Dendritic solidification of binary alloys with free and forced convection

Dendritic solidification with forced convection and free convection driven by contraction and thermosolutal buoyancy is simulated in two-dimensional space using a sharp-interface model. Both pure substances and alloys are considered. The model is formulated using the finite element method and works directly with primitive variables. The coupled energy- and solutal concentration-equations, along with the Navier-Stokes equations for incompressible flow, are solved using different meshes. Temperature is solved in a fixed mesh that covers the whole domain (solid + liquid) where the solid-liquid interface is explicitly tracked using marker points. The concentration and momentum equations are solved in the liquid region using an adaptive mesh of triangular elements that conforms to the interface. The velocity boundary conditions are applied directly on the interface. The model is validated using a series of problems that have analytical, experimental and numerical results. Four simulations are presented: (1) crystal growth of succinonitrile with thermal convection under two small undercoolings; (2) dendritic growth into an undercooled pure melt with a uniform forced flow; (3) equiaxial dendritic growth of a pure substance and an alloy with contraction-induced convection; and (4) directional solidification of Pb-0.2 wt% Sb alloy with convection driven by the combined action of contraction, thermal and solutal buoyancy. Some of the simulation results are compared to those reported using other methods including the phase-field method; others are new. In each case, the effects of convection on dendritic solidification are analysed.