Application of the Meshless Element-Free Galerkin Method to Freckle Formation in Directional Solidification

Abstract

Freckles or channel segregates are the most severe form of the macrosegregation that can occur in unidirectionally solidified superalloy castings used in the manufacturing of gas turbine blades. These defects are formed due to thermosolutal convection during solidification. Mathematical modeling of the solidification process involves the simultaneous solution of the conservation equations of momentum, energy and solute concentration in all regions (liquid, mush and solid). Most numerical simulations of dendritic solidification processes have been performed using finite element or the finite volume techniques. The dependence of these methods on the mesh is not always advantageous for problems in which discontinuities or regions of sharp gradients do not coincide with the original mesh lines. In the present work, the meshless element free Galerkin (EFG) method has been investigated to simulate directional solidification processes in which sharp gradients in the field variables can occur as a result of the formation of channels. Simulations of a multicomponent Ni-Al-Ta-W alloy have been performed in a two dimensional domain. The calculations are started with the alloy in all-liquid state and the growth of the mushy zone is followed in time. A projection method is used to solve the momentum equation which makes the computation more efficient than the previously used penalty method. The accuracy of the EFG results is compared with that of the finite element calculations and the potential advantages of the meshless methods for this type of problems are discussed.