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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.
A numerical simulation model under low Péclet number of conditions dimensional solute dendritic growth. In this model solute equilibrium method Zhu and Stefanescu proposed, i.e. calculating the solid / liquid interface evolution from the difference between the equilibrium concentration of the solid / liquid interface and the actual concentration of the driving force of the interface is determined by the equilibrium concentration of the interface temperature and curvature, the actual concentration of the solute is obtained by numerically solving the diffusion equations using finite difference method. the method can be described quantitatively reasonably dendrite from an initial non-steady state to In order to describe the three-dimensional dendritic growth with different crystallographic orientation, a weighted average curvature algorithm is proposed for calculating the curvature of the solid / liquid interface, The algorithm of curvature is coupled with the anisotropy of interface energy.The algorithm is simple and easy to implement and can be easily extended from two-dimensional to three-dimensional system.In order to validate the model, the simulated steady-state growth data of dendrite tip and theoretical model The results show that the steady-state growth rate and radius of the dendrite tip of simulated Al-2wt% Cu alloy are close to those of undercooling Lipton-Glicksman-Kurz analytical results of the model prediction. Simulation of the steady-state tip dendrite morphology, dendritic tip found that three-dimensional non-axisymmetric to four symmetric manner offset from a rotational paraboloid. Finally, application of the established model The three-dimensional multidendritic growth morphology with developed branches and different crystallographic orientations was simulated.