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Liquid metal flow in horizontal rods MacAulay, Lyle Campbell 1972

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LIQUID METAL FLOW IN HORIZONTAL RODS  by LYLE CAMPBELL MACAULAY B.A.Sc. (Met. Eng.), U n i v e r s i t y  o f B r i t i s h Columbia, 1966  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  i n t h e Department of METALLURGY  We a c c e p t t h i s  t h e s i s as conforming to the  required standard  THE UNIVERSITY OF BRITISH COLUMBIA June, 1972  In p r e s e n t i n g an  thesis  advanced degree at  the I  this  Library  further  for  shall  agree  scholarly  by  his  of  this  written  the  fulfilment of  University  of  make i t f r e e l y  that permission  p u r p o s e s may  representatives. thesis  be  available  J  u  l  Y  granted  gain  Metallurgy  1 7  '  1972  for  for extensive  permission.  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  British  by  the  It i s understood  for financial  Department of  Date  in p a r t i a l  Columbia  shall  requirements  Columbia,  Head o f my  be  I agree  r e f e r e n c e and copying of  that  not  the  that  study.  this  thesis  Department  copying or  for  or  publication  allowed without  my  ABSTRACT  R a d i o a c t i v e t r a c e r techniques have been developed d i r e c t i n s i t u o b s e r v a t i o n o f the nature  of f l u i d  accuracy  o f the techniques  The  Extensive s e r i e s of  i n o r d e r t o c o n f i r m the a c c e p t a b i l i t y and  employed.  f i n d i n g s o f the i n v e s t i g a t i o n e s t a b l i s h  flow v e l o c i t y on temperature d i f f e r e n c e a c r o s s the melt, temperature and t o t a l melt increase l i n e a r l y with  at  length.  the dependence o f average melt  The flow v e l o c i t y was observed t o  the average temperature g r a d i e n t between the h o t  and c o l d ends of the melt. average melt  An i n c r e a s e i n flow v e l o c i t y w i t h i n c r e a s i n g  temperature was a l s o observed.  very s m a l l temperature g r a d i e n t s .  Flow was observed  two  t o occur  When the temperature g r a d i e n t was  zero a t any p o i n t between the hot and c o l d ends o f the m e l t , c e l l s developed.  allow  flow i n l i q u i d t i n  c o n t a i n e d i n a l o n g s h a l l o w covered h o r i z o n t a l boat. experiments have been conducted  which  two flow  C o n v e c t i v e mass t r a n s f e r d i d n o t occur between these  cells.  Autoradiography  o f quenched specimens showed the flow p a t t e r n  to be a l a m i n a r u n i c e l l u l a r l o n g i t u d i n a l flow upon which a t r a v e r s e  double  c e l l flow i s superimposed.  The  r e s u l t s o f the flow p a t t e r n and flow v e l o c i t y  experiments  are compared t o a m o d i f i c a t i o n o f B a t c h e l o r ' s s o l u t i o n o f thermal i n a rectangular enclosure. experimental  I n g e n e r a l , the agreement between the  r e s u l t s and t h e m o d i f i e d s o l u t i o n i s good.  convection  ii A s e p a r a t e i n v e s t i g a t i o n of the m a c r o s e g r e g a t i o n w i t h c a s t i n g s t r u c t u r e c o n t r o l l e d by f o r c e d sented.  associated  convection i s also pre-  ACKNOWLEDGEMENT  The author g r a t e f u l l y acknowledges t h e a d v i c e and encouragement g i v e n by h i s r e s e a r c h d i r e c t o r , Dr. F r e d Weinberg. due t o f e l l o w g r a d u a t e students f u l discussions. experimental  Thanks a r e a l s o  and members o f t h e F a c u l t y f o r many h e l p -  The a s s i s t a n c e o f t h e t e c h n i c a l s t a f f , throughout t h e  program, has been g r e a t l y a p p r e c i a t e d .  The f i n a n c i a l a s s i s t a n c e p r o v i d e d by the N a t i o n a l Reseach C o u n c i l and an A l c a n F e l l o w s h i p a r e g r a t e f u l l y  acknowledged.  iv TABLE OF CONTENTS Page PART I - THERMAL CONVECTION IN HORIZONTAL RODS OF MOLTEN TIN  1  1 - INTRODUCTION  1  2 - DETERMINATION OF FLOW VELOCITIES IN HORIZONTAL RODS OF MOLTEN TIN  17  2.1. Flow Velocity Determination by Manually Monitoring the Movement of Radioactive Tracer  17  2.1.1. General Experimental Apparatus and Procedure  ..  ..  17  2.1.2. Tracer Introduction by Melting Back Through a Region Containing Radioactive Material  22  2.1.2.1. Experimental Apparatus and Procedure  22  2.1.2.2. Results and Discussion  25  2.1.2.3. Evaluation of Technique  ..  33  ..  35  2.1.3. Tracer Introduction by Rotating a V e r t i c a l Cylinder Located at the End of the Graphite Boat 2.1.3.1. Experimental Apparatus and Procedure  35  2.1.3.2. Results and Discussion  35  2.1.3.3. Evaluation of Technique 2.1.4. Tracer Introduction by Rotating a V e r t i c a l Cylinder Situated i n the Covered Section of the Graphite Boat  40  2.1.4.1. Experimental Apparatus and Procedure  42  2.1.4.2. Results and Discuss  44  2.1.4.3. Evaluation of Technique  44  2.1.5. Tracer Introduction by Rotating a Horizontal Cylinder Located i n the Cover of the Graphite Boat  46  2.1.5.1. Experimental Apparatus and Procedure  46  2.1.5.2. Results and Discussion  46  42  V  Page 2.1.5.3. E v a l u a t i o n o f Technique  .50  2.1.6. T r a c e r I n t r o d u c t i o n by R o t a t i n g a H o r i z o n t a l C y l i n d e r L o c a t e d i n t h e Cover o f t h e boat and then G e n t l y Pushing T r a c e r i n t o the M e l t  52  2.1.6.1. E x p e r i m e n t a l Apparatus  52  and Procedure  2.1.6.2. R e s u l t s and D i s c u s s i o n  56  2.1.6.2.1. Flow V e l o c i t y Measurements  56  2.1.6.2.2. A u t o r a d i o g r a p h y  56  2.1.6.3. E v a l u a t i o n o f Technique  62  2.1.7. R e t u r n t o I n t r o d u c t i o n by R o t a t i n g a V e r t i c a l L o c a t e d i n t h e Covered S e c t i o n o f t h e Channel 2.1.7.1. E x p e r i m e n t a l Apparatus 2.1.7.2. R e s u l t s  Cylinder 63  and Procedure  and D i s c u s s i o n  ..  63  . *  68  2.1.7.2.1. V a r i a t i o n o f Flow V e l o c i t y w i t h Temperature D i f f e r e n c e Across the Melt 2.1.7.2.2. E f f e c t o f V a r y i n g Average M e l t Temperature 2.1.7.2.3. E f f e c t o f V a r y i n g T r a c e A l l o y and M e l t D e n s i t y 2.1.7.2.4. E v a l u a t i o n o f Technique 2.1.8. S i n g l e Aluminum Channel  68 ..  ..  68  ..  72 74  Supported by G r a p h i t e  Reservoirs  76  2.1.8.1. E x p e r i m e n t a l Apparatus  and Procedure  76  2.1.8.2. R e s u l t s and D i s c u s s i o n s  79  2.1.8.3. E v a l u a t i o n o f Technique  82  2.2. Flow V e l o c i t y D e t e r m i n a t i o n by Dual M o n i t o r i n g  83  2.2.1. E x p e r i m e n t a l Apparatus  83  and Procedure  2.2.2. A n a l y s i s o f A c t i v i t y Versus Time Data  83  2.2.3. R e s u l t s and D i s c u s s i o n  94  2.2.3.1. V a r i a t i o n o f Flow V e l o c i t y w i t h Temperature D i f f e r e n c e between the Hot and C o l d Ends  94  vi Page 2.2.3.2. Variation of Flow Velocity with Average Melt Temperature .  94  2.2.3.3. Variation of Flow Velocity with Total Melt Length  97  2.2.3.4. Evaluation of Technique  104  2.2.3.4.1. E f f e c t on Flow Velocity of Varying the Nature of the Temperature D i s t r i b u t i o n 2.2.3.4.2. E f f e c t of Flow Velocity of Varying the Position of the Monitoring Interval  106 108  2.2.3.4.3. E f f e c t of Flow V e l o c i t y of Varying the Height of Metal i n the Reservoirs  I l l  2.2.3.4.4. E f f e c t on Flow Velocity of Introducing Tracer i n the Cold End of the Melt  117  2.2.3.4.5. Extent of Inductive Mixing ..  117  2.2.3.4.6. Reproducibility of Results  119  2.2.3.4.7. Summary of Technique Evaluation  120  2.3. Summary of Flow Velocity Determination Results  i.  ..  120  3 - FLOW PATTERNS IN HORIZONTAL RODS OF MOLTEN TIN  ..  ..  122  3.1. Introduction  122  3.2. Experimental Apparatus and Procedure  122  3.3. Results from Quenching Wired Top U-Channel  123  3.4. Autoradiography of Quenched Specimens Using a Completely Closed Square Aluminum Channel  124  3.4.1. Experimental Apparatus and Procedure 3.4.2. Results from Square Aluminum Channel With No Water Shield . . . .  124  vii Page 3.4.3. R e s u l t s and D i s c u s s i o n o f Experiments Aluminum Channel w i t h a Water S h i e l d  Using 125  3.4.4. R e s u l t s and D i s c u s s i o n o f Attempts t o Confirm the V a l i d i t y o f Observed Flow P a t t e r n s  144  3.4.4.1. E f f e c t o f Quench C y l i n d e r on Observed Flow "Velocity  144  3.4.4.2. Quench Time D e t e r m i n a t i o n 3.4.4.3. Quenching i n a Prearranged  145 Tracer D i s t r i b u t i o n  ..  147  3.4.4.4. E x t e n t o f I n d u c t i v e M i x i n g  150  3.4.4.5. D e t e r m i n a t i o n o f T r a n s v e r s e Temperature G r a d i e n t s  154  3.5. I n t e r a c t i o n o f U n i c e l l a r Flow w i t h a Moving Solid Liquid Interface  161  3.6. Summary ..  165  4 - ANALYSIS OF RESULTS  167  4.1. I n t r o d u c t i o n  167  4.2. P r e v i o u s I n v e s t i g a t i o n s  175  (9)  4.2.1. S o l u t i o n o f U t e c h 4.2.2. S o l u t i o n o f C o l e  v  176  J  180  ( 5 )  (23) 4.2.3. S o l u t i o n o f B a t c h e l o r  v  1  185  (2k)  4.2.4. S o l u t i o n o f P o o t s  v  186  1  4.2.5. S o l u t i o n o f S t e w a r t ^ ^  186  4.3. M o d i f i c a t i o n o f t h e B a t c h e l o r S o l u t i o n  188  4.4. Comparison o f T h e o r e t i c a l P r e d i c t i o n s and E x p e r i m e n t a l R e s u l t s  193  4.4.1. V a r i a t i o n o f Flow V e l o c i t y w i t h Average Temperature G r a d i e n t A c r o s s the M e l t  193  1 7  viii Page 4.4.2. V a r i a t i o n of Flow V e l o c i t y with Total Melt Length ..  194  4.4.3. V a r i a t i o n of Flow V e l o c i t y with Average Melt Temperature ,  194  4,5. Summary  195  5 - CONCLUSIONS  196  6 - SUGGESTIONS FOR FUTURE WORK  198  PART I I - FLUID FLOW DURING SOLIDIFICATION  - ITS EFFECT  ON GRAIN STRUCTURE AND MACROSEGREGATION  ..  ..  199  1 - INTRODUCTION  199  1.1. Grain Structure  199  1.2. Macrosegregation  200  2 - MACROSEGREGATION IN CASTINGS ROTATED AND OSCILLATED DURING SOLIDIFICATION  202  2.1. Introduction  202  2.2. Experiment  ..  203  2.3. Results  2.4. Discussion  2.5. Conclusion  2.6. Appendix to Section 2  206  ,  214  ..  217  219  ix  LIST OF FIGURES Figure No. 1  2 3 4 5  6 7  8  9  10.  11.  12.  Page Segregation resulting from (a) complete mixing (b) no mixing and (p) p a r t i a l mixing i n the liquid  2  Convective flow pattern a r i s i n g from horizontal temperature gradient .. . . . . ,  5  Representation of the flow pattern i n the h o r i zontal boat.. .. ..  12  The apparatus employed f o r i n i t i a l series of experiments ,.  18  The graphite boat used for i n i t i a l studies of convective flow i n horizontal rods of molten tin  23  Results of the test to evaluate the accuracy of the collimated counting procedure ,.  26  (a) The temperature p r o f i l e s at the i n i d i c a t i v e times after the tracer had melted, (b) The d i s , t r i b u t i o n of tracer at the indicated times a f t e r melting . . ..  28  (a) The temperature p r o f i l e s at the indicated times, (b) The d i s t r i b u t i o n of tracer before and after moving the furnace  29  The change i n a c t i v i t y with time at various positions along the melt  30  (a) The temperature p r o f i l e 1/2 hour after the tracer melted. (b) The d i s t r i b u t i o n of tracer before and after melting  32  The expected flow pattern when a zero gradient i s present ..  34  (a) Top view of graphite boat with tracer i n t r o duction cylinder i n place. (b) Introduction cylinder, (c) Tracer loading block  36  (a) The temperature p r o f i l e a l o n g the m e l t a t the time o f t r a c e r i n t r o d u c t i o n , (b) The d i s t r i b u t i o n o f t r a c e r b e f o r e and 15 minutes a f t e r introduction (a) The temperature g r a d i e n t s along the m e l t . (b) The d i s t r i b u t i o n of t r a c e r b e f o r e and a f t e r p a s s i n g argon (a) The temperature p r o f i l e s b e f o r e and a f t e r p a s s i n g argon. (b) The d i s t r i b u t i o n o f t r a c e r at the times i n d i c a t e d (a) D e t a i l s o f the g r a p h i t e boat employed f o r experiments i n which the t r a c e r was i n t r o d u c e d i n the covered s e c t i o n o f the m e l t , (b) T r a c e r i n troduction cylinder 113 The d i s t r i b u t i o n of Sn ( i n a pure Sn m e l t h a v i n g z e r o h o r i z o n t a l temperature g r a d i e n t ) bef o r e and a f t e r (a) t r a c e r i n t r o d u c t i o n and (b) m e l t i n g w i t h the i n t r o d u c t i o n c y l i n d e r i n the open positions. D e t a i l s of t r a c e r i n t r o d u c t i o n covers  from the boat  (a) The temperature p r o f i l e a l o n g the m e l t , (b) The d i s t r i b u t i o n o f Tl204 b e f o r e and a f t e r t r a c e r introduction (a) The temperature p r o f i l e a l o n g the m e l t , (b) The d i s t r i b u t i o n o f A g H ^ b e f o r e and a f t e r t r a c e r i n troduction D e t a i l s o f mechanism used to f a c i l i t a t e t r a c e r i n t r o d u c t i o n from the boat c o v e r . (a) Top view-(b) Side s e c t i o n view. T y p i c a l a c t i v i t y v e r s u s time d a t a f o r experiments employing f o r c e d t r a c e r i n t r o d u c t i o n from the b o a t cover. The dependence of f l o w v e l o c i t y on the temperature d i f f e r e n c e between the hot and the c o l d ends of the melt. L o n g i t u d i n a l s e c t i o n a u t o r a d i o g r a p h s of specimens quenched (a) 0.5 minutes (b) 1 minute and (c) 10 minutes a f t e r t r a c e r i n t r o d u c t i o n i n t o a m e l t h a v i n g zero h o r i z o n t a l temperature g r a d i e n t  (a) P o s i t i o n from which a u t o r a d i o g r a p h s were obt a i n e d , (b) T r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s (from p o s i t i o n s i n d i c a t e d i n (a)) o f a specimen quenched 1 minute a f t e r t r a c e r i n t r o d u c t i o n i n t o a melt having zero h o r i z o n t a l temperature g r a d ient T r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s (from t i o n s i n d i c a t e d ) of a specimen quenched a f t e r i n t r o d u c t i o n of t r a c e r i n t o a melt 70 °C temperature d i f f e r e n c e between the c o l d ends. .  the p o s i 1 minute having a hot and  (a) Tube f u r n a c e w i r i n g diagram (b) D e t a i l s o f f u r n a c e temperature c o n t r o l l e r . T y p i c a l a c t i v i t y v e r s u s time d a t a f o r e x p e r i ments employing t r a c e r i n t r o d u c t i o n by r o t a t i n g a v e r t i c a l c y l i n d e r l o c a t e d i n the covered s e c t i o n o f the m e l t s . The dependence of flow v e l o c i t y on the temperature d i f f e r e n c e between the hot and the c o l d ends o f the melt. The e f f e c t on the flow v e l o c i t y of v a r y i n g melt temperature  the  average  The e f f e c t on the f l o w v e l o c i t y of h a v i n g i d e n t i c a l t r a c e r a l l o y and melt d e n s i t i e s . The e f f e c t on the f l o w v e l o c i t y of v a r y i n g the d e n s i t y d i f f e r e n c e between the t r a c e a l l o y and the m e l t . Comparison of the flow v e l o c i t y measurements o b t a i n e d employing the r o t a t e d v e r t i c a l c y l i n d e r and p i s t o n mechanism i n t r o d u c t i o n t e c h n i q u e s . D e t a i l s o f the g r a p h i t e and supported s i n g l e aluminum channel b o a t Comparison o f the flow v e l o c i t y measurements o b t a i n e d employing the two channel g r a p h i t e boat ( F i g u r e 29) and the s i n g l e aluminum c h a n n e l boat S e c t i o n a l view of the double s l i t two s c i n t i l l a t i o n counters  collimator with  F i e l d o f view o f 35 mm camera employed to c o l l e c t a c t i v i t y v e r s u s time data, (b) A s e c t i o n of the 35 f i l m showing some t y p i c a l data  mm  xii Figure No. 38 39  40  •41 42  43  44  45  Page The counting c h a r a c t e r i s t i c s of the double s l i t c o l l i m a t o r - s c i n t i l l a t i o n counter arrangement.  ..  87  F u l l s i z e schematic diagram showing the length of melt subtended by the s c i n t i l l a t i o n detector. ..  88  The response of the dual simultaneous counting to a constant a c t i v i t y source t r a v e l l i n g at a known velocity.  91  Typical a c t i v i t y versus time data obtained by the simultaneous dual monitoring.  93  The dependence of flow v e l o c i t y on the temperature difference between the hot and the cold ends of the melt.  95  The effect on flow v e l o c i t y of varying the average melt temperature (with a constant temperature difference across the melt of 214°C).  98  The dependence of flow v e l o c i t y f o r three d i f f e r ent melt lengths , on temperature difference across the melt  100  The dependence of flow v e l o c i t y f o r three d i f f e r e n t melt lengths, on the temperature gradient between the hot and cold ends of the melt  102  46  The dependence of flow v e l o c i t y on the temperature gradient across the melt with an average melt temperatur of 400 °C 103  47  Comparison of the v e l o c i t y versus temperature gradient results obtained using the two channel graphite boat and the single aluminum channel boat. Average melt temperature was approximately 310 °C  105  Temperature p r o f i l e s from two experiments designed to show that the temperature gradient across the melt, and not the gradient across the monitoring i n t e r v a l , i s the driving force f o r the observed v e l o c i t y . ..  107  Temperature p r o f i l e from an experiment undertaken to determine the effect on flow v e l o c i t y of changing the p o s i t i o n of the monitoring i n t e r v a l  109  Comparison of the results of Figures 48 and 49 with results of Figure 46.  HO  The e f f e c t on flow v e l o c i t y of varying the l i q u i d metal height i n the reservoirs and of introducing the tracer near the cold end.  H2  48  49  50  51  xlii F i g u r e No. 52(a)  52(b)  52(c)  53  54  55  Page A c t i v i t y v e r s u s time r e s u l t s when t h e r e was a 3 mm head o f l i q u i d t i n i n the h o t r e s e r v o i r .. ..  114  A c t i v i t y v e r s u s time r e s u l t s when t h e r e was no d i f f e r e n c e i n the l i q u i d t i n l e v e l i n the h o t and c o l d r e s e r v o i r s  115  A c t i v i t y v e r s i s time r e s u l t s when t h e r e was a 3 mm head o f l i q u i d t i n i n the c o l d r e s e r v o i r  ..  116  R e s u l t s o f the i n v e s t i g a t i o n o f the e x t e n t o f i n d u c t t i v e mixing  118  Schematic r e p r e s e n t a t i o n showing t h e p o s i t i o n a t which the specimen was s e c t i o n e d t o o b t a i n e d t r a n s verse s e c t i o n autoradiographs ..  126  L o n g i t u d i n a l s e c t i o n a u t o r a d i o g r a p h s o f specimens quenched (a) 40 s e c and (b) 1 minute a f t e r i n t r o d u c t i o n o f t r a c e a l l o y (0.85% Sb i n pure Sn c o n t a i n ing 3.5% Sn-'--'-). S u r f a c e a u t o r a d i o g r a p h was 0.04 i n c h e s below o u t s i d e s u r f a c e (X2)  127  T r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s o f a specimen quenched 40 seconds a f t e r i n t r o d u c t i o n o f Snll3_ Sb-Sn t r a c e r . S e c t i o n s a r e a t 1 cm i n t e r v a l s w i t h the s t a r t (top l e f t hand c o r n e r ) 4 cm from p o i n t of i n t r o d u c t i o n near the h o t end (X4)  129  Comparison o f t r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s from specimens quenched 40 seconds ( f i r s t , t h i r d and f i f t h rows) and 1 minute (second, f o u r t h and s i x t h rows) after introduction  131-132  Comparison o f t r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s from specimens quenched 1 minute ( f i r s t , t h i r d and f i f t h rows) and 2 minutes (second, f o u r t h and s i x t h rows) after introduction  133-134  T r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s o f a specimen quenched 1 minute a f t e r i n t r o d u c t i o n o f a t r a c e a l l o y c o n t a i n i n g 0.85% Sb i n S n 3.5% (0.994 pSn). ..  136  T r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s o f a specimen quenched 1 minute a f t e r i n t r o d u c t i o n o f a t r a c e a l l o y c o n t a i n i n g 3.5% S n i n Sn (1.0000 pSn) ..  137  T r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s o f a specimen quenched 1 minute a f t e r i n t r o d u c t i o n o f a t r a c e a l l o y c o n t a i n i n g 0.5% T I i n Sn (1.0020 pSn). •• ••  138  3  56  57  58  59  1 1 3  60  1 1 3  61  2 0 4  xiv Figure No. 62  63  Page The expected appearance of a transverse section autoradiograph i f only u n i c e l l u l a r longitudinal flow were present (X12)  140  Transverse section autoradiographs of a quenched 1 minute after introduction of a l l o y containing 0.5% T I i n Sn. The (top l e f t hand corner) i s 4 cm from the introduction near the cold end.  142  2 0 4  64  specimen a trace f i r s t section point of  Transverse section autoradiographs of a specimen quench 1 minute a f t e r introduction of a trace a l l o y composed of 60% Pb i n Sn contained 0.5% T I . Introduction took place near the cold end  143  Typical results of quench time determination experiments  146  Schematic representation of the prearranged tracer d i s t r i b u t i o n (a) transverse section and (b) l o n g i tudinal section  148  Transverse section autoradiographs of the specimen which had the prearranged tracer d i s t r i b u t i o n fhown in Figure 66.  151  2 0 4  65 66  67  68  Comparison of transverse section autoradiographs of specimens quenched 1 minute after introduction of 3.5% Sn - - i n Sn tracer into the melt, while the furnace power was on ( f i r s t , t h i r d and f i f t h rows) and 2 minutes after the furnace power had been turned off (second, fourth and s i x t h rows) J  69  70  L  )  152-153  Schematic representation of apparatus used to measure transverse temperature gradients (X2)  155  The numbering systems for locating positions on temperature tranverse  157  the  71  The r e l a t i o n between the horizontal and v e r t i c a l temperature gradients for an uncovered t i n melt of depth 0.94 cm (after Utech). .. 159  72  Transverse section autoradiograph of a d i r e c t i o n a l l y s o l i d i f i e d t i n melt containing 500 ppm T I (X20).  162  Transverse section autoradiographs of a d i r e c t i o n a l l y s o l i d i f i e d t i n melt contain 100 ppm T I (X6)..  163  2 0 4  73  2 0 4  XV F i g u r e No. 74  75  76  77  78  79  Page (a) Schematic r e p r e s e n t a t i o n o f t h e double s p i r a l flow observed d u r i n g f o r c e d c o n v e c t i o n through a tube.(b) Expected appearance o f t r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s i f double s p i r a l f l o w were p r e s e n t  168  The s i m p l i f i e d flow system i n the long rectangular enclosure . . ..  174  shallow  Comparison o f the r e s u l t s o f the p r e s e n t i n v e s t i g a t i o n w i t h the p r e d i c t i o n o f the s o l u t i o n of Utech ..  179  The v a r i a t i o n o f l o n g i t u d i n a l flow v e l o c i t y w i t h v e r t i c a l p o s i t i o n i n the melt  191  The e x p e r i m e n t a l apparatus used f o r p r o d u c i n g the s t a t i o n a r y , r o t a t e d , and o s c i l l a t e d c a s t i n g s .. ..  204  Representative ingots  cast  i n (a) s t a t i o n a r y ,  (b) r o t a t i n g , and (c) o s c i l l a t i n g moulds 80  81 .  82  83  84  85  Equiaxed g r a i n s i n the c e n t r a l r e g i o n o s c i l l a t e d casting  ..  ..  207  o f the  R e p r e s e n t a t i v e i n g o t s c a s t i n (a) s t a t i o n a r y , (b) r o t a t i n g , and ( c ) o s c i l l a t i n g moulds. ..  208  ..  208-209  The r a d i a l s i l v e r d i s t r i b u t i o n i n a s t a t i o n a r y c a s t i n g : (a) 1/4 i n c h d r i l l h o l e s i n 1/4 i n c h s t e p s , (b) 1/4 i n c h d r i l l h o l e s i n 1/8 i n c h s t e p s , (c) 0.030 i n c h l a t h e t u r n i n g s , and (d) 0.050 i n c h lathe turnings dissolved i n a c i d  211  The r a d i a l s i l v e r d i s t r i b u t i o n i n (a) s t a t i o n a r y (b) r o t a t e d , and (c) o s c i l l a t e d i n g o t s using method (b) of F i g u r e 82.  213  An a u t o r a d i o g r a p h o f the c r o s s s e c t i o n o f the o s c i l l a t e d i n g o t showing the s i l v e r d i s t r i b u t i o n i n the c a s t i n g  215  The development o f the r a d i a l m a c r o s e g r e g a t i o n i n an o s c i l l a t e d i n g o t , (a) p r i o r t o the time o f the CET, (b) a t the time o f the CET, and (c) t h e f i n a l s i l v e r d i s t r i b u t i o n i n the c a s t i n g . .. ..  218  xv i  LIST OF TABLES  T a b l e No.  Page  1  Properties  of Radioisotopes  21  2  Flow V e l o c i t y R e s u l t s  69  3  Flow V e l o c i t y R e s u l t s  80  4  R e s u l t s o f Dual C o l l i m a t o r S e n s i t i v i t y T e s t  5  Flow V e l o c i t y R e s u l t s  96  6  P r o p e r t i e s of M o l t e n T i n  99  7  Flow V e l o c i t y R e s u l t s f o r Three M e l t Lengths ..  ..  90  101  PART I - THERMAL CONVECTION IN HORIZONTAL RODS OF MOLTEN TIN  1 - INTRODUCTION  D u r i n g the s o l i d i f i c a t i o n o f m e t a l s , s o l u t e can  l e a d t o macro and m i c r o s e g r e g a t i o n  which i n t u r n can markedly i n -  f l u e n c e t h e m e c h a n i c a l p r o p e r t i e s o f the r e s u l t i n g s o l i d i f i c a t i o n of binary  alloys  redistribution  t h e extent  s o l i d metal.  In  o f m i x i n g i n the l i q u i d  m e t a l g r e a t l y i n f l u e n c e s the s o l u t e r e d i s t r i b u t i o n .  The two l i m i t i n g  cases a r e : (1) Complete m i x i n g i n the l i q u i d d u r i n g results  C  s  s o l i d i f i c a t i o n which  i n a solute d i s t r i b u t i o n given  =  o o  k  C  (  1  -  f  )  k  °  by^"^:  1  (2) No m i x i n g i n the l i q u i d , t h a t i s , s o l u t e t r a n s p o r t l i q u i d i s by d i f f u s i o n o n l y . bution  i n the i n i t i a l l y  The r e s u l t i n g  solute  i n the distri-  s o l i d i f i e d p o r t i o n o f t h e melt i s  . (2) g i v e n by  C s  k {(1 - k ) [ 1 - exp (- —  = C o  O  Rx )] + k }  (1.2)  o  p  where: C  q  i s the average c o m p o s i t i o n o f the s t a r t i n g  liquid  C  g  i s the c o m p o s i t i o n o f t h e r e s u l t i n g  C  T  i s the c o m p o s i t i o n o f the l i q u i d i n e q u i l i b r i u m  solid  J_i  with s o l i d k^ - g / C  C  = L  of composition  C  g  equilibrium distribution  coefficient.  2  f  i s the f r a c t i o n s o l i d i f i e d  R  i s the f r e e z i n g r a t e  D  i s the d i f f u s i o n c o e f f i c i e n t f o r s o l u t e i n the  x  i s the d i s t a n c e  liquid'  from the s t a r t of u n i d i r e c t i o n a l s o l i d i -  fication.  In a r r i v i n g at E q u a t i o n s t h a t the s o l i d - l i q u i d occurred  bution  and  (1.2)  i n t e r f a c e remained p l a n a r ,  i n the s o l i d and  i n t e r f a c e during  (1.1)  i t was  t h a t no  that e q u i l i b r i u m conditions  solidification.  the extent  solute d i f f u s i o n  e x i s t e d at  Figure 1 i l l u s t r a t e s  t h a t a r i s e s as a r e s u l t of v a r y i n g  assumed  the s o l u t e  of m i x i n g i n  the redistrithe  liquid.  Figure  1.  S e g r e g a t i o n r e s u l t i n g from (a) complete m i x i n g , (b) no m i x i n g and (c) p a r t i a l m i x i n g i n the l i q u i d .  From F i g u r e 1 i t i s apparent  t h a t complete m i x i n g  ( a ) , causes long range c o m p o s i t i o n a l v a r i a t i o n s whereas no m i x i n g ,  ( b ) , y i e l d s a uniform  ( c ) , can be r e p r e s e n t e d by  C  S  = k  e  C  q  curve  (macrosegregation)  solute distribution  f o r the i n i t i a l and t e r m i n a l t r a n s i e n t s ) . p a r t i a l mixing,  i n the l i q u i d ,  (except  The i n t e r m e d i a t e case o f (2)  :  k -1 (1 - f ) °  (1.3)  where k , the e f f e c t i v e d i s t r i b u t i o n c o e f f i c i e n t , i s d e f i n e d t o be e (2) C /C and i s g i v e n by s o J  k  o  (1 - k ) exp (- f  4-  )  Q  where 6 i s the t h i c k n e s s o f t h e d i f f u s i o n boundary l a y e r which e x i s t s at t h e i n t e r f a c e . minimum o f k liquid.  Q  The magnitude o f k  f o r complete mixing  I t i s apparent  i n an i n c r e a s e i n k . g  £  (assuming k  Q  < 1) ranges from a  t o a maximum o f 1 f o r no m i x i n g  from E q u a t i o n  i n the  (1.4) t h a t an i n c r e a s e i n 6 r e s u l t s  The boundary l a y e r t h i c k n e s s i s l a r g e l y dependent  on the e x t e n t o f l i q u i d m i x i n g .  Maximum v a l u e s o f 6 o c c u r when no mix-  i n g i s p r e s e n t and minimum v a l u e s a r i s e under c o n d i t i o n s o f e x t e n s i v e mixing.  Thus, c o n t r o l o f mixing  i n a solidifying  liquid  c o n t r o l over the s o l u t e r e d i s t r i b u t i o n i n t h e s o l i d i f i e d  Mixing sources.  can a f f o r d product.  i n the l i q u i d may a r i s e from one o r more o f s e v e r a l  F l u i d f l o w may r e s u l t  i n Part I of t h i s t h e s i s .  from n a t u r a l c o n v e c t i o n .  T h i s i s examined  Flow may a l s o r e s u l t from f o r c e d c o n v e c t i o n .  P a r t I I c o n s i d e r s the s o l u t e s e g r e g a t i o n which o c c u r s as a r e s u l t o f controlling  i n g o t g r a i n s t r u c t u r e by f o r c e d c o n v e c t i o n .  4 Natural convection  o c c u r r i n g d u r i n g s o l i d i f i c a t i o n can  d i v i d e d i n t o two main c a t e g o r i e s , s o l u t e c o n v e c t i o n Solute  c o n v e c t i o n may  and  thermal  be  convection.  occur when c o n c e n t r a t i o n d i f f e r e n c e s , a r i s i n g  solute r e j e c t i o n at a s o l i d - l i q u i d  from  i n t e r f a c e , cause the appearance o f (3)  d e n s i t y g r a d i e n t s i n the l i q u i d m e t a l . i n t e r a c t i o n of s o l u t e c o n v e c t i o n w i t h has  developed equations  Wagner  has  studied  the  the d i f f u s i o n boundary l a y e r  to d e s c r i b e the r e s u l t i n g  and  solute redistribution.  An e v a l u a t i o n of the e f f e c t of m i x i n g i n the l i q u i d on d i s t r i b u t i o n along  u n i d i r e c t i o n a l l y s o l i d i f i e d h o r i z o n t a l r o d s of  solute dilute  (4) s i l v e r i n t i n a l l o y s has been made by Weinberg • . flow i n a q u a l i t a t i v e way solidified.  by v a r y i n g  He v a r i e d the  the diameter o f the rods  rods, extensive mixing occurred  i n the  s o l i d i f i c a t i o n of a l l rods of diameter g r e a t e r than 2mm. causes f o r t h i s m i x i n g were (a) thermal c o n v e c t i o n c u r r e n t s s e t up by volume changes d u r i n g vection.  E v i d e n c e was  presented  s t u d i e s on thermal c o n v e c t i o n  (b)  f r e e z i n g , and  t h a t causes  marily responsible f o r solute mixing. extensive  being  Weinberg found t h a t , based on the d i s t r i b u t i o n o f  i n the s o l i d i f i e d  (b) and  fluid  liquid  silver during  Suggested convective (c) s o l u t e con-  (c) were not  pri-  T h i s c o n c l u s i o n l e d to s e v e r a l i n h o r i z o n t a l melts.  Thermal c o n v e c t i o n w i l l occur when the melt i s s u b j e c t e d to a h o r i z o n t a l temperature g r a d i e n t . i s q u i t e simple. with  The  e x p l a n a t i o n o f t h i s phenomenon  Because the d e n s i t y o f most l i q u i d m e t a l s d e c r e a s e s  i n c r e a s i n g temperature, the h o r i z o n t a l temperature g r a d i e n t  sults i n a h o r i z o n t a l density gradient.  .The  system i s u n s t a b l e  re-  and  liquid  can be expected to flow i n a f a s h i o n s i m i l a r to t h a t shown i n  Figure  2.  the  5  o X  Liquid  F i g u r e 2.  O  Solid  o  C o n v e c t i v e flow p a t t e r n a r i s i n g from h o r i z o n t a l temperature g r a d i e n t .  During i n v e s t i g a t i o n s to determine s o l i d i f i c a t i o n  conditions  n e c e s s a r y to e l i m i n a t e m a c r o s e g r e g a t i o n and i n t e r c e l l u l a r s e g r e g a t i o n , Cole  (5)  found t h a t one of the  most important parameters  i n controlling  these f e a t u r e s was the temperature g r a d i e n t i n the l i q u i d G^.  Con-  s e q u e n t l y , i n e a r l y experiments, s e n s i t i v e thermocouples were p l a c e d i n d i r e c t c o n t a c t w i t h the l i q u i d  i n o r d e r to measure G^.  t h a t the temperature i n the l i q u i d  Kramer  I t was  found  f l u c t u a t e d i n a random manner.  , Cole found t h a t the p r e s e n c e o f the s o l i d - l i q u i d  had no b e a r i n g on the appearance o f the f l u c t u a t i o n s .  interface  Thus, experiments  were d e s i g n e d to study the c h a r a c t e r o f temperature f l u c t u a t i o n s i n a completely l i q u i d  system.  From these experiments C o l e concluded t h a t  temperature  f l u c t u a t i o n s o c c u r r e d when the l o n g i t u d i n a l temperature g r a d i e n t exceeded  a c r i t i c a l value G .  G  L  The amplitude and frequency o f temperature  6  f l u c t u a t i o n s were found to decrease  (a) as  decreased,  a n g l e o f h e a t i n g was decreased from the h o r i z o n t a l of  (b) as t h e  (with t h e c o l d end  the l i q u i d b e i n g the lowest p o i n t o f the system) and ( c ) as t h e  h e i g h t o f t h e l i q u i d i n the system decreased.  I t was a l s o found  that  3 c the r e l a t i o n s h i p - (Height o f M e l t )  G^  = c o n s t a n t d e s c r i b e d the con-  d i t i o n s n e c e s s a r y f o r the onset o f temperature  fluctuations.  The  g r e a t e r the melt h e i g h t , the g r e a t e r the i n s t a b i l i t y o f the systems w i t h r e s p e c t t o thermal c o n v e c t i o n . C o l e f u r t h e r concluded t h a t the presence o f temperature f l u c t u a t i o n s r e s u l t e d from the e x i s t e n c e o f n a t u r a l thermal c o n v e c t i o n i n the l i q u i d m e t a l and t h e r e f o r e n a t u r a l thermal c o n v e c t i o n c o u l d be d e t e c t e d by s e n s i t i v e thermocouples suggested  p l a c e d i n the l i q u i d .  t h a t c o n v e c t i o n c o u l d be e l i m i n a t e d by s u i t a b l y  the temperature  controlling  d i s t r i b u t i o n i n the l i q u i d .  Subsequent experiments by Cole i n v e s t i g a t e d during s o l i d i f i c a t i o n .  was found to e x i s t .  fluid  flow  As a r e s u l t o f the i n t e r a c t i o n o f thermal  v e c t i v e flow w i t h the s o l i d - l i q u i d  i n t e r f a c e a "thermal boundary  T h i s was d e s c r i b e d by the parameter  ceeding away from the i n t e r f a c e , the f l o w i s f i r s t or  I t was  6^.  con-  layer" Pro-  laminar, a buffer  t r a n s i t i o n r e g i o n f o l l o w s and f o r d i s t a n c e s away from t h e i n t e r f a c e  g r e a t e r than 6 ^ the flow i s e s s e n t i a l l y t u r b u l e n t .  The t h i c k n e s s o f  the thermal boundary l a y e r , as a f u n c t i o n o f the f l u i d  properties of  the l i q u i d m e t a l and t h e growth v a r i a b l e s , was found to be g i v e n by t h e . (5) expression :  7  6, -  H ' 1  203a •^ -  5  . 203R L 2  T  R 6  (1 + 1.58  .  2  ~  ~  cJgg(G°)  where:  2  a  Pr  406RLa 77  +  C gB(G°)  3  , , ( 1 "  2  g  i s the a c c e l e r a t i o n  g  i s the c o e f f i c i e n t o f volume  a  i s the thermal  diffusivity  Pr  i s the P r a n d t l  number  H  i s the h e i g h t of the s o l i d - l i q u i d  G°  i s the temperature  C  i s the s p e c i f i c heat i s the growth  Using  T  . ' )  expansion  interface  calculated  f o r the e x p e r i m e n t a l  (0.001 < R cm/sec. < 0.005, 10 < G ° °C/cm < 20) These v a l u e s were i n good  a theory was  6  5  developed  which accounted  - 46 6 T  T  interface of a s o l i d i f y i n g alloy.  to determine  S  4  + 56;<S  J  T  S  +  agreement  boundary l a y e r t h i c k n e s s e s .  