Numerical Simulation of Macrosegregation Caused by Thermal–Solutal Convection and Solidification Shrinkage Using ALE Model

Solidification shrinkage has been recognized as an important factor for macrosegregation formation. An arbitrary Lagrangian–Eulerian (ALE) model is constructed to predict the macrosegregation caused by thermal–solutal convection and solidification shrinkage. A novel mesh update algorithm is developed to account for the domain change induced by solidification shrinkage. The velocity–pressure coupling between the non-homogenous mass conservation equation and momentum equation is addressed by a modified pressure correction method. The governing equations are solved by the streamline-upwind/Petrov–Galerkin-stabilized finite element algorithm. The application of the model to the Pb-19.2 wt%Sn alloy solidification problem is considered. The inverse segregation is successfully predicted, and reasonable agreement with the literature results is obtained. Thus, the ALE model is established to be a highly effective tool for predicting the macrosegregation caused by solidification shrinkage and thermal–solutal convection. Finally, the effect of solidification shrinkage is analyzed. The results demonstrate that solidification shrinkage delays the advance of the solidification front and intensifies the segregation.