Modeling Freckle Segregation with Mesh Adaptation

Modeling the formation of macroscopic segregation channels during directional solidification processes has important applications in the casting industry. Computations that consider thermosolutal convection involve different length scales ranging from the small solute boundary layer at the dendrite tips to the characteristic size of the casting. In general, numerical models of solidification in the presence of a developing mushy zone are computationally inefficient because of nonlinear transport in an anisotropic porous medium. In the current work, mesh adaptation with triangular finite elements is used in conjunction with an efficient fractional-step solver of the momentum equations to predict the occurrence of channel-type segregation defects or freckles. The triangulations are created dynamically using an unstructured grid generator and a refinement criterion that tracks the position of the channel segregates. The efficiency of mesh adaptation is illustrated with simulations showing channel formation and macrosegregation in directional solidification of a Pb–Sn alloy.