基于改进元胞自动机方法的强制对流作用下三维枝晶生长的数值模拟

建立了一种改进的元胞自动机模型来模拟熔体对流条件下的二元合金三维枝晶的生长。模型中考虑了界面能各向异性和溶质扩散对固/液界面推移的影响,在同一套网格中耦合求解质量传输和液相流动方程,从而可以模拟溶质扩散和熔体对流之间的相互作用。使用该模型模拟了一定过冷度条件下,强制对流对Al-7%Si(质量分数,下同)合金三维枝晶生长形貌的影响。模拟结果表明,熔体强制对流导致迎流侧尖端溶质富集层减薄,枝晶生长出现了迎流生长现象。将模拟得到的溶质过饱和度与Oseen-Ivantsov解析解进行对比,当流速较大时两者吻合较好。同时模拟了三维和二维强制对流作用下枝晶生长形貌的演化,由于三维条件下对流使得熔体能够绕过垂直于对流方向的一次枝晶臂主干将溶质带到背流侧,而二维条件下只能绕过垂直方向一次臂的尖端,因此三维MCA模型能更准确地反映强制对流对枝晶生长的影响。

Numerical Simulation of 3-D Dendritic Growth under Forced Convection Using the Modified Cellular Automaton Method

In order to simulate three-dimensional dendritic evolution of binary alloys under melt convection, a modified cellular automaton (MCA) model was developed. With considering the influence of surface energy anisotropy and solute diffusion on the evolution of solid/liquid interface, and solving the mass transport equation coupled with Navier-Stokes equations on the same grid, the MCA model could simulate the interaction between solute diffusion and melt convection. In this study, 3-D dendritic growth of Al-7wt%Si alloy was simulated with forced convection at constant undercooling by the MCA model. It is found that the upstream tip of the dendrite grows faster than that of the downstream tip under forced convection, due to lower solute concentration and larger solute gradient in the front of the upstream interface caused by forced convection. Meanwhile, the simulated dimensionless solute supersaturation agrees well with Oseen-Ivantsov solution at higher forced convection. The effect of forced convection on dendrite morphology was also studied under 3-D and 2-D simulation. The solute enriched at the upstream frontier of solid/liquid interface is washed away bypassing the primary dendrite arms from the upstream to downstream direction by 3-D forced convection. However, in 2-D convection, the solute could only go over the tips of the perpendicular dendrite arms from the upstream to downstream direction. Therefore, the 3-D MCA model is more accurate in simulating the influence of forced convection on dendritic growth than a 2-D model.