Simulating Die Swell in the Context of Profile Extrusion

Plastics extrusion is a manufacturing process suitable for continuous profiles such as floor skirtings, window frames, and pipes. In industrial applications, extrusion is a large-scale process, financially attractive only for mass products. This is due to the time consuming and costly regulation of the extrusion process and especially, the design of an extrusion die which relies on running-in experiments. The effect of changes in the die geometry on the flow through the die is completely non-intuitive since the flow of plastics melt behaves very nonlinear, e.g. due to viscoelastic effects. This motivates the development of numerical tools capable of simulating the flow through and behind extrusion dies in order to reduce the design costs. The most important design criteria for an extrusion die are a homogeneous velocity distribution at the outflow and homogeneous die swell. Especially, an accurate numerical representation of die swell profiles turns out to be a challenging task. On the one hand, viscoelastic models have to be considered to be able to predict the amount of die swell realistically. On the other hand, the free surface has to be represented. In this particular application interface tracking presents many advantages. However, the standard mesh deformation of a free surface fails if sharp edges, like corners, are part of the die geometry. This is due to inaccurate normal and mesh displacement computations. The aim of this study is the implementation of a numerical method which is able to predict die swell. As a basis, two viscoelastic models, the Oldroyd-B and the Giesekus model, are implemented in a Galerkin/Least-Squares finite element formulation with space-time discretization. Both models are tested in the context of twoand three-dimensional die swell simulations. In addition, a NURBS representation of free surfaces is presented to robustly compute three-dimensional free-surface flows.