Simulation of three-dimensional polymer mould filling processes using a pseudo-concentration method

Abstract

Mould filling processes, in which a material flow front advances through a mould, are typical examplesof moving boundary problems. The moving boundary is accompanied by a moving contact line at themould walls causing, from a macroscopic modelling viewpoint, a stress singularity. In order to be able tosimulate such processes, the moving boundary and moving contact line problem must be overcome. Anumerical model for both two- and three-dimensional mould filling simulations has been developed. Itemploys a pseudo-concentration method in order to avoid elaborate three-dimensional remeshing, andhas been implemented in a finite element program. The moving contact line problem has been overcomeby employing a Robin boundary condition at the mould walls, which can be turned into a Dirichlet(no-slip)! or a Neumann (free-slip) boundary condition depending on the local pseudo-concentration.Simulation results for two-dimensional test cases demonstrate the model?s ability to deal with flowphenomena such as fountain flow and flow in bifurcations. The method is by no means limited totwo-dimensional flows, as is shown by a pilot simulation for a simple three-dimensional mould. Thereverse problem of mould filling is the displacement of a viscous fluid in a tube by a less viscous fluid,which has had considerable attention since the 1960?s. Simulation results for this problem are in goodagreement with results from the literature