Shape prediction for complex polymer extrudates through 3D numerical simulation

In polymer extrusion shape of the extrudate depend largely on the process parameters such as die shape, extrusion speed and temperature. Especially for complex profiles, it is impossible to predict this dependence a priori. By performing 3D finite element analyses more insight can be obtained in how the process parameters influence the final shape. In the present study it is assumed that the polymer is a liquid of which the elastic response can be neglected. This assumption, together with a steady state approach and the low Reynolds numbers that characterize extrusion, justifies the modeling of polymer extrusion as a Stokes flow. This Stokes flow can be discretized in an Eulerian framework using the MINI-element. The resulting system of equations can subsequently be solved using an iterative solver. However, the accuracy of the solution is influenced considerably by the manner in which the shape of the extruded profile is meshed. The shape of the extrudate is not known a priori. As a result it is not possible to have the mesh of the domain coincide with the actual shape of the profile before hand. It is therefore necessary to solve a free boundary problem for that portion of the profile that has exited the die to determine the real shape of the profile. Then the mesh of the domain has to be adopted to coincide with the real shape. Results of numerical experiments will be presented which indicate that the solution of the velocity field changes considerably if the shape of the domain is updated to comply with the real shape of the polymer extrudate. Due to the steady state assumption the shape of the free surface can be computed exactly for the given velocity profile in one step. This makes it possible to determine the shape of the profile at little extra cost