Efficient Simulation of Random Fields for Fiber-Fluid Interactions in Isotropic Turbulence

Abstract

In some processes for spinning synthetic fibers the filaments are exposed to highly turbulent flows to achieve a high degree of stretching. The quality of the resulting fabric is thus determined essentially by the turbulent fiber-fluid interactions. Due to the required fine resolution, direct numerical simulations fail. Therefore we model the flow fluctuations as random field in ${\mathbb{R}}^{4}$ on top of a k-ε turbulence description and describe the interactions in the context of slender-body theory as one-way-coupling with a corresponding stochastic aerodynamic drag force on the fibers. Hereby we exploit the special covariance structure of the random field, namely isotropy, homogeneity and decoupling of space and time. In this work we will focus on the construction and efficient simulation of the turbulent fluctuations assuming constant flow parameters and give an outlook on applications.