Particle transport and deposition in wall-sheared thermal turbulence

We studied the transport and deposition behaviour of point particles in Rayleigh–Bénard convection cells subjected to Couette-type wall shear. Direct numerical simulations (DNSs) are performed for Rayleigh number (Ra) in the range 10⁷ ≤ Ra ≤ 10⁹ with a fixed Prandtl number Pr = 0.71, while the wall-shear Reynolds number (Re_w) is in the range 0 ≤ Re_w ≤ 12 000. With the increase of Re_w, the large-scale rolls expanded horizontally, evolving into zonal flow in two-dimensional simulations or streamwise-oriented rolls in three-dimensional simulations. We observed that, for particles with a small Stokes number (St), they either circulated within the large-scale rolls when buoyancy dominated or drifted near the walls when shear dominated. For medium St particles, pronounced spatial inhomogeneity and preferential concentration were observed regardless of the prevailing flow state. For large St particles, the turbulent flow structure had a minor influence on the particles’ motion; although clustering still occurred, wall shear had a negligible influence compared with that for medium St particles. We then presented the settling curves to quantify the particle deposition ratio on the walls. Our DNS results aligned well with previous theoretical predictions, which state that small St particles settle with an exponential deposition ratio and large St particles settle with a linear deposition ratio. For medium St particles, where complex particle–turbulence interaction emerges, we developed a new model describing the settling process with an initial linear stage followed by a nonlinear stage. Unknown parameters in our model can be determined either by fitting the settling curves or using empirical relations.