Deformation of flexible fibers in turbulent channel flow

Abstract

In this paper, we examine from a statistical point of view the deformation of flexible fibers in turbulent channel flow. Fibers are longer than the Kolmogorov length scale of the carrier flow and have finite inertia. Our aim is to examine the effect of local shear and turbulence anisotropy on fiber twisting and bending, when shape effects add to the inertial bias. To these aims, we use an Eulerian–Lagrangian approach based on direct numerical simulation of turbulence in dilute flow conditions. Fibers are modelled as chains of sub-Kolmogorov rods (referred to as elements hereinafter) interconnected by holonomic constraints that enable relative rotation of neighbouring elements. Statistics are computed from simulations at shear Reynolds number ${\text{Re}}_{\tau }=150$, based on the channel half height, for fibers with different aspect ratio, $\lambda _r$ (defined as the ratio between the length $l_r$ of each element r composing the fiber and its cross-sectional radius, a), and different inertia, parameterized by the Stokes number of the element, $St_r$. We show that bending of flexible fibers is in general stronger in the bulk of the flow, where they are subject to turbulent velocity fluctuations only. Near the wall, fibers are more easily stretched by the mean shear, especially for large-enough inertia ($St_r > 5$ in our simulations). In spite of this different dynamics, which is connected to the anisotropy of the flow, we find that the fiber end-to-end distance reaches a steady state regardless of fiber location with respect to the wall.