A novel lattice Boltzmann - phase field model of dendritic growth and sedimentation with melt flows

Abstract

The dendrites growing anisotropically during alloy solidification exhibit different crystallographic orientations, accompanied by the sedimentation and collision of free equiaxed dendrites. In this study, a novel lattice Boltzmann - phase field (LB-PF) scheme is developed for modeling simultaneous dendritic growth and motion in the melt of binary alloys. Unit quaternions are employed to handle anisotropy dependent on local crystallographic orientation. The LB method is applied to solve the PF model and melt flow, while the finite volume method is adopted to discretize the solute field. The model is validated by examining the preservation of equiaxed dendrite shapes after rotation and the sedimentation of solid particles in fluid. Using the present scheme, the evolution of solidification microstructures with different preferred crystalline orientations and the sedimentation of free equiaxed dendrites above the stationary columnar dendrites under varying gravity levels are numerically investigated. The preferred orientation significantly affects the transition from planar crystals to columnar dendrites. Motion and melt convection promote dendritic growth along the flow direction and alter its orientation. This work demonstrates the applicability of the LB-PF scheme with quaternions to simulate dendritic growth and sedimentation in both two and three dimensions.