Analysis of the effect of shrinkage on macrosegregation in alloy solidification

Numerical calculations based on a continuum model are used to examine the effects of solidification shrinkage on the redistribution of solute in a Pb-19.2 pct Sn mixture which is convectively cooled at a sidewall. For each of three different cooling rates, separate calculations are performed for shrinkage and buoyancy-induced flows, as well as for the combined influence of shrinkage and buoyancy effects. The calculations reveal that flow and macrosegregation patterns are more strongly influenced by buoyancy effects over a wide range of solidification rates. Although extremely large solidification rates yield small regions near the chilled wall in which shrinkage-induced flows control the redis-tribution of solute, the overall effect on macrosegregation is small relative to that associated with buoyancy. Scaling analysis of the governing equations produces reference shrinkage and buoyancy velocities which can be used to extend the current numerical results to other binary systems.