Combined effect of thermal anisotropy and shrinkage on growth of binary alloy equiaxed crystal

A numerical model for microscale binary alloy solidification is proposed taking the effect of both thermal anisotropy and shrinkage into consideration. The model couples an enthalpy based solidification model with a SIMPLER algorithm based flow solver. The effect of shrinkage is implemented in an incompressible framework with the addition of transient source terms in continuity and pressure correction equations. Shrinkage leads to the generation of shrinkage induced flow which affects the growth of the equiaxed crystal. Thermal anisotropy is modelled by considering anisotmpic conductivity within the solid crystal and implemented by splitting the diffusive part of the energy equation into its equivalent isotropic and anisotropic parts. The presence of thermal anisotropy leads to non-uniform temperature distribution within the solid crystal resulting in the unequal growth rate of dendrite arms. Simulations have been performed to investigate the combined effects of shrinkage and thermal anisotropy on growth and morphology of equiaxed dendrites for different sets of thermal anisotropy ratio (AR) and density ratio (rho(s)/rho(l)). Subsequently, based on parametric analysis, 3D contour diagrams have been developed to summarize the combined effect of thermal anisotropy and density ratio for different undercooling and Lewis number.