Influence of Discretization of Permeability Term and Mesh Size on the Prediction of Channel Segregations

Macro-and meso-segregations correspond to compositional heterogeneities at the scale of a casting. They develop during the solidification process. One of the parameters that have an essential effect on these segregations is the mush permeability, which is highly nonlinear, and varies over a wide range of magnitudes. We present simulation results for solidification of a Sn-Pb alloy in a two-dimensional cavity, highlighting the role of (i) the numerical interpolation schemes used for the finite-volume discretization of the highly-nonlinear permeability term and (ii) of the mesh size on the prediction of mesosegregations and macrosegregation. We observe that solute-rich liquid flowing through the mushy zone due to thermo-solutal convection results in patches of thin channel structures, which develop into mesosegregations. We notice little sensitivity of the predicted macrosegregation to different discretization schemes for the permeability term. However, we found their influence on the prediction of channel segregates to be significant when using coarse computational grids, customary in the simulation of industrial castings. Mesh refinement is crucial for capturing the complex phenomena in the formation of channel segregates. With a very fine mesh channels have been captured with more than one grid point along their width, allowing the determination of their width.