Simulation method based on phase-field lattice Boltzmann model for long-distance sedimentation of single equiaxed dendrite

In solidification of metals and alloys under earth’s gravity, the growing free equiaxed dendrites either settle or float because of the difference between the solid and liquid densities. In this study, we developed a two-dimensional computational method that can efficiently simulate the growth of free dendrite settling over a long distance. In the developed method, the growth of the dendrite is expressed by a phase-field method, the liquid flow is computed by a lattice Boltzmann method, and the settling of dendrite is expressed by equations of motion. A moving-frame algorithm is employed to track the dendrite settling over a long distance. The computation is accelerated using a multi-level mesh method and GPU computing. The validity of the developed method was evaluated through simulation of the settling of a single circular particle. Specifically, using the developed method, we simulated the growth of a single dendrite in an isothermal undercooled melt of a binary alloy under gravity, and evaluated the time evolutions of the growth velocity of the primary arms, settling velocity, and crystal orientation of the dendrite. The results confirmed that the developed computational method can efficiently express the dendrite growth and settling over a long distance at a reasonable computational cost.