient f o r AISI 1018 s t e e l and 321 s t a i n l e s s s t e e l electrodes. 22 III.2 Experimental III.2.1 Temperature Measurement A schematic diagram for the arrangement used i s shown i n F i g . (23). Measurements of the slag temperature were made with the W3Re/W25Re thermo- couple protected by boron-nitride. The thermocouple was attached to the electrode surface as shown i n f i g . (23) and read out to a Sargent Model SR 4 recorder. Measurements of the temperature gradient i n the electrode were made using chromel-alumel thermocouples placed i n wells d r i l l e d i n the electrode i n a x i a l sets of four at known i n t e r v a l s . The thermocouple measuring the slag temperature was placed one centimeter ahead of the leading electrode thermocouple, and provided an accurate "marker" of the slag/gas i n t e r f a c e r e l a t i v e to electrode p o s i t i o n . The electrode thermocouple readout was on a Texas Instruments Model FMW6B multi-channel recorder. II.2.2 ESR Operating Conditions Two sets of ingot and electrode sizes were used: 2.54 cm (1") diameter electrode, 5.85 cm x 40 cm mold 3.81 cm (1.5") diameter electrode, 8.0 cm x 45 cm mold with two materials, AISI 1018 s t e e l and 321 s t a i n l e s s s t e e l . The 9 experimental ESR unit has been e a r l i e r described and was operated with either electrode p o s i t i v e or negative, with the negative pole at ground p o t e n t i a l . The electrode current densities used were approximately -2 -2 100 A.cm for 2.54 cm diameter electrodes and 75 A.cm for 3.81 cm diameter electrodes. The slag used i n each case was CaF2~30 wt. % calcium aluminate, and i n a quantity to give a 4 cm deep slag bath. The electrode 23 p o s i t i o n was measured by a remote incremental counter to a p r e c i s i o n -2 of + 5 x 10 cm. In a l l cases, the electrode feed rate was held constant during the measurement period, but as the operation had previously s t a b i l i z e d f or some time using a constant-current control mechanism, t h i s override condition did not r e s u l t i n s i g n i f i c a n t departure i n current density. The electrode temperature p r o f i l e s are shown i n F i g . (24) to (29). These are obtained by a non-linear (cubic) regression analysis of the sequential-readings record from the multi-channel recorder. The slag temperature varied between 1775°K + 20°K at the surface, and a maximum of 1975°K + 50°K, at a point several millimeters below the electrode t i p . III.3 Discussion III.3.1 Formulation of the Problem The general formulation of the problem i n the present case i s s i m i l a r to that of a c y l i n d r i c a l f i n d i s s i p a t i n g heat from i t s surface by convection and r a d i a t i o n with no heat tran s f e r through the end of 24 the f i n . However, there are more complex boundary conditions i n the present case than are encountered i n the usual formulation. The electrode i s immersed i n the slag as shown i n F i g . (30). The temperature -2 gradient at B i s assumed to e x i s t across the t h i n (2 x 10 cm) layer of s o l i d slag skin, s i m i l a r to that found between the slag and the water cooled mold w a l l . The boundary temperature T q at z = 0 i s known from the experimental measurements and i s s p e c i f i c to the melting conditions used. I t i s also assumed that: 24 (1) the slag surface temperature i s uniform over a l l the effe c t i v e radiant area; black body conditions are assumed (2) the system has complete r a d i a l symmetry (3) the physical and surface properties of the electrode are temperature invariant (4) no heat transfer occurs from the cold end of the electrode (5) the electrode has radiation interaction with the slag, but multiple interactions are absent (6) steady state conditions (7) water cooled copper mold and the gas atmosphere are at known constant temperatures (8) two dimensional heat transfer One may then write the energy equation as: 2 2 S T + -(.~) + ^-l = 0 (3.1) 3 r 2 . r 9 r 9 z 2 which has boundary conditions at z = 0, T = T (3.2) o at z = £, ~ = 0 . ' • (3.3) 3 z at r = 0, |^ = 0 (3.4) 8r and a fourth condition at r = a. This condition involves an energy balance over an element of electrode surface area dA^, discussed below. A heat balance through dA^ involves three heat transfer terms through the electrode surface, and the electrode volume conduction term. 25 F i r s t l y , the electrode surface element has radiant energy i n t e r - change with water cooled copper mold d A l F d A l - * e l 0 Tr=a " a l e3 0 ( T * ) 4 V * + dA^ ( 3 " 5 ) Also, there i s convective interchange with the gas atmosphere within the mold dA. h (T - T ) (3.6) 1 r=a » v and f i n a l l y , radiant interchange with l i q u i d slag surface e l ° d A l F d A l - A 2 Tr=a " e2 ° A l \ - *A± T s " l a g a l ( 3 ' 7 ) (The configuration factor F introduced above denotes the f r a c t i o n m -> n of the t o t a l energy emitted by surface m that i s intercepted by surface n) . Using the r e c i p r o c i t y theorem for configuration f a c t o r s : A„F , A = dA^,. . (3.8) 2 A 2 -* dA 1 1 dA^ A 2 N A * F * + d A l = d A l F d A l - . * ( 3 ' 9 ) and the summation theorem F,, . = 1 - F . (3.10) dA 1 ->- * dA^ A 2 26 and assuming grey body properties for the electrode ( i . e . , ct^ = e^) the energy balance equation reduces to -K dA 3T 1 3r r=a d A l ( 1 " FdA x -> A 2 ) £1 0 Tr=a •e, E, o d A , ( T * ) 4 ( l - F d A ^ A ) + dA± h ( T ^ - Tj '1*3 1 1 2 -dA F, . c 0 o T 4 e. + dA F . e.. a T 4 (3.11) 1 dA^ A 2 2 slag 1 1 dA.̂  -> A^ 1 r=a where each side gives the amount of heat leaving the surface. On rearrangement: 5T 3r r=a E l a 4 e l E 3 a * 4 K r=a K dA^ A^ £ (T - T ) + T , F,. K v r=a oo' K slag dA^ ->• A,, (3.12) Equation (3.12) may be conveniently re-expressed using the following dimensionless terms: T-T X = T o T N = ^ K D = 3 e..aT a 1 o K R = _r a L = — , Z - * a a 27 In terms of these new v a r i a b l e s , eq. (3.1) and the boundary conditions (3.2), (3.3), (3.4) and (3.11) become r e s p e c t i v e l y , 9R 2 R 8 R 3Z' (3.13) where = 0 Z=0 (3.14) 11 8 Z Z=L = 0 (3.15) _9X 9R R=0 = 0 (3.16) 9X 3R R=l D ( l + X R = / + D(X*) 4 (1 - ^ £ 3 - N(l + i ) + NX + De_ F, . R=l °° 2 x 1 2 (3.17) Putting e 2 —^-B- = E, equation (3.17) becomes ax. 3R 1 R=l -D (1 + X R = 1 ) 4 + D e 3(xV (1 - F ^ ^ k ) - N(1 + X -) + NX + DEF,. R=l °° -*• A 2 (3.18) 28 Let the s o l u t i o n of eq. (3.13) be of the form X = P(R) 0(Z) (3.19) Substituting the value of X from (3.19) i n eq. (3.13) and s i m p l i f y i n g y i e l d s P d E 2 P R " « dZ 2 ' ' Separating the v a r i a b l e s , the two r e s u l t i n g equations are ^ | = - Qm2 (3.21) dZ The s o l u t i o n to (3.21) i s of the form Q = C 1 cos mZ + C 2 s i n mZ ( 3 . 2 3 ) where C^, are constants. 2 5 Equation (3.22) i s of a type reducible to Bessel's equation and i t s s o l u t i o n i s of the form P = C 3 I (mR) + C 4K 0(mR) (3.24) where C„ and C. are unknown constants, I i s the modified Bessel function 3 4 ' o 29 of the f i r s t k i n d of o r d e r z e r o and K i s the m o d i f i e d B e s s e l f u n c t i o n o of the second k i n d of o r d e r z e r o . An approximate . s o l u t i o n of the energy e q u a t i o n (3.13) i s X = (C. cos mZ + C n s i n mZ) (C.,1 (mR) + C.K (mR)) (3.25) 1 2 3 o 4 o The use of eq. (3.14) i n (3.25) y i e l d s C± = 0, then X = [ C C I (mR) + C^K (mR)]sin mZ (3.26) D O D O where and are'unknown c o n s t a n t s . A p p l y i n g boundary c o n d i t i o n (3.16)to (3.26) y i e l d C g = 0. T h e r e f o r e , X = C r I (mR)sin mZ (3.27) 5 o Assuming no heat t r a n s f e r from the c o l d end o f the e l e c t r o d e i . e . , a p p l y i n g boundary c o n d i t i o n (3.15) to (3.27) y i e l d s X = m cos(mL) = 0 (3.28) E q u a t i o n (3.28) i s s a t i s f i e d f o r a l l v a l u e s o f m g i v e n by m = 12|±lilL , n = 0 , 1, 2 . . (3.29) Thus the g e n e r a l s o l u t i o n of eq. (3.13) i s X = E,[C I ( r ^ -n R) s i n (^$1) TT Z) ] (3.30) _ n o zL zL n=0 The unknown c o e f f i c i e n t s C (n = 0, 1, 2...°°) can be determined n by l e a s t square f i t t i n g a t a f i n i t e number of p o i n t s on the boundary, 30 choosing equally spaced points along the electrode i . e . , the z axis and f i t t i n g them to the boundary condition (3.18). In the present analysis 7 c o e f f i c i e n t s (n = 0, 1, 2,...6) and 100 boundary points were used. The problem to be solved was to determine the values of the 7 c o e f f i c i e n t s so as to s a t i s f y the boundary condition (3.18) for the 100 boundary points i n the best possible manner. From the boundary condition (3.18) the expression to be minimized i s obtained a s 2 ^ 5 - ~ [" "Cl + W 4 + D ( A * ) 4 ( 1 " FdA + A> R=l 1 2 - N ( l + A R = 1 ) + N X r o + D E F d A i _ > A 2 ] } 2 (3.31) where £ denotes summation over a l l points i n the region 0 < Z < L. 1 Using the s e r i e s s o l u t i o n for X as expressed i n (3.30), eq. (3.31) takes the form Q - v r v rp f 2 n + 1-> T r(2n+l)-n-. r (2n+l) „ n n 1 n=0 + D { 1 + I [C I [-^Hjl] s i n f - ^ i ^ Z ] ] } 4 n=0 + N {1 + I [ C I [^1)JL] sin[-^±lhL z ] } ~ n o AL ZL n=0 & A - DeQX (1 - F.. ) - NX DEF, . } (3.32) 3 dA.̂  -* A 2 °° dA.̂  -> A 2 31 The function to be f i t t e d to zero at various boundary points i s Since the function i s non-linear i n the unknown parameters C^, i t i s f i r s t l o c a l l y l i n e a r i z e d arid then the least-square f i t c r i t e r i a applied to get a system of l i n e a r algebraic equations which are solved to give the c o e f f i c i e n t s C^. I n i t i a l guess i s made for the values of C and the process i s then i t e r a t e d upon u n t i l n cnew _ c o l d n n ' .old < 10 -7 The computer programme written to obtain the calculated temperature d i s t r i b u t i o n i s given i n Appendix ( I I I ) . The subroutine LQF, used 27 i n the programme was obtained from U.B.C. programme l i b r a r y . 24 The configuration factor used was evaluated by Sikka and i s given by the following expression dk1 + A 2 Z A - 1 1 - {-=- cos (-) - TT 2 8 J7~-43 tan L \l(3+1 -1) (cj)+2g) (0+1)($-23) , 1 " I r + - tan [ TT Z (3.33) 2 2 where tj) = Z + 3 + 1 and 3 = r^/a. F i g . (31) gives the plo t of ]?dA _̂  ̂  against a x i a l length for various values of 3. 32 111,3.2 C a l c u l a t e d Temperature P r o f i l e s P r o f i l e s o b t a i n e d by the above computation depend s i g n i f i c a n t l y on the t h r e e d i m e n s i o n l e s s parameters 3, D and N ( e x p e r i m e n t a l v a l u e s of T , T , and the p r o c e s s geometry were u s e d ) . o' s l a g r & j The parameter D, f o r a p a r t i c u l a r v a l u e of 3> depends upon the t h e r m a l c o n d u c t i v i t y of the e l e c t r o d e m a t e r i a l and the temperature T . Assuming an average thermal c o n d u c t i v i t y K = 0.075 c a l . c m "*"°K ''"sec ^ f o r m i l d s t e e l and K = 0.058 c a l cm "*"°K ''"sec "*" f o r s t a i n l e s s s t e e l , the v a l u e of D o b t a i n e d f o r the e x p e r i m e n t a l l y o b s e r v e d T q v a l u e s i s i n the range of 0.02 < D < 0.035 f o r d i f f e r e n t 3 v a l u e s . h a The parameter N (= — — ) i s not the N u s s e l t number at the K e l e c t r o d e s u r f a c e , but may be e v a l u a t e d by c o n s i d e r i n g h^ f o r a s i m i l a r g e o m e t r i c a l heat t r a n s f e r s i t u a t i o n . h c i s t y p i c a l l y i n the range -3 -3 -2 -1 -1 of 0.6 x 10 to 6 x 10 cal.cm °K sec depending upon the type of c o n v e c t i o n , g i v i n g v a l u e s f o r N of 0.05 < N < 0.5. T y p i c a l p r o f i l e s f o r two s e t s of parameters are shown i n F i g . (24) to ( 2 9 ) . I I I . 3 . 3 C o r r e l a t i o n w i t h Experiment Curves of the type shown i n F i g s . (24) to (29) were computed f o r the e x i s t i n g e x p e r i m e n t a l boundary c o n d i t i o n s . The parameters used i n the computation of the t h e o r e t i c a l curves a r e l i s t e d i n T a b l e I I . The c o r r e l a t i o n between the t h e o r e t i c a l l y computed and the e x p e r i m e n t a l l y observed curves i s found to be v e r y good. The s l i g h t d i f f e r e n c e i n the two c u r v e s may be a t t r i b u t e d t o e x p e r i m e n t a l e r r o r ( e s p e c i a l l y i n the measurement o f : T ) and to the f a c t t h a t o n l y an average v a l u e o f the t h e r m a l c o n d u c t i v i t y of the Table II. Parameters used i n the computations of the curves shown i n Figs.(24) to (29). A ESR Condition L A A e K h T , T 3 D N °° c slag o 2.54 cm (1") 1018 s t e e l 16.0 0.308 0.29 2.2 0.075 0.0041 1775 1225 2.25 0.0255 0.07 electrode negative 3.81 cm (1 1/2") 1018 s t e e l 16.0 0.318 0.302 2.6 0.075 0.0041 1775 1175 2.167 0.032 0.10 electrode negative 2.54 cm (1") 321 s t e e l 16.0 0.366 0.346 4.5 0.058 0.0041 1775 1025 2.25 0.0225 0.09 electrode negative 2.54 cm (1") 1018 s t e e l 16.0 0.306 0.240 2.2 0.075 0.0041 1775 1225 2.25 0.0255 0.07 electrode p o s i t i v e 3.81 cm (1 1/2") 1018 s t e e l 16.0 0.318 0.302 2.6 0.075 0.0041 1775 1175 2.167 0.032 0.10 electrode p o s i t i v e 2.54 cm (1") 321 s t e e l 16.0 0.366 0.348 4.5 0.058 0.0041 1775 1025 2.25 0.0225 0.09 electrode p o s i t i v e _————. , — . — (jj 34 electrode material was considered i n the a n a l y s i s . Secondly, only approximate values of e m i s s i v i t y were used. The model would require extensive refinement to accommodate a temperature dependent thermal conductivity. Accordingly one can not comment on the value used beyond the f a c t that i t i s numerically equal to that calculated using an average thermal conductivity for the pertinent temperature ranges. The value of N i s higher than expected as i t requires an -3 -2a -1 -1 average heat transfer c o e f f i c i e n t , h of 4.1 x 10 c a l . cm °K sec , for the electrode surface. The argon gas flow rate through the system would give a maximum average v e l o c i t y of 4 cm sec ^ over the electrode. This would lead to a much lower h value i n free convection conditions c and thus we have either selected too low a value for the average gas temperature, or there e x i s t s s i g n i f i c a n t l o c a l v a r i a t i o n i n the value of N due to changes i n the gas flow regime along the electrode. Relation to Process Variables: The observed gradients i n the electrode show the expected trends i n that the gradients i n electrode negative mode d i f f e r only s l i g h t l y from the equivalent electrode p o s i t i v e . < - 2 - 1 condition. At a feed rate of 3 x 10 cm sec , the electrode material spends approximately 60 sec between 950°K and the melting point, and 30 sec below the slag surface i n the region 1300°K to melting point. Under these conditions i t seems l i k e l y that i n any s o l u t i o n process only very small p a r t i c l e s (probably sub-micron sizes) of the d i s s o l v i n g phase w i l l maintain equilibrium composition and phase r e l a t i o n s h i p through the temperature gradient. ; Two further aspects of the model are worthy of note. A steady; state model was chosen, i n s p i t e of the f a c t that the electrode i s being 35 consumed, and i s , therefore moving with respect to the slag/metal i n t e r f a c e . The rate at which the electrode moves a f f e c t s the temperature gradients predicted by the model through the boundary value of T , and possibly also through . Both of these values are experimental parameters and w i l l be s p e c i f i c to the melting conditions used. I f the melt rate and power input are changed1 these temperatures w i l l vary i n a way co n t r o l l e d by the complex heat transfer regime e x i s t i n g on 28 the electrode surface submerged below the slag/gas i n t e r f a c e . Recently attempts have been made to ca l c u l a t e the temperature d i s t r i b u t i o n i n the submerged portion of the electrode using assumed heat trans f e r c o e f f i c i e n t s . No attempt has been made here to predict the complex heat trans f e r regime and hence of including the melt-rate parameter i n thi s analysis. Due to the small diameter of electrode used i n the present labora- tory experiments, any r a d i a l temperature gradient should be small (10-20°C). This was found to be the case. However, i n large eleptrode/ ingot configurations, a s i g n i f i c a n t r a d i a l gradient e x i s t s and can be predicted by the present two dimensional a n a l y s i s . It was i n i t i a l l y postulated that the electrode's time-temperature r e l a t i o n s h i p would a f f e c t the amount of electrode surface oxidation, and therefore the re a c t i v e a l l o y element loss on melting. Using the; 31 data of Kubashewski and Evans f o r the oxidation of i r o n i n th i s temperature range, the oxide thickness f o r an electrode being melted i n a i r was calculated. This was done by considering the electrode surface above 1000°K, summing the appropriate parabolic growth-rates, -2 -1 for the experimental melt rate of 3 x 10 cm sec , and thus d e r i v i n g 36 an integrated oxide coating at point B i n F i g . (30). This thickness -4 i s approximately 10 cm, which i n the present electrode s i z e range _2 would account f o r only 10 wt. % loss of, say, titanium i n an i r o n - titanium a l l o y . As the electrode surface-volume r a t i o decreases with electrode diameter, t h i s oxidation source becomes s t i l l l e s s important i n large ESR u n i t s . One can b r i e f l y comment on the p o s s i b l e differences which might be observed between VAR and ESR electrode temperature gradients, i n s p i t e of the fact that there e x i s t s no convenient demarcation l i n e i n VAR equivalent to the slag/gas i n t e r f a c e i n ESR. The r e l a t i v e parts played by r a d i a t i o n , conduction and convection are i l l u s t r a t e d i n F i g . (32). Here i t has been assumed that VAR electrode i s exposed to a uniform surface at 1900°K at z = 0, with T = 1800°K and with no o electrode thermal term due to convection. The equivalent ESR gradient at an equivalent distance from the ingot surface i s also shown. Although the two s i t u a t i o n s are not s t r i c t l y comparable, the difference between the gradients i l l u s t r a t e s the s i g n i f i c a n t cooling e f f e c t , of the convective gas flow i n ESR. 37 CHAPTER IV MEASUREMENT OF ELECTRICAL AND THERMAL PROPERTIES OF THE SLAG-SKIN REGION IV.1 Introduction One of the advantages claimed for the ESR processing of metals i s held to be the r e s u l t i n g control i n the d i r e c t i o n a l i t y of ingot s o l i d i f i - 32 cation. This a r i s e s i n a c o n t r o l l a b l e proportion of r a d i a l to a x i a l heat flow i n the s o l i d i f y i n g ingot. Since the r a d i a l flow i s determined l a r g e l y by the heat transfer c h a r a c t e r i s t i c s of the mold-wall region, i t i s of i n t e r e s t to have numerical values of the appropriate heat < 33 transfer c o e f f i c i e n t s f or c a l c u l a t i o n purposes. The e l e c t r i c a l properties of the same i n t e r f a c e region determine the current d i s t r i b u - t i o n . In the insulated mold configuration (Fig. 33(a)), although there i s no net current flow out of the system, a p o t e n t i a l d i f f e r e n c e e x i s t s along the path slag/mold/ingot, so as to give the current path shown. Should t h i s current be large, the l o c a l j o u l e heating, or arcing, w i l l r e s u l t i n the ingot welding to the mold, or i n a severe case, i n mold- wall puncture. In the s i t u a t i o n shown i n F i g . (33(b)), with the mold grounded, the above e f f e c t s are only of importance i n the region where the slag has a p o t e n t i a l s i g n i f i c a n t l y above ground. Thus, the s l a g - skin should have a s u f f i c i e n t l y high e l e c t r i c a l r e s i s t i v i t y to prevent 38 the above e f f e c t s . A second r e s u l t of the current passing from the slag to the mold i s to provide the h o r i z o n t a l current component necessary 34 for conventional electromechanical s t i r r i n g . Whether s t i r r i n g from t h i s l a t t e r cause i s s i g n i f i c a n t i s s t i l l unknown. The numerical values obtained are used i n explaining the r e s u l t s r e l a t i n g to a p a r t i a l heat balance of the process and a current d i s t r i b u t i o n model i n Chapter V. IV.2 Experimental IV.2.1 E l e c t r i c a l and Thermal Measurements The apparatus used i s shown i n F i g . (34) and consists of a graphite c r u c i b l e containing a large volume (̂  1 l i t r e ) of l i q u i d s l a g , heated by an induction c o i l . The copper cylinder (of diameter 3 cm, length 3 cm) was immersed at time zero, and i t s temperature measured simultaneous with the slag temperature and the e l e c t r i c a l resistance between the graphite counter-electrode and the cyl i n d e r . The copper cylinder was cleaned by mechanical abrasion. The e l e c t r i c a l resistance was measured on successive occasions at both 40 Hz and 1 KHz, with the same r e s u l t , i n d i c a t i n g that p o l a r i z a t i o n contributions were n e g l i g i b l e . The 1.0 KHz instrument i s a phase-discriminating bridge which r e g i s t e r s only the ohmic contributions to the test impedance, and the close c o r r e l a t i o n between the 40 Hz and 1.0 KHz measurements also therefore indicates that r e a c t i v e contributions to the impedance were n e g l i g i b l e . The temperature was measured using W3Re/W25Re thermocouple. In order to eliminate the e l e c t r i c a l interference from the , induction generator, a l l the measurements were made with r . f . power o f f , 39 and with ungrounded instrumentation. This l a t t e r step also allowed high impedance recorders to be used i n the thermocouple c i r c u i t s w hilst the thermocouples were i n contact with the resistance measuring c i r c u i t s . The slag skin thickness was determined using a micrometer, a f t e r removing the copper block from the s l a g , following a 10 seconds immersion time. In order to e s t a b l i s h that the slag s k i n thickness remained constant during the experimental period, the block was immersed for periods varying between one and ten seconds, and the s k i n thickness measured. I t was found that the equilibrium thickness was established i n less than one second. Results of the r e s i s t i v i t y measurement are shown i n F i g . (35) and F i g . (36) as a function of the cy l i n d e r temperature. The equivalent dimensionless temperature vs. time measurements are shown i n Fig... (37) and F i g . (38). Several features not shown i n these graphs are worthy of comment. F i r s t l y , the slag temperature was measured continuously during the runs, so that the s l i g h t f a l l i n the temperature could be accounted for i n the subsequent c a l c u l a t i o n . This temperature decrease was approximately 20°C and remained e s s e n t i a l l y constant during the time of the experiment. At high temperatures (1730°C) i t was found that Ca\F^ did not form a coherent skin, but formed a discontinuous "patchy" f i l m on the cylinder surface. The consequent heat t r a n s f e r was high and non-reproducible:. F i n a l l y , a c a l c u l a t i o n of the amount of heat l i b e r a t e d i n the s o l i d i f i c a - tion of slag showed that the copper block would undergo a temperature r i s e of approximately 100°C i f a l l t h i s heat was absorbed by the block. However the subsequent analysis indicates that the rate of heat exchange 40 between the l i q u i d and s o l i d s l a g i s high i n comparison to that between the s o l i d slag and the block. Thus, most of the heat of fusion should be transferred to the l i q u i d slag bath. A s l i g h t curvature could be detected i n the i n i t i a l part of the experimental time/temperature trace, but as t h i s was i n a time period close to the reaction time of the recording system, t h i s can not be unequivocally a t t r i b u t e d to the s o l i d i f i c a t i o n step. The d e r i v a t i o n of the r u l i n g expression for heat trans f e r i n the 35 experimental s i t u a t i o n used i s a standard one. For the transient heat flow i n systems, with n e g l i g i b l e i n t e r n a l resistance The change of i n t e r n a l energy of the copper cyl i n d e r during 'dt' Net flow of heat from slag to the copper cylinder C m dT = U A [T slag Tjdt (4.1) P i n t e g r a t i n g , (4.2) o s i m p l i f y i n g (4.2), 41 F i g s . (37) and (38) show the time dependence of the c y l i n d e r temperature, p r o c e s s e d f o l l o w i n g eq. (4.3). In a p p l y i n g eq. (4.3) to the p r e s e n t e x p e r i m e n t a l s i t u a t i o n , s e v e r a l assumptions a r e made. F i r s t l y , a l t h o u g h the system u n d e r g o i n g the heat t r a n s f e r r e a c t i o n c o n t a i n s two s u r f a c e and a volume term, i t i s assumed h e r e t h a t i t may be d e s c r i b e d by an o v e r a l l h eat t r a n s f e r c o e f f i c i e n t , U. The terms c o m p r i s i n g U a r e o u t l i n e d and d i s c u s s e d s u b s e q u e n t l y . S e c o n d l y an average v a l u e f o r (C ) i s used over n J J - p copper the temperature range c o n s i d e r e d . T h i r d l y , i t i s assumed t h a t the copper c y l i n d e r c o n t a i n s no s i g n i f i c a n t g r a d i e n t s , i n s p i t e of the u n s t e a d y - s t a t e c o n d i t i o n used. The j u s t i f i c a t i o n f o r t h i s l i e s i n the f a c t t h a t the B i o t number ( — , where L = s i g n i f i c a n t d i m e n s i o n , K C u v o l u m e / s u r f a c e a r e a ; K = t h e r m a l c o n d u c t i v i t y of copper) of the system i s l e s s than 0.01. Only i f t h i s v a l u e exceeds 0.1 w i l l the 35 assumption i n t r o d u c e s i g n i f i c a n t (>5%) e r r o r i n t o a subsequent c a l c u l a t i o n of U. Values of U o b t a i n e d t h i s way a r e l i s t e d i n T a b l e I I I . IV.2.2 ESR E x p e r i m e n t a l Data The method of o b t a i n i n g the t o t a l e l e c t r i c a l r e s i s t a n c e between the mold, e l e c t r o d e and the i n g o t , i n an o p e r a t i n g ESR u n i t has been 36 p r e v i o u s l y d e s c r i b e d . T a b l e IV g i v e s the v a r i o u s o p e r a t i n g r e s i s t a n c e s 36 i n the ESR u n i t used i n t h i s study as o b t a i n e d by Cameron e t a l . 