Author's Personal Copy Computers and Mathematics with Applications Lattice Boltzmann Modeling of Dendritic Growth in Forced and Natural Convection
Author's Personal Copy Computers and Mathematics with Applications Lattice Boltzmann Modeling of Dendritic Growth in Forced and Natural Convection
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通讯作者：
D. K. Sun;M. F. Zhu;S. Pan;C. Yang;D. Raabe
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作者：
D. K. Sun;M. F. Zhu;S. Pan;C. Yang;D. Raabe
建立了一个二维(2D)耦合模型，用于模拟强迫对流和自然对流作用下合金凝固过程中的枝晶生长。与传统的基于连续介质的Navier-Stokes(NS)求解方法不同，该模型采用了基于动力学的格子Boltzmann方法(LBM)，该方法通过运动伪粒子分布函数的演化来描述流动动力学，用于流动动力学以及热和溶质输运的数值计算。枝晶生长的模拟采用朱和Stefan escu(ZS)提出的溶质平衡方法，其中固/液界面的演化由局部平衡成分和局部实际液体成分之间的差异来驱动。根据局部温度和曲率计算了局部平衡成分。用格子Bhatnagar-Gross-Krook(LBGK)格式求解LB型方程，得到了由扩散和对流共同控制的局部温度和实际液体组成。通过将模拟结果与分析预测结果进行比较，对模型进行了详细的验证，验证了模型的定量能力。此外，将本模型预测的对流枝晶生长特征与使用NS求解器计算流体流动的朱-Stefan escu和Navier-Stokes(ZS-NS)模型的结果进行了比较。结果表明，两种模型计算的枝晶生长固相分数的演化规律吻合较好。然而，对于模拟熔体对流作用下的枝晶生长，本模型在数值稳定性和计算效率方面具有显著优势。
A two-dimensional (2D) coupled model is developed for the simulation of dendritic growth during alloy solidification in the presence of forced and natural convection. Instead of conventional continuum-based Navier–Stokes (NS) solvers, the present model adopts a kinetic-based lattice Boltzmann method (LBM), which describes flow dynamics by the evolution of distribution functions of moving pseudo-particles, for the numerical computations of flow dynamics as well as thermal and solutal transport. The dendritic growth is modeled using a solutal equilibrium approach previously proposed by Zhu and Stefanescu (ZS), in which the evolution of the solid/liquid interface is driven by the difference between the local equilibrium composition and the local actual liquid composition. The local equilibrium composition is calculated from the local temperature and curvature. The local temperature and actual liquid composition, controlled by both diffusion and convection, are obtained by solving the LB equations using the lattice Bhatnagar–Gross–Krook (LBGK) scheme. Detailed model validation is performed by comparing the simulations with analytical predictions, which demonstrates the quantitative capability of the proposed model. Furthermore, the convective dendritic growth features predicted by the present model are compared with those obtained from the Zhu–Stefanescu and Navier–Stokes (ZS–NS) model, in which the fluid flow is calculated using an NS solver. It is found that the evolution of the solid fraction of dendritic growth calculated by both models coincides well. However, the present model has the significant advantages of numerical stability and computational efficiency for the simulation of dendritic growth with melt convection.