# Optimizing Industrial Fiber Spinning Processes: A PhD at the Fraunhofer ITWM

My name is Raphael Hohmann and I am a PhD student in a collaboration of the Transport Processes department at the Fraunhofer Institute for Industrial Mathematics (ITWM) in Kaiserslautern with the University of Kassel, and due to the thematic and spatial proximity I also have close ties to the Technical University of Kaiserslautern. For me as a mathematician with preference for the more practical branches of the subject, ITWM is a great place to be due to its role ‘in between’ university and industry.

One part of my research at ITWM addresses the optimal design of distributor cavities for the industrial fiber spinning process. These distributors are used to guide a highly viscous fluid, often a polymer melt, from an inlet pipe onto a spinneret plate with many small capillary nozzles, where the material is spun to fibers and subsequently further processed to yield a nonwoven product.

The main optimization goal here is to transport the fluid in such a way, that it has approximately the same ‘material age’ everywhere on the spinneret plate once it gets there. Since the fluid, that will eventually reach the nozzles adjacent to the walls of the distributor, must cover a longer distance at lower velocities than the fluid in the interior, it will inevitably reside relatively long within the cavity. These long residence times within the externally heated geometry are unfavorable, since they can lead to irreversible changes of the fiber’s material properties and decrease the quality of the final product.

In order to improve the distributor, the goal of achieving an approximately constant material age at the spinneret plate has to be translated into a suitable objective functional and the corresponding PDE-constrained shape optimization problem has to be set up. Subsequent thereto a given initial design can be improved through iterative deformation steps based on the so-called shape derivative of the objective.

The main theoretical results of my research on this topic are the introduction of a transport equation for the material age of the fluid as well as a cost functional based on a penalization of excessively high residence times and the pressure energy drop in the cavity, and finally the computation of its shape derivative. Once this step was completed, I could turn my attention towards the more practical aspects of implementing the shape optimization algorithm and testing it for an industrial test case.

My experience at Fraunhofer has been through and through positive so far. I personally highly value the inspiring and friendly working environment, the good IT-infrastructure, the connection to the industrial application as well as the workshops and training courses offered by the High Performance Center Simulation and Software Based Innovation, and am happy and thankful to be able to work here.