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Thermal characteristics of the electroslag remelting process Joshi, Satish V. 1971

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THE THERMAL CHARACTERISTICS OF THE ELECTROSLAG REMELTING PROCESS  BY  SATISH V. JOSHI B.Tech.(Hons),  I n d i a n I n s t i t u t e o f 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 a c c e p t t h i s t h e s i s as conforming t o the required  standard  THE UNIVERSITY OF BRITISH COLUMBIA J u l y , 1971  In  presenting this  thesis  an advanced degree at  further  agree  fulfilment  the U n i v e r s i t y of  the L i b r a r y s h a l l make I  in p a r t i a l  it  freely  of  the  requirements  B r i t i s h C o l u m b i a , I agree  available  for  that permission for extensive copying of  of  this  representatives. thesis for  It  i s understood that c o p y i n g o r  financial  gain shall  written permission.  Department  of  M e.tg*. 11  ^TfpJ  The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada  Date  not  that  r e f e r e n c e and s t u d y . this  thesis  f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department by h i s  for  or  publication  be allowed without my  ii  ABSTRACT  The  t h e r m a l 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 r e m e l t i n g  process  have been i n v e s t i g a t e d on a l a b o r a t o r y s c a l e u n i t . The The  heat g e n e r a t i o n  voltage  gradients  network analogue and  and  d i s t r i b u t i o n i n the s l a g bed  i n the s l a g bed tested against  are p r e d i c t e d u s i n g  discussed.  a resistance  experimental r e s u l t s .  A s e l f - c o n s i s t e n t model f o r e l e c t r o d e i n the e l e c t r o s l a g r e m e l t i n g  is  p r o c e s s has  temperature  gradients  been t e s t e d a g a i n s t  experimental  results. An  u n s t e a d y - s t a t e method has  been used to determine the  r e s i s t a n c e and  the o v e r a l l heat t r a n s f e r c o e f f i c i e n t  region,  s l a g / s l a g s k i n / c o p p e r w a l l i n the e l e c t r o s l a g  An  liquid  accurate  of the i n t e r f a c e  heat b a l a n c e of the p r o c e s s i s c a r r i e d out  tory scale ingots.  A t t e n t i o n has  been devoted to the  electrical  furnace. on  labora-  influence.of  v a r i o u s melt parameters i . e . p o l a r i t y , power i n p u t , geometry, atmosphere e t c . on the melt r a t e .  The  power requirements and  i n d u s t r i a l i n g o t s are p r e d i c t e d and from the The  compared w i t h the d a t a c o l l e c t e d  literature. l i q u i d m e t a l p o o l volumes i n ESR  the o p e r a t i o n a l data.  The  d i f f e r e n c e t e c h n i q u e and profiles.  the melt r a t e f o r  i n g o t s are p r e d i c t e d  p o o l p r o f i l e s are computed u s i n g a  compared w i t h the e x p e r i m e n t a l l y  from finite  obtained  iii  TABLE OF CONTENTS Page TITLE PAGE  .  i  ABSTRACT  i i  TABLE OF CONTENTS  i i i  LIST OF FIGURES  x  LIST OF TABLES  xvi  LIST OF SYMBOLS . ..;  xvii  ACKNOWLEDGEMENTS  xxiv  CHAPTER I .  INTRODUCTION  1  1.1 . The E l e c t r o s l a g Remelting P r o c e s s  1  1.2  Statement o f the Problem  4  1.3  The U.B.C. E l e c t r o s l a g U n i t  6  1.4  Choice o f M a t e r i a l s  7  CHAPTER I I .  DETERMINATION OF VOLTAGE GRADIENTS IN THE SLAG BED OF THE ESR PROCESS  10  11.1  Mechanism o f Heat G e n e r a t i o n  ..  11.2  Measurement of Temperature i n the S l a g Bed  11.3  D e t e r m i n a t i o n o f I s o p o t e n t i a l Contours i n the  10 12  Molten S l a g Bed  13  I I . 3.1  Introduction  .13  11.3.2  S o l u t i o n 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  E l e c t r o c h e m i c a l p o l a r i z a t i o n i n ESR  11.5  E f f e c t o f Ca and A l D i s s o l v e d i n the S l a g  18  11.6  Measurement of V o l t a g e  19  Gradients  i n t h e S l a g Bed....  .18  iv Page CHAPTER I I I .  ELECTRODE TEMPERATURE GRADIENTS IN THE ELECTROSLAG PROCESS  20  III.l  Introduction  20  III. 2  Experimental  22  111.2.1  Temperature Measurement  22  111.2.2  ESR Operating Conditions  22  III. 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  C o r r e l a t i o n 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.2.2  V.2.3  V.2.1.4  S l a g Composition  55  V.2.1.5  Polarity  55  V.2.1.6  Continuous S l a g A d d i t i o n  55  V.2.1.7  Atmosphere C o n t r o l  V.2.1.8  E x p e r i m e n t a l Data  . 55 56  Measurement of Temperature P r p f i l e s i n the Mold Measurement of the Heat L e a v i n g  Through  the Bottom of the Mold V.3  65  D i s t r i b u t i o n of Heat Input i n the S l a g Bed  65  V.3.1  Power Input  65  V.3.2  Resistance  V.3.3  E f f e c t of D i s s o l v e d Ca and  V.3.4 V.4  56  Heating  of the S l a g A l on  66 the  C o n d u c t i v i t y of the S l a g  68  Heat G e n e r a t i o n  71  Due  to P o l a r i z a t i o n  An A n a l y s i s of the Heat T r a n s f e r r e d  to Mold  Cooling  Water  71  V.4.1  Introduction  V.4.2  Non-boiling  V.4.3  V. 4.4  71 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 T r a n s f e r C o e f f i c i e n t i n the N o n - b o i l i n g Region  75  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 D i s s o l v e d A i r  80  Calculations  80  V.4.4.1  Introduction  80  V. 4.4. 2  Region A  81  vi Page  V.5  V.4.4.3  Region C  82  V.4.4.4  Region B  82  A D e t a i l A n a l y s i s o f the Heat D i s t r i b u t i o n i n the L a b o r a t o r y ESR U n i t  85  V.5.1  Introduction  85  V.5.2  Heat B a l a n c e o f the S l a g Bed Region  85  V.5.2.1  Heat Input  85  V.5.2.2  Heat Output  85  V.5.2.2.1  V.5.2.2.2  Heat R e q u i r e d t o M e l t the E l e c t r o d e  85  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  86  Heat L o s t t o C o o l i n g Water A c r o s s the S l a g Bed  87  Heat P i c k e d up by the F a l l i n g L i q u i d Metal Droplets  87  V.5.2.2.3  V.5.2.2.4  V.5.2.3  Heat D i s t r i b u t i o n i n the S l a g Bed  88  V.5.2.3.1  Introduction  88  V.5.2.3.2  Heat Balance of the Region Above the Electrode Tip  89  Heat B a l a n c e of the Region Below the Electrode Tip  89  V.5.2.3.3  V.5.3  Approximate C a l c u l a t i o n of t h e Heat T r a n s f e r C o e f f i c i e n t Across the L i q u i d S l a g - L i q u i d Metal Interface  90  V.5.4  Heat Balance o f the L i q u i d M e t a l Region..  91  V.5.5  Heat B a l a n c e 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  vii Page V.5.5.2.1  Heat Going to Mold C o o l i n g Water  91  V.5.5.2.2. Heat Going to Base P l a t e C o o l i n g Water.. V.5.5.2.3  S e n s i b l e Heat by  V.5.5.2.4 V.5.6 V.6  92  T o t a l Heat Output 1, 10 and  ...  93  16  93  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  V.6.2  E f f e c t of E l e c t r o c h e m i c a l and Reactions  V.6.3  E f f e c t of P o l a r i t y on the S l a g Thickness  V. 6.4  CHAPTER VI.  PREDICTION OF POOL VOLUMES IN ESR  Introduction  VI.2  P r e d i c t i o n of the Height of the P o o l Volume  .. Skin  104  INGOTS  Explicit  VI.3.2  D e r i v a t i o n of the Formulae F o r the F i n i t e D i f f e r e n c e Method  VI.3.4  Results  CONCLUSIONS  116  118  Introduction  S a l i a n t Features  • 105  of the C y l i n d r i c a l P o r t i o n  VI. 3.1  VI.3.3  102  116  P r e d i c t i o n of P o o l P r o f i l e s Using D i f f e r e n c e Method  CHAPTER V I I .  93  Chemical  C o r r e l a t i o n and P r e d i c i t i o n of O p e r a t i n g Parameters f o r E l e c t r o s l a g P r o c e s s i n g . . . .  VI.1  VI.3  Retained  the Ingot  Heat Balance f o r Ingot Nos.  92  Finite 119 1.19 Explicit  of the Computer Programme  120 121 129  131  viii Page APPENDIX I .  THE PHYSICAL PROPERTIES OF ESR SLAGS  134  A.I.I  Introduction  134  A.I.2  Measurement o f D e n s i t y o f CaF^ Based S l a g s  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 A.I.3  Results  141  Measurement of V i s c o s i t y o f the CaF^ Based S l a g s .  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  Calibration  144  A.I.3.2.4  E r r o r s Involved  14,5  A.I.3.3  APPENDIX I I .  Results  CALCULATION  146  OF THE RESISTANCE  OF THE VOLUME  ELEMENTS IN THE VOLTAGE GRADIENT ANALYSIS A.II.l  Introduction  A. I I . 2  C a l c u l a t i o n of R  147 147 147  z A. I I . 3 A. I I . 4  C a l c u l a t i o n of R r C a l c u l a t i o n of R and R g  148 1 3  148  APPENDIX I I I . COMPUTER PROGRAMME TO DETERMINE THE TEMPERATURE GRADIENTS ON THE MOLD  150  ix Page APPENDIX IV.  CALCULATION OF POWER REQUIREMENT FOR MAKING AN INDUSTRIAL SCALE INGOT  APPENDIX V.  154  DERIVATION OF FORMULAE FOR THE EXPLICIT FINITE DIFFERENCE METHOD  APPENDIX V I .  157  COMPUTER PROGRAMME TO DETERMINE THE POOL PROFILES IN ESR INGOTS  BIBLIOGRAPHY  163  •/  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  2  V o l t a g e g r a d i e n t i n an a r c  3  ESR e x p e r i m e n t a l s e t up f o r temperature measurement  .  178 179  under an argon atmosphere  180  4  Details  181  5  Temperature d i s t r i b u t i o n i n the s l a g bed f o r d.c. negative ( a i r ) Temperature d i s t r i b u t i o n i n the s l a g bed f o r d.c. n e g a t i v e (argon)  183  Temperature d i s t r i b u t i o n i n the s l a g bed f o r a.c. (air)  184  Temperature d i s t r i b u t i o n i n the s l a g bed f o r a.c. (argon)  185  Temperature d i s t r i b u t i o n i n the s l a g bed f o r d.c. p o s i t i v e (argon)  186  Temperature d i s t r i b u t i o n i n the s l a g bed f o r d.c. p o s i t i v e - ' l i v e ' mold (argon)  187  6  7  8  9  10  11  o f the thermocouple arrangement  182  Assumed temperature d i s t r i b u t i o n i n the s l a g bed (ingot  no. 1)  188  12  S u b d i v i s i o n of the s l a g bed  189  13  R e s i s t a n c e of a volume element  189  14  R e s i s t a n c e network  190  15  Network r e s i s t a n c e  16  Isopotential  • 17  18  for a single junction  c o n t o u r s i n the ESR s l a g bed  191 192  E f f e c t of f i n i t e mold w a l l - s l a g s k i n r e s i s t a n c e on the i s o p o t e n t i a l c o n t o u r s Cslag s k i n r e s i s t i v i t y = 250 ohm cm)  193  E f f e c t of f i n i t e e l e c t r o d e - s l a g s k i n r e s i s t a n c e on the i s o p o t e n t i a l c o n t o u r s ( s l a g s k i n r e s i s t i v i t y = 0.2 ohm cm)  194  xi  Figure 19  20  Page E f f e c t of f i n i t e e l e c t r o d e - s l a g s k i n r e s i s t a n c e on the i s o p o t e n t i a l c o n t o u r s ( s l a g s k i n r e s i s t i v i t y = 20 ohm cm) (a)  Anodic p o l a r i z a t i o n curves f o r CaF2-Al20"3 s l a g s determined by g a l v a n o s t a t i c experiments !  196  C a t h o d i c p o l a r i z a t i o n curves f o r CaF2~Al203 s l a g s determined by g a l v a n o s t a t i c experiments-^7  196  Anodic p o l a r i z a t i o n curves on ESR CaF -Al 0 slags  197  12  (b)  21  (a)  electrodes i n  1 2  2  (b)  2  3  C a t h o d i c p o l a r i z a t i o n curves on ESR in CaF -Al 0 s l a g s  electrodes 197  1 2  2  22  23  24  25  26  27  28  29  30  31  195  2  3  Experimentally obtained voltage gradient bath  i n the s l a g 198  Schematic o u t l i n e of the e x p e r i m e n t a l s e t up f o r e l e c t r o d e temperature measurement  199  E l e c t r o d e temperature g r a d i e n t 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 e l e c t r o d e n e g a t i v e polarity  200  E l e c t r o d e temperature g r a d i e n t f o r 3.81 cm dimater e l e c t r o d e of AISI 1018 s t e e l i n e l e c t r o d e n e g a t i v e polarity  201  E l e c t r o d e temperature g r a d i e n t f o r 2.54 cm diameter e l e c t r o d e of AISI 321 s t e e l i n e l e c t r o d e n e g a t i v e polarity  202  E l e c t r o d e temperature g r a d i e n t 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 e l e c t r o d e p o s i t i v e polarity  203  E l e c t r o d e temperature g r a d i e n t f o r 3.81 cm diameter e l e c t r o d e of AISI 1018 s t e e l i n e l e c t r o d e p o s i t i v e polarity  204  E l e c t r o d e temperature g r a d i e n t f o r 2.54 cm diameter e l e c t r o d e of AISI 321 s t e e l i n e l e c t r o d e p o s i t i v e polarity  205  O u t l i n e diagram to 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  206  V a r i a t i o n of c o n f i g u r a t i o n f a c t o r w i t h a x i a l and 3  length 2  07  xii  Figure 32  33  34  35  36  37  38  Page E l e c t r o d e temperature g r a d i e n t s f o r 3.81 cm diameter e l e c t r o d e of AISI 1018 s t e e l i n e l e c t r o d e n e g a t i v e p o l a r i t y i n VAR and ESR p r o c e s s e s  208  C u r r e n t paths i n an ESR mold (b) mold grounded  209  (a) mold  insulated  E x p e r i m e n t a l apparatus f o r measuring the e l e c t r i c a l and thermal r e s i s t a n c e o f the s l a g s k i n  210  S l a g s k i n e l e c t r i c a l r e s i s t a n c e as a f u n c t i o n o f temperature ( s l a g temperature c o n s t a n t at 1600°C)...  211  S l a g s k i n e l e c t r i c a l r e s i s t a n c e as a f u n c t i o n of temperature f o r CaF£ s l a g a t d i f f e r e n t s l a g b a t h temperatures  212  Time dependence o f c y l i n d e r thermal parameter; temperature c o n s t a n t at 1650°C  slag 213  Time dependence of c y l i n d e r thermal parameter; c o m p o s i t i o n c o n s t a n t at CaF^ + 25 wt.% A ^ O ^  slag  39  R a d i a l dimensions of the m o l d - s l a g s k i n system  40  Mold r e g i o n temperature p r o f i l e d e r i v e d from eq. (4.8) by assuming t h a t k = 0.8 x 10~2 cm-l°C-lsec-l ft??  41  42  (a) (b)  view of the l a b o r a t o r y ESR powder f e e d e r  Mold  c o n n e c t i o n i n ESR  (a) l i v e  C  214 215  al 215  unit 216'  practice  (b) f l o a t i n g  Cc) i n s u l a t e d  217  43  Atmospheric s h i e l d  (type ( I ) )  218  44  Atmospheric s h i e l d  (type ( I I ) )  219  45  Atmospheric s h i e l d  (type ( I I I ) )  220  46  Mold c u r r e n t i n d.c. +ve  'live'  47  Thermocouple  on the mold  48  Thermocouples  49  Temperature  p r o f i l e on the mold f o r i n g o t no. 1 ....  224  50  Temperature  p r o f i l e on the mold f o r i n g o t no. 3 ....  225  arrangement  operation  c l a d copper molds  221 222 223  xiii Figure  Page  51  Temperature  profile  on  t h e mold  f o r ingot  no.  8  ....  226  52  Temperature  profile  on  the mold  f o r ingot  no.  9  ....  227  53  Temperature  profile  on  the mold  f o r ingot  no.  10  ...  228  54  Temperature  profile  on  the mold  f o r ingot  no.  13  ...  229  55  Temperature  profile  on  the mold  f o r ingot  no.  16  ...  230  56  Temperature  profile  on  the mold  f o r ingot,  57  Temperature  d i s t r i b u t i o n i n the mold  ingot 58  59  no.  cooling  19  ...  231  water f o r  1  232  P l o t of temperature v s . d i s t a n c e from the i n t e r f a c e f o r base p l a t e thermocouples Voltage  no.  gradients  i n the slag  bed  slag/metal 233  f o r ingot  no.  1  ..  234  45 47 60  Plot  of heat  f l u x vs. excess temperature  .'.  235  47 61  Correlation  of p o o l - b o i l i n g  heat transfer  data  236  48 62  Effect  63  Plot  of d i s s o l v e d  of  surface  (q/A) v s . AT  a i r on  f o r (a) n o n - b o i l i n g  237 and  (b)  b o i l i n g conditions  64  Heat  d i s t r i b u t i o n i n an ESR  65  Heat  generation  ingot  the heat f l u x  no.  1)  lost  by  238 unit  239  d i s t r i b u t i o n i n the s l a g  bed ( f o r 240  66  Heat  67  Block  diagram f o r the heat balance of the s l a g  68 69  radiation  from the s l a g  surface  Block  diagram f o r the heat b a l a n c e of the  metal  region  Block  diagram  241 region  liquid 242  f o r the heat balance o f the  solidified  ingot 70  ESR  71  Pictures ESR  242  unit's  melts  241  analog  of s l a g  circuit cap and  243 slag  skin  o f some o f  the 244  xiv Figure 72  Page P i c t u r e s of the s l a g ESR m e l t s  cap  73  Boehler single diameter6  phase  a.c.  74  Effect  rate  of melt  and  slag  s k i n o f some o f  the 246  on  ESR  melt  t h e shape  rate vs.  of the  ingot  liquid  metal pool  248  75  Subdivision  of the molten  76  Macrographs  o f ESR  77  S u b d i v i s i o n of the i n g o t  78  Average  metal pool  249  ingots  250 251  :  the  247  temperature  solidified points  distribution  on  the mold  across  ingot  252  79  Nodal  configuration  126  80  Predicted  pool  profile  f o r ingot  no.  (1)  253  81  Predicted  pool  profile  for ingot  no.  (10)  253  82  Predicted  pool  profile  f o r ingot  no.  (16)  254  83  Predicted  pool  profile  f o r ingot  no.  (21)  254  84  Predicted  pool  profile  for ingot  no.  (26)  255  85  Predicted  pool  profile  for ingot  no.  (28)  255 21  86  Electrical  87  A schematic diagram  c o n d u c t i v i t y of CaF2~Al20  ment o f d e n s i t y 88 . 89  External The  o f CaF^  circuitry  density  of  based  required  slags  3  the apparatus slags  257  to operate the  91  Density vs.  temperature  f o r CaF2~Al20  92  Density vs.  temperature  f o r CaF2~Ca0 system  A  94  A  o f o x i d e s on  schematic diagram of v i s c o s i t y  c l o s e up v i e w  the surface  of the  tension  apparatus  o f CaF2 b a s e d  of the v i s c o s i t y  258 259  Effect  ment  transducer  measurement a p p a r a t u s  90  93  256  f o r the measure-  3  o f CaF^^^'''^  system  f o r the  261 262 measure-  slags measurement  260  263 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 o f v i s c o s i t y w i t h % A1„0„ at 1600°C 7....  265  V a r i a t i o n of c o e f f i c i e n t f o v i s c o s i t y w i t h temperat u r e f o r CaF2-Al20.j system  266  98  Schematic  diagram of the s e c t i o n  of the s l a g bath  ..  267  99  Schematic  diagram of the s e c t i o n  of the s l a g bath  ..  267  97  100  G e n e r a l element  f o r case 1  268  101  G e n e r a l element  f o r case 2  269  102  G e n e r a l element  f o r case 3  269  103  G e n e r a l element  f o r case 5  270  104  G e n e r a l element  f o r case 6  270  105  G e n e r a l element  f o r case 8  270  xvi L I S T OF  TABLES  Table  Page  I  Composition  II  Parameters used  i n the  in  Fig.  III  Fig.  of  (24)  to  the  alloys studied  7  computation  of  curves  shown  (29)  33  V a l u e s o f t h e 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 f r o m t h e d a t a o f F i g . (37) and F i g . ( 3 8 ) .  42  36 IV  Operating  V  ESR  VI  Chemical  VII  C a l c u l a t i o n of bed u s i n g a . c . C a l c u l a t i o n of  heat input electrical heat input  d i s t r i b u t i o n i n the conductivity d i s t r i b u t i o n i n the  bed  electrical  conductivity  VIII  melt  resistances  i n the  process  43  record  57  analysis  using  d.c.  the  25  X  Physical properties  XI  Heat b a l a n c e  for ingot  XII  Experimental  r e s u l t s f o r the to  for  EN  Experimental  shunted  data  of  IX  and  ESR  ingot  of  ground  no.  water no.  steel  1  at  1,  Calculated  values  of  Z  for  10  XIV  Calculated  values  of  Z for  slag 67 slag 70  (Table  V)  74  and  74  16  94  i n s u l a t e d mold  the  62  40-50°C  t h r o u g h 0.5  XIII  ingots  ohm  unshunted  resistor36  laboratory  industrial  99  made i n g o t s  ingots  110 112  51 XV  Operating  XVI  Physical  XVII  Parameters used i n the EN 25 and FVE i n g o t s P h y s i c a l p r o p e r t i e s of  XVIII  conditions properties  f o r an of  pure  industrial i r o n used  p r e d i c t i o n of ESR  slags  scale i n the  pool  ingot  119  analysis'^  126  profiles  in 130 137  xvii  L I S T OF SYMBOLS CHAPTER I I cross  s e c t i o n a l area,  conductivity, potential, length,  resistivity  coordinate  _  r  ^ •= A  transference  Z  vertical  :  r  volts  t ,t_: +  ohm ''"cm ^ (  cm  radial ^ A c  cm^  resistance, numbers,  ohms  dimensionless  coordinate  CHAPTER I I I a  :  radius  AA  :  area,  C  :  n  of the electrode, cm  cm  2  constants  3 ae a  T  ±  D  :  F  :  i7  E  , radiation-conduction  configuration factor,  2  :  slag  T — ° —  ,  j  .  parameter,  dimensionless  dimensionless  1  dimensionless  T o h  :  c  heat  transfer coefficient,  c a l cm  -2  -1  sec  -1  °K  -1 K  :  thermal  I  :  length  L  :  c o n d u c t i v i t y of t h e e l e c t r o d e , of the electrode,  cm  I —  , dimensionless  electrode  length  c a l cm  -1 sec  -1  °K  XVI11  ha —rf—  . , c o n v e c t i o n parameter, d i m e n s i o n l e s s  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 ,  R,Z  :  r — , a  r  cm  temperature a t any p o i n t i n the e l e c t r o d e ,  T T  z — , dimensionless a  mold r a d i u s ,  2  cm  °K  e l e c t r o d e s u r f a c e temperature at the s l a g / g a s i n t e r f a c e ,  o  °K  average temperature of argon, °K  T oo  average temperature of the i n s i d e s u r f a c e 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 , d i m e n s i o n l e s s c o e f f i c i e n t of e m i s s i v i t y , d i m e n s i o n l e s s  E  -1  a Stefan-Boltzmann c o n s t a n t , c a l sec  B  :  r —  X  :  —^  -2 cm  -4 °K  2  Si  , dimensionless  T -  T  , d i m e n s i o n l e s s temperature at any p o i n t i n the e l e c t r o d e o  T oo  X^  :  — , d i m e n s i o n l e s s average temperature of argon o  X  :  Y~  , d i m e n s i o n l e s s average temperature of i n s i d e s u r f a c e of  °  the copper mold.  Subscripts electrode surface s l a g s u r f a c e at s l a g / g a s i n t e r f a c e mold  surface  argon b u l k  xix  Superscripts * :  e f f e c t i v e r a d i a t i o n environment  (water c o o l e d  copper mold)  CHAPTER IV A :  heat t r a n s f e r a r e a , cm  c :  conductivity  ( =  J  Cp  :  n  r^—.—r—-) r e s i s t i v i ty ty  , ohm  ^cm "*"  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. l  2  :  heat t r a n s f e r c o e f f i c i e n t o f the d i s c o n t i n u o u s i n t e r f a c e between ' -2 - l o -1 the s l a g s k i n and the i n n e r f a c e o f the mold w a l l , c a l cm sec °C  :  heat t r a n s f e r c o e f f i c i e n t , d e s c r i b i n g  t  h ..  the t r a n s f e r o f heat from -2 -1 -1 the b u l k s l a g to the s l a g s k i n , c a l cm sec °C  8  ^slag  1  a  v  e  r  a  S  e  thermal c o n d u c t i v i t y  of the s l a g s k i n , c a l cm ''"sec ^°C "*" -1  K  :  thermal c o n d u c t i v i t y  H :  sec  -1 °C  c h a r a c t e r i s t i c a x i a l l e n g t h , cm •c • J• • r ^v. - I - J s i g n i f i c a n t dimension of the copper c y l i n d e r =  T  L  of copper, c a l cm  -1  :  r  m :  mass of the copper c y l i n d e r , g  q  heat t r a n s f e r r e d per second, c a l sec ^  :  volume -z , cm surface area  r.. „ „: r a d i a l dimensions of the copper mold s l a g - s k i n system as shown i n F i g . (39), cm R :  resistance,  t  time, sec  T  : C, D, E  T^: T^  : temperatures at l o c a t i o n s as shown i n F i g . (40), °C temperature of the i n n e r  :  ''"slag T  ohm  :  surface  of the copper mold w a l l ,  copper c y l i n d e r temperature a t t = 0, 1  b lk u  °C  s l a g temperature,°C  copper c y l i n d e r temperature a t t = t , °C  °C  XX  U :  o v e r a l l heat t r a n s f e r c o e f f i c i e n t , c a l cm  -2  -1 -1 sec °C  CHAPTER V  2 A :  area,  c :  c o n d u c t i v i t y , ohm "*"cm  0^  :  cm  s p e c i f i c heat, c a l g "*"°C  d :  e l e c t r o d e diameter, cm  D :  i n g o t diameter, cm  D^,D2:  dimensions o f the annulus, cm  :  average bubble diameter, cm  :  h y d r a u l i c diameter, cm  D  G : G^ : h :  mass v e l o c i t y of f l u i d  flowing  through the annulus, g cm -2 -1 mass v e l o c i t y o f the bubbles p e r u n i t area, g cm sec -2 -1 -1 heat t r a n s f e r c o e f f i c i e n t , c a l cm s e c °C  -2 -1 sec  -2 h^k :  heat t r a n s f e r c o e f f i c i e n t  f o r n o n - b o i l i n g r e g i o n , c a l cm  h ^  -2 -1 -1 heat t r a n s f e r c o e f f i c i e n t c a l cm s e c °C  f o r the s u r f a c e b o i l i n g  I :  c u r r e n t , amperes -1  k :  thermal c o n d u c t i v i t y , c a l cm  I  :  l e n g t h , cm  L  :  l a t e n t heat, c a l g ^  m : MR  sec  -1 °C  mass, g :  melt r a t e , g sec  Nu :  Nusselt  P :  power, K c a l sec ^  Pr  P r a n d t l number, d i m e n s i o n l e s s  q  -1  : :  number, d i m e n s i o n l e s s  heat t r a n s f e r r e d p e r u n i t time, c a l sec ^  region,  -1 sec  °C  XXI  q.,q A  ,q : 15  t o t a l heat t r a n s f e r r e d a c r o s s t h e r e g i o n s shown i n F i g . ( 4 9 ) ,  L*  ^  K c a l sec Qi^'  as d e f i n e d i n F i g . ( 6 4 ) , c a l sec  r  resistivity,  :  ohm cm  R :  ^irA  Re:  Reynolds number, d i m e n s i o n l e s s  St:  Stanton number, d i m e n s i o n l e s s  T :  temperature,  V :  voltage, volts  W :  water r a t e through t h e annulus, g sec  > r e s i s t a n c e , ohms  V I'd D (|) 2  °C  „ -1 , Kcal g  2  1  MR  p :  d e n s i t y , g cm  u '  v i s c o s i t y , poise  AT :  temperature  3  d i f f e r e n c e , °C  CHAPTER VI 2  A  a r e a , cm  C P h  s p e c i f i c h e a t , c a l g ^°K ^ heat t r a n s f e r c o e f f i c i e n t , c a l cm  h. ^ : bottom  heat t r a n s f e r c o e f f i c i e n t c a l cm  h  ., : S  h  l  d  top  e  :  sec  -2  -1 s e c °K  f o r the bottom s u r f a c e ,  K  heat t r a n s f e r c o e f f i c i e n t f o r the f l o w o f heat from the mold -2 -1 -1 w a l l to the mold c o o l i n g water, c a l cm sec °K heat t r a n s f e r c o e f f i c i e n t -i -2 -lo^-l c a l cm sec K  f o r the top s u r f a c e ,  thermal c o n d u c t i v i t y , c a l cm  -1  -1 -1 s e c °K  xxii  k ^.j. : eff  e f f e c t i v e thermal c o n d u c t i v i t y , c a l cm '  £ :  l e n g t h , cm  L  l e n g t h o f the mold,  : :  MR  :  sec  J  °K  cm  l a t e n t heat, c a l g ^  C p. —TI— K AT  V , dimensionless '  2 .C Az — £ — K AJp  MZ  q  :  :  dimensionless  heat t r a n s f e r r e d p e r u n i t  time, c a l sec ^  r,(j),z :  c y l i n d r i c a l polar coordinates  T :  temperature,  t  time, sec  :  k —TT ,  a :  -  y  °K  thermal d i f f u s i v i t y ,  2 - 1 cm sec  P -3  p :  density, g  Ar :  l e n g t h o f the element  At  time element,  :  cm a l o n g the r a x i s ,  cm  sec  AT :  temperature  difference,  Az :  l e n g t h of the element  °K  a l o n g the z a x i s ,  cm  APPENDIX I d  :  diameter of the s u s p e n s i o n w i r e , t" o 1+3 {— } , dimensionless o L  E  :  g :  a c c e l e r a t i o n due :  L  :  cm  L  to g r a v i t y , cm  -2 sec  constant l e n g t h of the i n n e r c y l i n d e r immersed i n the s l a g ,  cm  xxiii  L  :  l e n g t h of the c y l i n d e r at room temperature,  L  :  l e n g t h of the  r^  :  r a d i u s of the i n n e r c y l i n d e r , cm  r^  :  r a d i u s of the o u t e r  Q  T  :  temperature, :  t  c y l i n d e r at t °C,  :  torque,  cm  cm  c y l i n d e r , cm  °C  dynes  cm  time of r o t a t i o n , sec  3 V  :  Q  volume of the bob  at room temperature,  W :  weight of the bob,  p :  d e n s i t y , g cm  y  :  surface  a  :  c o e f f i c i e n t of l i n e a r e x p a n s i o n , °C ^  g  3  t e n s i o n , dynes cm  n :  c o e f f i c i e n t of v i s c o s i t y ,  to :  --— , angular  Subscripts a :  air  m  :  melt  w  :  water  cm  ^  poise  v e l o c i t y of the o u t e r  c y l i n d e r , sec  xxiv  ACKNOWLEDGEMENTS  The  author would l i k e  to express h i s g r a t i t u d e to h i s r e s e a r c h  a d v i s o r , Dr. A. M i t c h e l l , f o r h i s keen i n t e r e s t [ a n d v a l u a b l e during  the course of t h i s r e s e a r c h  advice  project.  Thanks a r e a l s o due to Dr. J . Cameron and my f e l l o w graduate students helpful The  o f the ESR group, f o r t e c h n i c a l h e l p and innumerable discussions. a s s i s t a n c e o f 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 e x p e r i m e n t a l  programme i s g r e a t l y  appreciated. The and  f i n a n c i a l a s s i s t a n c e by t h e N a t i o n a l Research C o u n c i l of Canada  the American I r o n and S t e e l 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 p a s t decade  12 3 received  increasing  superior  q u a l i t y , h i g h performance s p e c i a l a l l o y s has been s t e a d i l y  rising.  The c h i e f c o m p e t i t o r s of the e l e c t r o s l a g p r o c e s s are the  vacuum a r c r e m e l t i n g  i n d u s t r i a l attention.  The demand f o r  (VAR) and to a lesser degree, the electron-beam  m e l t i n g and the vacuum i n d u c t i o n The s t r u g g l e  ' '  melting processes.  to improve the q u a l i t y of a l l o y s t e e l s and o t h e r  h i g h m e l t i n g s p e c i a l a l l o y s and r e a c t i v e Cl)  r e d u c i n g the i n c l u s i o n  C2)  r e d u c i n g the gas content  (3)  r e d u c i n g the s e g r e g a t i o n  (4)  retaining  the r e a c t i v e  metals i s aimed at  content  elements p r e s e n t .  4 T h i s i s a c h i e v e d u s i n g two methods of approach : (1)  increasing  the p u r i t y o f the l i q u i d  (2)  improving the s t r u c t u r e  metal.  of the i n g o t .  Two groups o f methods have found use i n the m e t a l l u r g i c a l for  increasing (1)  the q u a l i t y o f the  m e t a l i n the f u s e d  p r o c e s s i n g the m e t a l under vacuum,  state:  industry  2  (2)  treatment  of t h e m e t a l w i t h s p e c i a l s l a g s o u t s i d e the  furnace. The vacuum p r o c e s s i n g i s c a r r i e d out e i t h e r d u r i n g the s m e l t i n g or o u t s i d e the f u r n a c e .  Although  t h i s treatment  removes s u b s t a n t i a l  amounts of 0, N, H and o t h e r i m p u r i t i e s p r e s e n t , most o f these methods have some s e r i o u s shortcomings. contamination  from the r e f r a c t o r y l i n i n g as w e l l as the e v a p o r a t i o n  of Mn, S i and other'elements The  I n vacuum i n d u c t i o n m e l t i n g , the  o f h i g h vapor p r e s s u r e occurs f r e q u e n t l y .  o u t - o f - f u r n a c e treatment  o f the metal w i t h v a r i o u s o x i d i z i n g  s l a g s of the system CaF2-CaO-Al20 , on the o t h e r hand, i s q u i t e 3  e f f e c t i v e i n r e d u c i n g the s u l f u r , phosphorus and the n o n - m e t a l l i c inclusion  content of the m e t a l .  i  However, these methods do n o t p r o v i d e t h e p o s s i b i l i t y significant  improvement o f the i n g o t s t r u c t u r e which i s e s s e n t i a l f o r  the p r o d u c t i o n o f h i g h q u a l i t y  metal.  V a r i o u s methods a r e suggested ingot.  f o r improving  the s t r u c t u r e o f the  These i n v o l v e the h e a t i n g o f the i n g o t t o p , teeming,  c o n s t r u c t i o n of the c a s t i n g mold e t c .  attempted.  c o l d - c r u c i b l e p r o c e s s e s i . e . the vacuum a r c r e m e l t i n g , e l e c t r o -  s l a g and the e l e c t r o n beam r e m e l t i n g , combine b o t h  the o b j e c t i v e s o f  i n c r e a s i n g the g e n e r a l p u r i t y o f the metal and improving of the i n g o t and as such have found i n c r e a s i n g i n d u s t r i a l The  rational  To improve t h e i n g o t s t r u c t u r e ,  directional s o l i d i f i c a t i o n i s generally The  o f any  electron-beam  the s t r u c t u r e applications.  m e l t i n g p r o c e s s uses a c o n c e n t r a t e d f l u x o f .  e l e c t r o n s as the source o f h e a t .  The presence  o f h i g h vacuum t o g e t h e r  w i t h 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 o f the l i q u i d metal i n a  3  w a t e r - c o o l e d 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 m e t a l from the gases and the n o n - m e t a l l i c i n c l u s i o n s .  Although p o s s e s s -  i n g the p o t e n t i a l f o r l a r g e s c a l e i n d u s t r i a l usage, at the p r e s e n t , t h i s p r o c e s s i s used o n l y f o r r e f i n i n g some v e r y h i g h m e l t i n g metals and a l l o y s .  T h i s i s due  to the c o m p l e x i t y o f the equipment and  the  h i g h c a p i t a l and o p e r a t i n g c o s t s . In the e l e c t r o s l a g r e m e l t i n g p r o c e s s (ESR), a m e t a l e l e c t r o d e i s melted i n a molten  superheated s l a g p o o l .  by r e s i s t a n c e h e a t i n g .  The s l a g i s r e n d e r e d molten  High c u r r e n t at low v o l t a g e s i s d e l i v e r e d t o  the s l a g through the e l e c t r o d e and the r e f i n e d molten m e t a l i s immediately  s o l i d i f i e d i n a water  c o o l e d copper mold  The vacuum a r c r e m e l t i n g (VAR)  ( F i g . 1).  process c o n s i s t s of melting a  consumable e l e c t r o d e i n vacuum or i n an atmosphere of i n e r t gas, by means of a h i g h c u r r e n t e l e c t r i c a r c m a i n t a i n e d between the lower end of the e l e c t r o d e and a p o o l o f molten metal c o n t a i n e d i n a water c o o l e d copper mold. Except f o r the f a c t t h a t a consumable e l e c t r o d e i s remelted and t h a t the metal i s s o l i d i f i e d  i n a water  slag process i s d i s t i n c t l y d i f f e r e n t  c o o l e d m e t a l mold, the e l e c t r o -  from the vacuum a r c r e m e l t i n g  process. The main advantages summarized as  o f the ESR p r o c e s s over the VAR  may  be  follows:  Cl)  good s u r f a c e q u a l i t y of the i n g o t , r e a d i l y u s e a b l e f o r f o r g i n g  C2)  a c e r t a i n degree of r e f i n i n g  (3)  p o s s i b l e to use e i t h e r a.c. or d.c. power  C4)  lower c a p i t a l  cost  (mainly of s u l f u r ) i s p o s s i b l e  4  (5)  s a f e r i n o p e r a t i o n than VAR  (6)  can t o l e r a t e r e l a t i v e l y c o m p l i c a t e d mold shapes.  While i t i s u s u a l l y accepted complements VAR by i t s a b i l i t y  t h a t the e l e c t r o s l a g  remelting  t o change the i n g o t chemistry  as w e l l  as i t s s t r u c t u r e , the c o s t f a c t o r does n o t a l l o w one t o make a c l e a r choice f o r i n d u s t r i a l operation.^  The lower  c a p i t a l c o s t and the  s l i g h t l y h i g h e r p r o d u c t i o n r a t e o f the ESR equipment i s o f f s e t by the h i g h e r s p e c i f i c power r e q u i r e d and the c o s t of the s l a g The  t y p i c a l power consumption f o r ESR p r o c e s s  i s 1200 t o 2000 KWH  per t o n of the m e t a l w h i l e f o r VAR, i t i s s l i g h t l y ESR  itself.  