Shape-dependent regions for inertialess spheroids in turbulent channel flow

Abstract

The alignment between the inertialess spheroids and the directions of the fluid Lagrangian stretching or compression is sensitive to the particles shape near the wall but not near the center of the channel [Cui et al. “Alignment statistics of rods with the Lagrangian stretching direction in a channel flow,” J. Fluid Mech. 901, A16 (2020)]. This observation is further investigated in the current study to uncover the mechanism of particle alignment behavior in different regions of channel flows at Reτ≈180 and 1000. Meanwhile, by using the probability distributions of the sign of the discriminant of the linear term in the Jeffery equation, we find that the turbulent channel flow can be distinctly divided into strong and weak shape-dependent regions. In the weak shape-dependent region, the slender (flat) particles have extraordinarily similar alignments with the directions of fluid Lagrangian stretching (compression). However, in the strong shape-dependent region, the alignments of these inertialess particles are sensitive to the particles shape, especially with the particle positions approaching the wall. The ranges of these shape-dependent regions rely on the Reynolds number, but the probability distributions of the sign of the discriminant of the linear term in the Jeffery equation are a useful tool to distinguish these shape-dependent regions in the wall turbulence regardless of the Reynolds number.