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

Abstract

:Macro-and meso-segregations correspond to heterogeneities of composition at the scale of a casting. They develop during the solidification. One of the parameters that has an essential effect on these segregations is the mush permeability which varies over a wide range of magnitude. We present simulation results for solidification of Sn-Pb alloy in a two-dimensional cavity. The role of discretization schemes and mesh size on the formation of channel segregates and macrosegregation is discussed.

Channel segregation during columnar solidification influence of inertia

“…In the next section, numerical simulations illustrate the contribution of this inertia correction term. For conciseness, the whole solidification model is not presented here and all the details are provided in the following references [3,9,28].…”

“…This configuration corresponds to the benchmark problem defined by Hebditch and Hunt [23] where channel segregations were experimentally and numerically observed [3,6,9]. The cavity is cooled from the left side and the remaining three sides are thermally insulated.…”

“…Their characteristic length scales strongly affect the homogeneity of the casting and therefore the quality and the mechanical properties of the solidifying product can be altered. Channel segregates generally result from instabilities taking place in the interfacial region due to interdendritic liquid flow and by eventual local remelting in the vicinity of the tip of the dendrites [1][2][3][4][5][6][7][8][9]. The formation of defects in metal casting processes critically depends on the permeability of the mushy zone and on the interdendritic liquid flow.…”

“…In this context, momentum transport is given by the averaged Navier-Stokes equation where the drag in the porous region is taken into account by the Darcy term [3][4][5][6][7][8][9][10][11][12][13][14][15]16]. If the pore Reynolds number Re vd is larger than unity in some locations of the mushy zone, inertia has to be taken into account through the Forchheimer correction term [17][18][19][20][21].…”

“…If the pore Reynolds number Re vd is larger than unity in some locations of the mushy zone, inertia has to be taken into account through the Forchheimer correction term [17][18][19][20][21]. Although many numerical studies have been performed to investigate channel segregation [1][2][3][4][5][6][7][8][9]12], little attention has been given to the influence of inertia on this phenomena. This is the objective of the present study to consider the influence of the Forchheimer correction term on the flow in the mush and on the predictions of channel segregations applied to solidification of Sn-Pb alloy in a 2D rectangular cavity.…”