5 6 less. '  i n g o t s have a l r e a d y exceeded the maximum s i z e of VAR i n g o t s , 7  as a producer Except  r e p o r t s h a v i n g produced i n g o t s of 23 tons.  f o r R u s s i a , which does n o t have many VAR i n s t a l l a t i o n s , ; i n  the r e s t o f the w o r l d , mentary p r o c e s s mainly  the ESR p r o c e s s  today  i s , at the b e s t , a comple-  t o VAR, f o r r e f i n i n g h i g h q u a l i t y a l l o y s .  This i s  due to the i n s t a l l a t i o n of l a r g e VAR f u r n a c e s i n the a l l o y  s t e e l i n d u s t r y i n the e a r l y s i x t i e s , p r i o r t o the advent of the ESR process.  1.2  Statement of the Problem The  secondary due  e l e c t r o s l a g remelting process r e f i n i n g process  i s s u i t a b l e as a modern  l a r g e l y because o f i t s v e r s a t i l i t y .  t o the l a r g e number o f a v a i l a b l e combinations  the more f l e x i b l e power requirements  of s l a g  This i s  chemistry,  and the g r e a t e r freedom of c h o i c e  of e l e c t r o d e c h a r a c t e r i s t i c s . D e s p i t e r a p i d advances i n the d e s i g n and a p p l i c a t i o n o f the  5  e l e c t r o s l a g equipment, much work o f a fundamental  nature i s required  b e f o r e the p h y s i c a l and c h e m i c a l p r o c e s s e s i n h e r e n t t o the e l e c t r o s l a g system a r e understood. The purpose  o f the p r e s e n t work i s t o study the thermal  t i c s o f the e l e c t r o s l a g p r o c e s s .  characteris-  I t i s n e c e s s a r y t o understand  the mode  of heat g e n e r a t i o n and d i s t r i b u t i o n i n the ESR p r o c e s s t o a c h i e v e e f f e c t i v e control during i t s operation. I t i s convenient t o d i v i d e the study i n t o s i x s e c t i o n s . Cl)  Heat g e n e r a t i o n i n the s l a g b a t h :  important p a r t of the p r o c e s s . element.  The s l a g b a t h i s the most  I t i s the r e s i s t i v e and the r e f i n i n g  I t i s t h e r e f o r e n e c e s s a r y t o examine the form o f heat  g e n e r a t i o n i n the s l a g b a t h . (2)  Temperature g r a d i e n t s on the e l e c t r o d e :  know the temperature  I t i s n e c e s s a r y to  g r a d i e n t s on the e l e c t r o d e as i t c o n t r o l s the  extent o f e l e c t r o d e o x i d a t i o n , s t r u c t u r e o f the i n g o t , as w e l l as the degree o f thermal i n s t a b i l i t y d u r i n g e l e c t r o d e changes i n l a r g e industrial C3) region:  units. 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 o f the s l a g  skin  As a s i g n i f i c a n t p o r t i o n o f the heat l e a v e s the system  the l i q u i d  across  s l a g r e g i o n , the study o f heat t r a n s f e r i n the system  s l a g / s l a g skin/mold i s v i t a l t o the u n d e r s t a n d i n g o f the ESR o p e r a t i o n . The study o f 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 t h i s r e g i o n i s n e c e s s a r y 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  o f the d i f f e r e n t  electrical  configurations.  g (4)  Heat b a l a n c e o f the p r o c e s s :  e l i t e s and B e a l l  s t u d i e d the  heat t r a n s f e r to the w a t e r - c o o l e d copper mold d u r i n g vacuum a r c r e m e l t i n g  6  of z i r c o n i u m process.  and t i t a n i u m .  No such study i s r e p o r t e d  on the ESR  I t i s e s s e n t i a l t o c a r r y out an a c c u r a t e heat b a l a n c e o f  the p r o c e s s t o understand the mode o f heat d i s t r i b u t i o n . 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 v a r i o u s meters of the p r o c e s s f o r i n d u s t r i a l s c a l e (5)  operating  the ESR i n g o t s .  should para-  ingots.  P r e d i c t i o n o f p o o l volumes i n ESR i n g o t s :  c o n t r o l , i t i s n e c e s s a r y t o be a b l e  This  F o r an e f f e c t i v e  t o p r e d i c t the p o o l volumes i n  The p o o l volume and i t s shape, c o n t r o l the s u r f a c e  q u a l i t y and the s t r u c t u r e o f the i n g o t . (6)  Measurement of the p h y s i c a l p r o p e r t i e s  o f the s l a g :  s e r v e s many purposes, n o t a l l o f them b e i n g compatible. have the a p p r o p r i a t e  melting  p o i n t , vapor p r e s s u r e ,  r e s i s t i v i t y , v i s c o s i t y , density, or a b e s t  1.3  tension  The s l a g s h o u l d  electrical  and thermal  p o s s i b l e combination o f these p r o p e r t i e s .  here t o measure (1) the d e n s i t y based  surface  The s l a g  capacity  Attempt i s made  and (2) the v i s c o s i t y o f the CaF^  slags.  The U.B.C. E l e c t r o s l a g U n i t For  the purpose o f i n v e s t i g a t i n g the i n f l u e n c e o f v a r i o u s  para-  meters on the thermal c h a r a c t e r i s t i c s of the p r o c e s s , experiments have been c a r r i e d out w i t h the U.B.C. e l e c t r o s l a g u n i t . unit  The d e s i g n o f t h i s  i s s p e c i f i c a l l y adapted t o the requirements o f a range o f r e s e a r c h  9 projects remelting  and 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 .  i s one of the few m e t a l l u r g i c a l p r o c e s s e s which can be  s c a l e d down w i t h o u t l o o s i n g i t s i n t r i n s i c p r o p e r t i e s . possible  Electroslag  to p r e d i c t  the o p e r a t i o n  i  Thus i t i s  c h a r a c t e r i s t i c s of l a r g e i n d u s t r i c a l  s c a l e u n i t s by c o r r e l a t i n g the d a t a o b t a i n e d on the s m a l l  laboratory  unit.  7  1.4  Choice of M a t e r i a l s An important problem  and s l a g compositions A l l o y compositions: Armco i r o n , AISI 1018  has been the s e l e c t i o n of s u i t a b l e  alloy  f o r the p r e s e n t study. V i b r a c EN 25, 321 s t a i n l e s s s t e e l , F e r r o v a c E, 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 .  T a b l e I g i v e s t h e c o m p o s i t i o n o f the a l l o y s  studied.  Table I.  (1)  of a l l o y s s t u d i e d  V i b r a c EN 25 ( s u p p l i e d by B r i t i s h S t e e l C o r p o r a t i o n ) Fe  Bal  Mo.  0.6  (2)  Composition  C  0.28  _ Sn  0.028  Mn  Si  S  P  0.67  0.22  0.058  0.012  Cu  Al  0.27  0.01  Austenitic Stainless Steel:  321 grade.  Ni  A i r melted  Cr  2.5  0.72  ( s u p p l i e d by  A t l a s S t e e l s Company, Welland, O n t a r i o ) . Fe Bal  S  0.018  Cr  17.78  0 0.0009  Ni  10.60  Ti  Si  Mn  0.58  0.56  1.86  C  0.05  P  0.031  8  (3)  Ferrovac E:  vacuum melted  ( s u p p l i e d by C r u c i b l e S t e e l Company,  S o r e l , Quebec) Fe Bal  Mo  0.01  1018 S t e e l :  Bal  (5)  H  0.00092  S  Ni  Cr  0.006  0.01  <0.01  Cu  V  Si  0.004  Co  0.000018 0.006  ( s u p p l i e d by A t l a s S t e e l  0.006  W  <0.002  0.02  Ni  Company)  C  Mn  P max  S  0.15-0.20  0.6-0.9  0.04  0.05  max  AISI 630 ( s u p p l i e d by Armco) Fe Bal  (6)  0.002  0  0.0002  Fe  P  0.001  N  0.001  (4)  Mn  C  C  Mn  Si  P  S  Cr  0.07  1.0  1.0  0.025  0.025  16.5  Co + Ta  Cu  0.3  4.00  Mo 0.5  Armco I r o n ( s u p p l i e d by Armco) Fe Bal  C 0.012  Mn  P  S  Si  0  0.017  0.005  0.025  trace  0.065  4.0  9  Slags:  Calcium  material  f l u o r i d e i s the b a s i c c o n s t i t u e n t .  P a r t of  this  ( f l o t a t i o n c o n c e n t r a t e ) i s used as a dry powder to make up  f o r the r e q u i r e d p r o p o r t i o n of powder and  granules.  Most of the c a l c i u m f l u o r i d e used i s p r e f u s e d i n a g r a p h i t e crucible.  I n d u c t i o n h e a t i n g and argon b l a n k e t are used.  i m p u r i t i e s of C a F  2  are c a l c i u m o x i d e , s i l i c a and  measurement of d e n s i t y and v i s c o s i t y of C a F CaF^  ( B r i t i s h Drug House) was  2  i r o n oxide.  For  the  used.  (Norton Co.)  Calcium  oxide i s prepared  Calcium  t i t a n a t e i s commercially  p u r i t y ) or  granules  of e q u i v a l e n t p u r i t y .  from c a l c i u m carbonate  n o r m a l l y used f o r spray c o a t i n g . use.  main  base s l a g s , e x t r a pure  Alumina i s used e i t h e r as powder ( A l c a n , 99.9% of e l e c t r o f u s e d alumina  The  (technical  grade).  a v a i l a b l e as powder (Cerac Corp.)  I t i s c o l d p r e s s e d and  sintered  before  10  CHAPTER I I DETERMINATION OF VOLTAGE GRADIENTS IN THE SLAG BED OF THE ESR PROCESS  II.1  Mechanism o f Heat  Generation  Descriptions'^'"'"^'"''''" of the e l e c t r o s l a g r e m e l t i n g p r o c e s s have a t t r i b u t e d the heat and  g e n e r a t i o n mechanism v a r i o u s l y to ' s o f t '  to r e s i s t i v e h e a t i n g , but are n o t s p e c i f i c as to how  arcs  the r e s i s t a n c e  is constituted. In o r d e r to understand it  the mechanism of heat  i s l o g i c a l t o compare ESR and vacuum a r c r e m e l t i n g  s i n c e they are a p p a r e n t l y and o p e r a t i o n s .  s i m i l a r , i n both  processes  t h e i r m e t a l l u r g i c a l aims  i s generated.  In the h i g h i n t e n s i t y a r c p r e s e n t heat  (VAR)  i n ESR,  The major d i f f e r e n c e between the two p r o c e s s e s i s  the method by which the heat  of  generation  i n VAR,  t h e r e are three p o i n t s  generation  (1)  cathode  (2)  anode  (3)  the t r a n s f e r r e s i s t a n c e of the plasma  The heat  fall  fall  g e n e r a t i o n mechanism i n an a r c i s a mixture  of j o u l e  h e a t i n g , due to the t r a n s f e r r e s i s t a n c e of the plasma, and the p a r t i c l e emission  and bombardment  which g i v e s r i s e t o the observed  steep  v o l t a g e g r a d i e n t s i n the t e r m i n a l r e g i o n s , c a l l e d the anode and cathode  11  fall  (Fig. (2)). It  i s i n t e r e s t i n g to c o n s i d e r what e f f e c t ? , i f any,  from the i n t e r p o s i t i o n of a l i q u i d  s l a g between the  two  will  electrodes  which are at a p o t e n t i a l d i f f e r e n c e h i g h enough to cause a a r c i n the absence of the s l a g , extinguished e f f e c t s and by  whether or not  sustained  the a r c w i l l  be  depends upon the r e l a t i o n between the e l e c t r i c a l the h e a t i n g  e f f e c t s i n the s l a g .  the other hand, the heat can be  below the b o i l i n g p o i n t , e l e c t r i c a l  a very  transport  I f the heat generated  the v a r i o u s r e s i s t a n c e s i n v o l v e d i s g r e a t enough to b o i l  then the i o n i z a b l e vapor w i l l p r o v i d e on  result  the s l a g ,  s t a b l e a r c path.  If,  d i s s i p a t e d at a temperature w e l l , t r a n s p o r t i s by  i o n i c movement  i n the s l a g . 12 M i t c h e l l and  Beynon  4 5 order of 10 -10 Amp.  have shown t h a t a c u r r e n t d e n s i t y of  the  -2  i s n e c e s s a r y f o r the s u s t a i n e d e x i s t e n c e 13 of an a r c i n the e l e c t r o s l a g p r o c e s s . Mironov et a l . have a l s o r e p o r t e d s i m i l a r f i n d i n g s 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  cm  the maximum c u r r e n t d e n s i t y r a r e l y exceeds  150  -2 Amp.  cm  i n laboratory scale units  u n i t s ) , one  can  the s l a g bed by heating  (much lower f o r i n d u s t r i a l  conclude t h a t the b u l k the f r i c t i o n a l  i s generated by  the  scale  of the heat i s generated i n  d i s s i p a t i o n i n i o n i c movement.  Joule  opposing f l u x of 14-17  c a t i o n s and  anions.  There i s e v e r y reason  the s l a g s used are e n t i r e l y i o n i c w i t h current  i s c a r r i e d by  gradient.  t  - t_ - 0.5  to suppose t h a t and  that  the  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  There should  be no  beyond that accounted f o r by  asymmetry of heat g e n e r a t i o n the geometry of the system.  i n the s l a g This p r o v i s i o n  12  would  include  calculated  skin  that  approximately would  be  effects  t h e 60 Hz  40  cm,  required  and  at a large skin  thus  depth  enough  in liquid  a crucible  b e f o r e the heat  crucible  size,  calcium  showed  i t is  fluoride  diameter larger  generation  but  is  t h a n 100  significant  cm  radial  asymmetry. As  the e l e c t r o d e  arrangement resistive  i n the s l a g  heat  so, i t i s f i r s t  in  the s l a g  be m o d e l l e d  dependent  distribution  determined  II.2  Measurement o f Temperature  the form  the i s o p o t e n t i a l axially  b e d was  for various  i n the Slag  will  of the s l a g .  electrical  configurations.  Bed  o f t e m p e r a t u r e measurement  i n an  operating  been  studied  i n several  There  exists  difficulty  in  a system  in  a corrosive  ground. rapidly  containing slag  I f a bare dissolves  surface  i n measuring  and  at a.c.  thermocouple even  millivolt  intense magnetic  cermet  or d.c.  at a high  potentials  refractories)  unit  potentials  temperature  significantly  i n the s l a g i t will  t e m p e r a t u r e b e f o r e b e i n g d e s t r o y e d by  ESR  substantial  thermocouple  fields,  i s immersed  As  unknown, i t was  problem  experimental  to  contours  The  contexts.  able  of  symmetrical  analogue which  resistivity  i n the s l a g  experimentally  the  a symmetrical  I n o r d e r t o be  f o r an  of a r e s i s t a n c e network  first  has  constitute  bulk.  necessary to c a l c u l a t e  the temperature  temperature  do n o t  i n the s l a g  T h i s may  the use  accommodate the  bed.  the ingot  b a t h , i t i s n e c e s s a r y t o examine  generation  do  s y s t e m by  and  above  (which  transiently  the m e t a l l i c  record content  20 of  the s l a g .  Since the s l a g  temperature measuring  i s at a p o t e n t i a l  i n s t r u m e n t s must be  above ground,  floating  and  have  the .  adequate  13  common mode r e j e c t i o n .  T r i a l s established that boron n i t r i d e i s an  e x c e l l e n t m a t e r i a l f o r thermocouple p r o t e c t i o n tubes i n t h i s context as i t i s compatible w i t h the W-3Re/W-25Re thermocouple.used, i s an e l e c t r i c a l i n s u l a t o r at the temperatures experienced, and w i l l r e s i s t attack by the ESR s l a g f o r 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. F i g . (3) and F i g . (4) give a schematic diagram of the experimental assembly.  Temperature measurement was c a r r i e d out i n both argon  atmosphere and a i r f o r various e l e c t r i c a l configurations using CaF2~ 25 wt. % A^O^ s l a g .  In a l l the cases, 3.81 cm (1.5 inches) diameter  EN 25 s t e e l electrode was melted i n 8 cm x 45 cm mold.  F i g . (5) to  F i g . (10) give the observed temperature gradients i n the slag bed f o r the one v e r t i c a l s e c t i o n i n v e s t i g a t e d .  II.3  Determination of I s o p o t e n t i a l Contours i n the Molten Slag Bed  II.3.1  Introduction  ;  The i s o p o t e n t i a l l i n e s are determined here f o r an experimentally obtained geometrical c o n f i g u r a t i o n (I.N. 1, Table V).  The extent  of electrode immersion and the depth of the slag bed are as shown i n F i g . (11). The r e s i s t i v i t y of the s l a g depends upon the temperature. , Appendix I ( F i g . (86)) gives the v a r i a t i o n of e l e c t r i c a l c o n d u c t i v i t y with temperature f o r CaF2~25 wt. % A^O^ slag as obtained by M i t c h e l l and Cameron?"'" In order to c a l c u l a t e the i s o p o t e n t i a l contours i n the slag bed,  14  it  i s necessary  Fig.  to assume a temperature d i s t r i b u t i o n i n the s l a g bed.  (11) g i v e s 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 sufficient  to c o n s i d e r the  v o l t a g e 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 s l a g bath. convenience, a segment of one r a d i a n i s chosen. volume elements as shown i n F i g . ( 1 2 ) . volume elements i s 0.5 cm w h i l e  along  For  I t i s subdivided  The v e r t i c a l h e i g h t  into  o f the  the r a d i u s i t i s 1.0 cm.  The  volume o f the elements i n c r e a s e s away from the c e n t r e .  22 II.3.2  S o l u t i o n 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 o f each volume element i s c o n s i d e r e d at the c e n t r a l p o i n t .  In accordance w i t h  t o be  concentrated  the e l e c t r i c a l r e s i s t a n c e  concept, the r e s i s t a n c e of the volume of the s l a g may be s e t up approximately  as shown i n F i g . ( 1 3 ) .  Here, the r e s i s t a n c e s R  and R r e p r e s e n t the r e s i s t a n c e s i n the r z 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 r e s i s t a n c e e f f e c t i s R R r z l i k e w i s e shown, w i t h s e p a r a t e h a l f elements and — j r e p r e s e n t i n g 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 and t o t a l l i n g R r r  J  and R z  f o r the e n t i r e  volume element. Consider  F i g . (12).  i s a t 23.75 v o l t s w h i l e  In d.c. n e g a t i v e  ( I . N . I ) , the s u r f a c e AB  the s u r f a c e CD i s at 0 v o l t s .  at the s u r f a c e EF ( s l a g / g a s  i n t e r f a c e ) i s assumed to be  Due t o the assumed r a d i a l symmetry,  The r e s i s t a n c e infinite.  s u r f a c e BC has i n f i n i t e r e s i s t a n c e .  In the ESR u n i t , t h e r e i s always a s o l i d s l a g s k i n a g a i n s t c o o l e d mold.  As s o l i d  the water  s l a g s k i n has v e r y h i g h e l e c t r i c a l r e s i s t a n c e ,  15  it  i s not  the  unreasonable  surface  potential As  A'F'.  The  the  solid  the  surface  resistivity that  this  tance  of  this  Fig.  than  skin  s k i n has  gives  w h e r e i t i s assumed It  i s necessary  various the  melting  i s not  that  skin  point  of  solid  resistance  be  the  c a l c u l a t i n g the  area  '&'  on  at  the  at  skin. i t will  'A'  and  (R =  and  =  electrical  be  assumed  finite  resist  treated. for  and  0 0  the  at  length  ED  f o r a l l the  case -  for  ) , Appendix  'A'  a exists  The  network  A'F'  i s at there  e f f e c t of  resistance  study  metal,  slag  The  which  subsequently  resistance  c a l c u l a t e the  the  Initially  resistance.  equivalent  resistance  later.  known.  skin w i l l  the  is infinite  slag  t h i n l a y e r of  volume elements under  method o f  under  to  there  e x i s t s i n the, s l a g b e d  zero  thin slag  (14)  that  considered  the  a very  this  slag  be  electrode  ED  of  assume  e f f e c t of f i n i t e  contours w i l l  temperature higher on  to  0  ohms.  the  II  gives  volume  elements  consideration. The  without  numerical recourse  specific  s o l u t i o n of  to  the  the  resistance  experimental  interest, particularly  network of  electrical  i n view  of  the  Fig.  (14) ,  determination many n e t w o r k  is  of  branches  involved. At the  sum  any of  junction the  accumulation. surrounded  by  corresponding  point,  currents  under  flowing  Accordingly, points  M,  branches  N,  P  and  is R  currents  difference  i n the  , R  in potential  four 'e'  state  ' i n ' must  considering  m' The  steady  Q.  Fig.  The  , R n  , R p  be  electrical  zero  i . e . , there  (15),  the  resistance  of  point the  conditions, is  no  0 is  four  respectively. q  r  d i f f e r e n t branches,  between the  flow  dependent  outlying point  and  on the  the center  16  j u n c t i o n are n e x t The  considered.  f o l l o w i n g r e l a t i o n s h i p s may  m  n  be s e t up  q  p  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 ,  (  ih M e  ^  +  =  +  ^  m  (  ir  ) e  r  -JL  n  p  +  (  ir  ) e  Q  f  (2.2) q  I n the p r e s e n t case, i t i s assumed t h a t 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 m o l t e n m e t a l  bath  (23.75 v o l t s ) . Equations points.  s i m i l a r t o (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  T h i s l e a d s t o 29 l i n e a r simultaneous  equations  These can be e a s i l y s o l v e d w i t h the a i d of the computer. the v o l t a g e d i s t r i b u t i o n  II.3.3  i n 29 unknowns. F i g . (16)  gives  obtained.  t  Discussion  F i g . (16) i l l u s t r a t e s the manner by w h i c h the s l a g volume, the geometry, a p p l i e d v o l t a g e and r e s i s t i v i t y combine to determine the v o l t a g e g r a d i e n t s and hence the heat i n p u t i n the s l a g b a t h . The  r e g i o n of steep v o l t a g e g r a d i e n t l i e s below the e l e c t r o d e  t i p and most of the heat g e n e r a t i o n takes p l a c e below t h i s l e v e l . s l a g above the e l e c t r o d e t i p , due  t o low v o l t a g e g r a d i e n t s , does  The not  17  get heated to the same extent  and  performs a c o o l a n t  function i n  the  system. The  curvature  t i p , and  there  surface.  This  i n the c u r r e n t  The  stirring  comment, of c o u r s e , n e g l e c t s  infinite  f o r c e s imposed on the ESR  of c o n s i d e r i n g  a n a l y s i s i t was  electrical  a finite  cantly distort  the v o l t a g e  the e f f e c t of f i n i t e It  resistance.  that  s k i n e f f e c t which  lies  i n the  ESR  form of  a c o n f i g u r a t i o n of  melt.  assumed t h a t the s l a g s k i n on. the F i g . (17)  slag skin resistance  i s c l e a r from F i g . (17)  ingot  i n this l a t t e r region i n a larger  p a t t e r n which might be e s t a b l i s h e d by  In the p r e s e n t  It  curvature  the a.c.  s i g n i f i c a n c e of such a c u r r e n t p a t t e r n  electromechanical  mold has  electrode  i s n e g l i g i b l e h o r i z o n t a l c u r r e n t v e c t o r near the  would l e a d to i n t e n s e unit.  l i n e s i s l a r g e l y above the  (r  -  shows the e f f e c t  200-300  ohm.  t h i s c o n s i d e r a t i o n does not  gradients.  r e s i s t a n c e of the  F i g . (18)  and  s l a g s k i n on  cm).  signifi-  F i g . (19) immersed  i s c l e a r that except f o r an unreasonably h i g h v a l u e  of  consider  electrode.  skin  r e s i s t a n c e , 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 e l e c t r o d e i s not  significant.  temperature  I t w i l l be  (> 1 0 0 0 ° C ) , the  r e s i s t a n c e due  shown i n Chapter IV t h a t at a h i g h s l a g s k i n has  a relatively  to good c o n t a c t w i t h the e l e c t r o d e .  low e f f e c t i v e  Hence F i g .  i s adequate i n d e s c r i b i n g the v o l t a g e p r o f i l e s i n the ESR In the p r e s e n t  model, the a p p l i e d v o l t a g e was  equated to the p o t e n t i a l seen by interfaces. present  electrode  slag  (16) bed.  deliberately  the s l a g b u l k at the  electrode-slag  However, by doing so, the e l e c t r o c h e m i c a l p o l a r i z a t i o n  i n ESR  was  neglected.  18  11.4  Electrochemical P o l a r i z a t i o n i n With the e x c e p t i o n  ESR  of the s i t u a t i o n where the s l a g has  e l e c t r o n m o b i l i t y , i o n s must be d i s c h a r g e d  at the e l e c t r o d e and  s u r f a c e s i f the c u r r e n t passes through the system. c u r r e n t r e q u i r e s both the anodic  and  cathodic  The has  anodic  The  process  g i v i n g r i s e to o v e r -  i n the d.c.  e l e c t r o s l a g melting Beynon  12  to be  to be  the d e p o s i t i o n of A l  of  pure i r o n  the c o r r o s i o n of  * I | i r o n , g i v i n g an i n t e r f a c e l a y e r of s a t u r a t i o n of Fe . i s postulated  passage of  surfaces.  been p o s t u l a t e d by M i t c h e l l and  process  The  or Ca  cathodic  which  subsequently d i s s o l v e i n e i t h e r the m e t a l or the s l a g phases. (20)  and  F i g . (21)  g i v e the e x p e r i m e n t a l l y  curves f o r pure i r o n .  ingot  interfacial potentials  to be d i s p l a c e d from t h e i r e q u i l i b r i u m v a l u e s , p o t e n t i a l s on both the  a substantial  12  In a.c.  may Fig.  obtained p o l a r i z a t i o n  electroslag melting,  i t was  found  j |  t h a t there i s no p o l a r i z a t i o n w i t h Fe o c c u r r i n g at b o t h the Fig.  (20 and  mately 1.0 cantly.  volt.  (21)  ——*-  11.5  The The  to a.c.  Effect  T h i s w i l l not  T h i s w i l l be  a l t e r the i s o p o t e n t i a l l i n e s i n the m e t a l - s l a g  signifi-,  interfacial  considered  i n d e t a i l i n Chapter  V.  Slag  used i n the a n a l y s i s are a p p l i c a b l e o n l y  electroslag refining. operation  approxi-  through t h i s o v e r p o t e n t i a l i s  of Ca and A l D i s s o l v e d i n the  r e s i s t i v i t y values  product i n d.c.  2e r e a c t i o n  show t h a t the maximum o v e r p o t e n t i a l i s  However, the heat g e n e r a t i o n  important.  +  electrodes.  r e g i o n as a r e s u l t of c u r r e n t p a s s i n g very  Fe  •<  As  discussed  i s Ca and  Al.  earlier,  the c a t h o d i c  Both these elements  are  reaction  19 s o l u b l e i n the CaF^ based s l a g s .  A d d i t i o n o f these elements  significantly  i n c r e a s e s the e l e c t r i c a l c o n d u c t i v i t y o f CaF£ based s l a g s .  Its effect  on ESR o p e r a t i o n w i l l be d i s c u s s e d i n d e t a i l i n Chapter V.  The  voltage gradients w i l l  remain u n a l t e r e d 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 s l a g i n d.c. o p e r a t i o n i s p r o p o r t i o n a t e l y the same as the s l a g i n a.c. o p e r a t i o n . resistivity  Although  the e f f e c t i v e  i n d.c. o p e r a t i o n w i l l be l e s s s e n s i t i v e t o temperature,  as the temperature dependence i s unknown, i t has been assumed here t o be p r o p o r t i o n a t e l y s i m i l a r t o the a.c. o p e r a t i o n  II.6  Measurement o f V o l t a g e The  i n the S l a g Bed  p r e d i c t e d v o l t a g e g r a d i e n t s were e x p e r i m e n t a l l y v a r i f i e d r u s i n g  a v o l t a g e probe. (3.81  Gradients  slag.  V o l t a g e was measured i n CaF2~25 wt. % ^l^O^ s l a g  cm diameter EN 25 s t e e l e l e c t r o d e i n 8.0 cm diameter copper  mold) between the e l e c t r o d e and a boron n i t r i d e i n s u l a t e d molybdenum wire probe. at c o n s t a n t  The probe was lowered v e r t i c a l l y  down i n t o the s l a g  speed by a motor and the v o l t a g e r e c o r d e d  Model SR 4 r e c o r d e r .  bath  on a Sargent  F i g . (22) g i v e s the e x p e r i m e n t a l l y  obtained  v o l t a g e g r a d i e n t a c r o s s a v e r t i c a l s e c t i o n and compares i t w i t h t h e predicted gradient.  The agreement appears t o be r e a s o n a b l y  i n s p i t e of the many s i m p l i f y i n g f a i r estimate  good.;  Thus,  assumptions made, f i g . (16) g i v e s a  of the v o l t a g e g r a d i e n t s i n an o p e r a t i n g ESR s l a g  bath.  20  CHAPTER I I I ELECTRODE TEMPERATURE GRADIENTS IN THE ELECTROSLAG PROCESS  III.l  Introduction In the e l e c t r o s l a g r e m e l t i n g  out  process,  the amount o f heat  through the e l e c t r o d e p l a y s a s i g n i f i c a n t p a r t i n  a number of reasons.  Firstly,  heat b a l a n c e i n the m e l t i n g process  operating  i t i s a direct  flowing  the p r o c e s s f o r  c o n t r i b u t i o n to the  e l e c t r o d e t i p r e g i o n and t h e r e f o r e to the  temperature.  temperature above the slag/gas  I t a l s o determines the e l e c t r o d e i n t e r f a c e and thus the amount o f p o s s i b l e  e l e c t r o d e o x i d a t i o n i n cases where i n e r t  atmosphere i s n o t used and  the degree o f thermal i n s t a b i l i t y d u r i n g e l e c t r o d e changes i n l a r g e industrial units. whilst travelling  Finally,  the time the e l e c t r o d e m a t e r i a l spends  through the e l e c t r o d e temperature g r a d i e n t  the e x t e n t  t o which second phase p a r t i c l e s w i l l be d i s s o l v e d  the m a t r i x  melts.  determines before  T h i s l a t t e r e f f e c t has n o t been i n v e s t i g a t e d i n  e i t h e r the vacuum a r c r e m e l t i n g  (VAR) or ESR c o n t e x t ,  but i s l i k e l y t o  have a t l e a s t t h r e e 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 f o l l o w s .  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  d i s s o l v e p r o g r e s s i v e l y 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 p r e s e n t t i p w i l l be  i n the m e l t i n g  electrode  c l o s e r to t h a t i n the b u l k e l e c t r o d e than would be  by an e q u i l i b r i u m a n a l y s i s of the h e a t i n g p r o c e s s .  The way  predicted  i n which 23  t h i s may  affect  i n g o t i n c l u s i o n content  A l t e r n a t e l y , i f the second as a c a r b i d e  has  been b r i e f l y o u t l i n e d .  phase i s a more s o l u b l e m a t e r i a l , such  ( T i C i n a s t a i n l e s s s t e e l , f o r 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 p e r i o d i n both VAR ESR  (due  to a low  time) w i l l be  s o l u t i o n r a t e compared to the l i q u i d m e t a l  that any  i n g o t stage w i l l  a c t as n u c l e i f o r subsequent c a r b i d e growth.  d i s t r i b u t i o n i n the e l e c t r o d e . a lower m e l t i n g  carbide)  the  Thus,  carbide  In the case where the second phase  p o i n t than the m a t r i x  (as f o r example, an e u t e c t i c  then the p o i n t at which t h i s melts r e l a t i v e to the t i p of  the e l e c t r o d e w i l l l a r g e l y determine whether or not e l e c t r o d e become p h y s i c a l l y detached and f r o n t without m e l t i n g . processing The  residence  e l e c t r o d e c a r b i d e p a r t i c l e s p e r s i s t i n g to  the s t r u c t u r e of the i n g o t produced would depend upon the  has  and  high-speed  fall  large pieces  to the i n g o t  solidifying-  T h i s l a t t e r d e f e c t i s w e l l known i n the  ESR  steels.  problem of the e l e c t r o d e temperature g r a d i e n t  divided conveniently  of  i n t o two  may  be  s e c t i o n s , r e l a t i n g to the heat t r a n s f e r  regimes above and below the s l a g / g a s r e l a t e s to the g r a d i e n t s  i n ESR  interface.  above the s l a g / g a s  the e x p e r i m e n t a l  r e s u l t s obtained,  of t h i s g r a d i e n t  f o r AISI 1018  with  s t e e l and  The  present  interface  and  study  compares  the t h e o r e t i c a l computation 321  stainless steel  electrodes.  22  III.2  Experimental  III.2.1  Temperature Measurement  A schematic diagram f o r t h e arrangement used i s shown i n F i g . Measurements o f t h e s l a g temperature were made w i t h couple p r o t e c t e d by b o r o n - n i t r i d e .  (23).  the W3Re/W25Re thermo-  The thermocouple was a t t a c h e d t o  the e l e c t r o d e s u r f a c e as shown i n f i g . (23) and read o u t t o a Sargent Model SR 4 r e c o r d e r .  Measurements o f the temperature g r a d i e n t  e l e c t r o d e were made u s i n g chromel-alumel thermocouples p l a c e d drilled The  i n wells  i n the e l e c t r o d e i n a x i a l s e t s o f f o u r a t known i n t e r v a l s .  thermocouple measuring the s l a g temperature was p l a c e d one c e n t i m e t e r  ahead o f the l e a d i n g e l e c t r o d e "marker" o f the s l a g / g a s The  i n the  thermocouple, and p r o v i d e d  interface relative  an a c c u r a t e  to electrode p o s i t i o n .  e l e c t r o d e thermocouple readout was on a Texas Instruments Model FMW6B  multi-channel  II.2.2  recorder.  ESR Operating  Conditions  Two s e t s o f i n g o t and e l e c t r o d e s i z e s were used:  with  2.54  cm (1") diameter e l e c t r o d e , 5.85 cm x 40 cm mold  3.81  cm (1.5") diameter e l e c t r o d e , 8.0 cm x 45 cm mold  two m a t e r i a l s , 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 u n i t has been e a r l i e r d e s c r i b e d  and was operated  with  e i t h e r e l e c t r o d e p o s i t i v e or n e g a t i v e , w i t h t h e n e g a t i v e p o l e a t ground potential. The e l e c t r o d e c u r r e n t d e n s i t i e s used were a p p r o x i m a t e l y 100  -2 -2 A.cm f o r 2.54 cm diameter e l e c t r o d e s and 75 A.cm f o r 3.81 cm  diameter e l e c t r o d e s .  The s l a g used i n each case was CaF2~30 wt. % c a l c i u m  aluminate, and i n a q u a n t i t y t o g i v e a 4 cm deep s l a g b a t h .  The e l e c t r o d e  23  p o s i t i o n was  measured by  a remote i n c r e m e n t a l  counter  to a p r e c i s i o n  -2 of + 5 x 10 constant  cm.  In a l l c a s e s ,  the e l e c t r o d e feed r a t e was  d u r i n g the measurement p e r i o d , but  held  as the o p e r a t i o n  had  p r e v i o u s l y s t a b i l i z e d f o r some time u s i n g a c o n s t a n t - c u r r e n t mechanism, t h i s o v e r r i d e c o n d i t i o n d i d not departure The (29).  i n current  result i n significant  density.  e l e c t r o d e temperature p r o f i l e s are shown i n F i g . (24)  These are o b t a i n e d  by a n o n - l i n e a r  of the s e q u e n t i a l - r e a d i n g s The and  control  to  (cubic) regression a n a l y s i s  r e c o r d from the m u l t i - c h a n n e l  recorder.  s l a g temperature v a r i e d between 1775°K + 20°K at the s u r f a c e ,  a maximum of 1975°K + 50°K, at a p o i n t s e v e r a l m i l l i m e t e r s below  the e l e c t r o d e t i p .  III.3  Discussion  III.3.1  Formulation  The  of the Problem  g e n e r a l f o r m u l a t i o n of the problem i n the p r e s e n t  case i s  s i m i l a r to that o f 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 s u r f a c e by  convection  and  r a d i a t i o n w i t h no heat t r a n s f e r through the end  of  24 the f i n . present  However, there are more complex boundary c o n d i t i o n s i n the  case than are encountered i n the u s u a l f o r m u l a t i o n .  e l e c t r o d e i s immersed i n the s l a g as shown i n F i g . (30).  The  The  temperature  -2 g r a d i e n t at B i s assumed to e x i s t a c r o s s of s o l i d  the t h i n  (2 x 10  cm)  s l a g s k i n , s i m i l a r to t h a t found between the s l a g and  water c o o l e d mold w a l l . from the e x p e r i m e n t a l c o n d i t i o n s used.  