A lattice Boltzmann study on dendritic growth of a binary alloy in the presence of melt convection

A multi-relaxation-time (MRT) lattice Boltzmann (LB) based model is utilized to simulate the dendritic growth with melt convection in solidification of alloys. It models melt convection by the MRT-LB equation and solute transport by a conservation equation with a pseudo-potential function. The D2Q9 lattice vectors are proposed to describe interface advancement in the liquid-solid transition. Effects of undercoolings, interface curvature and preferred growth orientation are incorporated into the model implicitly. After model validation, dendritic growth under several conditions of pure diffusion and melt convection was numerically investigated, and the solidification entropies were proposed to quantitatively characterize the solidification system. The result shows that the growth behavior, microstructure formation and solute segregation are significantly influenced by melt convection. The solidification entropies reflecting complexity of the solidification system are useful to characterize dendritic growth and solute segregation. This work offers a potential solution for studies of microstructure evolution in solidification of alloys.