枝晶凝固过程溶质再分配的数值模型和快速算法

Numerical model and rapid algorithm of solute redistribution i n dendritic solidification

提出了固熔体合金在枝晶凝固过程中的溶质再分配模型 ,模型由扩散微分方程和溶质守恒方程组成 ,使用Crank Nicholson有限差分法和Trapezoid法则离散控制方程 ,导出了一个计算固相内溶质界面浓度的迭代公式 ,在TDMA算法基础上 ,仅用一步迭代 ,就可以解出凝固过程中的溶质浓度场。用此算法分析了Al 4 .5Cu和Al 1.5Cu 3Zn等合金的溶质再分配过程 ,通过与实验解析解的比较 ,发现数值模型和算法是严密内洽的。

Solute redistribution is controlled by solut e partition and solute diffusion during dendritic solidification of the solid solu tion alloy and is described by solute diffusion differential equation and specie s conserve equation. The Crank Nicholson finite difference scheme and the trapez oid law were used to solve these equations; a new iteration equation was derived to calculate the solute concentration at the solid and liquid interface. The so lute concentration field during solidification was calculated on TDMA-based rap id algorithm. The solute redistribution of Al-4.5Cu and Al-1.5Cu-3Zn alloys w as analyzed by the algorithm and compared with the results of analytical formula , and it is proved that the numerical model is efficient and consistent.