A phase-field-lattice Boltzmann method for modeling motion and growth of a dendrite for binary alloy solidification in the presence of melt convection

In this study, a combination of the lattice Boltzmann method (LBM) and the phase-field method (PFM) is used for modeling simultaneous growth and motion of a dendrite during solidification. PFM is used as a numerical tool to simulate the morphological changes of the solid phase, and the fluid flow of the liquid phase is described by using LBM. The no-slip boundary condition at the liquid-solid interface is satisfied by adding a diffusive-forcing term in the LBM formulation. The equations of motion are solved for tracking the translational and rotational motion of the solid phase. The proposed method is easily implemented on a single Cartesian grid and is suitable for parallel computation. Two-dimensional benchmark computations show that the no-slip boundary condition and the shape preservation condition are satisfied in this method. Then, the present method is applied to the calculation of dendritic growth of a binary alloy under melt convection. Initially, the solid is stationary, and then, the solid moves freely due to the influence of fluid flow. Simultaneous growth and motion are effectively simulated. As a result, it is found that motion and melt convection enhance dendritic growth along the flow direction.