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.
Highlights
Solidification is a phase change process that combines many different research areas ranging from continuum mechanics to thermodynamics
The present paper demonstrates that the results calculated with the diffuse approximate meshless method are in good agreement with reference results
Among many varieties of meshless methods developed in recent years [2,3,4,5,6], the diffuse approximate method (DAM) [7] is chosen for the model presented in this paper
Summary
Solidification is a phase change process that combines many different research areas ranging from continuum mechanics to thermodynamics. The growth in the popularity of this research topic is mainly due to the requirements from industry, those involving casting, as the solidification process plays an important role in the quality of the final cast product. Among many varieties of meshless methods developed in recent years [2,3,4,5,6], the diffuse approximate method (DAM) [7] is chosen for the model presented in this paper. A benchmark test case devised for macrosegregation with mesosegragtes in binary metallic alloy by [12] was chosen and tested for Sn-10%Pb. The problem describes the solidification of binary alloy in a rectangular cavity. The problem describes the solidification of binary alloy in a rectangular cavity It is described by a set of tightly coupled momentum, mass, energy and solute transport equations. The present paper provides the results for Sn-10%Pb alloy and compares them to reference results calculated in [14]
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