Collision rates of small ellipsoids settling in turbulence

Abstract

We propose that the collision rates of non-spherical particles settling in a turbulent environment are significantly higher than those of spherical particles of the same mass and volume. The theoretical argument is based on the dependence of the particle drag force on the particle orientation, thus varying gravitational settling velocities, which can remain different until contact due to the particle inertia. Therefore, non-spherical particles can collide with large relative velocities. Direct numerical simulations (DNS) of streamwise decaying isotropic turbulence seeded with small, heavy, rotationally symmetric ellipsoids of five different aspect ratios are performed to confirm these arguments. The motion of 21 million ellipsoids is tracked by a Lagrangian particle solver assuming creeping flow conditions and neglecting the influence of the particles on the flow. We find that ellipsoids collide considerably more often than spherical particles of the same volume and mass due to a drastically increased mean relative velocity at contact.

Point-Particle DNS and LES of Particle-Laden Turbulent flow - a state-of-the-art review

“…In this section we will only consider spherical particles. Collision algorithms for non-spherical particles have also been developed and studied [93, 122]. Zhao et al [122] considered ellipsoidal particles and used an extension of a collision search algorithm for spherical particles by treating each ellipsoid as a set of overlapping fictitious spheres, whose hull approximately corresponds to the shape of the ellipsoid.…”

Disks aligned in a turbulent channel

“…For neutrally buoyant particles, the instantaneous orientation should be a nearly continuous field whose rich topology has begun to be explored (Szeri 1993;Wilkinson, Bezuglyy & Mehlig 2011). The addition of particle inertia introduces the possibility of caustics in the orientation field (Gustavsson et al 2014;Siewert, Kunnen & Schröder 2014b), which can strongly affect collision probabilities.…”

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

“…The orientation of small ice crystals has manifestly a direct impact on the reflection properties of electromagnetic waves (including light) from clouds [2][3][4], with potentially important consequences for the albedo and the climate. In addition, it was noted that the dispersion in the orientation of identical crystals leads to differences in their settling velocities, which in turn affects the collision and aggregation rates [5,6], essential in the formation of precipitation. A second example highlighting the significance of particles settling in turbulence is the dynamics of small aggregates of organic matter in the oceans ('marine snow') [7].…”

“…Time-dependent spatially inhomogeneous flows present new challenges, and very little is known about the effect of fluid inertia for such flows, in particular for turbulence. In some studies, therefore, effects of fluid inertia were simply neglected [5,6,[47][48][49]. These models predict that the breaking of isotropy due to gravity causes a bias in the orientation distribution of the settling particles, so that rods tend to settle tip first, parallel to gravity.…”