Simultaneous pressure-velocity coupling in the two-phase zone for solidification shrinkage in an open cavity

Binary constituent shrinkage-induced flows during alloy solidification are examined with a continuum mixture model. The multiphase conservation equations are solved with a control-volume-based finite-element method. Free surface flow capabilities and an elliptic grid transformation scheme accommodate volumetric contraction due to the density differences between solid and liquid phases. The procedure treats the multiphase mass and momentum transport in an implicit manner with a direct velocity-pressure coupling. Boundary conditions at the free surface account for the gas pressure and external stresses. Numerical results for both one-dimensional and two-dimensional solidification problems are examined and compared with analytical and experimental results.