A CA-LBM model for simulating dendrite growth with forced convection

Abstract

A two-dimensional coupled model of the cellular automaton (CA) and the lattice Boltzmann method (LBM) was developed to simulate the solute dendrite growth of Fe–C–Mn–S alloy in the presence of forced convection. The model describes the transport phenomenon by the evolution of moving pseudo-particles distribution functions and utilizes the LBM to solve fluid flow and solute transport under forced convection numerically. Based on the solute field calculated by the CA technique, the dynamics of dendrite growth were determined by the previously proposed local solute balance method. The accuracy of the forced convection dendrite growth model was verified by comparing the CA-LBM model with Lipton–Glicksman–Kurz analytical model. It is revealed that the dendrite symmetry structure is destroyed compared to free diffusion, and the upstream arm is more developed than the downstream arm of the dendrite. The enriched solute segregates more at the downstream side than at the upstream side of the dendrite. The length of the upstream dendrite arm increases firstly and then becomes stable with the increase in the flow velocity, the dendrite necking is restrained, and the vertical dendrite arm becomes longer.