Lattice Boltzmann modeling of dendritic growth in a forced melt convection

A two-dimensional (2D) lattice Boltzmann-based model is developed to simulate solutal dendritic growth of binary alloys in the presence of forced flow. The model adopts the lattice Boltzmann method (LBM) that describes transport phenomena by the evolution of distribution functions of moving pseudoparticles to numerically solve fluid flow and solute transport governed by both convection and diffusion. Based on the LBM-calculated solutal field, the dynamics of dendritic growth is determined according to a previously proposed local solutal equilibrium approach. After detailed model analysis and validation, the model is applied to simulate single and equiaxed multidendritic growth of Al-Cu alloys with forced convection. The results demonstrate the quantitative, numerically stable and computationally efficient capabilities of the proposed model. It is found that the solute distribution and dendritic growth are strongly influenced by convection, producing asymmetrical dendrites that grow faster in the upstream direction, but mostly slower in the downstream direction.