The  boundary temperature T  measurements and  q  the  at z = 0 i s known  i s s p e c i f i c to the  I t i s a l s o assumed t h a t :  layer  melting  24 (1)  the s l a g surface temperature i s uniform over a l l the e f f e 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 p h y s i c a l and surface properties of the electrode are  temperature i n v a r i a n t (4)  no heat t r a n s f e r occurs from the cold end of the electrode  (5)  the electrode has r a d i a t i o n i n t e r a c t i o n w i t h the s l a g , but  m u l t i p l e i n t e r a c t i o n s are absent (6)  steady state conditions  (7)  water cooled copper mold and the gas atmosphere are at  known  constant temperatures (8)  two dimensional heat t r a n s f e r  One may then w r i t e the energy equation as: 2 S  T  3  r  2  + .  -(.~) r  +  9 r  2 ^-l z  =  0  (3.1)  2  9  which has boundary conditions  at z = 0,  T  at z = £,  ~  at r = 0,  3z  |^ 8r  =  T =  o 0  =  0  (3.2) . '  •  (3.3) (3.4)  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 t r a n s f e r terms through the electrode surface, and the electrode volume conduction term.  25  Firstly,  the e l e c t r o d e  change w i t h water cooled  d  A  l d  - *  F  A  l  A l s o , there  l  e  T  0  s u r f a c e element has r a d i a n t energy i n t e r -  copper mold  r=a "  i s convective  l3  a  e  0  ( T  *  V *  ) 4  interchange  + dA^  ( 3  "  5 )  w i t h the gas atmosphere w i t h i n  the mold  dA. h (T - T ) 1 r=a »  and  finally,  e  (The  l  °  d  A  (3.6) v  r a d i a n t interchange  l d  - A  F  A  l  T 2  r=a " 2 ° e  with l i q u i d slag  A  l  \ - *A  ±  configuration factor F introduced m -> n  of the t o t a l energy emitted  T  s"la  surface  a g  l  ( 3  '  7 )  above denotes the f r a c t i o n  by s u r f a c e m t h a t i s i n t e r c e p t e d by  s u r f a c e n) . Using t h e r e c i p r o c i t y theorem f o r c o n f i g u r a t i o n f a c t o r s :  A„F 2 A  A  and  * *  2  , -* d A  +  d  =  A  F  A  l  dA^,. 1 dA^  1  =  d  A  l  F  d  A  l  . A  (3.8)  N  2  - . *  ( 3  '  9 )  the summation theorem  F,, dA  1  . ->- *  =  1 - F dA^  . A  (3.10) 2  26  and assuming grey body p r o p e r t i e s f o r the e l e c t r o d e ( i . e . , ct^ = the energy  -K  balance e q u a t i o n reduces  dA  3T 1 3r  d  A  l  (  " dA  1  e^)  to  -> A  F  x  ) 2  £  1  0  T  r=a  r=a  •e, , o d A , ( T * ) ( l - F '1*3 1  ^  4  E  -dA F, 1 dA^  . A  2  c  o T  0  2  d A  A  1  4  ) + dA 2  h  ±  ( T ^  -  Tj  e. + dA F . e.. a T 1 1 dA.^ -> A^ 1 r=a 4  slag  (3.11)  where each s i d e g i v e s the amount of heat l e a v i n g the s u r f a c e . On  rearrangement:  5T 3r  E  l K  4 r=a  a  e  l 3 K E  * 4  a  dA^  A^  r=a  £ K  Equation dimensionless  v  (T r=a  - T ) + oo'  (3.12) may  F,. dA^ ->• A,,  terms:  T  X  N =  ^ K  — a  ,  (3.12)  be c o n v e n i e n t l y r e - e x p r e s s e d u s i n g the f o l l o w i n g  T-T  L =  T , slag  K  =  D  =  Z  -  o  3 e..aT a 1 o K  * a  T  R  =  _r a  27 In terms of these new v a r i a b l e s , eq. (3.1) and the boundary  (3.2), (3.3), (3.4)  conditions  9  R  (3.11)  and  become  respectively,  (3.13) 2  R  8  3Z'  R  where  = 0  (3.14)  Z=0  11 8Z  = 0  (3.15)  = 0  (3.16)  Z=L  _9X  9R  R=0 9X 3R  D(l + X  / + D(X*)  R =  4  (1 -  ^  £ 3  R=l  - N(l +  i  R=l  Putting  e  2  ax.  -D  3R 1  —^-B-  =  ) + NX + °°  2  x  E, e q u a t i o n  (1 + X  R = 1  )  4  F, 1  De_  + De3  (3.17)  (xV  . 2  (3.17)  becomes  (1 -  F ^  ^  k  )  R=l  - N(1 + X -) + NX R=l  °°  (3.18)  + DEF,. -*• A  2  28  Let  the s o l u t i o n of eq. (3.13) be o f the form  X  =  Substituting  P(R)  0(Z)  (3.19)  the v a l u e o f X from (3.19) i n eq. (3.13) and s i m p l i f y i n g  yields  d  P  Separating  2  P  the v a r i a b l e s ,  ^ | dZ  "  R  E  =  «  dZ  '  2  '  the two r e s u l t i n g e q u a t i o n s are  - Qm  (3.21)  2  The s o l u t i o n t o (3.21) i s of the form  Q  where C^,  =  C  1  cos mZ  +  C  2  (3.23)  s i n mZ  are c o n s t a n t s . 25  Equation  (3.22) i s of a type r e d u c i b l e  to B e s s e l ' s e q u a t i o n  and  i t s s o l u t i o n i s of the form  P  =  C  3  I (mR)  +  C K (mR) 4  0  where C„ and C. a r e unknown c o n s t a n t s , I i s the m o d i f i e d B e s s e l 3 4 ' o  (3.24) function  29 of  the f i r s t  kind  of order  zero  and K  i s the modified  Bessel function  o of  the second k i n d An  of order  zero.  approximate .solution  of the energy  X =  ( C . c o s mZ + C s i n mZ) (C.,1 (mR) + C.K (mR)) 1 2 3 o 4 o  The  u s e o f e q . (3.14) i n (3.25) y i e l d s  X =  [ C I (mR) + C^K C  D O  D O  and  (3.16)to  (3.26) y i e l d  (mR)]sin  are'unknown  X = C I (mR)sin 5 o r  C  = 0,  then  mZ  (3.26)  constants.  = 0.  g  C±  Applying  boundary c o n d i t i o n  Therefore,  mZ  A s s u m i n g no h e a t  (3.27)  transfer  from  the cold  end o f t h e e l e c t r o d e i . e . ,  b o u n d a r y c o n d i t i o n (3.15) t o (3.27)  yields  X = m cos(mL) = 0  Equation  m =  Thus  the general  X =  (3.28)  (3.28) i s s a t i s f i e d  12|±lilL  n  solution  E,[C I _ n o n=0  T h e unknown  ,  ( r ^ zL  (3.13) i s  (3.25)  n  where  applying  equation  =  0  ,  f o r a l l values  of m given  1, 2 . .  by  (3.29)  o f e q . (3.13) i s  -n R) s i n (^$1) zL  coefficients  C  TT Z) ]  ( n = 0, 1, 2...°°) c a n b e  (3.30)  determined  n by  least  square  fitting  at a f i n i t e  number  o f p o i n t s on t h e b o u n d a r y ,  30  choosing  e q u a l l y spaced p o i n t s along  z a x i s and  fitting  them to the boundary c o n d i t i o n  In the p r e s e n t and  100  the e l e c t r o d e i . e . , the  analysis 7 coefficients  boundary p o i n t s were used.  determine the v a l u e s boundary c o n d i t i o n  of the  The  100  (n = 0,  problem to be  7 coefficients  (3.18) f o r the  (3.18). 1,  2,...6)  s o l v e d was  so as to s a t i s f y  boundary p o i n t s  i n the  to  the best  p o s s i b l e manner. From the boundary c o n d i t i o n (3.18) the e x p r e s s i o n i s obtained  5  minimized  as ^ 2  -  ~ [" "Cl + W  R=l  -N(l  where  to be  + A  R = 1  )  +NX  r o +  DEF  4  d A i  +  _  D ( A  > A 2  *  ]}  ) 4 ( 1  " dA  + A> 1 2  F  (3.31)  2  £ denotes summation over a l l p o i n t s i n the r e g i o n 0 < Z < L. 1 Using  takes the  Q  -  the s e r i e s s o l u t i o n f o r X as e x p r e s s e d i n (3.30),  eq.  (3.31)  form  v r v 1  rp f  2 n + 1  ->  T  r(2n+l)-n-.  r  (2n+l) „  n n  n=0  + D{1+  + N {1 +  - De X 3 Q  &A  I n=0  I  ~ n=0  [C I  [-^Hjl]  [ C I [^1)JL] no  AL  s i n f - ^ i ^ Z ] ] }  sin[-^±lhL  (1 - F.. ) - NX dA.^ -* A °° 2  ZL  4  z ] }  DEF, . } dA.^ -> A 2  (3.32)  31  The  f u n c t i o n t o be f i t t e d  t o zero a t v a r i o u s boundary p o i n t s i s  S i n c e the f u n c t i o n i s n o n - l i n e a r 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 l e a s t - s q u a r e f i t  c r i t e r i a a p p l i e d to get a system of l i n e a r a l g e b r a i c e q u a t i o n s are s o l v e d to g i v e the c o e f f i c i e n t s C^. values  of C and t h e process n  c  The  new _ o l d n n ' .old  which  I n i t i a l guess i s made f o r the  i s then i t e r a t e d upon u n t i l  c  <  -7 10  computer programme w r i t t e n t o o b t a i n the c a l c u l a t e d temperature  d i s t r i b u t i o n i s g i v e n i n Appendix i n the programme was o b t a i n e d  (III).  The s u b r o u t i n e  LQF, used  from U.B.C. programme l i b r a r y .  27  24 The  c o n f i g u r a t i o n f a c t o r used was e v a l u a t e d by S i k k a  g i v e n by the f o l l o w i n g  dk  1  + A  2  and i s  expression  Z A -11 - {-=- cos (-) TT 2 8  J7~-  tan  -1) (cj)+2g)  L  (0+1)($-23) \l(3+1  43  , +  1 "Ir - tan [ TT  2 where tj) = Z ]?dA  _^ ^  (3.33)  Z  2 +3  +1  and 3 = r ^ / a .  F i g . (31) g i v e s the p l o t of  against a x i a l length f o r various values  o f 3.  32  111,3.2  C a l c u l a t e d Temperature  Profiles on  the  of  T  three  thermal  the  an  average and  K  =  range of  0.02  0.6  x  transfer  for  two  existing the  The  giving  of  the  correlation  10  values  type  of  for N  °K of  the  the  temperature  0.075 c a l . c m  T  the .  "*"°K ''"sec ^ f o r  steel, values  q  T  the is in  3 values. number  at  c o n s i d e r i n g h^  sec  the for a  i n the  depending  < N  < 0.5.  shown i n F i g . (24)  similar  range  upon the  Typical to  to  (29)  conditions.  The  theoretical  slight  difference  (24)  curves  theoretically  t o be  very  i n the  (especially average  depends upon  -1  0.05  boundary  The  an  3>  is typically  c  -1  shown i n F i g s .  i s found  that only  of  the N u s s e l t  h  values  type  of  profiles  (29).  Experiment  curves  fact  are  between the  error  =  e v a l u a t e d by  cal.cm  observed  experimental  i s not  -2  experimental  computation  value  "*"°K ''"sec "*" f o r s t a i n l e s s  situation.  Correlation with  Curves  in  6 x  (experimental  experimentally observed  be  s e t s of parameters  III.3.3  the  to  N  significantly  used).  conductivity K  h a (= — — ) K may  depend  e l e c t r o d e m a t e r i a l and  -3  10  D and  < 0.035 f o r d i f f e r e n t  s u r f a c e , but  convection,  the  f o r the  -3 of  3,  for a particular  < D  g e o m e t r i c a l heat  computation  geometry were & j  0.058 c a l cm  parameter N  electrode  above  parameters  thermal  of D o b t a i n e d  The  the  the process r  c o n d u c t i v i t y of  steel  value  and  p a r a m e t e r D,  Assuming mild  by  dimensionless  , T , o' slag The  obtained  Profiles  value  are  computed  parameters  listed  computed  and  used  i n Table the  for  II.  experimentally  good.  two  curves  may  i n the measurement of  were  the  thermal  be  attributed  of T :  ) and  to  c o n d u c t i v i t y of  to the the  Table  II.  Parameters used i n the computations of t h e curves shown i n Figs.(24) t o (29). A  ESR C o n d i t i o n  L  A  A  e  K  °°  2.54 cm (1") 1018 s t e e l electrode  _————.  D  N  16.0  0.308  0.29  2.2  0.075  0.0041  1775  1225  2.25  0.0255  0.07  16.0  0.318  0.302  2.6  0.075  0.0041  1775  1175  2.167  0.032  0.10  16.0  0.366  0.346  4.5  0.058  0.0041  1775  1025  2.25  0.0225  0.09  16.0  0.306  0.240  2.2  0.075  0.0041  1775  1225  2.25  0.0255  0.07  16.0  0.318  0.302  2.6  0.075  0.0041  1775  1175  2.167  0.032  0.10  16.0  0.366  0.348  4.5  0.058  0.0041  1775  1025  2.25  0.0225  0.09  positive  2.54 cm (1") 321 s t e e l electrode  3  positive  3.81 cm (1 1/2") 1018 s t e e l electrode  T o  negative  2.54 cm (1") 1018 s t e e l electrode  T , slag  negative  2.54 cm (1") 321 s t e e l electrode  c  negative  3.81 cm (1 1/2") 1018 s t e e l electrode  h  positive  , —  .  —  (jj  34  e l e c t r o d e m a t e r i a l was approximate v a l u e s extensive  considered  i n the a n a l y s i s .  of e m i s s i v i t y were used.  The  Secondly, o n l y  model would  refinement to accommodate a temperature dependent  conductivity.  Accordingly  one  can not  the f a c t t h a t i t i s n u m e r i c a l l y  equal  require thermal  comment on the v a l u e  used beyond  to t h a t c a l c u l a t e d u s i n g  an  average thermal c o n d u c t i v i t y f o r the p e r t i n e n t temperature ranges. The  value  of N i s h i g h e r  than expected as i t r e q u i r e s -3  average heat t r a n s f e r c o e f f i c i e n t , h of 4.1 f o r the e l e c t r o d e s u r f a c e .  The  argon gas  x 10  value  -1  -2a  c a l . cm  °K  sec ^ over the  i n f r e e convection  -1 sec ,  flow r a t e through the  would g i v e a maximum average v e l o c i t y of 4 cm T h i s would l e a d to a much lower h  an  system  electrode. conditions  c and  thus we  have e i t h e r s e l e c t e d too  low  temperature, or there e x i s t s s i g n i f i c a n t of N due  to changes i n the gas  R e l a t i o n to P r o c e s s V a r i a b l e s : show the expected trends  a value  l o c a l v a r i a t i o n i n the  flow regime along The  the  i n t h a t the g r a d i e n t s  At a feed r a t e of 3 x 10  cm  i n the  i n electrode  value  electrode  negative  electrode positive.  sec  spends a p p r o x i m a t e l y 60 sec between 950°K and  gas  electrode.  observed g r a d i e n t s  mode d i f f e r o n l y s l i g h t l y from the e q u i v a l e n t - 2 - 1 condition.  f o r the average  , the e l e c t r o d e the m e l t i n g  <  material  point,  and  30 sec below the s l a g s u r f a c e i n the r e g i o n 1300°K to m e l t i n g  point.  Under these c o n d i t i o n s i t seems l i k e l y  process  only very  small p a r t i c l e s  phase w i l l m a i n t a i n through the Two  (probably  t h a t i n any  solution  sub-micron s i z e s ) of the d i s s o l v i n g  e q u i l i b r i u m composition  and  phase r e l a t i o n s h i p  temperature g r a d i e n t .  f u r t h e r aspects  s t a t e model was  of the model are worthy of n o t e .  ; A steady;  chosen, i n s p i t e of the f a c t t h a t the e l e c t r o d e i s b e i n g  35  consumed, and i s , t h e r e f o r e moving w i t h interface.  respect  t o the s l a g / m e t a l  The r a t e a t which t h e e l e c t r o d e moves a f f e c t s t h e temperature  g r a d i e n t s p r e d i c t e d by the model through the boundary v a l u e and  p o s s i b l y a l s o through  .  Both o f these v a l u e s  parameters and w i l l be s p e c i f i c t o the m e l t i n g the melt r a t e and power i n p u t a r e changed  of T ,  are experimental  c o n d i t i o n s used.  If  these temperatures w i l l  1  vary  i n a way c o n t r o l l e d by the complex heat t r a n s f e r regime e x i s t i n g on 28 the e l e c t r o d e s u r f a c e submerged below the s l a g / g a s  interface.  Recently  attempts have been made t o c a 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 p o r t i o n o f the e l e c t r o d e u s i n g coefficients.  No  assumed heat t r a n s f e r  attempt has been made here t o p r e d i c t the complex  heat t r a n s f e r regime and hence o f i n c l u d i n g the m e l t - r a t e  parameter i n  this analysis. Due  to the s m a l l diameter o f e l e c t r o d e used i n the p r e s e n t  t o r y experiments, any r a d i a l temperature g r a d i e n t (10-20°C). ingot  T h i s was found t o be t h e case.  two d i m e n s i o n a l  I t was i n i t i a l l y p o s t u l a t e d r e l a t i o n s h i p would a f f e c t and  should be s m a l l  However, i n l a r g e  configurations, a s i g n i f i c a n t r a d i a l gradient  p r e d i c t e d by the p r e s e n t  analysis.  t h a t the e l e c t r o d e ' s  time-temperature  t h e r e f o r e the r e a c t i v e a l l o y element l o s s on m e l t i n g . 31  temperature range, the oxide i n a i r was c a l c u l a t e d .  eleptrode/  e x i s t s and can be  the amount o f e l e c t r o d e s u r f a c e  data o f Kubashewski and Evans  labora-  oxidation, U s i n g the;  f o r the o x i d a t i o n o f i r o n i n t h i s thickness  f o r an e l e c t r o d e being  melted  T h i s was done by c o n s i d e r i n g the e l e c t r o d e  s u r f a c e above 1000°K, summing the a p p r o p r i a t e p a r a b o l i c growth-rates, -2 -1 f o r the e x p e r i m e n t a l melt r a t e o f 3 x 10 cm s e c , and thus d e r i v i n g  36  an i n t e g r a t e d oxide i s a p p r o x i m a t e l y 10  c o a t i n g a t p o i n t B i n F i g . (30). -4  cm,  which i n the p r e s e n t _2  would account f o r o n l y 10 titanium a l l o y .  As  wt.  This  e l e c t r o d e s i z e range  % l o s s o f , say,  t i t a n i u m i n an  One  observed between VAR  and  ESR  to the slag/gas  a uniform  Here i t has  be  e l e c t r o d e temperature g r a d i e n t s , i n s p i t e convenient demarcation l i n e i n  i n t e r f a c e i n ESR.  p l a y e d by r a d i a t i o n , c o n d u c t i o n (32).  l e s s important  comment on the p o s s i b l e d i f f e r e n c e s which might  of the f a c t t h a t t h e r e e x i s t s no  Fig.  with  units.  can b r i e f l y  equivalent  iron-  the e l e c t r o d e surface-volume r a t i o decreases  e l e c t r o d e diameter, t h i s o x i d a t i o n source becomes s t i l l i n l a r g e ESR  thickness  and  The  convection  been assumed t h a t VAR  relative  VAR  parts  are i l l u s t r a t e d i n e l e c t r o d e i s exposed to  s u r f a c e at 1900°K at z = 0, w i t h T  = 1800°K and w i t h  no  o e l e c t r o d e thermal term due  to c o n v e c t i o n .  The  equivalent  ESR  gradient  at an e q u i v a l e n t d i s t a n c e from the i n g o t s u r f a c e i s a l s o shown. A l t h o u g h the two  s i t u a t i o n s are not  between the g r a d i e n t s the c o n v e c t i v e  gas  strictly  comparable, the d i f f e r e n c e  i l l u s t r a t e s the s i g n i f i c a n t  flow i n  ESR.  c o o l i n g e f f e c t , of  37  CHAPTER IV MEASUREMENT OF ELECTRICAL AND PROPERTIES OF THE  IV.1  THERMAL  SLAG-SKIN REGION  Introduction One  of the advantages claimed  f o r the ESR  processing  of metals  h e l d to be the r e s u l t i n g c o n t r o l i n the d i r e c t i o n a l i t y of i n g o t  is  solidifi-  32 cation.  T h i s a r i s e s i n a c o n t r o l l a b l e p r o p o r t i o n of r a d i a l to  heat flow i n the s o l i d i f y i n g  ingot.  Since  axial  the r a d i a l flow i s determined  l a r g e l y by the heat t r a n s f e r c h a r a c t e r i s t i c s of the mold-wall r e g i o n , it  i s of i n t e r e s t  to have n u m e r i c a l  values  of the a p p r o p r i a t e heat < 33  t r a n s f e r c o e f f i c i e n t s f o r c a l c u l a t i o n purposes.  The  electrical  p r o p e r t i e s of the same i n t e r f a c e r e g i o n determine the c u r r e n t tion.  In the i n s u l a t e d mold c o n f i g u r a t i o n ( F i g . 3 3 ( a ) ) , a l t h o u g h  i s no net  there  c u r r e n t 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 g i v e the c u r r e n t path  Should t h i s c u r r e n t be l a r g e , the l o c a l j o u l e h e a t i n g , result  distribu-  i n the i n g o t w e l d i n g  shown.  or a r c i n g , w i l l  to the mold, or i n a s e v e r e  case, i n mold-  w a l l puncture. In the s i t u a t i o n shown i n F i g . ( 3 3 ( b ) ) , w i t h the mold grounded, the above e f f e c t s are o n l y of importance i n the r e g i o n where the s l a g 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 -  s k i n should have a s u f f i c i e n t l y h i g h 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 o f the c u r r e n t p a s s i n g from the s l a g  to the mold i s t o p r o v i d e the h o r i z o n t a l c u r r e n t component n e c e s s a r y  34 for conventional electromechanical 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  v a l u e s o b t a i n e d a r e used  Whether unknown.  stirring The n u m e r i c a l  i n e x p l a i n i n g 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 b a l a n c e of the p r o c e s s and a c u r r e n t 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 c o n s i s t s o f a g r a p h i t e c r u c i b l e c o n t a i n i n g a l a r g e volume (^ 1 l i t r e ) o f l i q u i d by an i n d u c t i o n c o i l .  The copper c y l i n d e r  s l a g , heated  (of diameter 3 cm,  length  3 cm) was immersed at time z e r o , and i t s temperature measured simultaneous w i t h t h e s l a g temperature and the e l e c t r i c a l r e s i s t a n c e between the g r a p h i t e c o u n t e r - e l e c t r o d e and the c y l i n d e r . was c l e a n e d by m e c h a n i c a l a b r a s i o n .  The copper  cylinder  The e l e c t r i c a l r e s i s t a n c e was  measured on s u c c e s s i v e o c c a s i o n s at b o t h 40 Hz and 1 KHz, w i t h the same r e s u l t , i n d i c a t i n g  t h a t p o l a r i z a t i o n c o n t r i b u t i o n s were n e g l i g i b l e .  The 1.0 KHz i n s t r u m e n t i s a p h a s e - d i s c r i m i n a t i n g b r i d g e which  registers  o n l y the ohmic c o n t r i b u t i o n s t o the t e s t impedance, and the c l o s e c o r r e l a t i o n between the 40 Hz and 1.0 KHz measurements a l s o  therefore  i n d i c a t e s t h a t r e a c t i v e c o n t r i b u t i o n s to the impedance were n e g l i g i b l e . The temperature was measured u s i n g W3Re/W25Re thermocouple. In o r d e r to e l i m i n a t e the e l e c t r i c a l i n t e r f e r e n c e from the , i n d u c t i o n g e n e r a t o r , a l l the measurements were made w i t h r . f . power o f f ,  39  and w i t h ungrounded i n s t r u m e n t a t i o n .  T h i s l a t t e r step also allowed  high impedance r e c o r d e r s t o be used i n the thermocouple c i r c u i t s  whilst  the thermocouples were i n c o n t a c t w i t h the r e s i s t a n c e measuring  circuits.  The s l a g s k i n t h i c k n e s s was  determined u s i n g a micrometer,  removing the copper b l o c k from the s l a g , f o l l o w i n g a 10 seconds time.  In o r d e r t o e s t a b l i s h t h a t the s l a g s k i n t h i c k n e s s  c o n s t a n t d u r i n g the e x p e r i m e n t a l p e r i o d , the b l o c k was  I t was  i n l e s s than one  immersion  remained  immersed f o r  p e r i o d s v a r y i n g between one and t e n seconds, and the s k i n measured.  after  found t h a t the e q u i l i b r i u m t h i c k n e s s was  thickness established  second.  R e s u l t s of the r e s i s t i v i t y measurement a r e shown i n F i g . (35) and F i g . (36) as a f u n c t i o n of the c y l i n d e r temperature.  The  equivalent  d i m e n s i o n l e s s temperature v s . time measurements a r e shown i n Fig... (37) and F i g . (38). S e v e r a l f e a t u r e s not shown i n these graphs are worthy of comment. F i r s t l y , the s l a g temperature was measured c o n t i n u o u s l y d u r i n g the r u n s , so t h a t the s l i g h t f a l l i n the subsequent c a l c u l a t i o n .  i n the temperature c o u l d be accounted f o r T h i s temperature d e c r e a s e was a p p r o x i m a t e l y  20°C and remained e s s e n t i a l l y c o n s t a n t d u r i n g the time o f the experiment. At h i g h temperatures (1730°C) i t was  found t h a t Ca\F^ d i d not form a  coherent s k i n , but formed a d i s c o n t i n u o u s "patchy" f i l m on the c y l i n d e r surface.  The consequent heat t r a n s f e r was  h i g h 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 t i o n of s l a g showed t h a t the copper b l o c k would undergo a temperature r i s e of a p p r o x i m a t e l y 100°C i f a l l t h i s heat was  absorbed by the b l o c k .  However the subsequent a n a l y s i s i n d i c a t e s t h a t the r a t e o f heat exchange  40  between the the  solid  should be  liquid  and  s o l i d s l a g i s h i g h i n comparison to t h a t  s l a g and  the  block.  transferred  to the  Thus, most of the liquid  A s l i g h t c u r v a t u r e c o u l d be  slag  close  to the  reaction  time of the  unequivocally attributed The  derivation  to the  of the  fusion  bath.  d e t e c t e d i n the  e x p e r i m e n t a l time/temperature t r a c e , but  heat of  between  as  i n i t i a l part  t h i s was  in  a time  r e c o r d i n g system, t h i s can  solidification  of  the period  not  be  step.  r u l i n g e x p r e s s i o n f o r heat t r a n s f e r  in  the  35 e x p e r i m e n t a l s i t u a t i o n used i s a s t a n d a r d For  the  transient  one.  heat f l o w i n systems, w i t h n e g l i g i b l e  internal  resistance  The change of i n t e r n a l energy of the copper c y l i n d e r d u r i n g 'dt'  C  P  m dT  =  U A  [T  slag  Net f l o w of heat from s l a g to the copper c y l i n d e r  Tjdt  (4.1)  integrating,  (4.2) o simplifying  (4.2),  41  Figs.  (37)  temperature,  and  is  transfer  assumed h e r e  coefficient,  n  J  temperature  copper  cylinder  unsteady-state fact  that  (4.3)  a r e made.  reaction i t may  The  terms  Secondly J  range  c o n t a i n s two  surface  d e s c r i b e d by  an  and  Thirdly,  significant  used.  situation,  system  overall  heat  The  justification  transfer  and d i s c u s s e d i s used  i t i s assumed  gradients,  undergoing  a volume term, i t  v a l u e f o r (C ) p copper  considered.  number  although the  comprising U are outlined  c o n t a i n s no  the B i o t  Firstly,  be  cylinder  (4.3).  eq.  an a v e r a g e -  condition  dependence of the  to the present e x p e r i m e n t a l  that  U.  subsequently. the  eq.  assumptions  the heat  show t h e t i m e  processed following  In applying several  (38)  that  in spite for this  of  over the the  lies  i n the  (— , where L = s i g n i f i c a n t d i m e n s i o n , Cu = thermal c o n d u c t i v i t y of copper) of the K  volume/surface  area; K  system  t h a n 0.01.  i s less  Only  i f this  v a l u e exceeds  0.1  will  the  35 assumption calculation  introduce significant o f U.  (>5%)  error  V a l u e s o f U o b t a i n e d t h i s way  into  a  subsequent  are l i s t e d  i n Table  III.  IV.2.2 The  ESR  Experimental  Data  method o f o b t a i n i n g  the mold, e l e c t r o d e  and  36  previously  described.  in  unit  t h e ESR  used  the  total  the i n g o t , T a b l e IV  i n this  electrical  resistance  i n a n o p e r a t i n g ESR  unit  between has  been  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  s t u d y as  o b t a i n e d by  Cameron e t a l .  36  42  Table I I I .  V a l u e s of the o v e r a l l heat t r a n s f e r calculated  Slag Composition  from the d a t a of F i g s .  Slag Temperature  Skin Thickness mm + 0 . 2  CaF  CaF  2  2  2  2  37 and 38.  U x 10 c a l . s cm _ 1  2  °C  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  1640  4.05  1.07  1530  5.0  1.00  +  25 wt. % A 1 0 CaF  c o e f f i c i e n t , U,  3  +  35 wt. % C a T i 0  o  1  +  0.02  T a b l e IV. Ingot dia.  O p e r a t i n g r e s i s t a n c e s i n the ESR process  E l e c t r o d e No. of dia. ingots X  determination  36  Slag skin thickness  Moldelectrode resistance  Moldingot resistance  Ingotelectrode resistance  (cm)  (ohms)  (ohms)  (ohms)  Slag composition  (cm)  (cm)  5.08  2.54  3 x 4  .0.12  0.77±0.1  0.45±0.02  0.03510.005  CaF  5.08  2.54  5 x 5  0.08  0.60±0.1  0.0510.02  0.03710.005  5.08  2.54  5 x 4  0.09  0.15±0.05  1.0 ±0.1  7.62  3.81  4 x 4  0.12  0.7 ±0.1  7.62  3.81  5 x 4  0.08  7.62  3.81  5 x 4  0.09  Unshunted current i n mold  Unshunted current i n slag  (amps)  (amps)  Electrode Polarity  1315  659110  -ve  CaF + CA  3815  650110  -ve  0.03610.005  CaF + CA  9+2  630110  +ve  0.13±0.05  0.020+0.005  CaF  13±5  1205115  -ve  0.5510.1  0.06±0.02  0.01910.005  CaF + CA  1915  1180115  -ve  0.1510.02  0.4 ±0.1  0.02010.005  CaF + CA  20±5  1180115  +ve  2  2  2  2  2  2  4>-  44  IV.3  Discussion  IV.3.1  The  Thermal R e s i s t a n c e of the S l a g S k i n  The p r e s e n t e x p e r i m e n t a l s e t up and an ESR one d i f f e r e n c e .  In ESR  p r o c e s s the copper mold i s water c o o l e d where  as the copper b l o c k was was it  system are s i m i l a r w i t h  not and  e x p e r i m e n t a l l y found  consequently  to be independent  heated  up.  of copper b l o c k  i s j u s t i f i e d t o use the d a t a o b t a i n e d from the p r e s e n t  set  up i n d e s c r i b i n g the ESR  However as U temperature, experimental  thermal c h a r a c t e r i s t i c s i n the  slag-skin  region. The  o v e r a l l heat  up of the two  transfer coefficient  s u r f a c e terms and  of the system, U,  i s mader  the volume conductance of the s l a g  skin. -2  The n u m e r i c a l v a l u e of U so d e f i n e d i s seen to be a p p r o x i m a t e l y -2 cm  -1 sec  10  cal.  -1 °C  .  T h i s i s almost  the same v a l u e as t h a t found  m e t a l / s o l i d - m e t a l / c o p p e r mold w a l l system, as i n continuous  f o r the casting ,  37 practice,  or i n a VAR  unit.  Although  c o n t a i n a thermal r e s i s t a n c e due i n the l i q u i d  the ESR  necessarily  t o e i t h e r f r e e or f o r c e d c o n v e c t i o n  s l a g a d j a c e n t t o the s o l i d  s k i n , which w i l l not be  same as the e q u i v a l e n t term a t the l i q u i d / s o l i d example, a VAR  system w i l l  metal  the  interface i n , for  system, i t i s noteworthy t h a t the o v e r a l l heat  transfer  c o e f f i c i e n t s are c l o s e i n magnitude. In  steady s t a t e , from F i g . (39) and F i g . (40) q  3  slag  slag  [ T  3  E  "  (4.4)  - T J  E  V  J  (4.5)  45  2  * l r  A h  int  From ( 4 . 4 ) , (4.5) and  q n  where  A  o  U  =  U A  =  2irr  o  [T  D " V  ( 4  (T' - T_ ) slag Cu  (4.7)  £  1  n  (4. )  ±-  -, 3 0  h  + slag  8  r £n ( r / r ) - i — — — k slag  In the f o l l o w i n g c a l c u l a t i o n s f o r 8.0 as u n i t y and r ^ -  +  region. 140°C.  h. „ int  cm copper mold, £ i s taken  r^.  By u s i n g a method o f a p p r o x i m a t i o n , one v a l u e s of eq.  (4.8) and hence the temperature  One must make the assumption  can deduce the component profile  here t h a t T  i n the  mold-wall  i s approximately  T h i s v a l u e i s e s t i m a t e d from the mold w a l l t h i c k n e s s , and  o b s e r v a t i o n t h a t the mold w a l l o u t e r temperature (Chapter V ) .  6 )  (4.6) one o b t a i n s  = r  '  i s approximately  the 110°C  In a t y p i c a l case, such as t h a t i l l u s t r a t e d by T a b l e I I I  f o r a CaF„ s l a g , T .. = 1650°C and the s l a g s k i n t h i c k n e s s i s 0.12. 2 ° slag b  T h i s l e a d s to a v a l u e f o r q of 480  c a l . cm ''sec  f o r a 8 cm  diameter  -2 copper mold u s i n g the observed v a l u e f o r U o f 1.28 At t h i s v a l u e , one o b t a i n s a s e l f - c o n s i s t e n t mold w a l l i n n e r and o u t e r  temperatures.  x 10  cm.  - 2 - 1 cal.cm  sec  c o r r e l a t i o n between the  c  46  Fig.  (40) shows s c h e m a t i c a l l y the system at hand.  case a l l the temperatures  except  at E i s the m e l t i n g p o i n t of I t i s now calculate  possible  that  In the p r e s e n t  at D are known as the  temperature  CaF^-  t o s e p a r a t e the terms i n e q u a t i o n  (4.8), and  the v a l u e s f o r h. , h ., and T , u s i n g the d a t a xnt' slag D  developed v  above. Thus, i n the l i q u i d  where  slag:  q  =  A* AT h o EF slag  A' o  =  2rrr„ I 3  r^  =  r a d i a l dimension  ATgp  =  temperature  Substituting  h . slag  slag  shown i n F i g .  difference  the v a l u e s i n eq.  ~  7.5  x 10  In o r d e r to c a l c u l a t e k  (4.9)  2  between p o i n t s E and F of F i g .  (4.9)  cal.cm  (39)  2 S  one  ec  1  °C~  the temperature  gets  (4.10)  1  at D,  i . e . T^,  a value f o r  must be assumed, The v a l u e of k , = 0.8 slag  x 10  -2  c a l . cm  -1  sec  from the v a l u e s 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 s used  f o r the c a l c u l a t i o n .  Substituting  (4.8) one  -1  °C  -1  , estimated  in literature  38  the v a l u e s of k , and slag  b  in  (40)  hslag  obtains  h. int  = 2.05  x 10~  2  c a l . cm  2  sec  l o  C  1  (4.11)  47  Substituting  the known v a l u e s i n eq.  (4.5) and  (4.6)  l e a d s to the  value T  ~  D  1100°C  V a r y i n g the v a l u e s of k , one slag  for  k , slag T  and f o r  =10  -2  c a l . cm  =  1160°C  k , slag  =  0.6  T  =  1000°C  D  D  obtains  x 10  -2  -1  sec  -1  c a l . cm  w i t h c o r r e s p o n d i n g changes i n ^ n  n t  -  °C  -1  One  shown i n F i g . (40), w i t h the temperature 1100°C.  The  two  heat t r a n s f e r  h , slag  =  7.5  h. mt  =  2.05  x 10  -2  x 10  S i n c e the major f a c t o r  -2  -1  sec  may  -1  °C  -1  thus draw the  at D a p p r o x i m a t e l y  processes r  that  the ESR  c a l . cm  -2  sec  -1  °C  -1  " -2 -1 -1 c a l . cm sec °C  i n determining  the v a l u e s of the  system c l o s e l y resembles  i n i t s heat t r a n s f e r  characteristics.  are f u n c t i o n s of s l a g c o m p o s i t i o n and to the v a r i a t i o n s  equal to  c o e f f i c i e n t s have v a l u e s :  parameter, U, i s seen to be the s u r f a c e d i s c o n t i n u i t y surprising  profile  term, i t i s not  the other  cold-mold  As both h .. and k ., slag slag  temperature,  i n s l a g s k i n t h i c k n e s s observed  overall  this w i l l  lead  i n practice.  48  However, i t i s u n l i k e l y t h a t e i t h e r o f these parameters c a n t l y 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  int  J  3  of the p r o c e s s v a r i a b l e s , as was  IV.3.2  The  The  signifi-  insensitive function  observed  and  shown i n T a b l e I I I .  E l e c t r i c a l R e s i s t a n c e of the S l a g S k i n  curves  i n F i g . (35) and  skin resistance i s quite high. r e s i s t a n c e i s - 50 ohms.  F i g . (36)  clearly  show t h a t the  slag  At c y l i n d e r temperature o f 140°C,  the  T h i s g i v e s a r e s i s t i v i t y v a l u e of 14,600 ohm.cm  assuming a s l a g s k i n t h i c k n e s s of 0.12  cm  and  the s u r f a c e a r e a of  the  2 copper b l o c k as 35 drops d r a s t i c a l l y Using  cm  .  to 292  these v a l u e s  l a b o r a t o r y ESR  At a c y l i n d e r temperature of 500°C, the ohm.  cm  (R - 1  R = 20 ohms f o r 140°C and  (diameter =8.0  R = 0.39  c  cm,  % = 3.5  ohms f o r 500°C. 36  obtained experimentally i n e a r l i e r R  ohm).  to c a l c u l a t e the s l a g s k i n r e s i s t a n c e f o r the  u n i t s l a g bath  comparable to 5 Q Q O >  value  study  The  cm)  yields,  v a l u e of R  of 0.55-0.77 ohms i s  However as the copper mold  temperature i s below  150°C, the e x p e r i m e n t a l l y o b t a i n e d v a l u e of R = 0.55-0.77 ohms has to be e x p l a i n e d by The  e x p e r i m e n t a l l y o b t a i n e d v a l u e o f the r e s i s t a n c e of  s k i n i n t h i s study in series, polating  a d i f f e r e n t mechanism.  the s l a g  can be  c o n s i d e r e d as a combination  s k i n r e s i s t a n c e and  the v a l u e s of r e s i s t i v i t y  as o b t a i n e d from F i g . ( 4 0 ) ) , one to 20 ohm. is  cm.  From these v a l u e s  the c o n t a c t r e s i s t a n c e .  of two r e s i s t a n c e s  the c o n t a c t r e s i s t a n c e .  