Numerical modeling of equiaxed crystal growth in solidification of binary alloys using a lattice Boltzmann-finite volume scheme

A lattice Boltzmann-finite volume scheme is proposed to numerically study the equiaxed crystal growth during binary alloy solidification. In present model, the lattice Boltzmann method is extended to numerically model the growth of equiaxed crystal coupled with solute transfer. An anisotropic lattice Boltzmann equation fitting into the lattice Bhatnagar-Gross-Krook (BGK) scheme is applied to describe the liquid-solid phase changes with interfacial anisotropic effect. Solute transfer is described by the diffusion equation including an anti-trapping current term, which is solved by the finite volume scheme and coupled straightly with the anisotropic lattice Boltzmann equation. After model validation, the hybrid model is applied to numerically simulate the equiaxed crystal growth with single and multiple seeds during Al-Cu solidification. The results demonstrate that the hybrid model is an alternative approach for numerical simulations of equiaxed crystal growth during binary alloy solidification with reliable numerical accuracy and excellent computational efficiency, which has important instructional significance for understanding the underlying mechanism of alloy solidification.