Solidification of a binary alloy: finite-element, single-domain simulation and new benchmark solutions
Résumé
A finite-element simulation of binary alloy solidification based on a single-domain formulation is presented and tested. Resolution of phase change is first checked by comparison with the analytical results of Worster (1986) for purely diffusive solidification. Fluid dynamical processes without phase change are then tested by comparison with previous numerical studies of thermal convection in a pure fluid (de Vahl Davis 1983, Mayne et al. 2000, Wan et al. 2001), in a porous medium with a constant porosity (Lauriat & Prasad 1989, Ni et al. 1997) and in a mixed liquid-porous medium with a spatially variable porosity (Ni et al. 1997, Zabaras & Samanta 2004). Finally, new benchmark solutions for simultaneous flow through both fluid and porous domains and for convective solidification processes are presented, based on the similarity solutions in corner-flow geometries recently obtained by Le Bars & Worster (2006). Good agreement is found for all tests, hence validating our physical and numerical methods. More generally, the computations presented here could now be considered as standard and reliable analytical benchmarks for numerical simulations, specifically and independently testing the different processes underlying binary alloy solidification.
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