42 Table I I I . Values of the o v e r a l l heat transfer c o e f f i c i e n t , U, calculated from the data of Figs. 37 and 38. Slag Slag Skin U Composition Temperature Thickness x 10 mm +0.2 c a l . s _ 1cm 2°C 1 + 0.02 CaF 2 1460 4.4 0.92 1440 4.2 1.15 1500 3.56 1.15 1600 2.30 1.23 1666 1.20 1.28 1720 1.02 1.25 CaF 2 + 25 wt. % A1 20 3 1640 4.05 1.07 CaF 2 + 35 wt. % CaTi0 o 1530 5.0 1.00 Table IV. Operating resistances i n the ESR process 36 Ingot Electrode No. of Slag Mold- Mold- Ingot- Slag Unshunted Unshunted Electrode dia. dia. ingots skin electrode ingot electrode composi- current current P o l a r i t y X thickness resistance resistance resistance t i o n i n mold i n slag (cm) (cm) determin-ation (cm) (ohms) (ohms) (ohms) (amps) (amps) 5.08 2.54 3 x 4 5.08 2.54 5 x 5 5.08 2.54 5 x 4 7.62 3.81 4 x 4 7.62 3.81 5 x 4 7.62 3.81 5 x 4 .0.12 0.77±0.1 0.45±0.02 0.08 0.60±0.1 0.0510.02 0.09 0.15±0.05 1.0 ±0.1 0.12 0.7 ±0.1 0.13±0.05 0.08 0.5510.1 0.06±0.02 0.09 0.1510.02 0.4 ±0.1 0.03510.005 0.03710.005 0.03610.005 0.020+0.005 0.01910.005 0.02010.005 CaF 2 CaF 2 + CA CaF 2 + CA CaF 2 CaF 2 + CA CaF 2 + CA 1315 3815 9+2 13±5 1915 20±5 659110 650110 630110 1205115 1180115 1180115 -ve -ve +ve -ve -ve +ve 4>- 44 IV.3 Discussion IV.3.1 The Thermal Resistance of the Slag Skin The present experimental set up and an ESR system are s i m i l a r with one d i f f e r e n c e . In ESR process the copper mold i s water cooled where as the copper block was not and consequently heated up. However as U was experimentally found to be independent of copper block temperature, i t i s j u s t i f i e d to use the data obtained from the present experimental set up i n describing the ESR thermal c h a r a c t e r i s t i c s i n the s l a g - s k i n The o v e r a l l heat transfer c o e f f i c i e n t of the system, U, i s mader up of the two surface terms and the volume conductance of the slag skin. -2 The numerical value of U so defined i s seen to be approximately 10 c a l . -2 -1 -1 cm sec °C . This i s almost the same value as that found for the metal/solid-metal/copper mold w a l l system, as i n continuous casting , 37 p r a c t i c e , or i n a VAR u n i t . Although the ESR system w i l l n e c e s s a r i l y contain a thermal resistance due to e i t h e r free or forced convection i n the l i q u i d slag adjacent to the s o l i d s k i n , which w i l l not be the same as the equivalent term at the l i q u i d / s o l i d metal i n t e r f a c e i n , for example, a VAR system, i t i s noteworthy that the o v e r a l l heat trans f e r c o e f f i c i e n t s are close i n magnitude. In steady state, from F i g . (39) and F i g . (40) region. q 3 slag slag - T J E J (4.4) [ T E " V (4.5) 3 45 2 * r l A h i n t [ TD " V ( 4 ' 6 ) From (4.4), (4.5) and (4.6) one obtains q = U A (T' - T_ ) (4.7) n o slag Cu where A = 2 i r r n £ o 1 U = ±- (4. 8) -, r £n (r / r ) + - i — — — + r 0 h k h. „ 3 slag slag i n t In the following c a l c u l a t i o n s f or 8.0 cm copper mold, £ i s taken as unity and r ^ - r^. By using a method of approximation, one can deduce the component values of eq. (4.8) and hence the temperature p r o f i l e i n the mold-wall region. One must make the assumption here that T i s approximately 140°C. This value i s estimated from the mold w a l l thickness, and the observation that the mold wall outer temperature i s approximately 110°C (Chapter V). In a t y p i c a l case, such as that i l l u s t r a t e d by Table I I I for a CaF„ s l a g , T .. = 1650°C and the slag skin thickness i s 0.12. cm. 2 ° slag - b This leads to a value for q of 480 c a l . cm ''sec for a 8 cm diameter -2 - 2 - 1 copper mold using the observed value for U of 1.28 x 10 cal.cm sec c At t h i s value, one obtains a s e l f - c o n s i s t e n t c o r r e l a t i o n between the mold wall inner and outer temperatures. 46 F i g . (40) shows schematically the system at hand. In the present case a l l the temperatures except that at D are known as the temperature at E i s the melting point of CaF^- I t i s now possible to separate the terms i n equation (4.8), and ca l c u l a t e the values for h. , h ., and T , using the data developed xnt' slag D v above. Thus, i n the l i q u i d s l a g : q = A* AT h (4.9) o EF slag where A' = 2rrr„ I o 3 r ^ = r a d i a l dimension shown i n F i g . (39) ATgp = temperature d i f f e r e n c e between points E and F of F i g . (40) Substituting the values i n eq. (4.9) one gets h . ~ 7.5 x 10 2 cal.cm 2 S e c 1 ° C ~ 1 (4.10) slag In order to c a l c u l a t e the temperature at D, i . e . T^, a value for k must be assumed, slag -2 -1 -1 -1 The value of k , = 0.8 x 10 c a l . cm sec °C , estimated slag 38 from the values of c r y s t a l l i n e i o n i c s o l i d s found i n l i t e r a t u r e i s used for the c a l c u l a t i o n . Substituting the values of k , and h - b slag slag i n (4.8) one obtains h. = 2.05 x 10~ 2 c a l . cm 2 s e c l o C 1 (4.11) i n t 47 Substituting the known values i n eq. (4.5) and (4.6) leads to the value T D ~ 1100°C Varying the values of k , one obtains slag -2 -1 -1 -1 for k , = 1 0 c a l . cm sec °C slag T D = 1160°C -2 -1 -1 -1 and f o r k , = 0.6 x 10 c a l . cm sec °C slag T D = 1000°C with corresponding changes i n n ^ n t - One may thus draw the p r o f i l e shown i n F i g . (40), with the temperature at D approximately equal to 1100°C. The two heat trans f e r c o e f f i c i e n t s have values: -2 -2 -1 -1 h , = 7.5 x 10 c a l . cm sec °C slag -2 " -2 -1 -1 h. = 2.05 x 10 c a l . cm sec °C m t Since the major factor i n determining the values of the o v e r a l l parameter, U, i s seen to be the surface d i s c o n t i n u i t y term, i t i s not s u r p r i s i n g that the ESR system c l o s e l y resembles the other cold-mold processes i n i t s heat trans f e r c h a r a c t e r i s t i c s . As both h .. and k ., r slag slag are functions of slag composition and temperature, t h i s w i l l lead to the v a r i a t i o n s i n slag skin thickness observed i n p r a c t i c e . 48 However, i t i s u n l i k e l y that e i t h e r of these parameters s i g n i f i - cantly a f f e c t h. ^ and thus U w i l l be r e l a t i v e l y i n s e n s i t i v e function J i n t 3 of the process v a r i a b l e s , as was observed and shown i n Table I I I . IV.3.2 The E l e c t r i c a l Resistance of the Slag Skin The curves i n F i g . (35) and F i g . (36) c l e a r l y show that the slag skin resistance i s quite high. At c y l i n d e r temperature of 140°C, the resistance i s - 50 ohms. This gives a r e s i s t i v i t y value of 14,600 ohm.cm assuming a slag skin thickness of 0.12 cm and the surface area of the 2 copper block as 35 cm . At a cylinder temperature of 500°C, the value drops d r a s t i c a l l y to 292 ohm. cm (R - 1 ohm). Using these values to c a l c u l a t e the slag skin resistance for the laboratory ESR unit slag bath (diameter =8.0 cm, % = 3.5 cm) y i e l d s , R = 20 ohms for 140°C and R = 0.39 ohms for 500°C. The value of R 36 obtained experimentally i n e a r l i e r study of 0.55-0.77 ohms i s comparable to R5QQO c> However as the copper mold temperature i s below 150°C, the experimentally obtained value of R = 0.55-0.77 ohms has to be explained by a d i f f e r e n t mechanism. The experimentally obtained value of the resistance of slag skin i n t h i s study can be considered as a combination of two resistances i n s e r i e s , the slag skin resistance and the contact resistance. Extra- polating the values of r e s i s t i v i t y for CaF2-Al20 3 system from F i g . (86), for s l a g temperature of 1000-1200°C (average slag skin temperature as obtained from F i g . (40)), one obtains values ranging from r = 0.5 to 20 ohm. cm. From these values i t i s clear that the main resistance i s the contact resistance. At 500°C, there i s a better contact between 49 the s l a g s k i n and the copper c y l i n d e r y i e l d i n g a v a l u e of the combined r e s i s t a n c e 50 times s m a l l e r t h a n a t 140°C. Thus i n the ESR u n i t i f t h e r e i s good c o n t a c t between s l a g s k i n and the mold over even a s m a l l a r e a o f 0,1-2 sq. cm, the e x p e r i m e n t a l l y o b s erved v a l u e of s l a g s k i n r e s i s t a n c e i n ESR u n i t can be o b t a i n e d . With the i n n e r m o l d - w a l l temperature above 150°C, the p r o b a b i l i t y of a good c o n t a c t between the s l a g s k i n and the mold i s h i g h e r . T h i s may make the e l e c t r o d e - m o l d , and the i n g o t - m o l d r e s i s t a n c e s comparable i n magnitude to the working r e s i s t a n c e o f the l i q u i d s l a g . Thus, the main c u r r e n t p a t h would be e l e c t r o d e -> mold ->• i n g o t , w i t h con- sequent mold w a l l f a i l u r e . T h i s p r o b a b l y a c c o u n t s f o r the e x p l o s i o n s , o r i n g o t - m o l d w e l d i n g , o b served i n the ESR p r a c t i c e u s i n g s t e e l molds. The second p o i n t t o be o b s e r v e d i n F i g . (35) and F i g . (36) i s t h a t t h e r e i s an apparent r e s i s t a n c e drop a t low t e m p e r a t u r e s . T h i s a r i s e s from the f a c t t h a t t h e r e p o r t e d temperature i s p r o c e s s e d from a t ime-temperature r e c o r d , and t h e apparent r e s i s t a n c e drop i s the i n i t i a l c o n t a c t of the c y l i n d e r and the s l a g . The s i g n i f i c a n c e o f t h i s i s a momentary l o w - r e s i s t a n c e c o n t a c t a r i s i n g e i t h e r from the c o o l i n g o f the i n i t i a l s l a g s k i n , or the speed of f o r m a t i o n of the s k i n . D u r i n g the ESR p r o c e s s i n g , the l i q u i d s l a g c o n t i n u a l l y forms a s k i n a t the mold- s l a g - a i r i n t e r f a c e i n a r e g i o n where p o t e n t i a l d i f f e r e n c e of a t l e a s t 15 V e x i s t s between the s l a g and the mold w a l l . The momentary low r e s i s t a n c e c o n t a c t w i l l r e s u l t i n s m a l l a r e a s of t r a n s i e n t h i g h c u r r e n t - d e n s i t y and p o s s i b l e a r c i n g . T h i s has been observed i n i n d u s t r i a l ESR u n i t s as s m a l l , t r a n s i e n t " b r i g h t s p o t s " around the s l a g s u r f a c e boundary w i t h the mold w a l l . 50 CHAPTER V HEAT BALANCE OF THE PROCESS V . l Introduction The e l e c t r o s l a g r e f i n i n g process i s a r e l a t i v e l y i n e f f i c i e n t operation i n terms of thermal e f f i c i e n c y . However, the factors which make t h i s process i n e f f i c i e n t are the same ones which give t h i s process some unique advantages. In an ESR furnace, the e f f i c i e n c y i s s a c r i f i c e d f o r the sake of ingot structure by melting the metal i n a metal mold which i s very e f f e c t i v e l y cooled by a water jacket., It i s hot s u r p r i s i n g , therefore, that power consumption figures f o r el e c t r o s l a g remelting of 1200 to 2000 kilowatt hours per metric ton are 39 reported, although the t h e o r e t i c a l power required to melt ferrous a l l o y s i s about 400 KWH/metric ton. For laboratory scale process, the e f f i c i e n c y i s s t i l l lower (16-25%). ' Most of the heat energy supplied to the process i s passed immediately to the cooling water by conduction from the sides of the slag pool. An analysis of the heat balance of some of the e l e c t r o s l a g heats made at the Mellon Institute"'""'" has indicated that about 50-55% of the heat i s held i n the molten metal pool which i s extracted through the ingot and the water-cooled copper s t o o l . About 10 to 15% heat i s extracted through mold cooling, while 25% i s used i n heating the , electrode. The balance of the heat was accounted for as being , 51 l o s t by r a d i a t i o n and convection. 40 Holzgruber found that for 110 mm square ESR ingots (42 V, 4500 amp), 66% of the t o t a l heat introduced i s removed by the cooling water of the mold. A s l i g h t amount (=5%) remains as heat i n the ingot, while about 29% of the t o t a l heat i s l o s t by r a d i a t i o n from the slag surface. It i s quite c l e a r that the analyses of heat d i s t r i b u t i o n done to date"^'"^' 4^' 4"'" do not agree c l o s e l y . An accurate knowledge of the d i s t r i b u t i o n of heat i n the e l e c t r o s l a g remelting unit i s v i t a l to the better understanding and control of the process. As discussed e a r l i e r , there are a number of d i f f e r e n t ways i n which the e l e c t r i c a l energy can be supplied to the u n i t . The process can be operated using A.C. or D.C. supply. In D.C, one has the choice of having the electrode as the cathode (referred to as electrode negative) or anode (electrode p o s i t i v e ) . I t has been established for 12 some time now that both the anode and cathode are p o l a r i z e d to d i f f e r e n t extents i n an ESR u n i t . The two types of arrangement give d i f f e r e n t operating c h a r a c t e r i s t i c s . The mold can be insulated from or connected (referred to as ' l i v e ' ) to the ingot. The current path 36 has been found to be d i f f e r e n t i n the two cases for electrode p o s i t i v e arrangement. S i g n i f i c a n t disagreement e x i s t s i n the l i t e r a t u r e as to the power required to melt i n a p a r t i c u l a r configuration"!"^ The range of figures 6 42 quoted ' f o r steels and nickel-base a l l o y s i s a function of absolute s i z e , p o l a r i t y and electrode/mold diameter r a t i o , as w e l l as of the 42 material. Kammel et a l . have reported that D.C. with electrode 52 negative i s the most e f f i c i e n t mode, whilst Holzgruber et a l . found that D.C. with electrode p o s i t i v e was the most e f f i c i e n t . Although the e l e c t r i c a l energy can be supplied i n d i f f e r e n t ways, i t i s necessary to adjust the power supplied to the melt to within f i n e l i m i t s i f an ingot having good surface and structure i s to be produced. The same power input can be achieved by various combinations of voltage and current.' The choice of current within the required power l i m i t a t i o n i s rather c r i t i c a l , because while increased current increases the melt rate, i t also.deepens the slag pool, giving a les s 4 43 s a t i s f a c t o r y ingot structure. ' The e f f e c t of change i n voltage i s not as great as that of current. In c e r t a i n cases, high voltage gives a better s o l i d i f i c a t i o n front and hence an improvement i n ingot 4 properties. Medoyar et a l . report that the main e f f e c t of voltage i s to r a i s e the temperature of the slag bath and a high voltage i n t e n s i t i e s desulphurization. The power input to the process i s generally chosen such that the melt rate corresponds to a stable e l e c t r o s l a g process. At a very low rate of de l i v e r y of the electrode, the ESR process p e r i o d i c a l l y turns into an e l e c t r i c arc process. At the moment when the drop breaks o f f , 4 an arc discharge i s observed between the electrode and slag surface. At very high rate of electrode feed, p e r i o d i c arc discharge occurs between the end of the electrode and the surface of the m e t a l l i c bath, a r i s i n g at the moment when the drop breaks o f f . This u l t i m a t e l y leads to s h o r t - c i r c u i t i n g of the electrode on the m e t a l l i c bath. The volume of the slag bath also controls the structure of the 53 ingot obtained. As the depth of the slag bath i s increased (without changing the melt r a t e ) , the depth of the m e t a l l i c bath i s reduced. As the materials processed by the ESR process are quite expensive, very often i t i s not economically f e a s i b l e to t r y out various working conditions to determine the optimum working parameters. An attempt i s made here to predict the working conditions f or i n d u s t r i a l scale ingots. D i s t r i b u t i o n of, Heat i n the ESR Unit In a dynamic steady s t a t e , the heat generated i n the slag bath by resistance heating i s d i s t r i b u t e d i n the unit i n the following manner (1) heat consumed i n heating the consumable electrode to the melting point, i t s fusion and further heating of the drops of the electrode material as they f a l l through the slag bed (2) heat given to cooling water across the slag bed (3) heat given to cooling water across the length of the ingot (4) heat accumulated i n the ingot (5) heat given to base plate cooling water ) (6) heat l o s t by r a d i a t i o n from the surface of the slag bath to the furnace atmosphere (7) heat radiated by the slag bath on to the walls of the mold (8) heat radiated by the slag bath on to the electrode. A 54 V.2 E x p e r i m e n t a l V.2.1 ESR Ingot Schedule V.2.1.1 M e l t Record Experiments were c a r r i e d out on the U.B.C. e l e c t r o s l a g u n i t . F i g . (41a) g i v e s the g e n e r a l view o f the l a b o r a t o r y u n i t . The s t a r t i n g 9 p r o c e d u r e has been d e s c r i b e d i n d e t a i l by E t i e n n e . A f t e r s t e a d y o p e r a t i n g c o n d i t i o n s were e s t a b l i s h e d , r e a d i n g s of c u r r e n t , v o l t a g e , e l e c t r o d e t r a v e l , s l a g f e e d r a t e e t c . , were r e c o r d e d a t known time i n t e r v a l s . ; V.2.1.2 Molds S i x d i f f e r e n t w a t e r - c o o l e d copper molds (Cl) I.D.: 5.85 cm, h t : 40 cm, w a l l t h i c k n e s s : 0.5 cm; ( i i ) I.D.: 6.35 cm, h t : 40 cm, w a l l t h i c k n e s s : 0.5 cm; ( i i i ) I.D.: 6.35 cm, h t : 80 cm, w a l l t h i c k n e s s : 0.5 cm; ( i v ) I.D.: 8.0 cm, h t : 45 cm, w a l l t h i c k n e s s : 0.5 cm; Cv) I.D.: 8.0 cm, h t : 80 cm, w a l l t h i c k n e s s 0.5 cm; ( v i ) I.D.: 9.5 cm, h t : 90 cm, w a l l t h i c k n e s s 0.4 cm). were used i n the p r e s e n t s t u d y . V.2.1.3 E l e c t r o d e s E l e c t r o d e s of d i f f e r e n t c o m p o s i t i o n (EN 25 s t e e l , 321 S.S., 1018 s t e e l , AISI 630, F e r r o v a c E, Armco i r o n ) and s i z e (2.54 cm to 6.35 cm d iameter) were r e m e l t e d . In the non-consumable e l e c t r o d e e x periment, 3.81 cm d i a m e t e r EN 25 s t e e l e l e c t r o d e was t h r e a d e d to the 3.81 cm d i a meter molybdenum e l e c t r o d e . The p r o c e s s went non-consumable a f t e r the EN 25 s t e e l m e l t e d and formed an i n g o t a t the bottom. 55 V.2.1.4 Slag Composition Slag composition CaF^ ^ 25 wt. % Al^O• was used i n the study of the heat balance of the process. For some a u x i l l i a r y studies, 100% CaF^ and CaF^ ^ 30 wt. % TiO^ compositions were also used. V.2.1.5 P o l a r i t y Ingots were made using e i t h e r a.c. or d.c. (with electrode of ei t h e r p o l a r i t y ) power. F i g . (42) gives the three possible mold connections. 9 V.2.1.6 Continuous Slag Addition A s p e c i a l l y designed r o t a t i n g table ( Fig. (41b)) allowed the continuous d e l i v e r y of the slag during the melt. A v e r t i c a l cannister whose base i s closed by the r o t a t i n g plate delivered the material (powder or small granules) through a c a l i b r a t e d grate. The stream of material was then wiped over the edge of the p l a t e into the mold. The continuous addition of slag using t h i s apparatus was c a r r i e d out only while making t a l l ingots. V.2.1.7 Atmosphere Control Three types of hoods were used for melts done under argon atmosphere: Type I: F i g . (43) gives a schematic diagram of the hood, used i n the i n i t i a l melts, which provided an argon blanket and extraction of fumes. Type I I : A more elaborate design included a sealed chamber i n 56 which the e l e c t r o d e was h e l d onto a water c o o l e d s t u b . The r u b b e r b e l l o w s clamped to the s t u b a t the top o f the assembly p r o v i d e d the moving s e a l ( F i g u r e ( 4 4 ) ) . S p r i n g clamps and blowout windows a l l o w e d f o r a q u i c k r e l e a s e of i n s i d e p r e s s u r e s i n case of e x p l o s i o n . Type I I I : T h i s was used i n m e l t s where c o n t i n u o u s a d d i t i o n of the s l a g was n e c e s s a r y ( F i g . ( 4 5 ) ) . V.2.1.8 E x p e r i m e n t a l Data The e x p e r i m e n t a l d a t a o b t a i n e d i s t a b u l a t e d i n T a b l e V. The r e p o r t e d v a l u e s of t h e p r o c e s s parameters are the average v a l u e s d u r i n g s t a b l e w orking c o n d i t i o n s . T a b l e (VI) g i v e s the a n a l y s i s o f the e l e c t r o d e and i n g o t c o m p o s i t i o n s f o r some of the EN 25 s t e e l m e l t s . T h i s was c a r r i e d out by the M i n e r a l S c i e n c e s D i v i s i o n , Mines Branch, Ottawa. F i g . (46) g i v e s the p e r c e n t a g e of c u r r e n t g o i n g t o the mold d u r i n g a d.c. p o s i t i v e ( w i t h l i v e mold) m e l t . V.2.2 Measurement of Temperature P r o f i l e s on the Mold In o r d e r to c a l c u l a t e the heat l e a v i n g the mold, measurement of the temperature p r o f i l e s on the mold was c a r r i e d out f o r v a r i o u s e x p e r i m e n t a l c o n d i t i o n s . C o p p e r - c o n s t a n t a n thermocouples were used to measure the temperature d i s t r i b u t i o n on t h e mold. Con s t a n t a n w i r e (0.0254 cm diameter) were embedded i n 0.1 cm d i a m e t e r x 0.125 cm deep h o l e s i n the copper mold, pl u g g e d by 0.1 cm d i a m e t e r copper w i r e . F o r t y - e i g h t c o n s t a n t a n w i r e s were embedded i n the copper mold l o c a t e d i n a s p i r a l a t f i x e d d i s t a n c e s a p a r t , as shown i n F i g . ( 4 7 ) . The copper mold i t s e l f was used as the p o s i t i v e t e r m i n a l , f o r a l l the 48 thermo- c o u p l e s . The 300 cm l o n g c o n s t a n t a n w i r e s were i n d i v i d u a l l y e n c l o s e d Table V. ESR melt record Ingot mold electrode electrode electrode atmos- no. d i a - diameter comp. p o l a r i t y phere meter (cm) (cm) st a r t i n g slag voltage current melt wt. of the To t a l wt. and comp- osition' (g) (volt) (amp) rate slag cap at electrode , -1. the end of descend-(g.sec ) , , b the run (cm) (g) 3.81 8 3.81 5.08 3.5 3.81 3.81 7 6.35 3.5 EN 25 EN 25 -ve Argon III -ve A i r EN 25 -ve A i r EN 25 -ve Argon EN 25 -ve Argon II EN 25 -ve Argon EN 25 -ve Argon II 660 g CaF 2-27.3 wt. % A1 20 3 720 g CaF2~25 wt. % A1 20 3 660 g CaF2-27.3 wt. % A1 20 3 680 g CaF2-26.5 wt. % A1 20 3 660 g CaF 2-27.3 wt. % A1 20 3 720 g CaF 2-25 wt. % A1 20 3 440 g CaF 2-25 wt. % A l 0 23.75 . 