三维溶质枝晶生长数值模拟

建立了在低Péclet数条件下三维溶质枝晶生长的数值模拟模型.该模型采用Zhu和Stefanescu 提出的溶质平衡方法，即根据固/液界面的平衡浓度和实际浓度之差计算固/液界面演化的驱动力.界面的平衡浓度由界面温度和曲率所确定，实际浓度通过采用有限差分法对溶质扩散控制方程进行数值求解而获得.该方法能够合理定量地描述枝晶从初始的非稳态到稳态的生长过程，并且具有较高的计算效率.为了描述具有不同晶体学取向的三维枝晶生长，提出了一种权值平均曲率算法用于计算固/液界面的曲率，在权值平均曲率的算法中耦合了界面能各向异性的因素.该算法简单易实现，并易于从二维推广到三维系统.为了对模型进行验证，将模拟的枝晶尖端稳态生长数据和理论模型的预测结果进行了比较.结果表明，模拟的Al-2wt%Cu合金枝晶尖端稳态生长速率和半径随过冷度的变化接近于Lipton-Glicksman-Kurz解析模型的预测结果.模拟分析了稳态枝晶尖端的形貌，发现三维枝晶尖端是非轴对称的，以四次对称的方式偏离旋转抛物面.最后，应用所建立的模型模拟出具有发达分枝和不同晶体学取向的三维等轴多枝晶生长形貌. 关键词： 微观组织模拟 溶质枝晶生长 权值平均曲率 三维

Modelling of solutal dendritic growth in three dimensions

A three-dimensional （3D） model for the simulation of solutal dendritic growth in the low Pclet number region is presented. In the model is adopted a solutal equilibrium approach previously proposed by Zhu and Stefanescu to calculate the evolution of the solid/liquid（SL） interface， which allows the accurate simulation of dendritic growth from the initial unstable stage to the steady-state stage with a good computational efficiency. In this approach， the kinetics of dendritic growth is driven by the difference between the local equilibrium composition， calculated from the local temperature and curvature， and the local actual liquid composition，obtained by solving the solutal transport equation. To describe the specific crystallographic orientation of 3D dendritic growth， a weighted mean curvature （WMC） algorithm， which is incorporated with the anisotropy of surface tension， is proposed to calculate the local SL interface curvature. This approach is convenient to be implemented and to make the transformation for WMC calculation from two to three dimensions. The model is verified by the comparison of our numerical resuets with the analytical ones. The simulated steady-state tip velocity and radius varying with the degree of undercooling of an Al-2wt%Cu alloy are found to be close to the ones predicted by the Lipton-Glicksman-Kurz analytical model. The steady-state morphology of the needle dendrite tip is analyzed. It is found that the tip is nonaxisymmetric and deviates from a paraboloid in the manner of the fourfold symmetry. Finally， the simulated 3D multi-equiaxed dendrites with various crystallographic orientations are presented.