Finite Element Simulation of Turbulent Heat Transfer in Mold-Filling Problems

Abstract

Abstract This paper presents a finite element solution algorithm for solving the turbulent heat transfer and fluid flow on three-dimensional industrial mold-filling problems. The problems of interest present unusual challenges for both the physical modeling and the solution algorithm. The heat transfer on high Reynolds number transient turbulent flow with free surfaces has to be computed on complex 3D geometries. In this work a segregated algorithm is used to solve the Navier-Stokes, energy, turbulence and front tracking equations. The Streamline Upwind Petrov-Galerkin method is used to obtain stable solutions to convection dominated problems. Turbulence is modeled using a one-equation turbulence model and the k-ϵ two-equation model with wall functions. Turbulence equations are solved for the natural logarithm of the turbulence variables. The change of dependent variables allows for good predictions even on coarse meshes. The forced heat transfer in the cavity partly filled with fluid and partly filled with air is coupled with the solution of the conduction equation in the mold. The position of the flow front in the mold cavity is computed using a level set approach. Finally, equations are integrated in time using second order accurate schemes. The methodology presents the robustness and cost effectiveness needed to tackle such complex industrial applications.