Phase Field Simulation of Binary Alloy Dendrite Growth Under Thermal- and Forced-Flow Fields: An Implementation of the Parallel–Multigrid Approach

Dendrite growth and morphology evolution during solidification have been studied using a phase field model incorporating melt convection effects, which was solved using a robust and efficient parallel, multigrid computing approach. Single dendrite growth against the flow of the melt was studied under a wide range of growth parameters, including the Lewis number (Le) and the Prandtl number (Pr) that express the relative strengths of thermal diffusivity to solute diffusivity and kinematic viscosity to thermal diffusivity. Multidendrite growths for both columnar and equiaxed cases were investigated, and important physical aspects including solute recirculation, tip splitting, and dendrite tilting against convection have been captured and discussed. The robustness of the parallel–multigrid approach enabled the simulation of dendrite growth for metallic alloys with Le ~ 10⁴ and Pr ~ 10⁻², and the interplay between crystallographic anisotropy and local solid/liquid interfacial conditions due to convection on the tendency for tip splitting was revealed.