On Modeling and Simulation of Crystallization in Fiber Melt Spinning

This thesis addresses the modeling and simulation of physical processes in the context of the production of technical textiles. The process of fiber melt spinning presents a significant challenge from a mathematical and modeling perspective, given its inherent complexity. The thesis focuses on semi-crystalline polymers, where the degree of crystallization is a critical factor. Considering a viscoelastic two-phase fiber model class, asymptotically justified boundary conditions are derived, preventing the occurrence of artificial boundary layers. In the context of a viscoelastic model hierarchy, several dimensionally reduced fiber models are analyzed and compared with respect to their performance and application regime, with a particular focus on a novel stress-averaged one-two-dimensional model. For the efficient numerical solution of the boundary value problems of ordinary and partial differential equations resulting from the fiber models, suitable problem-specific solution algorithms are developed. The capabilities of the model-simulation framework are demonstrated by investigating an industrial spinning scenario with hundreds of fibers, incorporating two-way coupled fiber-air interaction.