Shape Optimization of a Polymer Distributor Using an Eulerian Residence Time Model

Abstract

We consider the optimal shape design of polymer distributors for the industrial spinning process, where long residence times are known to have a negative impact on the quality of the fibers. To this end we introduce a cost function based on the material age and the pressure energy required for the fluid transport. We obtain the shape derivative of the cost function without using the material derivative of the state based on a recent differentiability result for the Lagrangian formulation of shape optimization problems. Numerical experiments for a three-dimensional distributor verify the feasibility of our approach.