A three-dimensional sharp interface model for the quantitative simulation of solutal dendritic growth

A three-dimensional (3-D) sharp interface model is developed to simulate the solutal dendritic growth in the low Péclet number regime. The model adopts a previously proposed solutal equilibrium approach to calculate the evolution of the solid/liquid interface. To describe specific crystallographic orientations of 3-D dendritic growth, a weighted mean curvature algorithm incorporated with the anisotropy of surface energy is proposed, allowing the simulation of 3-D dendrites with various orientations in a straightforward manner. The model validation is performed by comparing the simulations with the analytical predictions and experimental data for both single and multi-dendritic growth, which demonstrates the quantitative capabilities of the proposed model. The model efficiently reproduces realistic 3-D multi-equiaxed and columnar dendrites with various orientations and well-developed side branches.