of c o n v e c t i o n w i t h the s o l u t e boundary l a y e r  formulated  (1.5)  a  In o r d e r to e s t i m a t e the e f f e c t o f thermal  the s o l i d - l i q u i d  5  rate  w i t h the e x p e r i m e n t a l l y observed  action  /  g r a d i e n t a t the i n t e r f a c e  g i v i n g v a l u e s o f the o r d e r o f 1 cm.  macrosegregation  1  due to g r a v i t y  t h i s e x p e r e s s i o n 6^, was  c o n d i t i o n s employed  )  p  i s l a t e n t heat of f u s i o n  R  R 6  2  L  P  T  the magnitude o f <5  6  g  The  c o n v e c t i o n on f o r the i n t e r which e x i s t s a t relationship  was:  g  806^ (R5 - 2D) ± § -r53.3 H [a + R (_L_ _ « 1 )] C G° p L 2  T  (1.6)  8  where D i s the d i f f u s i o n c o e f f i c i e n t o f t h e s o l u t e i n l i q u i d s o l v e n t .  To o b t a i n the s o l u t e d i s t r i b u t i o n s d u r i n g h o r i z o n t a l  solidi-  f i c a t i o n the f o l l o w i n g procedure was u t i l i z e d : (1) S u b s t i t u t e a p p r o p r i a t e v a l u e s o f f l u i d meters and G °  and R i n t o E q u a t i o n  flow para-  (1.5) and thus  c a l c u l a t e 6^,.  (2) S u b s t i t u t e t h i s v a l u e o f 6 ^ i n t o E q u a t i o n  (1.6) and  solve for 6 . s  (3) S u b s t i t u t e t h i s v a l u e o f 6 i n t o the e q u a t i o n : s  k  e  =  ^ _  (1 - k ) 6 R o s  (  *  1  7  )  2D and o b t a i n the v a l u e o f k .  When the growth parameters a r e such t h a t the v a l u e o f k = l , e  a s o l i d i f i e d p r o d u c t which has u n i f o r m c o m p o s i t i o n ( F i g u r e 1,, curve b) s h o u l d be o b t a i n e d cooling  over most o f i t s l e n g t h  (providing c o n s t i t u t i o n a l  does n o t occur and cause t h e p l a n a r t o c e l l u l a r  super-  interface trans-  ition) .  Cole a l s o o b t a i n e d an e x p r e s s i o n f o r c a l c u l a t i n g v e l o c i t y of f l u i d  um  53.3 .2 T 6  the maximum  f l o w p a r a l l e l to the i n t e r f a c e :  H  L a + R ( -±C G° p L T  -T1 )  6  -  2  (1.8)  from  (1.5) I t would be expected t h a t U i n c r e a s e s as the m  (1.8) and  h e i g h t of the melt i n c r e a s e s and as the temperature g r a d i e n t G°  increases,  Equation  This i s  (1.8) shows t h a t u  m  s h o u l d i n c r e a s e w i t h i n c r e a s i n g H.  c o n s i s t e n t w i t h the f i n d i n g t h a t the c r i t i c a l h o r i z o n t a l g r a d i e n t  G°  n e c e s s a r y f o r the o n s e t o f temperature f l u c t u a t i o n s d e c r e a s e s as H i n creases. the  That i s , i n c r e a s i n g  the m e l t h e i g h t decreases the s t a b i l i t y o f  melt w i t h respect to convective flow. For  a s t a t i o n a r y system  (R = 0) the e x p r e s s i o n f o r u  m  be-  comes :  u  or,  m  1  3/5 = 53.3 a H ' 2  (1 + 1.58  5  Pr)  f o r a g i v e n melt h e i g h t and average melt  Clearly  /  (1.9) 203a  u  2  m  a  (G  L  temperature:  )  then, f o r any non-zero h o r i z o n t a l temperature g r a d i e n t one would  expect c o n v e c t i v e f l o w , t h a t i s , u^ ^ 0.  T h i s i n d i c a t e s t h a t the de-  t e c t i o n o f temperature f l u c t u a t i o n s a t some c r i t i c a l g r a d i e n t G^ > 0 does not i n d i c a t e the onset o f f l u i d  flow.  The Cole t e c h n i q u e then i s c  not  sufficiently  s e n s i t i v e to d e t e c t f l u i d  flow a t G^ < G^.  No  attempt  was made to measure flow v e l o c i t i e s and thus v a l i d a t e the e x p r e s s i o n f o r m ( 8) M u l l e r and Wiehelm  have a l s o demonstrated  the e x i s t e n c e of  temperature f l u c t u a t i o n s i n the m e l t d u r i n g the growth o f m e t a l and  semi-  conductor c r y s t a l s by the h o r i z o n t a l normal f r e e z e , and zone m e l t i n g techniques.  Correlation of  the p e r i o d i c v a r i a t i o n i n temperature w i t h  the  s p a c i n g o f c o n c e n t r a t i o n s t r i a e i n c r y s t a l s o f InSb was e s t a b l i s h e d .  Experiments showed t h a t f o r m e l t s between 10 and 30 cm l o n g the amplitude  and f r e q u e n c y o f the observed temperature f l u c t u a t i o n s were  independent o f the m e l t l e n g t h p r o v i d e d t h a t t h e temperature and tempera t u r e g r a d i e n t were kept c o n s t a n t a t the measuring  point.  The f i r s t d i r e c t measurements o f f l o w v e l o c i t i e s  i n liquid (9)  metals c o n t a i n e d i n h o r i z o n t a l b o a t s were c a r r i e d out by Utech  . In  s t u d i e s o f thermal c o n v e c t i o n i n molten t i n the o b s e r v a t i o n was made t h a t a sequence o f temperature f l u c t u a t i o n s r e c o r d e d by a thermocouple i n s e r t e d i n t o the m e l t was r e p e a t e d a s h o r t time l a t e r by a second thermocouple l o c a t e d down stream. the  By measuring  the time r e q u i r e d f o r  temperature f l u c t u a t i o n to t r a v e l a known d i s t a n c e downstream, an  i n d i c a t i o n o f mean flow v e l o c i t y c o u l d be o b t a i n e d .  Utech found ( i n  agreement w i t h C o l e ) t h a t a c r i t i c a l h o r i z o n t a l temperature g r a d i e n t was n e c e s s a r y t o produce temperature f l u c t u a t i o n s .  E v i d e n c e t h a t flow  Q  o c c u r r e d a t g r a d i e n t s below G  was o b t a i n e d by o b s e r v i n g t h a t as the  h o r i z o n t a l temperature g r a d i e n t i n c r e a s e d from z e r o a c o r r e s p o n d i n g i n c r e a s e i n v e r t i c a l temperature g r a d i e n t appeared. resultant  (hot l i q u i d above c o l d )  S u p p r e s s i o n o f c o n v e c t i v e flow by a magnetic f i e l d d i s a p p e a r a n c e o f the v e r t i c a l g r a d i e n t showed  t h a t the v e r t i c a l  temperature g r a d i e n t was a d i r e c t  and t h e  conclusively  consequence o f con-  v e c t i v e flow. The r e s u l t s o f t h e i n v e s t i g a t i o n o f Utech f o r c o n v e c t i v e flow i n a h o r i z o n t a l boat w i t h an open top can be summarized as f o l l o w s . At  small h o r i z o n t a l  temperature g r a d i e n t s c i r c u l a t i o n o f l i q u i d b e g i n s ,  c a u s i n g a v e r t i c a l temperature g r a d i e n t t o appear.  This convective flow  may be c o n s i d e r e d l a m i n a r i n as much as the temperature a t any p o i n t i n  11  the system remains c o n s t a n t , once steady attained.  The flow p a t t e r n under t h e s e c o n d i t i o n s c o u l d n o t be d e t e r -  mined d i r e c t l y . observed  s t a t e c o n d i t i o n s have been  Utech i n f e r r e d  the p a t t e r n would be s i m i l a r to t h a t  i n low v i s c o s i t y o i l , t h a t i s , a narrow stream  a l o n g t h e bottom  f l o w i n g from t h e c o l d end t o t h e h o t end o f t h e b o a t , a r i s i n g of  column  l i q u i d a t the h o t end o f the boat w i t h the h o t l i q u i d which had been  c a r r i e d t o the top f a l l i n g more o r l e s s u n i f o r m l y along t h e e n t i r e l e n g t h , F i g u r e 2.  As breaks  the h o r i z o n t a l g r a d i e n t i s i n c r e a s e d , t h i s u n i f o r m  down and a number o f c e l l s o f c i r c u l a t i n g  l e n g t h o f the b o a t .  T h e i r presence  flow  l i q u i d appear along the  i s manifested  by t h e f l u c t u a t i o n s  i n temperature as measured by a thermocouple l o c a t e d a t any p o i n t i n the system.  The r e s u l t i n g " t u r b u l e n c e " becomes i n c r e a s i n g l y s e v e r e as the  temperature g r a d i e n t i s i n c r e a s e d .  When the l i q u i d t i n i s a p p r o x i m a t e l y  1 cm deep and the g r a d i e n t i n the l i q u i d i s about 12°C/cm, mean v e l o cities  i n the l i q u i d o f the o r d e r o f 1 cm/second a r e observed.  flow v e l o c i t i e s measured by Utech a r e a p p r o x i m a t e l y tude l e s s than would be p r e d i c t e d by the C o l e  The  an o r d e r o f magni-  analysis.  Utech employed the boundary l a y e r a n a l y s i s o f E c k e r t and Drake  f o r flow past a v e r t i c a l  immersed i n a f l u i d a t u n i f o r m f o r maximum f l o w  p l a t e w i t h s u r f a c e temperature T ,  temperature T ,  to o b t a i n t h e e x p r e s s i o n  velocity:  u  = 0.766V m  (0.952  +  Pr) ( ^  2  ^  < - > 1  11  12  where:  v  i s the k i n e m a t i c  viscosity  x  i s the v e r t i c a l d i s t a n c e from the l e a d i n g end  of  the  vertical wall T  i s the temperature d i f f e r e n c e a c r o s s the boundary  According  to Utech  (although i t i s not e v i d e n t from  layer.  an  (9)  examination  of h i s r e s u l t s  ) Equation  (1.11) agrees  reasonably w e l l  w i t h h i s v e l o c i t y measurements. A NaCl melt  ( t r a n s p a r e n t ) was  v e l o c i t y determination technique  and  used i n o r d e r t o v e r i f y  to d i r e c t l y observe  the  this  flow  p a t t e r n a s s o c i a t e d w i t h a h o r i z o n t a l temperature g r a d i e n t a c r o s s a melt The  flow p a t t e r n observed  the g e n e r a l l y steady p a t t e r n of c e l l s  i n NaCl appears i n F i g u r e 3.  flow along the bottom and  t h a t r e s u l t i n upward and  along the e n t i r e l e n g t h of the  F i g u r e 3.  Superimposed  top o f the boat  downward v e r t i c a l  boat.  R e p r e s e n t a t i o n o f the flow p a t t e r n i n the h o r i z o n t a l boat.  is a  currents  on  13  T h i s p a t t e r n o f c e l l s changed w i t h time. was  the v e r t i c a l f l o w always  number of  i n the same d i r e c t i o n .  (a d i m e n s i o n l e s s parameter  f l u i d s ) o f molten NaCl  ( t y p i c a l l y 0.1  - 0.01)  metals would resemble  The  classifying  (Pr = 0.13)  i t was  Only a t the c o l d and hot ends S i n c e the P r a n d t l  the c o n v e c t i v e b e h a v i o u r  approaches  those o f l i q u i d  metals  assumed t h a t f l o w p a t t e r n s i n l i q u i d  those observed i n m o l t e n N a C l .  f a c t t h a t l i q u i d NaCl i s t r a n s p a r e n t suggests t h a t heat  t r a n s f e r by r a d i a t i o n i s a p p r e c i a b l e and t h e r e f o r e the c o n v e c t i v e heat t r a n s f e r f o r NaCl and a l i q u i d m e t a l , c o n s t r a i n e d by the same t h e r m a l environment, would be a p p r e c i a b l y d i f f e r e n t .  I f the heat t r a n s f e r modes  were d i s s i m i l a r the flow p a t t e r n s would a l s o be  dissimilar.  (12) O b s e r v a t i o n s by H u r l e  t h a t the mode o f  temperature  f l u c t u a t i o n s c o u l d be changed by q u i t e s m a l l movements o f the thermocouple or by i n s e r t i n g a 50 u diameter w i r e v e r t i c a l l y clearly  i n t o the m e l t  i n d i c a t e d t h a t the presence o f any o b s t r u c t i o n i n the m e l t ,  i n c l u d i n g the thermocouple, had a profound e f f e c t on the oscillations.  T h i s o b s e r v a t i o n suggested t h a t the temperature  ations reported e a r l i e r the  temperature  m e l t s themselves.  fluctu-  (5,6,7,8,9) were p r o b a b l y not c h a r a c t e r i s t i c o f I t was  s u b s e q u e n t l y found t h a t , p r o v i d e d the  thermocouples were i n s e r t e d to a depth of. l e s s than 0.04  cm,  oscillations  c o u l d s t i l l be r e c o r d e d and these o s c i l l a t i o n s were not a f f e c t e d by moving the  thermocouples.  H u r l e a l s o observed t h a t above a c r i t i c a l  hori-  z o n t a l temperature g r a d i e n t temperature o s c i l l a t i o n s appeared. c r i t i c a l g r a d i e n t was (At  found to i n c r e a s e w i t h d e c r e a s i n g m e l t  a boat l e n g t h o f 4 cm i t was  5.0  °C/cm and a t 2.6  This  length.  cm i t was  7.5  °C/cm).  14  Davis and Fryzuk  s t u d i e d thermal c o n v e c t i v e m i x i n g  in  h o r i z o n t a l melts w i t h known i n i t i a l s o l u t e d i s t r i b u t i o n s . R e s u l t s showed that observable convective mixing h o r i z o n t a l temperature  ( i n rods 2 mm  g r a d i e n t s g r e a t e r than 5°C/cm and  s o l u t e r e d i s t r i b u t i o n o c c u r s f o r temperature  Cole and Winegard's f o r m u l a t i o n  temperature  fluctuations  3 , H  attained.  f l u c t u a t i o n s i n the melt presence  that extensive  c G  = 3.1,  p r e d i c t s that  ( i n d i c a t i v e o f the onset of t u r b u l e n t thermal  c o n v e c t i o n ) would not appear u n t i l a temperature 400°C/cm was  occurs at  g r a d i e n t s 15°C/cm o r  (5) greater.  i n diameter)  gradient of  O b v i o u s l y then, the o c c u r r e n c e o f  approximately  temperature  i s not s u f f i c i e n t l y s e n s i t i v e t o d e t e c t the  o f e x t e n s i v e thermal  convection. (14)  C a r r u t h e r s and Winegard f o r determining  a s o l i d h o r i z o n t a l r o d o f pure l e a d was  f u r n a c e a l o n g the r o d .  contained approximately  10%  is  liquid  m e l t e d by moving  i n c o n t a c t w i t h the s o l i d  A f t e r steady s t a t e m e l t i n g  the l i q u i d was  In  s o l i d i f i e d by  lead  had  removing  S i n c e the d i s t r i b u t i o n c o e f f i c i e n t of t h a l l i u m i n l e a d  c l o s e to u n i t y , v e r y l i t t l e  freezing.  The  thallium.  been a c h i e v e d over 5 to 10 cm, the f u r n a c e .  technique  the e x t e n t of c o n v e c t i v e m i x i n g i n h o r i z o n t a l m e l t s .  t h e i r experiments a tube  employed y e t another  solute r e d i s t r i b u t i o n occurred during  Concentration p r o f i l e s r e s u l t i n g  from boundary l a y e r f l o w at  the i n t e r f a c e were r e v e a l e d by a s u i t a b l e e t c h i n g t e c h n i q u e . a t i o n o f boundary l a y e r t h i c k n e s s and of the e x t e n t of c o n v e c t i v e flow.  The  shape was  The  vari-  then taken as a measure  f o l l o w i n g c o n c l u s i o n s were  ob-  tained: (1) C o n v e c t i v e m i x i n g temperature heat  increases with increasing  g r a d i e n t and  transfer.  horizontal  also with increasing  radial  15  (2) I n c r e a s i n g the l e n g t h of the melt promotes more v i g o r ous  (3) The  thermal  convection.  l i q u i d height exerts very l i t t l e  e f f e c t on  the e x t e n t o r the c o n f i g u r a t i o n o f m i x i n g  due  either to  thermal  convection. (4) The is  e f f e c t of i n t r o d u c i n g thermocouples i n t o the m e l t to cause i n c r e a s e d c o n v e c t i v e m i x i n g .  Another important is  c o n c l u s i o n of the work of C a r r u t h e r s  t h a t the onset of temperature  to a f l o w t r a n s i t i o n from l a y e r flow.  o s c i l l a t i o n s seen by C o l e  l a m i n a r boundary l a y e r to t u r b u l e n t boundary  Thus, i t i s a g a i n apparent  that a p p r e c i a b l e f l u i d flow  be p r e s e n t a t g r a d i e n t s w e l l below those n e c e s s a r y temperature  corresponds  f o r the onset  may  of  fluctuations.  Of the t e c h n i q u e s d e s c r i b e d above not one measuring flow v e l o c i t i e s g r a d i e n t s below G fluctuation.  i n melts  i s capable  s u b j e c t e d to h o r i z o n t a l  temperature  , the g r a d i e n t a s s o c i a t e d w i t h the onset of  T  Nor  i s i t p o s s i b l e to a c c e p t the flow p a t t e r n s  i n nonmetallic m e l t s ^ a s  of  temperature observed  b e i n g t y p i c a l of the c o n v e c t i v e f l o w  p a t t e r n s which o c c u r i n l i q u i d m e t a l s .  However, any  theory  attempting  to p r e d i c t the s o l u t e d i s t r i b u t i o n i n a s o l i d i f i e d m e t a l r e q u i r e s i n f o r m a t i o n c o n c e r n i n g the e x t e n t of f l u i d flow i n the l i q u i d m e t a l solidification.  during  In the absence of such i n f o r m a t i o n i t becomes n e c e s s a r y  to make assumptions about the f l u i d flow p r e s e n t i n the m e l t .  A c c o r d i n g l y , the p r e s e n t i n v e s t i g a t i o n was  undertaken  to  obtain direct serve f l u i d  i n s i t u measurements of f l u i d  flow p a t t e r n s i n l i q u i d m e t a l s .  flow v e l o c i t i e s T h i s was  and  to  ob-  accomplished  by  (16) the use of r a d i o a c t i v e t r a c e r s .  Stewart  p l o y e d r a d i o a c t i v e t r a c e r techniques patterns i n thin  and Weinberg  to observe  have  em-  flow v e l o c i t i e s  and  c e l l s w i t h l e n g t h t o h e i g h t r a t i o of a p p r o x i m a t e l y  However, f o r the purpose of  ( l e n g t h to h e i g h t r a t i o s between 40 and  since this i s  the geometry adopted i n most fundamental examinations  solute segregation during s o l i d i f i c a t i o n .  70) was  A l s o the boat  selected  s t a l s of a s p e c i f i e d  losses  to s i m u l a t e c o n d i t i o n s r e q u i r e d f o r growth of c r y size.  Although  t h i s geometry p r o v i d e s a  simple  c o n f i g u r a t i o n f o r s o l i d i f i c a t i o n s t u d i e s i t p r e s e n t s a complex and yet  unsolved problem from the thermal  p o i n t s of view.  of  used to con-  p r o v i d e d w i t h a cover to reduce asymmetric heat  from the system and  1.  the p r e s e n t i n v e s t i g a t i o n a h o r i z o n t a l r o d  configuration  t a i n the melt was  flow  c o n v e c t i o n and  fluid  dynamics  as  2 - DETERMINATION OF FLOW VELOCITIES IN HORIZONTAL RODS OF MOLTEN TIN  2.1.  Flow V e l o c i t y D e t e r m i n a t i o n by M a n u a l l y M o n i t o r i n g the Movement o f R a d i o a c t i v e T r a c e r  As o u t l i n e d i n t h e i n t r o d u c t i o n , one o f t h e purposes  of the  p r e s e n t i n v e s t i g a t i o n was to develop a t e c h n i q u e t h a t would p e r m i t  direct  measurement o f flow v e l o c i t i e s i n h o r i z o n t a l rods o f molten m e t a l .  It  was c o n s i d e r e d e s s e n t i a l t h a t t h e measurement t e c h n i q u e employed s h o u l d not p e r t u r b the l i q u i d m e t a l system.  Specifically,  t h e v e l o c i t y ob-  s e r v e d s h o u l d be due o n l y t o the f l u i d p r o p e r t i e s o f t h e system e x p e r i m e n t a l l y imposed c o n d i t i o n s .  and t h e  I t was d e c i d e d t h a t a method i n -  v o l v i n g t h e e x t e r n a l m o n i t o r i n g o f r a d i o a c t i v e t r a c e r as i t flowed a l o n g w i t h t h e melt would b e s t s a t i s f y the f l u i d  t h e c o n d i t i o n o f not i n t e r f e r i n g  flow t h a t would n o r m a l l y o c c u r .  with  The development o f such a  t e c h n i q u e i s p r e s e n t e d below.  2.1.1.  G e n e r a l E x p e r i m e n t a l Apparatus The  apparatus  i s shown i n F i g u r e 4.  and Procedure  employed f o r the f i r s t  The molten m e t a l  s e r i e s o f experiments  (pure t i n ) was c o n t a i n e d i n a  g r a p h i t e boat which was equipped w i t h a d e v i c e f o r i n t r o d u c i n g the r a d i o active tracer. surrounded  The boat was i n s e r t e d i n t o a 45 mm O.D. Vycor  by an 18 i n c h long tube f u r n a c e .  i n t h e f o l l o w i n g way.  tube  The f u r n a c e was c o n s t r u c t e d  An 18 i n c h l e n g t h o f 2 i n c h diameter  copper tube was  Tube , — Graphite  =1  1  Furnace -n=f Boat I  F=r—  ^-Thermocouple leads  o  to  ^ inch Lead  Collimator  Scintillation  Figure 4 .  The apparatus employed  fori n i t i a l  Counter  s e r i e s o f experiments.  wrapped w i t h a l a y e r o f 1/16 s i s t a n c e windings 1/2  inch t h i c k asbestos c l o t h .  Four r e -  (26 gauge nichrome) each 4 i n c h e s l o n g , s e p a r a t e d by  i n c h , and h a v i n g s e p a r a t e power t e r m i n a l s were wound on t o the  asbestos.  The r e s i s t a n c e o f each w i n d i n g was  Each w i n d i n g was tube was  coated w i t h S a i r s e t r e f r a c t o r y cement.  The wound  surrounded by g l a s s wool and p l a c e d i n an aluminum  The c o n t a i n e r was assembly  a p p r o x i m a t e l y 120 ohms.  container.  mounted on a s e t o f wheels so t h a t the e n t i r e f u r n a c e  c o u l d be moved.  T h i s f a c i l i t a t e d changing the thermal en-  vironment o f the melt w i t h o u t p h y s i c a l l y d i s t u r b i n g  the m e l t  itself.  The i n n e r two windings were connected i n s e r i e s t o a 0 t o 130 10 ampere, v a r i a c . second v a r i a c .  The  The o u t e r windings were s i m i l a r l y  volt,  connected to a  Vycor tube and tube f u r n a c e were s u p p o r t e d by a  Handy A n g l e framework.  A s c i n t i l a t i o n c o u n t e r surrounded by a l e a d  collimator  ( c o n s t r u c t e d from l e a d b r i c k s ) and mounted on a moveable c a r r i a g e  was  l o c a t e d below the g r a p h i t e b o a t , Vycor tube and f u r n a c e assembly.  A  l o c a t i n g d e v i c e was fixing  a t t a c h e d to the s i d e of the c a r r i a g e r a i l  the p o s i t i o n o f  assembly  to allow  the s c i n t i l a t i o n c o u n t e r - l e a d c o l l i m a t o r  a t any d e s i r e d p o s i t i o n .  The a r r i v a l o f r a d i o a c t i v e  i s o t o p e above a g i v e n c o l l i m a t o r s l i t  trace  p o s i t i o n would be d e t e c t e d by a  r a p i d i n c r e a s e i n the a c t i v i t y r e a c h i n g the s c i n t i l l a t i o n c o u n t e r through the  collimator s l i t .  The v e l o c i t y o f f l u i d  f l o w i n the m e l t above c o u l d  then be measured by d e t e r m i n i n g the time d i f f e r e n c e f o r the movement of r a d i o a c t i v e t r a c e r from one p o s i t i o n to a p o s i t i o n a known d i s t a n c e away.  The  a c t i v i t y passing  through the c o l l i m a t o r was  measured  w i t h a Quantum E l e c t r o n i c s Q-6A, v i d e o s c a l a r u s i n g a sodium i o d i d e s c i n t i l l a t i o n counter.  To e s t a b l i s h  the optimum o p e r a t i n g  f o r the c o u n t e r , a r a d i o a c t i v e source was the a c t i v i t y was steps.  The  voltage  p l a c e d above the counter  measured as a f u n c t i o n of a p p l i e d v o l t a g e , i n 25  optimum o p e r a t i n g v o l t a g e was  and volt  taken as the v o l t a g e i n the  c e n t e r of the p l a t e a u o b t a i n e d on the a c t i v i t y v e r s u s  applied voltage  curve.  R a d i o a c t i v e t r a c e i s o t o p e s used d u r i n g the course o f i n v e s t i g a t i o n were Ag^"*"^, Sn^^ p r o p e r t i e s of these i s o t o p e s . 59's  o r b e t t e r q u a l i t y was  and T l ^ . 2  4  Table 1 l i s t s  Non-radioactive  sent  Ag,  Sn,  the p e r t i n e n t  Sb and T I o f  to e i t h e r A.E.C.L. at Chalk R i v e r ,  Canada,or to R a d i o a c t i v e M a t e r i a l s C o r p o r a t i o n , B u f f a l o , New irradiation.  Trace  a l l o y s of v a r y i n g composition  the r e s u l t i n g i s o t o p e s . vertical  The  this  a l l o y was  York, f o r  were p r e p a r e d  from  melted i n a r e s i s t a n c e wound  tube f u r n a c e and mixed f r e q u e n t l y (by v i g o r o u s  s h a k i n g ) f o r at  l e a s t 15 minutes to i n s u r e homogeneous d i s p e r s a l of the r a d i o a c t i v e i s o t o p e throughout the t r a c e a l l o y . g r a p h i t e mold and sized pieces  the r e s u l t i n g  (2-4 gms  The  a l l o y was  c a s t i n g was  then c a s t i n t o a  cut i n t o  conveniently  i n w e i g h t ) , packaged, l a b e l l e d and  then s t o r e d  i n a l e a d c a s t l e u n t i l needed.  Throughout the f o l l o w i n g p r e s e n t a t i o n the d e n s i t y of t r a c e a l l o y s w i l l be g i v e n r e l a t i v e to the d e n s i t y of pure m o l t e n t i n at a s i m i l a r temperature. c a l c u l a t e d on the  The  r e l a t i v e d e n s i t i e s of the t r a c e a l l o y s ,  assumption o f independent b e h a v i o u r  a l l o y e d , were determined by  the  relation:  o f the  species  TABLE 1 Properties of Radioisotopes  Isotope  Ag  1 1 0  Half L i f e  Type o f R a d i a t i o n and Energy (Mev)  270d  6  112d  X-ray, y  (.53), y (.66 -  2.0)  113 Sn Sb TI  1 2 4  2 0 4  60d 4.1y  (.26)  f3~ (2.31), y (.60-2.11) B~  (.76)  22  / p  alloy  100  %(wt  %Sn)  p  +  l  (100 - wt %Sn)  where p^ i s the d e n s i t y o f the t r a c e  The major problem  P  pSn  isotope.  a s s o c i a t e d w i t h the measurement o f flow  v e l o c i t y by a r a d i o a c t i v e t r a c e r t e c h n i q u e l i e s i n t r o d u c e the t r a c e r w i t h o u t d i s t u r b i n g  i n d i s c o v e r i n g a way  the m e l t s .  to  The o b s e r v a t i o n s and  r e s u l t s o b t a i n e d from an e x t e n s i v e s e r i e s o f experiments  undertaken  to  develop a s u i t a b l e t r a c e r i n t r o d u c t i o n t e c h n i q u e a r e p r e s e n t e d seq u e n t i a l l y i n S e c t i o n s 2.1.2. to 2.1.8.  2.1.2. T r a c e r I n t r o d u c t i o n by M e l t i n g Back Through a Region C o n t a i n i n g R a d i o a c t i v e M a t e r i a l 2.1.2.1.  E x p e r i m e n t a l Apparatus  and  Procedure  The g r a p h i t e boat used f o r the i n i t i a l attempt  t o study  the e x t e n t of c o n v e c t i v e f l o w i n h o r i z o n t a l rods o f molten t i n i s shown i n F i g u r e 5.  The boat had two  channels which were covered f o r a p p r o x i -  mately 90% o f the channel l e n g t h w i t h a s h o r t uncovered  s e c t i o n a t each  end.  0.64  0.64  In the covered s e c t i o n the melt c r o s s s e c t i o n was cm h i g h .  The h e i g h t of m e t a l i n the uncovered  a p p r o x i m a t e l y 1 cm. by 2 hole-1/16  Thermocouples  i n c h O.D.  cm wide and  reservoirs  was  (30 gauge i r o n - c o n s t a n t a n , i n s u l a t e d  m u l l i t e t u b i n g ) were p o s i t i o n e d at 3 cm  inter-  v a l s along one of the channels w i t h the thermocouple beads s i t u a t e d i n the c e n t r e o f the channel.  Thus, the temperature  d i s t r i b u t i o n could  be measured i n one channel w h i l e study o f the f l u i d temperature measuring I t was  d e v i c e s , c o u l d be  assumed t h a t the two  channels had  f l o w , unimpeded by  c a r r i e d out i n the o t h e r c h a n n e l . i d e n t i c a l temperature  distributions.  (a) 27 cm h— 3 cm —*-  Sectional View  Figure 5.  The g r a p h i t e boat used f o r i n i t i a l s t u d i e s of c o n v e c t i v e flow i n h o r i z o n t a l rods of molten t i n .  The boat was f i l l e d with 59's t i n (supplied by Vulcan Metals) and allowed to s o l i d i f y .  Approximately 3 gms of t i n was removed  from one end of the " c l e a r " channel and i n i t s place was cast radioactive tracer, a Sn-0.2wt % A g trace isotope since i t  1 1 0  alloy.  Ag  1 1 0  was chosen as the  i s a strong gamma emitter capable of penetrating  the Vycor tube and furnace assembly and thus i t s presence over the collimator s l i t i s e a s i l y detected.  The loaded boat was then placed i n  the Vycor tube and the thermocouple leads were connected through a Leeds and Northrup multi-point switch to a Honeywell Electronik 194 recorder. An i c e water bath was employed as the cold junction and the.thermocouples were p e r i o d i c a l l y calibrated against the freezing point of pure t i n .  Temperatures measured were believed to be correct w i t h i n  ± 0.1 °C.  The d i s t r i b u t i o n of a c t i v i t y along the length of the channel was determined p r i o r to melting with the moveable collimators c i n t i l l a t i o n counter described e a r l i e r . and the t i n melted.  The furnace was switched on  When the thermocouple adjacent to the radioactive  tracer indicated the tracer was molten, monitoring of tracer movement began.  This Was accomplished by equal time i n t e r v a l counting at various  positions along the length of the channel. be accompanied  Any movement of tracer would  by a change i n the observed d i s t r i b u t i o n of a c t i v i t y  along the boat.  In order to evaluate the c a p a b i l i t y of the collimator to accurately determine the d i s t r i b u t i o n of a c t i v i t y along the boat the following test was devised.  Following the procedure outlined above,  the d i s t r i b u t i o n of t r a c e r was occured.  The melt was  determined some time a f t e r m e l t i n g had  then quenched  (by f i l l i n g  the Vycor tube w i t h  water) and, w i t h the boat s t i l l  i n the same p o s i t i o n , the  of t r a c e r was  The boat was  a g a i n monitored.  and the s o l i d i f i e d  t i n was  i n t o 1/4  taken from the f u r n a c e  removed from the c l e a r channel of the b o a t .  The d i s t r i b u t i o n of t r a c e r along the t i n was it  distribution  determined by  sectioning  i n c h p i e c e s , weighing each p i e c e , and measuring  i t s activity  by f i x e d geometry c o u n t i n g w i t h a T r a c e r l a b I n c . s c i n t i l l a t i o n and  counter  ampliscalar.  2.1.2.2.  R e s u l t s and D i s c u s s i o n R e s u l t s of the t e s t  t o e v a l u a t e the a c c u r a c y of the  c o l l i m a t e d c o u n t i n g procedure appear i n F i g u r e 6.  The open squares  are from the i n s i t u m o n i t o r i n g a f t e r quenching and the f i l l e d from the s e c t i o n i n g and c o u n t i n g p r o c e d u r e . n o r m a l i z e d .to f a c i l i t a t e  The a c t i v i t i e s have been  comparison of the r e s u l t s .  can be r e p r e s e n t e d by one curve.  circles  Both s e t s of d a t a  A c c o r d i n g l y , the a c t i v i t y v e r s u s  p o s i t i o n p r o f i l e determined by the c o l l i m a t o r - s c i n t i l l a t i o n  counter  arrangement can be taken as an a c c u r a t e r e p r e s e n t a t i o n o f the h o r i z o n t a l d i s t r i b u t i o n of r a d i o a c t i v e t r a c e r along the m e l t  F i g u r e s 7, 8, and 9 show r e s u l t s from p r e l i m i n a r y experiments  length.  t y p i c a l of those o b t a i n e d  to determine the amount of f l u i d  flow  a s s o c i a t e d w i t h s m a l l h o r i z o n t a l temperature g r a d i e n t s a l o n g the tin.  liquid  F i g u r e 7(a) shows the temperature d i s t r i b u t i o n along the t i n  melt 1/2 hour, 1 hour and 4 hours a f t e r m e l t i n g had o c c u r e d . the average temperature o f the m e l t changes,  the temperature  Although distri-  0  1  F i g u r e 6.  2  3 4 POSITION  Results of the t e s t  5 ALONG  6  7 BOAT  8 (SN)  9  to e v a l u a t e the accuracy o f the c o l l i m a t e d c o u n t i n g  10  procedure.  ho  bution across the melt remains e s s e n t i a l l y the same f o r the 4 hour period.  Figure 7(b) shows the d i s t r i b u t i o n of tracer before melting  and at approximately 1/2 hour, 1 hour and 4 hours after melting. The tracer has first  moved approximately half the length of the melt i n the  1/2 hour but very l i t t l e movement occurs over the subsequent  3h hours.  A gradual l e v e l i n g of the tracer d i s t r i b u t i o n i n the f i r s t  half of the melt was observed over the 4 hours.  Comparison of  Figures 7(a) and 7(b) indicates that the position of furthest  advance  of tracer and the position of zero temperature gradient are approximately coincident.  To establish whether the stoppage of flow was  uniquely determined by the p o s i t i o n of the zero temperature gradient the tube furnace was moved, thus changing the temperature d i s t r i b u t i o n in the melt.  Figure 8(a) shows the temperature d i s t r i b u t i o n 5, 10  and 20 minutes after moving the tube furnace.  Figure 8(b) shows the  effect of the temperature changes on the d i s t r i b u t i o n of tracer along the melt.  The coincidence of tracer r e d i s t r i b u t i o n with movement along the boat of the zero gradient i s made more obvious by comparing Figures 8(a) and 9.  Figure 9 i s a plot of a c t i v i t y at a p a r t i c u l a r  position along the boat at various times a f t e r melting. seen from Figure 8, positions  As can be  at 8.5, 11 and 13.5 cm are on one side  of the zero gradient whereas those at 18.5 and 21 cm are on the other side.  Very l i t t l e change i n the a c t i v i t y observed at each p o s i t i o n  occurred between 1 hour after melting and 4 hours a f t e r melting. S i g n i f i c a n t changes occur shortly a f t e r the furnace i s moved.  Figure  8(a) indicates that at between 5 minutes a f t e r and 10 minutes after  28  280  o 270  UJ  260 [  250 h 1000 h -  800 h  Heoo t 400 > o < 200 0  0  F i g u r e 7.  3 6 9 POSITION  12 15 ALONG  18 21 24 BOAT (CM)  (a) The temperature p r o f i l e s a t the i n d i c a t e d times a f t e r the t r a c e r had melted. (b) The d i s t r i b u t i o n o f t r a c e r a t the i n d i c a t e d times a f t e r m e l t i n g .  27  29  T  1  1  1  1  1  r  (a) ?  20 min after-  280  o: H 270 Before moving furnace 1000 h (b)  ~. 8 0 0 o  -  Before moving furnace  600  O  t 400 > r-  20 min after  o  < 200 0  J  0  F i g u r e 8.  L  3 6 9 POSITION  12 15 ALONG  18 21 BOAT  24 27 (CM)  (a) The temperature p r o f i l e s a t the i n d i c a t e d times. (b) The d i s t r i b u t i o n of t r a c e r b e f o r e and a f t e r moving the f u r n a c e .  1400  —i  1  A 8-5 cm from tracer end 110 cm  "  "  "  a 13-5 cm  "  "  "  ©18-5 cm  "  »  "  O  1200 -1000  A 210 cm from tracer end  3  800  t  600  o  < 400 Furnace  moved  200 JA.  120 180 240 300 TIME A F T E R TRACER MELTED F i g u r e 9.  The change i n a c t i v i t y with  360 (MIN)  420  time at v a r i o u s p o s i t i o n s along the melt,  Co O  moving the f u r n a c e the zero g r a d i e n t has moved p a s t the 18.5 position.  Correspondingly  the 18.5  cm p l o t on F i g u r e 9 shows t h a t  t r a c e r s t a r t s moving p a s t t h i s p o s i t i o n a p p r o x i m a t e l y moving the f u r n a c e .  cm  6 minutes  after  S i m i l a r l y the zero g r a d i e n t moves p a s t the 21  cm  p o s i t i o n about 10 minutes a f t e r f u r n a c e movement and F i g u r e 9 i n d i c a t e s t r a c e r movement p a s t t h i s p o s i t i o n a t a p p r o x i m a t e l y  the same time.  These r e s u l t s c l e a r l y show t h a t : (1) The  r e g i o n of  zero h o r i z o n t a l temperature g r a d i e n t i s  not permeable to thermal (2) An extremely  The  flow.  s m a l l h o r i z o n t a l temperature  a p p a r e n t l y any sufficient  convective  g r a d i e n t g r e a t e r than z e r o , p r o v i d e s  driving  c o n c l u s i o n t h a t thermal  difference,  f o r c e f o r thermal  convective  c o n v e c t i v e m i x i n g w i l l not pass  flow. through  a r e g i o n of zero h o r i z o n t a l temperature g r a d i e n t i s i n agreement w i t h (13) the f i n d i n g s of Davis and of  Fryzuk  a r a d i o a c t i v e s o l u t e along 2 mm  e v e r , they were unable  who  s t u d i e d the  diameter  redistribution  h o r i z o n t a l melts.  to d e t e c t c o n v e c t i v e mixing  How-  at temperature  g r a d i e n t s below 5 °C/cm. Evidence  that convective mixing  the r e g i o n of zero g r a d i e n t i s p r e s e n t e d d i s t r i b u t i o n was to  o c c u r s on b o t h  i n F i g u r e 10.  initial  a c h i e v e d , by a l l o w i n g t r a c e r to move down the boat  a r e g i o n of zero g r a d i e n t (at a p p r o x i m a t e l y  the t r a c e r d i s t r i b u t i o n i n the f i r s t quenching.  The  s i d e s of  The boat was  Sn-0.2 % Ag"*""^ was  21 cm), w a i t i n g  until  21 cm became homogeneous and  removed from the f u r n a c e and  c a s t i n t o the end of the b o a t .  a new  then  piece of  F i g u r e 10(a)  shows  32  265  i  - i —  1  1  1  1  1  r  (a) o  o  QJ  260 h i  LU  hr  after  melting  255 h  1200  h  1000 h  (b)  ~ hr  after  melting  o:800 d >-  600  >  P 400  < o  •  200 0  Figure  0 10.  3 6 9 12 15 18 POSITION ALONG BOAT  21 24 (CM)  (a) The temperature p r o f i l e 1/2 hour a f t e r the t r a c e r melted. (b) The d i s t r i b u t i o n of t r a c e r b e f o r e and a f t e r melting.  27  t h a t a zero g r a d i e n t o c c u r r e d Correspondingly 15 cm mark.  approximately  15 cm along  the boat.  t h e r e was movement o f t r a c e r up t o , b u t not p a s t t h e  A l s o , the d i s t r i b u t i o n o f t r a c e r t o the r i g h t o f the  15 cm mark had evened o u t .  Thus, thermal c o n v e c t i v e m i x i n g was t a k i n g  p l a c e on b o t h s i d e s o f the  zero g r a d i e n t , b u t the p r e s e n c e o f the  zero g r a d i e n t prevented  m i x i n g along  the e n t i r e l e n g t h o f t h e b o a t .  T h i s r e s u l t suggests the e x i s t e n c e o f a q u i e s c e n t of zero g r a d i e n t .  