Shape- and scale-dependent coupling between spheroids and velocity gradients in turbulence

Nimish Pujara,Michael Wilczek,Bérenger Bramas,José-Agustín Arguedas-Leiva,Cristian C Lalescu

doi:10.1017/jfm.2021.543

Abstract

Rotations of spheroidal particles immersed in turbulent flows reflect the combined effects of fluid strain and vorticity, as well as the time history of these quantities along the particle's trajectory. Conversely, particle rotation statistics in turbulence provide a way to characterise the Lagrangian properties of velocity gradients. Particle rotations are also important for a range of environmental and industrial processes where particles of various shapes and sizes are immersed in a turbulent flow. In this study, we investigate the rotations of inertialess spheroidal particles that follow Lagrangian fluid trajectories. We perform direct numerical simulations (DNS) of homogeneous isotropic turbulence and investigate the dynamics of different particle shapes at different scales in turbulence using a filtering approach. We find that the mean-square particle angular velocity is nearly independent of particle shape across all scales from the Kolmogorov scale to the integral scale. The particle shape does determine the relative split between different modes of rotation (spinning vs tumbling), but this split is also almost independent of the filter scale suggesting a Lagrangian scale-invariance in velocity gradients. We show how the split between spinning and tumbling can be quantitatively related to the particle's alignment with respect to the fluid vorticity.

Highlights

In the Lagrangian study of turbulence, a point-sized sphere is used to probe the flow since such a particle adopts the velocity and angular velocity of the fluid in its immediate vicinity
Extending this idea to spheroids offers a more intricate way to examine the Lagrangian flow structure since spheroids rotate due to both fluid rotation and strain, and the statistics of spheroid rotations reflect the Lagrangian dynamics of velocity gradients (Voth & Soldati 2017)
Spinning and tumbling rates can be predicted analytically for particles randomly oriented with respect to the velocity gradient tensor, but results from experiments and direct numerical simulations (DNS) have shown that this does not provide an accurate prediction of particle rotation rates in turbulence (Shin & Koch 2005; Parsa et al 2012; Chevillard & Meneveau 2013; Byron et al 2015; Pujara & Variano 2017)

Summary

Introduction

In the Lagrangian study of turbulence, a point-sized sphere is used to probe the flow since such a particle adopts the velocity and angular velocity of the fluid in its immediate vicinity. When spheroids follow Lagrangian fluid trajectories and rotate in response to the velocity gradients along those trajectories, the mean-square spinning ( (ωp · p)2 ) and tumbling ( p2 ) rates reflect the distribution of particle orientations with respect to principal directions of the velocity gradients. Spinning and tumbling rates can be predicted analytically for particles randomly oriented with respect to the velocity gradient tensor, but results from experiments and direct numerical simulations (DNS) have shown that this does not provide an accurate prediction of particle rotation rates in turbulence (Shin & Koch 2005; Parsa et al 2012; Chevillard & Meneveau 2013; Byron et al 2015; Pujara & Variano 2017). Pujara and others fairly robust scale-invariance for velocity gradients across the complete scale spectrum of turbulence when examined in the Lagrangian frame

Velocity gradients along Lagrangian trajectories

Scale-dependency in particle rotation statistics

Particle spinning and tumbling

Findings

Discussion