f o r CaF2-Al20  f o r s l a g temperature o f 1000-1200°C  slag  (average  3  Extra-  system from F i g . (86),  slag skin  obtains values ranging  temperature from r =  0.5  i t i s c l e a r t h a t the main r e s i s t a n c e  At 500°C, t h e r e i s a b e t t e r c o n t a c t between  49  the  s l a g s k i n and  resistance Thus and  the  50  times  i n the  mold  of  a good  may in  the  inner mold-wall  to  between  ingot-mold  that  path  arises  from  the  time-temperature contact  of  momentary  the  initial  the  ESR  slag-air 15  V  units with  as the  contact  the  the  the will  mold  i n the  the the  liquid  the  the  cm,  the  can  mold  the  probability  i s higher.  resistances  liquid  at  Thus,  speed  of  low  Fig.  explosions,  (36)  the  e i t h e r from  mold w a l l .  i n small This  has  areas been  of  of  The  This  the the  from  i s the this  cooling skin.  the  a  initial is  a  of  During  a s k i n at  the  at  momentary  mold-  least low  transient high  observed  around  is  i s processed  s l a g c o n t i n u a l l y forms  s l a g and  molds.  temperatures.  s i g n i f i c a n c e of  formation  con-  steel  r e s i s t a n c e drop  The  arising  f o r the  and  temperature  apparent slag.  (35)  This  comparable  slag.  p r a c t i c e using  in Fig.  skin  obtained.  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  result  combined  experimentally  be  150°C,  accounts  ESR  transient "bright spots"  wall.  the  between s l a g  unit  above  probably  reported  the  of  e l e c t r o d e -> m o l d ->• i n g o t , w i t h  contact  possible arcing.  small,  sq.  ingot-mold  observed  and  s l a g s k i n , or  interface in a  and  0,1-2  r e s i s t a n c e drop  c y l i n d e r and  e x i s t s between  density  that  record,  processing,  resistance  contact  s k i n and  the  This  t o be  low-resistance  the  of  resistance of  observed  apparent fact  slag  w o u l d be  welding,  i s an  area  and  failure.  second p o i n t  there  i s good  temperature  the  the working  current  The  a small  a value  140°C.  s l a g s k i n r e s i s t a n c e i n ESR  sequent mold w a l l or  than at  electrode-mold,  magnitude  the main  of  cylinder yielding  unit i f there  even  contact  make t h e  copper  smaller  ESR  over  observed value With  the  current-  in industrial slag surface  ESR  boundary  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 p r o c e s s i s a r e l a t i v e l y  o p e r a t i o n i n terms of thermal e f f i c i e n c y . make t h i s p r o c e s s i n e f f i c i e n t  inefficient  However, the f a c t o r s  which  a r e the same ones which g i v e t h i s  p r o c e s s some unique advantages.  I n an ESR f u r n a c e , 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 o f i n g o t s t r u c t u r e by m e l t i n g the m e t a l i n a m e t a l mold which i s v e r y e f f e c t i v e l y c o o l e d by a water  jacket.,  I t i s h o t s u r p r i s i n g , t h e r e f o r e , t h a t power consumption electroslag  figures f o r  r e m e l t i n g o f 1200 to 2000 k i l o w a t t hours p e r m e t r i c t o n a r e  39 reported,  a l t h o u g h the t h e o r e t i c a l power r e q u i r e d t o melt  a l l o y s i s about 400 KWH/metric ton. the e f f i c i e n c y i s s t i l l  lower  ferrous  For laboratory scale process,  (16-25%). ' Most o f the heat  energy  s u p p l i e d t o the p r o c e s s i s passed immediately t o the c o o l i n g water by c o n d u c t i o n from the s i d e s of t h e s l a g  pool.  An a n a l y s i s o f the heat b a l a n c e o f some o f the e l e c t r o s l a g h e a t s made a t t h e M e l l o n Institute"'""'" has i n d i c a t e d t h a t about 50-55% o f the heat i s h e l d i n the molten m e t a l p o o l which i s e x t r a c t e d through the i n g o t and the w a t e r - c o o l e d copper s t o o l .  About 10 to 15% heat i s  e x t r a c t e d through mold c o o l i n g , w h i l e 25% i s used i n h e a t i n g the , electrode.  The b a l a n c e o f the heat was accounted f o r as b e i n g ,  51  l o s t by  r a d i a t i o n and  convection.  40 Holzgruber 4500 amp),  66%  found t h a t f o r 110  mm  square ESR  of the t o t a l heat i n t r o d u c e d  water of the mold. w h i l e about 29%  A s l i g h t amount (=5%)  ingots  i s removed by  (42 the  V, cooling  remains as heat i n the  o f the t o t a l heat i s l o s t by  ingot,  r a d i a t i o n from the s l a g  surface. I t i s q u i t e c l e a r t h a t the analyses date"^'"^' ^' "'" do not 4  4  agree c l o s e l y .  of heat d i s t r i b u t i o n done to  An  accurate  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 r e m e l t i n g b e t t e r u n d e r s t a n d i n g and As  discussed  c o n t r o l of the  earlier,  there  the e l e c t r i c a l energy can be be  o p e r a t e d u s i n g A.C.  unit i s v i t a l  the to  the  process.  are a number of d i f f e r e n t ways i n which  supplied  or D.C.  knowledge of  to the u n i t .  supply.  In D . C ,  The  one  has  of having the e l e c t r o d e as the cathode ( r e f e r r e d to as n e g a t i v e ) or anode ( e l e c t r o d e p o s i t i v e ) .  I t has  process the  can  choice  electrode  been e s t a b l i s h e d  for  12 some time now  t h a t both the anode and  d i f f e r e n t extents  i n an ESR  d i f f e r e n t operating or connected  unit.  The  characteristics.  ( r e f e r r e d to as  cathode are p o l a r i z e d to two  The  types of arrangement mold can be  ' l i v e ' ) to the i n g o t .  give  i n s u l a t e d from  The  current  path  36 has  been found  to be  d i f f e r e n t i n the two  cases f o r  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 required  to melt i n a p a r t i c u l a r configuration"!"^  The  to the power  range of f i g u r e s  6 42 quoted ' f o r s t e e l s and n i c k e l - b a s e a l l o y s i s a f u n c t i o n of a b s o l u t e s i z e , p o l a r i t y and e l e c t r o d e / m o l d diameter r a t i o , as w e l l as of the 42 material. Kammel et a l . have r e p o r t e d t h a t D.C. w i t h e l e c t r o d e  52  negative  i s the most e f f i c i e n t mode, w h i l s t H o l z g r u b e r e t a l .  t h a t D.C. w i t h  e l e c t r o d e p o s i t i v e was the most  found  efficient.  A l t h o u g h the e l e c t r i c a l energy can be s u p p l i e d i n d i f f e r e n t ways, i t i s n e c e s s a r y t o a d j u s t the power s u p p l i e d t o the melt t o w i t h i n f i n e l i m i t s i f an i n g o t having  good s u r f a c e and s t r u c t u r e i s  to be produced. The same power i n p u t can be achieved voltage  and current.'  by v a r i o u s  The c h o i c e o f c u r r e n t w i t h i n the r e q u i r e d  l i m i t a t i o n i s r a t h e r c r i t i c a l , because w h i l e increases  combinations of  increased  power  current  the melt r a t e , i t also.deepens the s l a g p o o l , g i v i n g a l e s s 4 43  s a t i s f a c t o r y ingot structure. ' not  as g r e a t  as t h a t o f c u r r e n t .  The e f f e c t  of change i n v o l t a g e i s  In c e r t a i n cases,  high voltage  gives  a b e t t e r s o l i d i f i c a t i o n f r o n t and hence an improvement i n i n g o t 4 properties.  Medoyar e t a l .  r e p o r t that the main e f f e c t o f v o l t a g e i s  to r a i s e the temperature o f the s l a g b a t h and a h i g h v o l t a g e  intensities  desulphurization. The power i n p u t  to the p r o c e s s  i s g e n e r a l l y chosen such t h a t the  melt r a t e corresponds to a s t a b l e e l e c t r o s l a g p r o c e s s . r a t e of d e l i v e r y o f the e l e c t r o d e , the ESR p r o c e s s i n t o an e l e c t r i c a r c p r o c e s s .  an a r c d i s c h a r g e  A t a very low  periodically  turns  At the moment when the drop breaks o f f , 4  i s observed between the e l e c t r o d e and s l a g s u r f a c e .  At v e r y h i g h r a t e o f e l e c t r o d e f e e d , p e r i o d i c a r c d i s c h a r g e  occurs  between the end o f the e l e c t r o d e and the s u r f a c e of the m e t a l l i c b a t h , a r i s i n g a t the moment when t h e drop b r e a k s 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 o f the e l e c t r o d e on t h e m e t a l l i c b a t h . The volume of  the s l a g b a t h a l s o c o n t r o l s the s t r u c t u r e o f the  53  ingot obtained.  As the depth of the s l a g b a t h i s i n c r e a s e d  (without  changing the melt r a t e ) , the depth of the m e t a l l i c b a t h i s reduced. As the m a t e r i a l s p r o c e s s e d by the ESR p r o c e s s are q u i t e e x p e n s i v e , v e r y o f t e n i t i s not e c o n o m i c a l l y f e a s i b l e t o t r y out v a r i o u s working c o n d i t i o n s to determine  the optimum working parameters.  i s made here to p r e d i c t the working  An  attempt  conditions for 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 s l a g b a t h by r e s i s t a n c e h e a t i n g i s d i s t r i b u t e d (1)  i n the u n i t i n the f o l l o w i n g manner  heat consumed i n h e a t i n g the consumable e l e c t r o d e to the  m e l t i n g p o i n t , i t s f u s i o n and f u r t h e r h e a t i n g o f the drops of the e l e c t r o d e m a t e r i a l as they f a l l  through the s l a g  bed  (2)  heat g i v e n t o c o o l i n g water  a c r o s s the s l a g  bed  (3)  heat g i v e n to c o o l i n g water a c r o s s the l e n g t h o f the i n g o t  (4)  heat accumulated  (5)  heat g i v e n to base p l a t e c o o l i n g water  (6)  heat l o s t by r a d i a t i o n from the s u r f a c e of the s l a g b a t h  i n the i n g o t  to the f u r n a c e atmosphere (7)  heat r a d i a t e d by the s l a g b a t h on t o the w a l l s of the mold  (8)  heat r a d i a t e d by the s l a g b a t h on t o the e l e c t r o d e .  A  )  54  V.2  Experimental  V.2.1  ESR  V.2.1.1  Ingot  Melt  Schedule  Record  E x p e r i m e n t s were c a r r i e d out Fig.  (41a)  gives  the  general  on  the  U.B.C. e l e c t r o s l a g u n i t .  view of  the  laboratory  unit.  The  starting  9 p r o c e d u r e has  been d e s c r i b e d  operating  conditions  electrode  travel,  in detail  by  were e s t a b l i s h e d ,  slag feed  rate  Etienne.  readings  After  of  steady  current,  e t c . , were r e c o r d e d  at  voltage,  known  time  intervals.  V.2.1.2  Molds  Six cm,  ;  different  wall  thickness:  thickness: 0.5 Cv) 9.5  cm;  0.5  ht:  V.2.1.3  cm;  cm;  (iii) 8.0  8.0  cm,  ht:  90  cm,  wall  cm  AISI  630,  of  EN  6.35  ht:  cm,  different  Ferrovac  diameter  EN  d i a m e t e r molybdenum the  I.D.:  45  wall  thickness  d i a m e t e r ) were r e m e l t e d . 3.81  ( i i ) I.D.:  cm, 80  copper molds 6.35 cm, cm,  (Cl)  ht:  40  80  cm,  wall  thickness:  thickness 0.4  cm).  5.85  cm,  ht:  wall  I.D.:  0.5  cm;  were used  cm,  cm,  ht:  40  wall thickness:  0.5  cm;  (vi)  I.D.:  i n the  present  study.  Electrodes  Electrodes steel,  0.5  ( i v ) I.D.:  I.D.: cm,  water-cooled  25  steel  25  composition  (EN  25  E,  Armco  and  size  In  the  steel  electrode.  melted  and  iron)  (2.54  321  The  process an  ingot  threaded  to  S.S.,  the  the  bottom.  cm  experiment, 3.81  went n o n - c o n s u m a b l e at  1018  cm to 6.35  non-consumable e l e c t r o d e  e l e c t r o d e was  formed  steel,  cm after  55  V.2.1.4  Slag  Composition  S l a g c o m p o s i t i o n CaF^  ^ 25 wt.  the heat b a l a n c e of the p r o c e s s . CaF^  and CaF^  V.2.1.5  ^ 30 wt.  % Al^O•  was  used i n the study of  For some a u x i l l i a r y s t u d i e s ,  % T i O ^ compositions were a l s o  100%  used.  Polarity  Ingots were made u s i n g e i t h e r a.c. o r d.c. e i t h e r p o l a r i t y ) power.  (with e l e c t r o d e of  F i g . (42) g i v e s the t h r e e p o s s i b l e mold  connections.  9 V.2.1.6  Continuous  Slag A d d i t i o n  A s p e c i a l l y designed r o t a t i n g  table  ( F i g . (41b)) allowed  continuous d e l i v e r y of the s l a g d u r i n g the melt.  the  A v e r t i c a l cannister  whose base i s c l o s e d by the r o t a t i n g p l a t e d e l i v e r e d the m a t e r i a l (powder or s m a l l g r a n u l e s ) through a c a l i b r a t e d g r a t e . of  m a t e r i a l was  mold.  The  then wiped over the edge o f the p l a t e i n t o  continuous a d d i t i o n of s l a g u s i n g t h i s apparatus  c a r r i e d out o n l y w h i l e making t a l l  V.2.1.7  The  stream the was  ingots.  Atmosphere C o n t r o l  Three  types of hoods were used  f o r m e l t s done under  argon  atmosphere: Type I :  F i g . (43) g i v e s a schematic  diagram  of the hood, used i n  the i n i t i a l m e l t s , which p r o v i d e d an argon b l a n k e t and e x t r a c t i o n of fumes. Type I I : A more e l a b o r a t e d e s i g n i n c l u d e d a s e a l e d chamber i n  56  which  the  bellows moving for  e l e c t r o d e was  clamped seal  to the  (Figure  a quick  h e l d onto stub  (44)).  r e l e a s e of  used  s l a g was  necessary  V.2.1.8  Experimental  Data  experimental  data  reported  values  stable working electrode  and  Fig.  (46)  a d.c.  V.2.2  Measurement  the  experimental  (0.0254 cm holes  i n the  a spiral mold  itself  couples.  of  copper  the  on  continuous  allowed  addition  cm  are  f o r some o f  the  EN  of  mold)  of  the  t h e m o l d was  wires  the  long  positive  constantan  the melts.  Division,  Mines  Branch,  on  the  to  the  mold  Mold  the mold, measurement out  on  the mold. cm  cm  diameter diameter  wire  x  deep  0.125  copper  copper  cm wire.  mold  t e r m i n a l , f o r a l l the were  used  Constantan  shown i n F i g . ( 4 7 ) .  wires  of  for various  thermocouples were  w e r e embedded i n t h e a p a r t , as  of  during  steel  carried  i n 0.1 0.1  values  melt.  leaving  by  The  25  current going  Profiles  distribution  V.  average analysis  heat  mold, plugged  the the  w e r e embedded  as  i s tabulated i n Table  Copper-constantan  distances  used  300  the  of e x p l o s i o n .  gives  Temperature  constantan  The  i n case  where  (VI)  (with l i v e  temperature  was  b l o w o u t windows  the percentage  profiles  at f i x e d  and  the M i n e r a l Sciences  gives  diameter)  Forty-eight  by  conditions.  to measure the  clamps  parameters  Table  to c a l c u l a t e  temperature  rubber  assembly p r o v i d e d  i n melts  process  positive  order  The  the  pressures  compositions  out  during  In  the  ingot  Ottawa.  stub.  of  obtained  conditions.  carried  top  cooled  ( F i g . (45)).  of  T h i s was  the  Spring  inside  T y p e I I I : T h i s was  The  at  a water  located i n  The 48  individually  copper thermo-  enclosed  Table  V.  ESR melt  record  Ingot mold e l e c t r o d e e l e c t r o d e e l e c t r o d e atmosno. d i a - diameter comp. polarity phere meter (cm) (cm)  starting slag wt. and composition' (g)  voltage (volt)  current (amp)  melt rate  wt. of t h e T o t a l s l a g cap a t e l e c t r o d e , -1. the end o f descend(g.sec ) , , the run (cm) b  (g) 3.81  EN 25  -ve  Argon  III  660 g CaF -27.3 wt. % A1 0  23.75  . 1150  3.35  535  106.5  720 g CaF2~25 wt. % A1 0  22.25  1150  3.8  495  38.2  660 g CaF2-27.3 wt. % A1 0  23.0  1100  4.15  461  37.0  680 g CaF2-26.5 wt. % A1 0  22.5  1130  2.20  411  56.8  660 g CaF -27.3 wt. % A1 0  23.5  1250  2.2  400  55.9  720 g CaF -25 wt. % A1 0  23.0  1175  2.64  485  30.8  440 g CaF -25 wt. % Al 0  22.8  960  2.67  325  99.9  2  2  8  3.81  EN 25  -ve  Air  2  5.08  EN 25  -ve  Air  2  3.5  EN 25  -ve  Argon  2  3.81  EN 25  -ve  Argon  II  3  3  3  3  2  2  3.81  EN 25  -ve  Argon  II  3  2  2  7  6.35  3.5  EN 25  -ve  Argon  2  3  Table V.  (Continued)  Ingot mold electrode electrode electrode atmosno. d i a - diameter comp. p o l a r i t y phere meter (cm) (cm)  8  9.5  5.08  EN 25'  -ve  s t a r t i n g slag voltage current melt wt. of the T o t a l wt. and comp- ( i t ) ( ) rate s l a g cap at electrode osition . -1. the end of decend (g) g.sec ( ) (g) v o  a m  r u n  Air  cm  960 g CaF -25 wt. % A1 0  23.5  1575  4.10  875  66.8  440 g CaF2~25 wt. % Ai q  22.0  880  1.26  380  122.8  660 g CaF -27.3 wt. % A1 0  23.0  920  2.58  530  86.2  720 g CaF2-25 wt. % A1 0  22.0  975.0  2.58  517  30.2  22.5  925.0  2.58  480 •  48.3  2  2  9  6.35  3.18  Armco Iron  -ve  Air  2  10  8.0  3.81  EN 25  +ve  Argon  1 1 1  3  3  2  2  11  8  3.81  EN 25  +ve  Argon  11  2  12  8  3.81  EN 25  +ve  Argon  13  8  3.81  EN 25  +ve l i v e  Argon  11  1 1 1  8  3.81  EN 25  +ve l i v e  Argon  11  3  • " 660 g CaF2~27.3 wt. % A1 0  23.25  1175  2.59  602  80.0  720 g CaF -25 wt. % A1 0  23.5  950  2.58  400  36.3  2  14  3  3  2  2  3  oo  15  8  3.81  EN 25  a.c.  Air  "  26.0  840  4.15  442  29.5  T a b l e V.  (Continued)  Ingot mold e l e c t r o d e e l e c t r o d e e l e c t r o d e atmosno. d i a - diameter comp. polarity phere meter (cm) (cm)  starting slag wt. and composition (g)  voltage (volt)  current (amp)  melt rate  wt. o f the T o t a l s l a g cap a t e l e c t r o d e , -1. the end o f decend Cg.sec ) t  h  e  r  u  n  (  c  m  )  (g) 16  8  3.81  En 25  a.c.  1  1  1  Argon  ceo  23.5  850  3.5  355  95.7  720 g CaF2-25 wt. % A1 0  25.5  810  3.7  340  63.0  680 g CaF -26.5 wt. % A1 0  23.1  780  2.8  367  70.0  660 g CaF -27.3 wt. % A1 0  25.0  1100  non-consumable  375  72.4  600g CaF -13.3 wt. % A1 0  23.5  1300  3.4  400  50.0  980 g CaF -25 wt. % A1 0  23.5  1575  6.36  772  80.0  380 g 100 % C a F  22.3  650  1.22  345  40.0  660 g CaF -27.3 wt. % A1 0 2  2  17  8  3.81  EN 25  a.c.  Argon^  2  18  8  3.5  EN 25  a.c.  Argon  1  3  3  2  2  19  8  3.81  EN 25 + Mo  a.c.  Argon  III  2  2  20  8 .•  3.81  AISI 630  -ve  Argon  II  9.5  6.35  EN 25  3  2  2  21  3  -ve  Air  3  2  2  22  5.85  2.54  321 SS  +ve  Argon  3  2  Ln  T a b l e V.  (Continued)  Ingot mold e l e c t r o d e e l e c t r o d e e l e c t r o d e atmosno. d i a - diameter comp. polarity phere meter (cm) (cm)  starting slag wt. and comp• • osition / ^ (g)  voltage current . , . . ( v o l t ) (amp) N  melt rate  wt. o f the T o t a l s l a g cap a t e l e c t r o d e . ^, ° , r , , , - 1 the end of decend (g-sec ) , . . ° the run (cm) N  t  (g) 23  5.85  2.54  321 SS  +ve  Argon  380 g CaF -31.6 wt, % CaTi0„  22.3  630  2.0  195  45.0  380 g CaF2-31.6 wt, % CaTiO„  22.3  640  1.69  286  40.1  380 g CaF -23.7 wt, % A1 0  23.3  1010  2.5  217  32.5  400 g CaF -25 wt. % A1 0  23.5  1000  1.735  192  26.5  360 g CaF -25 wt. % A1 0  20.2  780  1.56  252  31.4  340 g CaF -25 wt. % A1 0  22.2  975  2.45  327  28.1  340 g CaF -25 wt. % Al 0  22.4  910  1.75  272  28.0  2  24  5.85  2.54  321 SS  +ve  25  5.85  3.18  FVE  -ve  Argon  Air  2  2  26  5.85  3.18  FVE  -ve  Argon  II  3  2  2  27  5.85  3.18  FVE  +ve  Air  3  2  2  28  29  5.85  5.85  3.18  3.18  FVE  FVE  +ve BN i n s u lated  Argon  +ve BN i n s u lated"  Argon  :  II  3  2  2  II  2  3  o  T a b l e V.  (Continued)  Ingot mold e l e c t r o d e e l e c t r o d e e l e c t r o d e atmosdiameter comp. no. diapolarity phere meter (cm) (cm)  starting slag wt. and composition  voltage current (volt)  (amp)  melt rate (g.sec  (g)  wt. of the T o t a l s l a g cap a t e l e c t r o d e the end of decend ) (cm) the run (g)  30  5.85  3.18  FVE  +ve l i v e  Argon  340 g. CaF -25 wt. % A1 0  21.5  870  1.3  158  26.6  340 g CaF -25 wt. % A1 0  24.2  650  2.25  167  28.2  340 g CaF -25 wt. % Al 0  23.0  810  2.43  158  28.6  2  2  31  5.85  FVE  3.18  a. c.  Argon  3  2  2  32  5.85  FVE  3.18  Atmosphere:  Argon  :  a. c. BN i n s u lated  2  Argon atmosphere u s i n g s h i e l d of type I  Argon*''': Argon''"''": 1  Argon  3  Argon atmosphere u s i n g s h i e l d o f type I I Argon atmosphere u s i n g s h i e l d o f type I I I  Table VI. Chemical analysis of the EN 25 s t e e l ingots Ingot composi- A l l o y electrode Atmosno. t i o n of composi- p o l a r i t y phere the tion  composition (wt. %) Si  Ni  0.675 0.225 0.06  0.013 2.475 0.72  0.60  0.028 0.27  0.013 2.50  0.66  0.62  0.028 0.275 0.13  0.062 0.012 2.55  0.73  0.65  0.028 0.29  Mn  Cr  Mo  Sn  Cu  Al  1  Electrode EN 25  -ve  Argon  1 1 1  0.29  1  Ingot  EN 25  -ve  Argon  1 1 1  0.285 0.51  0.135 0.05  2  Electrode EN 25  -ve  Air  0.28  0.24  2  Ingot  EN 25  -ve  Air  0.275 0.56  3  Electrode EN 25  -ve  Air  0.275 0.645 0.32  3  Ingot  EN 25  -ve  Air  0.29  0.53  5  Electrode EN 25  -ve  Argon  11  0.28  0.675 0.235 0.056 0.012 2.5  5  Ingot  EN 25  -ve  Argon  11  0.295 0.61  0.165 0.06  0.013 2.42  0.70  0.65 >0-10  6  Electrode EN 25  -ve  Argon  11  0.28  0.67  0.235 0.059 0.012 2.55  0.72  6  Ingot  EN 25  -ve  Argon  11  0.30  0.59  0.17  0.79  10  Electrode EN 25  +ve  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  10  Ingot  EN 25  +ve  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  11  Electrode EN 25  +ve  Argon  11  0.28  0.66  0.23  0.058 0.013 2.55  0.72  0.60  0.028 0.275' 0.015  11  Ingot  +ve  Argon  11  0.275 0.63  0.15  0.040 0.013 2.5  0.20  0.57  0.028 0.27  EN 25  0.69  0.155 0.056 0.013 2.37  0.01 ba  0.01  0.185 0.61  0.028 0.265 0.13  0.025 0.013 2.42  0.74  0.60  0.026 0.23  0.165 0.026 0.013 2.38  0.20  0.56  0.027 0.225 >0.2  0.05  0.015 2.42  0.725 0.61  0.027 0.27  0.01  0.015  0.29  0.14  0.63  0.028 0.28  0.01  0.62  0.03  0.15  0.27  Fe  0.015  Table VI.  (Continued) composition (wt. %)  Ingot composi- A l l o y electrode atmosno. t i o n of composi- p o l a r i t y phere the tion  Mn  Si  Ni  Cr  Mo  Sn  Cu  Al  12  Electrode EN 25  +ve  Argon  11  0.29  0.665 0.225 0.058 0.013 2.475 0.72  0.598 0.029 0.265 0.01  12  Ingot  +ve  Argon  11  0.27  0.65  0.59  13  Electrode EN 25  +ve l i v e  Argon  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  13  Ingot  EN 25  +ve l i v e  Argon  1 1 1  0.30  14  Electrode EN 25  +ve l i v e  Argon  14  Ingot  +ve l i v e  Argon  15  Electrode EN 25  a. c.  15  Ingot  EN 25  16  EN 25  0.20  0.015  0.062 0.013 2.57  0.63  0.029 0.29  >.0.2  11  0.275 0.675 0.23  0.062 0.012 2.45  0.725 0.625 0.027 0.28  0.01  11  0.28  0.35  0.055 0.067 0.013 2.47  0.19  0.60  0.029 0.27  0.04  Air  0.28  0.66  0.225 0.06  0.012 2.45  0.715 0.61  0.017 0.27  0.01  a.c.  Air  0.275 0.61  0.18  0.032 0.013 2.50  .215 0.62  0.029 0.27  0.04  Electrode EN 25  a.c.  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  16  Ingot  EN 25  a.c.  Argon  1 1 1  0.285 0.66  0.20  0.064 0.014 2.52  0.74  0.66  0.03  0.03  17  Electrode EN 25  a. c.  Argon  11  0.28  0.675 0.235 0.057 0.012 2.475 0.73  0.61  0.028 0.275 0.01  17  Ingot  a.c.  Argon  11  0.27  0.62  EN 25  0.195 0.045 0.012 2.48  0.66  0.029 0.27  0.09  EN 25  0.33  0.185 0.051 0.013 2.50  0.195 0.60  0.29  0.028 0.27  Fe  0.035  CT\  64  i n 0.2  cm d i a . p l a s t i c t u b i n g s (made by ICORE, C a l i f o r n i a ) .  j u n c t i o n s were m a i n t a i n e d at 0°C by immersing g l a s s tubes c o n t a i n i n g For  The  cold  them i n i c e c o o l e d  mercury.  melts u s i n g d.c. p o s i t i v e  ( l i v e mold) c o n f i g u r a t i o n , a  s i g n i f i c a n t f r a c t i o n o f the t o t a l c u r r e n t f l o w s through the mold and as such i t i s not p o s s i b l e to determine the temperature on the mold u s i n g copper mold as the +ve couples.  distribution  t e r m i n a l f o r a l l the thermo-  A number o f i n s u l a t e d thermocouple grade copper w i r e s were  embedded near the c o n s t a n t a n w i r e s i n the mold to g i v e an a c c u r a t e temperature d i s t r i b u t i o n on the mold. F i n s were a t t a c h e d to the mold to r e g u l a t e the water f l o w over the copper mold, a t the same time, e n a b l i n g chromel-alumel  thermocouples  to be l o c a t e d i n a s p i r a l along the l e n g t h of the mold. couples  These  (15 i n t o t a l ) were used to determine the temperature  b u t i o n i n the mold c o o l i n g Fig.  distri-  water.  (48) shows the thermocouples  generated was  thermo-  clad  copper molds.  r e c o r d e d on a Texas i n s t r u m e n t model FM W6B  The e.m.f. multi-  channel r e c o r d e r . As the i n g o t p r o g r e s s i v e l y b u i l t up, a p p r o p r i a t e  thermocouples  were connected to the,24 t e r m i n a l s r e c o r d e r to g i v e the temperature d i s t r i b u t i o n on the mold. Fig.  (49) to F i g . (56) g i v e s the temperature d i s t r i b u t i o n on  mold f o r d i f f e r e n t  experimental configurations.  temperature d i s t r i b u t i o n  the  F i g . (57) g i v e s ; t h e  i n the mold c o o l i n g x^ater.  65  V.2.3  Measurement o f the Heat In  L e a v i n g Through  the Bottom o f the Mold  o r d e r t o c a l c u l a t e t h e amount o f heat l e a v i n g through the  bottom o f the, mold, i n some m e l t s , two chromel/alumel  thermocouples  were p l a c e d , known d i s t a n c e a p a r t (1 cm), i n grooves made i n the s t e e l base p l a t e .  V.3  F i g . (58) g i v e s the temperature d i s t r i b u t i o n o b t a i n e d .  D i s t r i b u t i o n o f Heat  V.3.1  Power Input In  t h i s s e c t i o n , a d e t a i l e d a n a l y s i s o f t h e heat i n p u t i n t o the  u n i t w i l l be c a r r i e d o u t . (I.N. set  Input i n the S l a g Bed  1 of Table V). up were determined  It will  be c a r r i e d out f o r a t y p i c a l melt  The v o l t a g e g r a d i e n t s f o r t h i s e x p e r i m e n t a l i n Chapter I I and w i l l  There a r e 3 sources of heat  be used here.  input.  (1)  r e s i s t a n c e h e a t i n g o f the s l a g  (2)  p o l a r i z a t i o n of the e l e c t r o d e and the i n g o t  (3)  o x i d a t i o n of t h e e l e c t r o d e o r the cathode r e a c t i o n p r o d u c t  in a i r . From T a b l e V, the amount o f heat i n p u t be c a l c u l a t e d .  (due t o (1) and (2)) can  The a.c. r i p p l e i n a d.c. o p e r a t i o n i s not a s i n e  wave, but has an r.m.s. e q u i v a l e n t , r e g i s t e r e d by the 'r.m.s.' meters. D.C. power: A.C. r i p p l e :  V = ,23.75 v o l t s ;  A = 1150 amps.  r.m.s. v o l t a g e = 2.65 V r.m.s. c u r r e n t = 142 amp  Power i n p u t = 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 Fig.  (59) g i v e s the 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 melt  of Ingot No. 1. shown.  of the S l a g  The s l a g b a t h i s s u b d i v i d e d i n t o f i v e s e c t i o n s as  The average temperature and c o n d u c t i v i t y of each s e c t i o n are  shown i n F i g . (59).  The c o n d u c t i v i t y data was e x p e r i m e n t a l l y  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 c o n d u c t i v i t y  w i l l be d i s c u s s e d subsequently.  .  Each s e c t i o n i s - assumed to have a c o n s t a n t  Power  =  current density  2 I R watts  R  v  —— I  v  .  2  volume x c  2  Region A: Power  =  —^ I  V  =  8 volts  volume =  x volume x c  2TT cm^  I  =  0.9  c  =  2.46 ohm *cm  =  2 ^ (0.9)  P A  cm  x 2TT x 2.46 x 0.24  Table V I I g i v e s the heat regions  considered  T o t a l heat  1  = =  0.295 K c a l . s e c "  i n p u t d i s t r i b u t i o n i n the f i v e  here.  input  =  E P A+E  A  4.75 K c a l . s e c *.  1  different  Table VII.  Region  A  Calculation  o f heat input  electrical  conductivity  AV . (volts)  8  . volume  length  (cm)  (cm)  2TT  =0.9  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.  a.c. electrical conductivity  Amount of heat generated  T o t a l heat generated  (ohm  ( K c a l . sec "'")  ( K c a l . sec "*")  "'"cm "*") 2.46  .295  0.295 + 1.27 +1.60 + 1.10  B  18  C  D  E  8TT  = 2.1'  2.85  1.27  12.87  24TT  = 2.22  2.64  1.60  13.0  12Tf  =1.8  2.30  1.10  18TT  =2.1  2.08  0.485  8.75  +0.485 = 4.75  68  V.3.3  E f f e c t of Dissolved As  discussed  A l on the C o n d u c t i v i t y  e a r l i e r i n Chapter I I , the  i n a d.c.  ESR  different  extents,  Ca has  Ca and  operation  i s Ca,  A l or A l  and  +  cathodic  complete m i s i b i l i t y i n CaF^  the  Slag  r e a c t i o n product  these are  i n both the l i q u i d m e t a l and  of the  soluble  to  slag.  s l a g at the ESR  operating  44 temperatures. of CaF^  has  not  A l t h o u g h the e f f e c t of Ca on been s t u d i e d ,  the e l e c t r i c a l  d a t a i s a v a i l a b l e on the  conductivity  e f f e c t of  Na  44 a d d i t i o n to NaF c l e a r that  due  s i m i l a r h a l i d e systems.  30-40% i n c r e a s e  Ca or A l i n the To  and  obtain  in conductivity  s l a g i s not  From t h i s d a t a i t i s f o r 2-5  mole % a d d i t i o n  of  unreasonable.  a more r e a l i s t i c v a l u e f o r the i n c r e a s e  to the d i s s o l u t i o n of Ca and  A l i n s l a g the  in  conductivity  following  approach i s  adopted. From T a b l e V, and  I.N.  16  ( a . c ) , the ESR  very s i m i l a r . cell  i t i s c l e a r t h a t both f o r I.N.  Using  1 (d.c.  c e l l geometry below the e l e c t r o d e  s u b s t i t u t e i t i n the  for  d.c. melt to g i v e the v a l u e of r e s i s t i v i t y of the  For  I.N.  (a.c.  tip  was  t h i s assumption, i t i s p o s s i b l e to c a l c u l a t e  c o n s t a n t from the a.c. melt and  16  negative)  V I  =  23.5 850  R  V I  R  r  V amp. .0276 ohms  a.c.  (f) A  =  0.0276  .0276 r a.c.  the  calculations  slag.  69  For I.N. 1 (d.c. n e g a t i v e )  V  = 23.5 V ( a c t u a l l y 23.75 V)  I  =1150  R  =  amp  =  0.0204 ohm  r, .(f) = d.c. A ,jU  =  0.0204  0.0204  A  r  A  d.c.  Equating  the two v a l u e s  of (^-)  ' 0.0276 r  =  a.c.  0.0204 r, d.c.  d.c.  0.0204 0.0276  r, d.c.  =  .74 r a.c.  c, d.c.  =  1.35 c a.c.  r  a.c  Thus the c o n d u c t i v i t y o f the s l a g i n d.c. o p e r a t i o n i s i n c r e a s e d 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 l e s s s e n s i t i v e t o temperature v a r i a t i o n , t o simplify  the a n a l y s i s ,  of d.c. r e s i s t i v i t y gradients w i l l  i t i s assumed here t h a t the temperature  i s s i m i l a r to a.c. r e s i s t i v i t y .  variation  The v o l t a g e  t h e r e f o r e remain u n a l t e r e d .  Table V I I I g i v e s the heat i n p u t d i s t r i b u t i o n i n the v a r i o u s based on the d.c. c o n d u c t i v i t y v a l u e s .  .......... regions  Table VIII.  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. electrical  Region  conductivity  a.c. e l e c t r i c conductivity  amount of heat generated  (ohm  (Kcal.sec  "'"cm *)  *)  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  amount o f heat generated (Kcal.sec  "'"cm "*")  1  )  T o t a l heat g e n e r a t e d by resistance heating of the s l a g ( K c a l . 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 G e n e r a t i o n Due  to P o l a r i z a t i o n  As d i s c u s s e d e a r l i e r i n Chapter i n g o t and e l e c t r o d e are p o l a r i z e d . not a v a i l a b l e f o r EN f o r pure i r o n  (Fig.  25  steel,  I I , i n d.c.- ESR  p r o c e s s , both  Although p o l a r i z a t i o n d a t a i s  i t i s not unreasonable  to use the d a t a  (21)). Using t h i s d a t a , f o r the c u r r e n t  d e n s i t i e s e x i s t i n g on the e l e c t r o d e and i n g o t f o r d.c. n e g a t i v e u r a t i o n , one The  o b t a i n s n - 0.5  V f o r both cathode  amount of heat generated  due  .0.5 x 1150 x .24 + 0.5 x 1150 x .24 Adding t i o n one  config-  and anode p r o c e s s e s .  to these p o l a r i z a t i o n s =  =  0.275 K c a l . s e c " . 1  the heat i n p u t v a l u e s f o r r e s i s t a n c e h e a t i n g and  polariza-  gets  heat i n p u t  The v a l u e of  6.43  =  +  0.275 =  6.705 K c a l . s e c  - 1  6.705 K c a l / s e c compares v e r y f a v o u r a b l y w i t h  6.65  K c a l . s e c ^ o b t a i n e d from the e l e c t r i c a l energy  V.4  An A n a l y s i s of the Heat T r a n s f e r r e d to Mold C o o l i n g Water  V.4.1  the  i n p u t data.  Introduction In order to c a r r y out an a c c u r a t e heat b a l a n c e of the p r o c e s s ,  one must know the amount of heat  t r a n s f e r r e d t o mold c o o l i n g water a t  each p o i n t on the mold o u t e r s u r f a c e . On examining it  the temperature  i s c l e a r t h a t the temperature  liquid  d i s t r i b u t i o n on the copper  mold,  of the copper mold c o n t a i n i n g the  s l a g and metal p o o l i s above the b o i l i n g p o i n t of water a t  atmospheric  pressure.  When the s u r f a c e temperature  exceeds the  72  s a t u r a t i o n 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 s u r f a c e  take p l a c e even i f the b u l k water temperature i s below the point.  The  b o i l i n g process  i n a l i q u i d whose b u l k  may  boiling  temperature i s below  the s a t u r a t i o n temperature but whose boundary l a y e r i s s u f f i c i e n t l y superheated that bubbles form next to. the h e a t i n g s u r f a c e i s u s u a l l y 35  c a l l e d heat t r a n s f e r to a subcooled  boiling  l i q u i d or s u r f a c e  V a r i o u s mechanisms of heat t r a n s f e r i n s u r f a c e b o i l i n g but it  boiling.  are put  the v a p o r - l i q u i d mechanism^"' i s the p r e s e n t l y a c c e p t e d  forward  mechanism as  i s a b l e to e x p l a i n most of the observed phenomena. Thus the a n a l y s i s has  to be  carried  out  i n the  two  regions  of  the  mold/water i n t e r f a c e which are s e p a r a t e l y i n the: 1.  non-boiling  2.  surface b o i l i n g  V.4.2  Non-boiling  V. 4.2.1 The  region.  Region  Introduction f i n a l expressions  very complicated flow and  region  and  obtained  from more advanced a n a l o g i e s  the e v a l u a t i o n of the N u s s e l t number under  thermal boundary c o n d i t i o n s u s u a l l y r e q u i r e s a  integration.  For  at hand to use analogies.  t h i s reason  semi-empirical  i t i s more convenient equations,  Secondly, as w i l l be  are given  numerical  f o r the purpose  or graphs based on  apparent s u b s e q u e n t l y ,  advanced  the amount of  heat t r a n s f e r r e d to the c o o l i n g water i n the n o n - b o i l i n g r e g i o n , i s q u i t e s m a l l when compared to s u r f a c e b o i l i n g  region.  73  V.4.2.2  C a l c u l a t i o n o f the Reynolds  Number  T a b l e s IX and X g i v e the e x p e r i m e n t a l d a t a and the r e l e v a n t p h y s i c a l p r o p e r t i e s of water  respectively.  