A free surface finite element model for low Froude number mould filling problems on fixed meshes

Abstract

The simulation of low Froude number mould filling problems on fixed meshes presents significant difficulties. As the Froude number decreases, the coupling between the position of the interface and the resulting flow field increases. The usual two-phase flow model provides poor results for such flow. In order to overcome the difficulties, a free surface model that applies boundary conditions at the interface accurately is used. Moreover, the use of wall laws on curved boundaries also fails in the case of low Froude number flows. To solve this second problem, we combine wall laws with ‘do nothing’ boundary conditions. A special feature of our approach is that ‘do nothing’ boundary conditions are only applied in the normal direction. These two key ingredients together with the Level Set method allow us to simulate three-dimensional mould filling problems borrowed directly from the foundry.