Abstract

A two-dimensional model is developed to simulate dendrite growth and movement in a gravity environment. The model combines the features of cellular automaton and lattice Boltzmann methods. Two sets of distribution functions are adopted to calculate the melt flow and solute transport simultaneously. The fluid force acting on the dendrite is calculated by extending the basic flow simulation at the solid-liquid interface. Incorporating the force interaction between melt flow and solidified dendrite into the algorithm for dendritic growth, the movement of a growing dendrite in the flowing melt can be simulated. After model validation, the coupled model has been applied to simulate the evolution and motion of an individual nucleus that grows into a dendrite in the presence of gravitational force. It is found that the dendrite growth is strongly influenced by the fluid flow, producing an asymmetrical morphology that the dendrite grows faster in the upstream direction, whereas largely slower in the downstream direction. The growth process of dendritic side-branches is modeled in a high settling velocity without any artificial noise introduced. The melt flow triggered by the dendrite motion enhances the growth of the dendrite in the downward direction, which in turn influences the subsequent dendritic translation.

Graphical abstract

中文翻译：

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利用晶格玻尔兹曼方法对重力环境中自由枝晶生长进行建模。

摘要

开发了一个二维模型来模拟重力环境中枝晶的生长和运动。该模型结合了元胞自动机和格子Boltzmann方法的特征。采用两组分布函数同时计算熔体流动和溶质运移。通过扩展固液界面上的基本流动模拟来计算作用在枝晶上的流体力。将熔体流和凝固枝晶之间的力相互作用纳入树枝状晶体生长算法中，可以模拟正在生长的枝晶在流动熔体中的运动。在模型验证之后，已将耦合模型应用于模拟单个核的演化和运动，该单个核在存在重力的情况下会长成树枝状晶体。发现树枝状晶体的生长受到流体流动的强烈影响，产生了不对称的形态，即树枝状晶体在上游方向生长较快，而在下游方向生长较慢。树状枝的生长过程以高沉降速度建模，没有引入任何人工噪声。由树枝状晶体运动触发的熔体流动促进了树枝状晶体在向下方向上的生长，这又影响了随后的树枝状晶体的平移。

图形概要