A three-dimensional cellular automaton for the simulation of the dendritic growth of aluminum alloy

摘要

A modified cellular automaton model is used to simulate the dendritic growth of aluminum alloy.This model couples the finite difference method and the three dimensional cellular automaton.Different from the classical cellular automata,the three dimensional cellular automaton model includes both the solute diffusion in liquid and in solid and curvature undercooling,which have vital influence on the evolution of microstructure.We use the KGT(KurzGiovanola-Trivedi) model to calculating the relationship between the growth velocity of a dendrite tip and the local undercooling.The finite difference method is used to calculate the temperature and solute fields in the calculation domain.In the Macro-Micro model we use two kinds of grids to calculate the temperature field and the evolution of dendrite microstructure,which gear up the speed of compute.The model was applied to show the variation of grain size with different cooling speed and predicts the grain structures solidified in a cubic steel mold,and we got three classic results of columnar-to-equiaxed transition with three different pouring temperatures.