1150 22.5 1130 23.0 1175 22.8 960 3.35 22.25 1150 3.8 23.0 1100 4.15 2.20 23.5 1250 2.2 2.64 2.67 535 495 461 411 400 485 325 106.5 38.2 37.0 56.8 55.9 30.8 99.9 Table V. (Continued) Ingot mold electrode electrode electrode atmos- starting slag voltage current melt wt. of the Total no. dia- diameter comp. po l a r i t y phere wt. and comp- ( v o i t ) ( a m ) rate slag cap at electrode meter o s i t i o n . -1. the end of decend (cm) (cm) (g) g.sec r u n ( c m) (g) 8 9.5 5.08 EN 25' -ve Air 960 g 23.5 1575 4.10 875 66.8 CaF2-25 wt. % A1 20 3 9 6.35 3.18 Armco -ve A i r 440 g 22.0 880 1.26 380 122.8 Iron CaF2~25 wt. % A i 2 q 3 10 8.0 3.81 EN 25 +ve A r g o n 1 1 1 660 g 23.0 920 2.58 530 86.2 CaF2-27.3 wt. % A1 20 3 11 8 3.81 EN 25 +ve Argon 1 1 720 g 22.0 975.0 2.58 517 30.2 CaF2-25 wt. % A1 20 3 12 8 3.81 EN 25 +ve Argon 1 1 • " 22.5 925.0 2.58 480 • 48.3 13 8 3.81 EN 25 +ve l i v e A rgon 1 1 1 660 g 23.25 1175 2.59 602 80.0 CaF2~27.3 wt. % A1 20 3 14 8 3.81 EN 25 +ve l i v e Argon 1 1 720 g 23.5 950 2.58 400 36.3 CaF2-25 wt. % A1 20 3 15 8 3.81 EN 25 a.c. Air " 26.0 840 4.15 442 29.5 oo Table V. (Continued) Ingot mold electrode electrode electrode atmos- no. d i a - diameter comp. p o l a r i t y phere meter (cm) (cm) s t a r t i n g slag voltage current melt wt. of the To t a l wt. and comp- o s i t i o n (g) (volt) (amp) rate slag cap at electrode , -1. the end of decend Cg.sec ) t h e r u n ( c m ) (g) 16 8 17 18 8 21 9.5 3.81 8 3.81 3.5 19 8 3.81 20 8 . • 3.81 6.35 22 5.85 2.54 En 25 a.c. EN 25 a.c. EN 25 EN 25 + Mo AISI 630 EN 25 321 SS a.c. a.c. Argon -ve III -ve Argon +ve Argon 1 1 1 ceo Argon 660 g CaF 2-27.3 wt. % A1 20 3 Argon^ 720 g CaF2-25 wt. % A1 20 3 Argon 1 680 g CaF2-26.5 wt. % A1 20 3 660 g CaF 2-27.3 wt. % A1 20 3 600g CaF 2-13.3 wt. % A1 20 3 980 g CaF 2-25 wt. % A1 20 3 380 g 100 % CaF 2 II A i r 23.5 850 3.5 25.5 810 3.7 23.1 780 2.8 25.0 1100 23.5 1575 non-con- sumable 23.5 1300 3.4 6.36 22.3 650 1.22 355 340 367 375 400 772 345 95.7 63.0 70.0 72.4 50.0 80.0 40.0 Ln Table V. (Continued) Ingot mold electrode electrode electrode atmos- no. d i a - diameter comp. p o l a r i t y phere meter (cm) (cm) st a r t i n g slag voltage current melt wt. of the T o t a l wt. and comp- . , . . N rate slag cap at electrode • • (volt) (amp) . ,̂ ° , r , , o s i t i o n , -1 N the end of decend / ^ (g-sec ) t, . . (g) ° the run (cm) (g) 23 5.85 2.54 321 SS +ve Argon 380 g CaF 2-31.6 wt, % CaTi0„ 22.3 630 2.0 195 45.0 24 5.85 2.54 321 SS +ve Argon 380 g CaF2-31.6 wt, % CaTiO„ 22.3 640 1.69 286 40.1 25 5.85 3.18 FVE 26 5.85 3.18 FVE 27 5.85 3.18 FVE 28 5.85 3.18 FVE 29 5.85 3.18 FVE -ve A i r -ve Argon +ve A i r +ve BN insu- lated +ve BN insu- lated" : II Argon II Argon II 380 g CaF 2-23.7 wt, % A1 20 3 400 g CaF 2-25 wt. % A1 20 3 360 g CaF 2-25 wt. % A1 20 3 340 g CaF 2-25 wt. % A1 20 3 340 g CaF 2-25 wt. % A l 0 23.3 1010 2.5 217 23.5 1000 1.735 192 20.2 780 1.56 22.2 975 2.45 22.4 910 1.75 252 327 272 32.5 26.5 31.4 28.1 28.0 o Table V. (Continued) Ingot mold electrode electrode electrode atmos- s t a r t i n g slag voltage current melt wt. of the Tota l no. d i a - meter diameter comp. p o l a r i t y phere wt. and comp- o s i t i o n (volt) (amp) rate (g.sec ) slag cap at the end of electrode decend (cm) (cm) (g) the run (g) (cm) 30 5.85 3.18 FVE +ve l i v e Argon 340 g. CaF 2-25 wt. % A1 20 3 21.5 870 1.3 158 26.6 31 5.85 3.18 FVE a. c. Argon 340 g CaF 2-25 wt. % A1 20 3 24.2 650 2.25 167 28.2 32 5.85 3.18 FVE a. c. BN insu- lated Argon 340 g CaF 2-25 wt. % A l 0 23.0 810 2.43 158 28.6 Atmosphere: Argon : Argon atmosphere using s h i e l d of type I Argon*''': Argon atmosphere using s h i e l d of type II Argon1''"''": Argon atmosphere using s h i e l d of type III Table VI. Chemical analysis of the EN 25 steel ingots Ingot composi- Alloy electrode Atmos- no. tion of composi- polari t y phere the tion composition (wt. %) Mn Si Ni Cr Mo Sn Cu Al Fe 1 Electrode EN 25 1 Ingot EN 25 2 Electrode EN 25 2 Ingot EN 25 3 Electrode EN 25 3 Ingot EN 25 5 Electrode EN 25 5 Ingot EN 25 6 Electrode EN 25 6 Ingot EN 25 10 Electrode EN 25 10 Ingot EN 25 11 Electrode EN 25 11 Ingot EN 25 -ve -ve -ve -ve -ve -ve -ve -ve -ve -ve +ve +ve +ve +ve Argon 1 1 1 0.29 0.675 0.225 0.06 0.013 2.475 0.72 0.60 0.028 0.27 0.01 ba Argon 1 1 1 0.285 0.51 0.135 0.05 0.013 2.50 0.66 0.62 0.028 0.275 0.13 Air 0.28 0.69 0.24 0.062 0.012 2.55 0.73 0.65 0.028 0.29 0.01 A i r 0.275 0.56 0.155 0.056 0.013 2.37 0.185 0.61 0.028 0.265 0.13 Ai r 0.275 0.645 0.32 0.025 0.013 2.42 0.74 0.60 0.026 0.23 0.01 Ai r 0.29 0.53 0.165 0.026 0.013 2.38 0.20 0.56 0.027 0.225 >0.2 Argon 1 1 0.28 0.675 0.235 0.056 0.012 2.5 0.725 0.61 0.027 0.27 0.015 Argon 1 1 0.295 0.61 0.165 0.06 0.013 2.42 0.70 0.65 >0-10 0.29 0.14 Argon 1 1 0.28 0.67 0.235 0.059 0.012 2.55 0.72 0.63 0.028 0.28 0.01 Argon 1 1 0.30 0.59 0.17 0.05 0.015 2.42 0.79 0.62 0.03 0.27 0.15 Argon 1 1 1 0.28 0.675 0.24 0.056 0.012 2.475 0.73 0.625 0.028 0.285 0.015 Argon 1 1 1 0.27 0.57 0.11 0.049 0.013 2.45 0.20 0.59 0.029 0.275 0.03 Argon 1 1 0.28 0.66 0.23 0.058 0.013 2.55 0.72 0.60 0.028 0.275' 0.015 Argon 1 1 0.275 0.63 0.15 0.040 0.013 2.5 0.20 0.57 0.028 0.27 0.015 Table VI. (Continued) Ingot composi- Alloy electrode atmos- no. tion of composi- polari t y phere the t i o n composition (wt. %) Mn Si Ni Cr Mo Sn Cu Al 12 Electrode EN 25 12 Ingot EN 25 13 Electrode EN 25 13 Ingot EN 25 14 Electrode EN 25 14 Ingot EN 25 15 Electrode EN 25 15 Ingot EN 25 16 Electrode EN 25 16 Ingot EN 25 17 Electrode EN 25 17 Ingot EN 25 a. c. a.c. a.c. a.c. a. c. a.c. Fe +ve Argon 1 1 0.29 0.665 0.225 0.058 0.013 2.475 0.72 0.598 0.029 0.265 0.01 +ve Argon 1 1 0.27 0.65 0.185 0.051 0.013 2.50 0.20 0.59 0.029 0.27 0.015 +ve l i v e A rgon 1 1 1 0.295 0.675 0.235 0.064 0.014 2.50 0.725 0.61 0.029 0.275 0.010 +ve l i v e A r g o n 1 1 1 0.30 0.33 0.09 0.062 0.013 2.57 0.63 0.66 0.029 0.29 >.0.2 +ve l i v e Argon 1 1 0.275 0.675 0.23 0.062 0.012 2.45 0.725 0.625 0.027 0.28 0.01 +ve l i v e Argon 1 1 0.28 0.35 0.055 0.067 0.013 2.47 0.19 0.60 0.029 0.27 0.04 Ai r 0.28 0.66 0.225 0.06 0.012 2.45 0.715 0.61 0.017 0.27 0.01 A i r 0.275 0.61 0.18 0.032 0.013 2.50 .215 0.62 0.029 0.27 0.04 Argon 1 1 1 0.28 0.66 0.23 0.058 0.012 2.475 0.72 0.60 0.028 0.27 0.010 Arg o n 1 1 1 0.285 0.66 0.20 0.064 0.014 2.52 0.74 0.66 0.03 0.29 0.03 Argon 1 1 0.28 0.675 0.235 0.057 0.012 2.475 0.73 0.61 0.028 0.275 0.01 Argon 1 1 0.27 0.62 0.195 0.045 0.012 2.48 0.195 0.60 0.028 0.27 0.035 CT\ 64 i n 0.2 cm dia. p l a s t i c tubings (made by ICORE, C a l i f o r n i a ) . The cold junctions were maintained at 0°C by immersing them i n i c e cooled glass tubes containing mercury. For melts using d.c. p o s i t i v e ( l i v e mold) configuration, a s i g n i f i c a n t f r a c t i o n of the t o t a l current flows through the mold and as such i t i s not possible to determine the temperature d i s t r i b u t i o n on the mold using copper mold as the +ve terminal f or a l l the thermo- couples. A number of insulated thermocouple grade copper wires were embedded near the constantan wires i n the mold to give an accurate temperature d i s t r i b u t i o n on the mold. Fins were attached to the mold to regulate the water flow over the copper mold, at the same time, enabling chromel-alumel thermocouples to be located i n a s p i r a l along the length of the mold. These thermo- couples (15 i n t o t a l ) were used to determine the temperature d i s t r i - bution i n the mold cooling water. F i g . (48) shows the thermocouples clad copper molds. The e.m.f. generated was recorded on a Texas instrument model FM W6B m u l t i - channel recorder. As the ingot progressively b u i l t up, appropriate thermocouples were connected to the,24 terminals recorder to give the temperature d i s t r i b u t i o n on the mold. F i g . (49) to F i g . (56) gives the temperature d i s t r i b u t i o n on the mold for d i f f e r e n t experimental configurations. F i g . (57) gives;the temperature d i s t r i b u t i o n i n the mold cooling x^ater. 65 V.2.3 Measurement of the Heat Leaving Through the Bottom of the Mold In order to c a l c u l a t e the amount of heat leaving through the bottom of the, mold, i n some melts, two chromel/alumel thermocouples were placed, known distance apart (1 cm), i n grooves made i n the s t e e l base plate. F i g . (58) gives the temperature d i s t r i b u t i o n obtained. V.3 D i s t r i b u t i o n of Heat Input i n the Slag Bed V.3.1 Power Input In t h i s section, a de t a i l e d analysis of the heat input into the unit w i l l be c a r r i e d out. I t w i l l be c a r r i e d out for a t y p i c a l melt (I.N. 1 of Table V). The voltage gradients f o r t h i s experimental set up were determined i n Chapter II and w i l l be used here. There are 3 sources of heat input. (1) resistance heating of the sl a g (2) p o l a r i z a t i o n of the electrode and the ingot (3) oxidation of the electrode or the cathode reaction product i n a i r . From Table V, the amount of heat input (due to (1) and (2)) can be calculated. The a.c. r i p p l e i n a d.c. operation i s not a sine wave, but has an r.m.s. equivalent, registered by the 'r.m.s.' meters. D.C. power: V = ,23.75 v o l t s ; A = 1150 amps. A.C. r i p p l e : r.m.s. v o l t a g e = 2.65 V r.m.s. current = 142 amp Power input = 23.75 x 1150 + 2.65 x 1.42 = 27.60 Kwatts Heat Input = 27.60 x 0.24 = 6.65 K c a l . s e c " 1 . 66 V.3.2 Resistance Heating of the Slag F i g . (59) gives the voltage gradients i n the slag bed f o r melt of Ingot No. 1. The slag bath i s subdivided i n t o f i v e sections as shown. The average temperature and conductivity of each section are shown i n F i g . (59). The conductivity data was experimentally determined 21 by M i t c h e l l and Cameron. The e f f e c t of Ca and A l on conductivity w i l l be discussed subsequently. . Each section is- assumed to have a constant current density 2 Power = I R watts R v 2 . —— volume x c I v 2 Region A: Power = —^ x volume x c I V = 8 v o l t s volume = 2TT cm^ I = 0.9 cm c = 2.46 ohm *cm 1 2 P = ^ x 2TT x 2.46 x 0.24 = 0.295 Kcal. s e c " 1 A (0.9) Table VII gives the heat input d i s t r i b u t i o n i n the f i v e d i f f e r e n t regions considered here. T o t a l heat input = E P A+E A = 4.75 Kcal.sec *. Table VII. Calculation of heat input d i s t r i b u t i o n i n the slag bed using a.c. e l e c t r i c a l conductivity Region AV . (volts) . volume (cm) length (cm) a.c. e l e c t r i c a l conductivity (ohm "'"cm "*") Amount of heat generated (Kcal. sec "'") T o t a l heat generated (Kcal. sec "*") A 8 2TT =0.9 2.46 .295 0.295 + 1.27 +1.60 + 1.10 B 18 8TT = 2.1' 2.85 1.27 +0.485 = 4.75 C 12.87 24TT = 2.22 2.64 1.60 D 13.0 12Tf =1.8 2.30 1.10 E 8.75 18TT =2.1 2.08 0.485 68 V.3.3 E f f e c t of Dissolved Ca and A l on the Conductivity of the Slag As discussed e a r l i e r i n Chapter I I , the cathodic reaction product i n a d.c. ESR operation i s Ca, A l or A l + and these are soluble to d i f f e r e n t extents, i n both the l i q u i d metal and the s l a g . Ca has complete m i s i b i l i t y i n CaF^ slag at the ESR operating 44 temperatures. Although the e f f e c t of Ca on the e l e c t r i c a l conductivity of CaF^ has not been studied, data i s a v a i l a b l e on the e f f e c t of Na 44 addition to NaF and s i m i l a r h a l i d e systems. From t h i s data i t i s c l e a r that 30-40% increase i n conductivity for 2-5 mole % addition of Ca or A l i n the slag i s not unreasonable. To obtain a more r e a l i s t i c value for the increase i n conductivity due to the d i s s o l u t i o n of Ca and A l i n slag the following approach i s adopted. From Table V, i t i s c l e a r that both for I.N. 1 (d.c. negative) and I.N. 16 ( a . c ) , the ESR c e l l geometry below the electrode t i p was very s i m i l a r . Using t h i s assumption, i t i s possible to c a l c u l a t e the c e l l constant from the a.c. melt and substitute i t i n the c a l c u l a t i o n s for d.c. melt to give the value of r e s i s t i v i t y of the s l a g . For I.N. 16 (a.c. V = 23.5 V I 850 amp. R V I .0276 ohms R r a.c. A (f) = 0.0276 .0276 r a.c. 69 For I.N. 1 (d.c. negative) V = 23.5 V (ac t u a l l y 23.75 V) I =1150 amp R = = 0.0204 ohm r , .(f) = 0.0204 d.c. A ,jU = 0.0204 A r A d.c. Equating the two values of (̂-) ' 0.0276 = 0.0204 r r , a.c. d.c. 0.0204 r , = .74 r d.c. a.c. c, = 1.35 c d.c. a.c. r d.c. 0.0276 a.c Thus the conductivity of the slag i n d.c. operation i s increased by 35%. The temperature v a r i a t i o n of d.c. r e s i s t i v i t y i s unknown. Although i t w i l l be les s s e n s i t i v e to temperature v a r i a t i o n , to simp l i f y the ana l y s i s , i t i s assumed here that the temperature v a r i a t i o n of d.c. r e s i s t i v i t y i s s i m i l a r to a.c. r e s i s t i v i t y . The voltage gradients w i l l therefore remain unaltered. .......... Table VIII gives the heat input d i s t r i b u t i o n i n the various regions based on the d.c. conductivity values. Table VIII. Calculation of heat input d i s t r i b u t i o n i n the slag bed using d.c. e l e c t r i c a l conductivity Region a.c. e l e c t r i c conductivity (ohm "'"cm *) amount of heat generated (Kcal.sec *) d.c. e l e c t r i c conductivity =1.35 x a.c. e l e c t r i c cond. (ohm "'"cm "*") amount of heat generated (Kcal.sec 1) To t a l heat generated by resistance heating of the slag (Kcal. sec "*") A 2.46 0.295 3.32 0.40 0.40 + 1.72 + 2.16 + 1.44 B 2.85 1.27 3.85 1.72 + 0.665 = 6.43 C 2.64 1.60 3.57 2.16 D 2.30 1.10 3.11 1.485 E 2.08 0.485 2.81 0.665 71 V.3,4 Heat Generation Due to P o l a r i z a t i o n As discussed e a r l i e r i n Chapter I I , i n d.c.- ESR process, both the ingot and electrode are p o l a r i z e d . Although p o l a r i z a t i o n data i s not a v a i l a b l e f or EN 25 s t e e l , i t i s not unreasonable to use the data for pure i r o n (Fig. (21)). Using t h i s data, for the current densities e x i s t i n g on the electrode and ingot for d.c. negative config- uration, one obtains n - 0.5 V f o r both cathode and anode processes. The amount of heat generated due to these p o l a r i z a t i o n s = .0.5 x 1150 x .24 + 0.5 x 1150 x .24 = 0.275 K c a l . s e c " 1 . Adding the heat input values for resistance heating and p o l a r i z a - t i o n one gets heat input = 6.43 + 0.275 = 6.705 K c a l . s e c - 1 The value of 6.705 Kcal/sec compares very favourably with 6.65 Kcal.sec ^ obtained from the e l e c t r i c a l energy input data. V.4 An Analysis of the Heat Transferred to Mold Cooling Water V.4.1 Introduction In order to carry out an accurate heat balance of the process, one must know the amount of heat transferred to mold cooling water at each point on the mold outer surface. On examining the temperature d i s t r i b u t i o n on the copper mold, i t i s clear that the temperature of the copper mold containing the l i q u i d slag and metal pool i s above the b o i l i n g point of water at atmospheric pressure. When the surface temperature exceeds the 72 saturation temperature, l o c a l b o i l i n g i n the v i c i n i t y of the surface may take place even i f the bulk water temperature i s below the b o i l i n g point. The b o i l i n g process i n a l i q u i d whose bulk temperature i s below the saturation temperature but whose boundary layer i s s u f f i c i e n t l y superheated that bubbles form next to. the heating surface i s usually 35 c a l l e d heat transfer to a subcooled b o i l i n g l i q u i d or surface b o i l i n g . Various mechanisms of heat transfer i n surface b o i l i n g are put forward but the v a p o r - l i q u i d mechanism^"' i s the presently accepted mechanism as i t i s able to explain most of the observed phenomena. Thus the analysis has to be c a r r i e d out i n the two regions of the mold/water i n t e r f a c e which are separately i n the: 1. non-boiling region 2. surface b o i l i n g region. V.4.2 Non-boiling Region V. 4.2.1 Introduction The f i n a l expressions obtained from more advanced analogies are very complicated and the evaluation of the Nusselt number under given flow and thermal boundary conditions usually requires a numerical i n t e g r a t i o n . For this reason i t i s more convenient for the purpose at hand to use semi-empirical equations, or graphs based on advanced analogies. Secondly, as w i l l be apparent subsequently, the amount of heat transferred to the cooling water i n the non-boiling region, i s quite small when compared to surface b o i l i n g region. 73 V.4.2.2 Ca l c u l a t i o n of the Reynolds Number Tables IX and X give the experimental data and the relevant p h y s i c a l properties of water r e s p e c t i v e l y . G D R Reynolds number = y where G = mass v e l o c i t y of the f l u i d flowing through the annulus (g.sec cm ) G = - W 4 2 2 TT[D2 - D p _1 where W = water rate through the annulus (g sec ) w = 2 1 * 6 f * 1 = 350 g s e c ' 1 D^ and D^ : dimensions of the annulus (cm) -1 -2 G = 5.87 g sec cm D = hydraulic diameter (cm) H - 4 x flow cross s e c t i o n a l area wetted perimeter = 3.55 cm u = v i s c o s i t y of water (poise) 5.87 x 3.55 Re 0.00657 = 3200 35 The flow i s laminar when the Reynolds number i s below 2100. In the range of Reynolds number between 2100 and 10,000, the tra n s i - t i o n from laminar to turbulent flow takes place. The flow i n th i s 74 Table IX. Experiment data f o r ingot no. 1 (Table V) Inle t water temperature: 32°C Outlet water temperature: 50°C Water flow rate: „, , . -1 21 l i t r e s mm Cross-sectional dimensions of the water jacket: D 1 = 8.9 cm D_ = 12.45 cm 2 Table X. Ph y s i c a l properties of water at 40°C-50°C C o e f f i c i e n t of v i s c o s i t y at 40°C: C o e f f i c i e n t of v i s c o s i t y at 50°C: S p e c i f i c heat: Thermal conductivity: Density: 0.00657 poise 0.0055 poise 1 c a l g " l o C _ 1 15.2 x 10~ 4 c a l cm"1sec"1°c' 1 g cm 75 regime i s c a l l e d ' t r a n s i t i o n a l ' . At a Reynolds number of about 10,000, the flow becomes f u l l y turbulent. : Thus the experimental flow rate i s i n the ' t r a n s i t i o n a l r e g i o n 1 . There are no w e l l developed empirical formulae f o r t h i s region. For the purpose of c a l c u l a t i o n s , 'turbulent flow' condition w i l l be assumed. Naturally, the heat transfer c o e f f i c i e n t obtained i n t h i s way would be the upper l i m i t . V.4.2.3 Ca l c u l a t i o n of the Heat Transfer C o e f f i c i e n t i n the Non-boiling Region 35 Colburn's equation for heat transfer c o e f f i c i e n t f o r turbulent flow i n annular tubes i s S t . ( P r ) 2 / 3 ^ 0.023 (Re) °' 2 (5.1) h n b where St = Stanton number = c G P Re = Reynolds number = Pr = Prandtl number = ^- k f where a l l the symbols have the usual meaning. To account for the v a r i a t i o n i n p h y s i c a l properties due to the 35 temperature gradient, McAdams recommends that a l l the p h y s i c a l properties except c be evaluated at the average f i l m temperature of the f l u i d P defined as 76 T £ = 0.5[T + T, ] (5.2) r s b where T g = surface temperature of copper (°C) = bulk water temperature (°C). In the present case, both T and T, are v a r i a b l e s . However, for s b accuracy required i n the present c a l c u l a t i o n s , i t i s a reasonable approximation to assume s 50°C. h nb 0.023 [-^]°- 2[^-!£] 2 / 3 (5.3) c G D u G J 1 k £ p H f su b s t i t u t i n g the values and s i m p l i f y i n g , one obtains h n b » 1.15 x 10 2 c a l cm - 2 ° C 1 s e c - 1 (5.4) 46 A l t e r n a t i v e l y , Sieder and Tate suggest the following empirical r e l a t i o n s h i p to ca l c u l a t e h ^: £ * A H £ J L r l / 3 f ^ 0.14 = 0 - 0 2 3 ^ 0 . 8 5 K K. y y A l l the ph y s i c a l properties are evaluated at the average bulk temperature of the water (-40°C) except which i s evaluated at the average surface temperature of the copper (~60°C). y t 7 = 0.00469 poise . (5.6) W60°C On s u b s t i t u t i n g the values i n (5.5) and s i m p l i f y i n g , one obtains: i 77 h = 1.145 x 10 -2 c a l cm .-2o„-l C sec (5.7) nb Thus one may approximate the heat tran s f e r c o e f f i c i e n t for the -2 -2 -1 -1 non-boiling region to be = 1.15 x 10 c a l cm °C sec V.4.3 Surface B o i l i n g Region V.4.3.1 Introduction The analysis f o r the heat transfer c o e f f i c i e n t i n the surface 45 47 48 b o i l i n g conditions, i s at present, semi-empirical. ' ' In a l l cases, the analysis was c a r r i e d out for d i s t i l l e d water. The normal tap water used as a coolant i n the present experiments has a considerable amount of dissolved a i r . The s o l u b i l i t y of a i r i n water decreases with an increase of temperature. The a i r escapes i n the form of bubbles. As a r e s u l t of the increase i n the bubble population, the ag i t a t i o n of the l i q u i d caused by the motion of the bubbles i s more intense. This Increases the heat tran s f e r from the mold w a l l to the cooling water quite s i g n i f i c a n t l y . As a f i r s t step, the d i s t i l l e d water analysis w i l l be considered. The experimental data f o r forced convection without b o i l i n g can 35 be correlated by a r e l a t i o n of the type , Nu = K R e ) 4> (Pr) (5.8) Eq. (5.8) can be modified f o r nucleate b o i l i n g into the form Nu, V b = KReb) * (Pr A) (5.9) b 78 where P r 0 i s the Prandtl number of the saturated, l i q u i d ; h, i s the D b G b : nucleate b o i l i n g heat transfer c o e f f i c i e n t and Re, = i s a b \ measure of the a g i t a t i o n of the l i q u i d i n nuc l e a t e - b o i l i n g heat transfer = average bubble diameter (cm) •-1 -2 = mass v e l o c i t y of the bubbles, per unit area (g sec cm ) u = v i s c o s i t y of the l i q u i d (poise) A/ The mechanisms of bubble formation and heat t r a n s f e r are quite s i m i l a r i n nucleate and surface b o i l i n g and thus the analysis f o r nucleate b o i l i n g i s applicable for surface b o i l i n g conditions. 