Effect of computational domain size on the mathematical modeling of transport processes and segregation during directional solidification

Using a finite-element simulator, a directionally solidified hypoeutectic Pb-Sn alloy was modeled in two dimensions to determine the effect of the height of the overlying liquid on convective transport and macrosegregation. It was determined that, while the strength of the convection in the overlying liquid depends on the square root of its height, one need not model the entire domain to predict freckling. Furthermore, the assumption of a constant thermal gradient in the liquid causes the predicted convection to be somewhat weaker than the convection in the temperature field used in directional solidification processing.