Numerical modelling of equiaxed dendritic growth with sedimentation in the melt of binary alloys by using an anisotropic lattice Boltzmann-phase field model

An anisotropic lattice Boltzmann-phase field (LB-PF) model is developed to simulate the equiaxed dendritic growth with sedimentation in the melt of binary alloys under the effect of gravity. In present model, the anisotropic lattice Boltzmann scheme is applied to solve the phase field equation describing the evolution of dendritic morphologies, while the finite volume scheme is employed to solve the advection-diffusion equation of solute with anti-trapping current. The multiple-relaxation-time lattice Boltzmann scheme is employed to compute the complex melt flow. Validity of the present model is demonstrated by the quantitative agreement between the references and simulations of circular particle sedimentation, while the shape preservation performance is verified by the simulations of non-deformation dendrite movement. Then, the effects of solid-liquid density ratio, initial supersaturation and preferred crystallographic orientation on the growth and sedimentation behaviour of a single equiaxed dendrite in the supersaturated melt of binary alloys are numerically investigated. Moreover, the growth and sedimentation process of dendrites with multiple nuclei is successfully simulated. The results demonstrate that the present model has great application potential in the simulations of dendritic growth with sedimentation of binary alloys, which has important instructional significance for regulating the microscopic dendritic morphologies during solidification, and further improving the macroscopic mechanical properties of final components.