Numerical simulation on dendritic growth of Al–Cu alloy under convection based on the cellular automaton lattice Boltzmann method

Abstract

A numerical model is developed by coupling the cellular automaton (CA) method and the lattice Boltzmann method (LBM) to simulate the dendritic growth of Al–Cu alloy in both two and three dimensions. An improved decentered square algorithm is proposed to overcome the artificial anisotropy induced by the CA cells and to realize simulation of dendritic growth with arbitrary orientations. Based on the established CA-LBM model, effects of forced convection and gravity-driven natural convection on dendritic growth are studied. The simulation results show that the blocking effect of dendrites on melt flow is advanced with a larger number of seeds. The competitive growth of the converging columnar dendrites is determined by the interaction between heat flow and forced convection. Gravity-driven natural convection leads to highly asymmetric growth of equiaxed dendrites. With sinking downwards of the heavy solute, chimney-like or mushroom-like solute plumes are formed in the melt in front of the columnar dendrites when they grow along the gravitational direction. More details on dendritic growth of Al–Cu alloy under convection are revealed by 3D simulations.