Modeling of free dendritic growth in a gravity environment by lattice Boltzmann method

A two-dimensional model is developed to simulate dendrite growth and movement in a gravity environment. The model combines the features of cellular automaton and lattice Boltzmann methods. Two sets of distribution functions are adopted to calculate the melt flow and solute transport simultaneously. The fluid force acting on the dendrite is calculated by extending the basic flow simulation at the solid-liquid interface. Incorporating the force interaction between melt flow and solidified dendrite into the algorithm for dendritic growth, the movement of a growing dendrite in the flowing melt can be simulated. After model validation, the coupled model has been applied to simulate the evolution and motion of an individual nucleus that grows into a dendrite in the presence of gravitational force. It is found that the dendrite growth is strongly influenced by the fluid flow, producing an asymmetrical morphology that the dendrite grows faster in the upstream direction, whereas largely slower in the downstream direction. The growth process of dendritic side-branches is modeled in a high settling velocity without any artificial noise introduced. The melt flow triggered by the dendrite motion enhances the growth of the dendrite in the downward direction, which in turn influences the subsequent dendritic translation.