G Reynolds  where G  =  (g.sec  cm  number  =  D  R  y  mass v e l o c i t y o f the f l u i d  f l o w i n g through the annulus  )  G  =  2 2 TT[D -Dp W  4  2  _1 where W w  =  water r a t e through t h e annulus  =  2  1  *  D^ and D^  G D  H  u  :  6  f  *  1  =  350 g s e c '  (g s e c  )  1  dimensions of the annulus  =  -1 -2 5.87 g s e c cm  =  h y d r a u l i c diameter (cm)  -  4 x flow c r o s s s e c t i o n a l a r e a wetted p e r i m e t e r  =  3.55 cm  =  v i s c o s i t y o f water  (cm)  (poise)  5.87 x 3.55 0.00657  Re  =  3200  The f l o w i s l a m i n a r when the Reynolds In the range of Reynolds  number i s below 2100.  35  number between 2100 and 10,000, the t r a n s i -  t i o n from l a m i n a r to t u r b u l e n t f l o w takes p l a c e .  The f l o w i n t h i s  74  T a b l e IX.  Experiment d a t a f o r i n g o t no. 1 (Table V)  I n l e t water temperature:  32°C  O u t l e t water temperature:  50°C  Water flow  „, , 21 l i t r e s  rate:  . -1 mm  C r o s s - s e c t i o n a l dimensions of  the water j a c k e t :  D  1  D_ 2  T a b l e X.  =  8.9 cm  =  12.45 cm  P h y s i c a l p r o p e r t i e s o f water a t 40°C-50°C  Coefficient  of v i s c o s i t y  a t 40°C:  0.00657 p o i s e  Coefficient  of v i s c o s i t y  at 50°C:  0.0055 p o i s e  S p e c i f i c heat:  1 cal g"  Thermal c o n d u c t i v i t y :  15.2 x 1 0 ~ c a l cm" sec" °c'  Density:  1 g cm  l o  C 4  _ 1  1  1  75  regime i s c a l l e d  'transitional'.  the flow becomes f u l l y  At a Reynolds  number of about 10,000,  turbulent.  Thus the e x p e r i m e n t a l flow  :  r a t e i s i n the  'transitional  region . 1  There are no w e l l developed e m p i r i c a l formulae f o r t h i s r e g i o n . purpose of c a l c u l a t i o n s , ' t u r b u l e n t  flow'  c o n d i t i o n w i l l be  N a t u r a l l y , the heat t r a n s f e r c o e f f i c i e n t o b t a i n e d be  the upper  V.4.2.3  For  the  assumed.  i n t h i s way  would  limit.  C a l c u l a t i o n of the Heat T r a n s f e r  C o e f f i c i e n t i n the  Non-boiling  Region 35 Colburn's e q u a t i o n flow  f o r heat t r a n s f e r c o e f f i c i e n t f o r  turbulent  i n annular tubes i s St.(Pr)  2 / 3  ^  0.023 (Re)  h  where  St  =  Stanton  number  Re  =  Reynolds  Pr  =  P r a n d t l number  =  number  °'  (5.1)  2  nb  c  P  G  =  =  ^k  f  where a l l the symbols have the u s u a l meaning. To  account f o r the v a r i a t i o n i n p h y s i c a l p r o p e r t i e s due  temperature g r a d i e n t , McAdams except c defined  P  be as  evaluated  35  to  the  recommends t h a t a l l the p h y s i c a l p r o p e r t i e s  at the average f i l m temperature of the  fluid  76  T  where T  g  =  £  r  0.5[T  s  + T, ]  (5.2)  b  =  s u r f a c e temperature  o f copper  =  b u l k water temperature (°C).  In the p r e s e n t case, both T  and T, a r e v a r i a b l e s . b  s accuracy r e q u i r e d i n approximation h c  p  substituting  h  However, f o r  the p r e s e n t c a l c u l a t i o n s , i t i s a r e a s o n a b l e  t o assume  nb G  (°C)  s 50°C.  0.023 [ - ^ ] ° - [ ^ - ! £ ] D G k H f 2  J  /  2  1  u  (5.3)  3  £  the v a l u e s and s i m p l i f y i n g , one o b t a i n s  »  n b  1.15 x 10  2  c a l cm °C - 2  1  sec  (5.4)  - 1  46 A l t e r n a t i v e l y , S i e d e r and Tate  suggest  the f o l l o w i n g e m p i r i c a l  r e l a t i o n s h i p t o c a l c u l a t e h ^:  £*A £JL l/3 H  r  K.  K  All  f  ^ 0.14  =  0  -  0  2  3  ^ 0 . 8  y  the p h y s i c a l p r o p e r t i e s a r e e v a l u a t e d a t the average  temperature  of the water  the average  s u r f a c e temperature  y  t 7 W  =  5  y  (-40°C) except  bulk  which i s e v a l u a t e d a t  o f the copper  (~60°C).  0.00469 p o i s e  . (5.6)  60°C  On s u b s t i t u t i n g the v a l u e s i n (5.5) and s i m p l i f y i n g , one o b t a i n s :  i  77  h  -2 .-2o„-l c a l cm = 1.145 x 10 C sec  nb  (5.7)  Thus one may approximate the heat t r a n s f e r c o e f f i c i e n t  f o r the  -2 -2 -1 -1 n o n - b o i l i n g r e g i o n t o be = 1.15 x 10 c a l cm °C s e c  V.4.3  Surface  V.4.3.1  Boiling  Region  Introduction  The  a n a l y s i s f o r the heat t r a n s f e r c o e f f i c i e n t  i n the s u r f a c e  45 47 48 boiling cases,  conditions, i s at present,  semi-empirical.  '  In a l l  the a n a l y s i s was c a r r i e d out f o r d i s t i l l e d water.  tap water used as a c o o l a n t i n the p r e s e n t amount of d i s s o l v e d a i r .  The s o l u b i l i t y  w i t h an i n c r e a s e o f temperature. bubbles.  intense.  The  experiments has a c o n s i d e r a b l e  of a i r i n water  decreases  The a i r escapes i n the form o f  caused by the motion o f the bubbles i s more  This Increases  c o o l i n g water q u i t e As  The normal  As a r e s u l t o f the i n c r e a s e i n the bubble p o p u l a t i o n , the  a g i t a t i o n o f the l i q u i d  be  '  a first  the heat t r a n s f e r from the mold w a l l to the  significantly.  s t e p , the d i s t i l l e d water a n a l y s i s w i l l be  considered.  experimental  data f o r f o r c e d c o n v e c t i o n w i t h o u t b o i l i n g can 35 c o r r e l a t e d by a r e l a t i o n o f the type ,  Nu  Eq.  =  KRe)  4>  (5.8) can be m o d i f i e d  Nu, b  V b  =  (5.8)  (Pr)  f o r n u c l e a t e b o i l i n g i n t o the form  KRe ) b  *  (Pr ) A  (5.9)  78  where P r  i s the P r a n d t l number o f the saturated, l i q u i d ; h, i s t h e  0  D  n u c l e a t e b o i l i n g heat t r a n s f e r c o e f f i c i e n t  and Re, =  b  G  :  is a  \  b  measure o f the a g i t a t i o n o f the l i q u i d  b  i n n u c l e a t e - b o i l i n g heat  transfer =  average bubble diameter (cm) •-1  u  =  mass v e l o c i t y o f the bubbles, p e r u n i t area  =  v i s c o s i t y o f the l i q u i d  (g s e c  -2  cm  )  (poise)  A/  The mechanisms o f bubble f o r m a t i o n s i m i l a r i n nucleate nucleate  and s u r f a c e b o i l i n g  and heat t r a n s f e r a r e q u i t e and thus the a n a l y s i s f o r  b o i l i n g i s applicable f o r surface b o i l i n g 47  Using  experimental  data, Rohsenow  modified  means o f s i m p l i f y i n g assumptions t o o b t a i n * ^ = C [ - ^ I *<?  J  C  7  h  f  g  (Pr/'  7  f  S  f  V f g  conditions.  M r  p  v  eq. (5.9) by  0  '  3  (5.10)  3  }  -1 where q/A  g^ o p  s p e c i f i c heat o f s a t u r a t e d  =  heat f l u x , BTU h r  =  l a t e n t heat o f v a p o r i z a t i o n , BTU l b  =  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  •=  £ v  a Pr  =  £  _ 1  ft  density of saturated  l i q u i d > BTU l b  -1  °F  _ 2  liquid,lb  m  ft  ft  1  -3  -3  =  density of saturated vapor,lb  =  s u r f a c e t e n s i o n o f the l i q u i d - t o - v a p o r i n t e r f a c e , l b ^ f t  =  P r a n d t l number o f the s a t u r a t e d  =  v i s c o s i t y o f the l i q u i d ,  liquid  ; ; l b h r "'"ft m  1  -1  79  C ^  =  e m p i r i c a l c o n s t a n t which depends upon the n a t u r e o f the heating s u r f a c e / f l u i d water/copper  AT  ^ sat  =  temperature  combination  ( C ^ = 0.013 f o r a g  combination). excess of the heated w a l l over the s a t u r a t e d  water temperature: ( t - t ), °F w sat ' Fig.  (60) g i v e s the e x p e r i m e n t a l p l o t o b t a i n e d f o r (q/A) v s . AT  by Rohsenow.  47  q/A  Using eq. (5.10) f o r AT  =  1.5 x 1 0  However, from f i g .  q/A  =  3  S3C  S 3-t  = 10°C (18°F), one o b t a i n s  BTU/sq.ft.hr.  (5.11)  (60) the v a l u e i s  2.2 x 10  4  BTU/sq.ft.hr.  (5.12)  Thus the (5.10) does n o t f i t t h e e x p e r i m e n t a l d a t a v e r y a c c u r a t e l y . Fig.  ( 6 1 ) , as p l o t t e d by Rohsenow c l e a r l y shows a l l the  e x p e r i m e n t a l p o i n t s f o r 14.7 PSIA l y i n g above those p r e d i c t e d by eq.  (5.10). Using E n g e l b e r g - F o r s t e r and G r i e f ' s " ' a n a l y s i s , f o r AT  = 10°C  4  S3.L  (18°F) one o b t a i n s  (q/A)  Fig.  =  4 x 10  4  BTU f t h r 2  (5.13)  1  (60) shows the p l o t f o r (q/A) v s . AT  S 3. t  obtained  from  E n g e l b e r g - F o r s t e r and G r i e f ' s a n a l y s i s superimposed on Rohenow's experimental  data.  80  McAdams e t a l . ,  Cq/A)  =  i n t h e i r a n a l y s i s use t h e f o l l o w i n g e x p r e s s i o n :  c' A t * * 3  (5.14)  5 6  S a L  where b o t h c' and 3.86 were determined e m p i r i c a l l y as 'best f i t s ' experimental  to t h e ;  data.  From the above d i s c u s s i o n i t i s v e r y c l e a r t h a t t h e p r e d i c t e d c o r r e l a t i o n s a r e v e r y approximate and t h a t t h e b e s t approach i s t o use 47 the e x p e r i m e n t a l p l o t o b t a i n e d by Rohsenow  V.4.3.2  (Fig. (60)).  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 t h e p r e v i o u s a n a l y s e s were c a r r i e d out for  d i s t i l l e d water.  flux.  The e v o l u t i o n o f a i r b u b b l e s i n c r e a s e s t h e heat  There i s no d e t a i l e d s t u d y made as y e t w h i c h 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 e t a l .  have e x p e r i -  m e n t a l l y determined t h e e f f e c t o f d i s s o l v e d a i r on t h e heat f l u x (Fig.  (62)).  I n the present a n a l y s i s a s i m i l a r increase 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 s u r f a c e b o i l i n g r e g i o n = q , .,. + ° ° surface boiling q . . The e x p e r i m e n t a l (q/A) v a l u e s used h e r e g i v e t h e t o t a l ^convection heat f l u x f o r s u r f a c e b o i l i n g . c  n  r  V.4.4  Calculations  V.4.4.1  Introduction  F i g u r e (63) g i v e s t h e p l o t f o r (q/A) v s . AT and s u r f a c e b o i l i n g c o n d i t i o n s .  f o r both n o n - b o i l i n g  AT i n F i g . (63) i s t h e temperature  d i f f e r e n c e between copper mold and b u l k water  temperature.  81  Curve 1 i n F i g . (63) for  represents  non-boiling conditions.  1.15  x lCf  cal cnf sec  2  2  Curve 2 r e p r e s e n t s  - 1  the r e l a t i o n between (q/A)  I t i s obtained  °C  _ 1  and  AT  by u s i n g the v a l u e pf h =  .  the r e l a t i o n between (q/A)  b o i l i n g , u s i n g d i s t i l l e d water.  T h i s p l o t was  and  AT  obtained  for surface  from  the  47 experimental be  data of Rohsenow.  The water temperature i s assumed to  50°C. Curve 3 g i v e s the c o r r e l a t i o n between (q/A)  and  AT  b o i l i n g , u s i n g tap water ( c o n t a i n i n g d i s s o l v e d a i r ) . s i m i l a r to the e x p e r i m e n t a l l y Using  F i g . (63)  t r a n s f e r r e d to The  i t i s now  curve  T h i s i s drawn  of F i g . (62).  p o s s i b l e to c a l c u l a t e the amount of heat  mold c o o l i n g water a t every s e c t i o n .  c a l c u l a t i o n s w i l l be  g i v e s the e x p e r i m e n t a l l y mold f o r Ingot No. A, B and  obtained  f o r surface  1.  c a r r i e d out  obtained  The  f o r Ingot No.  1.  Fig.  temperature p r o f i l e on the  curve w i l l be s u b d i v i d e d  C as shown i n the f i g u r e .  Regions A and  (49)  copper  i n t o three  regions  C have n o n - b o i l i n g  c o n d i t i o n s whereas i n r e g i o n B s u r f a c e b o i l i n g i s p r e s e n t . V.4.4.2 The  Region A  ,  average water temperature I n t h i s r e g i o n = 32°C.  o u t s i d e r a d i u s of copper mold w i l l be s u b d i v i d e d  mold = 4.45  cm.  i n t o elements 0.5  assumed t h a t each element has  a constant  The  The  h e i g h t of the  cm h i g h and temperature.  copper  i t will  be  For each  element i  where  h  q  =  =  1.15  h  A AT x 10  i  2  c a l . cm  2  sec  l o  C  1  .  82  A  =  2irrj,  AT  =  T  =  - 32-0,(°C)  copper  2x17x4.45x0.5  / = i14 cm  n Z q  cm  2  n  i  =  h A  =  0.161 '  A  T.  n  E  Region A i s 30 cm h i g h n E i  q =  AT.  i  1  Ci.e. 60 /\T terms)  0.161[3 x 30 + 4 x 4 + 4 x 6 + 8 x 4 +  11 x 4 +  14 x 4  + 19 x 4 + 25 x 4 + 32 x 4 + 39 x 4]  q. ^A  V.4.4.3  =  0.161 x 876  =  0.141 K c a l s e c  Region C  Average temperature o f water = 50°C, h e i g h t  of r e g i o n C = 29.0 cm.  A c a l c u l a t i o n s i m i l a r t o t h a t performed f o r r e g i o n A l e a d s t o  q  -  0.102 K c a l s e c "  1  VJ  Therefore, boiling  V.4.4.4  the t o t a l heat t r a n s f e r r e d t o c o o l i n g water i n the non-  region =  0.141 + 0.102 = 0.243 K c a l s e c " .  !  Region B  Average temperature o f water = 50°C, t o t a l 16 cm.  1  l e n g t h o f the r e g i o n B =  83  In f i g u r e  (63) the l o c a t i o n o f the curves 2 and 3 depends upon  the water temperature.  The water temperature  i s assumed t o be 50°C,  as from F i g . (57) i t i s c l e a r t h a t the water temperature boiling  i n the s u r f a c e  r e g i o n r a p i d l y i n c r e a s e s t o 50°C and then remains  approximately  constant.  q  where A  =  13  32 E i=l  q.  =  32 E h . AT. i=l ;  A  2 14 cm .  =  From F i g . (63), the v a l u e s f o r hAT (= q/A) a r e read f o r AT o f 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 K c a l s e c . 1  T o t a l amount o f heat g i v e n to mold c o o l i n g water  =  =  q  A  +  q  B  +  q  C  6.025 K c a l s e c  1  From F i g . (63), i t i s c l e a r t h a t the p r e s e n t heat analysis c r i t i c a l l y obtained.  depends upon the curve 3 which i s e m p i r i c a l l y  The f o l l o w i n g c a l c u l a t i o n s j u s t i f y  i n F i g . (63) .  distribution  the l o c a t i o n o f curve 3  84  (1) it  Knowing the c o o l i n g water f l o w r a t e and r i s e i n water i s p o s s i b l e t o c a l c u l a t e the t o t a l heat accumulated  temperature,  by the c o o l i n g  water water f l o w r a t e :  20.5 - 21 l i t r e s min  s p e c i f i c heat o f water:  1 cal g  l o  C  1  1  -3 d e n s i t y o f water:  1 g cm  A T water:  18°C  .  ,  q = flow r a t e x d e n s i t y x sp. heat x A T = 6.15-6.3 K c a l sec l i t r e s min  1  1  f o r a f l o w r a t e of 20.5 and 21.0  respectively.  With the e x i s t i n g a c c u r a c y i n f l o w r a t e and A T measurement, the agreement w i t h the v a l u e of 6.025 K c a l sec a n a l y s i s appears (2)  1  o b t a i n e d from F i g . (63)  t o be v e r y good.  A c c o r d i n g to the p r e s e n t l o c a t i o n of curve  3, the maximum  heat  f l u x going to the c o o l i n g water (near the s l a g / m e t a l i n t e r f a c e ) has a v a l u e of (q/A)  =  -2 -1 22.5 c a l cm sec  q/A  =  h  AT  -2 =  hAT  In  the 'copper  22.5 c a l cm  - 2  c a l cm~ C sec" 2 o  q/A  _ 1  =  sec  .  c y l i n d e r ' experiments  v a l u e of the o v e r a l l heat 10  -1  : L  d i s c u s s e d i n Chapter  IV, the  t r a n s f e r c o e f f i c i e n t was o b t a i n e d as 1.28 x  w i t h A T = 1610°C  1610 x 1.28 x 1 0  _ 2  =  20.6 c a l c m  - 2  sec  _ 1  .  As the two v a l u e s o f (q/A) o b t a i n e d from the two d i f f e r e n t a n a l y s i s a r e q u i t e c l o s e (7-8% e r r o r ) one i s j u s t i f i e d  i n u s i n g F i g . (63)  85  i n s p i t e o f the e m p i r i c a l d e r i v a t i o n o f the c u r v e s .  V.5  A D e t a i l A n a l y s i s of the Heat D i s t r i b u t i o n i n the L a b o r a t o r y  ESR  Unit V.5.1  Indroduction As most o f the p r e v i o u s  present  c a l c u l a t i o n s were done f o r I.N. 1, the  a n a l y s i s w i l l a l s o be c a r r i e d out f o r the e x p e r i m e n t a l  conditions  of i n g o t no. 1. The 6.65  t o t a l heat i n p u t i n t o the u n i t , as c a l c u l a t e d e a r l i e r i s  K.cal/sec. Fig.  V.5.2  (64) g i v e s the p o s s i b l e ways t h i s heat l e a v e s  Heat Balance o f the S l a g Bed Region  V.5.2.1 As  Heat Input a l l the heat i s generated i n the s l a g bed, the t o t a l heat  input i n  the s l a g bed r e g i o n = 6.65 K c a l / s e c .  heat g e n e r a t i o n this  the u n i t .  F i g . (65) g i v e s the  d i s t r i b u t i o n i n the s l a g bed as c a l c u l a t e d e a r l i e r i n  chapter.  V.5.2.2 V.5.2.2.1  Heat Output Heat Required to Melt Q., c a l s e c IA  the E l e c t r o d e  1  melt r a t e i n I.N. 1 = 3.0 cm/100 sec o f e l e c t r o d e l e n g t h of the e l e c t r o d e melted =  travel  3 81 * x 3.0 = 4.06 cm/100 s e c . z. o l Q 1  l e n g t h of the e l e c t r o d e melted i n 1 second = 0.0406 cm.  86  A l t h o u g h the e l e c t r o d e gets heated by  conduction,  convection  r a d i a t i o n g r a d u a l l y ; i n steady s t a t e , when the temperature of  the  e l e c t r o d e f a r away from the s l a g s u r f a c e i s a t room temperature, can assume that 0.0406 cm temperature to m e l t i n g Table  (XVI)  s t e e l was used  not  (except  p o i n t i n one  gives  the c a l c u l a t i o n .  As  l e n g t h o f the e l e c t r o d e was  A  the average p h y s i c a l p r o p e r t i e s of i r o n used i n  the d a t a on  the p h y s i c a l p r o p e r t i e s of EN  divided  Q  2B  Q Q  =  3.36 m  of the 0  c  g sec p  1000  second  AT  1  + m L  cal  sec  - 1  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 : 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  Q^,cal  sec  can be  sub-  1  into:  =  heat r a d i a t e d to the water c o o l e d  =  heat l o s t  =  heat r a d i a t e d to the  has  9  are  P  ( f i g . (66))  Q  25  2  =  The  <  for melting p o i n t ) .  irr £  V.5.2.2.2  heated from room  a v a i l a b l e , the average p h y s i c a l p r o p e r t i e s of i r o n  =  =  IA  one  second,  Mass of the e l e c t r o d e m e l t e d i n one  Q,  and  copper mold  to a i r or gases electrode.  a l r e a d y been c o n s i d e r e d  i n the heat taken up  f o r heating  electrode. th.e a i r or the gases p r e s e n t .  A  s i g n i f i c a n t p a r t of the heat a c q u i r e d by the gases i s however l o s t  by  2B  i s the heat c a r r i e d away by  87  c o n v e c t i o n t o t h e copper mold and t h e e l e c t r o d e .  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 n e t heat c a r r i e d away By t h e gases i t i s a r e a s o n a b l e assumption  t o have Q  = 0.0 c a l sec  \  Heat l o s t by r a d i a t i o n from t h e s l a g s u r f a c e to coj>j>er mold; The  Q  2 A  temperature p r o f i l e on the copper mold above the s l a g / g a s  i n f e r f a c e i s known  Q  (fig.  (49)).  Q  9  can be c a l c u l a t e d u s i n g F i g . (63)  = 1 4 l 2 x 8 + 2 x 3.5 + 2 x 1.6 + 2 x 0.65] + 102.0 ,  2 A  = 487 c a l sec  V.5.2,2.3  Heat L o s t to C o o l i n g Water A c r o s s the S l a g Bed: Q^, c a l s e c  U s i n g F i g . (63) and F i g . ( 4 9 ) , previous  can be c a l c u l a t e d s i m i l a r t o •  calculations.  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 P i c k e d up by the F a l l i n g L i q u i d M e t a l Drops: Q  Assuming  1T>  I D  > c a l se  t h a t the l i q u i d m e t a l d r o p l e t s a r e superheated by 100°C  d u r i n g t h e i r descent through t h e s l a g bed, the amount o f heat p i c k e d up by the d r o p l e t s :  Q  1B  =  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  +  1 B  Q  =  1  0  0  0  +  6  6  '  5  =. 1060,5 c a l s e c Although  I s the heat  consumed i n m e l t i n g the e l e c t r o d e and i t s  subsequent h e a t i n g , i t i s n o t l o s t . as s e n s i b l e  heat.  Thus f o r c a l c u l a t i n g  slag/metal i n t e r f a c e , Fig.  I t e n t e r s t h e l i q u i d m e t a l bed the t o t a l  transferred  a c r o s s the  t h i s heat has to be c o n s i d e r e d .  C67) g i v e s a b l o c k diagram f o r the heat b a l a n c e  o f the s l a g  region. The  amount o f heat  leaving  across the slag/metal i n t e r f a c e per  second =  6650 - 487 - 2597  =  3566 c a l s e c *.  Amount of heat  transferred  a c r o s s t h e s l a g / m e t a l i n t e r f a c e by  c o n v e c t i o n p e r second  Q. 4B V.5.2.3 V.5.2.3.1  =  3566 - 1060.5  =  2505.5 c a l s e c  - 1  Heat D i s t r i b u t i o n i n the S l a g Bed Introduction  F o l l o w i n g the c a l c u l a t i o n o f the heat b a l a n c e s l a g bed, i t i s i n t e r e s t i n g  to see how the heat  f o r the e n t i r e  i s distributed  i n the  v a r i o u s r e g i o n s o f the s l a g bed. The  s l a g bed can be s u b d i v i d e d i n t o  the e l e c t r o d e t i p .  two r e g i o n s , above and below  89  V.5.2.3.2  Heat Balance o f the Region Above the E l e c t r o d e T i p  C o n s i d e r the heat b a l a n c e o f r e g i o n AJKB ( F i g . ( 6 5 ) ) . Heat Input:  + Q  Q  + Q  + heat generated i n the c a t h o d i c p o l a r i z a t i o n  £  =  400 + 1485  + 665 +  =  2687 c a l s e c . .  137  1  Heat Output: Q  Q  = 1000  =  2 A  cal sec"  1  '487 c a l s e c "  1  heat going t o -mold c o o l i n g water a c r o s s the  =  bed = 1412  x 15 + 2 x 21.5 +  = 1337.0 c a l sec  T o t a l heat output = 1337  slag  22.5]  1  + 1000 +  = 2824 c a l sec  487 1  Amount of heat o b t a i n e d by t h i s r e g i o n from the lower r e g i o n JKCD by c o n v e c t i o n = 2824 - 2687 = 137  V.5.2.3.3 Heat  Heat  Input:  = Heat  Output:  Q  Balance +  Q  +  of heat  the Region generated  1720 + 2160 + 1 3 7 Q^^  = heat bed  c a l sec  to mold  = 14[4  x 22.5]  = 1260  c a l sec  .  Below  the E l e c t r o d e T i p  i n anodic  = . 4017  going  1  cal sec"  polarization  1  c o o l i n g water  1  .  across the  slag  90  Q  IB  = heat r e q u i r e d  to super heat the f a l l i n g l i q u i d  drops by 1 0 0 ° C = 6 0 . 5 heat t r a n s f e r r e d  cal sec"  metal  1  to AJKB r e g i o n by c o n v e c t i o n  = 137 c a l s e c  1  T o t a l heat output = 1 2 6 0 + 6 0 . 5 + 1 3 7 =  1457.5  c a l sec  1  heat t r a n s f e r r e d by c o n v e c t i o n a c r o s s the s l a g / m e t a l interface  =  4017  -  =  2559.5  1457.5  cal sec" . 1  -1  The d i f f e r e n c e o f 5 4 . 0 c a l sec observed i n the two a n a l y s e s , i s the e r r o r i n v o l v e d V.5.3  i n the heat i n p u t d i s t r i b u t i o n a n a l y s i s .  Approximate C a l c u l a t i o n o f t h e Heat T r a n s f e r C o e f f i c i e n t A c r o s s the L i q u i d S l a g - L i q u i d M e t a l The amount o f heat t r a n s f e r r e d - 2500  interface  q  =  h.A.AT  where  A  =  Assuming (2)  c a l sec  Interface across the l i q u i d  s l a g - l i q u i d metal  1  2  irr = 5 0 cm  2  ( 1 ) u n i f o r m heat t r a n s f e r c o e f f i c i e n t a c r o s s the s e c t i o n ;  u n i f o r m temperature  i n the s l a g and m e t a l b a t h a c r o s s the e n t i r e  c r o s s s e c t i o n at the s l a g / m e t a l i n t e r f a c e , one can w r i t e  hAT  =.  q jJ-  =  I f AT = temperature =  25-50°C  2500  i_  Q  =  50  .  c a l cm  -2  sec  d i f f e r e n c e between l i q u i d  -1  s l a g and m e t a l  r  91  h  V.5.4  =  1  2 c a l cm ° C ''sec \ 2  r-  Heat Balance o f the L i q u i d M e t a l Region Fig.  (68) g i v e s the b l o c k diagram f o r t h e heat b a l a n c e o f t h e  l i q u i d metal region. Heat, Input:  Q  4  =  Q^  +  =  3566.0 c a l sec ,  A  Q^  B  1  Heat Output: The amount of h e a t g o i n g t o mold CN = Q  = 1417  5  c o o l i n g water  across  -x 22.5 + 1 -x 14]  = 2401 c a l sec  \  Heat l e a v i n g the s e c t i o n ON downwards Q  9  =  Q  4 "  Q  5  = 3566.0 - 2401.0 = 1165.0 c a l sec  V.5.5  Heat Balance o f the S o l i d i f i e d Fig.  Ingot Region  (69) g i v e s the b l o c k diagram f o r the heat b a l a n c e o f t h i s  region.  V.5.5.1  Heat Input:  V.5.5.2  Heat  7.5.5.2.1  Q  g  =  1165.0 c a l / s e c  Output:  Heat Going to Mold C o o l i n g Water; Q, o  1412  x  0.75' + 2  = 540 c a l sec . 1  x 1.5 + 2  3  Qg-, c a l s e c "  5 + 1  x 14] + 141  1  V.5.5.2.2 Fig.  Heat Going to Base P l a t e C o o l i n g (58)  with respect  gives  the e x p e r i m e n t a l l y  to s l a g / m e t a l  Water:  obtained  temperature  i n t e r f a c e p o s i t i o n f o r two  at the base of the i n g o t , known d i s t a n c e  profiles  thermocouples l o c a t e  apart.  k A Q  =  7  7 where  k  — Ax  AT  =  average • thermal c o n d u c t i v i t y of i r o n  =  0.075 c a l c m " " s e c " C ~ 1  lo  1  2 A  =  cross s e c t i o n a l area  =  Ax  =  d i s t a n c e between the  two  The  present  of i n g o t has  temperature between the  Q  34.4 7  I7o  =  =  V.5.5.2. 3  cm  thermocouples = 1  heat b a l a n c e i s c a r r i e d out  been formed.  A  34.4  410  Therefore  two  cm  a f t e r a s i g n i f i c a n t amount  the v a l u e  of AT  = difference i n  thermocouples = 160°C.  x .075  . X  1 6 0  c a l sec  S e n s i b l e Heat R e t a i n e d by  the I n g o t :  Q_ o  Under steady s t a t e c o n d i t i o n s , a l l the heat s u p p l i e d r e g i o n i s taken away by  the s o l i d i f i e d  s e n s i b l e heat of the e s c a p i n g  i n g o t as s e n s i b l e heat.  gases i s n e g l e c t e d  Amount of heat r e t a i n e d as s e n s i b l e heat by = mass of i n g o t formed per =  slag  the mold and base p l a t e c o o l i n g water except  t h a t which i s r e t a i n e d i n  where AT  i n the  sec x C  average temperature of the  P  ingot  x  i n the p r e s e n t the i n g o t / s e c AT  The analysis.  =  Q. <8  93  Q  8  =  3.36 x 0.16 x AT  =  0.538 x AT  cal sec" . 1  The v a l u e o f AT i s unknown and one must make a r e a s o n a b l e estimate. Assuming AT  V.5.5.2.4 The  = 750°C  Q„ o  =  0.538 x 750  Qg  =  404 c a l sec . 1  T o t a l Heat  Output  t o t a l heat output  =  Q  =  540 + 410 + 404  &  +  0  ?  +  Q  g  = 1354 c a l sec \ The ,  d i f f e r e n c e i n heat i n p u t and output v a l u e s i s o n l y 188.5  -1  c a l sec With the v a r i o u s approximations and assumptions of 188.5 c a l sec  1  f o r a t o t a l heat i n p u t of 6650 c a l sec  than 3% and t h i s i s w e l l w i t h i n the accepted V.5.6  made, a d i f f e r e n c e 1  i s less  limits.  Heat Balance f o r Ingot Nos. 1, 10 and 16 T a b l e X I g i v e s the heat b a l a n c e f o r i n g o t s made w i t h d.c. n e g a t i v e ,  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. V.6.1  Discussion Comparison o f the D i f f e r e n t E l e c t r i c a l C o n f i g u r a t i o n s As mentioned  earlier,  t h e r e has been a c o n s i d e r a b l e disagreement  between d i f f e r e n t workers on the e f f i c i e n c y o f the ESR p r o c e s s f o r  94 T a b l e XI.  Ingot  Heat  b a l a n c e f o r i n g o t no. 1, 10 and 16  10  16  3.36  2.58  3.50  X  1.5  0.4  0.25  Dimensions Y (cm) r e f e r F i g . (64) Z  1.0  1.6  0.85  4.5  4.5  3.1  A  2.5  0.75  0.5  B  !-5  2.00  2.5  Melt g sec  No.  1  rate -1  6650  Heat Input . -1 c a l sec  1060.5  Heat Output  5100  4800  785  1110  ( c a l sec ) 1  %  15.6%  C>2A ( c a l s e c "S  %  7.15%  ( c a l sec "*")  %  2597  38.0%  ( c a l sec ) 1  %  487  3566.0  52.3%  15.50%  738  14.5%  2606  51.4%  1756  34.6%  23.3%  637.2  13.4%  1872.5  39.4%  2290  48%  95  t a b l e XI.  '(Continued)  10  Ingot No. Q  ( c a l sec ) 1  4 A  1060.5  15.6%  Q  4 B  ( c a l sec  )  2505.5  36.7%  Q,. ( c a l sec "*")  6  ( c a l s e c "*")  ( c a l sec  )  Qg ( c a l sec *)  16  785  1110  15.5%  23.3%  971  1180  19.10%  24.7%  2401  704  1081.5  35.1%  13.7%  22.6%  540  316  333  7.8%  6.2%  7.0%  410  410  410  6.1%  8.10%  8.7%  404  310  420  5.85%  6.1%  8.9%  96  different  e l e c t r i c a l configurations.  The e f f i c i e n c y o f the p r o c e s s i s  u s u a l l y expressed i n terms o f the amount o f m e t a l remelted p e r KWH. Using the a v a i l a b l e e x p e r i m e n t a l d a t a , an attempt e x p l a i n the observed  i s made here t o  differences. 36  There a r e 9 p o s s i b l e d i f f e r e n t types o f e l e c t r i c a l Cl)  configurations.  d.c. w i t h e l e c t r o d e as the n e g a t i v e p o l e (commonly  referred  to as d.c. n e g a t i v e ) . (2)  d.c. w i t h e l e c t r o d e as the p o s i t i v e p o l e (commonly  referred  to as d.c. p o s i t i v e ) . i(3)  a.c. Each o f these can have the mold  or (b) f l o a t i n g o r (c) connected Fig.  (42) g i v e s t h e schematic diagrams f o r the d i f f e r e n t  arrangements.  the r e m e l t i n g of the i n g o t s  c a r r i e d out w i t h the p r o c e s s parameters  and melt  from the i n g o t  to the i n g o t ( r e f e r r e d t o as ' l i v e ' ) .  In t h e p r e s e n t s e t of experiments, was  (a) i n s u l a t e d  ( i . e . , voltage, current  r a t e ) so a d j u s t e d , as to a c h i e v e s t a b l e o p e r a t i n g c o n d i t i o n s .  An attempt  was made t o m a i n t a i n a p p r o x i m a t e l y  the same melt r a t e f o r the  d i f f e r e n t e l e c t r i c a l c o n f i g u r a t i o n s under s i m i l a r c o n d i t i o n s .  However  i n cases where the p r o c e s s became u n s t a b l e w h i l e a t t e m p t i n g a c o n s t a n t melt  r a t e , the p r o c e s s parameters  remelting  were so a d j u s t e d as t o a c h i e v e s t a b l e  conditions.  Ingots 1, 10, 13 and 16 can be compared t o study the e f f e c t o f e l e c t r i c a l configuration.  Attempt was made here to a c h i e v e a constant  melt  3.4-3.5 g s e c * (30 mm of e l e c t r o d e t r a v e l f o r  r a t e of approximately  every 100 s e c o n d s ) .  T h i s was a c h i e v e d i n b o t h d.c. n e g a t i v e and a.c.  In t h e p r e s e n t s e t of experiments,  the v o l t a g e was kept a p p r o x i m a t e l y \  97  constant  (20-24 v o l t s ) .  melt r a t e , i t was between the cases.  As  I t was  electrode discussed  calcium input d.c.  a.c. and  case.  t i p and earlier,  i n the d.c. and  It  i s now  850  -ve amp  the s l a g / m e t a l  d.c.  i s due  -ve  slag.  case.  been shown e a r l i e r  the mold c o o l i n g water a c r o s s extent  35%  compared to a.c.  less  dissolved current  (1150  amp  for  observed deep negative  cylindrical  configuration  (Fig.  To m a i n t a i n a dynamic steady s t a t e , i t i s n e c e s s a r y  e x t r a heat i n t r o d u c e d  to the  slag i s  r e s u l t s i n a higher  i n d.c.  to remove the I t has  two  a.c).  l i q u i d metal p o o l  (84)).  operation  This  cm)  s i m i l a r geometry,  t o the p r e s e n c e of the  c o n f i g u r a t i o n as for  (= 2.0  i n t e r f a c e i n the  f o r the same s l a g and  p o s s i b l e to e x p l a i n the  p o r t i o n of the (80), F i g .  This  aluminum i n the  -ve  to a c h i e v e a s i m i l a r  n e c e s s a r y to m a i n t a i n a s i m i l a r gap  the working r e s i s t a n c e of the than the  observed t h a t  in  that  the  the the  liquid  of heat produced i n the  s l a g bed  i n the  d.c.  amount of heat t r a n s f e r r e d to s l a g bed  s l a g bed.  i s quite i n s e n s i t i v e Thus the e x t r a heat  produced i s t r a n s f e r r e d to the mold c o o l i n g water by m a i n t a i n i n g deep c y l i n d r i c a l p o r t i o n o f the surface  contact  I t was 'live', g sec  1  and 13). low  not  p o s i t i v e w i t h mold  p o s s i b l e to a c h i e v e the  immersion i t was  found t h a t  The  i n f e r f a c e (2.6 cm  t o t a l power i n p u t was  melt r a t e  a good  On  examining the  10  and  also correspondingly was  and  extent  of  s t a b l e working of the  between the  f o r i n g o t no.  (=2.58 g sec "*") o b t a i n e d  'floating'  d e s i r e d melt r a t e of 2=3.4  f o r the  n e c e s s a r y to m a i n t a i n a l a r g e r gap  slag/metal  a  w i t h the mold.  under s t a b l e working c o n d i t i o n s .  electrode i t was  l i q u i d metal p o o l which has  found that i n both d.c.  i t was  negative  a result  unit  electrode t i p 2.3 less.  of the  cm  for ingot Thus.the  low  power  no.  98  i n p u t and  the l a r g e gap between the e l e c t r o d e t i p and  interface.  the  slag/metal  The n e c e s s i t y of m a i n t a i n i n g these to o b t a i n s t a b l e working  c o n d i t i o n s can be e x p l a i n e d as f o l l o w s . Fig.  (70) g i v e s the ESR  the e x p e r i m e n t a l r e s u l t s and  u n i t ' s analog c i r c u i t .  T a b l e IV g i v e s  the v a l u e s of the v a r i o u s r e s i s t a n c e s as  36 c a l c u l a t e d by Cameron e t a l . There are two (1)  paths  electrode  f o r the flow of c u r r e n t i n F i g .  liquid (working  slag  (70)  ingot  resistance) (2)  e l e c t r o d e -*- mold -> i n g o t .  The magnitude of the c u r r e n t f o l l o w i n g i n each c i r c u i t on the r e l a t i v e v a l u e s of the r e s i s t a n c e s R^, R^  and R^ are i n s e r i e s and  R^  and R^.  depends  Resistances  they t o g e t h e r are i n p a r a l l e l w i t h  In the case of d.c. p o s i t i v e w i t h mold f l o a t i n g , the  R^.  potential  36 on the mold was The  e x p e r i m e n t a l l y determined  as =18  f l o w of c u r r e n t i s as shown i n F i g . (70a).  of 18  v  on the mold can be e x p l a i n e d .  V  (Table X I I ) .  The  observed  Under s t a b l e working c o n d i t i o n s  the e l e c t r o d e i s not s i g n i f i c a n t l y immersed i n the s l a g b a t h . temperature  a t the s l a g / g a s i n t e r f a c e i s q u i t e h i g h .  the r e s i s t a n c e R^  i s q u i t e low as new  the e l e c t r o d e and  s l a g s k i n i s c o n t i n u o u s l y formed  of 5 v o l t s o c c u r s mostly  and  resistance.  i n the s l a g b a t h between  the s l a g s k i n as shown i n Chapter  the c a l c u l a t e d v a l u e s of R^,  The  The v a l u e of  at the s l a g / g a s i n t e r f a c e h a v i n g a momentary low v a l u e of The v o l t a g e drop  value  II.  T a b l e IV g i v e s  R^.  There i s thus a c o n s i d e r a b l e p o t e n t i a l d i f f e r e n c e between the mold and  the i n g o t .  A r c i n g would occur between the mold and  the i n g o t  Table X I I .  E x p e r i m e n t a l r e s u l t s f o r the i n s u l a t e d mold unshunted and shunted t o ground through 0.5 ohm  Ingot Size  Slag System  resistor  Applied Voltage  Electrode Polarity  Mold Potential  Unshunted Current  Mold P o t e n t i a l 1/2 shunt t o ground  Shunted Current  Slag s k i n Average -thickness  2"  CaF  2  23.7  -ve  22.4  672  20.5  704  0.U40"  2"  CaF  2  24.5  -ve  21.9  688  20.1  720  0.025"  22.8  +ve  19.0  640  15.4  710  D.035"  + CA 2"  CaF  2  + CA 3"  CaF  2  22.5  -ve  18.7  1 220  17.3  1 300  0.040"  3"  CaF  2  22.8  -ve  20.6  1 200  18.6  1 265  0.030"  22.5  +ve  17.0  1 200  16.1  1 240  0.035"  + CA 3"  CaF  2  + CA  100  if  significant  amount of c u r r e n t flows through v i a p a t h 2,  t h i s , the v a l u e of  s h o u l d be m a i n t a i n e d h i g h .  