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

## TL;DR

This paper investigates how fluid inertia influences the orientation of settling spheroids in turbulent flows, revealing that inertia dominates at high Reynolds numbers, affecting particle orientation and drag.

## Contribution

It combines effects of fluid inertia and turbulent velocity gradients to determine their relative influence on particle orientation in different flow regimes.

## Key findings

- Fluid inertia dominates at high Reynolds numbers, aligning particles broad side first.
- Velocity gradient effects dominate at low Reynolds numbers, aligning particles tip first.
- The ratio of torques predicts the dominant orientation mechanism in turbulent flows.

## 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.