Numerical simulation of three-dimensional dendritic growth of alloy Part I—model development and test
Numerical simulation of three-dimensional dendritic growth of alloy Part I—model development and test
复制标题
合金三维枝晶生长数值模拟第一部分——模型开发与测试
DOI：
10.1007/s11661-015-3304-7
复制
发表时间：
2016
影响因子：
2.8
通讯作者：
Miaoyong Zhu
中科院分区：
文献类型：
--
作者：
Weiling Wang;Sen Luo;Miaoyong Zhu
为了提高描述合金枝晶生长的三维元胞自动机有限体积法(CA-FVM)模型的计算效率，引入了块修正技术(BCT)和并行计算方法。在此基础上，对优化后的程序处理熔体流动和传热问题的效率进行了一系列的研究。此外，通过对熔体流动和热传导问题的解与解析方程和商业软件的结果的比较，对本程序的精度进行了评估。此外，通过将等轴枝晶尖端的稳定生长参数和柱状枝晶的形态和二次枝晶间距(SDAS)与LGK分析模型和高碳钢定向凝固实验结果进行比较，对CA模型的性能进行了评价。结果表明，随着3DBCT的引入，序列三对角矩阵算法(TDMA)码的迭代过程从起伏型变为光滑型，从而显著降低了运算量。此外，在本文编制的程序中，三维BCT中一次迭代的并行Jacobi程序被证明是最有效的，因此，它被用于模拟合金的三维枝晶生长。计算得到的速度分布和温度变化与解析方程和商业软件的计算结果吻合较好。当过冷度为6~7K时，预测的稳态尖端速度与LGK分析模型相吻合。此外，预测的高碳Fe-C合金定向凝固过程中的柱状枝晶形态和SDAS与实验结果相吻合。
To improve the computational efficiency of the three-dimensional (3D) cellular-automaton–finite-volume-method (CA-FVM) model for describing the dendritic growth of alloy, the block-correction technique (BCT) and the parallel computation approach are introduced. Accordingly, a serial of investigations on the efficiency of the optimized codes in dealing with the designed cases for the melt flow and the heat transfer problems is carried out. Moreover, the accuracy of the present codes is evaluated by the comparisons between the solution to the melt flow and the heat transfer problems and the results from analytical equations and the commercial software. Additionally, the capability of the present CA model is evaluated by comparing the steady growth parameters of the equiaxed dendritic tip and the morphology and the secondary dendrite arm spacing (SDAS) of columnar dendrites with the LGK analytical model and the experimental results of the unidirectional solidification of high-carbon steels. The results show that with the introduction of the 3D BCT, the iteration process of the serial tri-diagonal matrix algorithm (TDMA) code changes from the fluctuation type to the smooth one, and thus, the computational cost is reduced significantly. Moreover, the parallel Jacobi code with one two-dimensional (2D) iteration in 3D BCT is proved to be the most efficient one among the codes compiled in the present work, and therefore, accordingly it is employed to simulate the 3D dendritic growth of alloys. The calculated velocity distribution and temperature variation agree well with the results from the analytical equations and the commercial software. The predicted steady tip velocities agree with the LGK analytical model as the undercooling is 6 K to 7 K. Moreover, the predicted columnar dendritic morphology and SDAS of high-carbon Fe-C alloys during the unidirectional solidification agree with the experimental results.