47 Using experimental data, Rohsenow modified eq. (5.9) by means of s i m p l i f y i n g assumptions to obtain C * ^ 7 = C f [ - ^ I *<? J 0 ' 3 3 (5.10) h f g ( P r / ' 7 S f V f g M r p v } -1 -1 where = s p e c i f i c heat of saturated liquid> BTU lb °F q/A = heat f l u x , BTU h r _ 1 f t _ 2 = latent heat of vaporization, BTU lb 1 g^ = g r a v i t a t i o n a l a c c e l e r a t i o n f t hr -3 o •= density of saturated l i q u i d , l b f t £ m -3 p v = density of saturated vapor,lb f t a = surface tension of the liquid-to-vapor interface, l b ^ f t Pr = Prandtl number of the saturated l i q u i d £ = v i s c o s i t y of the l i q u i d , ; ; l b m hr "'"ft 1 -1 79 C ^ = empirical constant which depends upon the nature of the heating s u r f a c e / f l u i d combination (C g^ = 0.013 for a water/copper combination). AT ^ = temperature excess of the heated wall over the saturated sat water temperature: (t - t ), °F w sat ' Fig . (60) gives the experimental p l o t obtained f o r (q/A) vs. AT S 3-t 47 by Rohsenow. Using eq. (5.10) f or AT = 10°C (18°F), one obtains S 3 C q/A = 1.5 x 10 3 BTU/sq.ft.hr. (5.11) However, from f i g . (60) the value i s 4 q/A = 2.2 x 10 BTU/sq.ft.hr. (5.12) Thus the (5.10) does not f i t the experimental data very accurately. F i g . (61), as plo t t e d by Rohsenow c l e a r l y shows a l l the experimental points f o r 14.7 PSIA l y i n g above those predicted by eq. (5.10). Using Engelberg-Forster and Grief's 4"' a n a l y s i s , f o r AT = 10°C S 3 . L (18°F) one obtains (q/A) = 4 x 10 4 BTU f t 2 h r 1 (5.13) F i g . (60) shows the plo t for (q/A) vs. AT obtained from S 3. t Engelberg-Forster and G r i e f ' s analysis superimposed on Rohenow's experimental data. 80 McAdams et a l . , i n t h e i r a n a l y s i s use the f o l l o w i n g expression: Cq/A) = c' A t 3 * * 5 6 (5.14) S a L where both c' and 3.86 were determined e m p i r i c a l l y as 'best f i t s ' to ; the experimental data. From the above d i s c u s s i o n i t i s very c l e a r that the p r e d i c t e d c o r r e l a t i o n s are very approximate and that the best approach i s to use 47 the experimental p l o t obtained by Rohsenow ( F i g . (60)). V.4.3.2 E f f e c t of D i s s o l v e d A i r As mentioned e a r l i e r , a l l the previous analyses were c a r r i e d out f o r d i s t i l l e d water. The e v o l u t i o n of a i r bubbles increases the heat f l u x . There i s no d e t a i l e d study made as yet which would p r e d i c t 48 the r e s u l t i n g i n c r e a s e i n heat f l u x . McAdams et a l . have e x p e r i - mentally determined the e f f e c t of d i s s o l v e d a i r on the heat f l u x ( F i g . (62)). In the present a n a l y s i s a s i m i l a r i n c r e a s e i n f l u x w i l l be assumed. The t o t a l heat f l u x i n surface b o i l i n g region = q c , .,. + ° ° n s u r f a c e b o i l i n g q . . The experimental (q/A) values used here give the t o t a l ^convection r heat f l u x f o r surface b o i l i n g . V.4.4 C a l c u l a t i o n s V.4.4.1 I n t r o d u c t i o n Figure (63) gives the p l o t f o r (q/A) vs. AT f o r both n o n - b o i l i n g and surface b o i l i n g c o n d i t i o n s . AT i n F i g . (63) i s the temperature d i f f e r e n c e between copper mold and bulk water temperature. 81 Curve 1 i n F i g . (63) represents the r e l a t i o n between (q/A) and AT for non-boiling conditions. I t i s obtained by using the value pf h = 1.15 x l C f 2 c a l c n f 2 s e c - 1 ° C _ 1 . Curve 2 represents the r e l a t i o n between (q/A) and AT for surface b o i l i n g , using d i s t i l l e d water. This p l o t was obtained from the 47 experimental data of Rohsenow. The water temperature i s assumed to be 50°C. Curve 3 gives the c o r r e l a t i o n between (q/A) and AT f o r surface b o i l i n g , using tap water (containing dissolved a i r ) . This i s drawn s i m i l a r to the experimentally obtained curve of F i g . (62). Using F i g . (63) i t i s now p o s s i b l e to c a l c u l a t e the amount of heat transferred to mold cooling water at every section. The c a l c u l a t i o n s w i l l be c a r r i e d out for Ingot No. 1. F i g . (49) gives the experimentally obtained temperature p r o f i l e on the copper mold for Ingot No. 1. The curve w i l l be subdivided i n t o three regions A, B and C as shown i n the f i g u r e . Regions A and C have non-boiling conditions whereas i n region B surface b o i l i n g i s present. V.4.4.2 Region A , The average water temperature In t h i s region = 32°C. The outside radius of copper mold = 4.45 cm. The height of the copper mold w i l l be subdivided i n t o elements 0.5 cm high and i t w i l l be assumed that each element has a constant temperature. For each element i q = h A AT i where h = 1.15 x 10 2 c a l . cm 2 s e c l o C 1 . 82 A = 2irrj, cm AT = T - 32-0,(°C) copper = 2 x 1 7 x 4 . 4 5 x 0 . 5 i / 2 = 14 cm n n Z q = h A i AT. n = 0.161 E AT. ' i 1 Region A i s 30 cm high Ci.e. 60 /\T terms) n E q = 0.161[3 x 30 + 4 x 4 + 4 x 6 + 8 x 4 + 11 x 4 + 14 x 4 i + 19 x 4 + 25 x 4 + 32 x 4 + 39 x 4] = 0.161 x 876 q. = 0.141 Kcal sec ^A V.4.4.3 Region C Average temperature of water = 50°C, height of region C = 29.0 cm. A c a l c u l a t i o n s i m i l a r to that performed for region A leads to q - 0.102 Kcal s e c " 1 V J Therefore, the t o t a l heat transferred to cooling water i n the non- b o i l i n g region = 0.141 + 0.102 = 0.243 Kcal s e c " 1 . ! V.4.4.4 Region B Average temperature of water = 50°C, t o t a l length of the region B = 16 cm. 83 In fi g u r e (63) the l o c a t i o n of the curves 2 and 3 depends upon the water temperature. The water temperature i s assumed to be 50°C, as from F i g . (57) i t i s cl e a r that the water temperature i n the surface b o i l i n g region r a p i d l y increases to 50°C and then remains approximately constant. 32 32 q 1 3 = E q. = A E h . AT. i = l i = l ; 2 where A = 14 cm . From F i g . (63), the values for hAT (= q/A) are read f o r AT of each element q,, = 14 [2 x 0.75 + 2 x 1.5 + 2 x 5 + 2 x 14 + 12 x 22.5 + 2 x 21.5 + 2 x 15 + 2 x 8 + 2 x 3 . 5 + 2 x 1.6 + 2 x 0.65] = 14 x 413.0 = 5.782 Kcal sec 1 . To t a l amount of heat given to mold cooling water = qA + qB + qC = 6.025 Kcal sec 1 From F i g . (63), i t i s clear that the present heat d i s t r i b u t i o n analysis c r i t i c a l l y depends upon the curve 3 which i s em p i r i c a l l y obtained. The following c a l c u l a t i o n s j u s t i f y the l o c a t i o n of curve 3 i n F i g . (63) . 84 (1) Knowing the cooling water flow rate and r i s e i n water temperature, i t i s possible to ca l c u l a t e the t o t a l heat accumulated by the cooling water water flow rate: 20.5 - 21 l i t r e s min 1 s p e c i f i c heat of water: 1 c a l g l o C 1 -3 density of water: 1 g cm . , A T water: 18°C q = flow rate x density x sp. heat x A T = 6.15-6.3 Kcal sec 1 for a flow rate of 20.5 and 21.0 l i t r e s min 1 r e s p e c t i v e l y . With the e x i s t i n g accuracy i n flow rate and A T measurement, the agreement with the value of 6.025 Kcal sec 1 obtained from F i g . (63) analysis appears to be very good. (2) According to the present l o c a t i o n of curve 3, the maximum h e a t f l u x going to the cooling water (near the slag/metal interface) has a value of -2 -1 (q/A) = 22.5 c a l cm sec q/A = h A T -2 -1 h A T = 22.5 c a l cm sec . In the 'copper c y l i n d e r ' experiments discussed i n Chapter IV, the value of the o v e r a l l heat transfer c o e f f i c i e n t was obtained as 1.28 x 1 0 - 2 c a l cm~ 2 oC _ 1sec" : L with A T = 1610°C q/A = 1610 x 1.28 x 1 0 _ 2 = 20.6 c a l c m - 2 s e c _ 1 . As the two values of (q/A) obtained from the two d i f f e r e n t analysis are quite close (7-8% error) one i s j u s t i f i e d i n using F i g . (63) 85 i n s p i t e of the empirical d e r i v a t i o n of the curves. V.5 A D e t a i l Analysis of the Heat D i s t r i b u t i o n i n the Laboratory ESR Unit V.5.1 Indroduction As most of the previous c a l c u l a t i o n s were done for I.N. 1, the present analysis w i l l also be c a r r i e d out for the experimental conditions of ingot no. 1. The t o t a l heat input i n t o the u n i t , as calculated e a r l i e r i s 6.65 K.cal/sec. F i g . (64) gives the possible ways t h i s heat leaves the unit. V.5.2 Heat Balance of the Slag Bed Region V.5.2.1 Heat Input As a l l the heat i s generated i n the slag bed, the t o t a l heat input i n the slag bed region = 6.65 Kcal/sec. F i g . (65) gives the heat generation d i s t r i b u t i o n i n the slag bed as calculated e a r l i e r i n thi s chapter. V.5.2.2 Heat Output V.5.2.2.1 Heat Required to Melt the Electrode Q., c a l sec 1 IA melt rate i n I.N. 1 = 3.0 cm/100 sec of electrode t r a v e l 3 81 length of the electrode melted = * Q 1 x 3.0 = 4.06 cm/100 sec. z . o l length of the electrode melted i n 1 second = 0.0406 cm. 86 Although the electrode gets heated by conduction, convection and r a d i a t i o n gradually; i n steady s t a t e , when the temperature of the electrode f a r away from the s l a g surface i s at room temperature, one can assume that 0.0406 cm length of the electrode was heated from room temperature to melting point i n one second, < Table (XVI) gives the average p h y s i c a l properties of i r o n used i n the c a l c u l a t i o n . As the data on the p h y s i c a l properties of EN 25 s t e e l was not a v a i l a b l e , the average p h y s i c a l properties of i r o n are used (except for melting p o i n t ) . Mass of the electrode melted i n one second 2 = i r r £ P = 3.36 g sec 1 Q, A = m c AT + m L IA p = 1000 c a l s e c - 1 V.5.2.2.2 Heat Lost by Radiation from the Slag Surface: Q^,cal sec 1 The heat l o s t by r a d i a t i o n from the slag surface can be sub- divided ( f i g . (66)) i n t o : Q = heat radiated to the water cooled copper mold Q = heat l o s t to a i r or gases 2B Q = heat radiated to the electrode. Q 9 has already been considered i n the heat taken up f o r heating of the electrode. 0 i s the heat c a r r i e d away by th.e a i r or the gases present. A 2B s i g n i f i c a n t part of the heat acquired by the gases i s however l o s t by 87 convection to the copper mold and the electrode. As i t i s d i f f i c u l t to c a l c u l a t e the net heat c a r r i e d away By the gases i t i s a reasonable assumption to have Q = 0.0 c a l sec \ Heat l o s t by r a d i a t i o n from the slag surface to coj>j>er mold; Q 2 A The temperature p r o f i l e on the copper mold above the slag/gas i n f e r f a c e i s known ( f i g . (49)). Q 9 can be calculated using F i g . (63) Q 2 A = 14l2 ,x 8 + 2 x 3.5 + 2 x 1.6 + 2 x 0.65] + 102.0 = 487 c a l sec V.5.2,2.3 Heat Lost to Cooling Water Across the Slag Bed: Q^, c a l sec Using F i g . (63) and F i g . (49), can be calculated s i m i l a r to • previous c a l c u l a t i o n s . Q 3 =: 14[5 x 22.5 + 2 x 21.5 + 2 x 15] = 2597.0 c a l sec 1 . V.5.2.2.4 Heat Picked up by the F a l l i n g L i q u i d Metal Drops: Q 1 T >>cal se I D Assuming that the l i q u i d metal droplets are superheated by 100°C during t h e i r descent through the slag bed, the amount of heat picked up by the droplets: Q1B = V X m X A T = 0.18 x 3.36 x 100 = 60.5 c a l sec 88 Q 4 A = Q 1 A + Q 1 B = 1 0 0 0 + 6 6 ' 5 =. 1060,5 c a l sec Although Is the heat consumed i n melting the electrode and i t s subsequent heating, i t i s not l o s t . I t enters the l i q u i d metal bed as sensible heat. Thus f o r c a l c u l a t i n g the t o t a l transferred across the slag/metal i n t e r f a c e , t h i s heat has to be considered. F i g . C67) gives a block diagram f or the heat balance of the slag region. The amount of heat leaving across the slag/metal i n t e r f a c e per second = 6650 - 487 - 2597 = 3566 c a l sec *. Amount of heat transferred across the slag/metal i n t e r f a c e by convection per second = 3566 - 1060.5 Q. = 2505.5 c a l s e c - 1 4B V.5.2.3 Heat D i s t r i b u t i o n i n the Slag Bed V.5.2.3.1 Introduction Following the c a l c u l a t i o n of the heat balance for the e n t i r e slag bed, i t i s i n t e r e s t i n g to see how the heat i s d i s t r i b u t e d i n the various regions of the slag bed. The slag bed can be subdivided into two regions, above and below the electrode t i p . 89 V.5.2.3.2 Heat Balance of the Region Above the Electrode Tip Consider the heat balance of region AJKB (Fig. (65)). Heat Input: + Q Q + Q £ + heat generated i n the cathodic p o l a r i z a t i o n = 400 + 1485 + 665 + 137 = 2687 c a l s e c . 1 . Heat Output: Q = 1000 c a l s e c " 1 Q 2 A = '487 c a l s e c " 1 = heat going to -mold cooling water across the slag bed = 1412 x 15 + 2 x 21.5 + 22.5] = 1337.0 c a l sec 1 T o t a l heat output = 1337 + 1000 + 487 = 2824 cal sec 1 Amount of heat obtained by t h i s region from the lower region JKCD by convection = 2824 - 2687 = 137 c a l sec 1 . V.5.2.3.3 Heat Balance o f the Region Below the E l e c t r o d e T i p Heat In p u t : Q + Q + heat g e n e r a t e d i n a n o d i c p o l a r i z a t i o n = 1720 + 2160 +137 = . 4017 c a l s e c " 1 Heat Output: Q^^ = heat g o i n g to mold c o o l i n g water a c r o s s the s l a g bed = 14[4 x 22.5] = 1260 c a l sec 1 . 90 Q = heat required to super heat the f a l l i n g l i q u i d metal IB drops by 1 0 0 ° C = 6 0 . 5 c a l sec" 1 heat transferred to AJKB region by convection = 137 c a l sec 1 T o t a l heat output = 1 2 6 0 + 6 0 . 5 + 1 3 7 = 1 4 5 7 . 5 c a l sec 1 heat transferred by convection across the slag/metal i n t e r f a c e = 4 0 1 7 - 1 4 5 7 . 5 = 2 5 5 9 . 5 c a l s e c " 1 . - 1 The diffe r e n c e of 5 4 . 0 cal sec observed i n the two analyses, i s the error involved i n the heat input d i s t r i b u t i o n analysis. V . 5 . 3 Approximate C a l c u l a t i o n of the Heat Transfer C o e f f i c i e n t Across the L i q u i d Slag-Liquid Metal Interface The amount of heat transferred across the l i q u i d s l a g - l i q u i d metal i n t e r f a c e - 2 5 0 0 c a l sec 1 q = h.A.AT 2 2 where A = irr = 5 0 cm Assuming ( 1 ) uniform heat transfer c o e f f i c i e n t across the section; (2 ) uniform temperature i n the slag and metal bath across the e n t i r e cross s e c t i o n at the slag/metal i n t e r f a c e , one can write q 2 5 0 0 . - 2 - 1 hAT =. jJ- = i _ Q = 5 0 c a l cm sec r If AT = temperature diffe r e n c e between l i q u i d slag and metal = 2 5 - 5 0°C 91 h = 1 r- 2 c a l cm 2°C ''sec \ V.5.4 Heat Balance of the L i q u i d Metal Region F i g . (68) gives the block diagram f o r the heat balance of the l i q u i d metal region. Heat, Input: Q 4 = Q^A + Q^B = 3566.0 c a l sec 1 , Heat Output: The amount of heat going to mold cooling water across CN = Q 5 = 1417 -x 22.5 + 1 -x 14] = 2401 c a l sec \ Heat leaving the section ON downwards Q 9 = Q 4 " Q 5 = 3566.0 - 2401.0 = 1165.0 c a l sec V.5.5 Heat Balance of the S o l i d i f i e d Ingot Region F i g . (69) gives the block diagram f o r the heat balance of t h i s region. V.5.5.1 Heat Input: Q g = 1165.0 cal/sec V.5.5.2 Heat Output: 7.5.5.2.1 Heat Going to Mold Cooling Water; Qg-, c a l s e c " 1 Q, 1412 x 0.75' + 2 x 1.5 + 2 3 5 + 1 x 14] + 141 o = 540 c a l sec 1 . V.5.5.2.2 Heat Going to Base Plate Cooling Water: F i g . (58) gives the experimentally obtained temperature p r o f i l e s with respect to slag/metal i n t e r f a c e p o s i t i o n for two thermocouples locate at the base of the ingot, known distance apart. k A Q 7 = — - AT 7 Ax where k = average • thermal conductivity of i r o n = 0.075 c a l cm"" 1sec" l oC~ 1 2 A = cross s e c t i o n a l area = 34.4 cm Ax = distance between the two thermocouples = 1 cm The present heat balance i s c a r r i e d out a f t e r a s i g n i f i c a n t amount of ingot has been formed. Therefore the value of AT = difference i n temperature between the two thermocouples = 160°C. A 34.4 x .075 . Q7 = I7o X 1 6 0 = 410 c a l sec V.5.5.2. 3 Sensible Heat Retained by the Ingot: Q_ o Under steady state conditions, a l l the heat supplied i n the slag region i s taken away by the mold and base plate cooling water except that which i s retained i n the s o l i d i f i e d ingot as sensible heat. The sensible heat of the escaping gases i s neglected i n the present analysis. Amount of heat retained as sensible heat by the ingot/sec = Q. <8 = mass of ingot formed per sec x C x AT P where AT = average temperature of the ingot 93 Q 8 = 3.36 x 0.16 x AT = 0.538 x AT c a l s e c " 1 . The value of AT i s unknown and one must make a reasonable estimate. Assuming AT = 750°C Q„ = 0.538 x 750 o Qg = 404 c a l sec 1 . V.5.5.2.4 T o t a l Heat Output The t o t a l heat output = Q & + 0 ? + Q g = 540 + 410 + 404 = 1354 c a l sec \ The difference i n heat input and output values i s only 188.5 , -1 c a l sec With the various approximations and assumptions made, a difference of 188.5 c a l sec 1 for a t o t a l heat input of 6650 c a l sec 1 i s less than 3% and th i s i s w e l l within the accepted l i m i t s . V.5.6 Heat Balance for Ingot Nos. 1, 10 and 16 Table X I gives the heat balance f o r ingots made with d.c. negative, d.c. p o s i t i v e and a.c. p o l a r i t i e s . V.6. Discussion V.6.1 Comparison of the D i f f e r e n t E l e c t r i c a l Configurations As mentioned e a r l i e r , there has been a considerable disagreement between d i f f e r e n t workers on the e f f i c i e n c y of the ESR process for 94 Table XI. Heat balance for ingot no. 1, 10 and 16 Ingot No. 1 10 16 Melt rate 3.36 2.58 3.50 -1 g sec X 1.5 0.4 0.25 Dimensions Y 1.0 1.6 0.85 (cm) ref e r F i g . (64) Z 4.5 4.5 3.1 A 2.5 0.75 0.5 B !-5 2.00 2.5 Heat Input 6650 5100 4800 . -1 c a l sec Heat Output 1060.5 785 1110 ( c a l sec 1) % 15.6% 15.50% 23.3% C>2A ( c a l sec "S 487 738 637.2 % 7.15% 14.5% 13.4% ( c a l sec "*") 2597 2606 1872.5 % 38.0% 51.4% 39.4% ( c a l sec 1) 3566.0 1756 2290 % 52.3% 34.6% 48% 95 table XI. '(Continued) Ingot No. 10 16 Q 4 A ( c a l sec 1) 1060.5 785 1110 15.6% 15.5% 23.3% Q 4 B ( c a l sec ) 2505.5 971 1180 36.7% 19.10% 24.7% Q,. ( c a l sec "*") 2401 704 1081.5 35.1% 13.7% 22.6% ( c a l sec "*") 6 540 316 333 7.8% 6.2% 7.0% ( c a l sec ) 410 410 410 6.1% 8.10% 8.7% Qg ( c a l sec *) 404 310 420 5.85% 6.1% 8.9% 96 d i f f e r e n t e l e c t r i c a l configurations. The e f f i c i e n c y of the process i s usually expressed i n terms of the amount of metal remelted per KWH. Using the a v a i l a b l e experimental data, an attempt i s made here to explain the observed di f f e r e n c e s . 3 6 There are 9 possible d i f f e r e n t types of e l e c t r i c a l configurations. Cl) d.c. with electrode as the negative pole (commonly referred to as d.c. negative). (2) d.c. with electrode as the p o s i t i v e pole (commonly ref e r r e d to as d.c. p o s i t i v e ) . i(3) a.c. Each of these can have the mold (a) insulated from the ingot or (b) f l o a t i n g or (c) connected to the ingot (referred to as ' l i v e ' ) . F i g . (42) gives the schematic diagrams f o r the d i f f e r e n t arrangements. In the present set of experiments, the remelting of the ingots was c a r r i e d out with the process parameters ( i . e . , voltage, current and melt rate) so adjusted, as to achieve stable operating conditions. An attempt was made to maintain approximately the same melt rate f o r the d i f f e r e n t e l e c t r i c a l configurations under s i m i l a r conditions. However i n cases where the process became unstable while attempting a constant melt rate, the process parameters were so adjusted as to achieve stable remelting conditions. Ingots 1, 10, 13 and 16 can be compared to study the e f f e c t of e l e c t r i c a l configuration. Attempt was made here to achieve a constant melt rate of approximately 3.4-3.5 g sec * (30 mm of electrode t r a v e l f o r every 100 seconds). This was achieved i n both d.c. negative and a.c. In the present set of experiments, the voltage was kept approximately \ 97 constant (20-24 v o l t s ) . I t was observed that to achieve a s i m i l a r melt rate, i t was necessary to maintain a s i m i l a r gap (= 2.0 cm) between the electrode t i p and the slag/metal i n t e r f a c e i n the two cases. As discussed e a r l i e r , f or the same slag and s i m i l a r geometry, the working resistance of the d.c. -ve operation slag i s 35% l e s s than the a.c. case. This i s due to the presence of the dissolved calcium and aluminum i n the s l a g . This r e s u l t s i n a higher current input i n the d.c. -ve configuration as compared to a.c. (1150 amp for d.c. -ve and 850 amp for a . c ) . It i s now possible to explain the observed deep c y l i n d r i c a l portion of the l i q u i d metal pool i n d.c. negative configuration (Fig. (80), F i g . (84)). To maintain a dynamic steady state, i t i s necessary to remove the extra heat introduced i n the slag bed i n the d.c. negative case. I t has been shown e a r l i e r that the amount of heat transferred to the mold cooling water across the l i q u i d slag bed i s quite i n s e n s i t i v e to the extent of heat produced i n the slag bed. Thus the extra heat produced i s transferred to the mold cooling water by maintaining a deep c y l i n d r i c a l portion of the l i q u i d metal pool which has a good surface contact with the mold. It was found that i n both d.c. p o s i t i v e with mold ' f l o a t i n g ' and ' l i v e ' , i t was not possible to achieve the desired melt rate of 2=3.4 g sec 1 under stable working conditions. On examining the extent of electrode immersion i t was found that for the stable working of the unit i t was necessary to maintain a larger gap between the electrode t i p and slag/metal i n f e r f a c e (2.6 cm f o r ingot no. 10 and 2.3 cm for ingot no. 13). The t o t a l power input was also correspondingly l e s s . Thus.the low melt rate (=2.58 g sec "*") obtained was a r e s u l t of the low power 98 input and the large gap between the electrode t i p and the slag/metal i n t e r f a c e . The necessity of maintaining these to obtain stable working conditions can be explained as follows. F i g . (70) gives the ESR unit's analog c i r c u i t . Table IV gives the experimental r e s u l t s and the values of the various resistances as 36 calculated by Cameron et a l . There are two paths f o r the flow of current i n F i g . (70) (1) electrode l i q u i d slag ingot (working resistance) (2) electrode -*- mold -> ingot. The magnitude of the current following i n each c i r c u i t depends on the r e l a t i v e values of the resistances R^, R^ and R^. Resistances R^ and R^ are i n ser i e s and they together are i n p a r a l l e l with R^. In the case of d.c. p o s i t i v e with mold f l o a t i n g , the p o t e n t i a l 36 on the mold was experimentally determined as =18 V (Table XII). The flow of current i s as shown i n F i g . (70a). The observed value of 18 v on the mold can be explained. Under stable working conditions the electrode i s not s i g n i f i c a n t l y immersed i n the slag bath. The temperature at the slag/gas i n t e r f a c e i s quite high. The value of the resistance R^ i s quite low as new slag skin i s continuously formed at the slag/gas i n t e r f a c e having a momentary low value of resistance. The voltage drop of 5 v o l t s occurs mostly i n the slag bath between the electrode and the slag skin as shown i n Chapter I I . Table IV gives the calculated values of R^, and R^. There i s thus a considerable p o t e n t i a l difference between the mold and the ingot. Arcing would occur between the mold and the ingot Table XII. Experimental r e s u l t s f o r the insulated mold unshunted and shunted to ground through 0.5 ohm r e s i s t o r Ingot Slag Applied Electrode Mold Unshunted Mold P o t e n t i a l Shunted Slag s k i n Size System Voltage P o l a r i t y P o t e n t i a l Current 1/2 shunt to Current Average -thickness ground 2" 2" CaF 2 CaF 2 + CA 23.7 24.5 -ve -ve 22.4 21.9 672 688 20.5 20.1 704 720 0.U40" 0.025" 2" CaF 2 + CA 22.8 +ve 19.0 640 15.4 710 D.035" 3" 3" CaF 2 CaF 2 + CA 22.5 22.8 -ve -ve 18.7 20.6 1 220 1 200 17.3 18.6 1 300 1 265 0.040" 0.030" 3" CaF 2 + CA 22.5 +ve 17.0 1 200 16.1 1 240 0.035" 100 i f s i g n i f i c a n t amount of current flows through v i a path 2, To avoid t h i s , the value of should be maintained high. The existence of a deep c y l i n d r i c a l portion of the l i q u i d metal pool r e s u l t s i n a low value of R^. Thus to achieve stable working conditions, the working para- meters are so adjusted as to avoid the existance of a deep c y l i n d r i c a l portion of the l i q u i d metal pool. This i s achieved by maintaining a larger gap between the electrode t i p and the slag metal i n t e r f a c e r e s u l t i n g i n lower power input and hence a lower melt rate. If the argument put forward here i s true then f o r the d.c. p o s i t i v e case with insulated mold, i t should be possible to achieve a melt rate comparable to a.c. and d.c. negative configurations. The mold was insulated by coating the in s i d e surface of the mold with boron n i t r i d e paste and allowed to dry. Comparing FVE ingots 25, 28, 29, 31 s 32 i t i s found that the melt rates are comparable. In the case of d.c. p o s i t i v e with l i v e mold, as the ingot and the mold are connected, they are both at the same p o t e n t i a l (= 0 v o l t s ) with R^ = 0 ohms. The p o t e n t i a l difference between the mold and :the electrode i s 23.0 v o l t s . As the value of R^ i s quite low, s i g n i f i c a n t portion of the current goes to the mold (as much as 80% as shown i n F i g . (46)). The e f f e c t of the h o r i z o n t a l current component on the magnetohydrodynamics of the region i s not yet c l e a r , but i s outside the scope of the present work. Metal drops are drawn towards the mold by the h o r i z o n t a l current component and are embedded i n the slag skin. Continuous arcing occurs between the mold and the slag bath and i s unavoidable. The melt rate i s low as the current going to the mold i s not e f f e c t i v e l y used to heat the slag bath. f 101 In the d.c. negative case with mold f l o a t i n g , i t was found that the mold had a p o t e n t i a l of 21 v o l t s . This i s expected since the value of i s low due to the existance of a deep c y l i n d r i c a l portion of the l i q u i d metal pool. There i s thus a s i g n i f i c a n t p o t e n t i a l difference between the electrode and the mold. To avoid arcing between the mold and the slag , the value of R^ i s maintained high. This i s achieved by maintaining the electrode deeply immersed i n the slag bath (2.5 cm i n ingot no. 1). This decreases the temperature at the slag/gas i n t e r f a c e r e s u l t i n g i n a thicker slag skin at the slag/gas i n t e r f a c e . Comparing the values of R^, R 2 and R^ (Table IV) i t i s seen that the value of R^ i s maintained high (0.7 ohms) for d.c. negative as compared to d.c. p o s i t i v e (0.15 ohms). The value of R^ on the other hand i s low f o r d.c. negative (0.1-0.2 ohms) as compared to d.c. positive; (0.4- 1. 