A two-dimensional model for the quantitative simulation of the dendritic growth with cellular automaton method

Abstract

A two-dimensional cellular automaton model was developed for simulating the diffusion-controlled dendritic growth in the low Péclet regime. The growth velocity of the solid/liquid interface was determined by the local solute diffusion, and the modified decentered square growth was improved to capture the first eight neighboring cells of the interface cell. In order to quantitatively validate the developed model, the free dendritic growth from an undercooled melt was simulated and compared with the classic Lipton–Glicksman–Kurz (LGK) analytical model. The results show that the predicted steady state tip velocity is in a reasonable agreement with the analytical value, and the dendritic growth can be quantitatively determined by the present model. Meanwhile, the simulation of the dendritic growth with random crystallographic orientation shows that the effects of the mesh dependency of the model on the growth kinetics and crystallographic orientation can be reduced to an accepted level. Moreover, the single dendritic growth and the multi-dendritic growth from an undercooled melt and the competitive dendritic growth in a unidirectional solidification were simulated and the dendritic growth features, such as crystallographic orientation, dendrite arm growing and coarsening, side branching, and arms fusion were graphically revealed.