F i g u r e 11 i l l u s t r a t e s  would be expected under the e x p e r i m e n t a l  zone i n the r e g i o n  the type o f flow p a t t e r n which c o n d i t i o n employed here.  zero g r a d i e n t f u n c t i o n s as a v a l v e i n t h a t c o n v e c t i o n  occurs  The  on both  s i d e s o f the zero g r a d i e n t b u t t h e r e i s no mass t r a n s p o r t between the two  cells.  provided  Stewart's a u t o r a d i o g r a p h y ^ ^  v i s u a l c o n f i r m a t i o n o f the e x i s t e n c e o f a q u i e s c e n t  a zero g r a d i e n t  2.1.2.3.  o f double c e l l flow has now zone i n  region.  E v a l u a t i o n o f Technique  A l t h o u g h the t r a c e r i n t r o d u c t i o n technique  just  described  was r a t h e r u n s o p h i s t i c a t e d , i t d i d show t h a t d e t e c t a b l e thermal conv e c t i v e flow o c c u r s  a t any h o r i z o n t a l g r a d i e n t g r e a t e r than zero.  flow c o u l d n o t have been d e t e c t e d by temperature o s c i l l a t i o n Unfortunately  techniques.  i t was not p o s s i b l e to determine the c o n t r i b u t i o n o f  volume changes on m e l t i n g coming o f t h i s  This  t o the observed f l o w .  t r a c e r i n t r o d u c t i o n technique  The major s h o r t -  i s the l a c k o f c o n t r o l  over the time a t which the t r a c e r was i n t r o d u c e d i n t o t h e m e l t .  A  much more d e s i r a b l e technique would a l l o w i n t r o d u c t i o n o f t r a c e r a t any  specified  time, f o r example, a f t e r a c h i e v i n g a s t a b l e temperature  Zero  Figure 1 1 .  Gradient  The expected flow p a t t e r n when a zero g r a d i e n t i s p r e s e n t .  d i s t r i b u t i o n i n the m e l t .  2.1.3.  T r a c e r I n t r o d u c t i o n by R o t a t i n g a V e r t i c a l L o c a t e d at the End o f the G r a p h i t e Boat  2.1.3.1.  E x p e r i m e n t a l Apparatus  and  Cylinder  Procedure  The g r a p h i t e boat used f o r t h i s s e c t i o n o f the g a t i o n i s shown i n F i g u r e 12.  I t i s the same boat as was  investiused i n  the p r e v i o u s s e c t i o n but w i t h one m o d i f i c a t i o n ; one end of the c l e a r channel has been f i t t e d w i t h a h o l l o w c y l i n d e r which i s opened on s i d e , F i g u r e 12(b).  The c y l i n d e r was  one  loaded w i t h t r a c e r i n the  tracer  heated w i t h a Bunsen Burner u n t i l the  tracer  l o a d i n g b l o c k shown i n F i g u r e 1 2 ( c ) .  The b l o c k was  melted and flowed i n t o the i n t r o d u c i n g  cylinder.  r o t a t e d such t h a t the c y l i n d e r opening was to the t r a c e r r e s e r v o i r . introducing  c y l i n d e r was  The  F o l l o w i n g s o l i d i f i c a t i o n of the t r a c e r , removed from  then  not i n l i n e w i t h the channel the  the l o a d i n g b l o c k and p l a c e d i n  the g r a p h i t e boat such t h a t the c y l i n d e r opening was the c h a n n e l .  c y l i n d e r was  not a l i g n e d w i t h  I n t r o d u c t i o n of t r a c e r i n t o the melt was  a c h i e v e d , a t any  d e s i r e d time a f t e r m e l t i n g , by r o t a t i n g  the c y l i n d e r u n t i l  and c y l i n d e r opening were c o i n c i d e n t .  The movement of t r a c e r along  the melt was  2.1.3.2.  monitored by  R e s u l t s and  the method d e s c r i b e d  the c h a n n e l  earlier.  Discussion  In o r d e r to determine the e x t e n t of m i x i n g a s s o c i a t e d w i t h t r a c e r i n t r o d u c t i o n , experiments were c a r r i e d out i n which t h e r e was zero h o r i z o n t a l temperature  g r a d i e n t i n the m e l t j u s t ahead of the  a  (c)  (b)  Tracer  Introduction F i g u r e 12.  Cylinder  Tracer  Loading  (a) Top view of g r a p h i t e boat with t r a c e r i n t r o d u c t i o n c y l i n d e r i n p l a c e . d u c t i o n c y l i n d e r . (c) T r a c e r l o a d i n g b l o c k .  Block  (b) I n t r o -  ON  tracer introducer.  F i g u r e 13 shows r e s u l t s o f such an experiment.  From F i g u r e 13(a) i t can be seen t h a t t h e r e i s a r e g i o n o f zero i e n t approximately  3 cm ahead o f the t r a c e r i n t r o d u c e r .  grad-  Movement o f  t r a c e r p a s t the r e g i o n of zero g r a d i e n t i s c l e a r l y shown i n F i g u r e It  i s evident  t h a t t h e r e i s some a d d i t i o n a l d r i v i n g  ment o f t r a c e r along  the m e l t .  13(b).  f o r c e f o r the move-  T h i s flow may a r i s e from s o l u t e convec-  t i o n , s i n c e the Sn-0.2 wt % Ag"*""*"^ a l l o y i s more dense than pure t i n , (1.0005 pSn) or from some m e c h a n i c a l d i s t u r b a n c e  associated with  tracer  i n t r o d u c t i o n , o r from a combination o f b o t h .  To e l i m i n a t e the e f f e c t o f m i x i n g a s s o c i a t e d w i t h  intro-  d u c t i o n , experiments were conducted i n which t r a c e r was i n t r o d u c e d a melt which had a zero g r a d i e n t approximately tracer introducer.  With the zero g r a d i e n t  6 t o 10 cm ahead o f the  f u r t h e r down the m e l t  was the case i n the experiment shown i n F i g u r e 13 m i x i n g with  i n t r o d u c t i o n was not s u f f i c i e n t  g i o n o f zero g r a d i e n t .  After i n i t i a l  to carry the t r a c e r past flow along  along  the  the r e -  the m e l t had stopped  The temperature g r a d i e n t s  The " i n i t i a l "  at v a r i o u s p o s i t i o n s  gradient d i s t r i b u t i o n represents  d i t i o n s under which t r a c e r was i n t r o d u c e d  and flow along  the con-  the melt  One and one h a l f hours a f t e r i n t r o d u c t i o n the s t a b l e t r a c e r  d i s t r i b u t i o n marked " i n i t i a l " was observed. 14 are times a f t e r t u r n i n g on the argon. and  argon  boat appear i n F i g u r e 14(a) and t h e t r a c e r d i s t r i b u t i o n i n  F i g u r e 14(b).  stopped.  than  associated  the temperature d i s t r i b u t i o n i n the melt was changed by p a s s i n g through the Vycor tube.  into  The times shown on F i g u r e  Comparison o f F i g u r e s 14(a)  14(b) show t h a t i n c r e a s i n g the g r a d i e n t above zero r e s u l t s i n f l o w  along  the b o a t .  Figure  13. (a) The temperature p r o f i l e along the melt at the time of tracer introduction. (b) The d i s t r i b u t i o n of tracer before and 15 minutes after introduction.  3 9  0-6 o  ?  0-4  1 a:  0-2 h 00  UJ  -0-2 h  Initial (90 min after intro.) 3 min  o  < 200  3  6 9 POSITION  12 15 ALONG  18 21 24 BOAT (CM)  F i g u r e 14. (a) The temperature g r a d i e n t s along the m e l t . (b) The d i s t r i b u t i o n of t r a c e r b e f o r e and a f t e r p a s s i n g argon.  40  In the experiments temperature  d i s t r i b u t i o n was  d e s c r i b e d i n the p r e v i o u s s e c t i o n  changed by moving the f u r n a c e whereas  d u r i n g t h i s s e r i e s of t e s t s argon f l o w was temperature it  along the m e l t .  the  employed t o a l t e r  the  S i n c e the f u r n a c e i s i n d u c t i v e l y wound  c o u l d be s p e c u l a t e d t h a t e l e c t r o m a g n e t i c s t i r r i n g  e f f e c t s were  r e s p o n s i b l e f o r the flow which o c c u r r e d a f t e r moving the f u r n a c e . The  r e s u l t s of the experiments  g r a d i e n t along the melt section.  from  temperature  concluded  the f l u i d  flow.  t h a t i t i s the thermal The  average  driving  flow v e l o c i t y  estimated  the r a t e of advance of the p o i n t s of i n t e r s e c t i o n w i t h the a b s c i s s a  of a tangent curve  to a l t e r the  agree w i t h those o b t a i n e d i n the p r e v i o u s  Thus, i t can be  f o r c e t h a t causes  u s i n g argon  drawn along the l e a d i n g edge of the a c t i v i t y v e r s u s  ( F i g u r e 14(b))was 5 x 10  During t e n t and  _3  cm/sec.  the course of e x p e r i m e n t a t i o n  cause of m i x i n g  t o e v a l u a t e the  a t u r e p r o f i l e 25 minutes a f t e r t u r n i n g on the argon from p r e v i o u s r e s u l t s , be  c o n s i d e r e d extremely  c o n d i t i o n s t h e r e i s no m i x i n g between the uncovered  2.1.3.3.  E v a l u a t i o n of The  temper-  15(a))would, flow.  A p p a r e n t l y under some r e s e r v o i r where  the covered s e c t i o n of the boat.  Technique  e s t i m a t e of f l o w v e l o c i t y o b t a i n e d above i s of  v a l u e s i n c e the temperature changing  (Figure  The  favourable f o r f l u i d  shows t h a t no flow o c c u r r e d .  t r a c e r i s i n t r o d u c e d and  ex-  associated with tracer introduction occasional  anomalous r e s u l t s of the type shown i n F i g u r e 15 o c c u r r e d .  However, F i g u r e 15(b)  position  g r a d i e n t a l o n g the melt was  d u r i n g the v e l o c i t y measurement.  limited  continually  In o r d e r to determine  the  41  T  1  1  POSITION  1  1  ALONG  1  BOAT  1  r  (CM)  F i g u r e 15. (a) The temperature p r o f i l e s b e f o r e and a f t e r p a s s i n g argon, (b) The d i s t r i b u t i o n of t r a c e r a t the times i n d i c a t e d .  r e l a t i o n s h i p between temperature g r a d i e n t n e c e s s a r y to i n t r o d u c e  and  flow v e l o c i t y i t i s  the t r a c e r i n t o the m e l t a f t e r a steady  temperature d i s t r i b u t i o n has  been a t t a i n e d .  A l t h o u g h the amount of  m i x i n g a s s o c i a t e d w i t h t r a c e r i n t r o d u c t i o n may flow v e l o c i t i e s which would occur a t h i g h e r anomalous phenomenon d i s p l a y e d  i n Figure  be  s m a l l compared  to  temperature g r a d i e n t s ,  15 n e c e s s i t a t e d  sequents attempts at t r a c e r i n t r o d u c t i o n be  state  c a r r i e d out  that  the  sub-  i n the  covered  s e c t i o n of the b o a t .  2.1.4.  T r a c e r I n t r o d u c t i o n by R o t a t i n g a V e r t i c a l C y l i n d e r S i t u a t e d i n the Covered S e c t i o n of the G r a p h i t e Boat  2.1.4.1.  E x p e r i m e n t a l Apparatus and Introduction  was  accomplished u s i n g  boat was  of t r a c e r i n t o the  the apparatus shown i n F i g u r e  an o v e r a l l melt l e n g t h of 27  the a d d i t i o n of a g r a p h i t e h e a t i n g (coated w i t h a g r a p h i t e  flow  covered s e c t i o n of the b o a t 16.  The  graphite  e s s e n t i a l l y the same as t h a t used p r e v i o u s l y , t h a t i s , two  channels and  heating  Procedure  b l o c k was  through the  meter model 0158  and  Modifications  included  a copper c o o l i n g  block,  s u s p e n s i o n , Aquadag).  The  a r e s i s t a n c e winding powered by c o o l i n g b l o c k was flowmeter.  c y l i n d e r i n the same way  The  measured and  t r a c e r was  as d e s c r i b e d  of t r a c e r i n t o the melt was cylinder, Figure  block  cm.  i n t o the  i n S e c t i o n 2.1.3.1.  accomplished by  the  a V a r i a c . Argon  c o n t r o l l e d by  loaded  r o t a t i n g the  1 6 ( b ) , u n t i l the square h o l e  c l e a r channel were a l i g n e d .  heat source f o r  i n the  a Victro-  introduction Introduction  introduction  c y l i n d e r and (not  shown  i n the diagram) were employed to i n s u r e that the c y l i n d e r c o u l d be  mani-  pulated  S t a i n l e s s s t e e l g u i d e s and  to the f u l l y opened or f u l l y  stops  the  c l o s e d p o s i t i o n s remotely.  Overall  (a)  Copper  cooling  block  Graphite  heating  block  Argon j  Tracer Introducer (closed)  Push to  open Variac  (b)  Figure 16.  (a) Details of the graphite boat employed for experiments i n which the tracer was introduced i n the covered section of the melt. (b) Tracer introduction cylinder.  experimental  set-up  and m o n i t o r i n g  techniques  were the same as d e s c r i b e d  earlier.  2.1.4.2.  R e s u l t s and D i s c u s s i o n To  determine the amount o f flow a s s o c i a t e d w i t h  d u c t i o n technique  this  intro-  t r a c e r was i n t r o d u c e d when the melt had a s t a b l e z e r o  temperature g r a d i e n t along  i t s e n t i r e length.  t r a c e i s o t o p e t o remove the p o s s i b i l i t y  Sn  113  was used as t h e  of solute convection.  Figure  113 17(a)  shows the r e s u l t s o f i n t r o d u c i n g Sn  zero g r a d i e n t .  Appreciable  t r a c e r i n t o a melt  having  flow has accompanied t r a c e r i n t r o d u c t i o n as  the t r a c e r has moved approximately  10 cm i n 40 minutes.  To a s c e r t a i n  whether o r not the m i x i n g on i n t r o d u c t i o n was due s o l e l y t o r o t a t i n g the cylinder  (and p o s s i b l y d i s t u r b i n g the b o a t ) an experiment was under-  taken i n which the t r a c e r i n t r o d u c e r was p l a c e d i n the f u l l y p o s i t i o n p r i o r to melting (maintaining The  a flat  and the temperature was g r a d u a l l y r a i s e d  temperature d i s t r i b u t i o n ) u n t i l m e l t i n g  r e s u l t s o f t h i s experiment a r e shown i n F i g u r e 17(b).  of t r a c e r along  opened  the boat was almost as f a r as o c c u r r e d  The movement  i n Figure  T h i s i n d i c a t e d t h a t the r o t a t i o n o f t h e c y l i n d e r t o e f f e c t d u c t i o n was not the major cause o f the f l u i d  occurred.  17(a).  tracer intro-  flow a s s o c i a t e d w i t h the  i n t r o d u c t i o n of t r a c e r .  2.1.4.3. E v a l u a t i o n o f Technique The  r e s u l t s shown i n F i g u r e 17 i n d i c a t e d t h a t r o t a t i o n o f the  c y l i n d e r was not a major cause o f flow a s s o c i a t e d w i t h  i n t r o d u c t i o n ; they  a l s o c l e a r l y showed t h a t flow d i d occur under thermal c o n d i t i o n s which  45  1200  T  1  — i  1  1  1  1  r  (a)  Initial  a: 9 0 0 h d 600 -  24 min after intro. a <  300 0  4 0 min  12  0  15  18  21  24  27  1200 (b)  — Initial  a: 9 0 0 h d  >-  600 -  >  H 300 O <  0  15 min after melting 4 0 min  -  0  F i g u r e 17.  3 6 9 POSITION  12 15 18 21 24 ALONG BOAT (CM)  113 The d i s t r i b u t i o n of Sn ( i n a pure Sn melt having zero h o r i z o n t a l temperature g r a d i e n t ) b e f o r e and a f t e r (a) t r a c e r i n t r o d u c t i o n and (b) m e l t i n g with the i n t r o d u c t i o n c y l i n d e r i n the open p o s i t i o n s .  27  have h e r e t o f o r e been shown to be u n f a v o u r a b l e . was  Therefore,  t e m p o r a r i l y abandoned i n hopes o f d e v e l o p i n g  which would i n no way  a l t e r the f l u i d  this  technique  a method of i n t r o d u c t i o n  flow t h a t was  occurring prior  to  tracer introduction.  2.1.5.  T r a c e r I n t r o d u c t i o n by R o t a t i n g a H o r i z o n t a l C y l i n d e r L o c a t e d i n the Cover o f the G r a p h i t e Boat.  2.1.5.1.  Experimental The  Apparatus and  Procedure  o n l y d i f f e r e n c e between the g r a p h i t e boat used f o r t h i s  s e c t i o n of the i n v e s t i g a t i o n and method of t r a c e r i n t r o d u c t i o n . are shown i n F i g u r e 18.  shown i n F i g u r e 16  cribed  i n t e r a c t i o n between  the m e l t the i n t r o d u c t i o n c y l i n d e r was  w i t h the h o l e i n the cover.  s h o u l d then draw t r a c e r out i n t o the m e l t . the f l u i d  any  placed  To i n t r o d u c e t r a c e r the c y l i n d e r opening was  t a t e d i n t o alignment  to  i s the  D e t a i l s of the i n t r o d u c t i o n t e c h n i q u e  In o r d e r to p r e v e n t  the t r a c e r i n t r o d u c e r and i n the boat cover.  the one  ro-  Flow p a s t the  hole  The movement of t r a c e r ,  flow p r e s e n t , c o u l d then be monitored by  due  the p r o c e d u r e des-  earlier. i  2.1.5.2.  R e s u l t s and  Discussion  Three d i f f e r e n t t r a c e i s o t o p e s , S n ^ , 3  Ag"'"''"^ and T l ^ 2  were  4  used to e v a l u a t e the e f f e c t i v e n e s s of the t r a c e r i n t r o d u c t i o n t e c h n i q u e 113 shown i n F i g u r e 18.  I n i t i a l experiments were conducted u s i n g Sn  the t r a c e i s o t o p e , t h e r e f o r e , t h e r e would be no s o l u t e c o n v e c t i o n i n t e r f e r e with "gate" was  the thermal  convection.  as to  When the t r a c e r i n t r o d u c e r or  opened to the melt under c o n d i t i o n s o f zero h o r i z o n t a l  47  1  )  -ir-l ~  - -  "  - )  push to introduce tracer Tracer  V///////////////////////////A sectional  F i g u r e 18.  view  Details of tracer introduction from the boat cover.  temperature  g r a d i e n t no d e t e c t a b l e change i n the t r a c e r  o c c u r r e d over a h a l f hour p e r i o d . g r a d i e n t i n the melt was expected.  The gate was  The gate was  distribution  then c l o s e d and  the  changed such t h a t thermal c o n v e c t i o n would be then reopened.  Even under  conditions favourable  f o r flow no change i n the t r a c e r d i s t r i b u t i o n along the boat was served.  ob-  The t r a c e r had not e n t e r e d the m e l t .  To a s s i s t i n t r o d u c t i o n o f t r a c e r i n t o the melt a 30 wt ^,^204  a l l o y was  used i n a subsequent  experiment.  %  Since T l ^ ^ ^  g  a  204 s o f t 3-emmitter, the r e l a t i v e l y h i g h weight per cent o f T I t r a c e a l l o y was  n e c e s s a r y to f a c i l i t a t e m o n i t o r i n g .  a p p r e c i a b l y more dense than the pure t i n melt  i n the  T h i s a l l o y was  (1.133 pSn)  and would be  expected to e n t e r the m e l t by s o l u t e c o n v e c t i o n a f t e r opening T h i s was  then  the g a t e .  c o n f i r m e d e x p e r i m e n t a l l y as the t r a c e r p r o f i l e became u n i f o r m  a p p r o x i m a t e l y 4 minutes temperature  a f t e r opening the g a t e , F i g u r e 1 9 ( b ) .  d i s t r i b u t i o n shown i n F i g u r e 19(a) one would expect  movement to be p r e d o m i n a n t l y to the l e f t  With  tracer  o f i t s o r i g i n a l p o s i t i o n as  would f o l l o w the thermal c o n v e c t i v e flow p a t t e r n expected.  the  this  That i s , the  more dense f l u i d moving from the c o l d end t o the hot end a l o n g the bottom of the c h a n n e l .  A u t o r a d i o g r a p h y o f the quenched m e l t c l e a r l y showed  t h a t the t r a c e a l l o y had i n both d i r e c t i o n s .  f a l l e n to the bottom  o f the channel and spread  S o l u t e c o n v e c t i o n must then have overcome the therma  convective flow. To reduce the d e n s i t y o f the t r a c e a l l o y but s t i l l m a i n t a i n a h i g h enough s p e c i f i c a c t i v i t y an a l l o y of 0.5 wt pared.  % Ag"*""*"^ i n Sn was  pre-  T h i s a l l o y had a s p e c i f i c a c t i v i t y h i g h enough t o f a c i l i t a t e moni  t o r i n g and i t was  s l i g h t l y more dense than the pure t i n (1.0013 pSn)  thus  49  295 ? 290 |  285 |-  UJ I—  280 1000 (b)  -  800 Initial  H 600 h t 400 h >  4 min  o  < 200  0 F i g u r e 19.  12 15 ALONG  3 6 9 POSITION  after  intro. J  18 21 24 BOAT (CM)  27  (a) The temperature p r o f i l e along the m e l t . (b) The d i s t r i b u t i o n of T l ^ b e f o r e and a f t e r t r a c e r i n t r o d u c t i o n . 2  4  a i d i n g i n t r o d u c t i o n i n t o the m e l t .  Opening the gate w i t h a zero g r a d i e n t  along the melt produced n e g l i g i b l e flow along the channel over a minute i n t e r v a l .  The gate was  c l o s e d and the temperature  a d j u s t e d t o that shown i n F i g u r e 2 0 ( a ) . s u l t i n g movement o f t r a c e r . moved t o the l e f t  2.1.5.3.  F i g u r e 20(b)  20  distribution  shows the r e -  As expected the more dense t r a c e  alloy  o f the p l a c e o f i n t r o d u c t i o n .  E v a l u a t i o n of  Technique 113  Experiments  u s i n g Sn  showed t h a t .this t r a c e r  introduction  t e c h n i q u e depends on s o l u t e c o n v e c t i o n f o r e n t r y o f t r a c e a l l o y i n t o melt.  That i s , the t r a c e r must be more dense than the m e l t . 204  t r a c e r i s too dense, as was it  the case w i t h the 30 wt  % TI  I f the  i n Sn  alloy,  i n t e r f e r e d w i t h or overcame the t h e r m a l c o n v e c t i v e f l o w p r e s e n t .  Even the r e a s o n a b l y s u c c e s s f u l experiment  w i t h the 0.5 wt  % Ag"^^  i n Sn  t r a c e a l l o y r e q u i r e s t h a t the s l i g h t l y more dense t r a c e r drop from top  the  to the  flow. AI90,  How  the  bottom o f the melt i n o r d e r to f o l l o w the thermal c o n v e c t i v e t h i s i n t e r f e r e s w i t h the thermal c o n v e c t i o n i s not known.  t h i s method o f  tracer i n t r o d u c t i o n l e a d s to continuous  dilution  of  the t r a c e r even as the t r a c e r i s b e i n g i n t r o d u c e d thus making  of  the passage  o f t r a c e r over a g i v e n c o l l i m a t o r p o s i t i o n more  detection  difficult.  A f a r more d e s i r a b l e t e c h n i q u e would a l l o w i n t r o d u c t i o n o f a c o n c e n t r a t e d amount o f t r a c e r i n t o a s m a l l a r e a w i t h i n a s h o r t p e r i o d of time. a t e c h n i q u e i s d e s c r i b e d i n the f o l l o w i n g  section.  Such  i  51  300 F o  o  290  CL  UJ  280 5000  (b)  :4000  QL  Initial  3000 p2000 o <  5 min after intra  1000 0  _L_  L  0  F i g u r e 20.  3 6 9 POSITION  I  1  L  12 15 18 21 24 ALONG BOAT (CM)  (a) The temperature p r o f i l e a l o n g the melt, (b) The d i s t r i b u t i o n o f Az^® b e f o r e and a f t e r t r a c e r i n t r o d u c t i o n .  27  52  2.1.6.  T r a c e r I n t r o d u c t i o n by R o t a t i n g a H o r i z o n t a l C y l i n d e r L o c a t e d i n the Cover of the Boat and then G e n t l y Pushing T r a c e r i n t o the M e l t .  2.1.6.1.  E x p e r i m e n t a l Apparatus and Figure  introduction  Procedure  21 shows the m o d i f i c a t i o n s  technique i l l u s t r a t e d  i n Figure  t h a t were made to 18.  has  been added to f a c i l i t a t e r a p i d i n t r o d u c t i o n  and  thus a v o i d  section.  the  the open p o s i t i o n and  then g e n t l y  accomplished by f o r c i n g the  the p i s t o n mechanism shown i n F i g u r e  Detection  i n the  c a r r i e d out  as  described  Data t y p i c a l of t h a t o b t a i n e d employing the new  a c t i v i t y observed above two  collimator positions  place  m o n i t o r i n g p o s i t i o n s were 6.3  of i n t r o d u c t i o n . p o s i t i o n was  the e f f e c t s on  the  The  to  21(b).  of t r a c e r movement was  The  gate  t r a c e r i n t o the melt w i t h  22.  first  previous  r o t a t i n g the  technique appears i n F i g u r e  The  arrangement  of t r a c e r i n t o the m e l t  t r a c e r d i l u t i o n problem d i s c u s s e d  T r a c e r i n t r o d u c t i o n was  previously.  A piston  the  two  curves r e p r e s e n t the  a p p r o x i m a t e l y 3 cm  introduction change i n  "downstream" from cm  the  apart.  away from the gate to reduce  observed flow v e l o c i t y , o f t r a n s i e n t s  associated  introduction.  A c t i v i t i e s p l o t t e d are average count r a t e s over a 30  time i n t e r v a l .  The  time r e q u i r e d  c o l l i m a t o r p o s i t i o n s was tween the and  the  l a t e r i n the dividing  determined by measuring the  i n t e r s e c t i o n s of the  abscissa.  extrapolations  of the  time d i f f e r e n c e  Observed flow v e l o c i t y was  the known s e p a r a t i o n  of 6.3  cm by  second two be-  a c t i v i t y - t i m e curve  J u s t i f i c a t i o n of t h i s method of a n a l y s i s  thesis.  The  f o r movement of t r a c e r between the  with  i s presented  then c a l c u l a t e d  the measured time  v a r i a t i o n i n observed flow v e l o c i t y w i t h  by  difference.  temperature  53  F i g u r e 21.  D e t a i l s of mechanism used to f a c i l i t a t e t r a c e r i n t r o d u c t i o n from the boat c o v e r . (a) Top view (b) Side s e c t i o n a l view.  500  I  1  1  TIME F i g u r e 22.  1  1  AFTER  1  INTRO.  1  1  r  (MIN)  T y p i c a l a c t i v i t y v e r s u s time data f o r experiments employing f o r c e d i n t r o d u c t i o n from the boat cover.  tracer  55  d i f f e r e n c e between t h e hot and c o l d ends was s t u d i e d u s i n g a 1% Sb  124  124 i n pure Sn t r a c e a l l o y .  Sb  was chosen as the t r a c e isotope,  as i t i s  a s t r o n g y - emmitter o f h i g h s p e c i f i c a c t i v i t y and because i t i s s l i g h t l y l e s s dense  than pure Sn (0.9993 pSn).  S i n c e the t r a c e r i s l e s s  dense  than the t i n , i t s h o u l d tend t o remain near the top o f the melt i n moving from the hot end to the c o l d end. the top t o the bottom  Thus, motion o f t r a c e r  from  o f the m e l t by s o l u t e c o n v e c t i o n w i l l n o t o c c u r  as i t d i d w i t h the more dense Ag"*""^ and T l " ^ ^  alloys.  Sn'"^ i s n o t  a s u i t a b l e i s o t o p e f o r v e l o c i t y measurements s i n c e flow a l o n g t h e b o a t causes d i l u t i o n o f  the i s o t o p e , which has a l o w ' s p e c i f i c a c t i v i t y r e -  124 l a t i v e t o Sb  , and makes d e t e c t i o n o f i t s p r e s e n c e above a g i v e n  collimator position  difficult. 113  A l t h o u g h Sn  i s n o t a good t r a c e i s o t o p e f o r the c o l l i m a t e d  m o n i t o r i n g system used t o determine flow v e l o c i t i e s , i t s low energy r a d i a t i o n makes i t an a c c e p t a b l e t r a c e r f o r a u t o r a d i o g r a p h y experiments. 113 For t h i s reason Sn  t r a c e a l l o y s were used t o determine flow p a t t e r n s  i n the melt and t o e v a l u a t e the t r a c e r i n t r o d u c t i o n t e c h n i q u e . s e r i e s o f specimens the melt  (by f i l l i n g  to be a u t o r a d i o g r a p h e d  was p r e p a r e d by quenching  the Vycor tube w i t h water) a t v a r i o u s times  t r a c e r i n t r o d u c t i o n and w i t h d i f f e r e n t temperature d i s t r i b u t i o n s . r a d i o g r a p h s were o b t a i n e d by p l a c i n g emulsion X-ray f i l m i n l i g h t  the quenched  t i g h t boxes.  specimens  after Auto-  on double  Areas o f the f i l m a d j a c e n t t o  r e g i o n s o f t r a c e r appear darkened on d e v e l o p i n g . which  A  A l l autoradiographs  appear i n the t h e s i s have been p r i n t e d such that dark r e g i o n s i n -  d i c a t e the presence o f t r a c e r .  56  2.1.6.2.  Results  2.1.6.2.1.  v a r i a t i o n of flow v e l o c i t y w i t h temperature  between the hot  and  difference  c o l d ends of the boat i s shown i n F i g u r e  i n flow v e l o c i t y w i t h i n c r e a s i n g  the melt was possible  Discussion  Flow V e l o c i t y Measurements The  increase  and  expected, however, the  to determine the  23.  The  temperature d i f f e r e n c e  across  l a r g e degree of s c a t t e r made i t  form of the r e l a t i o n s h i p between these  im-  two  variables.  2.1.6.2.2.  Autoradiography The  was  e x t e n t of flow a s s o c i a t e d  e v a l u a t e d by  introducing  temperature g r a d i e n t  and  with tracer  introduction  t r a c e r i n t o a m e l t having zero  then quenching the  horizontal  resulting tracer  distribution. 113  The  possibility  of s o l u t e  the  trace isotope.  c o n v e c t i o n was  i s evident that appreciable  of the  the m e l t , under c o n d i t i o n s  f o r c i n g of the  i s shown to be  t r a c e r has  zero and  not  only  and 24.  tracer.  expected,  unexpected manner.  One with  t r a c e r i n t o the melt v i a the p i s t o n mechanism.  This  specimen which was  24(a).  to be  It  spread through  where c o n v e c t i v e flow would not be  amount of t r a c e r d i s p e r s i o n  so i n the  the  1  shown i n F i g u r e of  as  associated  i n t r o d u c t i o n , Figure was  the  a l s o spread i n a n o n r e p r o d u c i b l e and  might expect a s l i g h t the  t r a c e r are  m i x i n g accompanies i n t r o d u c t i o n  What i s more s i g n i f i c a n t i s t h a t  has  employing Sn  A u t o r a d i o g r a p h s of specimens quenched 0.5,  10 minutes a f t e r i n t r o d u c t i o n  but  a v o i d e d by  quenched 0.5  minutes a f t e r  Since the h o r i z o n t a l g r a d i e n t  t r a c e a l l o y the  same d e n s i t y  as  i n the melt  the m e l t , specimens .  TEMP. F i g u r e 23.  DIFF.  ACROSS  MELT  The dependence of flow v e l o c i t y on the temperature between the hot and the c o l d ends of the melt.  (°C) difference  Cn  Cold  Figure  end  24.  Hot  end  L o n g i t u d i n a l s e c t i o n a u t o r a d i o g r a p h s of specimens quenched (a) 0.5 minutes (b) 1 minute and (c) 10 minutes a f t e r t r a c e r i n t r o d u c t i o n i n t o a melt having zero h o r i z o n t a l temperature g r a d i e n t .  quenched a t times g r e a t e r than 0.5  minutes  show no f u r t h e r r e d i s t r i b u t i o n o f t r a c e r .  a f t e r i n t r o d u c t i o n should However, F i g u r e 24(b)  shows  movement o f t r a c e r towards the c o l d r e s e r v o i r and to the bottom of the channel.  The  specimen  quenced 10 minutes  a f t e r i n t r o d u c t i o n of  tracer  a g a i n shows movement o f t r a c e r to the bottom o f the channel but i n t h i s case the r e d i s t r i b u t i o n about  the p o i n t o f i n t r o d u c t i o n i s q u i t e  uniform.  F i g u r e 25 c o n t a i n s t r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s o f a specimen  quenched one minute a f t e r i n t r o d u c t i o n o f t r a c e r i n t o a melt  having zero h o r i z o n t a l temperature show a double c e l l  gradient.  These a u t o r a d i o g r a p h s  flow p a t t e r n i n the t r a n s v e r s e d i r e c t i o n .  suggests t h a t the t r a c e r must be more dense than the m e l t . 70 °C temperature  This Even w i t h a  d i f f e r e n c e between the hot and c o l d ends the t r a n s -  v e r s e flow p a t t e r n m a i n t a i n s i t s double c e l l  appearance,  F i g u r e 26.  S i n c e the average  time r e q u i r e d to quench the melt was  15 seconds  q u e s t i o n e d whether f l o w p a t t e r n s observed r e f l e c t e d  i t was  of the o r d e r o f  flow p a t t e r n s t h a t e x i s t e d p r i o r to quenching, o r , whether the c e l l appearance  was  a quench e f f e c t .  double  In o r d e r to study the e f f e c t  the quench on the observed flow p a t t e r n a s e r i e s o f experiments c a r r i e d out i n which the quench was melt.  initiated  bottom of the m e l t ) .  of  was  from the top s i d e o f the  ( R e c a l l , t h a t t o t h i s time quenching was  the Vycor tube w i t h water,  the  accomplished by  t h e r e f o r e , the quench was  filling  i n i t i a t e d a t the  Any major change i n the observed flow p a t t e r n f o r  a g i v e n s e t o f e x p e r i m e n t a l c o n d i t i o n s would then i l l u s t r a t e the p r e s e n c e of was  a quench e f f e c t .  A s p r a y tube over the covered s e c t i o n of the b o a t  employed t o f a c i l i t a t e quenching.  Both opened r e s e r v o i r s were  covered w i t h s t a i n l e s s s t e e l caps and s e a l e d w i t h S a i r s e t  cement to p r e -  (a) Cold  end  Hot  end  Top 10  8  2  >  ^  Outside  (b) Top  w 9  I  -  W 10  II  (a) P o s i t i o n from which a u t o r a d i o g r a p h s were o b t a i n e d . (b) T r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s (from p o s i t i o n s i n d i c a t e d i n (a)) of a specimen quenched 1 minute a f t e r t r a c e r i n t r o d u c t i o n i n t o a melt having zero h o r i z o n t a l temperature g r a d i e n t .  F i g u r e 26.  T r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s (from the p o s i t i o n s i n d i c a t e d ) of a specimen quenched 1 minute a f t e r i n t r o d u c t i o n of t r a c e r i n t o a melt having a 70 °C temperat u r e d i f f e r e n c e between the hot and c o l d ends.  vent quench water  c o n t a c t i n g the molten t i n .  proved t o be u n s u c c e s s f u l as i t was seeping i n t o the m e l t . throughout pattern. was  The top quench t e s t s  i m p o s s i b l e t o p r e v e n t water  This resulted i n  from  r a d i o a c t i v e t i n being sprayed  the Vycor tube y i e l d i n g an o b v i o u s l y u n r e p r e s e n t a t i v e f l o w In o r d e r t o reduce the quench time a d i f f e r e n t  type o f boat  developed and the r e s u l t s of a u t o r a d i o g r a p h y s t u d i e s u s i n g t h i s  boat w i l l be d i s c u s s e d i n S e c t i o n  2.1.6.3.  3.  E v a l u a t i o n of Technique Although i t was  not p o s s i b l e to c o n f i r m the a c c u r a c y o f  the a u t o r a d i o g r a p h s o b t a i n e d , i t was dense than the m e l t .  Quenching  s h o u l d c r e a t e an i n i t i a l  apparent t h a t the t r a c e r was  from the bottom  first  (normal  more  procedure)  c o n d i t i o n o f c o o l e r l i q u i d below warmer l i q u i d  and t h e r e f o r e one would not expect the double c e l l p a t t e r n observed a r e s u l t o f such quenching.  to be  S i n c e the melt and t r a c e a l l o y were o f  i d e n t i c a l c h e m i c a l c o m p o s i t i o n , t h a t i s , pure t i n and pure t i n cont a i n i n g r a d i o a c t i v e t i n , the p o s s i b i l i t y o f s o l u t e c o n v e c t i o n must be r u l e d out.  The h i g h e r d e n s i t y o f the t r a c e r must r e f l e c t  the t r a c e r i s at a lower temperature introduced.  the f a c t  than the m e l t i n t o which  that  it is  S i n c e the t r a c e r i s o r i g i n a l l y l o c a t e d i n the c o v e r o f the  boat and the t r a c e r i n t r o d u c t i o n mechanism extends a p p r o x i m a t e l y  5/16  i n c h above the cover (and c o u l d thus be e f f e c t e d more by a i r c o n v e c t i o n i n the Vycor t u b e ) , i t i s not unreasonable t h a t slightly  c o o l e r than the melt below i t .  the t r a c e r c o u l d  be  T h i s would account f o r the  double c e l l flow p a t t e r n observed i n the t r a n s v e r s e s e c t i o n a u t o r a d i o graphs.  From F i g u r e 24(b) i t was  apparent t h a t t h i s t r a c e r  introduction  t e c h n i q u e can cause a net a uniform  spread  flow of t r a c e r i n one  d i r e c t i o n rather  about the p o i n t o f i n t r o d u c t i o n .  the t r a c e r i n t o the m e l t was observed i n F i g u r e 23 and  probably  Flow due  than  to f o r c i n g  the main cause of the s c a t t e r  t h e r e f o r e t h i s i n t r o d u c t i o n t e c h n i q u e was  aban-  doned.  2.1.7.  Return to I n t r o d u c t i o n by R o t a t i n g a V e r t i c a l C y l i n d e r L o c a t e d i n the Covered S e c t i o n of the Channel  2.1.7.1.  E x p e r i m e n t a l Apparatus and  Procedure  Research to t h i s p o i n t i n the i n v e s t i g a t i o n has  (1) T r a c e r must be  introduced  i n the  covered s e c t i o n of the b o a t  to a v o i d  the anomalous r e s u l t s caused by  currents  i n the uncovered r e s e r v o i r s a t the end  g r a p h i t e boat  (2) T r a c e r  shown t h a t :  the  convective of  the  ( S e c t i o n 2.1.3.).  cannot be h e l d i n the boat cover as t h i s causes  t r a c e r to be  c o o l e r than the melt  r e s u l t s i n the f o r m a t i o n transverse  s e c t i o n and  ( S e c t i o n 2.1.6.2.2.). T h i s  of a double c e l l flow p a t t e r n i n  thus i n t e r f e r e s w i t h  flow that would n o r m a l l y  the  occur  the  under s i m i l a r  convective  experimental  conditions.  Of t r a c e r by  the f i v e i n t r o d u c t i o n techniques  r o t a t i n g a v e r t i c a l c y l i n d e r l o c a t e d i n the  the boat appears most s a t i s f a c t o r y . technique discussed readopted.  s t u d i e d i n t r o d u c t i o n of  In order  Therefore,  i n S e c t i o n 2.1.4.1. and to f a c i l i t a t e  covered s e c t i o n of  the i n t r o d u c t i o n  illustrated  greater f l e x i b i l i t y  i n F i g u r e 16  was  i n the e s t a b l i s h -  64  merit and c o n t r o l o f e x p e r i m e n t a l ing  temperature d i s t r i b u t i o n s t h e f o l l o w -  m o d i f i c a t i o n s were made t o the f u r n a c e and f u r n a c e power s u p p l y .  A 0 t o 92 ohms r h e o s t a t was p l a c e d i n s e r i e s w i t h one o f the end f u r n a c e windings t o enable  establishment  the f u r n a c e , F i g u r e 2 7 ( a ) .  