Modelling of macrosegregation with mesosegregates in a binary metallic cast by the diffuse approximate meshless method

Abstract

The solidification of binary metallic alloy (Sn-10%Pb) is simulated in 2D with a diffuse approximate meshless method. The macrosegregation with mesosegregates is described by a coupled set of volume-averaged partial differential equations. The incompressible Newtonian fluid is described by coupled mass and momentum equations and the mushy zone is treated as a Darcy porous media. The energy transport is described with enthalpy formulation and the species transfer is incorporated by considering the Lever rule approximation. The thermo-solutal Boussinesq hypothesis is applied in order to account for the double-diffusive effects in the melt. The mathematical model is solved by a diffusive approximate method on local subdomains with Euler time stepping. Pressure-velocity coupling is incorporated by applying the fractional step method. The instabilities due to the convective terms are smoothed out by applying the upwinding technique. The results are presented on a regular node arrangement and are compared to other benchmark results. The present paper demonstrates that the results calculated with the diffuse approximate meshless method are in good agreement with reference results.