Mathematical modeling of macrosegregation during solidification of binary alloy by Control Volume Finite Element Method

Abstract

• A mathematical model for solidification with CVFEM is implemented in a computer code. • Coupled heat and mass transfer in solidification of lead-tin alloy is described. • Thermo-solutal convection and freckle formation in phase-change are reported. • Effects of cavity aspect ratio and cooling direction in solidification are studied. • Macrosegregation maps for Pb-48%Sn alloy in rectangular cavities is investigated. Unsteady coupled natural convective heat and mass transfer with liquid to solid phase change is described to analyze the macrosegregation of a Pb–Sn alloy in a rectangular two-dimensional cavity. The effect of cooling direction is investigated, by comparing the numerical simulation of solidification in rectangular molds with one vertical side cooled and with bottom wall cooling, both with the cold wall temperature changing with time. Fluid mechanics, heat and mass transfer coupled equations with unsteady, convective, diffusion and sources terms are solved with the Control Volume Finite Element Method (CVFEM) in cavities with aspect ratios A = H / B = 1 / 3 , 0.6 and 3. Results for the evolution of the distribution of streamlines, solidification front, isotherms and iso-concentrations are obtained with a code developed to characterize coupled fluid, heat and mass transport phenomena. Complex physical processes such as thermo-solutal convection during solidification, freckle formation and the final pattern of macrosegregation are described in terms of the cavity aspect ratio by the mathematical model. A good description of freckle formation and its relation to direction of cooling and aspect ratio has been obtained by the transient-convective–diffusive mathematical model solved by CVFEM.