Investigating the parametric dependence of the impact of two-way coupling on inertial particle settling in turbulence

Tom et al.\ (J.\ Fluid Mech.\ 947, A7, 2022) investigated the impact of two-way coupling (2WC) on particle settling in turbulence. For the limited parameter choices explored, it was found that 2WC substantially enhances particle settling compared to the one-way coupled (1WC) case, even at low mass loading $\Phi_m$. Moreover, contrary to previous claims, it was demonstrated that preferential sweeping remains the mechanism responsible for the particles settling faster than the Stokes settling velocity in 2WC flows. However, crucial questions remain: 1) how small must $\Phi_m$ be for the effects of 2WC on particle settling to be negligible? 2) does the preferential sweeping mechanism remain relevant in 2WC flows as $\Phi_m$ is increased? To answer these, we explore a much broader portion of the parameter space, and our simulations cover cases where the impact of 2WC on the global fluid statistics ranges from negligible to strong. We find that even for $\Phi_m=7.5\times 10^{-3}$, 2WC can noticeably increase the settling for some choices of the Stokes and Froude numbers. We also demonstrate that even when $\Phi_m$ is large enough for the global fluid statistics to be strongly affected by the particles, preferential sweeping is still the mechanism responsible for the enhanced particle settling. The difference between the 1WC and 2WC cases is that, in the latter the particles are not merely swept around the downward-moving side of vortices, but they also drag the fluid with them as they move down

Direct Numerical Simulation of a Turbulent Channel Flow with Forchheimer Drag

We characterize the turbulent flow, using direct numerical simulations (DNS), within a closed channel between two parallel walls with a canopy of constant areal density profile on the lower wall. The canopy is modelled using different formulations of the Forchheimer drag, and the characteristic properties of the turbulent flows are compared. In particular, we examine the influence of the added drag on the mean profiles of the flow and the balance equations of the turbulent kinetic energy. We find that the different formulations of the drag strongly affect the mean and the turbulent profiles close to the canopy. We also observe the changes in the local anisotropy of the turbulent flow in the presence of the canopy. We find that there is an equal transfer of energy from the streamwise component to both the transverse components outside the canopy by the pressure and velocity-gradient correlation; inside the canopy, this correlation removes energy from both the streamwise and the wall-normal fluctuations and injects into the spanwise component. As a result, the energy content of the spanwise fluctuations is comparable to that of the streamwise components inside the canopy. Inside the canopy, we observe that the turbulent transport of Reynolds stresses acts as an important source of turbulent kinetic energy. The pressure-fluctuation transport plays a significant role inside the canopy close to the wall and is comparable to turbulent transport