Numerical Simulation of Solute Diffusion -Controlled Dendritic Growth with Cellular Automaton Method

"A two-dimensional CAFD model was developed for simulating the solute diffusion-controlled dentritic growth in the low Peclet number regime. Mass conservation and local equilibrium at the solid/liquid interface were solved to determine the growth velocity of interface with consideration of constitutional and curvature undercooling. The modified decentered square growth proposed by Wang et al was adopted to capture the first eight neighboring cells. The comparison between the classic Lipton-Glicksman-Kurz (LGK) analytical model for steady state tip variables and the simulated values showed that the present model was capable of quantitatively determining the dendritic growth, and the simulation tests demonstrated that the effects of the mesh anisotropy in growth kinetics and crystallographic orientation were eliminated. The numerical simulations were performed to the dendritic growth ofFe-0.6%C binary alloy in undercooled melt, and the results showed that the present model could predict the dendrite morphology with artificial growth orientation in acceptable level.IntroductionDuring the solidification of metals and alloys, the dendrite grows from the substance or the undercooling melt and solute redistributes between the dendrite and the interdendritic liquid. The solidification microstructure is close related to the phase and solute evenness and has a close linkage with the properties of final production.In the past few decades, various kinds of deterministic and stochastic models have been developed to predict the evolution of microstructures in solidification, with the fast development of computer power. Among these methods, Phase Field (PF) model [1, 2] has been known as one of the most adequate deterministic models for directly simulating the dendritic growth. However, there is a vital drawback that the PF method requires considerable computation time and is limited to simulate very small domains with a few dendrites [3]. On the other hand, stochastic models, such as Monte Carlo (MC) method [4, 5] and Cellular Automaton (CA) method [6-8], have been usually applied to predict the solidification microstructure evolution. Comparing with the MC method, the dendritic growth kinetics is explicitly integrated in the CA model, while the MC model doesn't. Therefore, the CA method is more reasonable to predict the dendritic growth during the solidification of melt."