0 ohm). As there e x i s t s , only a s l i g h t p o t e n t i a l difference between the, mold and ingot i n d.c. negative with mold ' f l o a t i n g ' , there i s no s i g n i f i c a n t difference observed between operations using d.c. negative with ' f l o a t i n g ' mold and ' l i v e ' mold configurations. In the case of insulated mold, as there i s no problem of mold-slag arcing, i t i s possible to operate having the electrode only s l i g h t l y immersed i n the slag bath. Measurement of the current flowing through the circuit,electrodes- mpld-^ingot for a.c. with mold ' f l o a t i n g and ' l i v e ' has shown that only a very small f r a c t i o n of the t o t a l current flows through t h i s c i r c u i t . This i s expected since the slag skin i s always thick i n operations using a.c. mode thereby maintaining a high value for both R.. and R~., 102 V.6.2 E f f e c t of the Electrochemical and Chemical Reactions In the e l e c t r o s l a g remelting of FVE electrodes, M i t c h e l l and 12 Beynon have shown that the following electrochemical reactions occur at the two poles using CaF2~25 wt.% Al^O^ slag. Reactions at the cathode (1) A l + 2e y A l (2) Al"1"4"*" + 3e y A l (5.15) (3) Ca 4 4" + 2e y Ca Reaction at the anode (1) Fe y Fe 4 4" + 2e In the case of remelting of EN 25 s t e e l , the following reactions also may occur at the anode Cr y Cr 4 4" + 2e +++ Cr >- Cr + 3e (5:16) Mn >• Mn 4 4 + 2e S i y S i + 4e etc... In the e l e c t r o - p o s i t i v e configuration, the anodic reactions occur at the electrode, i . e . Fe, Cr, Mn, etc. are oxidized at the electrode. At the ingot surface, the cathodic reactions (reduction of A l ' I | and Ca ) occur. The anodic reaction product, due to convection and 103 higher density, comes i n contact with the cathodic reaction product and reduction of Fe, Cr, Mn, etc. occurs A l + Fe — —>• Fe Ca C r 4 4 4 Cr A l + S i 4 + S i Mn Mn (5.17) There i s no net change i n the slag composition i f the hack reaction (5.17) i s complete. However i t i s found that t h i s reaction does not go to completion, r e s u l t i n g i n a net change of the slag composition. Table (VI) gives the analysis of the ingot and the electrode compositions. I t can be seen that remelting with d.c. p o s i t i v e always r e s u l t s i n the loss of the a l l o y i n g element chromium (reduced from 0.7 wt.% to = 0.2 wt.%). This i s due to the incompletion of reaction (5.17). As the oxidation i s electrochemical i n nature, i t does not depend upon the atmosphere present. i In the ESR remelting using d.c. negative, the s i t u a t i o n i s quite I | I I I d i f f e r e n t . At the electrode, the cathodic reduction of Ca and A l occurs. As the l i q u i d metal i s present on the electrode i n the form of a t h i n f i l m , the reduced aluminum i s very e f f e c t i v e l y dissolved i n the l i q u i d metal before i t f a l l s down as a droplet. At the ingot s i t e , the anodic oxidation of Fe, Cr, Mn, S i , etc. occurs. However, as the aluminum i s dissolved to a considerable extent i n the l i q u i d metal, , the back reaction (5.17) occurs very e f f e c t i v e l y . There i s thus p r a c t i c a l l y no change i n the slag composition. Here i t was assumed that an argon atmosphere prevail e d over the slag to avoid atmospheric 104 oxidation of the reduced A l and Ca. The ESR remelted ingots under argon using d.c. negative configuration show no loss of a l l o y i n g elements as can be seen from Table (VI). In ESR processing i n a i r using d.c. negative configuration, i t i s found that there i s a loss of the a l l o y i n g element chromium on remelting. This can be e a s i l y explained. 9 Etienne has shown the existance of the convection patterns i n the slag at the s l a g / a i r i n t e r f a c e of the type which may suggest that a s i g n i f i c a n t amount of the electrochemically reduced A l and Ca has an opportunity to become reoxidized by.the atmospheric oxygen. This oxidation prevents the e f f e c t i v e reduction of the anodic product at the ingot r e s u l t i n g i n the loss of a l l o y i n g element chromium (reduced from =0. 7 wt. % to =0.2 wt. % ) . 12 It i s proposed by M i t c h e l l and Beynon that i n the a.c. e l e c t r o s l remelting of pure i r o n (FVE), reaction (5.18) occurs at both the ingot Fe ~ * Fe"*-1" + 2e (5.18) and electrode surfaces. More experimental data i s needed to draw any ; d e f i n i t e conclusions regarding the e f f e c t of the atmosphere i n t h i s configuration. V.6.3 E f f e c t of P o l a r i t y on the Slag Skin Thickness I t i s i n t e r e s t i n g to study the e f f e c t of the p o l a r i t y on the: thickness of the slag skin. F i g . (71) and (72) show pictures of the v e r t i c a l section of the slag cap and the slag skin formed. 105 It i s observed that i n the remelting of pure i r o n (FVE) using d.c. p o s i t i v e (both a i r and argon) and d.c. negative ( a i r ) , the slag skin i s extremely t h i n . There i s also a considerable amount of i r o n oxide at the bottom of the slag cap. The above observations can be explained i n terms of the electrochemical and chemical reactions discussed e a r l i e r . In a l l the three cases, the back reaction (5.17) does not occur very s i g n i f i c a n t l y . This builds up the iron-oxide content i n the slag bed. This iron-oxide attacks the alumina r i c h slag skin and dissolves i t - p a r t i a l l y , forming a low melting e u t e c t i c . This r e s u l t s i n a t h i n slag skin. This can also be v a r i f i e d from the experimental data of Table (V). I t i s observed that d.c. p o s i t i v e (argon and a i r ) and d.c. negative (air) melts have a thicker slag cap a f t e r remelting approximately the same length of the electrode. In remelting EN 25 s t e e l , the presence of chromium oxide prevents the formation of lower melting e u t e c t i c . The slag skin i s therefore not very t h i n . V.6.4 C o r r e l a t i o n and P r e d i c t i o n of Operating Parameters for E l e c t r o s l a g Processing In industry, very often, large scale ingots have to be made without carrying out t r i a l runs to e s t a b l i s h the working conditions. One i s therefore interested i n knowing the approximate process parameters ( i . e . current, voltage and melt rate) f o r remelting these large scale ingots. An attempt i s made here to predict these process parameters f o r the i n d u s t r i a l scale ingots from the av a i l a b l e laboratory and i n d u s t r i a l data. 106 On observing the temperature p r o f i l e s on the mold f o r the Y a ri° u s e l e c t r i c a l and geometrical configurations (Fig, (49) to F i g . (56)), i t i s c l e a r that the temperature p r o f i l e s on the mold and hence the amount of heat going to the mold cooling water per unit area does not depend upon the e l e c t r i c a l and the geometrical configurations. I t i s thus possible to assume an approximate temperature p r o f i l e on the mold and c a l c u l a t e the heat input f o r any i n d u s t r i a l scale ingot. Appendix (IV) gives the d e t a i l c a l c u l a t i o n of the power requirement for a 61 cm (24 inches) diameter ingot. The melt rate depends upon the following parameters: (1) slag composition (2) electrode composition (3) e l e c t r i c a l configuration (4) atmosphere (5) diameter of the electrode (6) diameter of the ingot (7) distance between the electrode t i p and the slag/metal i n t e r f a c e . 49 50 Empirical equations are a v a i l a b l e i n l i t e r a t u r e ' giving the dependence of the melt rate on the power input, electrode diameter etc. 49 K l e i n gave the following empirical equation to f i t h i s experimental data f or Hastelloy X ingots R = -2.64 + 0.473 D + 0.391 x 1 0 _ 3 I + 0.689 x 10 _ 1E - 0.0558S (5.19) where R = melt rate (lb min "*") D = electrode diameter (inches) 107 1 = current (amperes) E = voltage (volts) S = slag weight (lbs) The equation (error + 20%) was only v a l i d f or a narrow range of ingot s i z e s . 50 Sun and Pridgeon arr i v e d at the following empirical equation: R = 0.3 E^ + 1.57 x 1 0 _ 3 I - 0.18 S„ - 1.167 (5.20) where R = melt rate ( f t hr "*") E D = ingot diameter (inches) I = current (amperes) S = slag weight ( l b s ) . The above.equation was v a l i d f or (1) 2.75 < E^ < 4.25, (2) 1.85 < I x 10~ 3 < 3.0, (3) 7.0 < S < 9.3 ranges. Present analysis The melt rate can be correlated to the other process parameters i n the following manner M.R a V d f (5.21) D ea/D) t where M.R = melt rate (g sec "*") V = applied voltage (volts) -3 I = current x 10 (amperes) d = diameter of the electrode (cm) D = diameter of the ingot (cm) I = distance betweeen the electrode t i p and the slag/metal i n t e r f a c e (cm). 108 For an approximate c o r r e l a t i o n , one can assume a= b = f e 1.0 and c = e =2.0. Relation (5.21) reduces to 2 M.R a "V_I_d ( 5 > 2 2 ) Or D 2 (A/D) 2 V I d M.R = constant D2 a/D) z - ( 5 - 2 3 ) D (£/D)MR where Z i s a constant. The value of Z depends upon the slag composi- t i o n , electrode composition, e l e c t r i c a l configuration and the atmosphere. Before going i n t o the d e t a i l s of e s t a b l i s h i n g the v a l i d i t y of equation (5.23), the general form of the equation w i l l be discussed. The units of the constant Z are K c a l g *. Thus onawould expect a higher value for Z, higher the melting point of the material being remelted. In equation (5.23) i t i s proposed that, the other parameters remaining constant, the melt rate i s proportional to the square of the electrode diameter. As most of the heat necessary to melt the electrode i s transferred to the electrode by convection, i t i s l o g i c a l to expect the melt rate to be proportional to the c r o s s - s e c t i o n a l area of the electrode. The c o r r e l a t i o n that the melt rate i s i n v e r s e l y proportional to 109 the square of the ingot diameter can be q u a l i t a t i v e l y j u s t i f i e d . Keeping a constant (d/D) r a t i o , an increase i n the diameter of the ingot by a factor of 2 r e s u l t s i n a s i m i l a r increase i n power input. This i s j u s t i f i e d since most of the heat leaves the ESR unit through the side walls of the mold to the mold cooling water. The increase i n surface area of the mold wall i s proportional to the diameter of the ingot. However as some heat also leaves through the mold bottom, an increase i n the diameter of the ingot by a factor of 2, keeping the (d/D) r a t i o constant w i l l r e s u l t i n an increase i n the power input and hence the melt rate by a f a c t o r of 2.0 to 2.2. F i g . (73) gives the experimentally obtained c o r r e l a t i o n between, the melt rate and the ingot diameter by Holzgruber et a l . From F i g . (73) one can see that an increase i n the diameter of the ingot from 15 inches to 30 inches, r e s u l t s i n an increase i n the melt rate from 800 lbs h r " 1 to 1700 lbs h r " 1 . The e f f e c t of the l o c a l i z e d heat input on the melt rate i s included i n the equation (5.23) by the c o r r e l a t i o n that the melt rate i s i n v ersely proportional to (&/D). Decreasing the distance l o c a l i z e s a s i g n i f i c a n t portion of the t o t a l heat input .in the narrow region between the electrode t i p and the slag/metal i n t e r f a c e , r e s u l t i n g i n an increase i n the melt rate. The v a l i d i t y of equation (5.23) i s checked (error + 10%) against the a v a i l a b l e laboratory and i n d u s t r i a l experimental data. A l l the laboratory experiments were c a r r i e d out using CaF2^25 wt.% A^O^ slag. Tables XIII and XIV give the calculated values of Z for the d i f f e r e n t ingots. 110 Table XIII. Calculated values of Z for the laboratory made ingots Ingot no. P o l a r i t y Atmosphere Electrode material (cm) (Kcal g 1 ) 1 2 3 4 5 6 7 8 10 11 12 13 14 15 16 17 18 20 25 26 - r v e -ve -ve -ve -ve -ve -ve -ve +ve +ve +ve +ve l i v e +ve l i v e a. c. a.c. a. c. a. c. -ve -ve -ve Argon A i r A i r I III Argon Argon II Argon II Argon Argon Argon Argon A i r III II II Argon III Argon II Argon Argon A i r III II Argon Argon II Argon A i r II EN 25 EN 25 EN 25 EN 25 EN 25 EN 25 EN 25 EN 25 EN 25 EN 25 EN 25 EN 25 EN 25 EN 25 EN 25 EN 25 EN 25 AISI 630 FVE FVE 2.0 2.0 3.0 2.0 2.0 1.5 1.8 2.6 2.6 2.8 2.6 2.3 1.4 1.8 1.9 1-7 1.6 2.0 1.6 1.6 2.28 1.7 1.81 2.46 3.36 3.42 2.35 1.8 1.585 1.52 1.56 2.32 3.08 1.48 1.50 1.65 1.49 2.26 3.16 4.15 I l l Table XIII. (Continued) Ingot P o l a r i t y Atmosphere Electrode £ Z -1 no. material (cm) (Kcal g ) 27 +ve A i r FVE 1.6 3.10 28 +ve A r g o n 1 1 FVE 1.3 3.19 (BN ins) 29 +ve A r g o n 1 1 FVE 1.7 3.33 (BN ins) 30 +ve A r g o n 1 1 FVE 1.7 4.12 l i v e 31 a.c. Argon 1 1 FVE 1.2 2.86 32 a.c. A r g o n 1 1 FVE 1.1 3.12 (BN ins) Table XIV. Calculated values of Z for i n d u s t r i a l ingots Ingot Mold Electrode Electrode P o l a r i t y Power Melt rate £/D Z no. diameter diameter Composition input , -1. ( v , -1 (cm) (cm) (Kwatts) ^ 8 S 6 C ' ^ K C a l S I I 5 1 30.5 15.25 1020 a.c. 240 24 =0.262 2.3 I 2 5 1 30.5 22.8 1020 a.c. 240 50.5 =0.262 2.46 AQ 13 20.3 15.25 Hastelloy a.c. 66 19.4 =0.30 1.53 X 14 60.96 45.72 EN 25 a.c. 760 258: =0.24 1.65 15 60.95 4.1.57 EN 25 a.c. 720 157 =0.24 1.65 113 (1) To study the e f f e c t of the electrode composition one can compare the ingots (5), (20) and (26). . As expected, the ingot (26) with the highest melting point (1539°C) has the highest value of Z. The values of Z calculated for i n d u s t r i a l ingots also show a s i m i l a r pattern. (2) To study the e f f e c t of the ingot diameter, one can compare the ingots (3) and (8),and (4) and (7). The calculated values of Z are 2 very s i m i l a r , thereby e s t a b l i s h i n g the r e l a t i o n s h i p R a 1/D . (3) Comparing the ingots (2) and (3) to study the e f f e c t of the electrode diameter, the distance between the electrode t i p and the slag/metal i n t e r f a c e i t i s seen that the calculated value of Z i n both the cases i s approximately the same. The AISI 1020 ingots II and 12 (Table XIV) also show a s i m i l a r value f o r Z for d i f f e r e n t (d/D) r a t i o s . (4) On comparing the ingots having the same composition but : d i f f e r e n t e l e c t r i c a l configuration and atmosphere, i t i s seen that except f o r the d.c. negative with argon and d.c. p o s i t i v e l i v e (both with a i r and with argon) configurations, a l l have approximately the same value of Z (Z - 1.65 for EN 25 and Z - 3.0 for FVE). An attempt i s made here to explain the observed behaviour. In d.c. p o s i t i v e ' l i v e ' configuration, as shown by F i g . (46), a s i g n i f i c a n t portion of the current goes to the mold w a l l . This portion of the t o t a l current i s not e f f i c i e n t l y u t i l i z e d i n the heating the slag bath. The current density below the electrode t i p i s also r e l a t i v e l y low. As a r e s u l t , the temperature of the slag i n the v i c i n i t y of the electrode i s not very high. The melt rate i s thereby reduced, and the value of Z increased. 114 In remelting with d.c. having the electrode as negative pole, the presence of the argon atmosphere prevents the oxidation of the A l and Ca at the slag/gas i n t e r f a c e . The n o n - a v a i l a b i l i t y of the heat of oxidation i n the v i c i n i t y of the electrode r e s u l t s i n a lower melt rate and an increase i n the value of Z. . j In the d.c. p o s i t i v e configuration, both with a i r or argon, the electrode i s s i g n i f i c a n t l y more po l a r i z e d than the d.c. negative configuration. However i n the laboratory scale ingots, the extra heat l i b e r a t e d at the electrode surface i n the d.c. p o s i t i v e due to the ., higher p o l a r i z a t i o n i s compensated i n the d.c. negative i n a i r config- uration by the exothermic heat of oxidation of A l and Ca at the s l a g / gas i n t e r f a c e . This r e s u l t s i n both configurations having approximately the game value of Z. In remelting larger scale ingots however, d.c. negative i n a i r would have a lower value of Z. The increase i n the electrode s i z e , decreases the current density on the electrode thereby decreasing the r e l a t i v e contribution by the p o l a r i z a t i o n i n the d.c. p o s i t i v e configuration. In remelting s t e e l s using a.c. (- 50 cycles) there i s no c o n t r i - bution by p o l a r i z a t i o n or oxidation. However, due to the higher e f f e c t i v e slag resistance (because of the absence of dissolved Ca or Al) i t i s possible to achieve a l o c a l i z e d heat generation (by reducing the value of £) i n the slag bed. This r e s u l t s i n a s i m i l a r value for Z as i n d.c. negative i n a i r or d.c. p o s i t i v e (insulated). P r e d i c t i o n of the Melt Rate It i s possible to approximately predict the melt rate for large scale ingots from the a v a i l a b l e experimental data. 115 For a 60.95 cm (24 inches) diameter ingot of EN 25 (d/D = 0.75; ingot 14, Table XIV), the value of the melt rate i s obtained,using the approximate power input calculated i n Appendix (IV) and the average value of Z for EN 25 s t e e l of 1.65. Substituting the values of the various parameters i n equation (5.23) y i e l d s a value for the melt rate of =258 g sec 1 . To compare the predicted values of the melt rate with the 6 experimentally obtained values by Holzgruber et a l . , melt rate i s calculated for a 60.95 cm diameter ingot (15) of EN25 with d/D =0.6 (Fig. (73) data i s f o r d/D = 0.6) using the approximate power input calculated i n Appendix IV). A melt rate of 157 g sec 1 i s calculated as compared to 177 g sec 1 (1400 lb hr 1) obtained experimentally. The c o r r e l a t i o n appears reasonable, considering the various approximations involved. Secondly F i g . (73) i s obtained b a s i c a l l y from data on highly alloyed s t e e l s . As shown e a r l i e r , lower melting compositions have a smaller value of Z and hence a higher melt rate. 116 CHAPTER VI PREDICATION OF POOL VOLUMES IN ESR INGOTS VI.1 Introduction One of the main advantages claimed by e l e c t r o s l a g melting technique i s the improvement of the ingot structure. The manner by which an ingot would s o l i d i f y depends upon the mode of heat ext r a c t i o n . The l i q u i d metal pool p r o f i l e which i s co n t r o l l e d by the rate and mode of heat extra c t i o n , i s a good i n d i c a t o r of the manner i n which the ingot would s o l i d i f y . Consider the two extreme cases as shown i n F i g . (74). A high melt rate i s generally characterized by a deep l i q u i d pool. As the dendrites grow perpendicular to the i n t e r f a c e , a higher melt rate r e s u l t s i n a r a d i c a l o r i e n t a t i o n of the dendrites. This i s not favoured for subsequent working. On the other extreme, a very slow melt rate r e s u l t s i n a f l a t l i q u i d pool having s i g n i f i c a n t microsegre- gation due to larger d e n d r i t i c arm spacing. Thus one would l i k e to haye an optimum shape of the l i q u i d pool. The pool volume of an ESR ingot can be subdivided i n t o two d i s t i n c t regions as shown i n F i g . (75). Besides the shape of the curved portion of the l i q u i d pool, i t i s important to have an optimum height for the c y l i n d r i c a l portion of the pool volume. In i n d u s t r i a l scale ingots 117 t h i s height i s about 10-15 cm.