Residence time optimization of spin pack polymer distributors.

We consider the optimal shape design of polymer distributors used for industrial fiber spinning. In this laminar flow problem the residence time, the volume‐averaged age distribution of the fluid particles, has to be controlled to avoid material degradation. The residence time is modelled by an advection‐diffusion‐reaction equation with the fluid velocity being the transport field. This approach is more suitable for PDE‐constrained shape optimization than the Lagrangian particle‐tracking approach, where the observable is a finite set of trajectories. In order to develop an efficient shape optimization algorithm we derive the shape gradient of a tracking‐type cost functional by introducing the adjoint state. [ABSTRACT FROM AUTHOR]