o f s t e e p e r temperature g r a d i e n t s along  The V a r i a c power s u p p l i e s were r e p l a c e d  by the d u a l zone power s u p p l y and temperature c o n t r o l l e r shown i n F i g u r e 27(b). tral  The c o n t r o l thermocouple was l o c a t e d between the two  furnace windings.  The temperature g r a d i e n t along the f u r n a c e  cencould  then be a d j u s t e d by m a n i p u l a t i o n o f the c e n t r a l and end w i n d i n g s power d i s c r i m i n a t o r s and the 0 to 92 ohm r h e o s t a t .  Average f u r n a c e  was a d j u s t e d and m a i n t a i n e d w i t h the thermocouple b u c k i n g Honeywell c o n t r o l l e r . the melt  temperature  p o t e n t i a l s and  As b e f o r e , the temperature d i f f e r e n c e a c r o s s  c o u l d be f u r t h e r a d j u s t e d by the h e a t i n g c o i l  and c o o l i n g b l o c k  shown i n F i g u r e 16.  Flow v e l o c i t y measurements w e r e . c a r r i e d out i n t h e f o l l o w i n g way.  The f u r n a c e  power, h e a t i n g c o i l power and argon flow r a t e  the c o o l i n g b l o c k were a d j u s t e d to g i v e a d e s i r e d temperature along the m e l t .  T h i s temperature p r o f i l e , as monitored  E l e c t r o n i c 194 r e c o r d e r , was m a i n t a i n e d i n s u r e steady was then  s t a t e heat  i n t r o d u c e d i n t o the melt  the boat  c o l l i m a t o r p o s i t i o n was approximately  c o l d end) from t h e p l a c e o f i n t r o d u c t i o n . t r a c e r had passed  and m e l t .  The t r a c e r resulting  by the moveable c o l l i m a t o r -  s c i n t i l l a t i o n counter assembly d e s c r i b e d e a r l i e r . the f i r s t  one hour t o  and the movement o f t r a c e r  from the c o n v e c t i v e flow p r e s e n t was monitored  distribution  by the Honeywell  f o r approximately  t r a n s f e r through  through  As i n S e c t i o n 2.1.6.,  3 cm away (towards the  Once i t was apparent  t h a t the  t h i s p o s i t i o n the c o l l i m a t o r was moved 6.3 cm "down-  (a) 0 - 9 2 X 2 Rheostat to  n  i/>  8  a  £ o o c C (D  _J  F i g u r e 27.  Tube furnace w i r i n g diagram.(b) D e t a i l s o f furnace temperature c o n t r o l l e r .  A B C&D E F&G H I J  0-5 mv Honeywell C o n t r o l l e r Ammeter f o r c e n t e r windings Power d i s c r i m i n a t o r s f o r c e n t e r windings Ammeter f o r end windings Power d i s c r i m i n a t o r f o r end windings C o n t r o l thermocouple input 0-50 mv (10 mv s t e p s ) b a c k i n g p o t e n t i a l 0-10 mv (1 mv s t e p s ) b a c k i n g p o t e n t i a l  O C O  stream" and c o u n t i n g was  c o n t i n u e d u n t i l the t r a c e r was  observed t o p a s s .  F i g u r e 28 shows a t y p i c a l a c t i v i t y - t i m e c u r v e ; the a c t i v i t i e s p l o t t e d are average count r a t e s over a 15 second time i n t e r v a l .  As b e f o r e , the time  r e q u i r e d f o r flow o f t r a c e r from one c o l l i m a t o r p o s i t i o n to another determined by measuring  was  the time d i f f e r e n c e between the i n t e r s e c t i o n of  the e x t r a p o l a t i o n of the a c t i v i t y - t i m e curves and the a b s c i s s a .  Experi-  ments were conducted t o determine:(1) The v a r i a t i o n o f flow v e l o c i t y w i t h temperature between the hot and c o l d ends o f the m e l t .  Sb  difference  124  was  used  as  the t r a c e i s o t o p e f o r reasons s i m i l a r to those p r e s e n t e d i n 124 S e c t i o n 2.1.6. tin.  The t r a c e a l l o y was  Average temperature  approximately 312  0.46  wt  % Sb  a c r o s s the m e l t was  °C, w i t h 309  i n pure  m a i n t a i n e d at  °C minimum and 320  °C maximum.  (2) The e f f e c t on the observed flow v e l o c i t y of a l l o w i n g age temperature  to be o u t s i d e the l i m i t s s e t above.  the a v e r This  was  accomplished by c o n d u c t i n g v e l o c i t y d e t e r m i n a t i o n experiments at 300  °C and 325  °C and then comparing  these v a l u e s w i t h the  r e s u l t s obtained i n (1). (3) The e f f e c t on observed flow v e l o c i t y o f v a r y i n g d i f f e r e n c e between t r a c e a l l o y and m e l t .  the d e n s i t y  To e v a l u a t e t h i s  f i v e experiments were undertaken i n which the t r a c e a l l o y melt were o f the same d e n s i t y .  T h i s was  effect and  accomplished by making  the melt c o m p o s i t i o n the same as t h a t of the t r a c e a l l o y , namel y 0.46  wt  % Sb i n Sn  (Sb used i n the m e l t was  nonradioactive).  The melt was  p r e p a r e d under an argon atmosphere and was  periodically  f o r appoximately one h a l f hour to i n s u r e homogeniety.  F u r t h e r comparison  stirred  of flow v e l o c i t y w i t h t r a c e a l l o y d e n s i t y  p r o v i d e d by i n c r e a s i n g  the amount o f Sb i n the t r a c e a l l o y t o  was  1600  Q: 1 2 0 0 -  o  v-  8 0 0 -  JT 4 0 0  <  *  1  I TIME F i g u r e 28.  3  AFTER  INTRO.  (MIN)  T y p i c a l a c t i v i t y v e r s u s time data f o r experiments employing t r a c e r i n t r o d u c t i o n by r o t a t i n g a v e r t i c a l c y l i n d e r l o c a t e d i n the covered s e c t i o n of the melt. ON  68  3.0 wt % (by adding n o n r a d i o a c t i v e Sb), thus making the t r a c e 124  a l l o y a p p r e c i a b l y l e s s dense than the 0.46  2.1.7.2.  R e s u l t s and  2.1.7.2.1.  wt  % Sb  used  above.  Discussion  V a r i a t i o n of Flow V e l o c i t y w i t h D i f f e r e n c e A c r o s s the M e l t  Temperature  The r e s u l t s o f experiments to determine the v a r i a t i o n o f flow v e l o c i t y w i t h temperature d i f f e r e n c e between the hot and c o l d ends o f the 27 cm long melt are t a b u l a t e d i n T a b l e 2 and p l o t t e d i n F i g u r e 29. p e c t e d f l o w v e l o c i t y i n c r e a s e s w i t h i n c r e a s i n g temperature along the m e l t .  As  ex-  difference  Furthermore, the r e s u l t s show flow v e l o c i t y  increases  l i n e a r l y w i t h temperature d i f f e r e n c e over the range of e x p e r i m e n t a l conditions  investigated.  2.1.7.2.2.  E f f e c t of V a r y i n g Average M e l t To e v a l u a t e the e f f e c t  Temperature  (on observed f l o w v e l o c i t y ) of v a r y i n g  the average melt temperature, the r e s u l t s of experiments c a r r i e d out w i t h average melt temperature of 300 °C and 325 30, f o r comparison  t o the r e s u l t s shown i n F i g u r e 29.  appears i n F i g u r e 30 i s t h a t which was i n F i g u r e 29.  °C have been p l o t t e d ,  The  The l i n e  Figure which  determined from the d a t a p l o t t e d  minimum and maximum average melt temperatures o f the  r e s u l t s which determined the r e l a t i o n s h i p o b t a i n e d i n F i g u r e 29 were °C and 320  °C.  I f average m e l t temperature had any major  309  e f f e c t on the  flow v e l o c i t y one might expect, due t o the temperature dependence o f v i s cosity T = 300  (Table 6 ) , to see the r e s u l t s o f the experiment conducted w i t h °C to l i e below the l i n e and those from the t e s t a t T = 325  l i e above  the l i n e .  S i n c e both p o i n t s are above the l i n e ,  °C t o  i t must be  concluded t h a t v a r i a t i o n i n average melt temperature, over the range  des-  TABLE 2 Flow V e l o c i t y  Results  Experiment Number  Average Temp. °C.  A Temperature °C  Velocity cm/sec.  1  312  5.5  0.014  2  309  7.1  0.018  3  309  14.5  0.042  4  312  17.6  0.047  5  311  20.2  0.052  6  311  22.7  0.060  7  312  24.2  0.083  8  310  27.2  0.075  9  314  33.2  0.080  10  320  41.8  0.111  11  313  55.5  0.140  12  310  60.8  0.167  13  311  61.6  0.162  0*20 i  1  F i g u r e 29.  1  1  1  1  1  The dependence of flow v e l o c i t y on the temperature hot and the c o l d ends o f the melt.  1  1  difference  1  T  between the  o  TEMP. F i g u r e 30.  DIFF.  ACROSS  The e f f e c t on the flow v e l o c i t y m e l t temperature.  MELT of v a r y i n g  (°C) the average  c r i b e d f o r these experiments, measured by  has no e f f e c t on the flow v e l o c i t y  the p r e s e n t l y employed m o n i t o r i n g  technique.  P o i n t s which  do not f a l l on the l i n e must then do so because of normal  experimental  scatter inherent i n  determination  the t r a c e r i n t r o d u c t i o n and v e l o c i t y  techniques.  2.1.7.2.3.  E f f e c t of V a r y i n g T r a c e A l l o y and M e l t  Density  124 S i n c e the t r a c e a l l o y , 0.46  % Sb  i n Sn, used  to o b t a i n  the r e s u l t s p l o t t e d i n F i g u r e 29 i s l e s s dense than the melt i t was  necessary  to determine  have on the observed periments 0.46  flow v e l o c i t y .  i n which the melt  % Sb i n pure  what e f f e c t  and  (0.9997  pSn)  t h i s d e n s i t y d i f f e r e n c e might  F i g u r e 31 shows the r e s u l t s of  ex-  t r a c e r were of the same c o m p o s i t i o n , namely  Sn.  As i n F i g u r e 30, the r e s u l t s are p l o t t e d along w i t h l i n e a r r e l a t i o n s h i p o b t a i n e d , i n F i g u r e 29.  There i s e x c e l l e n t  ment between f o u r of the f i v e e x p e r i m e n t a l p o i n t s and  the agree-  the l i n e .  There  was  no apparent  reason f o r the l a r g e d e v i a t i o n d i s p l a y e d by the one p o i n t .  The  r e s u l t s of F i g u r e 31 c l e a r l y show t h a t no d i s c r e p a n c y i n observed  flow  v e l o c i t y o c c u r s as a r e s u l t of the t r a c e a l l o y b e i n g s l i g h t l y l e s s dense than the m e l t .  F u r t h e r evidence  e f f e c t on observed  of t h e a b s e n c e o f  flow v e l o c i t y i s p r e s e n t e d i n F i g u r e 32.  time curves f o r t h r e e d i f f e r e n t  tracer-melt, combinations  1) T r a c e r and melt same d e n s i t y (both 0.46 2) T r a c e r s l i g h t l y 0.46  wt  any major t r a c e r d e n s i t y  l e s s dense (0.9997 pSn  % Sb i n Sn, melt pure Sn).  wt  Activity-  are p l o t t e d :  % Sb i n  Sn)  ) than the melt  (tracer  TEMP. F i g u r e 31.  DIFF.  ACROSS  MELT  The e f f e c t on the flow v e l o c i t y of having t r a c e a l l o y and melt d e n s i t i e s .  (°C) identical  74  3) T r a c e r a p p r e c i a b l y l e s s dense (0.9978 pSn ( t r a c e r 3.0  The  wt  % Sb i n Sn, m e l t pure  Sn).  temperature d i f f e r e n c e f o r a l l t h r e e experiments was  30 °C and  the s e p a r a t i o n between m o n i t o r i n g  p o s i t i o n s was  To s i m p l i f y comparison of the curves t e s t has  position i s coincident.  the i n c r e a s e i n a c t i v i t y  10  e s s e n t i a l l y the same.  Examination of the p o i n t s  at the second m o n i t o r i n g  The  flow v e l o c i t i e s  f o r e the same, from which i t may  be  t a i n i n g up  introduced  to 3.0  wt  % Sb  can be  solute density differences affecting  2.1.7.2.4.  Although p r e v i o u s  2.1.4.) had  positions i s  that t r a c e a l l o y s  i n t o pure t i n m e l t s  the flow  there-  conwithout  velocity.  for introducing tracer i s acceptably i n v e s t i g a t i o n s of t h i s technique  shown t h a t some f l u i d  d u c t i o n the magnitude of the  flow was  associated with  a r i s e s from the f a c t  (Section  tracer intro-  This  that the data p l o t t e d i n F i g u r e 29 l i e s  which passes through zero v e l o c i t y when zero t h e r m a l d r i v i n g When the v e l o c i t i e s o b t a i n e d those  repro-  flow must be n e g l i g i b l y s m a l l when compared  the v e l o c i t i e s which r e s u l t from thermal c o n v e c t i o n .  along w i t h  are  s m a l l s c a t t e r of the r e s u l t s p l o t t e d i n F i g u r e 29 i n -  d i c a t e s t h a t t h i s technique ducible.  represent-  p o s i t i o n shows t h a t  i n the t h r e e cases  concluded  first  E v a l u a t i o n of Technique  The  sent.  cm.  the time s c a l e of each  the time f o r movement of t r a c e r between the two m o n i t o r i n g  with  approximately  been a d j u s t e d so t h a t the time of a r r i v a l of t r a c e r at the  monitoring ing  ) than the melt  conclusion  on a l i n e force i s pre-  i n S e c t i o n 2.1.6.2.1. are p l o t t e d  of F i g u r e 29 i t becomes apparent t h a t i n t r o d u c t i o n of  6000  TIME F i g u r e 32.  (MIN)  The e f f e c t on the flow v e l o c i t y of v a r y i n g the d e n s i t y d i f f e r e n c e between the t r a c e a l l o y and the melt.  t r a c e r by a p i s t o n mechanism has more m e c h a n i c a l m i x i n g a s s o c i a t e d w i t h it  than does the t e c h n i q u e j u s t employed.  F i g u r e 33, the f i l l e d  T h i s comparison  appears i n  i n c i r c l e s are from F i g u r e 29 and the open  circles  which d i s p l a y s l i g h t l y l a r g e r s c a t t e r are the r e s u l t s o b t a i n e d when t r a c e r was  i n t r o d u c e d by the p i s t o n mechanism.  The  tracer  introduction  t e c h n i q u e of r e v o l v i n g a v e r t i c a l c y l i n d e r l o c a t e d i n the covered s e c t i o n of the b o a t was a l l subsequent  2.1.8.  t h e r e f o r e permanently  readopted and employed f o r  v e l o c i t y measurement and a u t o r a d i o g r a p h y experiments.  S i n g l e Aluminum Channel Supported by G r a p h i t e R e s e r v o i r s  Although a s a t i s f a c t o r y  t r a c e r i n t r o d u c t i o n t e c h n i q u e has  been developed the p r e l i m i n a r y a u t o r a d i o g r a p h y r e s u l t s p r e s e n t e d i n S e c t i o n 2.1.6.2.2. i n d i c a t e d t h a t m e l t s c o n t a i n e d i n the two g r a p h i t e boat c o u l d not be quenched r a p i d l y enough. quench time the g r a p h i t e boat was  channel  To decrease the  r e p l a c e d by a boat c o n s t r u c t e d o f a  s i n g l e aluminum channel w i t h both ends h e l d i n g r a p h i t e r e s e r v o i r s . The s i n g l e channel boat was quenching but was i t was  designed p r i m a r i l y to f a c i l i t a t e  rapid  a l s o used f o r v e l o c i t y measurement experiments  a n t i c i p a t e d t h a t the  aluminum boat might  lateral  since  temperature g r a d i e n t s i n the  differ significantly  from the l a r g e r  cross-section  graphite boat.  2.1.8.1.  E x p e r i m e n t a l Apparatus and  The new minum channel was l e n g t h was  37.5  boat i s shown s c h e m a t i c a l l y i n F i g u r e 34.  0.64  cm,  Procedure  cm square  The  alu-  ( i n s i d e dimensions) and the o v e r a l l m e l t  a p p r o x i m a t e l y 10 cm l o n g e r than that used i n p r e v i o u s  006 from  005  Figure 2 9  $ 0-04H o  -  o  003 002  Q  ©Rotating vertical cylinder  > 001  O Piston 000  0  4 Figure  6 TEMP.  33.  8 DIFF.  mechanism  10 12 14 16 ACROSS MELT (°C)  18  Comparison of the flow v e l o c i t y measurements o b t a i n e d employing the r o t a t e d v e r t i c a l c y l i n d e r and p i s t o n mechanism i n t r o d u c t i o n techniques.  20  iron-constantan thermocouples Figure 34.  D e t a i l s of the g r a p h i t e end supported s i n g l e aluminum channel boat. 00  experiments.  The channel was c o n s t r u c t e d by w i r i n g a 0.05 i n c h t h i c k  s t r i p o f aluminum over the top o f a l e n g t h o f 3 s i d e d aluminum U-channel having  a w a l l t h i c k n e s s o f 0.06  inches.  Thermocouples (30 gauge i r o n - c o n s t a n t a n 1/16 i n c h O.D. at  to  m u l l i t e tubing) were i n s e r t e d i n the g r a p h i t e r e s e r v o i r s  the p o s i t i o n s shown i n F i g u r e 34.  f i x e d along  the aluminum channel.  Four a d d i t i o n a l thermocouples were These thermocouples were  the aluminum channel by d r i l l i n g  then hammering  the h o l e shut  attached  1/8 i n c h l o n g , 0.02 i n c h diameter  h o l e s up the s i d e w a l l s o f the channel, and  i n s u l a t e d by 2 h o l e ,  i n s e r t i n g the thermocouple w i r e ,  around the w i r e .  t r o l of the temperature d i f f e r e n c e along  Selection  and con-  the melt and i n t r o d u c t i o n o f  t r a c e r were c a r r i e d out i n the same way as d e s c r i b e d i n S e c t i o n  2.1.7.1.  The f i r s t  (towards  c o l l i m a t o r p o s i t i o n was approximately  5 cm downstream  the c o l d end) from the p l a c e of i n t r o d u c t i o n and the second p o s i t o n was 20 cm beyond the f i r s t .  2.1.8.2.  Results  and D i s c u s s i o n s  The r e s u l t s of v e l o c i t y d e t e r m i n a t i o n lated i n Table  3 and p l o t t e d i n F i g u r e  F i g u r e 35 that the e x p e r i m e n t a l  35.  experiments are tabu-  I t i s c l e a r l y evident  from  r e s u l t s f i t a l i n e a r r e l a t i o n s h i p between  observed flow v e l o c i t y and temperature d i f f e r e n c e between the hot and c o l d ends of the m e l t .  The s l o p e of the l i n e o b t a i n e d  s i n g l e alumium channel boat i s l e s s than t h a t o b t a i n e d long two channel g r a p h i t e boat used e a r l i e r . difference i n slope are:  f o r the 37.5 cm f o r the 27 cm  P o s s i b l e causes f o r t h i s  TABLE 3 Flow V e l o c i t y  Experiment Number  Average Temp. °C.  Results  A Temperature °C  Velocity cm/sec.  1  306  20  0.04  2  310  43  0.07  3  310  56  0.12  4  300  85  0.16  5  303  135  0.21  6  322  177  0.32  7  325  182  0.33  0-5  TEMP. F i g u r e 35.  DIFF.  ACROSS  MELT  (°C)  Comparison.of the flow v e l o c i t y measurements o b t a i n e d employing the two channel g r a p h i t e boat ( F i g u r e 29) and the s i n g l e aluminum channel boat.  00  (1)  A d i f f e r e n c e i n the l a t e r a l  temperature  g r a d i e n t s i n t h e two  boats. (2)  A v a r i a t i o n o f flow v e l o c i t y w i t h t o t a l melt  length.  The e f f e c t o f m e l t l e n g t h on flow v e l o c i t y w i l l be d i s c u s s e d below when more e x p e r i m e n t a l r e s u l t s a r e a v a i l a b l e .  2.1.8.3.  E v a l u a t i o n o f Technique  The  a c c e p t a b i l i t y o f the t r a c e r i n t r o d u c t i o n technique has  been e s t a b l i s h e d .  However, measurement o f flow v e l o c i t i e s by the manual  c o l l e c t i o n o f a c t i v i t y versus  time d a t a i s extremely  flow v e l o c i t y exceeds 0.5 cm/second. i n t e r v a l used  d i f f i c u l t when the  Even w i t h the l a r g e r m o n i t o r i n g  i n t h i s l a s t s e r i e s o f experiments  (20 cm as opposed t o t h e  6.3 cm and 10 cm i n t e r v a l s used e a r l i e r ) t h e r e i s n o t s u f f i c i e n t than 40 seconds) t o c o l l e c t  data t h a t w i l l a c c u r a t e l y determine  of a r r i v a l o f t r a c e r above a g i v e n c o l l i m a t o r p o s i t i o n . flow v e l o c i t i e s  exceeding  f a r too long to y i e l d  c o l l e c t data w i t h count  the time  0.5 cm/sec a c o u n t i n g i n t e r v a l o f 15 seconds i s  I t i s , however, extremely  difficult  the time a v a i l a b l e f o r m o n i t o r i n g  the second c o l l i m a t o r p o s i t i o n .  determina-  to manually  time i n t e r v a l s a p p r e c i a b l y l e s s than 15  The n e c e s s i t y to move the c o l l i m a t o r from one p o s i t i o n decreased  (less  Furthermore, f o r  s u f f i c i e n t l y s e n s i t i v e data f o r accurate  t i o n of t r a c e r a r r i v a l .  time  seconds.  t o the next  further  the i n c r e a s e i n a c t i v i t y  over  Improvement i n the s e n s i t i v i t y o f the  t r a c e r m o n i t o r i n g system was n e c e s s a r y b e f o r e i n v e s t i g a t i o n o f the v a r i a t i o n o f flow v e l o c i t y w i t h thermal d r i v i n g velocities  above 0.5 cm/second.  f o r c e c o u l d c o n t i n u e , t o flow  These improvements and the r e s u l t s  from  them are d i s c u s s e d i n the next  2.2.  section.  Flow V e l o c i t y D e t e r m i n a t i o n by Dual M o n i t o r i n g  2.2.1.  E x p e r i m e n t a l Apparatus  and  Procedure  To f a c i l i t a t e measurement o f h i g h e r flow v e l o c i t i e s  two  c o l l i m a t o r s l i t s were used and the a c t i v i t y o f r a d i a t i o n p a s s i n g through the s l i t s was Q6-A  m o n i t o r e d c o n t i n u o u s l y w i t h two s e p a r a t e Quantum E l e c t r o n i c  s c i n t i l l a t i o n counters.  i n F i g u r e 36.  The  T h i s arrangement  c o l l i m a t o r s e p a r a t i o n was  i s shown s c h e m a t i c a l l y  20 cm.  In a t y p i c a l  ex-  periment the s i n g l e channel aluminum boat shown i n F i g u r e 34 was p l a c e d i n the tube f u r n a c e and a d e s i r e d temperature p r o f i l e along the melt was  e s t a b l i s h e d and m a i n t a i n e d f o r about one hour.  When the  tempera-  124 ture p r o f i l e had s t a b i l i s e d , introduced  the t r a c e a l l o y  i n t o the t i n m e l t .  (0.85 wt  % Sb  The v i s u a l d i s p l a y on the two  p l u s the v i s u a l d i s p l a y from a Hamner NT-15F-1 t i m e r was 35 mm  f i l m at 5 second i n t e r v a l s .  The  i n Sn)  was  scalers  photographed  on  f i e l d of view o f the camera i s  shown i n F i g u r e 37(a) and some t y p i c a l data i n F i g u r e 37(b).  A n a l y s i s of  the data c o l l e c t e d i s d i s c u s s e d below.  2.2.2.  A n a l y s i s o f A c t i v i t y Versus Time Data  As a c t i v e m a t e r i a l approaches of l i q u i d subtended by counter i n i t i a l l y  the c o l l i m a t o r s l i t  and p a s s e s through the s e c t i o n the a c t i v i t y  i n c r e a s e s s l o w l y and then r a p i d l y .  To  d e t e c t e d by establish  whether the shape of the a c t i v i t y - t i m e curves i s e n t i r e l y due c o r r e s p o n d i n g i n c r e a s e i n a c t i v i t y i n the l i q u i d slip  or p a r t l y due  the  to a  above the c o l l i m a t o r  to the c o l l i m a t i n g procedure used the f o l l o w i n g  ex-  8  miMi  Figure 3 7 .  Fuacrtoi  raiMR  (a) F i e l d of view of 3 5 mm camera employed to c o l l e c t a c t i v i t y versus time data. (b) A section of the 3 5 mm film showing some typical data.  5  86  periment was  c a r r i e d out.  A 0.6  cm square b y 16 cm l o n g rod o f t i n  was  p o s i t i o n e d along the Vycor tube a t  124 c o n t a i n i n g 100 ppm  of Sb  v a r i o u s d i s t a n c e s away from the r e g i o n i n t e r s e c t e d by the slit  and the a c t i v i t y r e a c h i n g the s c i n t i l l a t i o n  a 1 5 second i n t e r v a l .  The r e s u l t s of t h i s  monitored f o r  are:  There i s a marked i n c r e a s e i n the a c t i v i t y seen by the s c i n tillation  counters as the r a d i o a c t i v e s o u r c e approaches the  collimator  (2)  counter was  t e s t are shown i n F i g u r e 38.  The most important c h a r a c t e r i s t i c s of t h i s p l o t (1)  collimator  slots.  The r a p i d i n c r e a s e i n a c t i v i t y  as the r a d i o a c t i v e source moves  over the c o l l i m a t o r s l o t i s spread over an i n t e r v a l of approximately 1  (3)  The  cm.  count r a t e observed through c o l l i m a t o r n o . l i s l e s s  t h a t observed through  The  than  no.2.  c o l l i m a t o r s c l e a r l y do not e x h i b i t a step f u n c t i o n response to the  movement of a r a d i o a c t i v e source p a s t them. crease i n a c t i v i t y by examining  The  fact  that the r a p i d i n -  occurs over a 1 cm i n t e r v a l can be r e a d i l y  F i g u r e 39.  The  collimator s l i t  i s 1/8  understood  i n c h wide by 4 i n c h e s  long and the d i s t a n c e b e t w e e n the top o f the c o l l i m a t o r s l o t and the p l a n e along which the r a d i o a c t i v e s o u r c e passes i s 3 i n c h e s . be seen t h a t under these c i r c u m s t a n c e s t h e . s c i n t i l l a t i o n  From F i g u r e . 3 9 i t can counter sees  an  i n t e r v a l a p p r o x i m a t e l y 1 cm long a t the p l a n e o f the r a d i o a c t i v e s o u r c e . T h e r e f o r e , the r a p i d i n c r e a s e i n a c t i v i t y w i l l b e g i n b e f o r e the source i s d i r e c t l y over the c o l l i m a t o r s l i t . ing  the s c i n t i l l a t i o n  The g r a d u a l i n c r e a s e i n a c t i v i t y  reach-  counter which o c c u r s as the s o u r c e approaches the  Source  Figure 3 9 .  Level  F u l l size schematic diagram showing the length of melt subtended by the s c i n t i l l a t i o n detector.  89  the c o l l i m a t o r s l i t  i s a r e s u l t of ;  (1)  A decrease i n d i s t a n c e between the source and  detector.  (2)  A decrease i n the t h i c k n e s s o f l e a d s h i e l d through which the r a d i a t i o n must p a s s .  The reason f o r the i n c r e a s e d count r a t e observed c o l l i m a t o r no.2 d e t e c t o r no.2  through  i s t h a t the a c t i v i t y v e r s u s c o u n t e r v o l t a g e p l a t e a u f o r  o c c u r r e d a t a h i g h e r v o l t a g e than f o r n o . l .  i n a h i g h e r count r a t e b e i n g r e c o r d e d by s c a l e r  This  resulted  no.2.  To t e s t the response o f the c o l l i m a t o r t o a moving s o u r c e , the 0.6  cm square by 16 cm long r a d i o a c t i v e source was  Vycor tube at a c o n s t a n t v e l o c i t y of 0.32  cm/second.  t e s t appear i n T a b l e 4 and are p l o t t e d i n F i g u r e 40.  p u l l e d through the The r e s u l t s o f t h i s The  t i m e r and  s c a l e r r e a d i n g s appearing i n T a b l e 4 were read o f f the 35 mm ground r a d i a t i o n was of  film.  Back-  determined by f i x e d count t i m i n g p r i o r t o movement  tracer.  In F i g u r e 40 the average net count r a t e d u r i n g the time v a l has been p l o t t e d a g a i n s t the time a t the end of the i n t e r v a l . be more c o r r e c t  to p l o t  interI t would  count r a t e v e r s u s the time at the m i d d l e of the  i n t e r v a l , b u t , s i n c e a l l time i n t e r v a l s are f i v e seconds and the  differ-  ence i n time between the i n c r e a s e i n the a c t i v i t y a t each c o l l i m a t o r the only measurement of i n t e r e s t  t h i s was  not n e c e s s a r y .  The most  was  signifi-  cant f e a t u r e s of F i g u r e 40 a r e :  (1)  As expected t h e r e i s a g r a d u a l i n c r e a s e i n a c t i v i t y b e f o r e the t r a c e r appears over the c o l l i m a t o r .  TABLE 4 Results  Collimator  o f Dual C o l l i m a t o r  Scalar  Reading  Test  C o l l i m a t o r No .2  No .1  Background 30 cps  Background 58 cps Time sec.  Sensitivity  Net C R . cps  S c a l a r Reading  Net c;  5.0  440  10.0  695  0  14.9  965  0  19.9  1285  5  25.0  1760  35  29.8  2270  50  865  34.9  3500  180  1025  0  39.9  6000  440  1200  5  45.0  8640  460  1410  10  50.1  11300  465  1600  5  55.0  1815  15  60.0  2070  20  65.0  2365  30  70.1  2690  35  75.1  3100  50  80.0  3600  75  85.0  4190  90  90.0  4830  100  95.0  5510  105  100.0  6670  200  104.9  8930  430  110.0  11880  550  115.0  14870  570  120.1  17930  570  TIME F i g u r e 40.  (SEC)  The response of the d u a l simultaneous c o u n t i n g t o a constant source t r a v e l l i n g a t a known v e l o c i t y .  activity  (2)  In the r a p i d l y i n c r e a s i n g p o r t i o n are  o f the curves the s l o p e s  almost i d e n t i c a l .  S i n c e the t r a c e r was o f constant c o m p o s i t i o n and t r a v e l l i n g a t c o n s t a n t speed, the time r a t e o f change o f a c t i v i t y as the t r a c e r moved over each c o l l i m a t o r s h o u l d be the same, t h a t i s , the s l o p e s creasing  portion  For  i n the r a p i d l y i n -  o f the curves s h o u l d be i d e n t i c a l .  the case o f c o n s t a n t c o m p o s i t i o n t r a c e r moving a t c o n s t a n t  speed, v e l o c i t y d e t e r m i n a t i o n i s s i m p l i f i e d by the f a c t t h a t  the time  d i f f e r e n c e between appearance o f t r a c e r over the two c o l l i m a t o r s l o t s may be o b t a i n e d by t a k i n g see  Figure  agrees  40.  the time d i f f e r e n c e a t any average count  rate,  The e x p e r i m e n t a l l y measured v e l o c i t y o f 0.31 cm/second  w e l l w i t h the " t r u e " v e l o c i t y o f 0.32 cm/second.  During an a c t u a l experiment the t r a c e r w i l l be d i l u t e d as i t moves through the m e l t .  Even more important i s the f a c t t h a t  the l e a d -  i n g edge o f the t r a c e r i s more d i l u t e than the r e g i o n s b e h i n d the l e a d i n g edge.  This  i s shown i n the l o n g i t u d i n a l  appearing i n F i g u r e  55 ( S e c t i o n  3.4.3.).  section  autoradiographs  I t i s apparent from F i g u r e  55  t h a t i n moving from the c o l d end towards the hot end ( p l a c e o f t r a c e r introduction)  the average cross  s e c t i o n a l composition of t r a c e r  The  n e t r e s u l t o f . t h i s w i l l be t h a t  the  c o l l i m a t o r response curve w i l l be lower f o r c o l l i m a t o r no.2 than f o r  collimator no.l.  the s l o p e  increases.  o f the l i n e a r p o r t i o n o f  T h i s e f f e c t i s shown i n F i g u r e  were capable o f s h i e l d i n g the s c i n t i l l a t i o n  41.  I f the c o l l i m a t o r s  counters from a l l r a d i a t i o n  other than t h a t which reached them through the c o l l i m a t o r s l i t the  itself,  a c t i v i t y v e r s u s time curves would p r o b a b l y be a p p r o x i m a t e l y l i n e a r  600 j  1  1  1  1  TIME F i g u r e 41.  1  1  1  1  r  (SEC)  T y p i c a l a c t i v i t y v e r s u s time data o b t a i n e d by the simultaneous d u a l m o n i t o r i n g . vo  starting from zero a c t i v i t y .  Therefore, the i n t e r s e c t i o n of the extra-  polation of the rapidly increasing l i n e a r portion of the curve and the abscissa was taken to be the time at vihich the tracer f i r s t appeared over the collimator s l i t .  The time difference at zero a c t i v i t y was used  for a l l flow v e l o c i t y measurements reported i n this investigation.  2.2.3.  Results and Discussion  2.2.3.1. Variation of Flow Velocity with Temperature Difference between the Hot and Cold Ends  Figure 42 shows the increase i n flow Velocity which occurs as a r e s u l t of increasing the temperature difference between the hot and cold ends of the melt.  Data plotted i n Figure 42 appears i n Table 5.  As observed previously (Figures 23, 29 and 35), the relationship between flow v e l o c i t y and temperature difference i s l i n e a r .  The l i n e represent-  ing the data plotted i n Figure 35 also appears i n Figure 42. single aluminum channel boat was  The same  used for both series of experiments.  Flow  v e l o c i t y measurements plotted i n Figure 42 were obtained when the average melt temperature was melt temperature  approximately 400 °C (Table 4) whereas the average  for Figure 35 was 310 °C (Table 2).  In Section 2.1.7.2.2.  increasing the average melt temperature from 300 °C to 325 °C had no apparent e f f e c t on the observed flow v e l o c i t y .  ,  As can be seen from  Figure 42 an increase i n average melt temperature from 310 °C to 400 °C leads to a 25% increase i n flow v e l o c i t y .  This apparent d i s p a r i t y i s  discussed i n the next section.  2.2.3.2.  V a r i a t i o n of Flow Velocity with Average Melt Temperature  The dependence of flow velocity on average melt temperature i s  0  40  80 120 160 2 0 0 TEMR DIFF. A C R O S S  F i g u r e 42.  240 280 320 MELT (°C)  The dependence of flow v e l o c i t y on the temperature between the hot and the c o l d ends o f the m e l t .  difference  360  400  vo  TABLE 5 Flow V e l o c i t y  Experiment Number  Average Temp. °C.  Results  A Temperature °C .  Velocity cm/sec.  1  401  161  0.33  2  400  190  0.46  3  398  196  0.44  4  402  214  0.48  5  400  259  0.57  6  403  306  0.67  7  425  384  0.88  shown i n Figure 43.  The temperature difference across the melt was  214 °C f o r a l l three points.  The increase i n flow v e l o c i t y with increas-  ing average melt temperature might be anticipated since increasing the average melt temperature decreases the v i s c o s i t y of the molten t i n (Table 6).  From Figure 43, one would expect about a 7% increase i n flow veloc-  i t y as a r e s u l t of increasing the average melt temperature from 300 °C to 325 °C. Since this increase was not observed i n Section 2.1.7.2.2., i t must be concluded that manual c o l l e c t i o n of data from a single moveable collimator i s less sensitive than simultaneous dual monitoring of the flow v e l o c i t y .  2.2.3.3.  V a r i a t i o n of Flow Velocity with Total Melt Length The results of flow v e l o c i t y measurements i n melts of d i f f e r -  ing lengths appear i n Figure 44 and Table 7.  The average melt temperatures  were approximately 400 °C. Decreasing the t o t a l melt length from 48.5 cm to 37.5 cm and then to 28.8 cm leads to an increase i n the flow v e l o c i t y observed for a given temperature difference between the hot and cold ends. If flow v e l o c i t y i s plotted against the average temperature gradient across the melt, Figure 45, i t becomes apparent that v e l o c i t y increases linearly-with increasing average temperature gradient.  In Figure 46  data from Table 5 ( f i l l e d c i r c l e s ) has been.plotted along with the data in Table 7.  From Figure 46 i t can be concluded that for covered l i q u i d  t i n melts 0.64 cm high, ranging i n length from approximately 25 to 50 cm and at an average temperature of 400 °C, the flow v e l o c i t y i s l i n e a r l y dependent on the average temperature gradient across the melt such that Velocity (cm/sec) = 0.082 x Temperature gradient (°C/cm).  This r e l a t i o n -  F i g u r e 43.  The e f f e c t on f l o w v e l o c i t y o f v a r y i n g the average melt, temperature (with a c o n s t a n t temperature d i f f e r e n c e a c r o s s the melt o f 214 °;C).  TABLE 6 P r o p e r t i e s of Molten T i n  Temperature  Viscosity (51)  Specific Heat (52)  Thermal. Conductivity (52)  centipoise  cal/gm°C  cal/cm s e c °C  Coef. o f V o l . Exp. (17) 1/°C x .10  Density (53) gm/cm  Kinematic Viscosity 2, cm /sec x 10  Thermal Diff. /s e c cm / 2  250  1.70  1.0229  6.961  2.44  0.203  300  1.53  1.0284  6.925  2.21  0.204  0.0565  0.080  400  1.29  1.0393  6.854  1.88  0.206  500  1.15  1.0502  6.783  1.70  0.207  vo  TEMR F i g u r e 44.  DIFF.  ACROSS  MELT  (°C)  The dependence of flow v e l o c i t y f o r t h r e e d i f f e r e n t l e n g t h s on temperature d i f f e r e n c e a c r o s s the m e l t .  melt  101  TABLE 7 Flow V e l o c i t y R e s u l t s f o r Three M e l t Lengths  Experiment Number  1 2 3 4  5 6 7 8 9  10 11 12 13 14  Melt Length  A Temperature °C  Temperature Grad. °C/cm  Velocity cm/sec.  48.5cm  156 189 189 229  3.22 3.90 3.90 4.72  .27 .28 ,28 - .35 .39  37.5cm  92 156 158 196 231  2.46 4.16 4.22 5.22 6.17  .18 .36 .35 .43 .51  28.8cm  105 153 167 198 218  3.65 5.31 5.80 6.88 7.58  .29 .34 .52 .52 .54  AVERAGE F i g u r e 45.  TEMR  GRAD.  (°C/CM)  The dependence of flow v e l o c i t y f o r t h r e e d i f f e r e n t melt l e n g t h s on the temperature g r a d i e n t between the hot and c o l d ends of the m e l t .  0-9 0-8  o co 0 - 6  from Table 5 O from Table 7 2 3 AVERAGE F i g u r e 46.  4 5 6 TEMP. GRAD.  7 (°C/CM)  8  9  The dependence of flow v e l o c i t y on the temperature g r a d i e n t a c r o s s the melt w i t h an average melt temperature of 400 °C.  10  t—  1  o  104  ship holds l e a s t 10  t r u e up  to average h o r i z o n t a l temperature g r a d i e n t s of at  °C/cm.  In S e c t i o n 2.1.8.2., F i g u r e 35, i t was of the l i n e o b t a i n e d was  f o r the 37.5  l e s s than t h a t o b t a i n e d  boat.  Two  observed t h a t the  slope  cm l o n g s i n g l e aluminum channel boat  f o r the 27 cm  long two  channel g r a p h i t e  p o s s i b l e causes f o r t h i s d i f f e r e n c e i n s l o p e were o f f e r e d ,  namely, a d i f f e r e n c e i n l a t e r a l g r a d i e n t s and/or a dependence of v e l o c i t y on t o t a l melt l e n g t h . F i g u r e 29 and  When the flow v e l o c i t i e s  flow  appearing  35 are p l o t t e d a g a i n s t average temperature g r a d i e n t  opposed to t o t a l temperature d i f f e r e n c e ) a c r o s s  the m e l t ,  in (as  F i g u r e 47, i t  becomes apparent t h a t the s l o p e d i f f e r e n c e observed i n F i g u r e 35 was r e s u l t of flow v e l o c i t y dependence on t o t a l melt l e n g t h . d i f f e r e n t l a t e r a l g r a d i e n t s i n the two channel b o a t s they v e l o c i t y observed.  