• This i s necessary to achieve a good surface q u a l i t y f or the ingot, If the process i s stopped suddenly a f t e r a desired length of the ingot i s made, the l i q u i d metal volume present at the time of shut o f f would s o l i d i f y i n the conventional manner i . e . , with equiaxed structure i n the centre. As the ESR process i s generally used f o r r e f i n i n g expensive a l l o y s , i t i s not economical to r e j e c t the l a s t 10-15 cm of the ingot every time. In industry, t h i s i s overcome by adopting the p r a c t i c e of 'hot topping'. The power and feed rate are gradually reduced towards the end, so that the c y l i n d r i c a l portion i s reduced to a minimum and then the process i s stopped. : I t . i s quite important from t h i s point of view to know the exact pool volume for a normal set of working conditions. Now that the ESR process i s accepted i n the industry as a batch_ process, e f f o r t s are being made to make i t continuous; s i m i l a r to; ' continuous casting. In designing the copper mold f o r the continuous: process, i t i s necessary to know the volume of the l i q u i d metal pool and the p o s i t i o n of the s o l i d / l i q u i d i n t e r f a c e i n the copper mold. Having discussed the importance of knowing the pool volume, an attempt i s now made to predict i t f o r some known operating conditions. As shown i n F i g . (75), the pool volume can be subdivided into two; ; regions. The c y l i n d r i c a l portion can be predicted on the basis of a dynamic heat balance of the unit while the curved portion can he predicted using a f i n i t e difference technique. 118 VI.2 P r e d i c t i o n of the Height of the C y l i n d r i c a l Portion of the Pool Volume In Chapter V, an accurate heat balance of the process was c a r r i e d out. From i t , i t i s clear that knowing the operating conditions, the geometry and the volume of the slag cap, i t i s possible to c a l c u l a t e the height of the c y l i n d r i c a l portion of the l i q u i d metal pool. F i g . (76) shows the macrographs of ingots (26) and (32). The observed d i f f e r e n c e i n height of the c y l i n d r i c a l p ortion i n the two cases i s =3.5 cm. Using s i m i l a r boundary conditions as obtained experimentally for ingots (1), (10) and (16), a heat balance of the two ingots y i e l d s a value f o r the d i f f e r e n c e i n the height of the ; c y l i n d r i c a l portion of 3.0-3.3 cm. Similar c a l c u l a t i o n s were c a r r i e d out f o r ingots (4) and (18). A value of =3.0 cm was obtained which compared very favourably with the experimentally observed d i f f e r e n c e i n height of the c y l i n d r i c a l portion of 3.0-3.2 cm. Having being able to predict the height of the c y l i n d r i c a l portion of the l i q u i d metal pool i n laboratory scale ingots, attempt i s now . made to predict t h i s height for an i n d u s t r i a l scale ingot. Table (XV) 51 gives the. operating conditions for an i n d u s t r i a l scale ingot. On carrying out a heat balance s i m i l a r to the one done i n Appendix (IV), a value of 15 cm i s obtained f o r the height of the c y l i n d r i c a l portion of the l i q u i d metal pool. Considering the approximations involved, t h i s value agrees very well with the experimentally obtained value of 15-18 cm. 119 Table XV. Operating conditions f o r an i n d u s t r i a l scale ingot. 51 Mold Electrode Electrode Electrode Atm. Slag dia. d ia. comp. p o l a r i t y comp. (cm) (cm) Volts Amp. 50.8 40.5 Hastelloy X a.c. A i r CaF 2- 25 wt.% A1 20 3 32 15000 Melt Rate * Z * A * B (g/sec) (cm) (cm) (cm) 160 15 15-18 20 * Refer to Fi g . (75) VI.3 P r e d i c t i o n of Pool P r o f i l e s Using E x p l i c i t F i n i t e Difference Method VI.3.1 Introduction Mathetmatical models f or p r e d i c t i n g the s o l i d i f i c a t i o n pattern i n 37 50 52 53 castings have been studied by many investigators."' ' ' ' Sun and 50 Pridgeon used the f i n i t e d i f f e r e n c e method to predict the pool p r o f i l e s i n Hastelloy-X ingots. The model presented here can be con- sidered as a refinement of the Sun and Pridgeon analysis. For rounded ingots, the c y l i n d r i c a l polar system (r, <J> , Z) i s : generally used. Two dimensional heat transfer along the r and Z axes i s adequate i n describing the heat flow i n an e l e c t r o s l a g r e f i n i n g unit as angular symmetry e x i s t s i n the temperature d i s t r i b u t i o n . The Fourier equation reduces to 120 9T • 32T 1 8T • 3 2 T i 1? " + ^ » * ^ < 6 - 1 } where a = — — (6.2) P C P Equation (6.1) can be solved by means of d e f i n i t e difference methods knowing the appropriate boundary conditions. Both the 54 55 Dusinberre (explicit), and the Crank and Nicolson ( i m p l i c i t ) methods can be used. Use of the Dusinberre's e x p l i c i t method i s made i n the following analysis. ' . < In the e l e c t r o s l a g process, the ingot i s continuously b u i l t up. The v e r s a t i l i t y of the f i n i t e d ifference technique permits one to simulate the l i q u i d metal dropped continuously i n t o the pool by adding at the top, a th i n d i s c layer of l i q u i d metal of a given s i z e a f t e r every unit time i n t e r v a l . VI.3.2 Derivation of the Formulae for the E x p l i c i t F i n i t e Difference Method The f i r s t question concerns the subdivision of the system. The simple and obvious method i s i n equal increments of the radius. The system i s then l a i d out as i n F i g . (77). For convenience, an arc of one radian i s used and each element has the dimensions of 'Ar' along the ' r ' axis and 'Az' along the 'z' axis. As seen i n F i g . (77), there are, i n t o t a l nine d i f f e r e n t types of elements. Symbolically, they can be represented as follows \ 121 (1) ( 5 ) 11 (2) (6) (3) ( 7 ) (8) ¥ C9). The arcs halfway between the reference points are taken as defining the width of the heat flow path and also the volumes of the respective regions. Appendix (V) gives the d e r i v a t i o n of the formulae for each of the nine d i f f e r e n t types of elements. VI.3.3 Salient Features of the Computer Programme The dependence of the pool shape on the thermophysical properties of a given a l l o y i s obvious. Hence i n developing the computation model, the pool shape i s considered as a function of both the ingot melt rate and the thermo-physical properties of the a l l o y . The. following are the s a l i e n t features of the programme. (1) I t i s assumed that the temperature of the top layer elements remains constant, i . e . the top layer elements are assumed to be i n , steady state equilibrium with the elements below them and the l i q u i d slag or metal above them. (2) The temperature d i s t r i b u t i o n i p the top layer elements i s assumed. The temperature d i s t r i b u t i o n depends upon the height of the c y l i n d r i c a l portion of the l i q u i d metal pool above them. The c y l i n d r i c a l portion acts as a b u f f e r region and reduces the r a d i a l temperature grad- ient i n the top layer elements. 122 (3) A constant temperature at the bottom of the ingot i s assumed a f t e r s u f f i c i e n t ingot i s b u i l t up. Although i t i s possible to calculate the heat leaving at the bottom of the ingot from the ava i l a b l e experimental.data, the assumption s i m p l i f i e s the analysis without s c a r i f i c i n g accuracy. (4) The current passing through the ingot does not produce s i g n i f i c a n t heating of the ingot; hence i t s e f f e c t i s neglected by 2 assuming I R = 0. (5) As documented e a r l i e r i n Chapter V, temperature p r o f i l e s were obtained on the copper mold for various mold s i z e s , mold/electrode r a t i o s and p o l a r i t i e s . I t i s possible to non-dimensionalize the temperature vs. distance from the l i q u i d m etal/solid metal i n t e r f a c e p l o t s f o r distance. F i g . C78) shows the average temperature d i s t r i b u t i o n on the mold across the s o l i d i f i e d ingot. I t i s necessary to express t h i s ; curve i n the form of an equation. A polynomial of 8th degree was f i t t e d to the curve quite accurately. However, t h i s polynomial cannot be used as a boundary condition for / . i n d u s t r i a l scale ingots as F i g . (78) i s v a l i d only for 'L' =35.0 cm. i One i s interes t e d i n c a l c u l a t i n g the heat going to the mold cooling water i n elements of cases 3, 6 and 7 discussed i n Appendix (V). For case 3, the temperature of a nodal point X at time t = k + I , i . e . r , z T n i s given by the following equation TL J Z 9 K. "T" X 123 C p volume k - i A l —P- , r T _ x 1 = fx - T 1 At r,z,k+l r,z,k Ar *" r - l , z , k r,z,k + h : , A . [T ,. . - T ] + - ~ - [T - T ] side 2 r+l,z,k r,z,k Az r,z+l,k r,z,k + Az ^ r , z - l , k Tr,z,k'' (6.3) In Eq. C6.3), one i s i n t e r e s t e d i n c a l c u l a t i n g the term hg-j^e^ •^r+l,z,k Tr,z,k'' L e t q ^side A 2 ^ r + l , z , k '''rjZjk"' = h [T - T . ] (6,4) A 0 side water r,z,k In steady state f - = h AT (6.5) A„ where h AT i s obtained from F i g . (63), AT being the temperature d i f f e r - ence between the mold w a l l and the water temperature. As discussed e a r l i e r i n Chapter V, the heat transfer to the mold cooling water can be subdivided into two regions (a) surface b o i l i n g region (b) non-boiling region Ca) Surface B o i l i n g Region:. The heat f l u x in the surface b o i l i n g , region can be expressed i n an equation form as follows 124 ( J ) = e x p (6.12 S , n [ ( T - 5 0 ) > 22.13]} (6.6) Where T i s the temperature on the copper mold i n degrees centrigrade. Using (6.6) i t i s possible to c a l c u l a t e the heat going to the mold cooling water f o r elements across the surface b o i l i n g region. (b) Non-Boiling Region: As calculated e a r l i e r i n Chapter V h , .,. ° r non-boiling -2 -2 -1 -1 1.15 x 10 c a l cm °C sec . Knowing the temperature diffe r e n c e between mold and water temperature, the heat transferred to the mold cooling water for elements across the non-boiling region can be calculated (6) As the thermophysical properties of the various s t e e l s at elevated temperatures are not a v a i l a b l e i n l i t e r a t u r e , attempt i s made here to predict the pool p r o f i l e s i n pure i r o n and EN 25 s t e e l ingots only. EN 25 s t e e l has approximately 5% a l l o y i n g elements and as such, except for the melting point (= 50°C lower), i t i s assumed to have the same thermophysical properties as pure i r o n . (7) The latent heat of s o l i d i f i c a t i o n and also the a l l o t r o p i c transformations i n the case of pure i r o n are taken i n t o account by adjusting the s p e c i f i c heat, i n the c a l c u l a t i o n , as follows: where AT i s the temperature range over which the transformation occurs. (8) The data for thermal conductivity i s not a v a i l a b l e i n l i t e r a t u r e above 1600°K even f o r pure i r o n . The thermal conductivity i s estimated above 1600°K by making use of the Loren's r e l a t i o n s h i p , as the data for e l e c t r i c a l r e s i s t i v i t y i s a v a i l a b l e up to 2100°K. C (adjusted) = C (metal) + P P LH (6.7) AT 125 Ivoren'g r e l a t i o n s h i p : e l e c t r i c a l r e s i s t i v i t y x thermal conductivity o x —- J—. - = constant (6.8) temperature In the range where both the thermal and e l e c t r i c a l conductivity data i s a v a i l a b l e , the v a l i d i t y of the Loren's r e l a t i o n s h i p i s checked (error < 5%). > In the l i q u i d i f o n temperature range, i t i s very d i f f i c u l t to ca l c u l a t e the contribution of convection. I t i s taken i n t o account by way of the concept of ' e f f e c t i v e thermal conductivity' k = k + k , (6.9) ef f conv cond k „ = f k- (6.10) e f f cond It i s extremely d i f f i c u l t y to estimate the value of ' f . I t i s a function of temperature and flow conditions. £un and Pridgeon"^ use f = 3-5. Using Stewart's"^ non-dimensional analysis f o r the present;, case y i e l d s a s i m i l a r value for ' f and i s used i n the analysis. However the v a l i d i t y of using this analysis to phe present case i s i n doubt. In the present case, the temperature gradients are such that denser l i q u i d i s at the bottom and l i g h t e r at the top. Table XVI gives the p h y s i c a l properties of pure i r o n used i n the analysis."' 7 (9) The time i n t e r v a l 'At' between successive temperature evaluations at a node i s chosen such that the s t a b i l i t y c r i t e r i a i s s a t i f i e d . In F i g . (79)., the temperature at the nodal point 'a' a f t e r time At 126 Table XVI. Ph y s i c a l properties of pure i r o n used i n the analysis 57 Temperature Range (°K) Density (g cm 3) S p e c i f i c Heat ( c a l g " 1 ^ " 1 ) Thermal Conductivity ( c a l cm l o K "*"sec 1 ) 300-900 7.75 0.14 0.13 900-1350 7.59 0.18 0.072 1350-1660 7.45 0.15 0.076 1660-1670 7.35 0.53 0.082 1670-1800 7.31 0.164 0.085 1800-1801 7.187 65.7 0.12 1801-1825 7.073 0.18 0.24 1825-1900 7.04 0.182 0.30 1900-2050 6.94 0.183 0.40 can be written as F i g . (79) nodal points configuration . C . I T ' - T J a a a_ At k (T - T ) + k (x - T ) + ba b a ca c a (6.10) 127 where C = o C a P On s i m p l i f y i n g At k At Ek. At r - T b + ^ T c + . . + U - - f ] T a (6.11) T' « F, T, + F T + ... + F T (6.12) a ba b ca c aa a In equation (6.12) a l l F b a etc. are inherently p o s i t i v e but Ek At F a a - 1 " — 5 — ( 6 - 1 3 ) and this may become negative i f At i s chosen large enough. This would be absurd p h y s i c a l l y , because i t would say that, the warmer the region 'a' i s now, the colder i t i s going to be a f t e r the time i n t e r v a l At. More sophisticated c r i t e r i a have been devised f o r systems to which d i f f e r e n t i a l equations are applicable and can be solved. But, as a p r a c t i c a l matter, i t i s easy to obey a simple r u l e : 'avoid negative c o e f f i c i e n t s . Of the possible F values, the worst value i s selected to evaluate aa At. In the present analysis, as constant temperature i s assumed at both the top and bottom, the value of F to be considered i s obtained 3.3. from eq. (A.V.7) [Appendix V]. 128 The maximum allowable value of At i s obtained by solving F a a = 1 - k~ + w; + w; ( 6 - 1 5 ) C p A r 2 where MR„ = • f — . • 2 k 2 At MZ - C p Az 2 3 k 3 At 2 C p Az MZ, = -? : 4 k, At 4.0 k At k At k. At • — + A 2 + — - 2 = 1 (6.16) p C Ar p C Az p C Az P P P p C The minimum value of (-jr-T^) i s chosen f or evaluation, as i t leads to the maximum allowable value of At i n the worst case. -3 p = 6. 88 g cm C - 0.18 c a l g " l o C _ 1 P k = 0.4 c a l cm l o C sec Substituting these values i n (6.16) y i e l d s At = • , 1 - 5 5 (6.17) l 2 2 Ar Az Using (6.17) i t i s possible to ca l c u l a t e the value of At for any s i z e of the element. 129 VI.3.4 Results Appendix VI gives the computer programme written to p r e d i c t the pool p r o f i l e s i n ESR ingots. Pool p r o f i l e s f o r EN 25 s t e e l and FVE ingots were computed. Table XVII gives the assumed temperature d i s t r i b u t i o n i n the top elements and the values of the various parameters used i n the computation. F i g . (80) to F i g . (85) show the predicted pool p r o f i l e s superimposed on the experimentally obtained p r o f i l e s . The agreement appears to be good i n s p i t e of the numerous assumptions made. In ingot no. 21 (Fig. (83)), tungsten powder was added to define the pool p r o f i l e . To predict the pool p r o f i l e s for i n d u s t r i a l scale ingots, i t i s necessary, e i t h e r to experimentally determine or assume, a temperature p r o f i l e on the mold across the s o l i d i f i e d ingot. : Table XVII. Parameters used i n the pre d i c t i o n of pool p r o f i l e s i n EN25 and FVE ingots Ingot DELR DELZ DELT NRATE no. cm cm sec SIDE . -2 -1 0 -1 c a l cm sec C Temperature d i s t r i b u t i o n i n -the top layer (°K) Ingot Centre Ingot Edge 1 10 16 21 26 28 1.22 1.22 1.22 1.1625 0.9 0.9 1.0 1.0 1.0 1.0 0.5 0.5 0.5 0.5 0.5 0.5 0.18 0.18 178 232 178 169 308 185 0.0116 0.0116 0.0116 0.0116 0.0116 0.0116 1800 1810 1825 1800 1830 1850 1790 1795 1785 1795 1815 1825 1780 1780 1770 1790 1780 1810 1815 1750 1750 1750 1750 1800 1800 i—1 o 131 CHAPTER VII CONCLUSIONS The heat generation pattern i n the ^lag bed has been analysed using a resistance network analogue to predict the voltage gradients i n the slag bed. Most of the heat generation takes place below the electrode t i p . Self consistency between current, voltage, temperature, resistance and q i s obtained i n the slag bed. It i s possible to predict the temperature gradient on the electrode. This may be used to ca l c u l a t e the degree of thermal i n s t a b i l i t y , during electrode changes i n large i n d u s t r i a l ingots and the electrode oxidation. The r e s u l t s i n d i c a t e that when melting s t e e l i n the electrode and mold sizes studied, the electrode material spends approximately 30 seconds i n the temperature gradient 1000°C to the melting point. I t i s suggested that t h i s would lead to a s i g n i f i c a n t non-equilibrium retention of second-phase p r e c i p i t a t e s i n a melting a l l o y which contained these p r e c i p i t a t e s at a lower temperature i n the s o l i d . The o v e r a l l heat tran s f e r c o e f f i c i e n t of the i n t e r f a c e region, l i q u i d slag/slag skin/copper mold i s found to have a s l i g h t 132 dependency on the slag temperature, slag composition and the slag skin thickness. I t i s postulated that the major resistance to the transfer of heat across t h i s composite i n t e r f a c e l i e s i n the d i s c o n t i n u i t y between the slag-skin and the mold w a l l . The e l e c t r i c a l r e s i s t i v i t y of the slag skin p r i m a r i l y depends upon the contact resistance and i s a s e n s i t i v e function of the mold w a l l temperature. An approximate thermal gradient i n the slag skin region hasIbeen determined. An accurate heat balance of the process i s c a r r i e d out on labora- tory scale ingots. The r e s u l t s i n d i c a t e that a s i g n i f i c a n t i portion of the heat leaves the unit across the l i q u i d slag and the l i q u i d metal regions. The power requirements and the melt rate for i n d u s t r i a l scale ingots are predicted. Good agreement i s obtained between the predicted values and the data c o l l e c t e d from l i t e r a t u r e . Real differences are observed between d i f f e r e n t melting modes. It i s observed that i n d.c. negative, there i s a marked difference between melting under argon and a i r . 133 (9) The l i q u i d metal pool volumes i n ESR ingots can be predicted from the operational data. Good agreement i s obtained between pool p r o f i l e s computed using a f i n i t e d ifference technique and the experimentally obtained p r o f i l e s . 134 APPENDIX 1 PHYSICAL PROPERTIES OF ESR SLAGS A.I.I Introduction ! The correct choice of slag composition i s of prime importance i n the e l e c t r o s l a g r e f i n i n g process. The slag bath i s the most important unit i n the process. I t i s the resistance and r e f i n i n g element. The correct choice of slag i s therefore governed by the p h y s i c a l considerations such as e l e c t r i c a l conductivity, l i q u i d u s temperature, v i s c o s i t y , density, vapor pressure e t c . f and also the chemical considerations such as desulphurization, and removal of large oxide i n c l u s i o n s . No coherent picture has yet emerged from the published data; as'to what constitutes the requirements f o r a useable ESR s l a g , but one may e s t a b l i s h several boundary c o n d i t i o n s . ^ (1) the slag must be chemically compatible with the metal being processed. (2) the slag must have a l i q u i d u s temperature below t h e melting point of the metal but a primary phase melting point above that of the metal. (31 the p h y s i c a l properties must be such that the heat generation i s established i n a uniform volume, of a s i z e compatible with the required heat balance. The f i r s t condition i s imposed^ by one of the prime objectives of the process i . e . , c a p a b i l i t y of improving the c l e a n l i n e s s of the metal. Inclusions such as sulphides, oxides, s i l i c a t e s etc. can be removed. Generally speaking, the process Is one of oxidation, hence 135 precautions are necessary to minimize oxidation losses of these a l l o y i n g elements such as S i , T i , A l which are p a r t i c u l a r l y prone to oxidation. The second boundary condition i s imposed by the requirement that one must be able to immerse the electrode i n the slag while also allowing a metal pool to be bounded by a s o l i d slag skin. The t h i r d condition represents the dependence of process para<- meters i . e . , melt rate, voltage and current on the ph y s i c a l properties of the slag. However, the requirements of a sui t a b l e e l e c t r i c a l conductivity, v i s c o s i t y , vapor pressure, liquidus temperature etc., must be s a t i s f i e d before the s e l e c t i o n according to the chemical properties desired of the slag f o r a s p e c i f i c m e t a l l u r g i c a l a p p l i c a t i o n i s made. Slag components are selected p r i m a r i l y on account of t h e i r low vapor pressure and high temperature s t a b i l i t y . The slag should also have the appropriate e l e c t r i c a l conductivity to achieve the desired temperature. Other important c r i t e r i a are those of v i s c o s i t y , density, thermal conductivity, liquidus temperature, vapour pressure, i n t e r - f a c i a l tension and thermal capacity. E l e c t r i c a l conductivity, dpnsity and kinematic v i s c o s i t y are i n t e r r e l a t e d . Thus a low e l e c t r i c a l ) conductivity necessary for high resistance heating i s accompanied by high v i s c o s i t y . Although the viscous slag may slow down the oxidation of r e a c t i v e elements, i t also slows down the removal of unwanted; ; components. The most common choice of slag constituents i s between CaF^, CaO, A^O^, MgO and Si02. However, MgF2, BaF2> Ti02 etc. are sometimes added i n small quantities to achieve a close control of a p a r t i c u l a r 136 element. Although many slag compositions may represent equally acceptable optima, i n industry, only a few slag compositions, selected by empirical means, are used. Knowing the ph y s i c a l properties of the slags, i t i s possible to sim p l i f y the multicomponent slags used i n industry and at the same time propose several a l t e r n a t i v e compositions. At the present time, i n s u f f i c i e n t data i s av a i l a b l e on the various physical properties of the slags. Table XVIII summarises the av a i l a b l e l i t e r a t u r e on the physi c a l properties of ESR slags. F i g . (86) gives 21 the e l e c t r i c a l conductivity data for CaF2 _Al20 3 slags. Attempt i s made here to measure the density and v i s c o s i t y of CaF2 based slags. A.I.2 Measurement of Density of CaF2 Based Slags A.I.2.1 Introduction In addition to i t s use i n the analysis of such properties as v i s c o s i t y and e l e c t r i c a l conductivity, density measurement i s of considerable value i n the inve s t i g a t i o n s of the structure of l i q u i d s . I t i s quite d i f f i c u l t to measure accurately the density of l i q u i d s at temperatures of 1450-1750°C. Previous measurements of the density of CaF2 _Al20 3 and CaF2~CaO binary systems have been r e s t r i c t e d to below 6 8— 7 2 1600°C and confined mostly to the Russian l i t e r a t u r e . In the present work, density measurements have been made i n the two binary compositions: CaF2-Al20.j, CaF2~CaO over the temperature : range 1450-1750°C. 137 Table XVIII. Physical properties of ESR slags Property System Reference Phase structure Phase structure Phase structure Phase structure Phase structure Phase structure Phase structure Phase structure Phase structure Phase structure Density Density Density Density Density Interphase and i n t e r f a c i a l tension Interphase and i n t e r f a c i a l tension C a F 2 - A l 2 0 3 , CaF 2-CaO, CaF - Ca0-A1 2Q 3 CaF 2-CaO-Al 20 3 CaF2-CaO CaF2~CaO C a F 2 - A l 2 0 3 CaO-CaF 2-2CaO-Si0 2 CaF 2-CaO; C a F ^ A l ^ ; CaF^CaO- A1 20 3; CaF 2-CaO-2CaO.Si0 2; CaO-MgO; CaO-Al 20 3 2CaO.Si0 2-CaF 2 Ca,0,-Ca_F,-Si.. ,-F,-Si 1 0, 3 3 3 6 1.56 1.53 CaF 2-CaO-Al 20 3 CaF 2-MF 2, MF CaF 2-Al 20 3-CaO CaF 2-CaO-Al 20 3; CaF 2-Si0 2-CaO CaF 2~CaO-Al 20 3 CaF2-MgO; CaF^CaO; C a F ^ A l ^ ; C a F 2 - S i 0 2 ; CaF 2~Zr0 2 58 59 60 61 62 63 65 64 66 67 68 69 70 C a F 2 - A l 2 0 3 ; CaF 2-Ca0; C a F ^ Al 20 3-CaO; CaF 2~CaO-Si0 2; CaF 2-CaO-Al 20 3-MgO CaF 2; CaF2-MgO; CaF2-CaO; C a F ^ 71 A1 20 3; CaF 2 - S i 0 2 ; CaF 2-Zr0 2; Ca F 2 - S i 0 2 72 69 70 138 Table XVIII. (Continued) Property System Reference Interphase and CaF 2-CaO-Al 20 3 71 i n t e r f a c i a l tension V i s c o s i t y CaF 2-CaO-Al 20 3 73,74 V i s c o s i t y CaO-Al 20 3-Si0 2 75 E l e c t r i c a l conductivity CaO-Al 2C> 3-CaF 2; CaF 2-CaO, 69 BaO, MgO, T i 0 2 , Z r 0 2 , A 1 2 0 3 E l e c t r i c a l conductivity CaF 2 76 E l e c t r i c a l conductivity CaO-Si0 2-CaF 2 77 E l e c t r i c a l conductivity CaF 2-CaO-Al 20 3 21 E l e c t r i c a l conductivity CaF 2-Al 20 3-CaO 66 S p e c i f i c heat and CaF^CaO; CaF^CaO-Al^-MgO 78 heat content C a F 2 - A l 2 0 3 Vapour pressure CaF„ 79 139 A.I.2.2 Experimental A.I.2.2.1 Apparatus The apparatus i s based on 'the measurement of the buoyancy force'. It i s shown schematically i n F i g . (87). I t was supported on a s t a i n l e s s s t e e l base plate with r i g i d support on the two sides. The molybdenum l i n e d graphite c r u c i b l e K (5 cm <J>, 10 cm high) was supported by a hollow alumina tube N carrying a thermocouple 0 which was attached to the c o n t r o l l e r of the' induction furnace. The e n t i r e assembly was enclosed i n a Vycor glass tube P (7.8 cm d i a . , 48 cm long) l i n e d with graphite f e l t L i n the heating zone. Oxidation at elevated temperature was prevented by maintaining a s l i g h t p o s i t i v e argon atmosphere i n the apparatus. The water cooled induction c o i l M enabled the maintainence of a uniform temperature over the e n t i r e volume of the slag i n the c r u c i b l e . Precise temperature measurement of the slag was made by i n s e r t i n g a W-3Re/W-25Re thermocouple E ( i n a twin bored alumina tubing with a boron-nitride sheath protection) i n the melt J . A transducing c e l l 'A' (Statham's Universal transducing c e l l model UC3) was used to measure the weight change of the bob. F i g . (88) gives the external c i r c u i t r y required to operate the transducer. A change i n weight of the bob caused a change i n the resistance. This was measured i n m i l l i v o l t s and was c a l i b r a t e d to give the weight change in grams. A molybdenum bob I (=5 grams) i n the form of a r i n g was suspended from the transducer by a tungsten wire H (0.025 cm d i a . ) . Both the weight change and temperature were simultaneously recorded by two Sargent Model SR6 recorders. The absence of large systematic errors 140 owing to the thermal lag between the melt and temperature sensing element on continuous measurement was v a r i f i e d . In a l l the density measurements, the bob was completely immersed i n the melt, leaving surface forces acting only on the wire. The problem of bubbles getting attached to the bob, as indicated by e r r a t i c buoyancies, necessitated the process of removal, cleaning and re-immersion of the bob. The process was repeated u n t i l reproducible and minimum values of buoyancy were obtained. F i g . (89) shows the experimental setup. A.I.2.2.2 C a l i b r a t i o n and Measurement > The transducer was c a l i b r a t e d by suspending known weights and observing the change i n m i l l i v o l t s . Eq. (A.1.1) gives the c a l i b r a t i o n 1 g = 1.3 mV (A.1.1) expression and t h i s was v e r i f i e d frequently. The volume of the bob at room temperature, determined from i t s apparent weight loss upon immersion i n d i s t i l l e d water was obtained from the equation. W - W Try d V n = t 3 n W ] + [—£-] (A. 1.2) pw S Pw where the subscripts 'a' and 'w' r e f e r to a i r and water r e s p e c t i v e l y and 3 V = volume of bob at room temperature (cm ) o W = weight of the bob (g) p = density (g cm 3) 141 Y = surface tension (dynes/cm) d = diameter of suspension wire (cm) g = ac c e l e r a t i o n due to gravity (cm sec ) The volume of the bob at room temperature was determined each time before an experiment. The density of the melt was calculated from the following equation W - W irv d a m m , -. O N + -TT (A. 1.3) m V [1 + 3a(T-25)] V g o o where the subscripts 'a' and 'm' r e f e r to a i r and melt r e s p e c t i v e l y and T = temperature of the melt (°C) a = l i n e a r c o e f f i c i e n t of expansion for the material of the bob. i 81 For molybdenum, a x 10 6 = 5.05 + 0.31 x 10 _ 3T + 0.36 x 1 0 _ 6 T 2 (A.1.4) where T = temperature (°C). The surface tension data from the l i t e r a t u r e 7 ^ ' 7 " ' " f o r 1450-1600°C range was used at a l l the temperatures (Fig. (90)). A.I.2.3 Results CaF 2 r i c h side of two binary systems C a F 2 ~ A l 2 0 3 and CaF 2-Ca0 was investigated. In a l l the cases Ap w a s l i n e a r with temperature. F i g . (91) and F i g . (92) give the experimental data obtained. 142 A.I.3 Measurement of V i s c o s i t y of CaF^ Based Slags A. I.3.1 Introduction V i s c o s i t y i s an important p h y s i c a l property of fused s a l t s . I t determines, i n part, the rate of f a l l of metal droplets through the l i q u i d slag and may also influence the rates of c e r t a i n r e f i n i n g reactions through i t s i n t e r r e l a t i o n s with d i f f u s i o n rates. As i n the case of most of the other p h y s i c a l properties of CaF^ 73 74 based slags, previous work i s sparse and inconclusive. ' Davies 73 and Wright i n t h e i r recent paper have reported the v i s c o s i t y data for some CaF^ based slags up to 1500°C. As the operating temperatures i n ESR process are higher than 1500°C, measurement of v i s c o s i t y at higher temperatures (1500-1650°C) i s attempted here. A. I.3.2 Experimental A. I.3.2.1 Apparatus The apparatus i s based on the r o t a t i n g c r u c i b l e p r i n c i p l e . In t h i s method, the torque exerted on the suspension wire through the inner c y l i n d e r immersed i n the l i q u i d slag contained i n the ro t a t i n g outer c y l i n d r i c a l c r u c i b l e i s measured by the d e f l e c t i o n of a beam of l i g h t incident on the mirror attached to the suspended assembly. F i g . (93) gives a schematic diagram of the apparatus. The molybdenum li n e d outer c y l i n d r i c a l graphite c r u c i b l e V was supported on a shaft W connected to a v a r i a b l e speed motor (Boston Gear R a t i o t r o l 1/8 H.F. Motor, made by Boston Gear Works, Quincy, Mass., U.S.A.). The inner molybdenum cylinder T was attached to the end of;the alumina tube M carrying a thermocouple 0 (W/W-26% Re thermocouple i n 143 a twin bored alumina sheath). The e n t i r e assembly was attached to the suspension wire G (0.012 cm d i a . tungsten wire) by a s t a i n l e s s s t e e l frame I carrying the mirror H. The leads of the thermocouple 0 were brought out through a s l i t i n I and connected to molybdenum wires K supported i n a brass ri n g J . When the inner molybdenum cyl i n d e r T was immersed i n the l i q u i d s l a g , the molybdenum leads K were immersed i n separate pools of , mercury L which were connected to a Sargent recorder (Model SR 6) for temperature measurement. F i g . (94) gives a close-up view of the assembly. The e n t i r e assembly i s enclosed i n two Vycor tubes F and Q with water cooled bases N and X r e s p e c t i v e l y . Constant immersion of the ; inner cylinder was achieved by having a graduated stem A. To avoid oxidation, argon gas was flushed continuously through B at s l i g h t p o s i t i v e pressure. Uniform heating of the slag bath U was achieved by induction heating. The Vycor tube Q was protected with a graphite f e l t l i n i n g j • • S i n the heating zone. A gas l a s e r was used as a l i g h t source to obtain a undiffused r e f l e c t e d beam from the mirror H. F i g . (95) shows experimental equip- ment. The d e f l e c t i o n of the beam of l i g h t caused by the torque exerted on the suspension wire i s measured on a scale mounted behind the l a s e r . A.I.3.2.2 Procedure Weighed amount of slag was melted i n outer c r u c i b l e under argon by induction heating. Af t e r the slag was molten, the inner molybdenum 144 cylinder was slowly lowered into a desired p o s i t i o n by lowering the shaft A. The outer graphite c r u c i b l e was rotated at various known speeds and the d e f l e c t i o n measured. Both clockwise and anticlockwise r o t a t i o n was used and a mean d e f l e c t i o n measured f o r each speed of r o t a t i o n . By changing the power input, the slag was heated to various temperatures. Measurement was c a r r i e d out a f t e r steady temperature had been obtained. A.T.3.2.3 C a l i b r a t i o n 82 I t has been shown for the i d e a l case of i n f i n i t e l y long cylinders that when the outer cylinder i s rotated at constant v e l o c i t y , the torque produced on the inner cylinder i s 2 2 4rrLWnr r„ T r = (A.1.5) r -—r 2 1 The torque i s measured by the angle of twist caused i n the c a l i b r a t e d suspension. It i s equal to K6 where 6 i s the angular displacement of the inner cylinder. I f absolute measurement of the c o e f f i c i e n t of v i s c o s i t y i s desired, corrections for stem of the inner c y l i n d e r , end e f f e c t due to f i n i t e length of cylinders etc. have to be accurately calculated. However, a much easier approach i s to c a l i b r a t e the apparatus against l i q u i d s of known v i s c o s i t y . I f dimensions of the c y l i n d e r s , depth of immersion, bottom clearance and t o r s i o n wire are kept constant, equation (A. l.<5) reduces to 145 n = K ^ t (A. 1.6) where K^ i s found experimentally. The value of K^ was determined by c a l i b r a t i n g the apparatus against l i g h t o i l s , Hydrodrive and Dinonyl- phathalate. The v i s c o s i t y of these o i l s was f i r s t determined accurately using Brookfield s y n c h o - l e c t r i c viscometer. A.I.3.2.4 Errors Involved (1) Dimensions of the Cylinders: As the c a l i b r a t i o n of the apparatus was done at room temperature, co r r e c t i o n has to be made for the expansion of the inner cylinder K f l t n = -4~ (A. 1.7) L -L where E « 1 + 3 {-y—-} (A. 1.8) o where L = length of cy l i n d e r at t°C L q =. length of c y l i n d e r at room temperature. For molybdenum cyli n d e r , the. error introduced, i f the expansion factor i s omitted was 2.7% at 1600°C. (2) Depth of Immersion: The inner c y l i n d e r was lowered to the same extent i n each experiment. To achieve constant depth of immersion, the volume of the l i q u i d slag had to be kept constant as w e l l . Knowing the density at 1600°C for CaF2~Al20 3 binary slags, the t o t a l weight of the slag was so chosen, as to give a constant volume f o r each slag 146 composition at 1600°C. However, an error (= 1%) i s introduced by the increase i n the depth of immersion due to the decrease i n slag density with increase i n temperature of the slag from 1600°C and vice-versa. (3) The other possible sources of error are (a) lack of alignment of the cylinders (b) temperature measurement (c) turbulent motion i n slag at high speeds of r o t a t i o n (d) s l i p between cylinders and slag due to non-wetting (e) the suspension wire being not p e r f e c t l y e l a s t i c over the t o r i o n angles involved. Care was taken to see that errors due to (a), (b) and (c) were o avoided. As the CaF2-Al20 3 slags do wet molybdenum, error due to s l i p was not present. The error introduced by the non-ideal behaviour of the tungsten suspension wire i s n e g l i g i b l e . A.I.3.3 Results V i s c o s i t y measurement of the CaF2 r i c h side of CaF2~Al20 3 binary system was c a r r i e d out. F i g . (96) gives the v a r i a t i o n of c o e f f i c i e n t of v i s c o s i t y with composition at 1600°C. F i g . (97) gives the v a r i a t i o n of c o e f f i c i e n t of v i s c o s i t y with temperature and compares 73 the experimental data with the data of Davies and Wright. 147 APPENDIX II CALCULATION OF THE RESISTANCE OF THE VOLUME ELEMENTS IN THE VOLTAGE GRADIENT ANALYSIS A . I I . l Introduction A segment of one radian of the slag bath i s subdivided into volume elements as shown i n F i g . (12). A.II.2 C a l c u l a t i o n of R z R = ^ z A Cal c u l a t i o n of 'A': Fig. (98) gives a schematic diagram of the segment of the slag bath. The volume elements are c l a s s i f i e d i n t o groups M, N, 0 and P as shown. The volume elements 9 and 13 w i l l be considered subsequently. Hi = ^ r T X 3^0 X ^ 4 A r ) 2 - Obr)2] = 2 Ar S i m i l a r l y 3 . 2 . A r 2 \ = 2 A r ; A 0 = 2 A r ; h C a l c u l a t i o n of % : I = Az for each of the volume elements. I t i s possible to subdivide the resistance R^ into two equal halves of R 12. z 148 A,II.3 C a l c u l a t i o n of R r R - r 1 R r r A Ar C a l c u l a t i o n of £ : £ = —^ for each of the two subdivisions of Ca l c u l a t i o n of A : The value of A i s d i f f e r e n t f o r the two subdivisions of R̂_ (Fig. (99)). 180 1 2* r 4 A r + \ A r . \ H S = — X 360 X T [ 2 ] A z 1 5 A — Ar Az LES: l e f t hand side; RHS: r i g h t hand side. S i m i l a r l y K 1 1 A A 9 A H S = T Ar A Z ; A = - Ar Az RHS A°LHS = { Ar Az ; A = | Ar Az RHS H 3 . . 1_ 4 Ap = Ar Az; A^ = -7- Ar Az LHS RHS A. II.4 C a l c u l a t i o n of R̂  and R^^ The exact c a l c u l a t i o n of 'A' and ' £' f or elements 9 and 13 i s complicated. Approximate values of A and £ are used i n the analysis and are given below: R : A = - Ar 2- I = — V l 2 A 4 A r »• * 3 R 9^ g: A = - Ar Az; 2, = -~ Ar 5/5* 2 ^ R9->electrode ! A " ~2 A z ; i l * ~ 5 2 R 1 3^ 1 7 : A = j-j- Ar ; Jl = Az/3 5 1 R13->-12: A = 6" A r A z ' ^ = 3" A r R A — 2 13+electrode* 6 ; £ APPENDIX I I I COMPUTER PROGRAMME TO DETERMINE THE TEMPERATURE GRADIENTS ON THE MOLD FORTRAN IV 6 COMPILER MAIN 05-23-71 12:07:08 P45E 0001 PROGRAM : PREDICTION OF TEMPERATURE PROFILES ON E . S . R . ELECTRODES C C C C c c PROGRAMMER : SATISH JOSHI L IST OF ABBREVIATIONS USED LQF : LEAST SQUARE FIT ROUTINE AVAILABLE IN UBC'S GENERAL PROGRAMME LIBRARY REFER TD THE WRITE-UP LQF FOR THE i E A N l l G 3F THE PARAMETERS NOT DEFINED IN THE PROGRAMME F - SHAPE FACTOR c c L I - LAMDA INFINITY c c LS= LAMOA STAR c c MA= NUMBER OF TERNS IN THE SERIES NA= NUMBER OF POINTS ON THE BOUNDARY A » D AS DEFINEO IN THE TEXT L - L AS DEFINED IN THE TEXT E • E AS DEFINED IN THE TEXT B = BETA AS DEFIMED IN THE TEXT T0= TO AS DEFINED IN THE TEXT T I I J - TEMP AT THE CENTRE OF THE ELECTRODE IS I 11= TEMP AT THE SURFACE OF THE ELECTRODE NU= NU AS DEFINED IN THE TEXT 0001 0002 0003 0004 0005 0006 0007 0008 0009 0010 0011 REAL X I 3 0 0 1 , Y ( 3 0 0 ) , Y F ( 3 0 0 > . H I 1 0 0 1 , E 1 ( 1 0 0 1 , E 2 ( 1 0 0 1 , P ( 1 0 0 » . T l 3 0 0 11 1 T S ( 3 0 0 I , A , L . N U , L I . L S . E COMMON A , L , P Y , M A , N U , L I , L S , E , B COMMON/A1 / P EXTERNAL AUX P Y - 3 ; U 1 5 9 3 READI5,1)EP FORMAT! E10.5) R E A D I 5 . 2 I L . L I . L S . E . T O FORMAT! 8F10.3I U R I T E ( 6 , 3 I L , L I , L S . E , T O ' FORMAT! IHO,*HL » ,F8.2,3X,11HLAHDAINF > , F B . 2 , 3X, 12HL AMDAST A* • , 1F8.2 .3X.13HENISSIVITY • , F 8 . 2 , 3 X , 5 H T 0 « .F10 .3 I FORTRAN IV 6 COMPILER MAIN 05-23-71 12:07:08 P»SE 0002 0012 READ! 5.41 NA.NA.II 001) 4 FORMAT 110 19 1 0014 WRITE 16,51 MA 0015 5 FORMAT! IH ,32HNUMBER OF TERMS IN SERIES » .15 1 > >~ 00l« WRITE(6 ,6) NA 001T A F0RNATI1H .35HNUMBER OF POINTS ON BOUNDARY - .151 ! 0018 DO 7 1-l.MA j 0019 7 XII l»(L/FLOAT INAI»« (0.5 + FLOAT I 1-111 I 0020 8 REA0(5.9>B>NU.AilP( I) iI>l,MA) 0021 9 FORMAT I3FB.3, ITE8.1 II ! 0022 IFIB.EO.O.OIGO TO 20 0023 WRITEI6.10IB.NU.A i 0024 10 FORMAT 11H0 .7KBETA • , F16.7. 5X. 5HHU » ,F8.2,5Xt4HA = .F16.7I | 0025 00 11 1*1,NA 0026 11 Y( 11-0.0 i 0027 CALL LQFIX,Y,YF,W,El,E2,P,0.0,NA,MA,(ll,MO,EP,»UXl 0028 I F I N O . E Q . O IG O TO 18 I 0024 WRITEI6.12I I 0030 12 FORMAT(69H ESTIMATES OF ROOT MEAN SQUARE TOTAL ERROR IN TH IE PARAMETERS! 0031 WRITE(6,13I <E2(II,I«1,MAI 0032 13 F0RMATI1X,(8E15.5II 0033 WR1TE(6,14> 0034 14 FORMAT(12X,lHX,17X,10HAXIAL TEMP,12X,12HSURFACE TEMP) 0035 00 17 I-l.NA 0036 SUN'O.0 0037 sum=0.0 0038 00 15 NN-l.MA 0039 N«NN-1 0040 Fl«(2.0*FLOAr(NI»l.0 1*PY/(2.0»LI 0041 S1«P(NN)*SIN(F1*X(I II 1 0042 SUM*SUM+S1 0043 SUM1-SUM1* S1*BESSI0IF1I 0044 15 CONTINUE 0045 TII)»1.0*SUN 0046 T i l l - TO*T(Il 0047 TS(I)=1.0*SUN1 0048 TSH)=TO*TS(II 1 0049 WRITE(6.16I X I I ) , T i l l , T S U I 0050 16 F0RMAT(7X,F12.7,8X,F14.7, 8X.F14.7I 0051 17 CONTINUE ! 0052 GO TO 8 0053 18 WRITE(6,19) 0054 19 FORMATI1X.19HEQUATI0NS UNSOLVED//) 0055 GO TO 8 ! 0056 20 CONTINUE 0047 END ! i TOTAL MEMORY REQUIREMENTS 00241C BYTES COMPILE TME - 2.7 SEC0N3S FORTRAN IV G COMPILER AUX 05-23-71 12:07:10 PAGE 0001 0001 0002 0003 000* boos 0006 0007 0008 0009 0010 0011 0012 0013 001* 0015_ 0016 3017 0018 0019 0020 0021 0022 0023 002* 0025 0026 0027 FUNCTION AUXIP.O.X.II COMMON A,LtPY,MAtNU,Ll,LS,E,B DIMENSION PI130I.OI100I HEAL L.NU.LI.LS 21 22 ALPHA-X*X*B*B*1.0 IFIIIS0RTIB*B-1.311*1.0E-36I.GT.X) GO TO 21 C-ATAN(SQRT|B*B-1.0>/X>/PY GO TO 22 C«0.5 F-C*IX/PY)«I0.5«ATANI SQR T I B*B-1. OH-( ALPM A/SORT I ALPHA* ALP HA-» ,0«B 1*B))*ATANISQRT((8-1.0 I*tALPHA*2.0*BI/I(B*l.01*(ALPHA-2.0*B» »I I) 00 2* NN-l.NA N»NN-1 F l - I2.0*FL0ATIN1*1 .0 )*PY/(2 .0*L » F2* BESSI 1(F1)*SIN(F1*XI F3- BESSIOIFl >»S1N1F1»X) SUM2-0.0 SUM3-0.0 00 21 JJ-l.MA J-JJ-1 F4=(2.0*FLOAT(J1*1.0)*PY/(2.0*1 I F5"F*»X F6-SlN(F5t F7-BESS10 (F4) F8-BESSH(F*I SUM2=SUM2 *P( JJ)*F**F8*F6 SUM3-SUM3 +P(JJ>*F7*F6 23 CONTINUE , 0028 0029 00 30 0031 0032 AUX"=SUM2*A*(1.0»SUM3I***-A*( l.-F I*LS****NU*< I. 0* SUM 31 -NU*L I - A*E*F D(NNI-F1*F2**.0*A*<1.0-SUM3 >**3*F3 +MU*F3 CONTINUE RETURN END TOTAL MEMORY REQUIREMENTS 00O5D8 BYTES COMPILE TIME = 1.4 SECONDS 154 APPENDIX IV CALCULATION OF POWER REQUIREMENT FOR MAKING AN INDUSTRIAL SCALE INGOT Assumed Data: 1. diameter of the electrode: 45.72 cm (18 inches) 2. diameter of the ingot: 61.0 cm (24 inches) 3. electrode composition: Vibrac EN 25 (B.S.C.) 4. slag composition: CaF 2~25 wt. % Al^O^ 5. height of slag cap: 16 cm 6. Electrode immersion: 1.5 cm 7. height of the c y l i n d r i c a l p ortion of the l i q u i d metal pool: 7.5 cm 8. height of the ingot 250 cm 8. approximate melt rate: 258 g sec 1 To c a l c u l a t e the power requirements, the t o t a l heat leaving the system w i l l be calculated and then equated to the required heat input. From the experimental data (Fig. (49) to F i g . (56)) i t i s clear that the themperature p r o f i l e s on the mold are independent of the s i z e of the electrode and the ingot. Thus assuming an approximate temperature p r o f i l e i t i s possible to calculate the heat leaving the system. A temperature p r o f i l e on the mold, s i m i l a r to F i g . (49) w i l l be assumed. The heat leaving the 61 cm diameter mold w i l l be assumed proportional to the r a t i o of the areas between the 61 cm diameter i n d u s t r i a l scale ingot and the 8 cm diameter ingot (ingot no. 1). 155 Heat Output: (1) = heat required to melt the electrode and superheat the metal droplets by 100°C 1066.5 0_ f t = -3736- X 2 5 8 = 82 Kcal sec 1 C2) = heat l o s t by r a d i a t i o n from the slag surface to the mold cooling water n « n 61.0 0.650 x — g — 5.0 Kcal sec 1 (3) = heat l o s t to mold cooling water across the slag bed 2.597 x ( ^ ) x (^5) 70 Kcal sec 1 CA) Qc, = heat l o s t to the cooling water across the l i q u i d metal pool 2401 ,61.0. ,10, = — C — ) x c—) - 45.6 Kcal sec 1 (5) Q, = heat l o s t to the cooling water across the s o l i d i f i e d ingot o = 540 x (~^- ) = 4.1 Kcal s e c " 1 The increase i n the length of ingot should also be considered. However, i t i s reasonable to assume Q =5.0 Kcal sec 1 as very l i t t l e 156 heat l e a v e s a c r o s s the e x t r a l e n g t h o f the s o l i d i f i e d i n g o t to the mold c o o l i n g water. (6) = heat l o s t t o base p l a t e c o o l i n g w ater = 0.410 X ( ^ r V o = 31.2 K c a l sec 1 However as the h e a t l e a v i n g the bottom o f the i n g o t d e c r e a s e s as the h e i g h t o f the i n g o t i n c r e a s e s , a v a l u e o f = 25 K c a l s e c 1 appears more r e a s o n a b l e . C7) Qg - S e n s i b l e heat r e t a i n e d by the i n g o t •PIT- x 0.404 = 31.4 K c a l s e c 1 3. 36 T o t a l heat output = 0 o . + Q. + 0 C + Q, + Q_ + Q Q = ZA 5 5 o / o = 182 K c a l s e c " 1 Thus the t o t a l heat i n p u t s h o u l d be a p p r o x i m a t e l y 182 K c a l s e c 1 . The above c a l c u l a t i o n i s v e r y approximate. However most o f the e r r o r can be accommodated i n the term Q^ i . e . , heat l o s t t o the c o o l i n g water a c r o s s the l i q u i d m e t a l p o o l . The h e i g h t o f the c y l i n d r i c a l p o r t i o n of the l i q u i d m e t a l p o o l a d j u s t s i t s e l f to the, a c t u a l power i n p u t . T o t a l power i n p u t = 182 K c a l s e c 1 - 760 Kwatts I f V => 40 v o l t s , the t o t a l c u r r e n t i n p u t s h o u l d be =19000 amperes. 157 APPENDIX V DERIVATION OF THE FORMULAE FOR THE EXPLICIT FINITE DIFFERENCE METHOD Case 1 The element i s surrounded on a l l sides by homogeneous material (Fig. 100(a)). The temperature of a general nodal point X at r, z time t = k i s designated as T . . One i s interes t e d i n c a l c u l a t i n g r,z,k the temperature of this nodal point at time t = k + 1, knowing the temperatures of the surrounding nodal points at t = k. 54 Using the f i n i t e difference form of eq. (6.1), the temperature of the nodal point X at t = k + 1 i s given by the following equation C p k A - 2 — volume [T , ., - T . ] = — — [T . . - T ] At r,z,k+l r,z,k Ar r - l , z , k r,z,k k A k A k A + — — - TT - T 1 + fx - T 1 + [T Ar r+l,z,k r,z,k Az r,z+l,k r,z,k Az r , z - l , k T r , z , k J ( A - V - 1 ) where (1) k^ i s the average conductivity for the temperature range of T 1 , to T , etc. r - l , z , k r,z,k (2) volume of the element: volume = area of the base x height = ^ - [(rAr + ^ ) Z - (rAr - ^ f ) 2 ] Az = r A r 2 Az 2TT I I 158 (3) calculation of the area Fig. (100(b)) gives a schematic diagram for the area A^ A^ = shaded area l4 Let MR MR, MZ MZ 2TT , fr + r - L. . , . 2x7 [ ( 2 ) A r ] ( 2 r 2 *) Ar Az 2r" + 1 s i m i l a r l y A^ = ( 2 — ) Ar Az A^ = r Ar 2 2 A. = r i r p C Ar 2  P 1 k± At p C A r 2 = P 2 k 2 At p C Az 2 = 1 P. 3 k 3 At 2 p C Az = P 4 . k. At 4 On substituting these values i n eq. (A.V.I), one obtains T - T = c?-r~^—1 TT - T 1 + f 2 r + 1 ) TT - T 1 r,z,k+l r,z,k 2rMR^ r - l , z , k r,z,k J v2rMR 2' L r+l,z,k r,z,k J + MZ^ [ Tr,z+l,k " T r , z , k ] + MZ^ [ T r , z - l , k _ T r , z , k ] (A.V.2) 159 Case 2 For a general point on the upper surface as shown i n F i g . (101), the temperature at t = k+1 i s given by the following equation. C p volume k , A i ^ ? A ? —2 [T - T 1 = [T - T ] + x At r,z,k+l r,z,k Ar r - l , z , k r,z,k Ar k 4 A 4 r+l,z,k r,z,k top 3 r,z+l,k r,z,k Az r , z - l , k T ] (A.V.3) r,z,k r A r 2 where volume = • — - — Az ^ r - l . . . A x = (—4 - ) Ar Az A 2 = (—^j—) Ar Az 2 A^ = r Ar 2 A 4 « r Ar h. i s the heat transfer c o e f f i c i e n t for the top surface, top Oil s u b s t i t u t i n g these values i n (A.V.3) one obtains Tr,z,k+1 T r , z , k ^2rMR * [ T r - l , z , k T r , z , k ] + ( 2 r M R 2 ) [ T r + l , z , k 2 h t Q p At 2 T r , z , k J + p C Az [ T r , z + l , k _ T r , z , k ^ + MZ^ [ T r , z - l , k _ T r , z , k * (A.V.4) 160 Case 3 For a general point as shown i n F i g . (102) i f f ) I \ 8 h . , r At i T _ T = 4(2r-l) r T _ T i + side r,z,k+l r,z,k MR 1(4r-l) L r - l , z , k r,z,k J (4r-l) p C p Ar [ T r + l , z , k " T r 5 z , k - 1 + MẐ " [ T r , z + l , k ~ T r , z , k ^ + MẐ ~ [ T r , z - l , k ~ T r , z , k ] ' <A'V-5> Case 4 TT - T 1 = f 2 r 1 U T _ T 1 + / 2 r + 1 \ r T r,z,k+l r,z,k J ^rMR^ 1 r - l , z , k r,z,k J 4 r M R 2 M r+l,z,k 2 h At 9 T 1 + P-2JE TT - T 1 + —— TT r,z,k J C p p Az L r , z - l , k r,z,k J MZ 3 L r,z+l,k T r , z , k ] ( A - V ' 6 ) Case 5 For a general point as shown i n F i g . (103) 4 1 C _ X = —— TT - T 1 H — TT r,z,k+l r,z,k MR 1 r+l,z,k r,z,k J MZ 1 r,z+l,k T i ] + [ T , , - T . ] (A.V.7) r,z,k MZ^ r , z - l , k r,z,k 161 Case 6 For a general point as shown i n F i g . (104) T _ T = r^2v-l) , _ , • 8 r h s i d e A t : r,z,k+l r,z,k 1 ( 4 r - l ) M R 1 ' 1 r - l , z , k r,z,k J l ( 4 r - l ) p C p Ar ' 2 h f c o At l T r + l , z , k _ T r , z , k J + { p C At * [ T r , z + l , k _ T r , z , k ] + {_?