Modeling of equiaxed solidification is vital for understanding the solidification process of metallic alloys. In this work, an extended literature review is given for the models currently used for equiaxed solidification simulations. Based on this analysis, we present a three-phase multiscale equiaxed solidification model in which some approximations regarding solute transport at microscopic scale are put together in a new way and incorporated into macroscopic transport equations. For the latter, a term relating to the momentum exchange between the two phases is revised, and a modification for the grain packing algorithm is proposed. A modernized model for equiaxed dendrite growth is tested using a case of solidification of Sn-5 wt pct Pb alloy in a parallelepiped cavity that mimics the Hebditch–Hunt experiment. The results obtained using two approaches to calculate diffusion length are presented and compared both with each other and with numerical results from elsewhere. It is demonstrated that diffusion length has a crucial effect on the final segregation pattern.

中文翻译：

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扩散长度对 Hebditch-Hunt 实验配置中浮力流下等轴枝晶凝固建模的影响

等轴凝固建模对于理解金属合金的凝固过程至关重要。在这项工作中，对当前用于等轴凝固模拟的模型进行了扩展文献综述。在此分析的基础上，我们提出了一个三相多尺度等轴凝固模型，其中一些关于微观尺度溶质输运的近似以一种新的方式组合在一起，并纳入宏观输运方程。对于后者，修改了与两相之间的动量交换有关的术语，并提出了对颗粒包装算法的修改。使用 Sn-5 wt pb 合金在模拟 Hebditch-Hunt 实验的平行六面体腔中凝固的案例，对等轴枝晶生长的现代化模型进行了测试。展示了使用两种方法计算扩散长度获得的结果，并相互比较，并与其他地方的数值结果进行比较。结果表明，扩散长度对最终的偏析模式具有至关重要的影响。