Importance of fluid inertia for the orientation of spheroids settling in turbulent flow

Abstract

How non-spherical particles orient as they settle in a flow has important practical implications in a number of scientific and engineering problems. In a quiescent fluid, a slowly settling particle orients so that it settles with its broad side first. This is an effect of the torque due to convective inertia of the fluid set in motion by the settling particle, which maximises the drag experienced by the particle. Turbulent flows tend to randomise the particle orientation. Recently the settling of non-spherical particles in turbulence was analysed neglecting the effect of convective fluid inertia, but taking into account the effect of the turbulent fluid-velocity gradients on the particle orientation. These studies reached the opposite conclusion, namely that a rod settles preferentially with its tip first, wheras a disk settles with its edge first, therefore minimizing the drag on the particle. Here, we consider both effects, the convective inertial torque as well as the torque due to fluctuating velocity gradients, and ask under which circumstances either one or the other dominate. To this end we estimate the ratio of the magnitudes of the two torques. Our estimates suggest that the fluid-inertia torque prevails in high-Reynolds number flows. In this case non-spherical particles are expected to settle with a maximal drag. But when the Reynolds number is small then the torque due to fluid-velocity gradients may dominate, causing the particle to settle with its broad side first. I. INTRODUCTIONThe settling of non-spherical particles in a flow is of importance in several scientific and engineering problems [2]. One example is given by deep cumulus clouds. In such clouds, the temperature falls well below 0 o C, inducing the formation of small ice crystals, which play a very significant role in the formation of precipitation [8,37]. The orientation of such small ice crystals also determines how electromagnetic radiation is reflected from clouds [42]. A second example is the sedimentation of organic and anorganic matter in the turbulent ocean [27,38]. The dynamics of motile micro-organisms in turbulence [4,12,16,43], usually slightly heavier than water, has important consequences for the population dynamics and the ecology of the ocean system.More generally, understanding the angular dynamics of non-spherical particles in turbulent flows is a challenging fundamental problem [41]. When the particles are heavier than the surrounding fluid, the problem is significantly complicated. Even in the simplest case of spherical particles suspended in a turbulent flow, a detailed understanding of their settling properties is only beginning to emerge [3,15,20,33,36]. Clearly, understanding the angular dynamics is essential to describe the settling of non-spherical particles.An exact theoretical description of the problem requires the solution of the full Navier-Stokes equations, imposing no-slip boundary conditions at the surface of the solid [7,22,35]. An alternative, much more tractable approach consists in using simplified desc...

Effect of fluid inertia on the orientation of a small prolate spheroid settling in turbulence

“…The question is thus whether one can find regions where inertial torque does not dominate. This is considered in [62]. The simulations described there show that the fluid-inertia torque can be smaller than Jeffery's torque only when l Re is small.…”

“…In this limit one therefore expects the fluid-inertia torque t ( ) 1 to dominate over Jeffery's torque t ( ) 0 , so that the inertial torque cannot be neglected (as was done in [5,6,[47][48][49]). It is argued in [62] that the orientation bias predicted in [5,47,48] can possibly be observed in smalll Re flow, but not at high l Re . In the following we neglect the contribution from ( ) f 1 .…”

Kinematics and dynamics of freely rising spheroids at high Reynolds numbers

“…Furthermore, the particle alignment relative to the incoming flow induces additional circulation around the body which results in a lift force contribution that is non-existent for spheres. Recent work by Sheikh et al (2020) underlines the importance of fluid inertia for the alignment of particles settling in turbulence. To date, related studies have focused on the transitional dynamics at low Ga. A classification into regimes is reported for spheroids in the numerical work by Zhou, Chrust & Dusek (2017).…”

“…Recent work by Sheikh et al. (2020) underlines the importance of fluid inertia for the alignment of particles settling in turbulence. To date, related studies have focused on the transitional dynamics at low .…”

Correlations for inclined prolates based on highly resolved simulations

“…for , the ellipsoid is subject to a pitching torque which rotates the ellipsoid towards the most stable orientation . Even for such low Reynolds numbers, it is estimated that the pitching contributions can dominate the torque due to fluid velocity gradients (Sheikh et al 2020). Although comparable analytical results are not reliable for higher Reynolds numbers (Clift et al 2005), the pitching torque should be included in correlations for ellipsoidal dynamics.…”