Die shape optimization for extrudate swell using feedback control

In this paper we propose a novel approach to solve the inverse problem of three-dimensional die design for extrudate swell, using a real-time active control scheme. To this end, we envisioned a feedback connection between the corner-line finite element method, used to predict the positions of the free surfaces of the extrudate, and the controller. The corner-line method allows for local mesh refinement and transient flow to be taken into account (Spanjaards et al., 2019). We show the validity of this method by showing optimization results for 2D axisymmetric extrusion flows of a viscoelastic fluid for different Weissenberg numbers. In 3D we first give a proof of concept by showing the results of a Newtonian fluid exiting dies with increasing complexity in shape. Finally, we show that this method is able to obtain the desired extrudate shape of extrudates of a viscoelastic fluid for different Weissenberg numbers and different amounts of shear-thinning.