Phase-field-lattice Boltzmann method for dendritic growth with melt flow and thermosolutal convection–diffusion
Phase-field-lattice Boltzmann method for dendritic growth with melt flow and thermosolutal convection–diffusion
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DOI：
10.1016/j.cma.2021.114026
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发表时间：
2021-11
影响因子：
7.2
通讯作者：
Nanqiao Wang;David Korba;Zixiang Liu;R. Prabhu;M. Priddy;Sheng-wu Yang;Lei Chen;Like Li
中科院分区：
文献类型：
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作者：
Nanqiao Wang;David Korba;Zixiang Liu;R. Prabhu;M. Priddy;Sheng-wu Yang;Lei Chen;Like Li
提出了一种新的相场模型，该模型建立在格子Boltzmann(LB)方程组中，用于模拟完全耦合熔体流动和热溶质对流扩散的凝固和枝晶生长。由于相场和输运现象的演化都被模拟和集成在同一个LB框架内，该方法保留并结合了相场方法(PFM)和格子Boltzmann方法(LBM)的固有优点。与现有相场模型相比，PFM/LBM模型有几个改进的特点：(1)提出了一种新的相场演化的多重松弛时间(MRT)LB格式，有效地模拟了凝固与熔体流动和热溶质对流扩散的耦合，提高了数值稳定性和精度；(2)对熔体流动和热溶质输运进行了方便的扩散界面处理，无需跟踪界面，即可应用于整个区域；(3)相场、流动、浓度和温度的演化。在LB格式中，微观分布函数水平上的温度场被多重时间尺度策略解耦(尽管它们是完全物理耦合的)，因此可以方便地模拟高Lewis数(液体热扩散系数与溶液扩散系数之比)下的凝固过程。通过等温、等溶和热溶质对流扩散问题的四个数值试验，验证了PFM/LBM模型的适用性和准确性，在相场分布、热溶质分布、枝晶尖端生长速度和半径等方面与文献报道的结果吻合较好。考虑到LBM的高可伸缩性，所提出的PFM/LBM模型可以成为大规模枝晶生长模拟的有力工具。
We propose a new phase-field model formulated within the system of lattice Boltzmann (LB) equation for simulating solidification and dendritic growth with fully coupled melt flow and thermosolutal convection–diffusion. With the evolution of the phase field and the transport phenomena all modeled and integrated within the same LB framework, this method preserves and combines the intrinsic advantages of the phase-field method (PFM) and the lattice Boltzmann method (LBM). Particularly, the present PFM/LBM model has several improved features compared to the existing phase-field models including: (1) a novel multiple-relaxation-time (MRT) LB scheme for the phase-field evolution is proposed to effectively model solidification coupled with melt flow and thermosolutal convection–diffusion with improved numerical stability and accuracy, (2) convenient diffuse interface treatments are implemented for the melt flow and thermosolutal transport which can be applied to the entire domain without tracking the interface, and (3) the evolution of the phase field, flow, concentration, and temperature fields on the level of microscopic distribution functions in the LB schemes is decoupled with a multiple-time-scaling strategy (despite their full physical coupling), thus solidification at high Lewis numbers (ratios of the liquid thermal to solutal diffusivities) can be conveniently modeled. The applicability and accuracy of the present PFM/LBM model are verified with four numerical tests including isothermal, iso-solutal and thermosolutal convection–diffusion problems, where excellent agreement in terms of phase-field and thermosolutal distributions and dendritic tip growth velocity and radius with those reported in the literature is demonstrated. The proposed PFM/LBM model can be an attractive and powerful tool for large-scale dendritic growth simulations given the high scalability of the LBM.