(清华大学 机械工程系 先进成形制造教育部重点实验室，北京 100084)
摘 要: 通过耦合溶质扩散方程，并考虑成分过冷和曲率过冷对界面平衡溶质成分的影响，建立改进的元胞自动机模型来模拟溶质扩散控制的立方晶系合金的枝晶生长过程。模型在计算固液界面生长速率时考虑立方晶系枝晶择优生长取向 的影响，同时采用斜中心差分格式对界面生长速率方程进行离散，从而能够模拟择优生长取向与坐标轴成不同夹角的枝晶生长形貌演变。为验证模型的可靠性，模拟NH4Cl-H2O系透明合金单个等轴枝晶以及不同择优生长取向角的多个等轴枝晶和柱状枝晶的形貌演化，模拟结果与实验结果吻合较好。
关键字: 改进的元胞自动机；择优生长取向；枝晶生长；数值模拟
（Key Laboratory for Advanced Materials Processing Technology, Ministry of Education,
Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China）
Abstract:By coupling solute diffusion equation, and considering the effects of constitutional and curvature undercooling on interface equilibrium composition, a modified cellular automaton model (MCA) was proposed to simulate dendrite growth controlled by solute diffusion for cubic metals. The model considers the influence of preferred growth orientation on the normal velocity of solid and liquid interface for cubic metals. Meanwhile, a skew central difference scheme was used to discrete the normal velocity of solid and liquid interface. Therefore, the MCA model could simulate the dendrite morphology with preferred growth orientation misaligned with the x-axis. In order to validate the MCA model, single equiaxed dendrite, multiple equiaxed dendrites and columnar dendrites of NH4Cl-H2O transparent alloy with different preferred growth orientation angles ranging from 0° to 90° with respect to the horizontal direction were simulated, which has good agreement with the experimental data.
Key words: modified cellular automaton; preferred growth direction; dendritic growth; numerical simulation
