Combined Effect of Thermal Anisotropy and Forced Convection on the Growth of Binary Alloy Equiaxed Dendrites

Abstract

A numerical model has been developed to simulate the growth of an equaixed binary alloy dendrite under the combined effect of thermal anisotropy and forced convection. A semi implicit–explicit approach is used where the velocity and pressure fields are solved implicitly using the SIMPLER algorithm, while energy and species conservation equations are treated explicitly. The effect of thermal anisotropy present in the solid crystal is implemented by the addition of a departure source term in the conventional isotropic heat transfer based energy equation. The departure source represents the anisotropic part of the diffusive term in the isotropic heat transfer based energy equation. Simulations were performed to find the relative effect of convection strength and thermal anisotropy on the growth rate and morphology of a dendrite. Subsequently, parametric studies were conducted to investigate the effect of thermal anisotropy ratio, inlet flow velocity, undercooling temperature, and the relative strength of the thermal to mass diffusivity ratio by analyzing the variation of the equilibrium tip velocity of the top and left arms, the arm length ratio (ALR), and the equivalent grain radius. Based on simulations, a chart has been developed, which demarcates different regimes in which convection or thermal anisotropy is the most dominant factor influencing the dendrite growth rate. The model has also been extended to study the growth of multiple dendrites with random distribution and orientation. This can be useful for the simulation of microstructure evolution under the combined effect of convection and thermal anisotropy.