I f t h e r e were  channel g r a p h i t e and  d i d not s i g n i f i c a n t l y  s i n g l e aluminum  e f f e c t the l o n g i t u d i n a l . flow  F i g u r e 47 shows, i n agreement w i t h F i g u r e 45,  flow v e l o c i t y i s . l i n e a r l y ature gradient across  dependent on  the m e l t .  The  a  that  the average h o r i z o n t a l temper-  s l o p e o f the l i n e i n F i g u r e  47  i s l e s s than t h a t i n F i g u r e 45 s i n c e the average melt temperature  was  lower.  2.2.3.4.  E v a l u a t i o n of Technique  In o r d e r to e v a l u a t e measurement technique experimental was  a s e r i e s of experiments was  velocity  performed i n which  p r o c e d u r e s and parameters were v a r i e d from the norm.  done to determine what e f f e c t  perimental  the s e n s i t i v i t y of t h i s f l o w  This  i n a d v e r t e n t v a r i a t i o n s from normal  procedure would have on the observed flow v e l o c i t y .  ex-  Results  0-4 i  1  —  AVERAGE F i g u r e 47.  r  TEMR  GRAD.  (°C/CM)  Comparison of the v e l o c i t y v e r s u s temperature g r a d i e n t r e s u l t s o b t a i n e d u s i n g the two channel g r a p h i t e boat and the s i n g l e aluminum channel b o a t . Average melt temperature was approximately 310 °C.  of these t e s t s appear below.  2.2.3.4.1.  E f f e c t on Flow V e l o c i t y o f V a r y i n g t h e Nature o f the Temperature D i s t r i b u t i o n  F i g u r e 48 compares the temperature d i s t r i b u t i o n  imposed  d u r i n g two s e p a r a t e experiments designed t o show t h a t i t i s t h e average temperature g r a d i e n t between the h o t and c o l d ends o f the m e l t s , and not the average temperature g r a d i e n t between the two c o l l i m a t o r  slots  ( m o n i t o r i n g i n t e r v a l ) t h a t determines the r e s u l t a n t flow v e l o c i t y .  As  can be seen i n F i g u r e 48, the average temperature, g r a d i e n t a c r o s s the monitoring  i n t e r v a l i s the same f o r both experiments.  The average g r a d -  i e n t s between the h o t and c o l d ends a r e however q u i t e d i f f e r e n t .  The  flow v e l o c i t i e s observed f o r t h e two t e s t s were 0.39 cm/sec f o r the experiment w i t h the lower g r a d i e n t , 5.0 °C/cm, and 0.47 cm/sec when t h e average g r a d i e n t between the ends o f the melt was 5.8 °C/cm.  When these  r e s u l t s a r e compared, F i g u r e 50, t o the r e s u l t s o f F i g u r e 46 e x c e l l e n t agreement i s found.  C l e a r l y then,the average g r a d i e n t a c r o s s the t o t a l  melt l e n g t h and n o t t h a t i n the m o n i t o r i n g i n t e r v a l i s r e s p o n s i b l e f o r the flow v e l o c i t y o b s e r v e d .  A l s o , from F i g u r e s 48 and 50 i t can be concluded t h a t t h e flow v e l o c i t y i s independent o f the shape o f the temperature  profile,  t h a t i s , whether the temperature d i s t r i b u t i o n between the h o t and c o l d ends i s n o n - l i n e a r o r n e a r l y l i n e a r  (as was g e n e r a l l y the case) the same  flow v e l o c i t y w i l l be observed when the average g r a d i e n t s a r e the same. The l i m i t i n g case o c c u r s when t h e r e i s a maximum  (or minimum) i n the  temperature p r o f i l e between the h o t and c o l d ends which s t o p s f l u i d  flow  250  1  0  1  5 F i g u r e 48.  * 10 15 20 POSITION ALONG 1  1  1  25 BOAT  1  30 (CM)  35  Temperature p r o f i l e s from two experiments, designed to show t h a t the tempera t u r e g r a d i e n t across the melt, and not the g r a d i e n t a c r o s s the m o n i t o r i n g i n t e r v a l , i s the d r i v i n g f o r c e f o r the observed v e l o c i t y .  108  at that point (Section 2.1.3.).  2.2.3.4.2.  Effect on Flow Velocity of Varying the Position of the Monitoring Interval Although the position of the monitoring i n t e r v a l  reasonably constant during a given series of experiments,  remained  experiments  were conducted to determine whether changing the p o s i t i o n of the monitoring  i n t e r v a l would change the measured flow v e l o c i t y .  ments a shorter i n t e r v a l of 13.8 cm was  employed.  For these experi-  The temperature pro-  f i l e shown i n Figure 49 was established and f o r the f i r s t test the monitoring i n t e r v a l was between thermocouples boat was emptied and reloaded, the  °C/cm.  carried out with the monitoring  The average gradient across the melt was  The gradient between A and C was  and D 6.0 °C/cm.  The graphite .  temperature p r o f i l e of Figure 49 re-  established, and the second experiment i n t e r v a l between B and D.  A and C.  5.1  4.3 °C/cm and that between B  Flow v e l o c i t i e s determined from both i n t e r v a l s were  approximately the same, 0.42  and 0.43  cm/sec respectively.  I f these  v e l o c i t i e s are plotted against the average temperature gradient between the hot and cold end,  Figure 50, i t i s found that they are i n excellent  agreement with the results of Figure 46.  Thus, i t can be concluded that  the position of the monitoring i n t e r v a l does not affect the flow v e l o c i t y observed.  However, i t was necessary to keep the f i r s t collimator s l i t  approximately 5 cm downstream of the place of tracer introduction and thus avoid any spurious effects which may be associated with introduction of tracer.  Figure  49.  Temperature p r o f i l e from an experiment undertaken to determine the e f f e c t on flow v e l o c i t y of changing the p o s i t i o n of the m o n i t o r i n g interval.  0 '9  I  0  1  1  1  1  2 3 AVERAGE F i g u r e 50.  —r  4 5 TEMP.  1  1  6 GRAD.  1  1—  7 8 (°C/CM)  Comparison o f the r e s u l t s o f F i g u r e s 48 and 49 w i t h  r  9  r e s u l t s of F i g u r e  10 46.  2.2.3.4.3.  E f f e c t on Flow V e l o c i t y o f V a r y i n g the Height o f M e t a l i n the R e s e r v o i r s  E a r l i e r i n the t h e s i s i t was for  a p p r o x i m a t e l y 90% o f i t s l e n g t h w i t h each end h a v i n g an  reservoir.  about 1 cm deep i n b o t h r e s e r v o i r s .  l i q u i d m e t a l i s a major parameter  i n any f l u i d  periments were conducted t o determine the e f f e c t v a r y i n g the h e i g h t o f m e t a l i n the r e s e r v o i r s .  I t was  the  flow v e l o c i t y .  effect  cm h e i g h t i s p l o t t e d on the l i n e  46, where the h e i g h t o f m e l t i n the r e s e r v o i r was  on  1.0  0.50  from  cm.  Thus,  concluded t h a t the h e i g h t of melt i n the r e s e r v o i r s does not  the observed flow v e l o c i t y and, t h e r e f o r e , i t i s a p p r o p r i a t e to  a n a l y z i n g the  cm,  f o r the purpose o f  h o r i z o n t a l m e l t system s t u d i e d h e r e .  Another v a r i a t i o n i n e x p e r i m e n t a l procedure which may  affect  observed flow v e l o c i t y i s a d i f f e r e n c e i n h e i g h t of m e t a l i n ; t h e  reservoirs.  The  w i t h pure t i n .  then t h a t the h e i g h t of m e t a l i n one r e s e r v o i r was other.  Thus, when the t r a c e r was  d i f f e r e n t than i n the  i n t r o d u c e d i n t o the boat by  t h i s would most a s s u r e d l y cause f l u i d motion was  conducted i n which  i n the hot and c o l d r e s e r v o i r s was  a 0.3  the  It i s quite possible  rotating  c y l i n d e r t h e r e would be a head of l i q u i d m e t a l i n one r e s e r v o i r  experiment  two  t r a c e r i n t r o d u c e r i s i n the c l o s e d p o s i t i o n ( b l o c k i n g  channel) when the boat i s loaded  the  ex-  found t h a t r e d u c i n g  cm had no e f f e c t  use the h e i g h t i n the covered s e c t i o n , namely 0.64  the  cm  S i n c e the h e i g h t  T h i s i s shown i n F i g u r e 51 were the v e l o c i t y o f  cm/second measured f o r the 0.7  can be  0.64  on flow v e l o c i t y of  melt h e i g h t i n the r e s e r v o i r s from. 1 cm to 0.7  it  uncovered  dynamics a n a l y s i s ,  the  Figure  covered  The h e i g h t o f l i q u i d m e t a l i n the oovered p o r t i o n was  w h i l e the melt was of  s t a t e d t h a t the m e l t was  through the c h a n n e l .  cm d i f f e r e n c e i n l i q u i d  and An  level  e s t a b l i s h e d p r i o r to r o t a t i o n of the  0*9 i  0  i  1  f  2 Figure 51.  1  —  i  3 4 AVERAGE  1  5 TEMP  — i  1  6 GRAD.  7 8 (°C/CM)  1  r  9  The e f f e c t on flow velocity of varying the l i q u i d metal height i n the reserviors and of introducing the tracer near the cold end.  10  tracer introducer. of the  cylinder  to the  l e v e l i n what had fluctuations in  10  to 15  V i s u a l o b s e r v a t i o n of the m e l t f o l l o w i n g  open p o s i t i o n showed a r a p i d r i s e i n the  been the  i n the  low  l e v e l end.  reservoir levels.  T h i s was  The  the  liquid  f o l l o w e d by o s c i l l a t o r y  o s c i l l a t i o n s disappeared with-  seconds.  To determine the e f f e c t of l i q u i d head i n the on  rotation  flow v e l o c i t y a s e r i e s of experiments was  reservoirs  conducted i n which  there  was:  The  (1)  A 0.3  cm head i n the hot  (2)  L e v e l s i n hot  (3)  A 0.3  cold reservoirs  °C/cm.  e q u a l , G = 6.1  cm head i n the c o l d r e s e r v o i r , G = 5.6  °C/cm.  °C/cm.  a c t i v i t y v e r s u s time curves f o r these t h r e e experiments are  F i g u r e s 5 2 ( a ) , 52(b) to  and  r e s e r v o i r , -G = 5.5  ( c ) , t h e r e i s an  first end).  collimator  and  52(c)  increase  slit.  However, when the  respectively.  i n the  the  from F i g u r e 46.  The  of t r a c e r i n the  l e v e l i n g d i r e c t i o n , but  difference  initial  the p o i n t s  no net  coincide  l e v e l i n g of the  e f f e c t on  i n r e s e r v o i r l e v e l was  the  f o r t r a c e r to  i n melt l e v e l i n the  flow v e l o c i t i e s observed.  reach  v e r s u s average w i t h the  reservoirs  a p p a r e n t l y , the  line  c o u l d not  hot  taken  causes a surge subsequent  concluded  os0.3  much l a r g e r than t h a t which c o u l d  reservoirs  the  gradient  flow v e l o c i t y . S i n c e the  n o r m a l l y o c c u r r e d d u r i n g a s e r i e s of experiments i t was differences  52(a)  t r a c e r i s i n t r o d u c e d a t the  flow v e l o c i t y i s p l o t t e d  (opened c i r c l e s i n F i g u r e 51),  c i l l a t o r y motion has  In going from F i g u r e  time r e q u i r e d  ( R e c a l l that  shown i n  have  that  have e f f e c t e d  cm  the  114  F i g u r e 52 ( a ) .  A c t i v i t y v e r s u s time r e s u l t s when t h e r e was a 3 mm head o f l i q u i d t i n i n the hot r e s e r v o i r .  115  F i g u r e 52(b),, A c t i v i t y v e r s u s time r e s u l t s when t h e r e was no d i f f e r e n c e i n the l i q u i d t i n l e v e l i n the hot and c o l d r e s e r v o i r s .  116  Figure 52(c).  A c t i v i t y v e r s u s time r e s u l t s when t h e r e was a 3 mm head of l i q u i d t i n i n the c o l d reservoir.  117  2.2.3.4.4.  E f f e c t on Flow V e l o c i t y o f I n t r o d u c i n g T r a c e r i n the C o l d End o f t h e M e l t  In almost a l l the v e l o c i t y measurement experiments was i n t r o d u c e d near t h e h o t end o f the m e l t . t i o n near the hot end, as opposed  tracer  To determine whether a d d i -  t o near the c o l d end, was s i g n i f i c a n t  an experiment was conducted i n which t r a c e r was i n t r o d u c e d near t h e c o l d end.  The r e s u l t s a r e p l o t t e d  i n F i g u r e 51 (open t r i a n g l e ) .  The ex-  1  c e l l e n t agreement w i t h the l i n e taken from F i g u r e 46 l e a d s t o the conc l u s i o n t h a t the s i t e o f i n t r o d u c t i o n , e i t h e r near the hot end o r c o l d end, has no b e a r i n g on the flow v e l o c i t y measured by the p r e s e n t t r a c e r monitoring technique.  2.2.3.4.5.  Extent o f I n d u c t i v e M i x i n g  The f a c t t h a t the tube f u r n a c e which surrounded t h e melt was i n d u c t i v e l y wound n e c e s s i t a t e d i n v e s t i g a t i o n o f the e x t e n t o f e l e c t r o magnetic s t i r r i n g . s e r i e s of"power  T h i s was p a r t i a l l y accomplished by c o n d u c t i n g a  off"experiments.  In these experiments a d e s i r e d  temper-  a t u r e g r a d i e n t was e s t a b l i s h e d , the f u r n a c e power was then t u r n e d o f f and introduction  o f t r a c e r took p l a c e some time l a t e r .  The s o l i d  circles  a p p e a r i n g i n F i g u r e 53 a r e the r e s u l t s o f f o u r experiments i n which t h e furnace power was t u r n e d o f f a t 1, 3, 3 and 5% minutes p r i o r t o t r a c e r introduction.  The s c a t t e r about the r e s u l t s o f F i g u r e 46  t h a t t h e r e i s no s i g n i f i c a n t i n d u c t i v e s t i r r i n g  indicates  i n the l o n g i t u d i n a l  direction.  F u r t h e r evidence o f the absence o f i n d u c t i v e m i x i n g was obt a i n e d from the f o l l o w i n g experiments.  The f u r n a c e power, h e a t i n g b l o c k  Q .  9  1  0  —  i  I F i g u r e 53.  j  1  2 3 AVERAGE  1  4 5 TEMR  1  1  1  6 7 8 GRAD. (°C/CM)  R e s u l t s o f the i n v e s t i g a t i o n of the extent  1  9  of inductive.mixing.  r  10  power and argon flow rate were adjusted to give a temperature gradient of approximately Employing  6 °C/cm and the resulting flow v e l o c i t y  determined.  the same furnace power settings; the heating block power and  argon flow rate were adjusted to give a gradient of approximately and the resulting v e l o c i t y measured.  4 °C/cm  The tube furnace windings are the  only possible cause of electromagnetic s t i r r i n g i n the l i q u i d metal. induced flow due to the furnace windings contributes i n a major way driving force of the observed  If to the  flow, then, since the furnace power settings  were i d e n t i c a l for the two experiments just described, one would expect to observe s i m i l a r flow v e l o c i t i e s .  The results 'of these experiments  are the open c i r c l e s plotted i n Figure 53. results and  The agreement between these  the results of Figure 46 i s very good.  Clearly then, i t i s  the average temperature gradient across the melt, that i s , the thermal driving force, and not an electromagnetic driving force, which  determines  the v e l o c i t y dependence obtained i n Figure 46.  2.2.3.4.6.  Reproducibility of Results Most of the experiments presented i n this "Evaluation of  Technique"  Section were conducted  during d i f f e r e n t phases of the project  The f i r s t stage of any series of experiments was results  to the results of Figure 46.  average melt temperature was  It was  approximately  to correlate the i n i t i a l  found that as long as the  400 °C agreement between experi  ments to reconfirm the v e l o c i t y versus average temperature gradient depend ence and the results shown i n Figure 46 when the appearance,that  was good.  This occurred even  i s , the slope of the rapidly increasing portion  and maximum a c t i v i t y of the a c t i v i t y versus time curves changed.  Changes  120  i n the appearance o f the a c t i v i t y v e r s u s time curves o c c c u r r e d as a r e s u l t of weakening of the t r a c e r , due  t o r a d i o a c t i v e decay, and as a r e s u l t  s l i g h t i r r e g u l a r i t i e s accompanying t r a c e r  2.2.3.4.7.  Summary of Technique  The s c a l e r and  introduction.  Evaluation  d u a l c o l l i m a t o r system w i t h photography of the v i d e o  t i m e r outputs a l l o w s a c c u r a t e and r e p r o d u c i b l e measurement of  flow v e l o c i t i e s up t o approximately  1 cm/second.  I t has been e s t a b l i s h e d  p r e v i o u s l y t h a t the i n t r o d u c t i o n technique of r o t a t i n g a v e r t i c a l l o c a t e d i n the covered s e c t i o n of the melt normally o c c u r r i n g f l u i d gated.  of  Furthermore,  causes  less interference with  flow than any of the o t h e r t e c h n i q u e s  the i n s e n s i t i v i t y of observed  employed.  investi-  flow v e l o c i t y  r e s p e c t to s l i g h t v a r i a t i o n s i n e x p e r i m e n t a l procedure a c c e p t a b i l i t y of the data a n a l y s i s  cylinder  confirms  with the  R e p r o d u c i b i l i t y of d a t a  has been e x c e l l e n t and the accuracy of the r e s u l t s , from F i g u r e 46,appears to be of the o r d e r of ± 10% o r b e t t e r .  The  s c a t t e r of r e s u l t s about  l i n e drawn i n F i g u r e 46 would p r o b a b l y have decreased taken i n h o l d i n g average melt  2.3.  Summary of  temperature  the  had more c a r e been  constant.  ELow V e l o c i t y D e t e r m i n a t i o n  Results  A summary of a l l r e s u l t s o b t a i n e d throughout  the course o f  this  i n v e s t i g a t i o n l e a d s t o the f o l l o w i n g important c o n c l u s i o n s :  (1)  Fluid  flow a r i s i n g  t r a n s f e r through gradient.  from  thermal c o n v e c t i o n w i l l not cause mass  a r e g i o n of zero h o r i z o n t a l  temperature  (2)  An extremely  s m a l l h o r i z o n t a l temperature g r a d i e n t , a p p a r e n t l y  any non-zero g r a d i e n t , p r o v i d e s s u f f i c i e n t force for f l u i d  (3)  The  thermal  driving  flow.  flow v e l o c i t i e s observed  are the r e s u l t of the  presence  of buoyancy f o r c e s c r e a t e d by the h o r i z o n t a l temperature d i f f e r e n c e a c r o s s the m e l t .  These v e l o c i t i e s are not  pendent on e l e c t r o - m a g n e t i c s t i r r i n g  (4)  The melt  v e l o c i t y of f l u i d temperature,  the m e l t ,  and  temperature  (5)  For  de-  effects.  flow i n c r e a s e s w i t h ; i n c r e a s i n g average  i n c r e a s i n g temperature d i f f e r e n c e a c r o s s  d e c r e a s i n g t o t a l melt  length (for a given  difference).  the covered h o r i z o n t a l rod c o n f i g u r a t i o n i n v e s t i g a t e d  h e r e i n the flow v e l o c i t y i s l i n e a r l y dependent on the average temperature g r a d i e n t between the h o t and  c o l d ends of the  melt.  122  3 - FLOW PATTERNS IN HORIZONTAL RODS OF MOLTEN TIN  3.1.  Introduction  To c o m p l e t e l y d e f i n e f l u i d  f l o w i n l i q u i d m e t a l s t h e flow  p a t t e r n i n the m e l t , as w e l l as t h e f l o w v e l o c i t i e s , must be s p e c i f i e d . P r e l i m i n a r y a u t o r a d i o g r a p h y r e s u l t s p r e s e n t e d i n S e c t i o n 2.1.6.2.2. i n d i c a t e d the presence o f a t r a n s v e r s e double c e l l flow p a t t e r n . was  There  no e v i d e n c e o f t h e l o n g i t u d i n a l m u l t i - c e l l flow p a t t e r n s suggested  by Utech e t a l ^ " ^  and Stewart  However, i t c o u l d n o t be e s t a b l i s h e d  unambiguously t h a t the flow p a t t e r n s shown i n F i g u r e 25 and 26 were d i r e c t l y a s s o c i a t e d w i t h the f l u i d effects.  The r e l a t i v e l y l o n g time  quenching p l u s the of  f l o w and n o t p a r t i a l l y due to quenching ( g r e a t e r than 15 seconds) r e q u i r e d f o r  the f a c t the t r a c e r i n t r o d u c t i o n was from t h e cover o f  boat suggested t h a t t h e f l o w p a t t e r n s observed were n o t r e p r e s e n t a t i v e the f l u i d  ing  I n o r d e r t o a p p r e c i a b l y reduce the quench-  time the s i n g l e channel t h i n w a l l e d aluminum boat was adopted f o r sub-  sequent  3.2.  flow i n the m e l t .  flow p a t t e r n o b s e r v a t i o n experiments.  E x p e r i m e n t a l Apparatus  and Procedure  The aluminum boat used t o c o n t a i n the melt i s t h a t shown p r e v i o u s l y i n F i g u r e 34.  The square channel p o r t i o n o f t h e boat was s u r -  rounded by a 3/4 i n c h I.D. open ended copper quenching j a c k e t .  Quench-  ing  The water  water was d i r e c t e d from the c o l d end towards the h o t end.  123  s u p p l y t o the quenching j a c k e t was c o n t r o l l e d by a p r e s s u r e r e d u c e r and valve. the  I n a t y p i c a l experiment a d e s i r e d temperature d i f f e r e n c e a c r o s s  melt was e s t a b l i s h e d and m a i n t a i n e d f o r a p p r o x i m a t e l y one hour, t h e  t r a c e r was then i n t r o d u c e d i n t o the melt and quenching some s p e c i f i e d time a f t e r i n t r o d u c t i o n .  took p l a c e a t  The water p r e s s u r e a t the b e -  g i n n i n g o f the quench was 5 p s i g and was q u i c k l y i n c r e a s e d t o about 15 p s i g once quenching had been i n i t i a t e d . the  Water p r e s s u r e was kept low a t  b e g i n n i n g o f t h e quench to p r e v e n t any water surges from p h y s i c a l l y  disturbing  the b o a t .  A f t e r quenching, the t i n f i l l e d  was cut from the g r a p h i t e ends w i t h a j e w e l l e r s saw.  aluminum c h a n n e l The sample was  then s e c t i o n e d , m e c h a n i c a l l y p o l i s h e d , and p l a c e d on double emulsion X-ray f i l m f o r a p e r i o d o f time s u f f i c i e n t  to y i e l d  a s a t i s f a c t o r y auto-  radiograph.  The a u t o r a d i o g r a p h r e s u l t s from the r a d i a t i o n r e c e i v e d a finite  t h i c k n e s s o f m a t e r i a l a d j a c e n t t o the p h o t o g r a p h i c f i l m .  from The  t h i c k n e s s o f t h i s c o n t r i b u t i n g l a y e r i n c r e a s e s w i t h i n c r e a s i n g energy o f r a d i a t i o n , thus r e d u c i n g the r e s o l u t i o n o b t a i n e d i n the a u t o r a d i o g r a p h . 113 S i n c e the r a d i a t i o n from Sn  (X-ray and gamma l e s s than 0.4 Mev) i s  much l e s s e n e r g e t i c than t h a t from Sb  12 ^  used f o r the flow p a t t e r n experiments. for  (gamma up t o 2 Mev), Sn  1X3  was  The t r a c e a l l o y commonly used  the flow p a t t e r n experiments was 0.85% n o n - r a d i o a c t i v e Sb i n pure 113  Sn w i t h a p p r o x i m a t e l y 3.5% Sn  .  T h i s a l l o y has the same d e n s i t y as  the  t r a c e a l l o y used f o r the v e l o c i t y d e t e r m i n a t i o n measurements  out  i n the p r e v i o u s s e c t i o n .  3.3.  carried  R e s u l t s from Quenching Wired Top U-Channel In  initial  experiments the square aluminum c h a n n e l had been  124  c o n s t r u c t e d by w i r i n g an aluminum cover over aluminum U-channel. attempts failed  to o b t a i n s u i t a b l e quenched specimens  s i n c e quench water was  v i o l e n t l y w i t h the l i q u i d  All  f o r autoradiography  a b l e to seep under the cover and  react  metal.  3.4. A u t o r a d i o g r a p h y o f Quenched Specimens U s i n g a Completely C l o s e d Square Aluminum Channel 3.4.1.  E x p e r i m e n t a l Apparatus  In  and  Procedure  o r d e r to a v o i d the d i s a s t e r o u s r e s u l t s brought on by  c o n t a c t o f quench water w i t h the melt i t became n e c e s s a r y to o b t a i n totally  e n c l o s e d square c h a n n e l .  I t was  not p o s s i b l e to o b t a i n 1/4  inch  square aluminum channel from commercial s o u r c e s and t h e r e f o r e an a p p r o x i mately square channel was  manufactured  w a l l t h i c k n e s s aluminum t u b i n g . t u b i n g over a 1/4  was  i n c h O.D.,  a p p r o x i m a t e l y 0.26  0.038 i n c h  accomplished by f o r c i n g  (with s l i g h t l y  i n a horizontal rolling m i l l .  rounded  corners)  The r e s u l t i n g  inches.  o v e r a l l m e l t l e n g t h was  The  channel was  channel  cut to l e n g t h such  namely 37.5  quenching j a c k e t , was  i n s e r t e d i n t o the g r a p h i t e r e s e r v o i r s and  cm.  The c h a n n e l , surrounded by  j o i n t s were s e a l e d w i t h S a i r s e t cement.  R e s u l t s from Square Aluminum With No Water S h i e l d  the  the  G e n e r a l e x p e r i m e n t a l procedure  o b t a i n i n g a u t o r a d i o g r a p h s has a l r e a d y been d e s c r i b e d i n S e c t i o n  3.4.2.  that  the same, as t h a t used i n S e c t i o n 2.1.8. and  most of S e c t i o n 2.2.,  for  the  i n c h e s square w i t h the c o r n e r s h a v i n g a r a d i u s o f  c u r v a t u r e of about 0.03 the  T h i s was  i n c h square mandrel  f o l l o w e d by r o l l i n g  from 3/8  3.2.  Channel  Even w i t h the t o t a l l y e n c l o s e d square aluminum c h a n n e l quench-  125  i n g of m e l t s to p r o v i d e specimens f o r subsequent  autoradiography  r e s u l t e d i n the s p r a y i n g o f melt out o f the hot r e s e r v o i r .  usually  T h i s caused  a decrease i n the l i q u i d m e t a l l e v e l i n the hot end o f the c h a n n e l and a g a i n r e s u l t e d i n specimens which were u n a c c e p t a b l e f o r a u t o r a d i o g r a p h y . I t appeared  t h a t quench water, which was  wards the hot end o f the c h a n n e l , was  d i r e c t e d from the c o l d and t o -  a b l e to l e a k through the S a i r s e t  cemented aluminum c h a n n e l - g r a p h i t e r e s e r v o i r j o i n t and cause v i o l e n t  dis-  r u p t i o n of the melt a t the hot end.  that  Another p o s s i b l e cause c o u l d be  quench water h i t the hot g r a p h i t e r e s e r v o i r c r e a t i n g a spray o f water i n the v i c i n i t y o f the r e s e r v o i r w i t h some of the s p r a y f i n d i n g i n t o the uncovered  3.4.3.  i t s way  s e c t i o n o f the r e s e r v o i r .  R e s u l t s and D i s c u s s i o n of Experiments Aluminum Channel w i t h a Water S h i e l d  Using  To p r e v e n t water from l e a k i n g through the aluminum c h a n n e l g r a p h i t e r e s e r v o i r j o i n t and t o remove the p o s s i b i l i t y o f water  finding  i t s way  thick,  3/4  i n t o the uncovered  i n c h O.D.  s e c t i o n o f the r e s e r v o i r a 3/32  aluminum water s h i e l d was  channel at a p p r o x i m a t e l y 1/8  appear average how  the aluminum  i n c h from the hot end s u p p o r t .  the c h a n n e l , equipped w i t h water s h i e l d j a c k e t , was  welded around  inch  As b e f o r e ,  and surrounded by the quench  cemented i n t o the r e s e r v o i r s .  A l l a u t o r a d i o g r a p h s which  i n t h i s s u b s e c t i o n were o b t a i n e d from quenched m e l t s which had temperature  g r a d i e n t o f a p p r o x i m a t e l y 6 °C/cm.  an  F i g u r e 54 shows  most of the specimens were s e c t i o n e d f o r a u t o r a d i o g r a p h y .  Sections  were taken p e r p e n d i c u l a r to the l o n g i t u d i n a l a x i s o f the r o d a t 0.5 i n t e r v a l s s t a r t i n g a t 4 cm from the p o i n t of i n t r o d u c t i o n .  cm  Several other  specimens were s e c t i o n e d p a r a l l e d to the " o u t s i d e " w a l l i n o r d e r to  Water shield  Outside End of— sectioning  Start (~4cm from introduction point)  1  F i g u r e 54.  Schematic r e p r e s e n t a t i o n showing the p o s i t i o n s at which the specimen was s e c t i o n e d to o b t a i n the t r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s .  (a) Hot  Cold  (b) Hot  Cold Figure  55.  L o n g i t u d i n a l s e c t i o n a u t o r a d i o g r a p h s of specimens quenched 1 minute a f t e r i n t r o d u c t i o n of t r a c e a l l o y Sn  )  Surface  autoradiograph  was  0.04  (a) AO s e c . and  (0.85% Sb i n pure Sn c o n t a i n i n g  inches below o u t s i d e  (b) 3.5%  s u r f a c e (X2).  S3  128  determine t h e flow p a t t e r n  i n the l o n g i t u d i n a l d i r e c t i o n .  F i g u r e 55 shows a u t o r a d i o g r a p h s o f l o n g i t u d i n a l s e c t i o n s o f specimens which have been quenched 40 seconds (Figure  55(b)) a f t e r t r a c e r i n t r o d u c t i o n .  (Figure  55(a)) and 1 minute  The s u r f a c e  was a p p r o x i m a t e l y 0.04 i n c h e s below the o u t s i d e s u r f a c e  autoradiographed o f the t i n .  The  d i s t r i b u t i o n o f t r a c e r i n both specimens i s e s s e n t i a l l y i d e n t i c a l and, as e x p e c t e d , t h e t r a c e r has  moved f a r t h e r along t h e melt i n the specimen  that was quenched one minute a f t e r i n t r o d u c t i o n , the  F i g u r e 55(b), than i n  specimen quenched 40 seconds a f t e r t r a c e r i n t r o d u c t i o n .  evidence o f m u l t i - c e l l flow.  I t appears that  There i s no  the l o n g i t u d i n a l flow i s  u n i c e l l u l a r w i t h l i q u i d moving from the h o t end to t h e c o l d end along the  top o f  the bottom.  the m e l t and r e t u r n i n g This  F i g u r e 55 s i n c e  from the c o l d end to t h e h o t end along  statement i s n o t confirmed by t h e a u t o r a d i o g r a p h s o f  i t i s apparent that  of the m e l t and t h e r e f o r e  t r a c e r has n o t reached t h e c o l d end  the t r a c e r which appears a t t h e bottom o f t h e  melt d i d n o t a r r i v e t h e r e as a r e s u l t o f u n i c e l l u l a r l o n g i t u d i n a l The  flow.  t r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s , F i g u r e 56, o f another specimen  which was quenched 40 seconds a f t e r t r a c e r i n t r o d u c t i o n  show t h a t the  t r a c e r has been c a r r i e d towards the bottom o f the melt by a t r a n s v e r s e flow which i s superimposed on the u n i c e l l u l a r l o n g i t u d i n a l flow. sections  i n F i g u r e 56 a r e a t 1 cm i n t e r v a l s along the r o d s t a r t i n g a t  4 cm from the p o i n t hot  of i n t r o d u c t i o n  i n the h o t r e s e r v o i r .  end t o the c o l d end o f the m e l t the flow p a t t e r n  Going from the  becomes l e s s com-  p l e x but t h i s i s most p r o b a b l y due t o the f a c t t h a t as the t r a c e r the  The  approaches  c o l d end i t has spent l e s s time a t a g i v e n p o s i t i o n and t h e r e f o r e  the  t r a n s v e r s e flow has had l e s s time to sweep the t r a c e r w i t h i t i n o r d e r t o  Top  Figure  56.  T r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s of a specimen quenched 113 Sn  -Sb-Sn t r a c e r .  4 cm  from p o i n t  Sections  are  at 1 cm  40 s e c .  i n t e r v a l s w i t h the s t a r t  of i n t r o d u c t i o n near the hot  end  (x 4 ) .  after introduction (top  of  l e f t hand corner  130  o u t l i n e the  complete flow p a t t e r n .  In  o r d e r t o study t h e development o f t h e t r a n s v e r s e f l o w  p a t t e r n , F i g u r e s 57 and 58 have been p r e p a r e d s o t h a t a comparison can be made between the t r a n s v e r s e flow observed AO seconds, 1 minute, and 2 minutes a f t e r t r a c e r i n t r o d u c t i o n . of  The f i r s t ,  t h i r d and f i f t h  rows  F i g u r e 57 a r e t r a n s v e r s e s e c t i o n s from the 40 second specimen and the  second, f o u r t h and s i x t h rows a r e from e q u i v a l e n t p o s i t i o n s along the specimen quenched 1 minute a f t e r i n t r o d u c t i o n o f t r a c e r .  As e x p e c t e d ,  and i n agreement w i t h F i g u r e 55, t r a c e r has moved f u r t h e r a l o n g t h e specimen quenched  1 minute a f t e r i n t r o d u c t i o n .  Comparison o f rows  t h r e e and f o u r shows t h a t i n c r e a s e d time b e f o r e quenching has a l s o allowed more e x t e n s i v e t r a n s v e r s e f l o w o f the t r a c e r .  F i g u r e 58 compares the specimens quenched 1 minute one, t h r e e and f i v e ) and 2 minutes introduction.  (rows  (rows two, f o u r and s i x ) a f t e r  There i s no obvious d i f f e r e n c e i n the t r a n s v e r s e  p a t t e r n s observed a t each p o i n t along the m e l t .  tracer  flow  The e x t r a minute b e f o r e  quenching has no doubt allowed more e x t e n s i v e d i l u t i o n o f the t r a c e r by the  melt.  This i s reflected  i n the f a c t t h a t t h e time r e q u i r e d t o  o b t a i n e d a s u i t a b l e a u t o r a d i o g r a p h o f the 2 minute specimen was 240 hours whereas o n l y 24 hours was r e q u i r e d f o r t h e 1 minute specimen. S i n c e 1 minute was s u f f i c i e n t of  time f o r t h e t r a c e r t o t r a v e l from the p l a c e  i n t r o d u c t i o n to the c o l d end o f the aluminum c h a n n e l , i t would be ex-  p e c t e d t h a t 2 minutes would be enough time f o r t h e t r a c e r to pass through the  c o l d r e s e r v i o r and, a t the c o l d w a l l , move to the bottom o f the boat  and proceed along the bottom o f the melt back towards the h o t end.  Thus,  one would expect t o observe t r a c e r along the bottom o f t h e t r a n s v e r s e  F i g u r e 57.  Comparison of t r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s from specimens quenched 40 seconds (first,  t h i r d and f i f t h  rows) and 1 minute  (second, f o u r t h and s i x t h rows) a f t e r i n t r o d u c t i o n .  r  f  k  *  ^ p  r  r  m F i g u r e 57 - Continued.  n  <  o >  —  —  i  F i g u r e 58.  Comparison of t r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s from specimens quenched (first,  t h i r d and f i f t h  introduction.  1 minute  rows) and 2 minutes (second, f o u r t h and s i x t h rows) a f t e r  F i g u r e 58 - Continued.  135  s e c t i o n a u t o r a d i o g r a p h s o f the m e l t which was quenched 2 minutes a f t e r tracer introduction.  The f a c t t h a t t r a c e r i s n o t observed along the  bottom o f these s e c t i o n s can be e x p l a i n e d by r e c a l l i n g d i l u t i o n o f t h e t r a c e r has o c c u r r e d it  i s conceivable  that  extensive  over the two minutes and t h e r e f o r e  t h a t by the time t h e t r a c e r has moved t o the bottom  of the melt v i a t h e u n i c e l l u l a r e n t l y d i l u t e d t o be u n d e t e c t a b l e  l o n g i t u d i n a l flow i t has become by a u t o r a d i o g r a p h i n g  for a  suffici-  reasonable  l e n g t h o f time.  The transverse ject.  e f f e c t o f s m a l l v a r i a t i o n s i n t r a c e a l l o y d e n s i t y on the  flow p a t t e r n was a l s o s t u d i e d during, t h i s phase o f the p r o -  As o u t l i n e d p r e v i o u s l y , the t r a c e a l l o y used t o o b t a i n the a u t o -  radiographs slightly  shown i n F i g u r e s 55-58 c o n t a i n e d  l e s s dense (0.9994 pSn) than the m e l t .  transverse  flow p a t t e r n s  greater density  obtain Figure  Figures  therefore  59-61 show t h e  observed one minute a f t e r i n t r o d u c i n g  a l l o y whioh i s o f lower d e n s i t y and  0.85% Sb and was  ( F i g u r e 5 9 ) , equal  ( F i g u r e 61) than the m e l t .  density  trace  ( F i g u r e 60)  The t r a c e a l l o y used t o  59 was 0.85% Sb i n pure Sn (with 3.5% Sn  0.9994 times the d e n s i t y o f the pure t i n m e l t .  113  A 3.5% Sn  ) and was 113  i n pure t i n  204 was the equal  d e n s i t y t r a c e a l l o y and a 0.5% T I  i n Sn t r a c e a l l o y was  p r e p a r e d t o observe the e f f e c t on the flow p a t t e r n o f h a v i n g more dense than the m e l t  (1.0020 p S n ) .  Although these d e n s i t y  ences due t o a l l o y i n g a r e s m a l l , they must be c o n s i d e r e d comparison t o the d e n s i t y changes a r i s i n g For a l i q u i d  the t r a c e r  significant i n  from temperature d i f f e r e n c e s .  the r e l a t i v e change i n d e n s i t y due to a temperature  ence i s g i v e n by: pT„ - ~ pT  = 1 - B (T 2  differ-  - T ) 1  differ-  •••nnnnn F i g u r e 59.  T r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s of a specimen quenched a trace a l l o y  containing  0.85%  Sb i n S n  1 1 3  1 minute a f t e r i n t r o d u c t i o n of  w i t h 3.5% Sn (0.9994  pSn).  F i g u r e 60.  Transverse s e c t i o n autoradiographs of a t r a c e a l l o y  containing  o f a specimen quenched 1 minute a f t e r 113 3.5% Sn i n Sn (1.0000 pSn).  introduction  where $ i s the volume c o e f f i c i e n t of thermal expansion. -4  molten t i n i s of the order of 10  Since g for  /o / C the change i n density a r i s i n g  from small l o c a l temperature differences w i l l be of the same order of magnitude as those caused by the addition of a small amount of a l l o y i n g element-  The flow pattern i l l u s t r a t e d i n Figures 59-61 are e s s e n t i a l l y  i d e n t i c a l and therefore i t can be concluded that the thermal convective flow i s s u f f i c i e n t l y strong to overcome the solute convection which might be expected i n view of the density difference between the trace alloys and the melt.  