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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.

Freckle formation during directional solidification of binary alloy is a well-researched subject area. However, the influence of shrinkage induced flow (SIF) on freckling phenomena is barely reported. The focus of this work is to investigate this effect during bottom-up solidification of binary alloys. A fixed grid-based numerical scheme involving volume averaging of conserved parameters is proposed. The solidification geometry under consideration is a two-dimensional mold cavity with a central riser allowing continuous melt flow into the cavity. Model validation is obtained against existing numerical results involving directional solidification of Al-4.1 wt. % Cu alloy. However, heavier solute (Cu) rejection in the melt during solidification renders the validation case study devoid of freckling phenomena. The postvalidation investigations involve bottom up solidification of Al-30 wt. % Mg alloy with lighter solute (Mg) rejection, leading to solutal instability and freckle formation. The effect of SIF on solutal instability, channel formation, and overall macro-segregation is investigated. The intensity of SIF hinges on both cooling condition and opening size. The penetration depth of SIF into the solidification domain gives rise to either early or late onset of solutal instability. SIF penetration depth till the melt domain adjacent to the mushy layer promotes early onset of solutal instability. However, SIF penetration into the mushy layer itself triggers redistribution of solute-rich melt inside this layer, leading to delayed onset of solutal instability. Since the macro-segregation is a direct consequence of advection of solute inside and adjacent to the mushy region, the influence of SIF is manifested by unprecedented macro-segregation pattern.

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