Effect of thermal anisotropy on binary alloy dendrite growth

A numerical model to study the effect of thermal anisotropy on binary alloy dendrite growth is presented. The model is based on the volume averaged enthalpy method with explicit surface tension anisotropy for crystal orientation. Thermal anisotropy is incorporated using anisotropic thermal conductivity in the energy equation. This is done by splitting the anisotropic conductivity into two parts, equivalent isotropic conductivity and anisotropic departure source term, enabling the use of a conventional isotropic solver to model anisotropic heat transfer. The proposed model is applied to study the effect of thermal anisotropy ratio on tip velocity, aspect ratio and equivalent radius of an equiaxed grain growing in an undercooled binary alloy melt. It is found that the thermal energy stored in the grain during solidification plays an important role in interface evolution, and thus anisotropic conductivity in the solid affects the grain morphology. There is a consistent increase in the aspect ratio of grains with increase in thermal anisotropy ratio, although the grain volume remains almost invariant. Due to unequal growth rates of the perpendicular arms, severe distortion of the solid crystal is seen at higher thermal anisotropy ratios. The model is further extended to study the growth of multiple dendrites in order to simulate microstructure evolution with thermal anisotropy. It is observed that thermal anisotropy significantly affects the grain morphology at low grain density but has a smaller influence at high grain density as compared to other governing factors such as solute transport.