To a v o i d  The e x i s t e n c e of a  deep 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 r e s u l t s i n a low v a l u e of R^.  Thus t o a c h i e v e s t a b l e working  c o n d i t i o n s , the working  meters are so a d j u s t e d as to a v o i d the e x i s t a n c e of a deep p o r t i o n of the l i q u i d m e t a l p o o l .  para-  cylindrical  T h i s i s a c h i e v e d by m a i n t a i n i n g a  l a r g e r gap between the e l e c t r o d e t i p and the s l a g m e t a l r e s u l t i n g i n lower power i n p u t and hence a lower melt  interface  rate.  I f the argument put forward here i s t r u e then f o r the d.c.  positive  case w i t h i n s u l a t e d mold, i t should be p o s s i b l e to a c h i e v e a melt comparable to a.c. and d.c. n e g a t i v e c o n f i g u r a t i o n s .  The mold  was  i n s u l a t e d by c o a t i n g the i n s i d e s u r f a c e of the mold w i t h boron paste and allowed to dry. it  Comparing FVE  i n g o t s 25, 28, 29,  31  rate  nitride 32  s  i s found t h a t the melt r a t e s are comparable. In the case of d.c. p o s i t i v e w i t h l i v e mold, as the i n g o t and  mold are connected, w i t h R^ = 0 ohms. e l e c t r o d e i s 23.0  they are  both at the same p o t e n t i a l  (46)). The  (= 0 v o l t s )  The p o t e n t i a l d i f f e r e n c e between the mold a n d t h e :  volts.  As the v a l u e of R^  p o r t i o n of the c u r r e n t goes t o the mold Fig.  the  effect  i s q u i t e low,  significant  (as much as 80% as shown i n  of the h o r i z o n t a l c u r r e n t component on  the  magnetohydrodynamics of the r e g i o n i s not y e t c l e a r , but i s o u t s i d e the scope of the p r e s e n t work.  M e t a l drops are drawn towards the mold  by the h o r i z o n t a l c u r r e n t component and are embedded i n the s l a g Continuous  a r c i n g occurs between the mold and  unavoidable.  The melt  not e f f e c t i v e l y used  skin.  the s l a g b a t h and i s  r a t e i s low as the c u r r e n t going to the mold i s  to heat  the s l a g b a t h .  f  101  In the d.c. n e g a t i v e case w i t h mold f l o a t i n g , i t was found the mold had a p o t e n t i a l o f v a l u e of  21 v o l t s .  T h i s i s expected  s i n c e the  i s low due to t h e e x i s t a n c e of a deep 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  pool.  There i s thus a s i g n i f i c a n t  d i f f e r e n c e between the e l e c t r o d e and the mold.  a c h i e v e d by m a i n t a i n i n g  potential  To a v o i d a r c i n g between  the mold and the s l a g , the v a l u e o f R^ i s m a i n t a i n e d  high.  Comparing the v a l u e s of R^, R v a l u e of R^ i s m a i n t a i n e d  2  high  (0.15 ohms).  f o r d.c. n e g a t i v e  bath  the temperature a t the s l a g / g a s  i n t e r f a c e r e s u l t i n g i n a t h i c k e r s l a g s k i n a t the s l a g / g a s  to d.c. p o s i t i v e  This i s  the e l e c t r o d e deeply immersed i n the s l a g  (2.5 cm i n i n g o t no. 1 ) . T h i s decreases  low  that  interface.  and R^ (Table IV) i t i s seen t h a t the (0.7 ohms) f o r d.c. n e g a t i v e as compared The v a l u e of R^ on the o t h e r hand i s  (0.1-0.2 ohms) as compared t o d.c. p o s i t i v e ; (0.4-  1. 0 ohm). As t h e r e e x i s t s , o n l y a s l i g h t p o t e n t i a l d i f f e r e n c e between the, mold and i n g o t i n d.c. n e g a t i v e w i t h mold s i g n i f i c a n t d i f f e r e n c e observed with  ' f l o a t i n g ' , t h e r e i s no  between o p e r a t i o n s u s i n g d.c. n e g a t i v e  ' f l o a t i n g ' mold and ' l i v e ' mold c o n f i g u r a t i o n s .  i n s u l a t e d mold, as t h e r e i s no problem o f m o l d - s l a g to o p e r a t e h a v i n g Measurement mpld-^ingot  I n the case o f  arcing, i t i s possible  the e l e c t r o d e o n l y s l i g h t l y immersed i n the s l a g o f the c u r r e n t f l o w i n g through  bath.  the c i r c u i t , e l e c t r o d e s -  f o r a.c. w i t h mold ' f l o a t i n g and ' l i v e ' has shown t h a t o n l y  a v e r y s m a l l f r a c t i o n of the t o t a l c u r r e n t flows through T h i s i s expected  this  circuit.  s i n c e the s l a g s k i n i s always t h i c k i n o p e r a t i o n s  u s i n g a.c. mode thereby  m a i n t a i n i n g a h i g h v a l u e f o r both R.. and R~.,  102  V.6.2  Effect  of the E l e c t r o c h e m i c a l  In the e l e c t r o s l a g r e m e l t i n g  and Chemical R e a c t i o n s  of FVE e l e c t r o d e s , M i t c h e l l and  12 Beynon  have shown t h a t the f o l l o w i n g e l e c t r o c h e m i c a l  at the two p o l e s  using  reactions  occur  CaF2~25 wt.% Al^O^ s l a g .  R e a c t i o n s at the cathode (1)  Al  (2)  (3)  Reaction  (1)  +  2e  y  Al  Al" " "*"  +  3e  y  Al  Ca "  +  2e  y  Ca  1  4  44  at the anode  Fe  y  Fe " 44  +  2e  In the case o f r e m e l t i n g a l s o may  (5.15)  o f EN 25 s t e e l ,  the f o l l o w i n g  reactions  occur at the anode  Cr  y  Cr  >- Cr  Mn  >• M n  Si  y  Cr " 44  +  +++  2e +  3e (5:16)  +  4 4  Si  +  2e 4e  etc...  In the e l e c t r o - p o s i t i v e c o n f i g u r a t i o n , the anodic r e a c t i o n s at the e l e c t r o d e , i . e . Fe, Cr, Mn, At and  Ca  the i n g o t s u r f a c e ,  I | ) occur.  occur  e t c . are o x i d i z e d a t the e l e c t r o d e .  the c a t h o d i c  reactions  ( r e d u c t i o n of A l '  The a n o d i c r e a c t i o n p r o d u c t , due to c o n v e c t i o n  and  103 h i g h e r d e n s i t y , comes i n c o n t a c t w i t h the c a t h o d i c r e a c t i o n and  r e d u c t i o n of Fe, Cr, Mn,  Al  +  Fe  Ca Al  Cr Si  +  ——>• 4 4 4  etc.  product  occurs  Fe  (5.17)  Cr Si  4 +  Mn  Mn  There i s no net change i n the s l a g c o m p o s i t i o n i f the hack r e a c t i o n (5.17) i s complete.  However i t i s found  t h a t t h i s r e a c t i o n does not  go to c o m p l e t i o n , r e s u l t i n g i n a net change of the s l a g Table  (VI) g i v e s the a n a l y s i s of the i n g o t and  compositions.  composition.  the e l e c t r o d e  I t can be seen t h a t r e m e l t i n g w i t h d.c. p o s i t i v e  r e s u l t s i n the l o s s of the a l l o y i n g element chromium (reduced 0.7  wt.%  (5.17).  As  to = 0.2  wt.%).  T h i s i s due  from  to the i n c o m p l e t i o n of r e a c t i o n  the o x i d a t i o n i s e l e c t r o c h e m i c a l i n n a t u r e , i t does not i  depend upon the atmosphere p r e s e n t . In  always  the ESR  r e m e l t i n g u s i n g d.c. n e g a t i v e , the s i t u a t i o n i s q u i t e I |  different. occurs. of  At the e l e c t r o d e , the c a t h o d i c r e d u c t i o n of Ca  III  and A l  As the l i q u i d m e t a l i s p r e s e n t on the e l e c t r o d e i n the  a t h i n f i l m , the reduced  form  aluminum i s v e r y e f f e c t i v e l y d i s s o l v e d i n  the l i q u i d metal b e f o r e i t f a l l s  down as a d r o p l e t .  the anodic o x i d a t i o n of Fe, Cr, Mn,  S i , etc. occurs.  At the i n g o t s i t e , However, as  the  aluminum i s d i s s o l v e d to a c o n s i d e r a b l e e x t e n t i n the l i q u i d m e t a l , , the back r e a c t i o n  (5.17) o c c u r s v e r y e f f e c t i v e l y .  p r a c t i c a l l y no change i n the s l a g c o m p o s i t i o n .  There i s thus  Here i t was  that an argon atmosphere p r e v a i l e d over the s l a g to a v o i d  assumed atmospheric  104  o x i d a t i o n of the reduced A l and argon u s i n g d.c.  negative  elements as can be In ESR  Ca.  ESR  remelted  c o n f i g u r a t i o n show no  seen from T a b l e  processing  The  i n g o t s under  l o s s of  alloying  (VI).  i n a i r u s i n g d.c.  negative  configuration, i t  i s found that t h e r e i s a l o s s of the a l l o y i n g element chromium on remelting.  T h i s can be e a s i l y  explained.  9 Etienne  has  shown the e x i s t a n c e of the c o n v e c t i o n  the s l a g at the s l a g / a i r i n t e r f a c e of the type which may  patterns i n suggest  a s i g n i f i c a n t amount of the e l e c t r o c h e m i c a l l y reduced A l and an o p p o r t u n i t y  to become r e o x i d i z e d by.the atmospheric oxygen.  o x i d a t i o n prevents  the e f f e c t i v e r e d u c t i o n of the anodic  i n g o t r e s u l t i n g i n the l o s s of a l l o y i n g element chromium =0. 7 wt.  % to  Ca  =0.2  that has This  product  at  (reduced  the  from  wt. % ) . 12  It  i s proposed by M i t c h e l l and  r e m e l t i n g of pure i r o n Fe  and  ~ *  Beynon  t h a t i n the a.c.  (FVE), r e a c t i o n (5.18) o c c u r s  Fe"* " -1  +  electrosl  at b o t h the  2e  (5.18)  e l e c t r o d e s u r f a c e s . More e x p e r i m e n t a l  d e f i n i t e conclusions regarding  ingot  data i s needed to draw any ;  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 S l a g S k i n I t i s i n t e r e s t i n g to study  t h i c k n e s s of the s l a g s k i n .  the e f f e c t of the p o l a r i t y on  F i g . (71)  v e r t i c a l s e c t i o n of the s l a g cap  Thickness  and  and  (72)  the:  show p i c t u r e s of  the s l a g s k i n formed.  the  105  I t i s observed t h a t i n the r e m e l t i n g o f pure i r o n d.c.  p o s i t i v e (both a i r and argon) and d.c. n e g a t i v e  i s extremely t h i n .  (air),  the s l a g s k i n  There i s a l s o a c o n s i d e r a b l e amount o f i r o n  at t h e bottom of the s l a g cap. The above o b s e r v a t i o n s i n terms o f the e l e c t r o c h e m i c a l and chemical In a l l the t h r e e cases, significantly.  (FVE) u s i n g  oxide  can be e x p l a i n e d  reactions discussed  the back r e a c t i o n (5.17) does n o t occur  T h i s b u i l d s up the i r o n - o x i d e content  earlier. very  i n the s l a g bed.  T h i s i r o n - o x i d e a t t a c k s the alumina r i c h s l a g s k i n and d i s s o l v e s i t partially, skin. (V).  forming  a low m e l t i n g e u t e c t i c .  T h i s can a l s o be v a r i f i e d  This results i n a thin slag  from the e x p e r i m e n t a l  I t i s observed t h a t d.c. p o s i t i v e (argon  negative  d a t a of Table  and a i r ) and d.c.  ( a i r ) melts have a t h i c k e r s l a g cap a f t e r r e m e l t i n g  approximately  the same l e n g t h o f the e l e c t r o d e . In  r e m e l t i n g EN 25 s t e e l ,  the f o r m a t i o n not very  V.6.4  o f lower m e l t i n g  the presence o f chromium oxide eutectic.  prevents  The s l a g s k i n i s t h e r e f o r e  thin.  C o r r e l a t i o n and P r e d i c t i o n o f O p e r a t i n g  Parameters f o r E l e c t r o s l a g  Processing In without One  i n d u s t r y , v e r y o f t e n , l a r g e s c a l e i n g o t s have t o be made c a r r y i n g out t r i a l  runs t o e s t a b l i s h the working c o n d i t i o n s .  i s t h e r e f o r e i n t e r e s t e d i n knowing the approximate p r o c e s s  (i.e. ingots.  c u r r e n t , v o l t a g e and melt r a t e ) f o r r e m e l t i n g  these  An attempt i s made here to p r e d i c t these p r o c e s s  parameters  large scale  parameters f o r  the i n d u s t r i a l s c a l e i n g o t s from the a v a i l a b l e l a b o r a t o r y and i n d u s t r i a l data.  106  On o b s e r v i n g  the temperature p r o f i l e s on the mold f o r the Y  e l e c t r i c a l and g e o m e t r i c a l it  configurations  a r  i°  u s  ( F i g , (49) to F i g . ( 5 6 ) ) ,  i s c l e a r t h a t the temperature p r o f i l e s on the mold and hence the  amount of heat going to the mold c o o l i n g water p e r u n i t area does not depend upon the e l e c t r i c a l and the g e o m e t r i c a l  configurations.  It i s  thus p o s s i b l e 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 i n p u t f o r any i n d u s t r i a l s c a l e i n g o t .  (IV) g i v e s  Appendix  the d e t a i l c a l c u l a t i o n of the power requirement f o r a 61 cm  (24 i n c h e s ) diameter i n g o t . The melt r a t e depends upon the f o l l o w i n g parameters: (1)  slag  composition  (2)  electrode  (3)  electrical  (4)  atmosphere  (5)  diameter of the e l e c t r o d e  (6)  diameter of the i n g o t  (7)  d i s t a n c e between the e l e c t r o d e  composition configuration  t i p and the s l a g / m e t a l  E m p i r i c a l equations are a v a i l a b l e i n l i t e r a t u r e  interface.  49 50 ' g i v i n g the  dependence of the melt r a t e on the power i n p u t , e l e c t r o d e diameter e t c . 49 Klein  gave the f o l l o w i n g e m p i r i c a l e q u a t i o n to f i t h i s  e x p e r i m e n t a l data f o r H a s t e l l o y X i n g o t s R  =  -2.64 + 0.473 D + 0.391 x 1 0  _ 3  I + 0.689 x 1 0 E _ 1  - 0.0558S (5.19)  where R  =  melt r a t e  ( l b min "*")  D  =  e l e c t r o d e diameter  (inches)  107  1  =  current  (amperes)  E  =  voltage  (volts)  S  =  s l a g weight  The  equation  of i n g o t Sun  ( e r r o r + 20%)  Pridgeon  R = 0.3  E^ + 1.57  E  = ingot  ( f t hr  diameter  S  = s l a g weight  3  Present  f o r a narrow range  (3)  S„ - 1.167  equation:  (5.20)  "*") (inches)  (amperes) (lbs).  above.equation was < 3.0,  - 0.18  _ 3  = current  I x 10~  only v a l i d  a r r i v e d at the f o l l o w i n g e m p i r i c a l  x 10 I  I  The  7.0  valid  < S  f o r (1) 2.75  < 9.3  < E^  < 4.25,  (2) 1.85  <  ranges.  analysis  The i n the  50  = melt r a t e D  was  sizes. and  where R  (lbs)  melt r a t e can be  c o r r e l a t e d to the o t h e r p r o c e s s parameters  f o l l o w i n g manner  M.R  a  V  (5.21)  d f  D a/D) e  where M.R  =  melt r a t e  (g sec  V  =  applied voltage  t  "*") (volts)  -3 I  =  current  x 10  d  =  diameter of the e l e c t r o d e  D  =  diameter of the i n g o t  I  =  distance interface  (amperes) (cm)  (cm)  betweeen the e l e c t r o d e (cm).  t i p and  the  slag/metal  108  For an approximate c o r r e l a t i o n , one and  c = e  can assume a=  b = f e  1.0  =2.0.  Relation  (5.21) reduces  to  2  M.R  a  "V_I_d D  2  ( 5 > 2 2 )  ( /D) A  Or M.R  z  = constant  D2  2  a/D)  -  ( 5  D  where Z i s a c o n s t a n t .  V I d  ( /D)MR £  The v a l u e of Z depends upon the s l a g  t i o n , e l e c t r o d e composition, e l e c t r i c a l  c o n f i g u r a t i o n and  composi-  the atmosphere.  B e f o r e 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 equation The  2 3 )  of  (5.23), the g e n e r a l form of the e q u a t i o n w i l l be d i s c u s s e d . u n i t s of the constant Z are K c a l g *.  Thus onawould  expect  a h i g h e r v a l u e f o r Z, h i g h e r the m e l t i n g p o i n t of the m a t e r i a l b e i n g remelted. In e q u a t i o n remaining  (5.23) i t i s proposed  c o n s t a n t , the melt  e l e c t r o d e diameter. is  t h a t , the o t h e r parameters  r a t e i s p r o p o r t i o n a l to the square  As most of the heat n e c e s s a r y  t o melt  of the  the e l e c t r o d e  t r a n s f e r r e d t o the e l e c t r o d e by c o n v e c t i o n , i t i s l o g i c a l to expect  the melt  r a t e to be p r o p o r t i o n a l t o  the c r o s s - s e c t i o n a l a r e a of the  electrode. The  c o r r e l a t i o n t h a t the melt  r a t e i s i n v e r s e l y p r o p o r t i o n a l to  109  the square of the i n g o t 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 . a constant  (d/D)  r a t i o , an i n c r e a s e i n the diameter of the i n g o t by  f a c t o r of 2 r e s u l t s i n a s i m i l a r i n c r e a s e i n power i n p u t . justified  s i n c e most of the heat l e a v e s  the ESR  w a l l s of the mold to the mold c o o l i n g water.  u n i t through the  The  However as some heat a l s o l e a v e s through  will  result  Fig.  (73)  gives  to  the e x p e r i m e n t a l l y  obtained  Fig.  see  can  from 15 inches from 800 The  to 30  lbs h r " effect  1  (d/D) hence  t h a t an i n c r e a s e i n  lbs  the  From  the diameter of the  ingot  i n c h e s , r e s u l t s i n an i n c r e a s e i n the melt  to 1700  ratio  c o r r e l a t i o n between,  the i n g o t diameter by H o l z g r u b e r et a l .  one  increase  2.2.  the melt r a t e and (73)  ingot.  keeping the  i n an i n c r e a s e i n the power i n p u t and  melt r a t e by a f a c t o r of 2.0  side  increase i n surface  the mold bottom, an  i n the diameter of the i n g o t by a f a c t o r of 2,  a  This i s  a r e a of the mold w a l l i s p r o p o r t i o n a l to the diameter of the  constant  Keeping  rate  hr" . 1  of the l o c a l i z e d heat i n p u t on the melt r a t e i s  i n c l u d e d i n the e q u a t i o n  (5.23) by  i s i n v e r s e l y p r o p o r t i o n a l to  (&/D).  the c o r r e l a t i o n t h a t the melt Decreasing  rate  the d i s t a n c e  localizes  a s i g n i f i c a n t p o r t i o n of the t o t a l heat i n p u t .in the narrow r e g i o n between the e l e c t r o d e t i p and  the s l a g / m e t a l  i n t e r f a c e , r e s u l t i n g i n an  i n c r e a s e i n the melt r a t e . The  v a l i d i t y of e q u a t i o n  the a v a i l a b l e l a b o r a t o r y and  (5.23) i s checked  ( e r r o r + 10%)  i n d u s t r i a l experimental  data.  l a b o r a t o r y experiments were c a r r i e d out u s i n g CaF2^25 wt.% Tables ingots.  X I I I and  XIV  g i v e the c a l c u l a t e d v a l u e s  of Z f o r the  against  A l l the A^O^  slag.  different  110  Table XIII.  Ingot no.  Calculated values  Polarity  Atmosphere  III  of Z f o r the l a b o r a t o r y made i n g o t s  Electrode material  (cm)  (Kcal g  EN  25  2.0  2.28  Air  EN  25  2.0  1.7  Air  EN  25  3.0  1.81  EN  25  2.0  2.46  EN  25  2.0  3.36  EN  25  1.5  3.42  EN  25  1.8  2.35  EN  25  2.6  1.8  EN  25  2.6  1.585  EN  25  2.8  1.52  EN  25  2.6  1.56  EN  25  2.3  2.32  EN  25  1.4  3.08  EN  25  1.8  1.48  EN  25  1.9  1.50  EN  25  1-7  1.65  EN  25  1.6  1.49  2.0  2.26  FVE  1.6  3.16  FVE  1.6  4.15  1  -rve  Argon  2  -ve  3  -ve  4  -ve  Argon  5  -ve  Argon  6  -ve  Argon  7  -ve  Argon  8  -ve  10  +ve  Argon  11  +ve  Argon  12  +ve  Argon  13  +ve live  Argon  14  +ve live  Argon  15  a. c.  16  a.c.  Argon  17  a. c.  Argon  18  a. c.  Argon  20  -ve  Argon  25  -ve  26  -ve  I II II  Air III II II III  II  Air III II  II  Air Argon  II  AISI  630  1  )  Ill Table  Ingot no. 27  XIII.  (Continued)  Polarity  +ve  Atmosphere  Air  Electrode material  £ (cm)  -1 (Kcal g ) Z  FVE  1.6  3.10  28  +ve (BN i n s )  Argon  1 1  FVE  1.3  3.19  29  +ve (BN i n s )  Argon  1 1  FVE  1.7  3.33  30  +ve live  Argon  1 1  FVE  1.7  4.12  Argon  1 1  FVE  1.2  2.86  Argon  1 1  FVE  1.1  3.12  31 32  a.c. a.c. (BN i n s )  Table  Ingot no.  XIV.  Calculated values  Mold diameter (cm)  of Z f o r i n d u s t r i a l  Electrode diameter (cm)  Electrode Composition  ingots  Polarity  Power input (Kwatts)  Melt , ^ 8 S  6  C  rate -1. '  £/D (  v  ^  Z , -1 K C a l  S  II  5 1  30.5  15.25  1020  a.c.  240  24  =0.262  2.3  I2  5 1  30.5  22.8  1020  a.c.  240  50.5  =0.262  2.46  13  20.3  15.25  a.c.  66  19.4  =0.30  1.53  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  AQ  Hastelloy X  113  (1)  To study the e f f e c t o f the e l e c t r o d e c o m p o s i t i o n  compare the i n g o t s with The  ( 5 ) , (20) and (26). . As e x p e c t e d , the i n g o t (26)  the h i g h e s t m e l t i n g values  one can  point  (1539°C) has the h i g h e s t  value  of Z.  o f Z c a l c u l a t e d f o r i n d u s t r i a l i n g o t s a l s o show a s i m i l a r  pattern. (2)  To study the e f f e c t o f t h e i n g o t diameter, one can compare  the i n g o t s  (3) and (8),and  (4) and ( 7 ) .  The c a l c u l a t e d v a l u e s  of Z a r e  2 very  s i m i l a r , t h e r e b y 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 i n g o t s  (2) and (3) t o study the e f f e c t of the  e l e c t r o d e diameter, the d i s t a n c e between the e l e c t r o d e t i p and the slag/metal  i n t e r f a c e i t i s seen that the c a l c u l a t e d v a l u e  o f Z i n both  the cases i s a p p r o x i m a t e l y the same.  The AISI 1020 i n g o t s I I and 12  (Table XIV) a l s o show a s i m i l a r v a l u e  for Z for different  (4)  On comparing the i n g o t s having  (d/D) r a t i o s .  the same composition b u t  :  d i f f e r e n t e l e c t r i c a l c o n f i g u r a t i o n and atmosphere, i t i s seen that except f o r the d.c. n e g a t i v e with  with  argon and d.c. p o s i t i v e l i v e  (both  a i r and w i t h argon) c o n f i g u r a t i o n s , a l l have a p p r o x i m a t e l y the  same v a l u e  o f Z (Z - 1.65 f o r EN 25 and Z - 3.0 f o r FVE).  An attempt  i s made here to e x p l a i n the observed b e h a v i o u r . In d.c. p o s i t i v e ' l i v e '  c o n f i g u r a t i o n , as shown by F i g . (46), a  s i g n i f i c a n t p o r t i o n o f the c u r r e n t goes t o the mold w a l l . of the t o t a l c u r r e n t s l a g bath.  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 h e a t i n g the  The c u r r e n t d e n s i t y below the e l e c t r o d e t i p i s a l s o  r e l a t i v e l y low. vicinity  This portion  As a r e s u l t , the temperature of the s l a g i n the  o f the e l e c t r o d e i s n o t v e r y h i g h .  reduced, and the v a l u e  of Z i n c r e a s e d .  The melt r a t e i s thereby  114  In r e m e l t i n g w i t h  d.c.  having  the e l e c t r o d e as n e g a t i v e  pole,  presence of the argon atmosphere p r e v e n t s the o x i d a t i o n of the A l Ca at the s l a g / g a s  interface.  The  the and  n o n - a v a i l a b i l i t y of the heat of  o x i d a t i o n i n the v i c i n i t y of the e l e c t r o d e r e s u l t s i n a lower melt and  .  an i n c r e a s e i n the v a l u e of Z. In the d.c.  p o s i t i v e c o n f i g u r a t i o n , both w i t h  a i r or argon,  e l e c t r o d e i s s i g n i f i c a n t l y more p o l a r i z e d than the d.c. configuration.  higher  negative  p o l a r i z a t i o n i s compensated i n the d.c.  the exothermic heat of o x i d a t i o n of A l and  interface.  the game v a l u e negative  of Z.  In r e m e l t i n g  to the .,  i n a i r config-  Ca at the s l a g /  T h i s r e s u l t s i n both c o n f i g u r a t i o n s having  approximately  l a r g e r s c a l e i n g o t s however,  i n a i r would have a lower v a l u e  of Z.  The  the r e l a t i v e c o n t r i b u t i o n by  d.c.  i n c r e a s e i n the  e l e c t r o d e s i z e , decreases the c u r r e n t d e n s i t y on the e l e c t r o d e decreasing  the  However i n the l a b o r a t o r y s c a l e i n g o t s , the e x t r a heat p o s i t i v e due  gas  j  negative  l i b e r a t e d at the e l e c t r o d e s u r f a c e i n the d.c.  u r a t i o n by  rate  thereby  the p o l a r i z a t i o n i n the  d.c.  positive configuration. In r e m e l t i n g  s t e e l s u s i n g a.c.  b u t i o n by p o l a r i z a t i o n or o x i d a t i o n .  (- 50 c y c l e s ) t h e r e i s no However, due  to  the  contri-  higher  e f f e c t i v e s l a g r e s i s t a n c e (because of the absence of d i s s o l v e d Ca A l ) i t i s p o s s i b l e to achieve the v a l u e  a l o c a l i z e d heat g e n e r a t i o n  of £) i n the s l a g bed.  Z as i n d.c.  negative  P r e d i c t i o n of the Melt  (by  reducing  This r e s u l t s i n a s i m i l a r value  i n a i r or d.c.  or  for  positive (insulated).  Rate  I t i s p o s s i b l e to a p p r o x i m a t e l y p r e d i c t the melt r a t e f o r l a r g e s c a l e i n g o t s from the a v a i l a b l e e x p e r i m e n t a l  data.  115  For a 60.95 cm  (24 i n c h e s ) diameter  i n g o t of EN  i n g o t 14, T a b l e XIV), the v a l u e of the melt the approximate power i n p u t average  v a l u e of Z f o r EN  melt  r a t e of =258 g sec  1  (d/D =  0.75;  rate i s obtained,using  c a l c u l a t e d i n Appendix  25 s t e e l of 1.65.  of the v a r i o u s parameters i n e q u a t i o n  25  (IV) and  the  S u b s t i t u t i n g the v a l u e s  (5.23) y i e l d s a v a l u e f o r the  .  To compare the p r e d i c t e d v a l u e s of the melt  rate with  the  6 e x p e r i m e n t a l l y o b t a i n e d v a l u e s by H o l z g r u b e r c a l c u l a t e d f o r a 60.95 cm diameter (Fig.  (73) d a t a i s f o r d/D  = 0.6)  c a l c u l a t e d i n Appendix I V ) . as compared t o 177  g sec  1  i n g o t (15) of EN25 w i t h d/D  =0.6  u s i n g the approximate power i n p u t  A melt  (1400  e t a l . , melt r a t e i s  r a t e of 157  l b hr ) 1  g sec  1  i s calculated  obtained experimentally.  The  c o r r e l a t i o n appears  r e a s o n a b l e , c o n s i d e r i n g the v a r i o u s  involved.  F i g . (73) i s o b t a i n e d b a s i c a l l y from d a t a on h i g h l y  Secondly  alloyed steels.  approximations  As shown e a r l i e r , lower m e l t i n g compositions  s m a l l e r v a l u e of Z and hence a h i g h e r melt  rate.  have a  116  CHAPTER VI PREDICATION OF POOL VOLUMES IN ESR INGOTS  VI.1  Introduction One of the main advantages claimed  i s t h e improvement would s o l i d i f y pool p r o f i l e  by e l e c t r o s l a g m e l t i n g  of the ingot s t r u c t u r e .  technique  The manner by which an i n g o t  depends upon t h e mode of heat e x t r a c t i o n .  The l i q u i d metal  which i s c o n t r o l l e d by t h e r a t e and mode o f heat  e x t r a c t i o n , i s a good i n d i c a t o r o f t h e manner i n which t h e i n g o t would solidify. Consider  the two extreme cases as shown i n F i g . (74).  A high  m e l t r a t e i s g e n e r a l l y c h a r a c t e r i z e d by a deep l i q u i d p o o l . dendrites  grow p e r p e n d i c u l a r  t o t h e i n t e r f a c e , a h i g h e r melt r a t e  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 o f the d e n d r i t e s . favoured  f o r subsequent working.  melt rate r e s u l t s i n a f l a t  On the  liquid  haye an optimum shape of the l i q u i d  T h i s i s not  o t h e r extreme, a v e r y  p o o l having  g a t i o n due t o l a r g e r d e n d r i t i c arm s p a c i n g .  significant  as shown i n F i g . (75).  of t h e l i q u i d cylindrical  microsegre-  pool.  Besides  p o o l , i t i s important  slow  Thus one would l i k e t o  The p o o l volume o f an ESR i n g o t can be s u b d i v i d e d regions  As the  i n t o two d i s t i n c t  the shape o f t h e curved  to have an optimum h e i g h t  p o r t i o n o f the p o o l volume.  In i n d u s t r i a l scale  portion  f o r the ingots  117  t h i s h e i g h t i s about  10-15  cm.•  s u r f a c e q u a l i t y f o r the i n g o t ,  T h i s i s n e c e s s a r y to a c h i e v e a good I f the p r o c e s s i s stopped  suddenly  a f t e r a d e s i r e d l e n g t h of the i n g o t i s made, the l i q u i d m e t a l volume p r e s e n t a t the time o f shut o f f would s o l i d i f y  i n the c o n v e n t i o n a l  manner i . e . , w i t h equiaxed s t r u c t u r e i n the c e n t r e . i s g e n e r a l l y used to r e j e c t  As the ESR  f o r r e f i n i n g expensive a l l o y s , i t i s not  the l a s t  10-15  cm of the ingot every time.  towards the end,  economical  In i n d u s t r y , t h i s  i s overcome by a d o p t i n g the p r a c t i c e of 'hot t o p p i n g ' . feed r a t e are g r a d u a l l y reduced  process  The power and  so t h a t the  cylindrical  p o r t i o n i s reduced  to a minimum and  i s q u i t e important  from t h i s p o i n t of view to know the exact p o o l volume  f o r a normal s e t of working Now  t h a t the ESR  then the p r o c e s s i s stopped. : I t .  conditions.  p r o c e s s i s accepted i n the i n d u s t r y as a batch_  p r o c e s s , e f f o r t s are b e i n g made t o make i t c o n t i n u o u s ; s i m i l a r to; continuous  casting.  In d e s i g n i n g the copper mold f o r the continuous:  p r o c e s s , i t i s n e c e s s a r y t o know the volume of the and the p o s i t i o n of the s o l i d / l i q u i d Having attempt  d i s c u s s e d the importance  i s now  l i q u i d metal pool  i n t e r f a c e i n the copper mold. of knowing the p o o l volume, an  made to p r e d i c t i t f o r some known o p e r a t i n g c o n d i t i o n s .  As shown i n F i g . (75), the p o o l volume can be s u b d i v i d e d i n t o two  ;  regions.  The  '  ;  c y l i n d r i c a l p o r t i o n can be p r e d i c t e d on the b a s i s of a  dynamic heat b a l a n c e of the u n i t w h i l e the curved p o r t i o n 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 P o r t i o n of  the  P o o l Volume In Chapter V, an a c c u r a t e heat b a l a n c e out.  of the p r o c e s s was  carried  From i t , i t i s c l e a r t h a t knowing the o p e r a t i n g c o n d i t i o n s , the  geometry and  the volume of the s l a g cap,  i t i s p o s s i b l e to c a l c u l a t e  the h e i g h t of 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 . Fig. observed cases  (76)  (26) and  is  =3.5  cm.  Using  for ingots  s i m i l a r boundary c o n d i t i o n s as ( 1 ) , (10) and  The two  obtained  (16), a heat b a l a n c e  of  the  i n g o t s y i e l d s a v a l u e f o r the d i f f e r e n c e i n the h e i g h t of the  c y l i n d r i c a l p o r t i o n of 3.0-3.3  v a l u e of =3.0  cm was  (4) and  (18).  o b t a i n e d which compared v e r y f a v o u r a b l y w i t h  e x p e r i m e n t a l l y observed 3.0-3.2  ;  cm.  S i m i l a r c a l c u l a t i o n s were c a r r i e d out f o r i n g o t s  of  (32).  d i f f e r e n c e i n h e i g h t of the c y l i n d r i c a l p o r t i o n i n the  experimentally two  shows the macrographs of i n g o t s  A  the  d i f f e r e n c e i n h e i g h t of the c y l i n d r i c a l p o r t i o n  cm.  Having b e i n g a b l e to p r e d i c t the h e i g h t of 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 i n l a b o r a t o r y s c a l e i n g o t s , attempt i s now  made to p r e d i c t t h i s h e i g h t  f o r an i n d u s t r i a l s c a l e i n g o t .  Table  . (XV)  51 g i v e s the. 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 . c a r r y i n g out a heat a v a l u e of 15 cm of  balance  s i m i l a r to the one  i s obtained  the l i q u i d m e t a l p o o l .  f o r the h e i g h t  15-18  cm.  done i n Appendix ( I V ) ,  of the c y l i n d r i c a l p o r t i o n  C o n s i d e r i n g the approximations  t h i s v a l u e agrees v e r y w e l l w i t h  On  involved,  the e x p e r i m e n t a l l y o b t a i n e d v a l u e  of  119  T a b l e XV.  Mold dia. (cm)  Operating conditions  Electrode dia. (cm)  50.8  Electrode comp.  Hastelloy X  40.5  f o r an i n d u s t r i a l s c a l e  Electrode polarity  a.c.  Atm.  Air  Slag comp.  160  *  *  *  *  A (cm)  B (cm)  Refer to F i g .  VI.3  15-18  15000  3  20  (75)  P r e d i c t i o n o f P o o l P r o f i l e s Using E x p l i c i t  VI.3.1  32  2  Amp.  25 wt.% A1 0  Z (cm) 15  51  Volts  CaF -  2  Melt Rate (g/sec)  ingot.  F i n i t e D i f f e r e n c e Method  Introduction  M a t h e t m a t i c a l models f o r 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 p a t t e r n i n 37 50 52 53 c a s t i n g s have been s t u d i e d by many i n v e s t i g a t o r s . " ' '  '  '  Sun and  50 Pridgeon  used the f i n i t e d i f f e r e n c e method to p r e d i c t the p o o l  p r o f i l e s i n Hastelloy-X sidered For  ingots.  The model p r e s e n t e d here can be con-  as a r e f i n e m e n t o f t h e Sun and P r i d g e o n a n a l y s i s . rounded i n g o t s , the c y l i n d r i c a l p o l a r system  g e n e r a l l y used.  ( r , <J> , Z) i s  Two d i m e n s i o n a l heat t r a n s f e r a l o n g the r and Z axes  i s adequate i n d e s c r i b i n g  t h e heat f l o w i n an e l e c t r o s l a g r e f i n i n g  u n i t 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  :  F o u r i e r e q u a t i o n reduces to  120  9T  •  1? where  a  =  3T  1  2  "  +  ^  8T  »  • 3 Ti 2  *  ^  < 6  — — P C  (6.2)  methods knowing the a p p r o p r i a t e boundary c o n d i t i o n s . 54  1 }  P  E q u a t i o n (6.1) can be s o l v e d by means o f d e f i n i t e  Dusinberre  -  difference Both  the  55 ( e x p l i c i t ) , and the Crank and N i c o l s o n ( i m p l i c i t ) methods  can be used.  Use of the D u s i n b e r r e ' 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 p r o c e s s , the i n g o t i s c o n t i n u o u s l y b u i l t  up.  The v e r s a t i l i t y o f the f i n i t e d i f f e r e n c e technique p e r m i t s one t o s i m u l a t e the l i q u i d m e t a l dropped  c o n t i n u o u s l y i n t o the p o o l by  adding a t the top, a t h i n d i s c l a y e r of l i q u i d metal of a g i v e n s i z e a f t e r every u n i t time  VI.3.2  interval.  D e r i v a t i o n o f the Formulae f o r the E x p l i c i t F i n i t e  Difference  Method The  first  q u e s t i o n concerns the s u b d i v i s i o n of the system.  The  simple and obvious method i s i n e q u a l increments of the r a d i u s .  The  system i s then l a i d out as i n F i g . (77). For convenience, an a r c of one r a d i a n i s used and each has the dimensions  of 'Ar' a l o n g the ' r ' a x i s and  element  'Az' along the 'z'  axis. As seen i n F i g . (77), t h e r e a r e , i n t o t a l n i n e d i f f e r e n t elements.  types of  S y m b o l i c a l l y , they can be r e p r e s e n t e d as f o l l o w s  \  121  (1)  (5) 11  (2)  (3)  (6)  (7)  (8)  ¥  C9).  The a r c s halfway between the r e f e r e n c e p o i n t s are taken as d e f i n i n g the width of the heat flow p a t h and a l s o the volumes respective  o f the  regions.  Appendix  (V) g i v e s the d e r i v a t i o n of the formulae f o r each of the  n i n e d i f f e r e n t types o f elements.  VI.3.3  S a l i e n t F e a t u r e s o f the Computer Programme  The dependence  of the p o o l shape on the t h e r m o p h y s i c a l p r o p e r t i e s  of a g i v e n a l l o y i s o b v i o u s . model,  Hence i n d e v e l o p i n g the computation  the p o o l shape i s c o n s i d e r e d as a f u n c t i o n of both the i n g o t melt  r a t e and the t h e r m o - p h y s i c a l p r o p e r t i e s o f the a l l o y . the s a l i e n t (1)  The. f o l l o w i n g are  f e a t u r e s of the programme.  