Abstract
The dry spinning of fibers can be described by three-dimensional multi-phase flow models that contain key effects like solvent evaporation and fiber-air interaction. Since the direct numerical simulation of the three-dimensional models is in general not possible, dimensionally reduced models are deduced. We recently developed a one-two-dimensional fiber model and presented a problem-tailored numerical solution strategy in Wieland et al. (J Comput Phys 384:326–348, 2019). However, in view of industrial setups with multiple fibers spun simultaneously the numerical schemes must be accelerated to achieve feasible simulation times. The bottleneck builds the computation of the radial concentration and temperature profiles as well as their cross-sectionally averaged values. In this paper we address this issue and develop efficient numerical algorithms.
Highlights
In dry spinning processes a polymer solvent mixture is extruded from multiple nozzles into a spinning duct with a tempered air stream
In [19] we recently developed a dimensionally reduced fiber model which consists of one-dimensional equations for tangential fiber velocity and stress and two-dimensional advection-diffusion equations covering the cross-sectional variations of polymer mass fraction and fiber temperature
3 Reduced fiber dry spinning model Due to the complexity of the three-dimensional problem (System 1) that prevents the simulations of industrial dry spinning setups, we proposed a dimensionally reduced model in [19] that is of good approximation quality and efficiently evaluable
Summary
In dry spinning processes a polymer solvent mixture is extruded from multiple nozzles into a spinning duct with a tempered air stream. Governing the key effects, like solvent evaporation and interaction between multiple slender fibers and air [21], rises the computational complexity of the multiphase-multiscale problem such that the direct numerical simulation of the three-dimensional models is in general not possible. In [19] we recently developed a dimensionally reduced fiber model which consists of one-dimensional equations for tangential fiber velocity and stress and two-dimensional advection-diffusion equations covering the cross-sectional variations of polymer mass fraction and fiber temperature. We extended this uni-axial fiber model to curved fibers utilizing the theory of Cosserat rods in [20]. Based on a generalized problem description we give details for an efficient implementation of the underlying routines and demonstrate their performance for an industrial example
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