Numerical simulation of filling and solidification of permanent mold castings

Filling of a mold is an essential part of the permanent mold casting process and affects significantly the heat transfer and solidification of the melt. For this reason, accurate prediction of the temperature field in permanent mold castings can be achieved only by including simulation of filling in the analysis. In this work we consider two problems dealing with the mold-filling analysis which are of great interest for both the research community and the metal-casting industry. The first problem consists of the development of finite element formulations of the Level Set interface tracking method. The main motivation here is to develop a high-order interface tracking scheme to model industrial mold-filling processes on unstructured triangulated grids. The second problem consists of three-dimensional numerical modeling and validation of permanent mold castings produced under industrial conditions. The purpose is to assess the accuracy and the computational cost of this type of simulations.; In the first part of the work, we develop and test two finite element formulations of the level set method: the Steamline-Upwind/Petrov-Galerkin (SUPG) and the Runge-Kutta Discontinuous Galerkin (RKDG) schemes. In the SUPG scheme the numerical diffusion inherently present in the scheme is reduced by implementing a special mass-correction procedure. The RKDG level set formulation is an original model and presents the first attempt to apply the discontinuous Galerkin Finite Element method for interface tracking. The performances of the schemes are demonstrated on two-dimensional problems. Both level set formulations allow easy extension to three-dimensional simulations.; In the second part of the work we use the finite element method and the volume-of-fluid interface tracking scheme to model the filling and solidification of an industrial permanent casting. The work is performed for the casting of an actual automotive piston produced from an aluminum alloy. Comparisons of numerical results to available experimental data show that the formulated model provides a solution of acceptable accuracy despite some uncertainty in material properties and boundary conditions. This implies that the model can be a viable tool to design permanent molds.