In going from the less dense to the more dense trace  alloy i t might be expected that there would be an increased tendency for tracer to move v i a solute convection from the top to the bottom of melt. This was not observed. To this point i n the autoradiography studies, trace a l l o y has been introduced near the hot end of the melt and i f i t followed a u n i c e l l u l a r longitudinal flow i t would be expected to move along the top of the melt from the hot to cold end and then return along the bottom of the melt.  A transverse autoradiograph of the u n i c e l l u l a r flow would then  look l i k e Figure 62 (providing there had been s u f f i c i e n t time for tracer to make a complete c i r c u i t with the flow).  Under the experimental condition  of an average temperature gradient along the melt of approximately 6 °C/cm, 2 minutes should be s u f f i c i e n t time for tracer to outline the return flow (from cold to hot) along the bottom of the melt.  Figure 58 (rows two,  four and s i x ) showed the 1 cm i n t e r v a l transverse sections from a specimen which had been quenched 2 minutes after tracer introduction and there was no evidence of a tracer r i c h region along the bottom of the melt.  The  fact that tracer did not appear along the bottom of melt has been ex-  ure 62. The expected appearance of a t r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s i f on u n i c e l l u l a r l o n g i t u d i n a l flow were present (X12).  141  plained by assuming that the tracer became d i l u t e d to the extent that i t was not detectable by autoradiographing  (for a reasonable  length of  time).  To f a c i l i t a t e observation of flow along the bottom of the melt two experiments were conducted i n which tracer was the cooler section of the melt.  (This was  introduced i n  accomplished by  interchanging  the heating and cooling blocks so that the graphite end support i n which the introduction took place became the cold end). temperature gradient along the melt was  6 °C/cm.  As before the average Quenching was  one minute after tracer introduction i n both cases. verse section autoradiographs  initiated  Figure 63 shows the trans-  (the f i r s t being 4 cm from the place of  introduction i n the cold reservoir and subsequent sections at 1 cm i n t e r 204 vals towards the hot end) obtained after introducing a 0.5% TI tracer into the melt.  As expected the tracer moves from the cold end to  the hot end along the bottom of the melt. the way  i n Sn  Approximately one-third of  along the channel transverse flow i s observed.  Although the  trace a l l o y i s s l i g h t l y more dense than the melt (1.0020 pSn)  the trans^  verse flow i s s u f f i c i e n t l y strong to cause mixing of tracer throughout the cross section .  The nature of the transverse flow i s s i m i l a r to  that observed i n Figures 56-61.  The flow travels down the sides of the  section and as i t returns to the top, through the middle of the section, the radioactive tracer i s drawn upwards by i t .  The transverse flow i s  greatly suppressed by using a dense (1.257 pSn)  trace a l l o y composed of  60% Pb i n Sn containing 0.5% TI In Figures 56-61  , Figure 64.  the apparent extent of transverse flow de-  creases with increasing distance from the point of introduction near the  F i g ure 63.  T r a n s v e r s e sect i o n a u t o r a d i o g r a p h s of a specimen quenched 1 minute a f t e r i n t r o d u c t i o n  20A of a t r a c e a l l o y i s 4 cm  from  c o n t a i n i n g 0.5%  the p o i n t  TI  i n Sn.  The  first  of i n t r o d u c t i o n near the c o l d  section  (top l e f t hand  corner)  end. •plo  Transverse section autoradiographs  of a s p e c i m e n q u e n c h e d 1 m i n u t e a f t e r  introduction  O A /  of a t r a c e  alloy  place near  the  composed o f  c o l d end.  60% Pb i n Sn c o n t a i n e d 0.5% TI  .  Introduction  took  144  hot end. T h i s has been e x p l a i n e d by n o t i n g t h a t as t h e d i s t a n c e from the i n t r o d u c t i o n s i t e i n c r e a s e s t h e t r a c e r has had c o n t i n u o u s l y dec r e a s i n g time i n which t o f u l l y o u t l i n e t h e t r a n s v e r s e The  n e t r e s u l t i s t h a t one would observe move e x t e n s i v e  flow  present.  transverse  flow near t h e h o t end ( p l a c e o f i n t r o d u c t i o n ) t h a n near t h e c o l d end.  In F i g u r e s 63 and 64 i t i s observed that t h e e x t e n t o f transverse flow increases with  i n c r e a s i n g d i s t a n c e from t h e p l a c e o f  introduction.  This observation i s not consistent with  the explanation  just offered.  R e c a l l i n g t h a t F i g u r e s 56-61 were o b t a i n e d by i n t r o d u c i n g  t r a c e r i n t h e h o t end whereas f o r F i g u r e s 63 and 64 i n t r o d u c t i o n took p l a c e i n the c o l d end (and t h e f i r s t  s e c t i o n i n . each f i g u r e i s a p p r o x i -  mately 4 cm from t h e p l a c e o f i n t r o d u c t i o n ) , i t i s apparent t h a t t r a n s v e r s e flow i s more e x t e n s i v e near t h e h o t end than t h e c o l d end.  Since  more heat must be removed from t h e h o t end than t h e c o l d end o f t h e melt d u r i n g quenching i t i s p o s s i b l e t h a t more time i s r e q u i r e d f o r s o l i d i f i c a t i o n i n t h e h o t end and t h a t d u r i n g extensive  t r a n s v e r s e flow may o c c u r .  t h i s a d d i t i o n a l time more  A l s o , l a t e r a l temperature  gradients  which a r i s e d u r i n g quenching may cause t r a n s v e r s e flow t h a t i s more ext e n s i v e than was o c c u r r i n g p r i o r quench time d e t e r m i n a t i o n to c o n f i r m  t o quench i n i t i a t i o n .  experiments and s e v e r a l other  The r e s u l t s o f t e s t s t o attempt  the v a l i d i t y o f t h e observed flow p a t t e r n s as w e l l as t h e  d r i v i n g f o r c e f o r the t r a n s v e r s e flow a r e d i s c u s s e d  i n t h e next s e c t i o n .  3.4.4. R e s u l t s and D i s c u s s i o n o f Attempts t o Confirm the V a l i d i t y o f Observed Flow P a t t e r n s 3.4.4.1.  E f f e c t o f Quench C y l i n d e r on Observed Flow V e l o c i t y In o r d e r  to determine what, i f any, e f f e c t  the presence o f  145  the quenching cylinder had on the flow taking place i n the melt a v e l o c i t y determination experiment was carried out i n which the quench cylinder was i n place.  The results of this experiment were v e l o c i t y equals 0.36  cm/sec for an average temperature gradient across the melt of 4.16 °C/cm. Figure 46 shows that for a gradient of 4.16 observe a flow v e l o c i t y of 0.35 cm/sec.  °C/cm one would expect to  From this i t can be assumed that  the quench cylinder does not a f f e c t the longitudinal flow.  3.4.4.2.  Quench Time Determination The time required for complete s o l i d i f i c a t i o n was  determined  at both the hot and cold ends of the square aluminum channel. thermocouples  (30 gauge iron-constantan insulated by 1/16" O.D.  The mullite  tubing) were inserted through the top of the channel such that the beads were located i n the cross sectional centre of the melt.  The hot end  thermocouple was positioned 5 mm downstream from the water s h i e l d and the cold end thermocouple was 5 mm  ahead of the cold end support.  The  thermocouples were connected through a multipoint switch to the Honeywell recorder.  Results of t y p i c a l quench time determination tests are  shown i n Figure 65.  On the basis of s i x tests the average time for  t o t a l s o l i d i f i c a t i o n at the hot end was 2\ seconds and at the cold end was h\ seconds.  At f i r s t glance a somewhat surprising r e s u l t .  The latent heat of fusion of t i n i s 14.5 cal/gm and the heat capacity of l i q u i d t i n at 350 °C i s approximately 0.06 If the hot end of the melt was  cal/gm °C.  200 °C higher than the cold end the amount  of heat that would have to be removed from the hot end would be roughly 1.2 cal/gm more than that removed from the cold end.  Since t h i s i s less  146  F i g u r e 65.  T y p i c a l r e s u l t s of quench time d e t e r m i n a t i o n experiments.  147  than 10% of  the heat o f f u s i o n i t would not be unreasonable  hot and c o l d ends to s o l i d i f y  f o r the  i n a p p r o x i m a t e l y the same l e n g t h o f time.  A l s o , s i n c e the quench water e n t e r s the chamber 3 cm ahead o f the c o l d r e s e r v o i r and the stream i s d i r e c t e d towards the water s h i e l d at the hot end, the o b s e r v a t i o n that the hot end of the channel s o l i d i f i e s seconds b e f o r e the c o l d end i s u n d e r s t a n d a b l e . time t e s t s c o n c l u s i v e l y show s o l i d i f y than the c o l d end.  In any c a s e , the quench  t h a t the hot end does not take l o n g e r t o The p o s s i b i l i t y t h a t  the more e x t e n s i v e  t r a n s v e r s e flow i n the hot end r e s u l t s from d e l a y e d quenching r e g i o n must be r u l e d  3.4.4.3.  2  i n this  out.  Quenching i n a P r e a r r a n g e d T r a c e r D i s t r i b u t i o n The p o s s i b i l i t y  t h a t the quenching  o p e r a t i o n was  the  prime  d r i v i n g f o r c e f o r the development of the observed t r a n s v e r s e f l o w p a t t e r n was quenching bution.  f u r t h e r i n v e s t i g a t e d by c o n d u c t i o n experiments which  a melt which had a p r e a r r a n g e d and thus known t r a c e r  involved  distri-  The p r e a r r a n g e d t r a c e r d i s t r i b u t i o n i s shown i n F i g u r e 66.  d i s t r i b u t i o n was  a c h i e v e d by the f o l l o w i n g t e c h n i q u e .  A 0.04  inch  This thick,  113 0.24  i n c h wide by 11 i n c h long l a y e r o f 0.5%  Sn  i n Sn was  along the bottom o f a square aluminum channel which was than the u s u a l channel l e n g t h . boat p l a c e d i n the f u r n a c e .  an i n c h l o n g e r  The g r a p h i t e ends were a t t a c h e d and  A f u r n a c e temperature  of 200  m e l t i n g p o i n t o f pure t i n ) was  e s t a b l i s h e d and m a i n t a i n e d .  temperature  200  along the boat was  at a p p r o x i m a t e l y 210  °C was  of the e u t e c t i c the boat was  placed  poured  the  °C(30 °C below the When the  °C l e a d - t i n e u t e c t i c  (m.p.  i n t o the b o a t .  solidification  Upon  183  °C)  removed from the f u r n a c e and the channel  (a)  F i g u r e 66.  Schematic r e p r e s e n t a t i o n of the prearranged t r a c e r d i s t r i b u t i o n (a) t r a n s v e r s e s e c t i o n and (b) l o n g i tudinal section. i—  1  00  149  which now  had l e a d - t i n e u t e c t i c over the 3.5%  removed w i t h a j e w e l l e r s saw.  Sn  i n Sn l a y e r  was  The r e s e r v o i r s were r e h e a t e d t o remove  the e u t e c t i c and the ends o f the aluminum channel which were l e f t  after  113 sawing.  The  channel was  then i n v e r t e d so t h a t the Sn  the e u t e c t i c , the boat was  reassembled  and  l a y e r was  above  the r e s e r v o i r s r e f i l l e d .  The  aluminum b l a n k s were p l a c e d a c r o s s each end of the c h a n n e l t o i n s u r e t h a t , once m o l t e n , no movement o f the melt  (due to d i f f e r e n c e s i n head  between the hot and c o l d r e s e r v o i r s or due t o p h y s i c a l d i s t u r b a n c e ) c o u l d o c c u r through the channel and In d e s c r i b e d , was heat o f about  the f i r s t  test  g r a d u a l l y heated t o a p p r o x i m a t e l y 285 100  °C.  o f the o r d e r o f 100  T h i s superheat was  p o s s i b l e c a r e was  °C.  distribution.  the b o a t , w i t h the t r a c e r d i s t r i b u t i o n  c o n d i t i o n s of e a r l i e r quenching was  thus change the t r a c e r  °C t o g i v e a super-  chosen so as to reproduce  experiments where the average  During the m e l t i n g and s u p e r h e a t i n g a l l  taken to m a i n t a i n a zero h o r i z o n t a l  temperature  be s t a b l e .  similar  should y i e l d  should  to F i g u r e 6 6 ( a ) .  t r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s which R e s u l t s of t h i s f i r s t  p l e t e l y u n i f o r m d i s t r i b u t i o n of t r a c e r .  as a r e s u l t o f the quench.  t e s t showed a com-  T h i s showed t h a t m i x i n g  e i t h e r o c c u r r e d d u r i n g the s u p e r h e a t i n g p e r i o d  ( a p p r o x i m a t e l y 3/4  had hour)  The i d e a t h a t the quench (which from p r e -  v i o u s t e s t s i s known t o take l e s s than 5 seconds) was for  (1.257 pSn)  S i n c e n e i t h e r s o l u t e nor thermal c o n v e c t i o n i s expected,the  quenched specimen  or  con-  S o l u t e c o n v e c t i o n should not occur s i n c e the c o n f i g u r a t i o n o f  the l e s s dense t i n l a y e r over the more dense e u t e c t i c  are  the  superheat  g r a d i e n t a l o n g the melt and thus a v o i d the p o s s i b i l i t y o f thermal vection.  just  t h i s complete m i x i n g i s t o t a l l y u n a c c e p t a b l e .  solely responsible  I t was  not  possible  150  to maintain a p e r f e c t l y f l a t temperature p r o f i l e during the superheating and therefore some thermal convection must have occurred.  The second test was conducted  i n a similar manner but this  time quenching was started shortly a f t e r the melting point of t i n (232 °C) was passed.  The t o t a l time from the melting of the eutectic to the time  of quenching was 12 minutes. Figure 67.  The results of this test are shown i n  The sections are at 1 cm i n t e r v a l s .  Although some mixing  113 of Sn  into the eutectic has occurred, there i s no evidence of the  transverse flow observed i n previous autoradiographs.  The conclusion  that the quench technique i s not responsible f o r the transverse flow observed would now appear v a l i d . 3.4.4.4.  Extent of Inductive Mixing In Section 2.2.2.5. evidence was presented to show that i n -  ductive mixing i s not the  driving force for the longitudinal flow of  the l i q u i d t i n . The extent to which inductive mixing e f f e c t s the trans113 verse flow pattern was determined by introducing tracer (3.5 % Sn  )  into the melt two minutes after the furnace power had been turned o f f . The gradient across the melt was 6 °C/cm and quenching took place one minute after tracer introduction.  Rows two, four and s i x of Figure 68  show the results of the power o f f test.  The r e s u l t s of a test with the  same temperature gradient and tracer but with the furnace power on (normal procedure) are shown i n rows one, three and f i v e .  Comparison of  rows one and two, and three and four shows the transverse flow patterns i n the power on and power o f f experiments to be v i r t u a l l y i d e n t i c a l . The only apparent  difference between the two being that the power o f f  F i g u r e 67.  T r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s of the specimen which had the prearranged tracer d i s t r i b u t i o n  shown i n F i g u r e 66.  Figure 6 8 .  Comparison of t r a n s v e r s e s e c t i o n autoradiographs  of specimens quenched 1 minute a f t e r  113  introduction (first, (second,  of 3 . 5 % Sn  t h i r d and fourth  fifth  i n Sn t r a c e r i n t o the melt; w h i l e the furnace power was  on  rows) and 2 minutes a f t e r the furnace power had been turned o f f  and s i x t h  rows).  ^>  F i g u r e 68 - Continued.  flow seems to be somewhat more d i f f u s e . t r a n s v e r s e m i x i n g towards  There i s c o n s i d e r a b l y more  the c o l d end i n the power o f f t e s t  rows f i v e and s i x ) and t h i s c o u p l e d w i t h the f a c t  (comparing  t h a t the f l o w i n t h i s  t e s t i s g e n e r a l l y more d i f f u s e suggests a s l i g h t i n c r e a s e i n the d r i v i n g f o r c e f o r t r a n s v e r s e flow when the power i s o f f .  The p r o b a b l e s o u r c e o f  t h i s d r i v i n g f o r c e would be an i n c r e a s e i n t r a n s v e r s e temperature g r a d i e n t s which a r i s e a f t e r t u r n i n g o f f the f u r n a c e power.  3.4.4.5.  D e t e r m i n a t i o n o f T r a n s v e r s e Temperature  Gradients  Measurements were made o f the temperature d i s t r i b u t i o n  on  p l a n e s t r a n s v e r s e t o the boat a x i s u s i n g the apparatus i l l u s t r a t e d i n F i g u r e 69.  T h i s apparatus a l l o w e d complete  freedom  of two d i m e n s i o n a l  movement of the thermocouple bead i n a g i v e n t r a n s v e r s e p l a n e . moveable thermocouple was that accurate  chosen over a s e r i e s of f i x e d thermocouples  so  r e l a t i v e temperature d i f f e n c e s c o u l d be measured w i t h o u t  having t o be concerned about boat i n which  One  thermocouple  calibration corrections.  the t r a n s v e r s e g r a d i e n t s were measured was  g r a p h i t e boat used i n S e c t i o n 2.1.6.. much e a s i e r t o adapt  T h i s boat was  the moveable thermocouple  have been f o r the s i n g l e channel aluminum b o a t .  The  the two. c h a n n e l  chosen s i n c e i t was  i n t h i s case than i t would S i n c e the t r a n s v e r s e  flow p a t t e r n s observed i n the two channel g r a p h i t e boat  ( F i g u r e s 25  and  26) are s i m i l a r to ones observed i n the s i n g l e channel aluminum boat i t was  assumed t h a t t r a n s v e r s e temperature g r a d i e n t s would a l s o be  ( e s p e c i a l l y so i n the g r a p h i t e end s u p p o r t s used on the s i n g l e  similar channel  aluminum b o a t ) .  F i g u r e 69(a) i s a top view of the boat showing mechanism used t o move  the thermocouple  the wedging  from one s i d e o f the channel .  F i g u r e 69.  Schematic r e p r e s e n t a t i o n of apparatus used to measure t r a n s v e r s e temperature g r a d i e n t s (x2).  Ul  to the  the o t h e r .  The s t a i n l e s s s t e e l r o d was f a s t e n e d on to the boat a t  c o l d end and had s u f f i c i e n t e l a s t i c i t y  original position  t o cause i t t o r e t u r n t o i t s  (1) when the wedge was withdrawn.  A cam mechanism,  which c o u l d be o p e r a t e d remotely by a l e v e r system, was employed t o r a i s e and lower t h e thermocouple, F i g u r e 69(b). would  The s t a i n l e s s s t e e l r o d  r e t u r n t o t h e low p o s i t i o n due to i t s own e l a s t i c i t y .  The thermo-  c o u p l e was connected t o the end o f t h e s t a i n l e s s s t e e l r o d such t h a t i t was s e l f a l i g n i n g boat c o v e r .  ( i n the p l a n e o f F i g u r e 69(b)) w i t h t h e s l o t i n the  The thermocouple was 38 gauge chromel-alumel w i r e and was  i n s u l a t e d by two h o l e 1/32 i n c h O.D. m u l l i t e t u b i n g .  To s t r e n g t h e n t h e  thermocouple probe the m u l l i t e was surrounded f o r a p p r o x i m a t e l y 90% o f its  length  drilling  (2 cm) by s t a i n l e s s s t e e l t u b i n g which had been produced by  out a 0.050 i n c h O.D. hypepdermic  n e e d l e on a j e w e l l e r s  lathe.  The temperature t r a v e r s e o f the c r o s s s e c t i o n was done w h i l e the average temperature g r a d i e n t a c r o s s the melt was A °C/cm. F i g u r e 70 shows the numbering r e s u l t s o f the t r a o v e r s e . was  on the 0.1 mv f u l l  employed not  system which w i l l be used t o d e s c r i b e the  During the t r a v e r s e t h e Honeywell  s c a l e span  this represents a f u l l  ( f o r the chromel-alumel  recorder thermocouple  s c a l e span o f l e s s than 2.5 ° C ) .  I t was  p o s s i b l e t o determine t h e a b s o l u t e temperature a t each p o i n t shown  on F i g u r e 70 s i n c e temperature v a r i a t i o n s a s s o c i a t e d w i t h c y c l i c f u r n a c e temperature c o n t r o l l i n g were p r e s e n t i n the m e l t .  The t e c h n i q u e  adopted was t o move t h e thermocouple bead t o a bottom p o s i t i o n and then move  (1,4, o r 7)  the bead up and down between t h i s bottom and the c o r r e s -  ponding top p o s i t i o n a t 2 second i n t e r v a l s .  A f t e r about 3 c y c l e s t h e  temperature d i f f e r e n c e between the upper and lower p o s i t i o n s d e c r e a s e d indicating  the probe was c a u s i n g some m i x i n g .  The temperature  157  F i g u r e 70.  The numbering systems f o r l o c a t i n g p o s i t i o n s on the temperature t r a v e r s e .  158 d i f f e r e n c e s s t a t e d below a r e the average v a l u e s a f t e r 3 c y c l e s between the top and bottom p o s i t i o n s .  The r e s u l t s o f the t r a v e r s e were:  (a) P o s i t i o n 3 i s c o l d e r than p o s i t i o n 1 by  0.25  approximately  °C.  (b) P o s i t i o n 6 i s c o l d e r than p o s i t i o n 4 by a p p r o x i m a t e l y  0.25  °C.  (c) P o s i t i o n 9 i s c o l d e r than p o s i t i o n 7 by  approximately  0.1 °C.  No d i f f e r e n c e s i n temperature were d e t e c t e d i n the h o r i z o n t a l  direction.  The r e s u l t s show t h a t the top of the melt i s s l i g h t l y c o o l e r than the  (9) bottom.  T h i s i s a d i r e c t c o n t r a d i c t i o n o f the f i n d i n g s o f Utech  The r e s u l t s Utech o b t a i n e d f o r the i n c r e a s e i n v e r t i c a l gradient  (hot l i q u i d  temperature  above c o l d ) w i t h i n c r e a s i n g h o r i z o n t a l  g r a d i e n t a r e shown i n F i g u r e 71.  the v e r t i c a l and h o r i z o n t a l temperature Utech demonstrated  t h a t the v e r t i c a l  Sequence of c o n v e c t i o n . w i t h a magnetic zero.  field  temperature  T h i s was  (longitudinal)  A c c o r d i n g to F i g u r e 71  g r a d i e n t s are n e a r l y e q u a l .  temperature  a r o s e as a d i r e c t  con-  accomplished by s u p p r e s s i n g c o n v e c t i o n  and o b s e r v i n g t h a t the v e r t i c a l g r a d i e n t went t o  I t must be p o i n t e d out t h a t the experiments  i n an open top boat w i t h a melt depth o f 0.94  of Utech were  conducted  cm whereas the e x p e r i -  ments p r e s e n t e d i n t h i s t h e s i s were c a r r i e d out i n c l o s e d top boat w i t h a melt depth o f 0.64 understandable.  cm.  A d i f f e r e n c e i n the n a t u r e of the flow i s  F i r s t , the melt whose depth i s 0.64  s t a b l e w i t h r e s p e c t to f l u i d  f l o w than a melt 0.94  cm would be more cm deep.  the c l o s e d top g r a p h i t e b o a t , a good thermal c o n d u c t o r , might the e s t a b l i s h m e n t o f a v e r t i c a l g r a d i e n t i n the m e l t .  Secondly, prevent  159  HORIZONTAL  GRAD.  (°C/CM)  F i g u r e 71. The r e l a t i o n between the h o r i z o n t a l and v e r t i c a l temperature g r a d i e n t s f o r an uncovered t i n melt of depth 0.94 cm ( a f t e r Utech).  C o l e , i n a l i t e r a t u r e review o f c o n v e c t i o n  , stated  t h a t r e c e n t i n v e s t i g a t i o n s i n a r e c t a n g u l a r c a v i t y bounded by p l a t e s i n d i c a t e that a weak u n i c e l l u l a r motion zero temperature  differences.  Furthermore,  vertical  i s g e n e r a t e d f o r a l l non-  the heat t r a n s p o r t e d by  this  flow i s n e g l i g i b l e , except f o r s m a l l c o n t r i b u t i o n s near the c o r n e r s o f the w a l l s .  The n u m e r i c a l a n a l y s i s o f thermal c o n v e c t i o n i n l i q u i d Stewart  showed t h a t l a r g e flow r a t e s may  by  be developed i n a melt  w h i l e the thermal p r o f i l e i s s t i l l u n a l t e r e d from the pure c o n d u c t i o n form. At  T h i s i s i n t o t a l agreement w i t h the r e s u l t s o f the p r e s e n t work.  a h o r i z o n t a l temperature  g r a d i e n t of 4 °C/cm F i g u r e 46 shows t h a t a  flow v e l o c i t y o f g r e a t e r than 0.3  cm/sec would be observed.  h o r i z o n t a l g r a d i e n t the temperature  At  t r a v e r s e has shown t h a t heat  p o r t i n the melt must be almost c o m p l e t e l y c o n d u c t i v e .  In f a c t ,  this transthe  v e r t i c a l g r a d i e n t measured here i s o p p o s i t e t o t h a t which would be expected, t h a t i s , the temperature v e r t i c a l g r a d i e n t ( l e s s than 0.3 above the hot l i q u i d .  t r a v e r s e has shown a v e r y s m a l l  °C/cm) i n which the c o l d l i q u i d i s  T h i s g r a d i e n t may  r e s u l t from the f a c t t h a t  the  bottom o f the g r a p h i t e boat i s i n c o n t a c t w i t h the Vycor tube whereas the top s u r f a c e o f the boat may w i t h i n the Vycor tube.  The  be c o o l e d by the c o n v e c t i v e a i r c u r r e n t s  t r a n s v e r s e flow observed i s the type of f l o w  one would expect i n a c e l l which i s heated from below and above, namely, a double c e l l top  c o o l e d from  flow p a t t e r n w i t h c o o l e r l i q u i d  from  moving down the c e l l w a l l s , b e i n g heated at the bottom and  rising  i n the middle o f the c e l l .  the  then  For the case o f the square aluminum  c h a n n e l supported by the g r a p h i t e ends i t would be expected  t h a t the most  e x t e n s i v e f l o w would occur i n the v i c i n i t y o f the g r a p h i t e ends.  This  i s e s p e c i a l l y apparent i n the a u t o r a d i o g r a p h s shown i n rows one and  five  o f F i g u r e 58. but  I t i s a l s o observable  to a l e s s e r degree, p r o b a b l y  due  i n rows two  and  s i x of Figure  to the f a c t t h a t t h i s specimen  quenched 2 minutes a f t e r i n t r o d u c t i o n (specimen i n rows one, f i v e was  quenched at 1 minute) and  more d i l u t e .  The  and  t h e r e f o r e the t r a c e r becomes much  o b s e r v a t i o n t h a t t r a n s v e r s e flow i n the v i c i n i t y  c o l d r e s e r v o i r must r e f l e c t  was  three  the hot r e s e r v o i r i s more e x t e n s i v e than the t r a n s v e r s e flow near the f a c t  t h a t the adverse  i n the hot r e s e r v o i r i s g r e a t e r than t h a t p r e s e n t  3.5.  58,  vertical  i n the c o l d  of the  gradient reservoir.  I n t e r a c t i o n of U n i c e l l a r Flow w i t h a Moving Solid Liquid Interface  Fluid  flow a c r o s s a s o l i d - l i q u i d  i n t e r f a c e at which s o l u t e  s e g r e g a t i o n i s t a k i n g p l a c e i s prime o f importance i n d e t e r m i n i n g s o l u t e d i s t r i b u t i o n that appears i n the r e s u l t a n t s o l i d . s o l i d i f i c a t i o n of an a l l o y , s o l u t e b u i l d - u p w i l l o c c u r at the i n t e r f a c e and supercooling.  Q  t h i s i n t u r n can l e a d to  F o l l o w i n g the onset  morphology of the i n t e r f a c e w i l l then p o s s i b l y t o d e n d r i t i c  (assuming k  the  During i s l e s s than  constitutional  of c o n s t i t u t i o n a l supercooling  change from p l a n a r to c e l l u l a r  ( p r o v i d e d the growth r a t e and  g r a d i e n t a r e f a v o u r a b l e f o r such a t r a n s i t i o n ) .  1)  the  and  temperature  A general  observation  i n experiments used to determine the growth c r i t e r i a f o r the p l a n a r  to  c e l l u l a r t r a n s i t i o n i s t h a t breakdown o c c u r s f i r s t at the  melt-container  interface.  73.  Examples of t h i s a r e shown i n F i g u r e s 72 and  f i g u r e s are from u n p u b l i s h e d autoradiograph 1/4  work by F. Weinberg.  of a transverse  i n c h square r o d .  The  Both  F i g u r e 72 i s an  (to the growth d i r e c t i o n ) s e c t i o n of a  rod was  a m e l t o f pure t i n c o n t a i n i n g 500  produced by d i r e c t i o n a l l y ppm  of TI  204  .  The  solidifying  autoradiographs  of  F i g u r e 72.  T r a n s v e r s e s e c t i o n a u t o r a d i o g r a p y of a solidified  t i n melt c o n t a i n i n g 500 ppm  directionally TI  (X20).  163  F i g u r e 73.  T r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s of a solidified  t i n melt  containing  100 pom  directionally 204 TI (X6) .  164  F i g u r e 73 a r e from 3 d i f f e r e n t t r a n s v e r s e s e c t i o n s o f a d i r e c t i o n a l l y 204 s o l i d i f i e d pure t i n p l u s 100 ppm T I  melt.  The c r o s s - s e c t i o n a l  dimensions o f t h i s r o d a r e 1/2 i n c h wide by 1/4 i n c h h i g h . r a t e i n b o t h cases was approximately  2 x 10  The growth  cm/sec and t h e temperature  g r a d i e n t i n the melt was o f the o r d e r o f 0.5 °C/cm. The most w i d e l y  accepted  mechanism f o r p r e f e r e n t i a l break-  down o f the p l a n a r i n t e r f a c e near the c o n t a i n e r w a l l s invokes of an e n l a r g e d  s o l u t e r i c h boundary l a y e r ( 6 - l a y e r ) i n t h i s  the concept region.  s That i s , thermal c o n v e c t i o n  i s reasonably  e f f e c t i v e i n removing r e -  2 OA jected solute  (in this  case T I  ) from the c e n t r a l r e g i o n o f the s o l i d -  l i q u i d i n t e r f a c e , b u t i s much l e s s e f f e c t i v e i n removing r e j e c t e d s o l u t e t h i s i s t h a t l i q u i d s m e t a l s w i t h t h e i r low P r a n d t l numbers ( t y p i c a l l y o f from r e g i o n s where the i n t e r f a c e and c o n t a i n e r meet. The reason f o r _2 the o r d e r o f 10 ) tend to m a i n t a i n c i r c u l a r flow paths r a t h ear r tl than conform to the shape o f the c o n t a i n e r i n which they Therefore,  the extent  are f l o w i n g  (17)  of c o n v e c t i v e m i x i n g i n the i n t e r f a c e - c o n t a i n e r  r e g i o n w i l l be s m a l l i n comparison to the m i x i n g which occurs c e n t r a l region of the i n t e r f a c e .  T h i s w i l l r e s u l t i n the b u i l d - u p o f  a much l a r g e r s o l u t e r i c h l a y e r ahead o f the p e r i p h e r y The  net r e s u l t  supercooling  a t the  of the i n t e r f a c e .  i s that conditions s u i t a b l e f o r c o n s t i t u t i o n a l  and thus p l a n a r t o c e l l u l a r breakdown w i l l occur  first in  r e g i o n s where the i n t e r f a c e and c o n t a i n e r meet.  The main o b j e c t i o n to t h i s mechanism i s that the s i z e o f the 6 - l a y e r r e q u i r e d to produce as pronounced an e f f e c t as i s shown i n Figures systems.  72 and 73 i s much l a r g e r than i s n o r m a l l y  observed i n l i q u i d m e t a l  (& ~ l a y e r s i z e s a r e g e n e r a l l y c o n s i d e r e d s  to range from a low  lOu f o r complete mixing  t o lOOOu when no mixing  i s present  ).  The  type o f c o n v e c t i v e flow d e s c r i b e d i n t h e p r e v i o u s s e c t i o n s , t h a t i s , u n i c e l l u l a r l o n g i t u d i n a l flow w i t h a superimposed t r a n s v e r s e double cell to  flow would c e r t a i n l y encourage the onset o f i n t e r f a c e breakdown  occur near  the i n t e r f a c e c o n t a i n e r j u n c t i o n .  The t r a n s v e r s e flow  would tend t o d i s t r i b u t e s o l u t e , which had been p i c k e d up by the u n i c e l l u l a r l o n g i t u d i n a l f l o w , around the o u t s i d e edges o f the m e l t . Although  the t r a n s v e r s e double  c e n t r a l r e g i o n o f the m e l t ,  cell  flow would b r i n g s o l u t e i n t o  t h i s s o l u t e would not be seen by the i n t e r -  f a c e s i n c e the l o n g i t u d i n a l f l o w i s c o n s t a n t l y sweeping the c e n t r a l r e g i o n o f the i n t e r f a c e .  The r e s u l t i s t h a t t h e i n t e r f a c e would be  growing i n t o a melt which had g r e a t e r p o r t i o n o f t h e r e j e c t e d s o l u t e d i s t r i b u t e d around the o u t e r edges, t h a t i s , a d j a c e n t t o t h e melt tainer walls. down o f the  As b e f o r e , t h e n e t r e s u l t would be p r e f e r e n t i a l  con-  break-  planar interface i n this region.  The  c l a s s i c a l mechanism r e q u i r e s the e s t a b l i s h m e n t o f an  u n r e a l i s t i c a l l y l a r g e s o l u t e l a y e r a t the c o n t a i n e r w a l l s .  The f a c t  that t h e 5 - l a y e r around the p e r i p h e r y i s l a r g e r than t h a t which at  the c e n t r a l p o r t i o n o f the i n t e r f a c e cannot be denied.  exists  I t would  appear t h a t the most a c c e p t a b l e mechanism f o r the p r e f e r e n t i a l onset o f the p l a n a r t o c e l l u l a r t r a n s i t i o n near a combination  3.6.  the melt  c o n t a i n e r w a l l s must be  o f the c l a s s i c a l mechanism and the mechanism j u s t  proposed.  Summary The  flow which o c c u r s i n the h o r i z o n t a l melt  system s t u d i e d  here i s an u n i c e l l u l a r l o n g i t u d i n a l flow i n which the l i q u i d moves from the hot end to the c o l d end along the top o f the melt  and r e t u r n s from  the c o l d end to the h o t end along been suggested  the bottom.  T h i s mode o f flow has  b u t n o t observed by C a r r u t h e r s .  However, C a r r u t h e r s  made no mention o f the p o s s i b i l i t y o f t r a n s v e r s e flow. movement o f f l u i d observed  from the top t o t h e bottom o f the c e l l has been h e r e i n  t o occur by a double  on the l o n g i t u d i n a l motion. is  an adverse  cell  t r a n s v e r s e flow which i s superimposed  The d r i v i n g  f o r c e f o r the t r a n s v e r s e flow  v e r t i c a l temperature g r a d i e n t  The  Additional  driving  ( c o l d l i q u i d above h o t ) .  f o r c e f o r the l o n g i t u d i n a l u n i c e l l u l a r flow i s  the imposed h o r i z o n t a l temperature g r a d i e n t . flow i s n e g l i g i b l e .  Although  t h e heat  The heat  t r a n s f e r r e d by the flow i s  n e g l i g i b l e , the flow v e l o c i t i e s and the r e s u l t i n g be c o n s i d e r e d important  t r a n s f e r r e d by t h i s  i n the s o l i d i f i c a t i o n  convective mixing  process.  must  167  4 - ANALYSIS OF RESULTS  4.1.  Introduction  I n o r d e r t o a n a l y s e the f l o w v e l o c i t y r e s u l t s o b t a i n e d ing t h i s i n v e s t i g a t i o n i t i s f i r s t necessary c a l n a t u r e of the v e l o c i t y measured. g i v e s r i s e t o the observed v e r s e double  to determine  dur-  the exact p h y s i -  In p a r t i c u l a r , i s the flow which  v e l o c i t y simply a s u p e r p o s i t i o n of a t r a n s -  c e l l flow on a l o n g i t u n d i n a l u n i c e l l u l a r f l o w o r c o u l d i t  be more a c c u r a t e l y d e f i n e d as a double  s p i r a l flow of the type  observed  (19) during forced  c o n v e c t i o n through  The broken l i n e s i n F i g u r e 74(a)  a c y l i n d r i c a l tube show the path  a p a r t i c l e as i t moved along w i t h the s p i r a l  , Figure  t h a t would be  flow.  74.  f o l l o w e d by  I f t r a c e r was  injected  i n t o t h i s system, the r o t a t i o n a l flow would cause t r a n s v e r s e s e c t i o n radiographs  t o have the appearance of F i g u r e 7 4 ( b ) .  S i n c e the a u t o r a d i o -  graphs a p p e a r i n g i n F i g u r e s 56-64 do n o t , f o r the most p a r t , d i s p l a y outlined of s p i r a l herein.  t r a n s v e r s e double  cell  f l o w , i t may  be  auto-  concluded  t h a t the  fully  concept  flow does not a c c u r a t e l y d e s c r i b e the flow system i n v e s t i g a t e d I t i s p o s s i b l e , however, t h a t the f l o w c o u l d be d e s c r i b e d as a  slow s p i r a l flow  ( r a t h e r than a s t r i c t l y  t r a n s v e r s e flow) superimposed  the more dominant u n i c e l l u l a r l o n g i t u d i n a l motion. c o n t r i b u t i o n to the observed The  velocity  In any  on  case, the major  comes from the l o n g i t u d i n a l  flow.  l o n g i t u d i n a l flow v e l o c i t y c l o s e to the top and bottom o f  the e n c l o s e d melt must be much g r e a t e r than the v e l o c i t i e s  i n the  cen-  168  F i g u r e 74,  ( ) Schematic r e p r e s e n t a t i o n of the double s p i r a l flow observed d u r i n g f o r c e d c o n v e c t i o n through a tube .(b) Expected appearance of t r a n s verse s e c t i o n a u t o r a d i o g r a p h s i f double s p i r a l flow were p r e s e n t . a  t r a l region.  