Effect of Variable Density in Dendritic Solidification

Abstract

Dendritic solidification with natural convection caused by solidification contraction and thermal and solutal buoyancy in two-dimensional space is numerically studied using a sharp-interface model. The model is formulated using the finite element method and works directly with primitive variables. Both pure substances and binary alloys are considered. The model solves the coupled energy and solutal concentration equations and the Navier-Stokes equations for incompressible flow while tracking the solid-liquid interface explicitly using marker points. The energy equation is solved on a fixed mesh that covers the whole domain of the solid and liquid phases. The solutal concentration and Navier-Stokes equations are solved on an adaptive mesh of triangular elements that covers only the liquid phase. The adaptive mesh conforms to the interface and the velocity boundary conditions are applied directly at the nodes on the interface. Three examples that consider solidification contraction, thermal buoyancy and all three of contraction and thermal and solutal buoyancy are presented. The simulations show that, for equiaxial dendritic growth into an undercooled pure melt, the contraction-induced convection enhances the solidification rate symmetrically while the thermal convection causes the dendrite to grow faster in the downward direction and slower in the upward direction. For directional solidification with the growth direction perpendicular to the gravity, thermo-solutal buoyancy causes circulatory convection while contraction induces unidirectional flow. The mixed convection alters the concentration distribution in the solutal-boundary layer ahead of the interface and changes the local solidification rate.