Variational formulation of a quantitative phase-field model for nonisothermal solidification in a multicomponent alloy
Variational formulation of a quantitative phase-field model for nonisothermal solidification in a multicomponent alloy
复制标题
多元合金非等温凝固定量相场模型的变分公式
DOI：
10.1103/physreve.96.033311
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发表时间：
2017
影响因子：
2.4
通讯作者：
Y. Shibuta
中科院分区：
文献类型：
--
作者：
M. Ohno;T. Takaki;Y. Shibuta
本文提出了一个定量相场模型的变分形式，用于描述具有双侧非对称扩散的多元合金的非等温凝固过程。该公式的基本组成部分是液体和固体中守恒变量的扩散通量分别由总熵的函数导数导出，然后这些通量根据局部平衡条件相互关联。在本公式中，相场和守恒变量之间的交叉耦合项自然出现在相场方程和扩散方程中，其中之一对应于反捕获电流，早期非变分模型中的唯象校正项。此外，该公式导致在界面内的张量形式的扩散率。渐近分析表明，该模型可以精确地再现薄界面极限下的自由边界问题。本模型是广泛适用的，因为近似和简化没有正式引入到散装的自由能密度，因为非对角元素的扩散矩阵被明确考虑。此外，我们提出了一个非变分形式的本模型，以实现高的数值性能。对二元合金的非等温凝固进行了数值试验。结果表明，随着界面厚度的减小，计算结果收敛速度很快。
A variational formulation of a quantitative phase-field model is presented for nonisothermal solidification in a multicomponent alloy with two-sided asymmetric diffusion. The essential ingredient of this formulation is that the diffusion fluxes for conserved variables in both the liquid and solid are separately derived from functional derivatives of the total entropy and then these fluxes are related to each other on the basis of the local equilibrium conditions. In the present formulation, the cross-coupling terms between the phase-field and conserved variables naturally arise in the phase-field equation and diffusion equations, one of which corresponds to the antitrapping current, the phenomenological correction term in early nonvariational models. In addition, this formulation results in diffusivities of tensor form inside the interface. Asymptotic analysis demonstrates that this model can exactly reproduce the free-boundary problem in the thin-interface limit. The present model is widely applicable because approximations and simplifications are not formally introduced into the bulk's free energy densities and because off-diagonal elements of the diffusivity matrix are explicitly taken into account. Furthermore, we propose a nonvariational form of the present model to achieve high numerical performance. A numerical test of the nonvariational model is carried out for nonisothermal solidification in a binary alloy. It shows fast convergence of the results with decreasing interface thickness.