Computational Modeling of Heat Mass and Solute Transport in Directional Solidification Processes

"A computational model to investigate solid/liquid phase change transitions for binary alloy under directional solidification is presented. Conservation equations are developed by using an homogeneous formulation. A second order accuracy method of time and space based on finite volume approximation has been evaluated by comparing results to spectral solution for time-dependent solutal convection developping in a melted alloy. For extended model to solid/liquid interface effects time amplification of solutal perturbation injected near the interface is described before considering solutal convection is melt.IntroductionThe enthalpy method gives a front fixing approach for energy equation without introducing coordinate transformation. The interfare position is recovered a posteriori [1]. A number of authors have extended this approach so as to include the convection phenomena within the two phase 'mushy region' [2, 3, 4, 5, 6].We have developed a time-dependent enthalpy-porosity formulation for directional solidification [4, 6, 8]. The interaction between solid and liquid phases is modelised by a Darcien type force in the phase change area. The behaviour of the melt is similar with the flow of an incompressible fluid in a porous medium. This force is proportional to the relative phase velocity. It corresponds to a damping force depending on the anisotropic permeability of the 'mushy zone'. The permeability depends on the liquid fraction and on the size of·solidification microstructures. An informative discussion of a new slant on the general approach of continuum mechanics needed to analyze the formation of mushy zone is given in [12]. The method is extended to the presence of species diffusion: the solutal Stefan condition which expresses the solute incorporation or rejection across the interface is accounted implicitly in a species equation valid in all the domain [14, 15]."