Sensitivity of mesh spacing on simulating macrosegregation during directional solidification of a superalloy

The sensitivity of mesh spacing on simulations of macrosegregation, particularly ‘freckles’, during vertical directional solidification of a superalloy in a rectangular mold was systematically analyzed to achieve accurate predictions in finite element calculations. It was observed that a coarser mesh spacing in the x-direction horizontal tends to minimize the simulated macrosegregation, whereas a coarser mesh spacing in the y-direction vertical artificially tends to make the system appear to have more macrosegregation. When solidification conditions either lead to a well-established freckling case or to a well-established non-freckling case, the simulated results are not sensitive to the mesh spacing provided the elements are no larger than about 2d1 by 2 D/V and 3d1 by 4 D/V respectively, where d1 is the primary dendrite arm spacing, D is the diffusivity of the alloy solute with the smallest diffusivity in the liquid, and V is the growth rate. However, when solidification conditions are very close to the transition between freckling and no freckling, the simulated results are sensitive to the mesh spacing, especially in the y-direction. Based on the mesh sensitivity analysis from the two-dimensional simulations of rectangular castings of René N5, the mesh with element dimensions no larger than 2d1 in the x-direction and 1.5 D/V in the y-direction are recommended as the most stringent element size.