I t i s assumed t h a t the temperature of the top l a y e r  elements  remains c o n s t a n t , i . e . the top l a y e r elements are assumed t o be i n , steady s t a t e e q u i l i b r i u m w i t h the elements below them and the l i q u i d  slag  or m e t a l above them. (2) assumed.  The temperature d i s t r i b u t i o n i p the top l a y e r elements i s The temperature d i s t r i b u t i o n depends upon 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 above  them.  The  cylindrical  p o r t i o n a c t s as a b u f f e r r e g i o n and reduces the r a d i a l temperature g r a d i e n t i n the top l a y e r elements.  122  (3)  A c o n s t a n t temperature a t the bottom of the i n g o t 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 p o s s i b l e  to c a l c u l a t e the heat l e a v i n g a t the bottom of the i n g o t from the a v a i l a b l e e x p e r i m e n t a l . d a t a , the assumption s i m p l i f i e s  the a n a l y s i s  without s c a r i f i c i n g a c c u r a c y . (4)  The c u r r e n t p a s s i n g through the i n g o t does not produce  s i g n i f i c a n t h e a t i n g o f the i n g o t ; hence i t s e f f e c t i s n e g l e c t e d 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  o b t a i n e d on the copper mold and p o l a r i t i e s .  f o r v a r i o u s mold s i z e s , m o l d / e l e c t r o d e r a t i o s  I t i s p o s s i b l e t o n o n - d i m e n s i o n a l i z e the temperature  v s . d i s t a n c e from the l i q u i d m e t a l / s o l i d m e t a l i n t e r f a c e p l o t s f o r distance. mold  F i g . C78) shows the average temperature d i s t r i b u t i o n on the  a c r o s s the s o l i d i f i e d i n g o t .  curve i n the form of an e q u a t i o n . fitted  I t i s necessary to express t h i s A p o l y n o m i a l of 8th degree was  to the curve q u i t e a c c u r a t e l y .  be used as a boundary  However, t h i s p o l y n o m i a l cannot  c o n d i t i o n f o r / . i n d u s t r i a l s c a l e i n g o t s as F i g . (78) i  i s v a l i d o n l y f o r 'L' =35.0 cm. 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 heat going to the mold  water i n elements of cases 3, 6 and 7 d i s c u s s e d i n Appendix case 3, the temperature o f a n o d a l p o i n t X T  n  TL J Z 9  K.  "T"  r, z i s g i v e n by the f o l l o w i n g e q u a t i o n X  ;  cooling  (V). For  a t time t = k + I , i . e .  123  C  —P-  p volume  A  , At  r  T  r,z,k+l  _ x  r,z,k  1  =  Ar  h : , A . [T ,. . - T ] + -~side 2 r+l,z,k r,z,k Az  +  Az  ^r,z-l,k  In Eq.  C6.3), one  +  •^r+l,z,k  L  k-i l  e  t  T  T  [T  - T  - T  r,z+l,k  r,z,k  r,z,k  1  ]  r,z,k''  (6.3)  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,z,k''  ^side 2 ^ r + l , z , k  q  '''rjZjk"'  A  A  fx  *" r - l , z , k  =  h  0  [T - T .] water r,z,k  side  (6,4)  In steady s t a t e  f- = A„  where h AT  h AT  (6.5)  i s obtained  from F i g . (63), AT b e i n g  ence between the mold w a l l and As  discussed  e a r l i e r i n Chapter V,  c o o l i n g water can be  Ca)  subdivided  (a)  surface b o i l i n g  (b)  non-boiling  Surface  r e g i o n can be  the water  the  temperature  temperature. the heat t r a n s f e r to the  i n t o two  differ-  mold  regions  region  region  B o i l i n g Region:.  The  heat f l u x i n the s u r f a c e b o i l i n g ,  expressed i n an e q u a t i o n  form as  follows  124  (J)  =  exp  (6.12  S,n[(T-50)>  22.13]}  (6.6)  Where T i s the temperature on the copper mold i n degrees Using  (6.6) i t i s p o s s i b l e to c a l c u l a t e the heat going to the mold  c o o l i n g water (b)  centrigrade.  f o r elements  a c r o s s the s u r f a c e b o i l i n g  region.  N o n - B o i l i n g Region: As c a l c u l a t e d e a r l i e r i n Chapter V h , .,. ° non-boiling -2 -2 -1 -1 x 10 c a l cm °C sec . Knowing the temperature d i f f e r e n c e r  1.15  between mold and water c o o l i n g water (6)  temperature, the heat t r a n s f e r r e d to the mold  f o r elements  a c r o s s the n o n - b o i l i n g r e g i o n can be  As the t h e r m o p h y s i c a l p r o p e r t i e s of the v a r i o u s s t e e l s at  e l e v a t e d 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 here to p r e d i c t only.  i s made  the p o o l p r o f i l e s i n pure i r o n and EN 25 s t e e l  EN 25 s t e e l has a p p r o x i m a t e l y 5% a l l o y i n g elements  except f o r the m e l t i n g p o i n t  ingots  and as such,  (= 50°C l o w e r ) , i t i s assumed to have  the same t h e r m o p h y s i c a l p r o p e r t i e s as pure (7)  calculated  iron.  The l a t e n t heat of s o l i d i f i c a t i o n and a l s o the a l l o t r o p i c  t r a n s f o r m a t i o n s i n the case o f pure i r o n are taken i n t o account by a d j u s t i n g 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:  H AT  L  C (adjusted) P  =  where AT i s the temperature (8)  C (metal) P  +  range over which  (6.7)  the t r a n s f o r m a t i o n o c c u r s .  The d a t a f o r thermal c o n d u c t i v i t y 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 c o n d u c t i v i t y  i s e s t i m a t e d above 1600°K by making use of the Loren's r e l a t i o n s h i p , the d a t a f o r 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.  as  125  Ivoren'g  relationship:  e l e c t r i c a l r e s i s t i v i t y x thermal c o n d u c t i v i t y —- —. - = constant temperature J  In  the range where b o t h the thermal and e l e c t r i c a l  i s a v a i l a b l e , the v a l i d i t y (error  o f the Loren's r e l a t i o n s h i p i s checked >  the l i q u i d i f o n temperature range, i t i s v e r y d i f f i c u l t  c a l c u l a t e the c o n t r i b u t i o n o f c o n v e c t i o n . by way  o x  conductivity data  < 5%).  In  (6.8)  to  I t i s taken i n t o account  of the concept of ' e f f e c t i v e thermal c o n d u c t i v i t y '  k  k  eff  „ eff  =  k  =  f -  conv  +  k  , cond  (6.9)  (6.10)  k  cond  I t i s extremely d i f f i c u l t y t o e s t i m a t e the v a l u e of ' f . f u n c t i o n o f temperature and f l o w c o n d i t i o n s . f = 3-5.  It i s a  £un and P r i d g e o n " ^ use  U s i n g S t e w a r t ' s " ^ n o n - d i m e n s i o n a l a n a l y s i s f o r the present;,  case y i e l d s a s i m i l a r v a l u e f o r ' f and i s used i n the a n a l y s i s . the  validity  the  p r e s e n t case, the temperature g r a d i e n t s are such t h a t denser  of u s i n g t h i s a n a l y s i s t o phe p r e s e n t case i s i n doubt.  i s at the bottom and l i g h t e r at the top.  The time i n t e r v a l  In  liquid  T a b l e XVI g i v e s the 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 . " ' (9)  However  7  'At' between s u c c e s s i v e  temperature  e v a l u a t i o n s at a node i s chosen such t h a t the s t a b i l i t y c r i t e r i a i s satified. In  F i g . (79)., the temperature at the n o d a l p o i n t  'a' a f t e r time At  126  Table  XVI.  57  P h y s i c a l p r o p e r t i e s o f pure i r o n used i n the a n a l y s i s  Temperature Range (°K)  Density  Specific  (g cm )  (cal  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  1801-1825  7.073  0.18  0.24  1825-1900  7.04  0.182  0.30  1900-2050  6.94  0.183  0.40  3  Heat  Thermal  g" ^" )  ( c a l cm  1  1  65.7  Conductivity l o  K  "*"sec  1  )  0.12  can be w r i t t e n as  Fig.  .C.  a  IT'  (79) n o d a l p o i n t s  a At  - TJ a_  k  ba  configuration  (T b  T )+ k a  ca  (x - T ) + c  a  (6.10)  127 where C  a  = o C  P  On s i m p l i f y i n g  r  At  -  T' a  «  T  k  b  F, T, + ba b  In e q u a t i o n  F T  ca c  and  aa -  1  T  + ... +  (6.12) a l l F Ek  F  At  + ^  b a  c  +  . .  Ek. At  + U - - f  ]T  a  F T  (6.11)  (6.12)  aa a  e t c . a r e i n h e r e n t l y p o s i t i v e but  At  " — 5 —  ( 6  t h i s may become n e g a t i v e i f At i s chosen l a r g e enough.  -  1 3 )  T h i s would  be absurd p h y s i c a l l y , because i t would say t h a t , the warmer the r e g i o n 'a' i s now, t h e c o l d e r i t i s going  t o be a f t e r the time i n t e r v a l A t .  More s o p h i s t i c a t e d c r i t e r i a have been d e v i s e d f o r systems t o which d i f f e r e n t i a l equations p r a c t i c a l matter,  a r e a p p l i c a b l e and can be s o l v e d .  i t i s easy  t o obey a simple r u l e :  But, as a  'avoid n e g a t i v e  coefficients . Of the p o s s i b l e F At.  aa  v a l u e s , the worst v a l u e i s s e l e c t e d t o e v a l u a t e  In the p r e s e n t a n a l y s i s , as c o n s t a n t temperature i s assumed a t  b o t h the top and bottom, the v a l u e o f F  t o be c o n s i d e r e d i s o b t a i n e d 3.3.  from eq. (A.V.7) [Appendix V ] .  128  The maximum a l l o w a b l e v a l u e o f A t i s o b t a i n e d by s o l v i n g  F  aa  =  - k~  1  w;  +  +  w;  ( 6  -  1 5 )  C p Ar •f — . • k At 2  where MR„ 2  =  2  C MZ  3  MZ, 4 4.0 k  -  p Az k  At  3  C p Az -? : k, At  =  At  — p C Ar P  2  2  k +  At  A p C  k. At +  2  — -2 p C Az P  Az  P  • =  1  (6.16)  p C The minimum v a l u e o f (-j ^) i s chosen f o r e v a l u a t i o n , as i t l e a d s -T  r  t o the maximum a l l o w a b l e v a l u e o f At i n the worst -3  p  =  6. 88 g cm  C P  -  0.18 c a l g "  =  0.4 c a l cm  k  case.  l o  l o  C  C  _ 1  sec  S u b s t i t u t i n g these v a l u e s i n (6.16) y i e l d s  At  =  • , 1  l  Using  Ar  2  5  (6.17)  5  2  Az  (6.17) i t i s p o s s i b l e to c a l c u l a t e the v a l u e  of the element.  of At f o r any s i z e  129  VI.3.4  Results  Appendix VI g i v e s the computer p o o l p r o f i l e s i n ESR i n g o t s were computed. distribution  ingots.  programme w r i t t e n t o p r e d i c t the  Pool p r o f i l e s  f o r EN 25 s t e e l and  FVE  T a b l e XVII g i v e s the assumed temperature  i n the top elements and t h e v a l u e s of the v a r i o u s parameters  used i n the computation. Fig.  (80) to F i g . (85) show the p r e d i c t e d p o o l p r o f i l e s  on the e x p e r i m e n t a l l y o b t a i n e d p r o f i l e s . good i n s p i t e  The agreement  of the numerous assumptions made.  ( 8 3 ) ) , tungsten powder was  superimposed  appears t o be  I n i n g o t no. 21 ( F i g .  added t o d e f i n e the p o o l p r o f i l e .  To p r e d i c t the p o o l p r o f i l e s  for industrial scale ingots, i t i s  n e c e s s a r y , e i t h e r t o e x p e r i m e n t a l l y determine or assume, a p r o f i l e on the mold a c r o s s the s o l i d i f i e d  ingot.  temperature :  T a b l e XVII.  Ingot no.  Parameters  DELR cm  DELZ cm  used i n the p r e d i c t i o n o f p o o l p r o f i l e s i n EN25 and FVE i n g o t s  DELT sec  NRATE  SIDE . -2 - 1 -1 c a l cm s e c C 0  Temperature d i s t r i b u t i o n i n -the top l a y e r (°K) Ingot Centre Ingot Edge  1  1.22  1.0  0.5  178  0.0116  1800  1790  1780  1750  10  1.22  1.0  0.5  232  0.0116  1810  1795  1780  1750  16  1.22  1.0  0.5  178  0.0116  1825  1785  1770  1750  21  1.1625  1.0  0.5  169  0.0116  1800  1795  1790  26  0.9  0.5  0.18  308  0.0116  1830  1815  1810  1800  28  0.9  0.5  0.18  185  0.0116  1850  1825  1815  1800  1780  1750  i—  1  o  131  CHAPTER V I I CONCLUSIONS  The  heat g e n e r a t i o n  p a t t e r n i n the ^ l a g bed has been  analysed  u s i n g a r e s i s t a n c e network analogue to p r e d i c t the v o l t a g e gradients  i n the s l a g bed.  Most of the heat g e n e r a t i o n  p l a c e below the e l e c t r o d e t i p .  Self consistency  between  takes current,  v o l t a g e , temperature, r e s i s t a n c e and q i s o b t a i n e d  i n the s l a g bed.  It  on the e l e c t r o d e .  i s p o s s i b l e t o p r e d i c t the temperature g r a d i e n t  T h i s may be used t o c a l c u l a t e the degree o f thermal  instability,  d u r i n g e l e c t r o d e changes i n l a r g e i n d u s t r i a l i n g o t s 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 e l e c t r o d e and mold s i z e s s t u d i e d , the e l e c t r o d e m a t e r i a l spends a p p r o x i m a t e l y 30 seconds i n the temperature g r a d i e n t to the m e l t i n g  point.  I t i s suggested t h a t t h i s would l e a d t o a  s i g n i f i c a n t non-equilibrium i n a melting  1000°C  r e t e n t i o n o f second-phase p r e c i p i t a t e s  a l l o y which c o n t a i n e d  these p r e c i p i t a t e s a t a lower  temperature i n the s o l i d .  The  o v e r a l l heat t r a n s f e r c o e f f i c i e n t o f the i n t e r f a c e r e g i o n ,  liquid  s l a g / s l a g skin/copper  mold i s found t o have a s l i g h t  132 dependency on  the  s l a g temperature, s l a g c o m p o s i t i o n and  slag skin thickness. to the  I t i s postulated  that  the major  the  resistance  t r a n s f e r of heat a c r o s s t h i s composite i n t e r f a c e l i e s  the  d i s c o n t i n u i t y between the  The  e l e c t r i c a l r e s i s t i v i t y of the  the  contact  resistance  and  s l a g - s k i n and  in  the mold w a l l .  s l a g s k i n p r i m a r i l y depends upon  i s a sensitive function  of the mold w a l l  temperature.  An  approximate thermal g r a d i e n t  i n the  slag skin region  hasIbeen  determined.  An  a c c u r a t e heat b a l a n c e of  tory scale ingots.  The  the p r o c e s s i s c a r r i e d out  r e s u l t s i n d i c a t e that  p o r t i o n of the heat l e a v e s the the  l i q u i d metal  The  power requirements and  ingots  v a l u e s and  Real d i f f e r e n c e s It  u n i t a c r o s s the  labora-  significanti liquid  slag  and  regions.  are p r e d i c t e d .  predicted  a  on  are  i s observed t h a t  the melt r a t e f o r i n d u s t r i a l  scale  Good agreement i s o b t a i n e d between the  d a t a c o l l e c t e d from  the  literature.  observed between d i f f e r e n t m e l t i n g modes. i n d.c.  n e g a t i v e , t h e r e i s a marked  between m e l t i n g under argon and  air.  difference  133  (9)  The l i q u i d m e t a l p o o l volumes i n ESR i n g o t s can be p r e d i c t e d from the o p e r a t i o n a l d a t a . pool p r o f i l e s  Good agreement i s o b t a i n e d  between  computed u s i n g a f i n i t e d i f f e r e n c e technique  the e x p e r i m e n t a l l y o b t a i n e d  profiles.  and  134 APPENDIX 1 PHYSICAL PROPERTIES OF ESR  A.I.I !  SLAGS  Introduction The  c o r r e c t c h o i c e of s l a g c o m p o s i t i o n 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 p r o c e s s . The  s l a g b a t h i s the most important  the r e s i s t a n c e and  r e f i n i n g element.  t h e r e f o r e governed  by the p h y s i c a l c o n s i d e r a t i o n s such as  c o n d u c t i v i t y , l i q u i d u s temperature, etc.  The  u n i t i n the p r o c e s s .  It is  correct choice of slag i s electrical  v i s c o s i t y , d e n s i t y , vapor  pressure  and a l s o the c h e m i c a l c o n s i d e r a t i o n s such as d e s u l p h u r i z a t i o n ,  f  and removal No  of l a r g e o x i d e  inclusions.  coherent p i c t u r e has y e t emerged from the p u b l i s h e d data; a s ' t o  what c o n s t i t u t e s the requirements e s t a b l i s h s e v e r a l boundary (1)  f o r a u s e a b l e ESR  s l a g , but one  may  conditions.^  the s l a g must be c h e m i c a l l y compatible w i t h the m e t a l b e i n g  processed. (2)  the s l a g must have a l i q u i d u s temperature  below t h  e  melting  p o i n t of the m e t a l but a primary phase m e l t i n g p o i n t above t h a t of the metal. (31  the p h y s i c a l p r o p e r t i e s must be such t h a t the heat g e n e r a t i o n  i s e s t a b l i s h e d i n a u n i f o r m volume, o f a s i z e compatible w i t h r e q u i r e d heat The  balance.  first  c o n d i t i o n i s imposed^ by one of the prime o b j e c t i v e s of  the p r o c e s s i . e . , c a p a b i l i t y of improving metal.  the c l e a n l i n e s s o f the  I n c l u s i o n s such as s u l p h i d e s , o x i d e s , s i l i c a t e s e t c .  be removed.  the  can  G e n e r a l l y s p e a k i n g , the p r o c e s s I s one o f o x i d a t i o n , hence  135 precautions  a r e n e c e s s a r y t o minimize o x i d a t i o n  l o s s e s of these a l l o y i n g  elements such as S i , T i , A l which a r e p a r t i c u l a r l y prone t o o x i d a t i o n . The  second boundary c o n d i t i o n  i s imposed by the requirement  one must be a b l e t o immerse t h e e l e c t r o d e allowing The  a metal pool  i n the s l a g w h i l e  that  also  t o be bounded by a s o l i d s l a g s k i n .  t h i r d condition represents  meters i . e . , melt r a t e , v o l t a g e  the dependence o f p r o c e s s para<-  and c u r r e n t  on the p h y s i c a l  properties  of the s l a g . However, the requirements of a s u i t a b l e e l e c t r i c a l v i s c o s i t y , vapor p r e s s u r e ,  conductivity,  l i q u i d u s temperature e t c . , must be s a t i s f i e d  b e f o r e the s e l e c t i o n a c c o r d i n g  t o the c h e m i c a l p r o p e r t i e s  desired of  the s l a g 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. S l a g components a r e s e l e c t e d p r i m a r i l y on account o f t h e i r low vapor p r e s s u r e and h i g h have the a p p r o p r i a t e temperature.  temperature s t a b i l i t y .  e l e c t r i c a l conductivity  also  t o a c h i e v e the d e s i r e d  Other important c r i t e r i a are those o f v i s c o s i t y , d e n s i t y ,  thermal c o n d u c t i v i t y ,  l i q u i d u s temperature, vapour p r e s s u r e ,  f a c i a l t e n s i o n and thermal c a p a c i t y . and  The s l a g should  E l e c t r i c a l conductivity,  kinematic v i s c o s i t y are i n t e r r e l a t e d .  conductivity necessary f o r high high v i s c o s i t y .  dpnsity  Thus a low e l e c t r i c a l )  resistance heating  A l t h o u g h the v i s c o u s  inter-  i s accompanied by  s l a g may slow down the o x i d a t i o n  of r e a c t i v e elements, i t a l s o slows down the removal o f unwanted;  ;  components. The  most common choice  A ^ O ^ , MgO and Si02. added i n s m a l l  of s l a g constituents  i s between CaF^, CaO,  However, MgF2, BaF2> Ti02 e t c . a r e sometimes  q u a n t i t i e s to a c h i e v e a c l o s e c o n t r o l o f a p a r t i c u l a r  136  element. A l t h o u g h many s l a g compositions may r e p r e s e n t  equally  acceptable  optima, i n i n d u s t r y , o n l y a few s l a g c o m p o s i t i o n s , s e l e c t e d by e m p i r i c a l means, a r e used.  Knowing the p h y s i c a l p r o p e r t i e s o f the s l a g s , i t i s  p o s s i b l e to s i m p l i f y the multicomponent s l a g s used i n i n d u s t r y and a t the same time propose s e v e r a l a l t e r n a t i v e c o m p o s i t i o n s . At  the p r e s e n t  time, i n s u f f i c i e n t  p h y s i c a l p r o p e r t i e s o f the s l a g s .  d a t a i s a v a i l a b l e on the v a r i o u s  T a b l e XVIII summarises the a v a i l a b l e  l i t e r a t u r e on the 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 . the e l e c t r i c a l c o n d u c t i v i t y d a t a f o r C a F 2 A l 2 0 _  3  F i g . (86) g i v e s  slags.  21  Attempt i s made here t o measure the d e n s i t y and v i s c o s i t y of CaF2 based s l a g s .  A.I.2  Measurement o f D e n s i t y  A.I.2.1  of CaF2 Based  Slags  Introduction  In a d d i t i o n to i t s use i n the a n a l y s i s o f such p r o p e r t i e s as v i s c o s i t y and e l e c t r i c a l c o n d u c t i v i t y , d e n s i t y measurement i s o f considerable  value  i n the i n v e s t i g a t i o n s o f the s t r u c t u r e o f l i q u i d s .  It i s quite d i f f i c u l t  t o measure a c c u r a t e l y  temperatures of 1450-1750°C. CaF2 Al20 _  3  and CaF2~CaO b i n a r y  Previous  the d e n s i t y o f l i q u i d s a t  measurements o f the d e n s i t y of  systems have been r e s t r i c t e d t o below 6 8— 7 2  1600°C and c o n f i n e d mostly t o the R u s s i a n In t h e p r e s e n t two  binary  work, d e n s i t y measurements have been made i n the  compositions:  range 1450-1750°C.  literature.  CaF2-Al20.j, CaF2~CaO over the temperature  :  137  Table XVIII.  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  Property Phase s t r u c t u r e  Reference  System C a F - A l 0 , CaF -CaO, CaF 2  2  Ca0-A1 Q 2  3  2  58  3  Phase s t r u c t u r e  CaF -CaO-Al 0  Phase s t r u c t u r e  CaF -CaO  60  Phase s t r u c t u r e  CaF ~CaO  61  Phase s t r u c t u r e  CaF -Al 0  Phase s t r u c t u r e  CaO-CaF -2CaO-Si0  Phase s t r u c t u r e  CaF -CaO; C a F ^ A l ^ ;  2  2  59  3  2  2  2  2  62  3  2  63  2  CaF^CaO-  2  65  A 1 0 ; CaF -CaO-2CaO.Si0 ; 2  3  2  2  CaO-MgO; C a O - A l 0 2  3  64  Phase s t r u c t u r e  2CaO.Si0 -CaF  Phase s t r u c t u r e  Ca,0,-Ca_F,-Si.. ,-F,-Si 0, 33 36 1.56 1.53  66  Phase s t r u c t u r e  CaF -CaO-Al 0  67  Density  CaF -MF , MF  68  Density  CaF -Al 0 -CaO  69  Density  C a F - A l 0 ; CaF -Ca0; C a F ^  2  2  1  2  2  2  2  2  2  2  3  2  3  2  Al 0 -CaO; 2  3  70  CaF ~CaO-Si0 ;  3  2  2  CaF -CaO-Al 0 -MgO 2  Density  2  3  C a F ; CaF -MgO; CaF -CaO; C a F ^ 2  2  2  A1 0 ; CaF -Si0 ; 2  3  CaF -Si0 2  2  2  CaF -Zr0 ; 2  2  2  Density  CaF -CaO-Al 0 ;  I n t e r p h a s e and i n t e r f a c i a l tension  CaF ~CaO-Al 0  I n t e r p h a s e and i n t e r f a c i a l tension  CaF -MgO; C a F ^ C a O ;  2  2  2  2  CaF -Si0 -CaO  3  2  CaF -Si0 ; 2  2  72 69  3  CaF^Al^;  2  2  71  CaF ~Zr0 2  2  70  138 Table XVIII.  (Continued)  Property  System  Reference  I n t e r p h a s e and i n t e r f a c i a l tension  CaF -CaO-Al 0  3  Viscosity  CaF -CaO-Al 0  3  Viscosity  CaO-Al 0 -Si0  Electrical  2  2  2  2  2  conductivity  3  71  73,74 75  2  CaO-Al C> -CaF ; CaF -CaO, 2  3  2  BaO, MgO,  Ti0 , Zr0 , A1 0 2  69  2  2  2  3  E l e c t r i c a l conductivity  CaF  76  Electrical  conductivity  CaO-Si0 -CaF  Electrical  conductivity  CaF -CaO-Al 0  3  21  Electrical  conductivity  CaF -Al 0 -CaO  66  S p e c i f i c heat and  CaF^CaO; C a F ^ C a O - A l ^ - M g O  78  heat content  CaF -Al 0  Vapour p r e s s u r e  CaF„  2  2  2  2  2  2  2  77  2  3  2  3  79  139  A.I.2.2  Experimental  A.I.2.2.1  Apparatus  The apparatus i s based on 'the measurement o f the buoyancy It  i s shown s c h e m a t i c a l l y i n F i g . (87).  s t e e l base p l a t e w i t h r i g i d  force'.  I t was s u p p o r t e d on a s t a i n l e s s  support on t h e two s i d e s .  The molybdenum  l i n e d g r a p h i t e c r u c i b l e K (5 cm <J>, 10 cm h i g h ) was s u p p o r t e d by a h o l l o w alumina tube N c a r r y i n g a thermocouple the  c o n t r o l l e r o f the' i n d u c t i o n f u r n a c e .  0 which was a t t a c h e d to  The e n t i r e assembly was  e n c l o s e d i n a Vycor g l a s s tube P (7.8 cm d i a . , 48 cm long) l i n e d w i t h graphite f e l t was  L i n the h e a t i n g zone.  Oxidation at elevated  temperature  p r e v e n t e d by m a i n t a i n i n g a s l i g h t p o s i t i v e argon atmosphere  i n the  apparatus. The water c o o l e d i n d u c t i o n c o i l M e n a b l e d the maintainence o f a u n i f o r m temperature over t h e e n t i r e volume of t h e s l a g i n the c r u c i b l e . P r e c i s e temperature measurement o f t h e s l a g 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 t u b i n g w i t h a b o r o n - n i t r i d e sheath p r o t e c t i o n ) i n the melt J . A transducing c e l l  'A' (Statham's U n i v e r s a l t r a n s d u c i n g c e l l  model UC3) was used t o measure the weight  change o f the bob. F i g .  (88) g i v e s the 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 to operate the t r a n s d u c e r . A change i n weight of the bob caused a change i n the r e s i s t a n c e .  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 t o g i v e the weight  change  i n grams.  A molybdenum bob I (=5 grams) i n the form o f a r i n g was  suspended  from the t r a n s d u c e r by a tungsten w i r e H (0.025 cm d i a . ) .  Both t h e weight  change and temperature were s i m u l t a n e o u s l y r e c o r d e d by  two Sargent Model SR6 r e c o r d e r s .  The absence o f l a r g e s y s t e m a t i c e r r o r s  140  owing t o the thermal l a g between the melt and temperature s e n s i n g element  on c o n t i n u o u s measurement was  measurements, the bob was  varified.  c o m p l e t e l y immersed i n the m e l t ,  s u r f a c e f o r c e s a c t i n g o n l y on the w i r e . a t t a c h e d to the bob,  The  getting  as i n d i c a t e d by e r r a t i c b u o y a n c i e s , n e c e s s i t a t e d of the bob.  The  r e p e a t e d u n t i l r e p r o d u c i b l e and minimum v a l u e s of buoyancy  were o b t a i n e d .  A.I.2.2.2  leaving  The problem o f bubbles  the p r o c e s s of removal, c l e a n i n g and re-immersion p r o c e s s was  In a l l the d e n s i t y  F i g . (89) shows the e x p e r i m e n t a l s e t u p .  C a l i b r a t i o n and Measurement t r a n s d u c e r was  c a l i b r a t e d by suspending known weights  o b s e r v i n g the change i n m i l l i v o l t s .  1 g  =  Eq.  (A.1.1) g i v e s the  1.3 mV  e x p r e s s i o n and t h i s was  and  calibration  (A.1.1)  verified  The volume o f the bob apparent weight  >  frequently.  a t room temperature, determined  l o s s upon immersion  i n d i s t i l l e d water was  from i t s obtained  from the e q u a t i o n .  V  n  =  W t  3  - W ] w W  n  +  p  where the s u b s c r i p t s V  volume of bob  W  =  weight  p  =  density  o  'w'  r e f e r to a i r and water  at room temperature  of the bob (g cm  (A. 1.2)  SP  'a' and  =  Try d [—£-] w  3  )  (g)  3 (cm )  respectively  and  141  Y  =  surface tension  (dynes/cm)  d  =  diameter of s u s p e n s i o n w i r e  (cm)  g  =  a c c e l e r a t i o n due to g r a v i t y  (cm sec  )  The volume of the bob at room temperature was  determined each time  b e f o r e an experiment. The d e n s i t y o f the  melt was  c a l c u l a t e d from the f o l l o w i n g  equation W  - W a m V [1 + 3a(T-25)] o  m  where the s u b s c r i p t s  'a' and  'm'  +  =  temperature of the melt  a  =  linear coefficient i  where T  x  =  temperature (°C).  6  O N  and  (°C)  of expansion f o r the m a t e r i a l of the bob.  81  a  10  , -. (A. 1.3)  r e f e r to a i r and melt r e s p e c t i v e l y  T  For molybdenum,  irv d m T V g o  -T  =  5.05  + 0.31  x 10 T _ 3  + 0.36  x 10  _ 6  T  2  (A.1.4)  The s u r f a c e t e n s i o n data from the l i t e r a t u r e ^ ' " ' " f o r 1450-1600°C 7  range was  A.I.2.3 CaF  used a t a l l the temperatures  ( F i g . (90)).  Results 2  r i c h s i d e of two b i n a r y systems C a F ~ A l 0  investigated. Fig.  7  2  I n a l l the cases  Ap  w a  s  2  3  and CaF -Ca0 2  was  l i n e a r w i t h temperature.  (91) and F i g . (92) g i v e 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 .  142 A.I.3  Measurement o f V i s c o s i t y of CaF^  A. I.3.1  Based  Slags  Introduction  V i s c o s i t y i s an important p h y s i c a l p r o p e r t y of f u s e d s a l t s . determines, i n p a r t , the r a t e of f a l l s l a g and may  It  of m e t a l d r o p l e t s through the  a l s o i n f l u e n c e the r a t e s of c e r t a i n r e f i n i n g  through i t s i n t e r r e l a t i o n s w i t h d i f f u s i o n  liquid  reactions  rates.  As i n the case of most o f the o t h e r p h y s i c a l p r o p e r t i e s of 73 based s l a g s , p r e v i o u s work i s s p a r s e and i n c o n c l u s i v e .  CaF^  74 '  Davies  73 and Wright  i n t h e i r r e c e n t paper have r e p o r t e d the v i s c o s i t y  f o r some CaF^ i n ESR  based  s l a g s up to 1500°C.  data  As the o p e r a t i n g temperatures  p r o c e s s are h i g h e r than 1500°C, measurement of v i s c o s i t y at  h i g h e r temperatures A. I.3.2  (1500-1650°C) i s attempted  here.  Experimental  A. I.3.2.1  Apparatus  The apparatus  i s based on the r o t a t i n g  crucible principle.  t h i s method, the torque e x e r t e d on the s u s p e n s i o n w i r e through i n n e r c y l i n d e r immersed i n the l i q u i d s l a g c o n t a i n e d i n the  In the  rotating  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 o f light  i n c i d e n t on the m i r r o r a t t a c h e d t o the suspended Fig.  assembly.  (93) g i v e s a schematic diagram of the a p p a r a t u s .  l i n e d o u t e r c y l i n d r i c a l g r a p h i t e c r u c i b l e V was W connected  The molybdenum  supported on a s h a f t  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  i n n e r molybdenum c y l i n d e r T was  alumina tube M c a r r y i n g a thermocouple  a t t a c h e d t o the end o f ; t h e  0 (W/W-26% Re thermocouple  in  143  a twin bored alumina s h e a t h ) .  The e n t i r e assembly was  a t t a c h e d to the  s u s p e n s i o n w i r e G (0.012 cm d i a . t u n g s t e n w i r e ) by a s t a i n l e s s frame I c a r r y i n g  the m i r r o r H.  brought out through a s l i t  The l e a d s of the thermocouple  steel 0 were  i n I and connected to molybdenum w i r e s K  supported i n a b r a s s r i n g J . When the i n n e r molybdenum c y l i n d e r T was  immersed i n the  liquid  s l a g , the molybdenum l e a d s K were immersed i n s e p a r a t e p o o l s of , mercury  L which were connected t o a Sargent r e c o r d e r (Model SR 6) f o r  temperature measurement.  F i g . (94) g i v e s a c l o s e - u p view o f the  assembly. The e n t i r e assembly water  i s e n c l o s e d i n two Vycor tubes F and Q w i t h  c o o l e d bases N and X r e s p e c t i v e l y .  i n n e r c y l i n d e r was  Constant immersion  a c h i e v e d by h a v i n g a graduated stem A.  o x i d a t i o n , argon gas was  To  of the  ;  avoid  f l u s h e d c o n t i n u o u s l y through B at s l i g h t  p o s i t i v e pressure. Uniform h e a t i n g of the s l a g bath U was heating.  The Vycor tube Q was  a c h i e v e d by  induction  protected with a graphite f e l t  j  •  lining  •  S i n the h e a t i n g zone. A gas l a s e r was  used as a l i g h t  r e f l e c t e d beam from the m i r r o r H. ment.  source to o b t a i n a u n d i f f u s e d  F i g . (95) shows e x p e r i m e n t a l e q u i p -  The d e f l e c t i o n of the beam of l i g h t  caused by the torque e x e r t e d  on the s u s p e n s i o n w i r e i s measured on a s c a l e mounted behind the l a s e r .  A.I.3.2.2  Procedure  Weighed amount of s l a g was induction heating.  melted i n o u t e r c r u c i b l e under argon by  A f t e r the s l a g was  molten, the i n n e r molybdenum  144  c y l i n d e r was  s l o w l y lowered i n t o a d e s i r e d  s h a f t A.  o u t e r g r a p h i t e c r u c i b l e was  The  speeds and  the  r o t a t i o n was  d e f l e c t i o n measured.  used and  p o s i t i o n by  rotated  lowering  the  at v a r i o u s known  Both c l o c k w i s e and  anticlockwise  a mean d e f l e c t i o n measured f o r each speed  of  rotation. By  changing the power i n p u t ,  temperatures.  Measurement was  the  s l a g was  c a r r i e d out  heated to v a r i o u s  a f t e r steady temperature  had  been o b t a i n e d .  A.T.3.2.3  Calibration 82  I t has  been shown  that when the  f o r the i d e a l case of i n f i n i t e l y  outer cylinder  torque produced on  the  inner cylinder  4rrLWnr T  2  r„  2  -—r  suspension.  the  a n g l e of  I t i s e q u a l to K6  inner  the  where 6 i s the  inner cylinder,  e t c . have to be  I f dimensions of  bottom c l e a r a n c e and  caused i n  the  angular  c o e f f i c i e n t of v i s c o s i t y i s end  accurately  approach i s to c a l i b r a t e the  known v i s c o s i t y .  twist  cylinder.  f o r stem of the  l e n g t h of c y l i n d e r s  reduces to  is  1  I f a b s o l u t e measurement of  a much e a s i e r  the  (A.1.5)  displacement of the  corrections  cylinders  2  torque i s measured by  calibrated  at c o n s t a n t v e l o c i t y ,  =  r  r  The  i s rotated  long  the  e f f e c t due calculated.  to  desired,  finite  However,  apparatus a g a i n s t l i q u i d s of  cylinders,  depth of  immersion,  t o r s i o n w i r e are kept c o n s t a n t , e q u a t i o n (A. l.<5)  145  n  where K^  =  K^t  (A. 1.6)  i s found e x p e r i m e n t a l l y .  The v a l u e o f K^ was  calibrating  the apparatus a g a i n s t l i g h t o i l s ,  phathalate.  The v i s c o s i t y o f these o i l s was  determined  by  H y d r o d r i v e and D i n o n y l first  determined  accurately  using Brookfield s y n c h o - l e c t r i c viscometer.  A.I.3.2.4 (1)  Errors Involved Dimensions  apparatus was  of the C y l i n d e r s :  As the c a l i b r a t i o n o f the  done at room temperature, c o r r e c t i o n has  the expansion o f the i n n e r  to be made f o r  cylinder  Kflt  -4~  n =  (A. 1.7)  L -L where  E  «  where L  =  l e n g t h o f c y l i n d e r at t°C  =.  l e n g t h o f c y l i n d e r at room  L  q  1 + 3 {-y—-} o  (A. 1.8)  temperature.  For molybdenum c y l i n d e r , the. e r r o r i n t r o d u c e d , i f the expansion f a c t o r i s o m i t t e d was (2)  2.7% at  1600°C.  Depth of Immersion:  The i n n e r c y l i n d e r was  same e x t e n t i n each experiment. the volume of the l i q u i d  s l a g had  To a c h i e v e c o n s t a n t depth of to be kept c o n s t a n t as w e l l .  the d e n s i t y a t 1600°C f o r C a F 2 ~ A l 2 0 the s l a g was  lowered to the  3  immersion, Knowing  b i n a r y s l a g s , the t o t a l weight  so chosen, as to g i v e a c o n s t a n t volume f o r each  slag  of  146  composition a t 1600°C.  However, an e r r o r  (= 1%) i s i n t r o d u c e d by the  i n c r e a s e i n the depth of immersion due to the decrease w i t h i n c r e a s e i n temperature (3)  i n slag density  o f the s l a g from 1600°C and v i c e - v e r s a .  The o t h e r p o s s i b l e sources of e r r o r a r e  (a)  l a c k of alignment  of the c y l i n d e r s  (b)  temperature  (c)  t u r b u l e n t motion i n s l a g a t h i g h speeds o f r o t a t i o n  (d)  s l i p between c y l i n d e r s and s l a g due to non-wetting  (e)  the s u s p e n s i o n w i r e b e i n g n o t p e r f e c t l y e l a s t i c over the t o r i o n  measurement  angles  involved. Care was taken to see t h a t e r r o r s due to ( a ) , (b) and (c) were o  avoided.  