_} fx ' - T , 1 (A.V.8) lMZ 4 J 1 r , z - l , k r,z,k J Case 7 . rr, -, \ 8 r h . , At f 4 ( 2 r - l ) i r^r _ T I 4. / S L D E p - T - r ̂  ; i I"T - T 1 + l > r,z,k=l r,z,k - 1(4r-l)MR 1^ 1 r - l , z , k r,z,k J 1 ( 4 r - l ) p C p Ar' 2 2 h b o t A t [ T r + l , z , k " T r , z , k ] + {MZ3"} [ T r , z + l , k ~ T r , z , k ] + {Az p C ? } [ T r z-1 k " T r z k ] ( A ^ - 9 > Case 8 For a general point as shown i n F i g . (105) 2 h At T - T = ( -} \T - T 1 + { ^ 2 } r,z,k+l r,z,k lMR/ 1 r+l,z,k r,z;,kJ p C Az fT - T 1 + {-2—} [T „ , - T , ] (A.V.10) 1 r,z+l,k r,z,k J x m ^ J 1 r , z - l , k r,z,k J Case 9 T - T = { r,z,k+l r,z,k MR„'} ^ Tr+l,z,k ~ Tr,z,k-' + *MZ, •} [T r,z+l,k 163 APPENDIX VI COMPUTER PROGRAMME TO DETERMINE THE POOL PROFILES IN ESR INGOTS ow chart of the computer programme Q~Start~A Read Data Assign an i n i t i a l temperature for every nodal point C l a s s i f y every nodal point i n t o one of the 9 possible cases C a l l the subroutine to read the p h y s i c a l properties at a l l 1=1,NN J = 1,N Compute the temperatures at a l l nodal points, i . e . evaluate A „. The physi c a l properties 1, J , z being taken for temperature A I , J , 1 - C a l l the subroutine to read the physic a l properties at AI,J,2 I = 1,NN J = 1,N t Compute the new A „ at a l l 1, J , z nodal points, taking average temperature between A - and 1, J , l A 9 for evaluating the p h y s i c a l 1, J , z properties Yes Define A .. = A „ L , J , Z Increase the time step [ s u n i t time i n t e r v a l reached Yes P r i n t out the temperature at each node Has the Z axis reached the maximum ingot length Yes ' " i t . Vt ' V .» C J . V I U . ' . ( W . J O - i i - II ItHliftt PAkic 0031 i: L rc1Pc .<^ru<r f>-kJFILES IN A\ E . S . R . l ^ l k i O T AbdREVlATI J * S U S E D I U r i u h t AXIS C J :U^.>1 M Jl 'JAL AXI i k, (. f. : ( M c AXIS C C .kl I . J . O : I ct;';.< ATU*e AT N J J 4 L P U 1 N T ( I . J i K I _C f. n i . J . M ^ c ' ^ . w W * TEMPERATURE LUC4TI0N FOR NOJAL POINT l i . J . O C k. J d . ^ . i W M E M P c K A T U K c UF THE ELEMENTS IN THE TOP LAYER t C ; ) I I . J . U - k o l l « 'JF VDLJrtc ELEMcHT AT I I . J . l O _C C k..'( I . J . K I : jf'Lk.1 i-'iC H E A T ;JF VJLU.1E ELEMENT AT ( I . J . K I C 0 i d • J . i O : | . - I L * 1 A L CjNIJJCriVirY (JF VOLUME ELEMENT AT (I.J.K.1 L C J tL I : I iHc i ' .C. i l I L M T C JIILK l o l i i : J r 1 He VdiJ.' l t ELEHeNT IN K J IRECTi : ) * C >. JcL£ J>= T H C V J L U M L E L E ^ E N T I N I D I R E C T U M c C <l : J f 1 <lik)T A T A N Y T I M E C N N !iWrtJc« OF cl c 1; -\ \ 3 IN THt R A D I A L UIKECT I3H C C JF : NF»ocL^: MAAliiJiH lNJJT HfclliHT C C i » : IJ'V-IUL A I I VL ALLJrfAdLE E^ROR L C NAJRY : I PJR AKHVIXI felr. EVALUATION k. •i^jif : I F J \ .UXJRAIE c V.iLUA TI J->» C C "4.(AIE : \\\*S u ' J t l . r : I ' M C : t tT«r:S^ Nfc* VflLUMt ELEMENT AkldlTION C k- H.,13,- : riEAl r .-iA.NJF E K l JE F F I C 1 :-N T F iR THE S U E XAI 1 S k. k. HjiJl : ( J / A ) ACK'JbS I H L ELEMt^I A(1.*N.K> FOR SURFACE B O l L l N j FilRTB»N IV ^ o J H P l L t x C J J Y 4 C k Ha J l HAi.« J 6 - ^ ' . - / I is : l2 :<»4 l ' J / A I F J * S j K F A C t u U R l . v ; : J/» ACMISS Trtt U J I I . M JF THE 1NGIH PACE J J 0 2 H l J r l A i . . w i b I HE >LAi»/METAL I>'Uti<rACr : J / M I-U* MuLU COOLING rfAIER A l THE i lUI FUH Pi|Y*>*. , : i j i t ^ j . J T I He JO e V A L U A f t T. lc P H Y S I C A L C<Ur»t: R T 1 fc S u S S d M r U U N S JJt.il r i iu n ii-i : .2-<•>. j T i-u 11:4 : j J d . J -.11'-."..* T !•->•) 0 0 0 4 n'»0 *: J i Mt " l i 1 urt A( I J , ] U , i I . I ( 1 J . S J . J I . i l l i J l 1 Lr* t I J . j u « <i I . L ( i J . 5 J . 2 I i.Ui1Mu:i A , J , O f . i . , .«.N.«. I . J . K . K L A J l b . i U - t L K . J E L Z . M i l J t . l i t U P , HBO T .HMjr.OELI. .-IJOI r u K M a T l o f l j . : > ) >ml I r In . . T j l , J I L K . , i r L / . D r l T Ml l j . J U l . D < 1 J . 5 0 . 2 I . 'U '0 7 0:10:) ? . )K 'UI | iX . /H)LL« = . F 1 J . 3 . 2 H C M . S X . 7 H D E L Z = . F 13 . 5 . 2 HCM. S X . 1 7 n j L L I = . r I J . •> , J H S L C ) «*1 Ictu.u iJ . 1 i l L , r .HIDr>,Hoyr . H M U r .HSOT r J K M A I ( j X . J H H j i U c = . H O . 5 . 5 X . 7HHTdr = ,F 1 0 . 5 . 5X . t = . t JA .7HH . - l j r = , f l 0 . b O X , 7 H H S j r = . F 1 J . 5 I KLAOI S. n 2<i<KAIt . .MF . N . . J N . 7 Y 0 0 1 1 101 J •1014 l-ii;<1AI < * I 3 , F o . 2 ) n U i Tc. ( j , 0 3 1 .'MA I E . N F , N . N N . Z Y F j ^ A I I i X . d H ' l i t A r E = . I J . b X . 5 H H E l i X o r i Z Y = , r ( > . 2 l N A J < Y = I Y ' J . J ! = . I 2 . 5 X . 4 H N = . 1 2 . S X . 5 H N N 0 0 1 S 0 0 l h 0 0 1 7 0 0 1 8 0 0 1 " 0 O ? l 0 0 2 ? 1 0 2 3 ao?s 1 1 7 4 i l l = :>l-i N2 =MN-1 «IR1 r t ( o , 6 < t l r . l K M A l I 10X,< . jHA:> iU1Eu I N I T I A L TEMPERATURE • I SIR 1 BUT I ON I U J 2 J = l . N l KfcALH j . j B l l T l l . J . l l . H . N H I F.jrfMAr < S F i a . u 1 O K I T c ( o . 9 d l I I I I . J . l ! C J i l T i H J t I K l ' y j 1=1 . i )J J = l . N i A l l . J . l l * T I l . J . l l ,1=1 .NNI 0 O ? 7 0O?R 0 0 2 9 C U r t M N U t KeALl i 5,ydll t i l I I t l ' l . N N I rfKlTE<o.o5J . O i 167 H N ii ii n I ^ N 3 • » • Z ' X X — . — — ^ ' . — — *3 II 2 • o — x r T T : > G O C O ^ * \ * ^ er i f r r c i ' o e o e c o e c o e c C -« t \ j t*> <t rr # •* * «ff o o o o o c c o c c c c i / \ *o r - cc a o * r ^ * r «» i n c o o o c o c o o o c c tM f o ^ i r NC IP IT <^ i f I f IT c c c c c c o c c c c c r̂ - c r <7* o •— rv IT IT IT -O ^ ' >f e o o o c c c o c c e o r ^ IT O K (T I - r -o - c o «£ • c c o o o c < c c c c c o < UJ — — • —< h- h» -̂ I c c c • c o c o J3 — — rv f~ a <r x o c c c c c 168 j o <r <r <r - O O "3 ?V « . . . .-r IMW \ ** ^ ^. -\j -t * t — - i $5 H i J J •* ** -T c . - ^ I J T <I <T "1 I If >l 1 * -1 - J J FORTRAN IV G COMPILER H U t 06-2*^/1 16312:** PASt UU05 ^ . 0137 A l ' I A I l - l . J . l l - A I I . J . l l l 0133 A * M A M , J - l . l ) - A < I . J . l l l I 0139 * X < A W . J . I > . D I M GO TO 20 • ' 01*1 17 C l - I C I I - l . J . l l * C l I . J . 1 1 1 / 2 . 0 01*2 C3>ICIl.J»l.ll*C(I.J.lll/2.0 01*3 A l - l A U - l . J . l l - A U . J . l l l i 01** A 3 ' I A I 1 . J * 1 . 1 I - A I I . J . 1 I I j 01*9 X-AI1,J.1I*C1*S3*A1»S5*C3*A3-S6*H«0T-S*«HNDT i 01*6 GO TU 20 01*7 18 C2-I C4 1*1. J . l ) * C I I . J . I 11/2.0 | 01*8 C * ' ( C < i . J - l . l l * C ( i . J . 1 ) 1 / 2 . 0 j 01*9 A 2 M A I U 1 . J . 1 1 - 4 ( 1 . J . I l l n w A*«tAU,J-l,ll-A(I.J.lll i 0151 X"AI1.J.11**.J*C2*A2/AH*S6»HTiP*C*»A*»S5 0152 GO TO 20 j 01S3 19 C2»IC(1*1.J.1I*CI1.J.111/2.0 015* C3MCI1. J*1.1)*CI I . J , 111/2.0 ! 0155 A2°|AU*l.J.l)-All,J.lll 0156 A 4 * t A ( l . J * l . l l - A ( I . J . l l ) 01 57 X>A(I.J.I»**.0*C2*A2/AH*A3*C3*S5-S6*HBDT .j 0158 20 Ui.J.2l«X 0159 21 CONTINUE 1 0160 00 22 1-l.NN 0161 00 22 J»2,Nl • .. . j 0162 A U . 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Ai.^SkUx^J.jJ.i.-Mlj,i»lijl - ... . • i J 170 r\l — — — r\J J \ r\J - » I " J ;» -» T '5 I -A —. — f\i r\i <NJ — — '.1 r \ i t \ ' \ j . ^ 1 » < - — — » -< — — -t <N -) - — — — — <t i <4( < f - i I I 1 • « » O "J O *T <T < r*\ -I -1 — i ' T -) • o o I . 1 • . * O -5 J _) * T 4 • o J _ ) _ ) - * < 4 o - J -J _> <* <r II II .i H — f -« -o * — •_) «* -T 1 <T ~ -vj n j - -j -n t n ^3 J J - j •< r c N» i; c r C £7 c c c o.c c c o t c c c >r u" •t >5" IN. ^ c e o 171 ~i * —• V iv r r, o c r C O — fv. •* *T IT IT IT T <T r . f*. «\ r . *\ e c c c c c -? -i -> r\j -î -j-J-g -1 J J 4 1 • II -t 'I tt _) 1 < >< V IT. x r» o .c O if *r tr ir if * f, <N: Cv fN c c c r c — • CN. r if\ J ^ »C -C •£ c. f\ r\j f\. r\, r-. c c C C C C NJ -J -3 o N IT C - \ •C O O f* r- r-r r\ fM r\ cv c r c c o c -» —< <* — • II < <-\J ll r~> «J in >c p» to J H - M 7 * > X . I • -« .1 -4 • a c — oi " T? x cf. (r tr tM f\> f \J rsj ev c c c c c u -f • r- T t x a. : i/> «c a" c c x o? c  cr or. a C ' fV C; f\ f\. f\. c c c o c o 172 — — n < C C c o o c i O O f> Ol O O O I -t O D - * O O T J • ! o ̂  . 3 n *- !*• x *f I T ^ r- rr c r O O Cj C c- c o c o c c c o c o c I -i — > "3 : 3 II II I — ^ - - 5 "3 II II -) • T O 1 • T O ~ «c p- cn f c --t — —' - * cv c c o o c o o c o c c C' c o o o c cc O* O —< rv r\j f\ m ro f c. o o c c c o o o c c rr «r ir *f cr ^ C C -"" |T f II — 11 < —4 A —• — c — M s t i r ^ -a" * »t C Q O O O O o c- O O O " sc co tr - T • * O C O C o c o c 173 BIBLIOGRAPHY 1. G.K. Bhat: Proc. Second Int. Symp. on ESR Technology, Vol. I, Mellon I n s t i t u t e , Pittsburgh, (IX, 1969). 2. W. Holzgruber, A. Schneidhofer, M. Kroneis: Proc. Second Int. Symp. on ESR Technology, Vol. I, Mellon I n s t i t u t e , Pittsburgh, (IX, 1969). 3. B.E.Paton, B.I. Medovar, Yu. V. Latash, L.V. Chekotilo: Proc. Second. Int. 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Sedina, A. Ia, Stomahin: Izv. Vysshikh. Uchebn. Zavedonii (Ferr. Met.), 5_, p 54-56 (1969). 79. D.A. Shulz and A.W. Searcy: J . Phys. Chem., 6_7, pp 103-106 (1963). 80. S. Cantor, W.T. Ward, C.T. Moynihan: J . Chem. Phys., 50(7), pp 2874-79 (1969). 81. J. Om Bockris, J.L. White, J.D. Mackenzie: Physico-chemical Measurements at High Temperatures, Butterworth's S c i e n t i f i c Pub., London, p. 347 (1959). 82. J.R. Rait: Trans. B r i t . Ceram. S o c , 40, pp 1941 (1941). 178 Figure 1. Schematic diagram of the e l e c t r o s l a g remelting unit. 179 y V > V C a t h o d e A n o d e Figure 2. Voltage gradient i n an arc. 180 N X - Water - cooled copper electrode -Color li th Rubber bellows •Thermocouple E l e c t r o d e •Gas seal Cu mold Water - jackel Figure 3. ESR experimental setup f or temperature measurement under an argon atmosphere. 181 thermocouple Cu mold elect rode mullite spacer boron nitride slag liquid metal Figure 4. D e t a i l s of the thermocouple arrangement. I 1— I I I I I . I I I I 1 3 5 7 9 Distance cm Figure 5. Temperature d i s t r i b u t i o n i n the slag bed for d.c. negative ( a i r ) .  1 3 5 7 9 D i s t a n c e cm Figure 7. Temperature d i s t r i b u t i o n i n the slag bed f o r a.c. ( a i r ) . Distanee c m Figure 8. Temperature d i s t r i b u t i o n i n the slag bed for a.c. (argon).  I 1 I 1 I I ' ' 1 1 1 1 3 5 7 9 Dis tance cm Figure 10 . Temperature d i s t r i b u t i o n i n the slag bed for d.c. positive - ' l i v e ' mold (argon). 0 5 cm 4, 1550 C 1550 1600 1600 1620 16 20 1630 16 30 1650%^ 1650 1650 1700 1 6 5 0 S ^ | 1675 1 700 1725 1725 I 1700 1700 1750 176 0 1725 1740 1760 1760 I 1725 1740 1760 1760 ] 1-5 cm 1-0 cm 4-5cm 4 0 cm Figure 11. Assumed temperature d i s t r i b u t i o n i n the slag bed (ingot no. 1). R = oo ohms 2 El c 3 4 5 6 / D D 0 v o l t s 7 8 10 11 12 14 15 16 17 1 8 1 9 20 21 22 2 3 24 25 X 2 6 2 7 2 8 2 9 R r oo ohm B 23-75 v o l t s Figure 12. Subdivision of the slag bed. Figure 13. Resistance of a volume element. R z / - W — M r RJ>2 R ^ 2 190 Figure 14. Resistance network. 191 Figure 15. Network resistance for a s i n g l e junction.  Figure 17. E f f e c t of f i n i t e mold wall-slag skin resistance on the i s o p o t e n t i a l contours Cslag skin r e s i s t i v i t y = 250 ohm cm). Figure 18. E f f e c t of f i n i t e electrode-slag skin resistance on-the i s o p o t e n t i a l contours (slag skin r e s i s t i v i t y =0.2 ohm cm). Figure 19. E f f e c t of f i n i t e electrode-slag skin resistance on the i s o p o t e n t i a l contours (slag skin r e s i s t i v i t y = 20 ohm cm). 1000 196. (a) Anodic p o l a r i z a t i o n curves f or CaF2-Al2C>3 slags determined by galvanostatic experiments.^ -m In i 0 A . Ci (b) Cathodic p o l a r i z a t i o n curves f or CaF2-Al2C>3 slags determined by galvanostatic experiments•12 Figure 20. 197 1-25H 2 3 _ 2 4 5 In i Q A . c m (a) A n o d i c p o l a r i z a t i o n c r u v e s on ESR e l e c t r o d e s i n CaF2-Al20.2 s l a g s 12 1-5 10 T wt-/. A l 2 0 3 0 Furnace Result I n i n A . c m-2 O 12 (b) C a t h o d i c p o l a r i z a t i o n c u r v e s on ESR e l e c t r o d e s i n CaF^-Al^O^ s l a g s . F i g u r e 21. n t e r f a c e D i s t a n c e C m interface Figure 22. Experimentally obtained voltage gradient i n the slag bath. 199 50 mV shunt -ve Recorder E lectrode Feed Control Unit Argon W3Re/W25Rl +ve 2x Hobart 750 powe r supplies Recorder Elect rode Set of 4 chromel -a lumel thermocouples Slag Figure 23. Schematic outline of the experimental set up for electrode temperature measurement. 200 Figure 24. Electrode temperature gradient for 2.54 cm diameter electrode AISI 1018 s t e e l i n electrode negative p o l a r i t y . of 201 electrode axis CM Figure 25. Electrode temperature gradient for 3.81 cm diameter electrode of AISI 1018 steel i n electrode negative p o l a r i t y . 202 electrode a x i s cm Figure 26. Electrode temperature gradient f o r 2.54 cm diameter electrode of AISI 321 s t e e l i n electrode negative p o l a r i t y . 2 0 3 electrode axis CM Figure 27. Electrode temperature gradient f o r 2.54 cm diameter e l e c t r o d e of AISI 1018 s t e e l i n el e c t r o d e p o s i t i v e p o l a r i t y . 204 e l e c t r o d e axis CM Figure 28. Electrode temperature gradient f o r 3.81 cm diameter electrode of AISI 1018 s t e e l i n electrode p o s i t i v e p o l a r i t y . 205 206 •oo Tslct I, z f / .1 z " 7? z V •B .TV S L^- eleptrode mold wqll a rgo n slag F i g u r e 30. O u t l i n e diagram t o i l l u s t r a t e the parameters used i n the computation of the e l e c t r o d e temperature g r a d i e n t .  208 32. Electrode temperature gradients f or 3.81 cm diameter electrode of AISI 1018 s t e e l i n electrode negative p o l a r i t y i n VAR and ESR processes. 209 electrode water slag I mold (a) mold insulated (b) mold grounded metal pool water mold i elect rode slag metal pool Figure 33. Current paths in an ESR mold 210 R e c o rd e r 3 Ohm ^ M e t e r H P 4 3 2 8 A ^ - R e c o r d e r 1 • • R e c o r d e r 2 u 2 3 4 5 6 8 Figure 34. Experimental apparatus for measuring the e l e c t r i c a l and thermal resistance of the slag skin. (1) 0.5 cm diameter graphite rod, (2) 450 kHz induction c o i l , (3) thermal i n s u l a t i o n , (4) graphite c r u c i b l e , (5) boron n i t r i d e i n s u l a t i n g sleeve, (6) 3.0cm diameter x 3 cm high copper cylinder, (7) approximately 1 l t r . of l i q u i d s l a g , (8) boron n i t r i d e i n s u l a t o r for slag temperature thermocouple. 211 o' l 1 1 J i Cl 0 100 200 300 400 500 T e m p e r a t u r e C Figure 35. Slag skin e l e c t r i c a l resistance as a function of temperature (slag temperature constant at 1600°C). 212 Figure 36. Slag skin e l e c t r i c a l resistance as a function of temperature for CaF„ slag at different slag bath temperatures,. 2 X 3 T i me s e c Figure 37. Time dependence of cy l i n d e r thermal parameter; slag temperature constant at 1650°C. 214 0 4 8 10 T i me sec re 38. * Time dependence of cylinder thermal parameter; slag compos tio n constant at CaF„ + 25 wt.% M „ 0 - . 215 slag skin interface - mold Figure 39. Radial dimensions of the mold-slag skin system. i nterf ac e D / 1100 water mold / slag skin 110 — 14C B f C 5 ° A - > 1420 1650 slag radius Temperature C Figure 40. Mold region temperature p r o f i l e derived from eq. (4.8) by -2 -1 -1 -1 assuming that k g i a g = 0.8 x 10 c a l cm °C sec Figure 41. (a) View of the laboratory ESR unit. (b) Powder feeder h-1 ON 217 a Figure 42. Mold connection i n ESR p r a c t i c e . (a) l i v e (b) f l o a t i n g (c) insulated 218 Figure 43. Atmospheric shield (type ( I ) ) . Figure 44. Atmospheric s h i e l d (type ( I I ) ) . 220 electrode sliding sea argon in 1 mold cap Polyethylene bag / slag adding ] { unit / I Cu mold slag solidified ingot Figure 4 5 . Atmospheric shield (type ( I I I ) ) . height of the ingot Figure 46. Mold current i n d.c. +ve ' l i v e ' operation. 34 C M ho 222 Figure 47. Thermocouple arrangement on the mold. Figure 48. Thermocouples clad copper molds. gure 49. Temperature p r o f i l e on the mold for ingot no. 1. 225 T e m p e r a t u r e ( ° C ) Figure 50. Temperature p r o f i l e on the mold for ingot, no. 3. Figure 51. Temperature p r o f i l e on the mold for ingot no. 8. Figure 52. Temperature p r o f i l e on the mold for ingot no. 9. Figure 53. Temperature p r o f i l e on the mold for ingot no. 10. 229 Temperature °C Figure 54. Temperature p r o f i l e on the mold for ingot no. 13. i Figure 55. Temperature p r o f i l e on the mold for ingot no. 16. 231 Temperature °C 110 9 0 7 0 5 0 Figure 56. Temperature p r o f i l e on the mold for ingot no. 19. 232 gure 5 7 . Temperature d i s t r i b u t i o n i n the mold cooling water for ingot no. 1.  2 err em T = 1590°C c = 2.08 ohm ''"cm ̂ T = 1640°C c = 2.30 ohm "'"cm ̂ T = 1712.5°C c •= 2.64 ohm "*"cm "*" T=1675 c=2.46 _ A ohm cm T = 1750°C c = 2.86 ohm "'"cm ̂ I. 23-75 Vo l ts Figure 59. Voltage gradients i n the slag bed for ingot no. 1. 2 3 5 236 > 1 O N 1 h - — CO cn C r | < J C y5 C | . A T s a t h f g • P r | 1 - 7 Figure 61. C o r r e l a t i o n of p o o l - b o i l i n g heat t r a n s f e r data 47 237 F 600- CN • D CO CO o X cr l< 2 60 10 L L L L L 5 90 p s i a o water tempera ture = 2 70 F o s a t u r a t i o n t e m p e r a t u r e = 3 2 0 F v e l o c i t y = 1 f t . sec -6— s t e a m p r e s s u r i z e d 0-3 cc a i r . I it re -^ -X— a i r p r e s s u r i z e d 6 9 cc a i r . l i t re • i i i • ' M l 20 A T = Two II - Twater ( ° F ) 48 Figure 62. E f f e c t of d i s s o l v e d a i r on the heat f l u x 238 50 h i o g (a surface boiling (distil led water) 1 — - non - bo i l ing I I M i l l _L 40 60 100 20 0 AT = Tmold - Twate r = T m o l d (°C) - 5 0 Figure 63. Plot of (q/A) vs. AT for (a) non-boiling and (b) surface b o i l i n g conditions. 239 <1A >1B •4A M B Q 4 = Q 4 A + Q 4 B I iquid metal Q 7 solidified i ngot B i heat required to melt the el e c t r o d e heat required to superheat the l i q u i d metal drops heat l o s t by r a d i a t i o n from the s l a g surface to (A) mold c o o l i n g water, (B) gases, (C) ele c t r o d e heat l o s t to mold c o o l i n g water across the s l a g bed heat t r a n s f e r r e d across S/M i n t e r f a c e as s e n s i b l e heat of the f a l l i n g metal drops heat t r a n s f e r r e d across S/M i n t e r f a c e by convective heat t r a n s f e r heat l o s t to mold c o o l i n g water across the l i q u i d metal pool heat l o s t to mold c o o l i n g water across the s o l i d i f i e d ingot heat l o s t to base p l a t e c o o l i n g water s e n s i b l e heat r e t a i n e d by the s o l i d i f i e d i n g o t . Figure 64. Heat d i s t r i b u t i o n i n an ESR u n i t . Q A P = 1 3 7 J L Cal.secl gure 65. Heat generation d i s t r i b u t i o n i n the slag bed (for ingot no, 1) Q 2 A = 487 cal.sec -1 Heat Input = 6 6 5 0 cal .sec 1 JL^>Q3 = 2597 cal. sec 4 -1 0.4^ = 1060-5 cal.sec - i Q 4 B = 2505-5 cal .sec -1 Figure 67. Block diagram for the heat balance of the slag region. l iquid metal Q 4 - 3566 Cal .sec -1 Q 9 = H65Ca l .sec Ca l Q 5 = 2401 ^ v - u i . s e c N 2 4 2 Figure 68. Block diagram for the heat balance of the l i q u i d metal region. Q 9 =H65Cal.sec -1 so l id i f ied ingot Q 3 = 4 0 4 C o l . sec -1 C*6 = 5 4 0 Cal-sec -1 -1 Q 7 = 410 C a l . sec Figure 69. Block diagram for the heat balance of the s o l i d i f i e d ingot. ( a ) d.c. +ve mold 18 v Rj= '' - ingot R3= mold - > > 11 ( b ) d.c.-ve mold 20-5 v «1 + ve electrode 23 v l 2 h R- resistance R3 ingot -ve electrode -ve 0 v R2 R3 i ngot 23v +• ve Figure 70. ESR unit's analog c i r c u i t . (a) I.N. 27 ( b ) | . N . 2 9 Figure 71. Pictures of slag cap and slag skin of some of the ESR melts of FVE 4>   247 e s r with cover. 400C- y~ without cover 200( 11_ . 100C 5 700 400 for 12 ton urnac Boehler ESR ave. a l l grades f o r optimum pool depth ^ Boehler ESR ave. for die s t e e l , low a l l o y s , s t a i n l e s s s t e e l s and high temperature a l l o y s . 200 i i 10 20 40 60 80 Ingot diameter in Figure 73. Boehler si n g l e phase a.c. ESR melt rate vs. ingot A- , 6 diameter. radial _ dend rites High melt rate Low melt rate Figure 74. E f f e c t of melt rate on the shape of the l i q u i d metal pool. N3 00 e l e c t r o d e molten slag mol ten metal D t Z + A + ABC D : cyl ind rical por t ion of the molten metal pool D E F G C : curved por t ion of the mol ten metal pool Figure 75. Subdivision of the molten metal pool. N3 2 5 0 Figure 77. Subdivision of the ingot. 110f  Figure 82. Predicted pool p r o f i l e for ingot no. (16). Figure 83. Predicted pool p r o f i l e for ingot no. (21). r o 4--  7 257 Figure 87. A schematic diagram of the apparatus of the measurement of density of CaF2 based slags. (A) transducer, (B) l u c i t e box, (C) argon gas i n l e t , (D) s t a i n l e s s s t e e l support, (E) thermocouple, (F) water cooled s t a i n l e s s s t e e l l i d , (G) AI2O3 tube, (H) 0.025 cm diameter tungsten wire, (I) molybdenum bob, (J) l i q u i d s l a g , (K) molybdenum l i n e d graphite c r u c i b l e , (L) graphite f e l t , (M) induction c o i l , (N) AI2O3 tube to support the c r u c i b l e , (0) thermocouple connected to induction f/c c o n t r o l l e r , (P) vycor glass tube, (Q) water cooled s t a i n l e s s s t e e l base, (R) argon gas e x i t . 1 A 10 slow blow 5 V 2 0 0 mA 50K bloc green shield white 1 V 100 m A _L_A slow 1 0 blow ( W v v v ^ w w c W 1 | offset | on o off tranducer offset zero balance recorder 0 0 output Figure 88. External c i r c u i t r y required to operate the transducer. Figure 89. The density measurement apparatus. «3   Dens i ty g r a m s - c m ro ro ro • • . Z9Z 263 Figure 93. A schematic diagram of the apparatus f or the measurement of v i s c o s i t y of CaF£ based slags. (A) graduated stem, (B) argon gas i n l e t , (C) thermocouple junction,(D) s t e e l frame support, (E) brass l i d , (F) vycor glass tube, (G) suspension wire (5 thou W), (H) mirror, (I) s t a i n l e s s s t e e l frame, (J) brass r i n g to support thermocouple leads, (K) molybdenum thermocouple leads, (L) mercury pool, (M) alumina tube, (N) water cooled base, (0) thermocouple (W-W-26% Re), (P) s t e e l l i d f or the glass tube Q, (Q) vycor glass tube, (R) water cooled copper induction c o i l , (S) graphite wool, (T) inner molybdenum c y l i n d e r , (U) l i q u i d s l a g , (V) outer molybdenum l i n e d graphite c y l i n d r i c a l c r u c i b l e , (W) shaft connected to the motor, (X) water cooled base, (Y) s t e e l frame to support the l i d P, (Z) argon gas o u t l e t .  265 266 120 tA o a c a> u 100 80 60 \ \ \ v° \ \ \ \ \ \ \ N x \ N \ \ . \ \ \ \ \ \ \ \10 \ 1500 X : present work 0 : Davis & Wr ight 7 3 w t o / o A l 2 0 3 1600 Temperature C Figure 97. V a r i a t i o n of c o e f f i c i e n t of v i s c o s i t y with temperature f or C a F 2 - A l 2 0 3 system. 267 268 269 Figure 102. General element for case 3. 270

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