Computer simulation of consumable melted slabs
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A. CAMPAGNA
A m a t h e m a t i c a l model has b e e n developed to s i m u l a t e t w o - d i m e n s i o n a l heat flow for a slab ingot produced as a r e m e l t e d product. V a r i o u s heat flow p a r a m e t e r s have b e e n studied to det e r m i n e the influence of c h a n g e s in them on local solidification t i m e . The p a r a m e t e r s which show the g r e a t e s t influence a r e the heat t r a n s f e r coefficient and the t h i c k n e s s of the s l a b . The rate of addition of m a t e r i a l c h a n g e s the depth of the m o l t e n pool, but does not affect local s o l i d i f i c a t i o n time. T H E p r o c e s s of v a c u u m a r c r e m e l t i n g is a welding p r o c e s s c a r r i e d out in v a c u u m in a w a t e r - c o o l e d c y l i n d r i c a l m e t a l mold. C o n s u m a b l e m e l t e d ingots produced in this p r o c e s s show all of the expected s t r u c t u r a l v a r i a t i o n s that c o n v e n t i o n a l l y c a s t ingots do. Due to the cost and difficulty of r u n n i n g a l a r g e n u m b e r of e x p e r i m e n t s to study this p r o c e s s , it was felt that a m a t h e m a t i c a l model could b e t t e r provide useful i n f o r m a t i o n about f r e e z i n g c o n d i t i o n s and hence about g r a i n s t r u c t u r e of the ingot. A s c h e m a t i c view of the e n t i r e s y s t e m which was m o d e l e d is shown in Fig. 1. The m e t a l mold is c o p p e r , and the model i s pict u r e d as a t w o - d i m e n s i o n a l slab r a t h e r than a s a three-dimensional cylinder. The v a c u u m a r c m e l t i n g p r o c e s s has not b e e n ext e n s i v e l y modeled. In fact the only known work i s that of d u M a n o i r and P i e r c e 1 who p r o d u c e d a pool configu r a t i o n in s m a l l ingots of m o l y b d e n u m . C l i t e s and B e a l l 2 have c a l c u l a t e d the t h e r m a l flux as a function of position in 5-in. and 8 - i n . diam ingots of z i r c o n i u m and t i t a n i u m . C r e m i s i o 3 has d i s c u s s e d s o l i d i f i c a t i o n theory and its r e l a t i o n s h i p to this p r o c e s s . Buehl and McCauley 4 and Shcherbakov el al. s have r e p o r t e d on e x p e r i m e n t a l s t u d i e s in production size heats. It was the a i m of this study, however, to produce a m a t h e m a t i c a l model which would e x p l o r e the effects that c h a n g e s in v a r i o u s t h e r m a l p a r a m e t e r s would have on the local s o l i d i f i c a t i o n time in the r e s u l t a n t slab. Local solidification time was chosen as the m o s t m e a n i n g f u l value to study b e c a u s e it is the one on which g r a i n size is m o s t d i r e c t l y dependent, 7'B and the g r a i n size o r d e n d r i t e a r m s p a c i n g is known to affect the t h e r m o - m e c h a n i c a l p r o p e r t i e s of any ingot or slab. The t h e r m a l p a r a m e t e r s that were of g r e a t e s t i n t e r e s t were the rate of m e l t i n g , the rate at which h
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