A New Growth Kinetics in Simulation of Dendrite Growth by Cellular Automaton Method

Abstract

A modified cellular automaton model was proposed to simulate the dendrite growth of alloy. Different from previous models, this model used neither an analytical equation(such as KGT model) nor an interface solute gradient equation to solve the velocity of solid-liquid interface, but used the interface solute and energy conservation and thermodynamic equilibrium condition to describe the solid/liquid interface growth kinetics process. In present model, once the temperature field and solute field were solved by finite different method in the entire domain, the material thermodynamic properties can be substituted into four algebraic equations to easily determine the variation of solid fraction, interface temperature and solute concentration, instead of calculating interface moving velocity. As a result, the complexity of the calculation can be largely reduced. The simulated dendrite growth was in a good agreement with the Lipton–Glicksman–Kurz (LGK) model for free dendritic growth in undercooled melts.