Columnar front tracking algorithm for prediction of the columnar-to-equiaxed transition in two-dimensional solidification

A novel algorithm to track the columnar front in one- (1D) and two-dimensional (2D) solidification problems has been developed and coupled with the governing equations of a deterministic model to predict the columnar-to-equiaxed transition (CET). The new algorithm, inspired by the cellular automaton (CA) technique, requires a CA mesh as coarse as that for the numerical solution of the governing equations. Front positions predicted with the new algorithm during transient and steady-state growth under given 1D and 2D temperature fields matched the results from analytical solutions. The time evolution of the columnar front agreed well with the published results for the 1D and 2D solidification of an Al-3(wt%) Cu alloy. Some discrepancy observed in the CET position was attributed to the different implementation of the columnar front blocking criterion and to the nonisothermal character of the front line.