A unified lattice Boltzmann- phase field scheme for simulations of solutal dendrite growth in the presence of melt convection

A unified lattice Boltzmann (LB) -phase field (PF) scheme is proposed to simulate the dendrite growth of binary alloys in the presence of melt convection. The solute transfer with phase transition is modeled by using the passive scalar equation fitting into the LB framework, and the melt convection is governed by the multiple-relaxation-time (MRT) LB equation. The evolutions of all the fields during solutal dendrite growth are described by the LB equations, and the macroscopic equations can be recovered by the Chapman-Enskog analysis. Model validation and verification are accomplished through comparisons with benchmark solutions and mesh-independence examination. The growths of the single/multiple equiaxial and columnar dendrites are numerically investigated by using the present model. The effects of supersaturation, anisotropy, thermal gradient and forced convection are concluded in terms of morphologies, growing kinetics and solute segregation.