Vortex dynamics of fiber-laden free shear flows

The objective of this study is to investigate the effects of high aspect-ratio fiber additives on the temporal hydrodynamic instabilities of free shear flows. Nonlinear numerical simulations are conducted on a two-dimensional semi-dilute fiber-laden flow model coupled with a three-dimensional orientation distribution. An averaged-based approach is adopted to describe the orientation of the fiber using orientation tensors defined as moments of the orientation distribution function. The resulting system of differential equations is solved using a combination of a pseudo-spectral method based on the Hartley transform and a finite difference technique. The results of the study show that higher volume fraction and/or larger fiber aspect-ratio weaken the roll-up of the flow. More importantly, it is found that weak hydrodynamic interactions lead to fundamental structural changes in the flow and result in either a spatial phase shift of the vorticity or the growth of higher harmonics that compete with the fundamental and prevent the completion of the roll-up. A detailed analysis of the distribution of the fiber stresses and orientation allowed us to explain the physical mechanisms responsible for the observed changes in the structures of the flow. These mechanisms are compared to those developing in a polymer flow in order to understand the similarities and differences in the effects of these two additives on the mechanisms of transition to turbulence in free shear flows.