Abstract A multi-relaxation-time (MRT) lattice Boltzmann (LB) based model is utilized to simulate the dendritic growth with melt convection in solidification of alloys. It models melt convection by the MRT-LB equation and solute transport by a conservation equation with a pseudo-potential function. The D2Q9 lattice vectors are proposed to describe interface advancement in the liquid-solid transition. Effects of undercoolings, interface curvature and preferred growth orientation are incorporated into the model implicitly. After model validation, dendritic growth under several conditions of pure diffusion and melt convection was numerically investigated, and the solidification entropies were proposed to quantitatively characterize the solidification system. The result shows that the growth behavior, microstructure formation and solute segregation are significantly influenced by melt convection. The solidification entropies reflecting complexity of the solidification system are useful to characterize dendritic growth and solute segregation. This work offers a potential solution for studies of microstructure evolution in solidification of alloys.

中文翻译：

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存在熔体对流的二元合金枝晶生长的晶格玻尔兹曼研究

摘要 利用多松弛时间(MRT) 晶格玻尔兹曼(LB) 模型来模拟合金凝固过程中伴随熔体对流的枝晶生长。它通过 MRT-LB 方程模拟熔体对流，并通过具有赝势函数的守恒方程模拟溶质输运。提出了 D2Q9 晶格向量来描述液固转变中的界面进展。过冷度、界面曲率和首选生长方向的影响被隐式地合并到模型中。经过模型验证，对几种纯扩散和熔体对流条件下的枝晶生长进行了数值研究，并提出了凝固熵来定量表征凝固系统。结果表明，生长行为，微结构形成和溶质偏析受熔体对流的显着影响。反映凝固系统复杂性的凝固熵可用于表征枝晶生长和溶质偏析。这项工作为研究合金凝固中的微观结构演变提供了潜在的解决方案。