T h i s c o n c l u s i o n r e s u l t s from a c o n s i d e r a t i o n o f the t r a c e r  i n t r o d u c t i o n technique employed.  Essentially,  tracer introduction i n -  v o l v e s p l a c i n g a 0.64 cm cube o f t r a c e a l l o y i n the covered  channel.  the l o n g i t u d i n a l v e l o c i t y d i d not v a r y s i g n i f i c a n t l y with v e r t i c a l t i o n i n the melt one would not expect autoradiographs)  t o observe  If  posi-  (as i s shown by the  the t r a c e r t o be c o n c e n t r a t e d i n the top and bottom  l a y e r s o f the melt.  The observed  predominance o f flow c l o s e t o the top and  bottom s u r f a c e s o f the melt suggests  t h a t i t may be a p p r o p r i a t e to apply  boundary l a y e r theory to a n a l y s e the flow v e l o c i t y r e s u l t s o b t a i n e d i n S e c t i o n 2.  . The  temperature  •  r a t i o of the buoyancy f o r c e s generated  as a r e s u l t o f  d i f f e r e n c e s i n the f l u i d to the v i s c o u s f o r c e i n the f l u i d , i s  g i v e n q u a l i t a t i v e l y by the d i m e n s i o n l e s s Grashof e n c l o s u r e w i t h heated  number.  For a rectangular  and c o o l e d v e r t i c a l w a l l s the Grashof  number i s  g e n e r a l l y w r i t t e n as: G  r  =  ^  (4.1)  v where:  Gr  i s the Grashof  number  g  i s the a c c e l e r a t i o n of g r a v i t y  8  i s the c o e f f i c i e n t o f volume  AT  i s the temperature  L  i s the d i s t a n c e between the hot and c o l d w a l l s  v  i s the k i n e m a t i c  a  i s the thermal  expansion  d i f f e r e n c e between the h o t and c o l d w a l l s  viscosity  diffusivity  In o r d e r t h a t the buoyancy f o r c e be c o n s i s t e n t w i t h the r e s u l t s o f the p r e s e n t i n v e s t i g a t i o n , i t i s n e c e s s a r y  to r e d e f i n e the  170  Grashof number.  I t has  been e s t a b l i s h e d above t h a t the d r i v i n g  force  f o r the observed flow i s the average temperature g r a d i e n t between the and  c o l d ends o f the m e l t .  i s s l i g h t l y modified  I f the Grashof number as p r e s e n t l y  hot  defined  to a l l o w i n c o r p o r a t i o n of the average h o r i z o n t a l  temperature g r a d i e n t a c r o s s  the melt, G , i t becomes: i-j  G  "  r  — —  (4.2)  L  v .  Thus the buoyancy f o r c e , which i s the d r i v i n g f o r c e f o r the  observed  flow, would appear to be s t r o n g l y dependent on the melt l e n g t h f o r a g i v e n average g r a d i e n t .  T h i s g r o s s l y c o n t r a d i c t s the e x p e r i m e n t a l  s u l t s which c l e a r l y show ( f o r two lengths  ranging  from 27 to 48.8  of t o t a l melt l e n g t h , p r o v i d e d mains c o n s t a n t .  d i f f e r e n t boat designs  cm)  and  re-  4 melt  t h a t flow v e l o c i t y i s independent  the average g r a d i e n t a c r o s s  the melt re-  When the Grashof number i s f u r t h e r m o d i f i e d  to remove  the melt l e n g t h dependence i t becomes:  g3H Gr =  v where the melt h e i g h t H has now  has  the e x p e r i m e n t a l l y  on average g r a d i e n t and  4  G  j-±  (4.3)  r e p l a c e d the l e n g t h L.  T h i s Grashof number  determined p r o p e r t i e s of l i n e a r  i s independent of t o t a l melt  dependence  length.  T h i s m o d i f i c a t i o n i s s i m i l a r to t h a t employed by C o l e ^ ^ 2  d e s c r i b e the dependence of the c r i t i c a l h o r i z o n t a l temperature  to  gradient  c r e q u i r e d f o r the onset  of thermocouple o s c i l l a t i o n , G  C o l e r e d e f i n e d the R a y l e i g h  number (Grashof  , on the melt  x Prandtl) for a l i q u i d  height. heated  171  from below, namely:  g3H G _. . 1 Yertrcal 4  t  R  a  =  (  4  >  4  )  av  by assuming that H x G ( v e r t i c a l ) could be replaced by L x G (horizontal) The new Rayleigh number then became:  g3H LG 3  Ra =  (4.5) av  from which can be obtained the expression:  H  G  3  T  =  ^ SSL  (4.6)  Cole established experimentally that H  3  G  c  c = 3.1 (cgs units) where G i s Li  Lj  the c r i t i c a l h o r i z o n t a l gradient required for the onset of thermocouple fluctuations which i n turn were taken to be i n d i c a t i v e of the onset of turbulent convection. Rayleigh number Ra  Using this r e s u l t , an expression for the c r i t i c a l  necessary for the onset of turbulent convection was  obtained:  R  a  c  =  (3-D g3L  (  4  >  ?  )  av  Thus i t would appear that Ra did  i s a function of the melt length L.  not determine whether i n fact Ra  since Ra  varied with melt length.  Cole  However,  i s a dimensionless parameter of dynamic s i m i l a r i t y i t i s  reasonable to assume that i t should not vary with melt length.  Therefore,  since g i s a constant and a , 3 and v remain e s s e n t i a l l y constant, provided  the  average melt temperature does n o t v a r y g r e a t l y , the p r o d u c t H  must a l s o remain c o n s t a n t .  L G  For a melt o f h e i g h t H i t f o l l o w s t h a t  couple f l u c t u a t i o n s s h o u l d be observed once the a p p r o p r i a t e v a l u e c which makes Ra > Ra ) of the p r o d u c t G  L exceeds  a constant G  c  thermo(that  L.  (12) Hurle's of  4.0  of  G  r e s u l t s noted i n S e c t i o n 1.1. cm, G£ = 5.0  °C/cm and f o r L = 2.6  L f o r these two  showed t h a t f o r a melt cm, G^ = 7.5  experiments are 20°C and 19.5°C  Thus i t becomes apparent t h a t whereas flow v e l o c i t i e s the  °C/cm.  length  The v a l u e s  respectively. are dependent  on  average temperature g r a d i e n t ( i n d e p e n d e n t of melt l e n g t h ) a c r o s s the  m e l t , the onset o f t u r b u l e n t c o n v e c t i o n i s determined by a temperature d i f f e r e n c e  critical  ( a g a i n independent of melt l e n g t h ) between the hot  and c o l d ends of the m e l t . ( 8) The f i n d i n g that  r e s u l t s of M i i l l e r  flow v e l o c i t i e s  and Wiehelm  indirectly  s u p p o r t the  are independent of melt l e n g t h f o r a g i v e n  h o r i z o n t a l temperature g r a d i e n t .  They found t h a t f o r melts between 10  and 30 cm l o n g the observed temperature f l u c t u a t i o n s were independent of melt l e n g t h p r o v i d e d the temperature and temperature g r a d i e n t constant at the measuring p o i n t . temperature f l u c t u a t i o n s  remain  I f the amplitude and frequency of the  can be taken as b e i n g r e p r e s e n t a t i v e of the ex-  t e n t of c o n v e c t i v e flow and thus an i n d i r e c t measure of flow v e l o c i t i e s , then the r e s u l t s of M i i l l e r and Wiehelm are i n agreement w i t h those of the present i n v e s t i g a t i o n . driving  buoyancy  f o r c e , as r e p r e s e n t e d by a Grashof number, w i l l be g i v e n by  Equation  (4.3). In  liquid  T h e r e f o r e , f o r t h i s i n v e s t i g a t i o n the  S e c t i o n 2.2.3.4.3. i t was  shown t h a t v a r y i n g the h e i g h t o f  metal i n the open r e s e r v o i r s had n e g l i g i b l e e f f e c t on the flow  velocity. being  I t s h o u l d , t h e r e f q r e , be p o s s i b l e to c o n s i d e r the system as  covered  f o r the e n t i r e melt  In summary one  length.  obtains  the f o l l o w i n g p i c t u r e o f f l u i d  i n a covered h o r i z o n t a l rod of l i q u i d  (1) The  flow  metal:  flow which g i v e s r i s e to the observed  v e l o c i t y i s laminar  l o n g i t u d i n a l u n i c e l l u l a r flow c o n f i n e d t o the o u t e r t r e m e t i e s of the m e l t , F i g u r e 75.  The  ex-  t r a n s v e r s e flow  will  be n e g l e c t e d thus r e d u c i n g the mathematical a n a l y s i s to a d i m e n s i o n a l problem.  The  2-  assumption t h a t the t r a n s v e r s e  flow can be n e g l e c t e d i s based on a u t o r a d i o g r a p h y  experiments  which show t h a t the t r a n s v e r s e flow does not make a s i g n i ficant  c o n t r i b u t i o n t o the l o n g i t u d i n a l  (2) The buoyancy f o r c e s which generate be  the l o n g i t u d i n a l flow  r e p r e s e n t e d by a m o d i f i e d Grashof  g3H  4  G  flow.  number o f the  can  form:  T  Gr =  v . (3) The  covered h o r i z o n t a l rod w i t h the two  can be  c o n s i d e r e d to be  as shown i n F i g u r e  a totally  s m a l l open r e s e r v o i r s  e n c l o s e d r e c t a n g u l a r system  75.  S u c c e s s f u l mathematical a n a l y s i s o f the s i m p l i f i e d mensional  two d i -  problem must p r e d i c t : (1) A l i n e a r r e l a t i o n s h i p between flow v e l o c i t y temperature g r a d i e n t a c r o s s the  melt.  and  average  Figure  75.  The  simplified  flow system i n the long shallow  retangular  enclosure  175  (2) A l a c k of v e l o c i t y dependence on t o t a l l e n g t h . (3) A dependence of flow v e l o c i t y on average m e l t  4.2.  Previous Investigations Hydrodynamic a n a l y s i s of n a t u r a l thermal  l i q u i d metals has  temperature.  having  received l i t t l e  c o n v e c t i v e flow i n  the h o r i z o n t a l rod c o n f i g u r a t i o n i n v e s t i g a t e d h e r e a t t e n t i o n i n the l i t e r a t u r e .  e x i s t i n g s o l u t i o n s have been p r i m a r i l y concerned  The v a s t m a j o r i t y of w i t h the heat t r a n s f e r r e d  v i a c o n v e c t i o n , r a t h e r than the magnitude of the flow v e l o c i t i e s . though heat  t r a n s f e r i s a i n t e g r a l p a r t of the s o l i d i f i c a t i o n  the purpose of the p r e s e n t i n v e s t i g a t i o n was  to study  Al-  process,  flow p a t t e r n s  and  flow v e l o c i t i e s .  Attempts t h a t have been made to a n a l y s e f l u i d metal  c o n t a i n e d i n a h o r i z o n t a l boat  (5 9) ' and  flow i n a  thus p r e d i c t flow  liquid  velocities  have s u f f e r e d from a l a c k of a c c u r a t e r e p r o d u c i b l e r e s u l t s w i t h which to (9) c o n f i r m or d i s p u t e the mathematical s o l u t i o n . and  Cole^  viewed and  which were o u t l i n e d b r i e f l y discussed with  investigation.  The  a n a l y s e s of Utech  i n S e c t i o n 1.1.  w i l l now  r e s p e c t to the r e s u l t s o b t a i n e d i n the  be r e present  4.2.1.  (9)  S o l u t i o n o f Utech^ ' The  D r a k e f o r  s o l u t i o n used by Utech was developed by E c k e r t and  l a m i n a r flow a l o n g a v e r t i c a l p l a t e a t a temperature  T w  immersed i n a f l u i d  T .  a t temperature  The momentum e q u a t i o n f o r the  q  boundary l a y e r a d j a c e n t t o the w a l l i s :  f  6  d dxj  The heat  *  dy  = gS  J  0dy -  v  ( ^u )  ( 4 w  a  i  i  '  8 )  flow e q u a t i o n i s :  4" ax  where:  2 U  y  )  uGdy = - a (  dy  ) wall i n  x  i s the d i s t a n c e a l o n g t h e w a l l  y  i s the d i s t a n c e p e r p e n d i c u l a r t o the w a l l  6  i s the boundary l a y e r t h i c k n e s s  u  i s the v e l o c i t y i n t h e x  •3  T  (4.9)  direction  = T - T o i s the temperature  at some y p o s i t i o n i n s i d e the boundary  layer  (21) *  Merks  . has shown t h a t the thermal  and hydrodynamic boundary  are e q u a l f o r f r e e c o n v e c t i o n i n l i q u i d s m e t a l s , hydro  so t h a t ^  t  n  e  r  layers m  a  ^  =  By assuming a temperature d i s t r i b u t i o n i n the boundary  layer of:  - w - V <!-i>  s  w  (4  . ) 10  and a v e l o c i t y p r o f i l e o f the form:  =  u  where u^ i s an a r b i t r a r y Equations  u  i1 J 6  ^  "  v  A6 >  (4.1D  2  f u n c t i o n w i t h the dimension of v e l o c i t y ,  (4.8)and (4.9) assume the form:  ±-  ^  105  dx  3o  (T  w  (u 6) = i g B ( T - T ) 6 - v i 2  o  w  3  " o T  k  )  (  u  i  5  =  )  2 a  (  ~^T~  £ )  Solving  these e q u a t i o n s s i m u l t a n e o u s l y employing the  u^ =  x  and 6 =  x  substitutions  gives:  ^iJ^lIsf^ ^ 2  u  r  -  5,17V  (0.952  Pr)-  +  1 / 2  From E q u a t i o n (4.11) i t can be seen t h a t boundary  l a y e r , u^, i s 0.148  u^.  (4.12)  the maximum v e l o c i t y i n the  I n t r o d u c i n g t h i s i n t o E q u a t i o n (4.12)  gives: u  m  = 0.766v  (0.952 + P r ) ~  1 / 2  (  g  B  (T  W  ^ v  " V)  ^  x  1 / 2  . (.4.13)  178  For molten t i n a t an average melt temperature o f 400 °C i n t r o d u c t i o n o f the a p p r o p r i a t e f l u i d parameters  (Table 6) y i e l d s the f o l l o w i n g e x p r e s s i o n  f o r the maximum flow v e l o c i t y i n the boundary l a y e r :  <V400 - ° '  The  2 5  (T  W  "  V  *  1 / 2  1/2  ( 4  '  1 4 )  average v e l o c i t y a l o n g a w a l l o f h e i g h t H would be:  <V400 = ° -  < W-V T  2 5  lJ  1 / 2  dx Hx l / 2  (4.15) = 0.166 ( T - T ) W o  1  /  2  TT  H  1 / 2  The  melt h e i g h t  The  temperature d i f f e r e n c e which c r e a t e d the bouyancy f o r c e s i n the melt  i s obtained  f o r t h e system s t u d i e d i n S e c t i o n s 2 and 3 was 0.64 cm.  from E q u a t i o n  (4.3) and i s H G .  Thus the average maximum  J-i  v e l o c i t y r e s u l t i n g from a h o r i z o n t a l temperature g r a d i e n t between t h e v e r t i c a l w a l l s a t the ends o f the melt would be:  <»m>400 - ' 0  1  0  6 G  L  1  /  2  ( 4  '  1 6 )  In F i g u r e 76, the l i n e from F i g u r e 46 i s p l o t t e d along the m o d i f i e d E c k e r t and Drake s o l u t i o n g i v e n i n E q u a t i o n though the c a l c u l a t e d v e l o c i t i e s the e x p e r i m e n t a l l y  with  (4.16). A l -  a r e o f t h e same o r d e r o f magnitude as  determined v a l u e s , the l i n e a r dependence o f flow  v e l o c i t y on temperature g r a d i e n t i s n o t s a t i s f i e d by t h i s  solution.  Furthermore, when the v a l u e o f (u )„__ i s c a l c u l a t e d , the p r e d i c t e d r a t i o m 300 ^m^ 300^ m^400 * U  i s 0.78.  u  S  whereas e x p e r i m e n t a l l y , F i g u r e 43, t h i s  ratio  09  I  1  1—  1  AVERAGE F i g u r e 76.  1  1—  TEMR  s  GRAD.  —  i  —  r  —  (°C/CM)  Comparison of the r e s u l t s of the present i n v e s t i g a t i o n w i t h the p r e d i c t i o n of the s o l u t i o n of Utech.  r  180  4.2.2.  Solution of C o l e ^ The  s o l u t i o n used by Cole t o c a l c u l a t e  was the E c k e t t  and Drake a n a l y s i s m o d i f i e d t o i n c l u d e t h e l a t e n t heat o f s o l i d i f i c a t i o n X and t h e growth r a t e R i n t h e heat v e l o c i t y and temperature  flow E q u a t i o n  (4.9).  Assuming the  d i s t r i b u t i o n s were those g i v e n by E q u a t i o n s  (4.10) and (4.11) (except C o l e made u^ = u ) , t h e d i f f e r e n t i a l m  equations  which have t o be s o l v e d s i m u l t a n e o u s l y a r e then:  1 — 105  , 2 1 „ . „ - - ( u 5) - 3 g 3 ( T - T ) 6 dx  'd  m  w  T - T W o — — 40 Employing  / m  T d ,: , W — (u 5) = a ( dx x  S  the s u b s t i t u t i o n s  fi  =  o  U  v  m  -  - T o \ ,R/X • _ ) + -j < —  x  1 7 2  (  4  a  ?  )  o  . " <w  "  T  p  T  o »  (4-18)  , 6 = A.^ x " ^ C o l e o b t a i n e d a 4  r e l a t i o n f o r u , which f o r the case o f R = 0 (no s o l i d p r e s e n t or a m' (22) s t a t i o n a r y s o l i d - l i q u i d i n t e r f a c e ) becomes : r  u  =  4  .2  (  _  M  ) ! / (RAT) 2  1 7 2  (4.19)  .63 + Pr  m  I f the a p p r o p r i a t e f l u i d parameters from T a b l e 6 a r e i n s e r t e d , and as bef o r e AT i s taken t o be H G  , then E q u a t i o n  (4.19) becomes:  •Li  (  % 400 = °' }  7 1 5  ^L  (4.20)  The C o l e a n a l y s i s has the same p a r a b o l i c dependence o f u  on  temperature g r a d i e n t G^ as the E c k e r t and Drake r e l a t i o n of E q u a t i o n but the c a l c u l a t e d v a l u e o f  from E q u a t i o n  (4.16)  (4.20) i s a p p r o x i m a t e l y  an o r d e r o f magnitude l a r g e r than t h a t c a l c u l a t e d  from E q u a t i o n  (4.16).  S i n c e Cole's s o l u t i o n i s e s s e n t i a l l y the E c k e r t and Drake s o l u t i o n w i t h the a d d i t i o n of terms a c c o u n t i n g f o r the l a t e n t heat of s o l i d i f i c a t i o n and the growth r a t e R, E q u a t i o n  (4.2.0) should be i d e n t i c a l t o E q u a t i o n  (4.16) when no s o l i d i f i c a t i o n or m e l t i n g (R = 0) i s o c c u r r i n g . a t i o n of C o l e ' s a n a l y s i s r e v e a l s the f o l l o w i n g e r r o r . velocity profile  C o l e assumed the  was:  u = u  £ mo  (1 - £ ) o  (4.21)  2  and e v e n t u a l l y o b t a i n e d a s o l u t i o n f o r u^, the maximum v e l o c i t y to the i n t e r f a c e .  By d i f f e r e n t i a t i n g E q u a t i o n  (4.21) and  u  m  = 0.148  u  This value  m  C l e a r l y then, C o l e ' s c a l c u l a t e d v a l u e s o f When t h i s  parallel  setting  du/dy = 0, one can o b t a i n the v a l u e o f y f o r which u = u . m i s 1/36 and s u b s t i t u t i n g t h i s i n t o E q u a t i o n (4.21) y i e l d s :  f a c t o r of 6.85.  Examin-  x j i l l be too l a r g e by a  c o r r e c t i o n i s a p p l i e d to Equation  (4.20) the  result i s :  (  V400 =  °- V 106  /2  which agrees w i t h the E c k e r t and Drake r e l a t i o n .  In view o f the l a c k o f agreement between the E c k e r t and Drake type of s o l u t i o n and the r e s u l t s o b t a i n e d d u r i n g t h i s i t becomes n e c e s s a r y  investigation,  to examine more c a r e f u l l y the assumptions i n v o l v e d i n  182  deriving  the v e l o c i t y r e l a t i o n s h i p p r e d i c t e d  of the major assumptions o f t h i s a n a l y s i s boundary l a y e r  by E q u a t i o n  i s that  fully  flow e x i s t s a l o n g the v e r t i c a l w a l l .  can be n e g l e c t e d and t h e i n t e g r a t e d  One  developed  Thus, corner  boundary l a y e r E q u a t i o n s ( 4 . 8 )  r e s u l t s as a s i m p l i f i c a t i o n o f t h e g o v e r n i n g e q u a t i o n s vection,  (4.16).  o f thermal  effects and (4.9) con-  namely:  Momentum e q u a t i o n i n the x - d i r e c t i o n  |H + d t  u  |H + - | u = _ 3x dy • v  G  3  A  , I |£l +  T  p  v  (  v  2  u  )  (  O X  4  >  2  2  )  v  Momentum e q u a t i o n i n t h e y - d i r e c t i o n  3v 3t  Energy  3v • 3v 1 u — + v — = - — 3x 3y p  V_ , ,„2 Tf— + v (V v) 3y  (4.23)  equation  Continuity  equation  -^ + ^ = 0 3x 3y where:  (4.25)  x  i s the d i s t a n c e i n the v e r t i c a l  direction  u  i s the v e l o c i t y i n the v e r t i c a l  direction  y  i s the d i s t a n c e i n t h e h o r i z o n t a l  direction  v  i s the v e l o c i t y i n the h o r i z o n t a l  direction  p'  i s the pressure d e v i a t i o n  from t h e i n i t i a l  static  pressure.  183  The  assumptions used i n o b t a i n i n g t h e above equations are:  (1) A l l f l u i d p r o p e r t i e s , w i t h the e x c e p t i o n o f t h e d e n s i t y changes which g i v e r i s e t o the buoyancy f o r c e s , a r e cons t a n t f o r a g i v e n average melt  temperature.  (2) The temperature d i f f e r e n c e a c r o s s the melt  i s s m a l l compared  w i t h 1/3. (3) The v i s c o u s d i s s i p a t i o n i s n e g l e c t e d . (4) C o m p r e s s i b i l i t y e f f e c t s a r e n e g l e c t e d .  P u r e l y a n a l y t i c a l attempts t o s o l v e t h e flow and heat t r a n s fer  c h a r a c t e r i s t i c s o f c o n v e c t i o n a r e s e v e r e l y . handicapped by the com-  p l e x i t y o f the governing  The  equations.  i n t e g r a l boundary l a y e r s o l u t i o n j u s t d i s c u s s e d i s l i m i t e d  by a minimum h e i g h t t o l e n g t h r a t i o o f the c e l l . the r e s u l t s o f the p r e s e n t concluded  i n v e s t i g a t i o n a r e not i n agreement i t must be  t h a t the h e i g h t t o l e n g t h r a t i o s employed h e r e i n were o u t s i d e  the range o f a p p l i c a b i l i t y  o f the i n t e g r a l boundary l a y e r  Approximate s o l u t i o n s o f the governing (23) developed  S i n c e t h i s s o l u t i o n and  by B a t c h e l o r  solution.  e q u a t i o n s have been  (24) and Poots  s i o n a l forms o f the governing  equations.  .  Both s o l u t i o n s use non-dimenThese non-dimensional  o b t a i n e d by u s i n g the f o l l o w i n g d i m e n s i o n l e s s  parameters:  forms a r e  184  X  u  =  =  Y = * L  -  L'  ii  H  L  0  and T  where  v  9 ¥  L  T - T ioi T, - T 1 o  =  = _ i*  8Y  jr_  =  _  ( 4 . 2 6 )  8X  „ 2 „  a r e the temperature o f the v e r t i c a l w a l l s , Y i s d e f i n e d  q  as the d i m e n s i o n l e s s stream f u n c t i o n and z; i s d e f i n e d as the d i m e n s i o n less v o r t i c i t y .  S u b s t i t u t i n g the r e l a t i o n s h i p s i n  ( 4 . 2 2 )  to  ( 4 . 2 2 )  w i t h r e s p e c t to Y and  ( 4 . 2 5 )  1 _  Pr  and e l i m i n a t i n g the p r e s s u r e terms by  c  IS. ^ 3X 3Y  !§.  II  Ra  BY  i®.  with respect to  ( 4 . 2 3 )  5V 8g ax  9X 3Y ~ 8Y  W  +  v  X  i n t o Equations  differentiating results i n :  2  ( 4 . 2 7 )  C  v0  ( 4 . 2 8 )  2  =  SX  In o b t a i n i n g E q u a t i o n s vatives  ( 4 . 2 6 )  ( 4 . 2 7 )  and  ( 4 . 2 8 )  all  the time d e r i -  (3/3t) have been equated to z e r o s i n c e only the steady s t a t e  t i o n i s of i n t e r e s t .  The boundary c o n d i t i o n s i n d i m e n s i o n l e s s  0 = Y  solu-  form a r e :  (4.29) Y = 1  4.2.3.  <j/ =  Solution  |X = Q  0 = 1  of Batchelor  B a t c h e l o r developed s e r i e s s o l u t i o n f o r 0 and ¥ by expanding them i n power s e r i e s o f the R a y l e i g h number, namely:  (4.30)  (4.31)  These s e r i e s can be s u b s t i t u t e d  i n t o Equations  (4.27) and (4,28) and upon  e q u a t i n g c o e f f i c i e n t s of l i k e powers of the R a y l e i g h number e q u a t i o n s describing  0^, 0^,  ^  and ^  c  a  n  be o b t a i n e d .  For values of Rayleigh  3 l e s s than 10  and f o r H/L  r a t i o s close  to u n i t y  the v a l u e o f 4^ can be  approximated by:  (4.32)  Thus, under these c o n d i t i o n s , suffiently  and assuming t h a t  series  (4.31) converges  r a p i d l y , the s o l u t i o n f o r the stream f u n c t i o n  can be  written  as: .¥ = RaH' (X,Y) 1  (4.33)  186  The  flow v e l o c i t i e s  can be o b t a i n e d d i r e c t l y  from E q u a t i o n  the use o f the v e l o c i t y r e l a t i o n s h i p s i n E q u a t i o n  (4.33) w i t h  (4.26).  B e f o r e c o n t i n u i n g w i t h the development of the B a t c h e l o r (24) s o l u t i o n , i t i s convenient and Stewart  4.2.4.  to b r i e f l y d i s c u s s the s o l u t i o n s of Poots  .  S o l u t i o n of Poots Employing  (24)  the d i m e n s i o n l e s s  g o v e r n i n g e q u a t i o n s , Poots by expanding  forms of the  two-dimensional  o b t a i n e d approximate s o l u t i o n s  them as s e r i e s o f o r t h o g o n a l p o l y n o m i a l s .  f o r 0 and ¥  The g e n e r a l con-  c l u s i o n s o f t h i s i n v e s t i g a t i o n were t h a t : (1) The  s o l u t i o n of Poots was  i n agreement w i t h the B a t c h e l o r  3 s o l u t i o n up to R a y l e i g h equals 10 . (2) The  labour involved i n obtaining Poots' solutions for 4  R a y l e i g h g r e a t e r than 10  and H/L  g r e a t e r than 4 was  p r o h i b i t i v e by the slow convergence of the s e r i e s  4.2.5.  S o l u t i o n of Stewart,  made  solutions.  Stewart employing  a r a d i o a c t i v e t r a c e r t e c h n i q u e , measured  flow v e l o c i t i e s a s s o c i a t e d w i t h n a t u r a l c o n v e c t i o n of l i q u i d metal t a i n e d i n a c e l l w i t h a h e i g h t to l e n g t h r a t i o of u n i t y . v e s t i g a t i o n the R a y l e i g h number ranged  from 10  1  t o 10^.  During  con-  this i n -  These v a l u e s o f  R a y l e i g h are w e l l o u t s i d e the range i n which the s o l u t i o n s of B a t c h e l o r and Poots may Stewart  be a p p l i e d .  developed  In order to a n a l y s e h i s e x p e r i m e n t a l  a f i n i t e d i f f e r e n c e s o l u t i o n of the g o v e r n i n g  results, equations.  The s o l u t i o n was based  on the work o f Wilkes  (25)  and Samuels and  (26) Churchill  .  I t was n e c e s s a r y t o modify  these s o l u t i o n s s i n c e t h e  Wilkes a n a l y s i s became u n s t a b l e a t l a r g e v a l u e s o f R a y l e i g h , and the r e s u l t s o f Samuels and C h u r c h i l l d i d n o t apply as t h e i r s o l u t i o n was f o r a system w i t h a v e r t i c a l l y a p p l i e d temperature  g r a d i e n t whereas  Stewart  worked w i t h a h o r i z o n t a l d i f f e r e n c e i n temperature. The  f i n i t e d i f f e r e n c e n u m e r i c a l t e c h n i q u e used by Stewart  f o r the s o l u t i o n o f a d i m e n s i o n l e s s form o f the g o v e r n i n g e q u a t i o n s (slightly  different  form than t h a t used by B a t c h e l o r ) was the i m p l i c i t  a l t e r n a t i n g d i r e c t i o n technique.  Stewart  found t h a t t h e s o l u t i o n ob-  t a i n e d f o r the flow v e l o c i t y was i n e x c e l l e n t agreement w i t h t h e s o l u t i o n o f B a t c h e l o r up t o Grashof equals 10  5  3 ( R a y l e i g h a p p r o x i m a t e l y 10 ) .  For Grashof g r e a t e r than 10^ Stewarts s o l u t i o n d e v i a t e d from the B a t c h e l o r s o l u t i o n and then approached  the E c k e r t and Drake boundary l a y e r  solution  9 f o r v a l u e s o f Grashof o f the o r d e r o f 10 . D u r i n g the course o f the p r e s e n t i n v e s t i g a t i o n the v a l u e s of Grashof  ( f o r an average melt temperature  o f 400 ° C ) , as d e f i n e d by  E q u a t i o n 4.3, was:  (Gr)  4 Q 0  = 4800 G  (4.34)  L  and (Ra)  The maximum v a l u e o f G than 10 °C/cm. apparent  4 0 0  ^43.7G  (4.35)  L  f o r which v e l o c i t y measurements were made was l e s s  T h e r e f o r e , from E q u a t i o n s  (4.34) and (4.35) i t becomes  that the c o n d i t i o n s s t u d i e d d u r i n g t h i s  investigation f a l l  well  w i t h i n the range i n which t h e r e i s good agreement between the s o l u t i o n s of B a t c h e l o r , Poots and  Stewart.  S i n c e the s o l u t i o n of B a t c h e l o r i s by  f a r the s i m p l e s t of the t h r e e i t i s a p p r o p r i a t e to i n v e s t i g a t e i t f u r t h e r i n the hopes of f i n d i n g a s u i t a b l e a n a l y s i s f o r the e x p e r i m e n t a l s u l t of t h i s  4.3.  re-  investigation.  M o d i f i c a t i o n of the B a t c h e l o r S o l u t i o n I t w i l l be shown below t h a t the s o l u t i o n of B a t c h e l o r can  m o d i f i e d and  extended so as to adequately  investigation. the stream  this  As s t a t e d i n S e c t i o n 4.2.3. an approximate s o l u t i o n f o r  function i s given  ¥ - | R a  where  A(X)  Although  =  by:  A (X) Y  (1 +  (fA  (1-Y)  2  1  2 (  X ( ~ - X) 2  ^  3  (  >  )  2  the e x p e r i m e n t a l v a l u e s of R a y l e i g h l i e w i t h i n the  range f o r which t h i s approximation H/L  d e s c r i b e the r e s u l t s of  be  i s useful,  the e x p e r i m e n t a l v a l u e s  of  are much l e s s than u n i t y . However, B a t c h e l o r s t a t e s t h a t i t i s un-  likely  t h a t the convergence of the s e r i e s would v a r y a p p r e c i a b l y w i t h  the  (27) v a l u e of H/L.  Furthermore, C a r r u t h e r s  has  (4.36) i s v a l i d  f o r flows i n the neighbourhood of a v e r t i c a l  even f o r low v a l u e s of the aspect r a t i o n H/L. ing the e x p r e s s i o n f o r obtained:  suggested  that  Equation  interface  A c c o r d i n g l y , the f o l l o w -  the v e l o c i t y p a r a l l e l to the v e r t i c a l w a l l i s  U  =  a L  8¥  (4.26)  W  | ~  A  (  x  )  ( 4 Y  I f i t i s f u r t h e r assumed valid  3 _ 2 6 y  +  2  y  )  that Equation  (  4  3  ?  )  (4.36) i s a l s o  f o r flow p a r a l l e l t o the much l o n g e r h o r i z o n a l b o u n d a r i e s ,  then  the l o n g i t u d i n a l flow v e l o c i t y as d e f i n e d by;  i s g i v e n by the e x p r e s s i o n :  v = - £  |  Ra Y ( l - Y ) ( l + (|)) 2  2  Vx  4  3  - 6 ^  + 2 (f) 2  X)  (4.38) The R a y l e i g h number, as o b t a i n e d by n o n d i m e n s i o n l i z i n g  the g o v e r n i n g  equations, i s :  Ra= fiSlAl av  The aspect r a t i o s employed d u r i n g t h i s i n v e s t i g a t i o n were:  0.013 < - < 0.024 XJ  Therefore, reduces cribing  (H/L)  4  << 1 and the (1 + ( H / L ) ) 4  - 1  term i n E q u a t i o n  (4.38)  t o u n i t y where upon one o b t a i n s the f o l l o w i n g e x p r e s s i o n desthe dependence  o f l o n g i t u d i n a l flow v e l o c i t y on l i q u i d  metal  properties,  m e l t geometry, temperature g r a d i e n t between t h e h o t and  c o l d ends o f the m e l t and p o s i t i o n i n the m e l t :  v  =  2  SBL 3v  3  At  g  y  first  2  ( 1  _  Y )  2  ( 4 x  3 _  6  I  2 x  appearance, E q u a t i o n  pendence o f flow v e l o c i t y on m e l t l e n g t h group o f terms i n E q u a t i o n  +  2  A  X)  2  (4.39)  (4.39) p r e d i c t s L.  a s t r o n g de-  However, when the l a s t  (4.39) i s a l t e r e d such that  the v a r i a t i o n o f  flow v e l o c i t y w i t h v e r t i c a l p o s i t i o n i n the m e l t i s d e s c r i b e d by a new v a r i a b l e XL/H , the f o l l o w i n g  4X  3  - 6f X  Substitution  2  + 2  2 3 3 2 ) X = ( f ) ( 4 ( ^ ) - 6 (|^) + 2(f^)) (4.40)  o f the r i g h t hand s i d e o f E q u a t i o n  (4.39) y i e l d s the f o l l o w i n g  M j f - ^  The  Y (l-Y) 2  2  (4.40) i n t o E q u a t i o n  expression:  3  v o  appears:  (  4,(1^)3 - 6 (f^) 2 + 2 f  expression 4(XL/H)  3  - 6(XL/H)  2  - )  (4.41)  + 2XL/H d e s c r i b e s t h e  v a r i a t i o n o f l o n g i t u d i n a l flow v e l o c i t y w i t h v e r t i c a l p o s i t i o n i n the melt.  T h i s v e l o c i t y dependence on p o s i t i o n i s shown i n F i g u r e 77, and  i s consistent  w i t h the r e s u l t s o f the a u t o r a d i o g r a p h y experiments which  * S i n c e X = x/L (by E q u a t i o n s (4.26)) the new v a r i a b l e XL/H i s x/H, that i s , XL/H i s t h e d i m e n s i o n l e s s d i s t a n c e i n the v e r t i c a l d i r e c t i o n whose magnitude ranges from 0 to 1.  -0-3  -0-2  -0-1  00  +0-1  +0-2  +0-3  ^relative F i g u r e 77.  The v a r i a t i o n of l o n g i t u d i n a l flow v e l o c i t y w i t h v e r t i c a l p o s i t i o n i n the melt.  VO  show t h a t the r e g i o n s o f more predominant' flow e x i s t  c l o s e t o the top  and bottom o f the m e l t .  The v e l o c i t y measured by t h e t r a c e r m o n i t o r i n g p l o y e d d u r i n g t h i s i n v e s t i g a t i o n would be expected the maximum v e l o c i t y i n the  boundary l a y e r s .  a t XL/H = 0.212 (and 0.788).  technique  em-  to be v e r y c l o s e t o  The maximum v e l o c i t y  Thus t h e expected maximum l o n g i t u d i n a l  occurs flow  v e l o c i t y w i l l be g i v e n by:  3 v = 0.128 ^  Equation  (4.42) s t i l l  G  V  Y (l-Y) 2  2  (4.42)  .Li  c o n t a i n s t h e flow v e l o c i t y dependence on p o s i t i o n  along the melt w i t h v b e i n g 0 a t the v e r t i c a l w a l l s and r e a c h i n g a maximum  a t Y = 0.5 ( h a l f way along  the m e l t ) .  T h i s maximum v a l u e o f v i s  g i v e n by:  3 v = 0.008  G  (4.43)  T  The i n t e g r a t e d average v a l u e o f v between Y = 0 and Y - 1 i s g i v e n by:  3 v = 0.0043  v  Comparison o f t h e e x p e r i m e n t a l (4.43) and (4.44) appear below.  _ GL T  r e s u l t s with  ,,\ (4.44)  ( l  the p r e d i c t i o n s o f E q u a t i o n s  193  4.4.  Comparison of T h e o r e t i c a l P r e d i c t i o n s and E x p e r i m e n t a l R e s u l t s  4.4.1. V a r i a t i o n of Flow V e l o c i t y w i t h Average Temperature G r a d i e n t Across the M e l t When the a p p r o p r i a t e f l u i d parameters from T a b l e 6 a r e i n s e r t e d i n t o Equations average  (4.43) and  and maximum flow v e l o c i t i e s  400°C and melt h e i g h t of 0.64  cm)  < m>400 = ° v  (  The  (4.44), the t h e o r e t i c a l l y  V400 - ' 0  0 6 1  e x p e r i m e n t a l l y determined  V  1 1 3  (at an average m e l t  =  G  L  (4.43(b)) and  G  L  °'  0 8 2  (from F i g u r e  G  and maximum v e l o c i t i e s o f  (4.44(b)).  E x p e r i m e n t a l l y i t has been determined  temperature Equations  of t o t a l melt  Length t h a t the f l o w v e l o c i t y  l e n g t h p r o v i d e d the average  g r a d i e n t remains c o n s t a n t .  (4.43) and  46);  L  4.4.2. V a r i a t i o n of Flow V e l o c i t y w i t h T o t a l M e l t  i s independent  of  (4.43(b))  f a l l s midway between the p r e d i c t e d average Equations  temperature  are g i v e n by:  relation  400  expected  horizontal  As can be seen by i n s p e c t i o n of  (4.44), t h i s e x p e r i m e n t a l o b s e r v a t i o n i s i n agree-  ment w i t h the p r e d i c t i o n s of the m o d i f i e d B a t c h e l o r s o l u t i o n .  4.4.3. V a r i a t i o n of Flow V e l o c i t y w i t h Average M e l t Temperature From F i g u r e 43  the e x p e r i m e n t a l l y measured r a t i o o f the  ,  194  v e l o c i t y a t an average melt  temperature o f 300°C and 400°C i s :  ^ 400  - 0.78  V  Equations  (4.43) and (4.44) p r e d i c t t h a t t h i s r a t i o s h o u l d be 0.84.  Since F i g u r e 43 was c o n s t r u c t e d w i t h o n l y t h r e e data p o i n t s , and the o v e r a l l experimental  accuracy  the o p i n i o n o f t h i s  author  i s b e l i e v e d to be ± 10% (or b e t t e r ) , i t i s  t h a t the t h e o r e t i c a l and e x p e r i m e n t a l  of flow v e l o c i t y dependence  on average melt  values  temperature a r e i n good  agreement.  4.5.  Summary Although  B a t c h e l o r ' s s o l u t i o n o f f r e e thermal  convection i n  r e c t a n g u l a r e n c l o s u r e s o f h i g h a s p e c t r a t i o i s not g e n e r a l l y a p p l i e d t o low a s p e c t r a t i o e n c l o s u r e s , the m o d i f i e d B a t c h e l o r s o l u t i o n above does adequately investigation. the observed temperature.  d e s c r i b e the e x p e r i m e n t a l  appearing  r e s u l t s obtained i n t h i s  There i s v e r y good agreement between t h i s s o l u t i o n and  dependence o f flow on t o t a l melt Equations  l e n g t h and average m e l t  (4.43) and (4.44) both p r e d i c t the observed  l i n e a r dependence between flow v e l o c i t y and the average h o r i z o n t a l temperature g r a d i e n t a c r o s s t h e m e l t .  Furthermore, the magnitude o f  the p r e d i c t e d average and maximum v e l o c i t y o f l o n g i t u d i n a l flow i s i n r e a s o n a b l y good agreement w i t h the r e s u l t s o f the p r e s e n t  Since the s o l u t i o n s o f B a t c h e l o r and Stewart agreement  (over the range o f  Grashof  investigation.  a r e i n good  and R a y l e i g h numbers employed  here), i t i s reasonable  to expect t h a t Stewart's more e l a b o r a t e  d i f f e r e n c e s o l u t i o n c o u l d have been used to a n a l y s e this investigation. clearly  the r e s u l t s of  However, the s o l u t i o n s used by C o l e and  do not d e s c r i b e the flow i n a long h o r i z o n t a l r o d o f  m e t a l f o r the  experimental  finite  c o n d i t i o n s employed h e r e i n .  Utech liquid  196  5 - CONCLUSIONS  A r a d i o a c t i v e t r a c e r t e c h n i q u e has been developed the n a t u r e o f f l u i d  flow i n l i q u i d  to examine  t i n contained i n a lpng h o r i z o n t a l  covered b o a t .  E x t e n s i v e t e s t s have shown t h a t t h e t r a c e r i n t r o d u c t i o n  and m o n i t o r i n g  techniques  employed a l l o w a c c u r a t e and r e p r o d u c i b l e  measurement o f the flow v e l o c i t i e s .  Further experimentation  has r e -  v e a l e d the appearance o f the flow p a t t e r n s which occur i n the m e l t . most s i g n i f i c a n t  The  f i n d i n g s o f t h i s i n v e s t i g a t i o n a r e summarized below:  (1) An extremely  s m a l l h o r i z o n t a l g r a d i e n t , a p p a r e n t l y any non-  zero g r a d i e n t , p r o v i d e s s u f f i c i e n t convective  driving  f o r c e f o r thermal  flow.  (2) Laminar flow a r i s i n g mass t r a n s f e r through  from thermal  c o n v e c t i o n w i l l n o t cause  a r e g i o n o f zero h o r i z o n t a l temperature  gradient. (3) The flow v e l o c i t i e s observed  a r e the r e s u l t o f the presence  of buoyancy f o r c e s c r e a t e d by a temperature g r a d i e n t between the hot and c o l d ends o f the melt.  These v e l o c i t i e s a r e n o t  dependent on e l e c t r o m a g n e t i c s t i r r i n g  effects.  (4) F o r the covered h o r i z o n t a l r o d c o n f i g u r a t i o n i n v e s t i g a t e d h e r e i n the flow v e l o c i t y i s l i n e a r l y dependent on t h e average temperature g r a d i e n t a c r o s s t h e melt z o n t a l temperature g r a d i e n t s ) .  (and n o t on l o c a l  hori-  (5) The  flow v e l o c i t y i n c r e a s e s w i t h i n c r e a s i n g average  melt  temperature. (6) Although second,  the flow v e l o c i t i e s measured were l e s s than 1  cm/  they a r e l a r g e r e l a t i v e to the slow grow r a t e s  commonly employed i n 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 e x p e r i ments and, (7) The  t h e r e f o r e , must be c o n s i d e r e d  significant.  flow p a t t e r n o c c u r r i n g i n the m o l t e n t i n i s a l a m i n a r  u n i c e l l u l a r l o n g i t u d i n a l f l o w upon which i s superimposed a t r a n s v e r s e double  c e l l flow.  not c o n t r i b u t e s i g n i f i c a n t l y  The  t r a n s v e r s e f l o w does  to the l o n g i t u d i n a l  flow  velocity. (8) The  t r a n s v e r s e f l o w observed would be expected  tributing  t o be a  f a c t o r t o the p r e f e r e n t i a l breakdown of  con-  solid-  l i q u i d i n t e r f a c e morphology near the melt c o n t a i n e r . (9) When the s o l u t i o n o f B a t c h e l o r i s extended  and m o d i f i e d ,  t h e r e i s good agreement between t h i s s o l u t i o n and s u l t s of the p r e s e n t  investigation.  the r e -  198  6 - SUGGESTIONS FOR FUTURE WORK  Employing  t h e t r a c e r i n t r o d u c t i o n and m o n i t o r i n g t e c h n i q u e s  developed i n t h i s i n v e s t i g a t i o n , the experiments  l i s t e d below c o u l d be  performed i n o r d e r t o p r o v i d e a d d i t i o n a l i n f o r m a t i o n on the n a t u r e o f fluid  f l o w i n h o r i z o n t a l rods o f l i q u i d m e t a l :  (1) Examination o f t h e dependence o f f l o w v e l o c i t y on temperat u r e g r a d i e n t i n uncovered m e l t s . (2) Examination o f the dependence o f flow v e l o c i t y on melt depth. (3) Examination o f t h e v a r i a t i o n o f flow v e l o c i t y w i t h d i f f e r e n t cross s e c t i o n a l geometries. (4) Examination o f the e f f e c t on flow v e l o c i t y o f i n t r o d u c i n g a moving s o l i d - l i q u i d  i n t e r f a c e i n b o t h pure m e t a l and a l l o y  systems. (5) A q u a n t i t a t i v e e v a l u a t i o n of the dependence of the e f f e c t i v e d i s t r i b u t i o n c o e f f i c i e n t on f l o w v e l o c i t y .  199  PART I I - FLUID FLOW DURING SOLIDIFICATION - ITS EFFECT  ___  ,  _  „.,.,,.  ,  ,—"T"-—  '  •  ON GRAIN STRUCTURE AND  .  , - ,-  .,-  -  MACROSEGREGATION  1 - INTRODUCTION  1.1.  Grain Structure Fluid  flow o f r e s i d u a l l i q u i d m e t a l d u r i n g i n g o t  solidifica-  t i o n i s n e c e s s a r y (under normal c o n d i t i o n s ) i f t h e columnar t o equiaxed transition  (CET) i s t o o c c u r .  The r e d u c t i o n o f temperature g r a d i e n t s i n  the  liquid  ahead o f the s o l i d - l i q u i d  the  convective mixing  i n t e r f a c e i s hastened by i n c r e a s i n g  ( f r e e or f o r c e d ) .  i n the melt w i l l a l l o w n u c l e i  (whatever  S i n c e l o w e r i n g o f temperatures t h e i r s o u r c e be  )to sur-  v i v e and grow, i n c r e a s e d f l u i d flow w i l l promote an e a r l i e r  CET.  Grain  s t r u c t u r e m a n i p u l a t i o n can, t h e r e f o r e , be accomplished by c o n t r o l l i n g the liquid  flow d u r i n g s o l i d i f i c a t i o n .  f o l l o w i n g ways:  Flow c o n t r o l may be accomplished i n the  .  ( 1 ) Magnetic  fields  can be used t o enhance o r reduce f l u i d  S i n c e metals a r e e l e c t r i c a l  motion.  conductors they a r e f o r c e d t o (35)  move i n the presence o f a r o t a t i n g magnetic  field  a c o n s t a n t magnetic  f i e l d i f a d.c. c u r r e n t i s passed  the  .  l i q u i d metal  f i x e d magnetic  through  Reduction of convection occurs i n a  f i e l d s i n c e t h e r e w i l l be a r e t a r d i n g u  to  , or i n  u  *•  force  ,,(11,37,38)  the motxon o f a conductor through the f i e l d  200 (2) Motion of the mold during s o l i d i f i c a t i o n can be used to control casting grain structure.  The e f f e c t of steady-  state mold rotation has been studied extensively by Cole and B o i l i n g  »^0) ^  Wo j ciechowski and Chalmers  f  as  well as Cole and B o i l i n g , have examined the e f f e c t on grain structure of o s c i l l a t i n g the mold during  solidification.  V e r t i c a l reciprocation of semi-continuous D.C. cast aluminum ingots has also proved e f f e c t i v e i n producing f i n e r  grained  , (42) ingots (3) The use of u l t r a - s o n i c energy to e f f e c t grain nucleation i s another mode of grain structure control.  whether i t should  be classed as a form of mechanical mixing i s s t i l l  contro-  , ,(43,44) versial  1.2.  Macrosegregation Various forms of macrosegregation occur as a r e s u l t of con-  vection.  Normal segregation has been discussed  i n Part I, Section 1.  Back-flow along i n t e r d e n d r i t i c channels (caused by volume changes on freezing), of normally segregated residual l i q u i d , i s generally accepted (45)  as the mechanism for inverse Solute convection  segregation cutting across dendrites  i s believed to  be responsible f o r 'A' type segregates i n ingots and for the formation of 'freckles' i n u n i d i r e c t i o n a l l y s o l i d i f i e d castings. theory i s provided^ by observation (46.47) water systems  Support of t h i s  of s o l i d i f i c a t i o n i n ammonium chloride-  201  S u p p r e s s i o n o f c o n v e c t i o n (by magnetic  fields)  eliminates (37)  temperature  f l u c t u a t i o n s which would o t h e r w i s e cause banding  , and  a l s o changes the m a c r o s e g r e g a t i o n ^ " ^ . 1  U n t i l r e c e n t l y , d i f f e r e n c e s i n macrosegregation  arising  from the r o t a t i n g and o s c i l l a t i n g modes o f i n g o t s o l i d i f i c a t i o n had not been s t u d i e d .  The remainder o f P a r t I I w i l l d i s c u s s the i n v e s t i g a t i o n  by t h e author and f e l l o w graduate s t u d e n t M.J. Stewart on macrossegregation a r i s i n g  from these v a r i o u s s o l i d i f i c a t i o n t e c h n i q u e s .  The study w i l l be p r e s e n t e d here i n the same form as i t appeared i n M e t a l l u r g i c a l T r a n s a c t i o n s ^ ^ . The t h e s i s o f M.J. 4 8  tains a s i m i l a r  section.  Stewartcon-  2 - MACROSEGREGATION IN CASTINGS ROTATED AND OSCILLATED DURING  •2.1.  SOLIDIFICATION  Introduction Castings  considered  which have a s m a l l  equiaxed g r a i n s t r u c t u r e a r e  t o be more homogeneous and t o have b e t t e r m e c h a n i c a l p r o -  p e r t i e s than e q u i v a l e n t  castings with a p a r t i a l l y  columnar s t r u c t u r e .  One way o f c o n t r o l l i n g the g r a i n s t r u c t u r e i s by m e c h a n i c a l l y m i x i n g the r e s i d u a l l i q u i d . d u r i n g s o l i d i f i c a t i o n . the mould.  This  can be done by moving  Constant r o t a t i o n o f a c y l i n d r i c a l mould,  radially  c o o l e d , w i l l suppress the columnar t o equiaxed t r a n s i t i o n (CET); oscillation  o f the mould w i l l promote an e a r l i e r  CET; and a s t a t i o n a r y (39  mould w i l l have a s t r u c t u r e between the r o t a t i o n and o s c i l l a t i o n The c o n t r o l o f g r a i n s t r u c t u r e by m e c h a n i c a l m i x i n g o f the l i q u i d c a s t i n g may cause m a c r o s e g r e g a t i o n - - (a f u n c t i o n of t h e k i n d tent of l i q u i d mixing). solute transport  cases during  and ex-  I n a d d i t i o n , r o t a t i o n a l f o r c e s might i n f l u e n c e  i n the l i q u i d  between s o l u t e and s o l v e n t .  i f there  i s a large density  difference  I f m a c r o s e g r e g a t i o n i s enhanced by l i q u i d  mixing t h i s c o u l d be d e t r i m e n t a l  to casting q u a l i t y .  The purpose of the p r e s e n t i n v e s t i g a t i o n i s t o determine the e x t e n t o f m a c r o s e g r e g a t i o n i n s t a t i o n a r y , r o t a t e d , and o s c i l l a t e d c a s t i n g s , and r e l a t e the r e s u l t s t o the c a s t  structure.  203  2.2.  Experiment The m a c r o s e g r e g a t i o n i n the c a s t i n g s was determined by a  r a d i o a c t i v e t r a c e r technique.  The a l l o y used was A l - 3 wt.% Ag made  up of 99.99% A l and 99.8% Ag.  The i n g o t s were c y l i n d r i c a l ,  i n diameter and a p p r o x i m a t e l y 6 i n c h e s h i g h .  The c a s t i n g  3h i n c h e s  apparatus  used, F i g u r e 78, enabled the c a s t i n g o f Al-Ag a l l o y s to be made i n s t a t i o n a r y , r o t a t i n g , or o s c i l l a t i n g moulds. graphite c r u c i b l e i n a resistance furnace. to  a p p r o x i m a t e l y 800 °C and immediately  M e l t i n g was done i n a The a l l o y was superheated  p r i o r to c a s t i n g , a small  110 amount o f r a d i o a c t i v e Ag  was added i n t o the m e l t .  The c a s t i n g s were  a l l poured a t 750 °C (90 °C superheat) i n t o s t a i n l e s s s t e e l moulds, water c o o l e d b e f o r e and d u r i n g c a s t i n g .  A g r a p h i t e h o t top was used  to keep the heat t r a n s f e r from the upper  s u r f a c e to a minimum.  Three  c a s t i n g c o n d i t i o n s were used: s t a t i o n a r y mould, r o t a t e d mould a t 126 rpm, and an o s c i l l a t e d mould.  The o s c i l l a t i o n was a r o t a t i o n o f 126 rmp  w i t h the d i r e c t i o n o f r o t a t i o n b e i n g r e v e r s e d every f i v e The etching of axis.  seconds.  c a s t i n g m i c r o s t r u c t u r e was determined by s e c t i o n i n g and  the c a s t i n g s p a r a l l e l and p e r p e n d i c u l a r to the c y l i n d r i c a l  E t c h i n g was done i n a M o d i f i e d Tucker e t c h (HCL, HNO^, HF, and  H^O i n a 2:2:1:15 r a t i o ) and the e t c h i n g p r o d u c t s were washed o f f immediately w i t h c o n c e n t r a t e d n i t r i c  acid.  To measure the m a c r o s e g r e g a t i o n  i n the i n g o t , the most ex-  p e d i e n t p r o c e d u r e , as commonly used, i s t o measure the s o l u t e c o n c e n t r a t i o n o f c u t t i n g s taken a t v a r i o u s p o i n t s i n the i n g o t by d r i l l i n g .  This  i s s a t i s f a c t o r y i f t h e r e i s no m i c r o s e g r e g a t i o n and no s h o r t range v a r i a t i o n s i n the m a c r o s e g r e g a t i o n , which i s r a r e l y the case.  To  improve  204  IOT TOP  S T E E L MOULD  WATER COOLING Al-Ag CASTING  MOTOR  F i g u r e 78.  The e x p e r i m e n t a l apparatus used f o r p r o d u c i n g the s t a t i o n a r y , r o t a t e d , and o s c i l l a t e d c a s t i n g s o f A l - 3 w t . % Ag.  the a v e r a g i n g p r o c e s s ,  more d r i l l i n g s and  analyses  c o u l d be made, or  a l t e r n a t i v e l y a l a y e r of the c a s t i n g can be machined o f f and taken from t h i s . concentration time and  the e n t i r e c a s t i n g can be machined and  of a l l the c a s t i n g by  e f f o r t involved increases  process l i s t e d initially sent  Finally,  above.  sections very  Accordingly,  can be measured.  g r e a t l y from the f i r s t  the  The to  final  a l l f o u r procedures were used  to determine t h e i r a c c u r a c y and  castings.  samples  r e p r o d u c i b i l i t y f o r the  pre-  Four methods of sampling were employed to determine thi  degree of r a d i a l m a c r o s e g r e g a t i o n .  (a) Holes of 1/4 in  1/4  i n c h steps  of s o l i d The  except 1/8 as method  packed i n t o a s t a n d a r d  moved.  i n c h steps were used.  counter.  The  a n a l y s i s was  (a)  the same  (a).  c y l i n d e r s one  0.030 i n c h t h i c k  i n c h long were p r o g r e s s i v e l y  From each cut a random f i v e gram sample was  the a c t i v i t y of the sample measured i n a  thick.  re-  taken  scintillation  of f i x e d geometry.  c a s t i n g s were machined as i n (c) except the cut  0.050 i n c h e s was  i n each  i n c h diameter were d r i l l e d as i n method  w e l l counter under c o n d i t i o n s  (d) The  container.  then measured w i t h a s c i n t i l l a t i o n w e l l  c a s t i n g s were mounted i n a l a t h e and  concentric  casting  A f i x e d weight  a c t i v i t y of the r a d i o a c t i v e s i l v e r p r e s e n t  (b) Holes of 1/4  and  through the  i n the r a d i a l d i r e c t i o n .  t u r n i n g s was  sample was  (c) The  i n c h diameter were d r i l l e d  was  A l l the m a t e r i a l removed i n each cut  d i s s o l v e d i n a concentrated  s o l u t i o n of n i t r i c  acid  c o n t a i n i n g a s m a l l amount of mercury i n s o l u t i o n . s o l u t i o n s were then made up adding water. and  A 10 ml.  to e i t h e r 250  sample was  The  or 500 ml.  by  taken from each s o l u t i o n  the a c t i v i t y of each sample measured.  In e v a l u a t i n g the r e s u l t s the c o n c e n t r a t i o n of s i l v e r i s taken to be p r o p o r t i o n a l to the measured a c t i v i t y . gamma e m i t t e r and  aluminum a weak a b s o r b e r .  Ag ^ 1 1  As a r e s u l t , s m a l l  c a l d i f f e r e n c e s i n samples counted i n ( a ) , (b) and be  i s a strong geometri-  (c) techniques  should  negligible.  A u t o r a d i o g r a p h y was segregation and  i n the i n g o t s .  the sample a b s o r p t i o n  used to show q u a l i t a t i v e l y  S i n c e the energy of the r a d i a t i o n i s h i g h i s low  the a u t o r a d i o g r a p h  a c t i v i t y of a l a r g e d i s t a n c e i n t o the i n g o t . reasonable  2.3.  w i l l represent  Therefore  r e s o l u t i o n t h i n s e c t i o n s are r e q u i r e d .  p e n d i c u l a r to the c y l i n d r i c a l a x i s were prepared ing  the macro-  the  to o b t a i n  Thin d i s c s perby machining  and  polish-  the d i s c s to a t h i c k n e s s of 0.020 i n c h e s .  Results V e r t i c a l s e c t i o n s of c a s t i n g s which were s t a t i o n a r y ,  r o t a t i n g , and 79(a),  79(b)  oscillating and  79(c)  during  s o l i d i f i c a t i o n a r e shown i n F i g u r e s  respectively.  The  s t a t i o n a r y c a s t i n g has  equiaxed r e g i o n i n the c e n t r e , the r o t a t e d c a s t i n g has to the c e n t r e of the c a s t i n g , and r e g i o n , i n agreement w i t h p r e v i o u s i n the o s c i l l a t e d i n F i g u r e 80,  the o s c i l l a t e d observations.  a columnar zone  c a s t i n g has The  a small  a large  equiaxed g r a i n s  i n g o t a r e c l e a r l y shown to have grown d e n d r i t i c a l l y  taken at h i g h e r  magnification.  I  F i g u r e 80.  Equiaxed g r a i n s i n the c e n t r a l r e g i o n of the o s c i l l a t e d c a s t i n g , m a g n i f i c a t i o n AO times.  209  The ingots  structures obtained  (Figures 81(a),  f l u i d motion on the  81(b),  on etched  c r o s s s e c t i o n s of  and 81(c)) show the e f f e c t  columnar zone.  In F i g u r e  81(a)  of the  f o r the r o t a t e d i n g o t itial  to the mould w a l l .  The  These g r a i n s are growing tov/ards In the o s c i l l a t e d i n g o t  columnar  the oncoming f l u i d  (Figure 81(c))the  A s i m i l a r observation  i n the  the i n -  liquid  d i r e c t i o n of the  has  region  to the mould w a l l s .  zone changes when the mould r o t a t i o n . i s r e v e r s e d grow i n t o the flow.  a l l the  ( F i g u r e 81(b))shows a s p i r a l shape w i t h  columnar g r a i n s growing n o n - p e r p e n d i c u l a r  applied  of the s t a t i o n a r y  c a s t i n g o t the columnar r e g i o n i s i n a r a d i a l d i r e c t i o n w i t h g r a i n s growing p e r p e n d i c u l a r  the  pool.  columnar  so t h a t they always  been made by Roth  and  (49) Schippen  .  In both the r o t a t e d and  o s c i l l a t e d ingot there  r e n u c l e a t i o n of the columnar g r a i n s to a c h i e v e There were no g r a i n s observed which curved  the curved  or had  that the c r y s t a l l o g r a p h i c growth o r i e n t a t i o n was The using  the  solute concentration  f o u r sampling techniques  Comparing the techniques  have v a r i o u s  The  described  1/4  i n c h steps  accuracy  i s shown i n F i g u r e t h a t the  82.  different them.  For  from the o u t e r mould w a l l to the c e n t r e l i n e . of the p o i n t s p l o t t e d i s such t h a t they  counter.  i n the c o n c e n t r a t i o n  always m a i n t a i n e d .  ( F i g u r e 82(a)) the macro-  a t r u e r e p r e s e n t a t i o n of the c o n c e n t r a t i o n the s c i n t i l l a t i o n  a kink, i n d i c a t i n g  degrees of s c a t t e r a s s o c i a t e d w i t h  appears c y c l i c  experimental  effects.  in.a stationary casting  f o u r s e t s of p o i n t s i t i s e v i d e n t  the d r i l l e d h o l e s w i t h segregation  of Ag  is a  along  b e h a v i o u r i s genuine the 1/8  of the sample measured i n  Thus the s c a t t e r must be the d r i l l h o l e .  are  To  test  due  to a change  i f this  cyclic  i n c h step h o l e method i s shown i n F i g u r e  82  211  3.2  r  3.0  (a)  2.8 3.2  (b)  3.0  2.8 cc Ul  >  CO  z o 3.0 a: u a x a  UJ  o  5.2 -  o  po »  o°  °  o/ooo°oo  °°  •o—tr— CP  o°  2.8  OO  o  o  (O  ° O o o  2.6  3.2 fa  3.0  0  0  - 0  O  o  n  . o °  o— 6 a  n  0  -  o  0  o"  (d)  o  2.8 JL  0  0.5  1.0  1.5  DISTANCE FROM MOULD WALL (INCHES)  Figure  82. The r a d i a l s i l v e r d i s t r i b u t i o n i n a s t a t i o n a r y c a s t i n g ; (a) 1/4 i n c h d r i l l h o l e s i n 1/4 i n c h s t e p s , (b) 1/4 i n c h d r i l l h o l e s i n 1/8 i n c h s t e p s , (c) 0.030 i n c h l a t h e t u r n i n g s , (d) 0.050 i n c h l a t h e t u r n i n g s d i s s o l v e d i n a c i d .  212 A g a i n the p o i n t s show a , c y c l i c b e h a v i o u r , but the c y c l e p e r i o d i s d i f f e r ent  f o r the two  cases.  Thus m i c r o s e g r e g a t i o n a l o n g the d r i l l  be the cause o f the c y c l i n g . ( F i g u r e 82(c))shows  h o l e must  The p l o t f o r the s o l i d l a t h e t u r n i n g s  an e x t e n s i v e s c a t t e r between p o i n t s .  This large  s c a t t e r c o u l d be caused by the m i c r o s e g r e g a t i o n , by the s e l e c t i o n o f the m a t e r i a l taken from the whole sample, o r by not having a s u f f i c i e n t l y s t a n t sample geometry due to the n a t u r e o f the l a t h e t u r n i n g s . method o f d i s s o l v i n g of  final  the t u r n i n g s o f the e n t i r e sample gave the r e s u l t s  F i g u r e 8 2 ( d ) , which shows much l e s s s c a t t e r than the o t h e r methods. In  t h i s case the c o u n t i n g geometry i s not a problem t a i n e d i n s t a n d a r d tube and the l i q u i d sample c o m p o s i t i o n . for  The  con-  the o t h e r two castings.  counted i s a t r u e average o f the used  m a c r o s e g r e g a t i o n measurements.  The r a d i a l m a c r o s e g r e g a t i o n  macrosegregation,  i s con-  T h i s method gave r e p r o d u c i b l e r e s u l t s and was  a l l the subsequent  shown i n F i g u r e 83.  as the l i q u i d  i n the t h r e e types o f i n g o t s i s  Three s e t s of d a t a were o b t a i n e d f o r the  radial  one from the c e n t r a l r e g i o n o f one group o f c a s t i n g s ,  from near the top and bottom o f a second s i m i l a r group  and  of  A l l the r e s u l t s f o r a p a r t i c u l a r type of c a s t i n g were v e r y  similar. The s i l v e r c o n c e n t r a t i o n i n the s t a t i o n a r y and i n g o t s , shown i n F i g u r e s 83(a) and 8 3 ( b ) , i s e s s e n t i a l l y dicating  l i t t l e macrosegregation,  constant i n -  except f o r a s m a l l drop i n concen-  t r a t i o n a t the c e n t r e l i n e o f the c a s t i n g . m a c r o s e g r e g a t i o n due  rotated  There i s no e f f e c t on  to the d i f f e r e n c e i n d e n s i t y o f the s i l v e r  aluminum i n the r o t a t e d c a s t i n g .  In the o s c i l l a t e d case  the and  macrosegregation  i s p r e s e n t , w i t h an i n i t i a l r i s e i n the s i l v e r c o n c e n t r a t i o n up to a peak.  The c o n c e n t r a t i o n then decreases to the c e n t r e l i n e o f the c a s t i n g  213  3.1 °  OO  o o  3.0  — ° -  »  o  o  o  0  °  o  j  (a)  o o°° °  o  1  o o  2.9  3.1 ° o °  ° o „ o  ^ O  o  "  n  G  o  o  c  0  6  °  o o  o  o  UJ  o  o  u  "  !  1  O  o  o  3.2  / X  / 1 °x  3.1 I  5  0  OO  -  UJ  UJ  I  (b)  3.0  2.9  o  o  o^-  i.  3.0  i  j  (c)  0.5  1.0  DISTANCE FROM MOULD WALL  1.5  ( INCHES )  F i g u r e 83.The r a d i a l s i l v e r d i s t r i b u t i o n i n (a) s t a t i o n a r y , (b) r o t a t e d , and (c) o s c i l l a t e d i n g o t s u s i n g method (d) o f F i g u r e 82.  214  to a v a l u e  over 0.25%  Ag below the C  q  value.  The  p o s i t i o n of the  i s shown on  the curve; t h i s p o s i t i o n corresponds to the CET  83(c).  r e s u l t s show t h a t the CET  The  CET  i n Figure  corresponds to the maximum s i l v e r  concentration.  An  a u t o r a d i o g r a p h of the o s c i l l a t e d  the m a c r o s e g r e g a t i o n q u a l i t a t i v e l y . c e n t r e o f the i n g o t r e p r e s e n t  The  ingot  l i g h t e r areas towards  s i l v e r depleted  i n the s i l v e r d i s t r i b u t i o n i t can  e a s i l y be  h o l e methods of a n a l y s i s c o u l d g i v e s p u r i o u s a n a l y s i s t h a t does not  2.4.  shows  the  areas which c o r r e s p o n d  to the q u a n t i t a t i v e measurements ( F i g u r e 8 3 ( c ) ) . Due effect  ( F i g u r e 84)  to t h i s m o t t l e d  seen t h a t the  r e s u l t s , as can  i n c l u d e the t o t a l r a d i a l  drill  any  sample.  Discussion  The  cast structure associated with stationary, rotated,  and (39)  oscillated  c a s t i n g s are s i m i l a r to those r e p o r t e d  and  and w i l l not be  others  discussed  here.  Two  by  C o l e and B o i l i n g  p o i n t s w i l l be  con-  sidered. (1) The  r e l a t i o n of the observed m a c r o s e g r e g a t i o n w i t h the  cast  structure. (2) The  shape of the s o l u t e  Conditions  f o r the CET  curves.  are met  much e a r l i e r i n the  c a s t i n g than i n e i t h e r the r o t a t e d or s t a t i o n a r y c a s t i n g . l i e v e d due region  to the lowering  of the  temperature g r a d i e n t  ( o s c i l l a t i o n causes e x t e n s i v e  produced by  oscillated  This i s  be-  i n the m o l t e n  m i x i n g ) thus a l l o w i n g " n u c l e i " ,  large, shear f o r c e s at the i n t e r f a c e , to s u r v i v e and  grow.  215  84. A" autoradiograph of tha cross-section of the oscillated i n g o t showing tha s i l v e r d i s t r i b u t i o n i n the casting. Actual size*  216  During r o t a t i o n r e v e r s a l these l a r g e shear f o r c e s w i l l  cause  remelting  (34 41) and/or b r e a k i n g "nuclei". liquid  o f f of d e n d r i t e  fragments  '  These can e a s i l y be swept i n t o the c e n t r a l r e g i o n o f  p o o l by the v i o l e n t t u r b u l e n t  oscillation.  flow  O b s e r v a t i o n o f t h i s flow  the e x i s t e n c e  occurring  liquid  I f the mould i s r o t a t e d a t a c o n s t a n t (39)  shows  a t the i n t e r f a c e .  Therefore,  n a t u r a l convection  will  no n u c l e i w i l l be produced F o r the s t a t i o n a r y  ingot  w i l l y i e l d low shear f o r c e s a t the i n t e r f a c e and t h e  temperature g r a d i e n t w i l l be o f some i n t e r m e d i a t e The  speed  and no shear f o r c e s  the CET w i l l be s u p p r e s s e d , as observed.  ingots  as a r e s u l t o f  i n a rheoscopic  the temperature g r a d i e n t w i l l remain h i g h be p r e s e n t  the  o f a t u r b u l e n t wave g e n e r a t e d a t the i n t e r f a c e and r a p i d l y  moving to the c e n t r e .  and  which can a c t as  value.  l a c k o f m a c r o s e g r e g a t i o n i n the r o t a t e d and s t a t i o n a r y  can be a t t r i b u t e d to the l a c k o f s i g n i f i c a n t  i n t e r d e n d r i t i c region.  Without f l u i d flow  f l u i d flow  i n the  t h e r e w i l l be no n e t s o l u t e  f l u x from the i n t e r f a c e r e g i o n , and t h e r e f o r e , no m a c r o s e g r e g a t i o n . For  the o s c i l l a t e d  of t h e s o l i d - l i q u i d flow. The  casting high  shear f o r c e s i n the v i c i n i t y  i n t e r f a c e w i l l produce more e x t e n s i v e i n t e r d e n d r i t i c  T h i s flow w i l l sweep s o l u t e r i c h  liquid  out o f the mushy zone.  s o l u t e d i s t r i b u t i o n near the mould w a l l w i l l  then tend t o conform  to the e q u a t i o n f o r complete m i x i n g :  c where C C  q  G  i s the s o l i d  s  =  kC^l-g)^  1  s o l u t e composition, k the d i s t r i b u t i o n c o e f f i c i e n t ,  the average i n i t i a l s o l u t e c o m p o s i t i o n and g the f r a c t i o n s o l i d i f i e d .  When the r o t a t i o n i s r e v e r s e d  a t u r b u l e n t wave i s produced which w i l l  217  transport this solute towards the centre of the s o l i d i f y i n g ingot.  During columnar growth the solute d i s t r i b u t i o n w i l l therefore be as shown i n Figure 85(a).  When the CET i s imminent the  d i s t r i b u t i o n w i l l be that shown i n Figure 85(b).  The i n i t i a l part of  the curve corresponds to a complete mixing s i t u a t i o n up to the peak. Beyond the peak the composition  gradually decreases towards the centre  due to the incomplete mixing of the solute r i c h l i q u i d generated at the interface.  Concurrent with this solute movement i s the reduction of  the temperature gradient which, u n t i l the CET occurs, does not allow s u r v i v a l of n u c l e i .  (At every rotation reversal high shear forces and  temperature fluctuations, due to turbulence, w i l l produce a large number of dendrite fragments).  When the temperature gradient i s  s u f f i c i e n t l y low these fragments w i l l be able to survive and grow and be swept by the turbulent wave throughout the remaining these fragments are of composition less than C  Q  liquid.  the o v e r a l l  i n this region w i l l be reduced as shown i n Figure 85(c).  Since  composition Also, due to  the lowering of the temperature gradient the mushy zone w i l l be i n creased i n length.  The mass and composition  of dendrite fragments  necessary to cause this reduction i n composition  (Figure 85(b) -  Figure 85(c)) i s calculated i n the Appendix, Section 2.6. The solute d i s t r i b u t i o n p r o f i l e of Figure 85(c) w i l l be that of an ingot o s c i l l a t e d during s o l i d i f i c a t i o n .  The macrosegregation predicted above was ob-  served i n the o s c i l l a t e d ingot, Figure 83(c).  2.5.  Conclusion The present investigation has shown that no s i g n i f i c a n t  218  DISTANCE FROM MOULD  WALL  F i g u r e 85. The development of the r a d i a l m a c r o s e g r e g a t i o n i n an o s c i l l a t e d i n g o t , (a) p r i o r t o the time o f the CET, (b) a t the time of the CET, and (c) the f i n a l s i l v e r d i s t r i b u t i o n i n the c a s t i n g .  219  m a c r o s e g r e g a t i o n accompanies s o l i d i f i c a t i o n i n s t a t i o n a r y o r r o t a t e d moulds f o r the system examined. d i f f e r e n c e between the s o l v e n t  This implies (Al) and s o l u t e  the r a d i a l s o l u t e d i s t r i b u t i o n .  t h a t the l a r g e  (Ag) has no e f f e c t on  However, a p p r e c i a b l e  macrosegregation  i s a s s o c i a t e d w i t h t h e o s c i l l a t i o n mode o f s o l i d i f i c a t i o n . r i s e i s a t t r i b u t e d t o s o l u t e m i x i n g i n the l i q u i d due  tothe  turbulent  flow.  centre  the i n g o t  2.6.  The i n i t i a l region  i s associated  The s o l u t e d e p l e t i o n i n t h e  o f the c a s t i n g i s caused by s m a l l g r a i n s  c e n t r a t i o n being  interfacial  The maximum c o n c e n t r a t i o n  w i t h the columnar t o equiaxed t r a n s i t i o n .  density  o f low s o l u t e  con-  swept, by the t u r b u l e n t waves, from the mushy zone t o  centre.  Appendix to S e c t i o n 2 The model proposed f o r m a c r o s e g r e g a t i o n i n t h e o s c i l l a t e d  i n g o t assumes s u f f i c i e n t liquid and  dendrite  fragments a r e swept i n t o t h e c e n t r a l  zone, t o g i v e the change i n t h e d i s t r i b u t i o n between F i g u r e 85(b)  85(c).  The f o l l o w i n g a n a l y s i s i s an approximate c a l c u l a t i o n f o r  the mass o f fragments which i s r e q u i r e d . Assume V p r i o r t o t h e CET.  i s the volume o f the c e n t r a l l i q u i d r e g i o n j u s t  The average c o m p o s i t i o n i n t h i s volume a f t e r t o t a l  s o l i d i f i c a t i o n assuming a l i n e a r d i s t r i b u t i o n p r o f i l e i n t h i s and  C^ = 3.0 wt % Ag, i s g i v e n by:  75  =  V  )  ° J  o  2TT r C ( r ) d r 2TT  rdr  where C ( r ) i s c o m p o s i t i o n as a f u n c t i o n o f r a d i u s CET.  region  From F i g u r e  83(c), C(r) =  and R i s r a d i u s o f  r + 2.70, therefore~C  = 3.02 wt % Ag.  Comparing F i g u r e s 85(b) and 85(c) in V  an e s t i m a t e  o f the average  j u s t p r i o r to the CET can be made ( C ( r ) =  composition  r + 3.00) and i s  e q u a l t o 3.10 wt % Ag.  Assuming the composition  o f d e n d r i t e fragments swept  the c e n t r a l r e g i o n i s ctk C , where a i s a f a c t o r o o crease  i n solute concentration  progresses, ation.  assumed t o be 1.5,  into  t o account f o r t h e i n -  i n the d e n d r i t e branches as s o l i d i f i c a t i o n k  i s 0.25 f o r t h e a l l o y under  consider-  Therefore: akC = (1.5)(0.25) (3.0) o o = 1.12 wt % Ag  L e t v be the volume o f d e n d r i t e fragments swept i n t o the c e n t r a l m o l t e n region  (V„) a t the time o f the CET.  concentration i n V  The r e s u l t i n g change i n the average  can then be used t o s o l v e f o r v.  Therefore:  3.10 V  + 1.12 v =• 3.02 (V  Therefore:  v = 0.04 V„  + v)  T h i s c a l c u l a t i o n shows t h a t a s m a l l amount o f s o l i d  frag-  ments i s r e q u i r e d r e l a t i v e to the t o t a l l i q u i d volume to cause the decrease low  i n c o n c e n t r a t i o n observed.  The l a r g e mushy zone, due t o the  thermal g r a d i e n t , and t h e l a r g e i n t e r d e n d r i t i c flow, due t o t h e  turbulence  produced d u r i n g  the r o t a t i o n r e v e r s a l ,  should  t h i s s m a l l volume o f fragments b e i n g made a v a i l a b l e served  effect.  result i n  to cause t h e ob-  221  BIBLIOGRAPHY  1.  W.G.  Pfann, Zone M e l t i n g , John W i l e y  2.  B. C h a l m e r s , P r i n c i p l e s of S o l i d i f i c a t i o n , 1964.  3.  C. Wagner, T r a n s . AIME, 1954,  4.  F. Weinberg, TMS-AIME, 1963,  5.  G.S.  Cole and W.C.  6.  K.A.  Jackson  7.  G.F.  B o i l i n g and J.R.  8.  A. M i i l l e r and M. Wiehelm, Z. N a t u r f . , 1964,  9.  H.P.  and  200, 227,  & Sons, New  York,  John Wiley  1958.  & Sons, New  York,  p.154. p.231.  Winegard, J . I n s t . Met.  1965,  ]_, p.153.  B. Chalmers, P r i v a t e communication i n R e f e r e n c e  Utech, Sc.D.  5.  Kramer, i b i d . A,  19, p.254.  T h e s i s , Dept. of M e t a l l u r g y , M.I.T.  10.  E. E c k e r t and R.M.  Drake, Heat and Mass T r a n s f e r , M c G r a w - H i l l ,  11.  H.P. U t e c h , W.S. Brower and J.G. E a r l y , " C r y s t a l Growth", P r o c e e d i n g s of an I n t e r n a t i o n a l Conference on C r y s t a l Growth, Boston, 20-24, June, 1966, p.201.  12.  D.T.J. H u r l e , P h i l . Mag.,  1966,  13.  K.G.  Davis  TMS-AIME, 1965,  14.  J.R.  C a r r u t h e r s and W.C.  15.  J.R. C a r r u t h e r s , Ph.D. Toronto, 1966.  16.  M.J.  17.  M.J. Stewart, Ph.D. Columbia, 1970.  18.  G.S. C o l e , Ford Motor Co. R e p o r t , " T r a n s p o r t Solidification", December 9, 1969.  19.  D.R.  20.  C.S. C o l e , Ph.D. 1963.  21.  H.J.  and P.  Stewart and  Fryzuk,  13,  #122,  Winegard, Can.  p.305. 233,  Met.  p.1796.  Quart. 6, p.223.  T h e s i s , Dept. of M e t a l l u r g y , U n i v e r s i t y of  F. Weinberg  (to be p u b l i s h e d ) .  T h e s i s , Dept. of M e t a l l u r g y , U n i v e r s i t y of  O l i v e r , Chem. Eng.  1959.  Sc.,  1962,  Process  and  Fluid  British  Flow i n  17, p.335.  T h e s i s , Dept. of M e t a l l u r g y , U n i v e r s i t y of  Merks, A p p l . S c i . R e s e a r c h , 1958,  [A], V o l . 8 , p.100.  Toronto,  222 22.  G.S. C o l e , TMS-AIME, 1967, Vol.239, p.1287.  23.  G.K. B a t c h e l o r , Quart. A p p l . Math., 12, 1954, p.209.  24.  G. P o o t s , Quart. Mech. A p p l . Math., 11, 1958, p.257.  25.  J . 0. W i l k e s , Ph.D. T h e s i s , U n i v e r s i t y o f M i c h i g a n , Ann Arbour, M i c h i g a n , 1963.  26.  M.R.  27.  J.R. C a r r u t h e r s , J . C r y s t a l Growth, 2^, 1968, p 1.  28.  W.R. M a r t i n i and S.W.  29.  Samuels and W. C h u r c h i l l , A.I.Ch.E. J . , J.3, 1967, p. 77.  C h u r c h i l l , A.I.Ch.E.J., 6, 1960, p.251.  S. Weinbaum, J . F l u i d Mech. 18, 1964, p.809.  30. J.W. E l d e r . J . F l u i d Mech, 23, p a r t 1, p.77. 31.  W.C. Winegard and B. Chalmers, TASM, 1954, 216, p.1214.  32. B. Chalmers, J . A u s t r a l i a n I n s t . M e t a l s , 1963, 8, p.255. 33.  R.T. S o u t h i n , TMS-AIME, 1967, 239, p.220.  34. K.A. J a c k s o n , J.D. Hunt, D.E. Uhlman and T.P, Seward I I I , 1966, 236, p. 149. 35.  TMS-AIME,  W.C. Johnson and W.A. T i l l e r , Westinghouse Research R e p o r t , " F l u i d Flow C o n t r o l During S o l i d i f i c a t i o n P a r t I " , December 15, 1959.  36. G.S. C o l e and G.F. B o i l i n g , TMS-AIME, .1966, 236, p. 1366. 37.  H.P. Utech and M.C. F l e m i n g s , " C r y s t a l Growth" P r o c e e d i n g s o f an I n t e r n a t i o n a l Conference on C r y s t a l Growth, Boston, 20-24, June, 1966, p.659.  38. D.R. Uhftman, T.P. Seward I I I and B. Chalmers, TMS-AIME, 1966, 236, p.527. 39.  G.S. C o l e and G.F. B o i l i n g , F o r d Motor Co. r e p o r t " E n f o r c e d F l u i d M o t i o n and the C o n t r o l o f G r a i n S t r u c t u r e s i n M e t a l Casting',' March 15, 1967.  40. G.S. C o l e and G.F. B o i l i n g , Ford Motor Co. r e p o r t , " M a n i p u l a t i o n o f S t r u c t u r e and P r o p e r t i e s " , October 30, 1969. 41.  S. Wojciechowski and B. Chalmers, TMS-AIME, 1968, 242, p.690.  42. N. Bryson, A l c a n Research, K i n g s t o n Ont., p r i v a t e 43.  discussion.  R.T. S o u t h i n , J . I n s t . Met., 1966, 94, p.401.  44. D.H. Lane, J.W. Cunningham and W.A.  T i l l e r , TMS-AIME, 1960, 218, p.985.  223  45.  J.S. K i r k a l d y and W.V. Y o u d e l i s , TMS-AIME, 1958, 212, p.833.  46.  R.J. MacDonald and J.D. Hunt, TMS-AIME, 1969, 245, p.1993.  47.  S.M. C o p l e y , A.F. Giamei, S.M. Johnson T r a n s . , 1970, 1, p.2193.  48.  M.J. Stewart, L.C. MacAulay and F. Weinberg, Met. T r a n s . , January 1971.  49.  W. Rother and M. Schippen, Z. M e t a l l k , 47_, 1956, p.78.  50.  J . K o h l , R.D. Zentner, and H.R. Lukens, R a d i o i s o t o p e A p p l i c a t i o n s Eng. D. Van Nostrand Company, P r i n c e t o n , N.J., 1961.  51.  H. T h r e s h , D r a f t M a n u s c r i p t of"The V i s c o s i t y o f L i q u i d T i n , Lead and T i n - L e a d A l l o y s " , Submitted t o TMS-AIME, Feb. 1969.  52.  R.N. Lyon, L i q u i d M e t a l s Handbook, The Committee on the B a s i c P r o p e r t i e s o f L i q u i d M e t a l s , O f f i c e o f N a v a l Research, Dept. o f t h e Navy, 1954.  53.  H.R.  Thresh,  and M.F. Hornbecker, Met.  A.F. Crawley and D.W.G. White, TSM-AIME, 1968, _242, p.819.  

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