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Particle transport and deposition in wall-sheared thermal turbulence

Published online by Cambridge University Press:  08 November 2024

Ao Xu Open the ORCID record for Ao Xu [Opens in a new window] ,
Ben-Rui Xu  and
Heng-Dong Xi Open the ORCID record for Heng-Dong Xi [Opens in a new window]
Ao Xu
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, PR China Institute of Extreme Mechanics, Northwestern Polytechnical University, Xi'an 710072, PR China National Key Laboratory of Aircraft Configuration Design, Xi'an 710072, PR China
Ben-Rui Xu
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, PR China
Heng-Dong Xi*
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, PR China Institute of Extreme Mechanics, Northwestern Polytechnical University, Xi'an 710072, PR China National Key Laboratory of Aircraft Configuration Design, Xi'an 710072, PR China
*
†Email address for correspondence: hengdongxi@nwpu.edu.cn
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Abstract

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 $10^{7} \leq Ra \leq ~10^9$ with a fixed Prandtl number $Pr = 0.71$, while the wall-shear Reynolds number ($Re_w$) is in the range $0 \leq Re_w \leq ~12\,000$. 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. Compared with DNS results, our model also accurately predicts the average residence time across a wide range of $St$ for various $Re_w$.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Turbulent Flows: Turbulent convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 999 , 25 November 2024 , A15
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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Temperature fields and particle positions in two-dimension.
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Slice of velocity component ν and particle positions in three-dimension.
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