Mechanisms governing the settling velocities and spatial distributions of inertial particles in wall-bounded turbulence

TL;DR

This study combines theory and DNS to analyze how inertial particles settle and distribute in wall-bounded turbulence, revealing mechanisms like preferential sweeping and turbophoresis affecting particle velocities and concentrations.

Contribution

It provides a detailed theoretical and numerical analysis of particle transport mechanisms near walls, highlighting differences caused by inertia and gravity, and proposes modifications to existing concentration models.

Findings

Vertical velocities can exceed Stokes settling velocity by ten times due to turbulence.

Near the wall, particle concentration follows a power-law with a Stokes number-dependent exponent.

Preferential sweeping dominates away from the wall, while turbophoresis is key near the wall.

Abstract

We use theory and Direct Numerical Simulations (DNS) to explore the average vertical velocities and spatial distributions of inertial particles settling in a wall-bounded turbulent flow. The theory is based on the exact phase-space equation for the Probability Density Function describing particle positions and velocities. This allowed us to identify the distinct physical mechanisms governing the particle transport. We then examined the asymptotic behavior of the particle motion near the wall, revealing the fundamental differences to the near wall behavior that is produced when incorporating gravitational settling. When the average vertical particle mass flux is zero, the averaged vertical particle velocity is zero away from the wall due to the particles preferentially sampling regions where the fluid velocity is positive, which balances with the downward Stokes settling velocity. When the average mass flux is negative, the combined effects of turbulence and particle inertia lead to average vertical particle velocities that can significantly exceed the Stokes settling velocity, by as much as ten times. Sufficiently far from the wall, the enhanced vertical velocities are due to the preferential sweeping mechanism. However, as the particles approach the wall, the contribution from the preferential sweeping mechanism becomes small, and a downward contribution from the turbophoretic velocity dominates the behavior. Close to the wall, the particle concentration grows as a power-law, but the nature of this power law depends on the particle Stokes number. Finally, our results highlight how the Rouse model of particle concentration is to be modified for particles with finite inertia.