As the C a F 2 - A l 2 0  was not p r e s e n t .  3  s l a g s do wet molybdenum, e r r o r due t o s l i p  The e r r o r i n t r o d u c e d by the n o n - i d e a l b e h a v i o u r  of the  tungsten s u s p e n s i o n w i r e 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 o f the CaF2 r i c h s i d e of C a F 2 ~ A l 2 0 system was c a r r i e d o u t . of  3  binary  F i g . (96) g i v e s the v a r i a t i o n of c o e f f i c i e n t  v i s c o s i t y w i t h c o m p o s i t i o n a t 1600°C.  F i g . (97) g i v e s 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 w i t h temperature the e x p e r i m e n t a l d a t a w i t h the d a t a of Davies  and compares  and Wright.  73  147  APPENDIX I I CALCULATION OF THE RESISTANCE  OF THE VOLUME ELEMENTS IN THE VOLTAGE  GRADIENT ANALYSIS  A.II.l  Introduction  A segment o f one r a d i a n o f t h e s l a g b a t h i s s u b d i v i d e d i n t o volume elements as shown i n F i g .  A.II.2  C a l c u l a t i o n of R  R  =  z  A  (12).  z  ^  C a l c u l a t i o n o f 'A': Fig. bath.  (98) g i v e s a schematic diagram o f the segment o f the s l a g  The volume elements a r e c l a s s i f i e d  as shown.  i n t o groups M, N, 0 and P  The volume elements 9 and 13 w i l l be c o n s i d e r e d s u b s e q u e n t l y .  Hi  =  =  ^rT  X  3^0  X  ^  4  A  A  r  )  r  2  -  Obr) ] 2  2 Ar  Similarly  3.2 \  =  2  A  r  ;  A  0  C a l c u l a t i o n of % : I  =  2  ;  .  Ar  2  h  = Az f o r each o f t h e volume elements.  i s p o s s i b l e t o s u b d i v i d e t h e r e s i s t a n c e R^ i n t o two e q u a l h a l v e s o f R 12. z  It  148 A,II.3  C a l c u l a t i o n of R  R  -  r  r  r  1  A Ar —^  C a l c u l a t i o n of £ : £ = R  f o r each o f the two s u b d i v i s i o n s of  r C a l c u l a t i o n of A :  s u b d i v i s i o n s of R^_  \  H  ( F i g . (99)).  180 —  = S  1  l e f t hand  K AHS  A  °LHS  =  Ar  2*  T  X  T  r  AZ;  RHS  Az ;  A  3 .  A. II.4  =  Ar  A  .  r  ]  A  z  Similarly  =  -  Ar  Az  =  |  Ar  Az  Ar  Az  H  .  Az;  C a l c u l a t i o n of R^ and  The exact  \  9  A  RHS  Ap LHS  +  2  A  Ar  { Ar  A  r i g h t hand s i d e .  A  1  4 r [  Az  s i d e ; RHS:  1  =  1 360  X  A  5  —  LES:  The v a l u e of A i s d i f f e r e n t f o r the two  1_  A^ RHS  =  -74-  R^^  c a l c u l a t i o n of 'A' and  ' £' f o r elements 9 and 13 i s  complicated.  Approximate v a l u e s o f A and £ are used i n the  and are g i v e n  below:  analysis  R : V l 2  R^: 9  R  A  =  4  A  =  - Ar Az;  A  g  9->electrode  R  1 3  ^  :  A  2  =  =  13+electrode*  =  2,  =  5 6" A  — 3  -~ Ar  2 A  5 2 j-j- Ar ; Jl  z  ^ * ~  ;il  =  Az/3  1 r  A  R  I *  5/5* " ~2  A  A  : 1 7  13->-12  R  !  Ar »•  A r  A z  '  ^  =  —  6  3"  A  r  2 ;  £  APPENDIX I I I  COMPUTER PROGRAMME TO DETERMINE THE TEMPERATURE GRADIENTS ON THE MOLD  PROGRAM :  C C C C  c c  PREDICTION OF TEMPERATURE PROFILES ON E . S . R .  PROGRAMMER :  SATISH  LEAST SQUARE FIT ROUTINE AVAILABLE PROGRAMME LIBRARY  F -  SHAPE FACTOR  LI-  LAMDA  0001  ELECTRODES  USED IN U B C ' S GENERAL  REFER TD THE WRITE-UP LQF FOR THE i E A N l l G NOT DEFINED IN THE PROGRAMME  c c c c c c  P45E  JOSHI  L I S T OF ABBREVIATIONS LQF :  12:07:08  05-23-71  MAIN  FORTRAN IV 6 COMPILER  3F THE PARAMETERS  INFINITY  LS= LAMOA STAR 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 TIIJ-  TEMP AT THE CENTRE OF THE ELECTRODE  IS I 11= TEMP AT THE SURFACE OF THE ELECTRODE NU=  0001 0002 0003 0004 0005 0006 0007 0008 0009  0010 0011  NU AS DEFINED IN THE TEXT  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 1TS(300I,A,L.NU,LI.LS.E COMMON A , L , P Y , M A , N U , L I , L S , E , B COMMON/A1 / P EXTERNAL AUX PY-3;U1593 READI5,1)EP FORMAT! E 1 0 . 5 ) READI5.2IL.LI.LS.E.TO FORMAT! 8 F 1 0 . 3 I URITE(6,3IL,L I,LS.E,TO' FORMAT! IHO,*HL » , F 8 . 2 , 3 X , 1 1 H L A H D A I N F > , F B . 2 , 3 X , 12HL AMDAST A * • , 1F8.2.3X.13HENISSIVITY • ,F8.2,3X,5HT0 « .F10.3I  FORTRAN IV 6 COMPILER  >~  1  !  !  i  0012 001) 0014 0015 00l« 001T 0018 0019 0020 0021 0022 0023 0024 0025 0026 0027 0028 0024 0030 0031 0032 0033 0034 0035 0036 0037 0038 0039 0040 0041 0042 0043 0044 0045 0046 0047 0048 0049 0050 0051 0052 0053 0054 0055 0056 0047  4 5 A 7 8 9 10 11  MAIN  13 14  15  16 17 18 19 20  P»SE 0002  >  !  j I !  i  |  t  TO  2.7  SEC0N3S  i  I  18  WRITEI6.12I FORMAT(69H ESTIMATES OF ROOT MEAN SQUARE TOTAL ERROR IE PARAMETERS! WRITE(6,13I <E2(II,I«1,MAI F0RMATI1X,(8E15.5II WR1TE(6,14> FORMAT(12X,lHX,17X,10HAXIAL TEMP,12X,12HSURFACE TEMP) 00 17 I - l . N A SUN'O.0 sum=0.0 00 15 NN-l.MA N«NN-1 Fl«(2.0*FLOAr(NI»l.0 1*PY/(2.0»LI S1«P(NN)*SIN(F1*X(I II SUM*SUM+S1 SUM1-SUM1* S1*BESSI0IF1I CONTINUE TII)»1.0*SUN T i l l - TO*T(Il TS(I)=1.0*SUN1 TSH)=TO*TS(II WRITE(6.16I X I I ) , T i l l , T S U I F0RMAT(7X,F12.7,8X,F14.7, 8X.F14.7I CONTINUE GO TO 8 WRITE(6,19) FORMATI1X.19HEQUATI0NS UNSOLVED//) GO TO 8 CONTINUE END  TOTAL MEMORY REQUIREMENTS 00241C BYTES COMPILE TME -  12:07:08  READ! 5.41 NA.NA.II FORMAT 110 19 1 WRITE 16,51 MA FORMAT! IH ,32HNUMBER OF TERMS IN SERIES » .15 1 WRITE(6 ,6) NA F0RNATI1H .35HNUMBER OF POINTS ON BOUNDARY - .151 DO 7 1-l.MA X I I l»(L/FLOAT INAI»« (0.5 + FLOAT I 1-111 REA0(5.9>B>NU.AilP( I) iI>l,MA) FORMAT I3FB.3, ITE8.1 I I IFIB.EO.O.OIGO TO 20 WRITEI6.10IB.NU.A FORMAT 11H0 .7KBETA • , F16.7. 5X. 5HHU » ,F8.2,5X 4HA = .F16.7I 00 11 1*1,NA Y( 11-0.0 CALL LQFIX,Y,YF,W,El,E2,P,0.0,NA,MA,(ll,MO,EP,»UXl IFINO.EQ.OIGO  12  05-23-71  IN  TH  I  1  !  FORTRAN IV G COMPILER 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 0028 0029 00 30 0031 0032  21 22  23  AUX  12:07:10  PAGE 0001  FUNCTION AUXIP.O.X.II COMMON A,LtPY,MAtNU,Ll,LS,E,B DIMENSION P I 1 3 0 I . O I 1 0 0 I HEAL L.NU.LI.LS 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. O H - ( 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 ( F 1 ) * S I N ( F 1 * X I F3- BESSIOIFl >»S1N1F1»X) SUM2-0.0 SUM3-0.0 00 21 J J - l . M A 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( J J ) * F * * F 8 * F 6 SUM3-SUM3 +P(JJ>*F7*F6 CONTINUE , 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 =  05-23-71  1.4  SECONDS  154 APPENDIX IV CALCULATION OF POWER REQUIREMENT FOR MAKING AN INDUSTRIAL SCALE INGOT  Assumed  Data:  1.  diameter o f the e l e c t r o d e :  45.72 cm (18 i n c h e s )  2.  diameter o f the i n g o t :  61.0 cm (24 i n c h e s )  3.  electrode composition:  V i b r a c EN 25 (B.S.C.)  4.  s l a g composition:  CaF ~25 wt. % A l ^ O ^  5.  height  16 cm  6.  E l e c t r o d e immersion:  7.  height  2  of s l a g cap:  1.5 cm  o f the c y l i n d r i c a l  portion  of the l i q u i d m e t a l p o o l :  7.5 cm  8.  height  250 cm  8.  approximate melt r a t e :  o f the i n g o t  258 g s e c  1  To c a l c u l a t e the power r e q u i r e m e n t s , the t o t a l heat l e a v i n g the system w i l l be c a l c u l a t e d and then equated  to the r e q u i r e d heat  input.  From the e x p e r i m e n t a l data ( F i g . (49) t o F i g . (56)) i t i s c l e a r t h a t the themperature  profiles  on the mold are independent  the e l e c t r o d e and the i n g o t . profile  of the s i z e o f  Thus assuming an approximate  temperature  i t i s p o s s i b l e to c a l c u l a t e the heat l e a v i n g the system.  A temperature assumed.  profile  The heat l e a v i n g the  p r o p o r t i o n a l t o the r a t i o industrial  on the mold, s i m i l a r to F i g . (49) w i l l be 61  cm diameter mold w i l l be assumed  o f the areas between the  s c a l e i n g o t and the 8 cm diameter i n g o t  61  cm diameter  ( i n g o t no. 1 ) .  155 Heat Output: (1)  =  heat r e q u i r e d to melt the e l e c t r o d e and  d r o p l e t s by  100°C  1066.5 =  =  C2)  =  superheat the m e t a l  0  -3736-  X  _  ft  2 5  8  82 K c a l sec  heat l o s t by  1  r a d i a t i o n from the s l a g s u r f a c e to the mold  c o o l i n g water  n «n 0.650 x  5.0  (3)  =  61.0 —g—  K c a l sec  heat l o s t  1  to mold c o o l i n g water across  2.597 x ( ^ ) 70 K c a l sec  CA)  Qc,  = heat l o s t 2401  = —  -  (5)  Q, o  =  540  1  x  c—)  1  to the  (~^-  )  c o o l i n g water a c r o s s  =  4.1  Kcal  sec"  to assume Q  =5.0  the s o l i d i f i e d  ingot  1  i n c r e a s e i n the l e n g t h of i n g o t should  However, i t i s reasonable  the l i q u i d m e t a l p o o l  ,10,  x  K c a l sec  heat l o s t  = The  ,61.0.  bed  (^5)  to the c o o l i n g water a c r o s s  C—)  45.6  x  the s l a g  a l s o be  K c a l sec  1  considered. as v e r y  little  156  heat  leaves  mold  cooling  (6)  across  the extra  length  lost  to base p l a t e  =  0.410 X  =  31.2 K c a l  sec  1  leaving  height  increases,a  of the ingot  cooling water  ( ^ r V o  However as t h e h e a t  the bottom of the ingot value  of  decreases  = 25 K c a l  sec  as t h e  appears  1  reasonable.  C7)  Qg  -  Sensible  •PIT3. 36  Total  heat  Thus above  error  =  0 . ZA o  the t o t a l  heat  calculation  cylindrical  across  portion  power  V  =>  31.4 K c a l  +  Q.  +  0  sec  C  +  1  Q, o  +  Q_ /  +  5  5  should  be a p p r o x i m a t e l y  Q  =  Q  o  1  i s very  approximate.  i n t h e t e r m Q^  the l i q u i d  However  i . e . , heat  metal pool.  of the l i q u i d metal p o o l  most lost  The h e i g h t adjusts  182 K c a l  sec . 1  of the  to the of the  itself  t o the,  input.  power i n p u t  If  =  input  c a n be accommodated  actual  r e t a i n e d by the i n g o t  182 K c a l s e c "  c o o l i n g water  Total  heat  x 0.404  output  =  The  to the  water.  = heat  more  of the s o l i d i f i e d ingot  =  182 K c a l  -  760 K w a t t s  40 v o l t s ,  sec  the t o t a l  1  current  input  should  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 s i d e s by homogeneous m a t e r i a l (Fig. 100(a)).  The temperature of a g e n e r a l n o d a l p o i n t X  time t = k i s d e s i g n a t e d as T  .. r,z,k  at  r, z 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 temperature of t h i s n o d a l p o i n t a t time t = k + 1, knowing the temperatures o f the s u r r o u n d i n g n o d a l p o i n t s a t t = k. 54 Using the f i n i t e d i f f e r e n c e form o f eq. ( 6 . 1 ) , of the n o d a l p o i n t X C p -2— At  +  at t = k + 1 i s g i v e n by the f o l l o w i n g e q u a t i o n  k A volume [T , ., - T .] = — — r,z,k+l r,z,k Ar  k A k A — — - TT - T 1 + Ar r+l,z,k r,z,k Az  T  r,z,k  the temperature  [T . . - T ] r-l,z,k r,z,k k A  fx  - T  r,z+l,k  1 +  [T  r,z,k  Az  J  r,z-l,k  ( A  - V  1 )  where (1) k^ i s the average c o n d u c t i v i t y f o r the temperature range o f T  , to T , etc. r-l,z,k r,z,k 1  (2)  volume of the element: volume =  =  a r e a of the base x h e i g h t  ^ - [(rAr + ^ ) 2TT  I  Z  - ( r A r - ^ f ) ] Az = 2  I  r Ar  2  Az  158 (3)  c a l c u l a t i o n of the area F i g . (100(b)) gives a schematic diagram f o r the area A^  A^  =  shaded area 2TT  , r  (  [  r - L. . , .  +  f  2x7  2  (  )  2  =  2r" + 1 ( — ) Ar Az  A^  =  r Ar  =  2 r ir  A. 4 MR  2  C Ar P k At  2  p C Az 1 P. k At  2  ±  p  MZ 3 MZ  2  C Ar P k At  1  MR,2  ]  2  p  Let  r  *) Ar Az  2 r  s i m i l a r l y A^  l  A  =  2  =  3  2 C Az P . k. At 4 p  4  =  On s u b s t i t u t i n g these values i n eq. (A.V.I), one obtains T  +  r,z,k+l  MZ^  [T  - T  = c?- ~^—1 TT r  r,z,k  2rMR^  r,z+l,k " r , z , k T  ]  +  r-l,z,k  MZ^  [ T  - T  r,z-l,k  r,z,k  _  T  1 +  J  r,z,k  v  f  2  r  +  )L TT  1  2rMR ' 2  ]  r+l,z,k  (A.V.2)  - T  r,z,k  J  1  159  Case 2 For a g e n e r a l p o i n t on the upper s u r f a c e as shown i n F i g . (101), the temperature a t t = k+1 i s g i v e n by the f o l l o w i n g e q u a t i o n .  C  p volume  k, i  ^? ?  A  —2  [T - T 1= r,z,k+l r,z,k  At  A  [T - T ] + r-l,z,k r,z,k  Ar  k  r+l,z,k  T  r,z,k  r,z,k  top  3  r,z+l,k  4  r,z,k  x Ar  A 4  Az  r,z-l,k  ]  (A.V.3)  r Ar •—-—  Az . . Ar Az  2  where volume =  A  x  =  ^r-l. (—4-)  A  2  =  (—^j—) Ar Az  A^  =  r Ar  A  «  r Ar  4  2  2  h. i s the heat top  transfer coefficient  f o r the top s u r f a c e ,  Oil s u b s t i t u t i n g these v a l u e s i n (A.V.3) one o b t a i n s  T  r,z,k+1  T  r,z,k  2h T  r,z,k  J  +  p  C  t Q p  ^2rMR *  [ T  r-l,z,k  T  r,z,k  At Az  ]  +  (  2rMR  ) [ T 2  r+l,z,k  2  [ 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 g e n e r a l p o i n t as shown i n F i g . (102)  _ T  T  r,z,k+l  [ T  iff) I\ 4(2r-l)  =  r,z,k  r+l,z,k " r z,kT  MR (4r-l) 1  1  MZ^"  +  5  T  r,z,k  r  [ T  L  _  T  i  T  r-l,z,k  r,z,k  r,z+l,k ~ r,z,k^ T  +  8 h .,  r At  side  +  (4r-l) p C  J  MZ^~  [ T  Ar  r,z-l,k ~  '  ]  p  i  <'-> A  V  5  Case 4  TT  -  T  r,z,k+l  r,z,k  1  f UT ^rMR^ r-l,z,k  =  2  J  1  2 h  1+  T  T  r,z,k  J  r,z,k  ]  p  p Az  +  /  2  r  +  \  1  4rMR  J  At  r  M 2  T  r+l,z,k  9  P-2JE  C  _ T 1 r,z,k  1  r  TT L  r,z-l,k  - T r,z,k  1 + —— TT J  MZ  L 3  r,z+l,k  ( A  - ' V  6 )  Case 5 For a g e n e r a l p o i n t as shown i n F i g . (103)  C  r,z,k+l  T  _ X  r,z,k  i] + r,z,k MZ^  4 = — — TTr + l , z , k MR 1  [  T  1 - T 1 H — r,z,k MZ  , , - T .] r,z-l,k r,z,k  J  1  TT r,z+l,k  (A.V.7)  161  Case 6 For a g e n e r a l p o i n t as shown i n F i g .  _  T  T  r,z,k+l  = r^2v-l) r,z,k (4r-l)MR '  ,  1  1  r+l,z,k  {_?_} MZ l  J  4  1  _  T  r,z,k  J  +  C  { p  _ r-l,z,k  1  2 h l T  (104)  , r,z,k  • side (4r-l)pC 8  J  r  h  p  : Ar '  At  f c o  At  * r,z+l,k [ T  _  T  r,z,k  ]  +  - T ,1 r,z,k  fx ' r,z-l,k  A t  l  (A.V.8)  J  Case 7  .  p  -  r,z,k=l  [ T  [ T  T r,z,k  -  1  i I"T 1  1  r+l,z,k " r,z,k  z-1 k " r z k T  ]  +  {  _ T  i r^r  (4r-l)MR ^  T  r  -, \  rr,  4 ( 2 r - ;l )  - r^ f  2 MZ " }  r-l,z,k  I 4. /  +l  - T 1 r,z,k J  1  3  r,z+l,k ~ r,z,k T  ]  +  S  L  D  E  >  ( 4 r - l ) p C Ar' p  bot Az p C 2  [ T  8 r h . , At  {  h  A  t  }  ?  ]  ( A  ^-  9 >  Case 8 For a g e n e r a l p o i n t as shown i n F i g .  T  - T = r,z,k+l r,z,k  fT  1  l  ( -} \T MR/ r+l,z,k 1  - T 1 + {- —} r,z,k m ^ 2  r,z+l,k  J  x  J1  (105)  2 h At - T 1 + { ^2 } r,z;,k p C Az  [T „ , r,z-l,k  J  - T ,] r,z,k J  (A.V.10)  Case 9  T  r,z,k+l  - T  r,z,k  =  { MR„'  }  ^ r + l , z , k ~ r,z,k-' T  T  +  *MZ,  •} [T  r,z+l,k  163  APPENDIX VI COMPUTER PROGRAMME TO DETERMINE THE POOL PROFILES IN ESR  INGOTS  ow c h a r t o f the computer programme  Q~Start~A Read Data  A s s i g n an i n i t i a l temperature f o r every n o d a l p o i n t  C l a s s i f y every n o d a l p o i n t i n t o one o f the 9 p o s s i b l e cases  C a l l the s u b r o u t i n e t o read the p h y s i c a l p r o p e r t i e s a t a l l  1=1,NN J = 1,N  Compute the temperatures at a l l nodal points, i . e . evaluate A „. The p h y s i c a l p r o p e r t i e s 1, J , z being A  taken f o r temperature  I,J,1-  C a l l the s u b r o u t i n e to read the p h y s i c a l properties at A  I,J,2  I = 1,NN J = 1,N  t Compute  the new A  „ at a l l 1, J , z n o d a l p o i n t s , t a k i n g average temperature between A - and 1, J , l A f o r e v a l u a t i n g the p h y s i c a l 1, J , z properties 9  Yes  Define  A  .. = A  „ L ,J , Z  I n c r e a s e the time  [sunit  step  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 a x i s reached the maximum i n g o t length  Yes  ' " i t . Vt  'V  .»  C J . V I U . ' .  J O - i i - II  ( W .  PAkic 0031  ItHliftt  i: L  f>-kJFILES IN A\ E . S . R .  rc1Pc.<^ru<r  AbdREVlATI  C k, (. C C _C f. C  k.  t  C _C C C  0 L  I  Uriuht  J  :U^.>1 M Jl 'JAL AXI i  f.  :(Mc  AXIS  ni.J.M^c'^.wW*  N J J 4 L  (I.JiKI  PU1NT  TEMPERATURE LUC4TI0N FOR NOJAL POINT l i . J . O  J d . ^ . i W M E M P c K A T U K c UF THE ELEMENTS IN THE TOP LAYER ;)II.J.U-koll« k..'(  JtL  JIILK  I  |.-IL*1AL  : I  HEAT  ;JF VJLU.1E ELEMENT AT ( I . J . K I  C j N I J J C r i V i r Y (JF VOLUME ELEMENT AT (I.J.K.1  iHc i'.C.il  ILMT  l o l i i : J r 1 He VdiJ.'lt ELEHeNT IN K J I R E C T i : ) *  JcL£  C  'JF VDLJrtc ELEMcHT AT I I . J . l O  : jf'Lk.1 i-'iC  I . J.KI  i d • J.iO :  C  J>=  THC  VJLUML  <l  :  NN  !iWrtJc« OF cl c 1; -\ \  Jf  E L E ^ E N T  1 <lik)T  AT  ANY  NAJRY  :  I PJR AKHVIXI felr. EVALUATION  k.  •i^jif  :  I  JF i»  3  IN THt  I  IN  C C C C C L C C C kk. k.  USED  AXIS  .kl I . J . O : I ct;';.< ATU*e AT  C C >. c  C  J * S  l^lkiOT  D I R E C T U M  TIME  RADIAL  UIKECT  I3H  : NF»ocL^: MAAliiJiH lNJJT HfclliHT :  IJ'V-IUL A I I VL ALLJrfAdLE E^ROR FJ\  .UXJRAIE  c V.iLUA TI J->»  "4.(AIE  : \\\*S u ' J t l . r : I ' M C :ttT«r:S^ Nfc* VflLUMt ELEMENT AkldlTION  H.,13,-  : riEAl r .-iA.NJF E K l JE F F I C 1 :-N T F i R THE S U E XAI 1 S  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 I V  ^ oJHPlLtx C C k  J6-^'.-/I  HAi.«  JJY4  l'J/AI  Ha J l  :  J/»  HlJrl  F J *SjKFACt ACMISS  Ai..wib  I HE  Trtt  : i j i t ^ j . J T I He  PACE  JJ02  uURl.v;  UJII.M  JF THE 1NGIH  >LAi»/METAL  J / M I - U * MuLU COOLING  : Pi|Y*>*.,  is:l2:<»4  I>'Uti<rACr  rfAIER  JO e V A L U A f t  Al  THE i l U I FUH  T.lc PHYSICAL  C<Ur»t: R T 1fcS  uSSdMrUUNS  JJt.il i i u n ii-i  r  T i-u 11:4 :  -.11'-."..* T !•->•) 0004 n'»0 *: 'U'0 7 0:10:)  : .2-<•>. j jJd.J  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 Ml l j . J U l . D < 1 J . 5 0 . 2 I . 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 ruKMaTlof lj.:>) >ml I r I n . . T j l , J I L K . , i r L / . D r l T ? . ) K ' U I | i X . / H ) L L « = . F 1 J . 3 . 2 H C M . S X . 7 H D E L Z = . F 13 . 5 . 2 H C M . S X . 1 7 n j L L I = . r I J . •> , J H S L C )  «*1  Ictu.uiJ.1ilL,r.HIDr>,Hoyr.HMUr.HSOT  r J K M A I ( j X . J H H j i U c = . H O . 5 . 5 X . 7 H H T d r = , F 1 0 . 5 . 5X . t = . tJA.7HH.-ljr = ,f l 0 . b O X , 7 H H S j r = . F 1 J . 5 I KLAOI S. 2<i<KAIt..MF . N . . J N . 7 Y 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 iX.dH'litArE = .IJ.bX.5HHE = . I 2 . 5 X . 4 H N = . 1 2 . 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(ro Jif..c^O »\C -r•C O £.CO V v i r r , r j f \ . r \ , r \ r r \ c v o c re c c c c ~ r>o «Jcin > c p» c r c c c c C C C C * f, <N:Cv N f M t f> \ c evc c o c o cccrc cc ccc *T I T  r.  —  IT IT T <T f*. «\ r . *\  IT.  — • CN.  *r  c  f\  r  N  T?  fM  to  f\J rsj  C ' fV C ; f\ f\. f\.  172  i O O I -t  O  O  f> Ol O O O D -*  T  J  O  •!  o ^ n *- *!• Ix  -i —  .3  > "3 II  :3  II  -5  "3  II  II II  — — n <  I —  -)  C  c o  C o c  ^  •  T  O  1  •  T  O  r- rr  O  O  Cj  c  c  o  c  o  c  C  c  «c  --t  p—  cn f c —' - * cv  11  <  —  ~  oc cc o co o co c- c o c o c c C' c o o o c *f I T ^  r  —  —4 A —•  -  cc r\j c. c  O* f\ o o  O m o o  —< rv rr «r i r C ro f ^ c c o c c  *f cr C -"" |T  oQ  »t  c— M stir f ^ -a" * C O O O c- O O O  sc  co t r  -T  OO C o " c  •*  O o  C c  173  BIBLIOGRAPHY  1.  G.K. Bhat: P r o c . Second I n t . Symp. on ESR Technology, M e l l o n I n s t i t u t e , P i t t s b u r g h , (IX, 1969).  Vol. I,  2.  W. H o l z g r u b e r , A. 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(Tokyo), 9_, pp 39  C1969). 78.  S.E. V a i s b u r d , P.P. E v s e e r , I.N. S e d i n a , A. I a , Stomahin: I z v . V y s s h i k h . Uchebn. Z a v e d o n i i ( F e r r . M e t . ) , 5_, p 54-56 (1969).  79.  D.A. Shulz and A.W.  80.  S. Cantor, W.T. Ward, C.T. Moynihan: pp 2874-79 (1969).  81.  J . Om B o c k r i s , J . L . White, J.D. Mackenzie: Physico-chemical Measurements a t High Temperatures, B u t t e r w o r t h ' s S c i e n t i f i c Pub., London, p. 347 (1959).  82.  J.R. R a i t :  Searcy:  Trans. B r i t .  J . Phys. Chem., 6_7, pp 103-106 J . Chem. Phys.,  (1963).  50(7),  Ceram. S o c , 40, pp 1941 (1941).  178  F i g u r e 1.  Schematic diagram of the e l e c t r o s l a g  remelting  unit.  179  yV  >  V  C a thode  F i g u r e 2.  Voltage  gradient  Anode  i n an  arc.  180  - Water - cooled copper electrode  -Color li th Rubber  bellows  •Thermocouple  Electrode  •Gas Cu  seal mold  Water -  jackel  NX  F i g u r e 3.  ESR e x p e r i m e n t a l setup f o r temperature measurement an argon atmosphere.  under  181  thermocouple  Cu  mold  elect rode mullite spacer  boron  nitride  slag  liquid  F i g u r e 4.  D e t a i l s o f t h e thermocouple  arrangement.  metal  I  1—  1  I  I  3  I  Distance F i g u r e 5.  I  I  5  .  I  I  7  cm  Temperature d i s t r i b u t i o n i n the s l a g bed f o r d.c. n e g a t i v e  (air).  I  9  I  1  3 Distance  F i g u r e 7.  5  7  cm  Temperature d i s t r i b u t i o n i n the s l a g bed f o r a.c.  (air).  9  Distanee F i g u r e 8.  Temperature d i s t r i b u t i o n  c m  i n the s l a g bed f o r a.c.  (argon).  I  1  1  I  1  3  I  I  '  5 Distance  7 cm  '  1  1  9  Figure 1 0 . Temperature d i s t r i b u t i o n i n the slag bed f o r d.c. p o s i t i v e - ' l i v e ' mold (argon).  1  0 5 cm  1550  C  1550  4, 1600  1600  1620  16 20  1630  16 30  1650  1650  1700  1675  1 700  1725  1725  1700  1700  1750  176 0  1725  1740  1760  1760  I  1725  1740  1760  1760  ]  1-5 cm  1650%^  1-0 cm 4-5cm  1650 ^| S  I  4 0 cm  F i g u r e 11.  Assumed temperature d i s t r i b u t i o n i n the s l a g bed ( i n g o t  no.  1).  R = oo o h m s El  2  X  3  4  5  6  c  /  D  D  0 volts  7  8  10  11  12  14  15  16  17  18  19  20  21  22  2 3  24  25  2 7  28  29  2  6  23-75  volts  F i g u r e 12.  S u b d i v i s i o n of the s l a g bed.  F i g u r e 13.  Resistance  of a volume element.  Rz/  -W—Mr R  J>2  R  ^2  R r oo o h m  B  190  F i g u r e 14.  R e s i s t a n c e network.  191  F i g u r e 15.  Network r e s i s t a n c e  for a single junction.  F i g u r e 17.  E f f e c t of f i n i t e mold w a l l - s l a g Cslag s k i n r e s i s t i v i t y  = 250  ohm  skin resistance cm).  on  the  i s o p o t e n t i a l contours  F i g u r e 18.  E f f e c t of f i n i t e e l e c t r o d e - s l a g (slag skin r e s i s t i v i t y  =0.2  ohm  skin resistance cm).  on-the i s o p o t e n t i a l contours  Figure  19.  E f f e c t of f i n i t e e l e c t r o d e - s l a g s k i n r e s i s t a n c e 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 o r CaF2-Al2C>3 s l a g s determined by galvanostatic experiments.^  In i (b)  Cathodic p o l a r i z a t i o n galvanostatic  F i g u r e 20.  0  A . Ci-m  curves f o r CaF2-Al2C>3 s l a g s determined by  experiments•12  197  1-25H  2  3 _  In (a) A n o d i c p o l a r i z a t i o n  1-5  cruves  i  Q  4  2  5  A.c m  o n ESR  electrodes  in  CaF2-Al20.2  slags  12  T wt-/. 0  Al 0 2  3  Furnace  Result  10  Ini (b)  Cathodic  Figure  21.  polarization  curves  n  O  o n ESR  A . c m-2 electrodes  i n CaF^-Al^O^  slags.  12  n t e r f a c e  F i g u r e 22.  Distance  Cm  E x p e r i m e n t a l l y o b t a i n e d v o l t a g e g r a d i e n t i n the s l a g bath.  interface  199  -ve E lectrode Feed  50  mV shunt  Control Unit  Recorder Recorder Elect rode Set  of 4  chromel - a l u m e l  Argon  thermocouples  W3Re/W25Rl Slag  +ve  2x Hobart 750 powe r supplies  Figure 23. Schematic o u t l i n e of the experimental set up f o r electrode temperature measurement.  200  F i g u r e 24.  E l e c t r o d e temperature g r a d i e n t 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 e l e c t r o d e n e g a t i v e p o l a r i t y .  201  electrode axis  CM  Figure 25. Electrode temperature gradient f o r 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 .  202  electrode  axis  cm  F i g u r e 26. E l e c t r o d e temperature g r a d i e n t f o r 2.54 cm diameter e l e c t r o d e of AISI 321 s t e e l i n e l e c t r o d e n e g a t i v e p o l a r i t y .  203  electrode  axis  CM  F i g u r e 27. E l e c t r o d e temperature g r a d i e n t f o r 2.54 cm d i a m e t e r e l e c t r o d e o f A I S I 1018 s t e e l i n e l e c t r o d e p o s i t i v e p o l a r i t y .  204  electrode F i g u r e 28.  Electrode  axis  temperature g r a d i e n t  CM f o r 3.81 cm diameter  of AISI 1018 s t e e l i n e l e c t r o d e p o s i t i v e  polarity.  electrode  205  206  eleptrode •oo  mold wqll I, z a rgo n  Tslct  f  z"7?  / z  V  •B .TV  .1  slag  L^-  S  Figure  30.  Outline  diagram  computation  to i l l u s t r a t e  of the e l e c t r o d e  the parameters temperature  used  gradient.  i n the  208  32.  E l e c t r o d e temperature g r a d i e n t s f o r 3.81  cm diameter e l e c t r o d e  of AISI 1018  polarity  and ESR  s t e e l i n electrode negative  processes.  i n VAR  209  electrode  slag  water  metal pool  I  mold  (a) mold insulated (b) mold grounded  elect rode  slag  water  metal  mold  i  Figure 33. Current paths i n an ESR mold  pool  210  Recorder  ^  Ohm  3  Meter HP4328A  ^-Recorder  1  ••Recorder  2  2 3 4 5 6  8  u  F i g u r e 34.  E x p e r i m e n t a l apparatus f o r measuring r e s i s t a n c e of the s l a g s k i n .  (2) 450 kHz i n d u c t i o n c o i l ,  the e l e c t r i c a l and thermal  (1) 0.5 cm diameter g r a p h i t e r o d ,  (3) thermal i n s u l a t i o n ,  (5) boron n i t r i d e i n s u l a t i n g s l e e v e ,  crucible,  (6) 3.0cm diameter x 3 cm h i g h  cylinder,  (7) a p p r o x i m a t e l y 1 l t r . o f l i q u i d  insulator  f o r slag  temperature  (4) g r a p h i t e  thermocouple.  slag,  (8) boron n i t r i d e  copper  211  o'l 0  1  1  100  200  J  300  i 400  Temperature  Cl 500 C  Figure 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).  212  Figure 36.  Slag s k i n 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,.  2X3  T i me F i g u r e 37.  sec  Time dependence o f c y l i n d e r temperature c o n s t a n t at  thermal parameter;  1650°C.  slag  214  0  4 T i me  r e 38. * Time dependence of c y l i n d e r  8  10  sec thermal parameter; s l a g  t i o n c o n s t a n t at CaF„ + 25 wt.%  M„0-.  compos  215  slag skin  interface  - mold  F i g u r e 39.  R a d i a l dimensions of the m o l d - s l a g s k i n system.  i nterf ac e 1420 1650  D 1100  /  water  mold  /  Temperature slag skin  C  slag  f 110 5  ° A -  —  B  14C  C  >  radius F i g u r e 40.  Mold r e g i o n temperature p r o f i l e d e r i v e d from eq. (4.8) by assuming  that k i g = 0.8 g  a  x 10  -2  c a l cm  -1 -1 °C  -1  sec  F i g u r e 41.  (a)  View of the l a b o r a t o r y ESR  unit.  (b)  Powder f e e d e r  h-  1  ON  217  a  F i g u r e 42.  Mold c o n n e c t i o n i n ESR (a) l i v e  (b) f l o a t i n g  practice. (c)  insulated  218  Figure 43.  Atmospheric s h i e l d (type ( I ) ) .  F i g u r e 44.  Atmospheric s h i e l d  (type  (II)).  220  Polyethylene  bag  electrode  sliding sea argon in  mold cap  1  / {  slag adding ] unit /  I  Cu  mold  slag  solidified ingot  Figure 4 5 .  Atmospheric s h i e l d (type ( I I I ) ) .  34 height of  the  ingot  Figure 46. Mold current i n d.c. +ve ' l i v e ' operation.  CM  ho  222  F i g u r e 47.  Thermocouple arrangement on the mold.  F i g u r e 48.  Thermocouples c l a d copper molds.  gure 49.  Temperature p r o f i l e on the mold f o r i n g o t no. 1.  225  Temperature  F i g u r e 50.  (°C )  Temperature p r o f i l e on the mold f o r i n g o t , no. 3.  F i g u r e 51.  Temperature p r o f i l e on the mold f o r i n g o t no.  8.  F i g u r e 52.  Temperature p r o f i l e on the mold f o r i n g o t no.  9.  F i g u r e 53.  Temperature p r o f i l e on the mold f o r i n g o t no. 10.  229  Temperature  °C  Figure 54. Temperature p r o f i l e on the mold f o r ingot no. 13.  i  F i g u r e 55.  Temperature p r o f i l e on the mold f o r i n g o t no.  16.  231  Temperature 110  F i g u r e 56.  90  70  °C 50  Temperature p r o f i l e on the mold f o r i n g o t 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 f o r ingot no. 1.  2 em  T = 1590°C c = 2.08 ohm ''"cm ^  T = 1640°C  err  T=1675 c = 2.30 ohm "'"cm ^ c=2.46 _ A ohm cm  T = 1712.5°C  T = 1750°C  c •= 2.64 ohm "*"cm "*"c = 2.86 ohm "'"cm ^  I.  23-75  F i g u r e 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.  Volts  235  236  > ON  1  1  h -—  CO  cn  JC  y5  Cr|<  F i g u r e 61.  C|.  ATsat  hf  • Pr| 7 1 -  g  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 60090  psia  water  temperature = 2 70  saturation  temperature  =  o  F 320  o  F  v e l o c i t y = 1 f t . sec  -6—  steam pressurized 0-3 cc a i r . I it re ^ -  CN  -X—  •  air pressurized 6 9 cc a i r . l i t r e  D  L L  CO  CO  o 2  60 L  X  L  L  crl<  10  • i i i  •  '  20  5 AT  = T w o II - T w a t e r  F i g u r e 62. E f f e c t o f d i s s o l v e d  air  48  on the heat f l u x  ( °F )  M l  238  50 h i a og(  surface  boiling  ( d i s t i l led  water)  1  — - non - b o i l i n g  I I Mill 40 60 100  _L  20 0  AT = T m o l d - T w a t e r = T m o l d - 5 0  (°C) F i g u r e 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 boiling conditions.  239  Q =  Q  4  4  A + Q 4 B  I iquid metal  B  i solidified i ngot  Q <1A >1B  7  heat r e q u i r e d  t o melt t h e e l e c t r o d e  heat r e q u i r e d  t o superheat t h e l i q u i d m e t a l drops  heat l o s t by r a d i a t i o n from t h e s l a g s u r f a c e t o (A) mold c o o l i n g w a t e r , (B) g a s e s , (C) e l e c t r o d e heat l o s t t o mold c o o l i n g w a t e r a c r o s s t h e s l a g bed •4A  heat t r a n s f e r r e d a c r o s s 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 m e t a l drops  MB  heat t r a n s f e r r e d a c r o s s S/M i n t e r f a c e by c o n v e c t i v e heat transfer heat l o s t t o mold c o o l i n g water a c r o s s t h e l i q u i d m e t a l pool heat l o s t t o mold c o o l i n g w a t e r a c r o s s t h e s o l i d i f i e d heat l o s t t o 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 t h e s o l i d i f i e d  F i g u r e 64. Heat d i s t r i b u t i o n i n an ESR u n i t .  ingot.  ingot  QAP=137JL  Cal.secl  gure 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)  Q  -1  2 A  = 487 cal.sec  Heat Input = 6 6 5 0 cal.sec  1  -1 JL^>Q = 2597 cal. sec  4  0.4^ = 1060-5 Q F i g u r e 67.  4 B  3  cal.sec- i  -1 = 2505-5 c a l .sec  B l o c k diagram f o r the heat b a l a n c e o f the s l a g  region.  2 4 2  Q 4  liquid  -1 - 3566 C a l . s e c  Q  metal  5  =  ^  2401 Cv -aul i . s e c  N Q  F i g u r e 68.  9  = H65Cal.sec  B l o c k diagram f o r the heat balance of the l i q u i d region.  Q  -1 =H65Cal.sec  9  solidified  metal  ingot C*6 = 5 4 0 -1 Cal-sec  Q3  -1 = 4 0 4 C o l . sec  Q F i g u r e 69.  7  =  -1 410 C a l . sec  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  ingot.  + ve electrode 23 v  ( a ) d.c. +ve mold  l  2  h  R-  18 v  resistance Rj=  ''  R=  mold -  3  R  3  ingot -ve  - ingot > >  11  «1  ( b ) d.c.-ve  electrode -ve 0v  mold  R  2  20-5 v  R  3  i ngot 23v +• ve  F i g u r e 70.  ESR u n i t ' s analog  circuit.  (a)  I.N.  27  ( b )  |.N.  29 4>  F i g u r e 71.  Pictures  of s l a g cap  and  s l a g s k i n of some of the  ESR  melts of  FVE  247  es r with cover.  400Cy~ without cover  200( 1  1_  . 100C  5  700 f o r 12 ton  urnac Boehler ESR ave. a l l grades f o r optimum p o o l depth  400 ^  200 10  40  20 Ingot  F i g u r e 73.  Boehler ESR ave. f o r d i e 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 h i g h temperature a l l o y s .  diameter  60 in  Boehler s i n g l e phase a.c. ESR melt A, diameter.  6  ii  80  rate vs. ingot  radial _ dend rites  H i g h melt  F i g u r e 74.  Effect  rate  Low melt  of melt r a t e on the shape of the l i q u i d m e t a l  pool.  rate  N3 00  electrode  molten  molten  t  slag  Z  +  metal  A  D  Figure  75.  S u b d i v i s i o n of the molten metal p o o l .  +  ABC D : cyl ind rical portion of the m o l t e n metal pool D E F G C : curved p o r t i o n of the m o l t e n metal pool  N3  250  F i g u r e 77.  Subdivision  of the  ingot.  110f  Figure  82.  Predicted pool p r o f i l e ingot no.  (16).  for  Figure  83.  Predicted pool p r o f i l e i n g o t no.  (21).  for  ro 4--  7  257  F i g u r e 87.  A schematic diagram of the apparatus of the measurement of d e n s i t y of CaF2 based s l a g s .  (A) t r a n s d u c e r , (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 s u p p o r t , (E) thermocouple, (F) water c o o l e d 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 w i r e , (I) molybdenum bob, (J) l i q u i d s l a g , (K) molybdenum l i n e d g r a p h i t e c r u c i b l e , (L) g r a p h i t e f e l t , (M) i n d u c t i o n c o i l , (N) AI2O3 tube to support the c r u c i b l e , (0) thermocouple connected t o i n d u c t i o n f / c c o n t r o l l e r , (P) v y c o r g l a s s tube, (Q) water c o o l e d s t a i n l e s s s t e e l base, (R) argon gas e x i t .  1  10  A  _L_A slow blow  slow blow  1 0  V 2 0 0 mA 5  1  100  V mA  (Wvvv ^ w w  1 c  W  | offset  50K  |  green shield white  bloc  on o off  Figure  88.  External c i r c u i t r y required  tranducer zero  to operate the t r a n s d u c e r .  offset balance  recorder 0  0  output  F i g u r e 89.  The d e n s i t y measurement a p p a r a t u s .  «3  Density ro  •  Z9Z  grams-cm ro  •  ro  .  263  F i g u r e 93.  A schematic diagram of the apparatus f o r the measurement of v i s c o s i t y o f CaF£ based s l a g s .  (A) graduated stem, (B) argon gas i n l e t , (C) thermocouple j u n c t i o n , ( D ) s t e e l frame s u p p o r t , (E) b r a s s l i d , (F) v y c o r g l a s s tube, (G) s u s p e n s i o n w i r e (5 thou W), (H) m i r r o r , (I) s t a i n l e s s s t e e l frame, (J) b r a s s r i n g to support thermocouple l e a d s , (K) molybdenum thermocouple l e a d s , (L) mercury p o o l , (M) alumina tube, (N) water c o o l e d base, (0) thermocouple (W-W-26% Re), (P) s t e e l l i d f o r the g l a s s tube Q, (Q) v y c o r g l a s s tube, (R) water c o o l e d copper i n d u c t i o n c o i l , (S) g r a p h i t e wool, (T) i n n e r molybdenum c y l i n d e r , (U) l i q u i d s l a g , (V) o u t e r molybdenum l i n e d g r a p h i t e c y l i n d r i c a l c r u c i b l e , (W) s h a f t connected t o the motor, (X) water c o o l e d base, (Y) s t e e l frame t o support the l i d P, (Z) argon gas o u t l e t .  265  266  120  X : present  work  0 : Davis & W r i g h t  7 3  \ \  v°  100  w t o  \ \  tA o a  /o  Al 0 2  3  \  c a> u  80  \ \ \ \ \  \ N  x  \  \  N  \.\ \  \  \  \  \10  60  \ \  1500  1600 Temperature  F i g u r e 97. V a r i a t i o n CaF -Al 0 2  2  of c o e f f i c i e n t 3  system.  C  o f v i s c o s i t y w i t h temperature f o r  267  268  269  F i g u r e 102.  G e n e r a l element  f o r case  3.  270  

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