Fiber melt spinning plays an important role in the production of polymer technical textiles. In the case of semi-crystalline polymers, crystallization occurs during the melt spinning process, which has a significant impact on the properties of the final product. Modeling and simulation of the process is essential for the design and optimization of industrial spinning machines to reduce material costs and improve fiber quality. The challenge is the establishment of models that cover as many physically relevant effects as possible, while being simulated with a reasonable amount of computational time and effort. In this talk, we present a two-way coupled simulation framework that combines airflow with fiber simulations to achieve fast and reliable simulations of industrial spinning plants. The fiber model employs viscoelastic, two-phase material laws to accurately model the crystallization process of the amorphous phase of the filaments. It also includes radial effects to capture the formation of core-sheath phenomena. Together with the realized fiber-air interaction, this opens the field for simulation-based process design and material optimization. Overall, our approach offers a comprehensive solution for modeling the melt spinning process, providing valuable insights for industrial applications.