A front-tracking method of predicting the solidification microstructure in shape castings

A numerical model has been developed that simulates the nucleation and growth of columnar and equiaxed grains from the liquid phase in a casting. This model uses a control volume finite difference method to solve conduction heat transfer over a two-dimensional domain. The evolving columnar front and equiaxed grain boundaries are represented by sharp fronts across the mesh. A front-tracking algorithm is used to predict the evolution of the grains across the grid according to dendrite kinetics. The heat equation is coupled to the front-tracking algorithm by a source term that represents the latent heat that evolves as the dendrite tips advance and the mushy zone solidifies. This model predicts the extent of liquid undercooling ahead of the growing columnar front and this computation is used to determine the likelihood of nucleation and growth of equiaxed grains in the liquid; in particular the columnar-to-equiaxed transition is predicted.