Multi-scale interactions in turbulent mixed convection drive efficient transport of Lagrangian particles

TL;DR

The paper addresses how turbulent mixed convection affects the suspension and vertical transport of strongly settling inertial particles in a turbulent channel. It uses coupled Eulerian-Lagrangian DNS spanning CF, FC, and MC via variation of $Ri_ au$, resolving near-wall ejections and interior convective superstructures. The key finding is a cooperative two-stage suspension mechanism: primary suspension from near-wall ejections (hairpin vortices with $u'<0$ and $w'>0$) and secondary suspension from streamwise-aligned interior plumes (with $w'>0$ and $θ'>0$), producing about a one-order-of-magnitude increase in midplane concentration at $Ri_ au o ext{O}(40)$ relative to limiting cases. This mechanism, absent in pure channel flow and free convection, has implications for atmospheric boundary-layer transport, particle residence times, and clustering, underscoring the importance of multi-scale coupling in heavy-particle dispersion.

Abstract

When turbulent convection interacts with a turbulent shear flow, the cores of convective cells become aligned with the mean current, and these cells (which span the height of the domain) may interact with motions closer to the solid boundary. In this work, we use coupled Eulerian-Lagrangian direct numerical simulations of a turbulent channel flow to demonstrate that under conditions of turbulent mixed convection, interactions between motions associated with ejections and low-speed streaks near the solid boundary, and coherent superstructures in the interior of the flow interact and lead to significant vertical transport of strongly settling Lagrangian particles. We show that the primary suspension mechanism is associated with strong ejection events (canonical low-speed streaks and hairpin vortices characterized by $u'<0$ and $w'>0$), whereas secondary suspension is strongly associated with large scale plume structures aligned with the mean shear (characterized by $w'>0$ and $θ'>0$). This coupling, which is absent in the limiting cases (pure channel flow or free convection) is shown to lead to a sudden increase in the interior concentration profiles as $\mathrm{Ri}_τ$ increases, resulting in concentrations that are larger by roughly an order of magnitude at the channel midplane.

Figures (4)

• Figure 1: A rectangular channel of dimensions $4\pi h\times 2\pi h\times 2h$. The flow is periodic in the horizontal and is driven by a constant streamwise pressure gradient. No-slip boundary conditions are enforced at the top and bottom boundaries. The solid boundaries are held at a temperature difference $\varDelta T=T_h-T_c$. Particles are emitted randomly from a reservoir (fixed $\mathcal{C}\approx 4000$) into the domain through the bottom boundary. Particles reflect elastically off the upper boundary.
• Figure 2: Slices of the fluctuating vertical velocity at the mid-plane for pure channel flow (a-b), mixed convection (c-d), and free convection (e-f). Fluctuating velocities are normalized by $u_\tau$ in panels (a-d) and by $w_*$ (the convective velocity scale) in panels (e-f). The left column shows $x-y$ slices and the right column shows $y-z$ slices. Shaded contours in panels (c-f) show regions of $w'\theta' > 0.12\kappa\varDelta T(2h)^{-1}\mathrm{Ra}^{1/3}$.
• Figure 3: As in figure \ref{['fig:wslices']}. Contours are regions where $w'\theta' > 0.12\kappa\varDelta T(2h)^{-1}\mathrm{Ra}^{1/3}$, and coloured based on the sign of the vertical fluid velocity (red is positive and blue is negative). Particles (not to scale) are overlaid highlighting their clustering behaviour.
• Figure 4: Profiles of slabwise correlation coefficients conditioned on ejection events (a-b), and positive heat fluxes (c). Panel (d) shows concentration profiles averaged in the horizontal dimensions. Also included is a case with $\mathrm{Ri}_\tau=5$ demonstrating the sudden onset of interior mixing as $\mathrm{Ri}_\tau$ increases.