When is settling important for particle concentrations in wall-bounded turbulent flows?

TL;DR

This paper investigates the influence of gravitational settling on inertial particle concentrations in wall-bounded turbulent flows, revealing that even small settling velocities can significantly affect concentration profiles and particle behavior near walls.

Contribution

It demonstrates that settling effects are important in boundary layers regardless of how small the settling parameter is, challenging previous assumptions about negligible settling at low velocities.

Findings

Settling impacts concentration profiles even when Sv is very small.

Near-wall particle concentration can decrease significantly with increasing Sv.

Particle sampling behavior shifts from ejection to sweep events as Sv increases.

Abstract

We explore the role of gravitational settling on inertial particle concentrations in a wall-bounded turbulent flow. While it may be thought that settling can be ignored when the settling parameter $Sv\equiv v_s/u_\tau$ is small ($v_s$ - Stokes settling velocity, $u_\tau$ - fluid friction velocity), we show that even in this regime the settling may make a leading order contribution to the concentration profiles. This is because the importance of settling is determined, not by the size of $v_s$ compared with $u_\tau$ or any other fluid velocity scale, but by the size of $v_s$ relative to the other mechanisms that control the vertical particle velocity and concentration profile. We explain this in the context of the particle mean-momentum equation, and show that in general, there always exists a region in the boundary layer where settling cannot be neglected, no matter how small $Sv$ is (provided it is finite). Direct numerical simulations confirm the arguments, and show that the near-wall concentration is highly dependent on $Sv$ even when $Sv\ll 1$, and can reduce by an order of magnitude when $Sv$ is increased from $O(10^{-4})$ and $O(10^{-2})$. The results also show that the preferential sampling of ejection events in the boundary layer by inertial particles when $Sv=0$ is profoundly altered as $Sv$ is increased, and is replaced by a preferential sampling of sweep events due to the onset of the preferential sweeping mechanism.