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Effect of discretization of permeability term and mesh size on macro- and meso-segregation predictions

The effect of interpolation schemes used for discretization of permeability in numerical simulations on macrosegregation and channel segregation (mesosegregation) during solidification has been studied. The different ways to discretize the permeability term and its effect on the interdendritic velocity are illustrated by a simplified 1D model which solves the Darcy equation for a porous medium. The Darcy equation is solved numerically using the SIMPLE algorithm for the coupled velocity–pressure fields. For this simplified case, an analytical reference solution can also be obtained. In the numerical solution four different interpolation schemes for permeability discretization have been employed, and the results obtained are compared. For coarse mesh, different interpolation schemes produce large differences from the analytical reference solution. We thereafter, present simulation results for solidification of Sn–Pb alloy in a two-dimensional rectangular cavity using different discretization schemes. It is observed that solute-rich liquid flowing towards the bottom of the rectangular cavity in the mushy zone due to thermosolutal convection results in patches of thin structure known as channels. These channels are formed by perturbation by the interdendritic fluid flow in the mushy zone and in some cases by the localized remelting in some portions of the solid/mush interface. The role of discretization schemes and mesh size on the formation of channel segregates and macrosegregation is discussed.