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Dynamic coupling between carrier and dispersed phases in Rayleigh–Bénard convection laden with inertial isothermal particles

Published online by Cambridge University Press:  11 November 2021

Wenwu Yang
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai200072, China
Yi-Zhao Zhang
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai200072, China
Bo-Fu Wang
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai200072, China
Yuhong Dong*
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai200072, China
Quan Zhou
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai200072, China
*
Email address for correspondence: dongyh@shu.edu.cn

Abstract

We investigate the dynamic couplings between particles and fluid in turbulent Rayleigh–Bénard (RB) convection laden with isothermal inertial particles. Direct numerical simulations combined with the Lagrangian point-particle mode were carried out in the range of Rayleigh number $1\times 10^6 \le {Ra}\le 1 \times 10^8$ at Prandtl number ${Pr}=0.678$ for three Stokes numbers ${St_f}=1 \times 10^{-3}$, $8 \times 10^{-3}$ and $2.5 \times 10^{-2}$. It is found that the global heat transfer and the strength of turbulent momentum transfer are altered a small amount for the small Stokes number and large Stokes number as the coupling between the two phases is weak, whereas they are enhanced a large amount for the medium Stokes number due to strong coupling of the two phases. We then derived the exact relation of kinetic energy dissipation in the particle-laden RB convection to study the budget balance of induced and dissipated kinetic energy. The strength of the dynamic coupling can be clearly revealed from the percentage of particle-induced kinetic energy over the total induced kinetic energy. We further derived the power law relation of the averaged particles settling rate versus the Rayleigh number, i.e. $S_p/(d_p/H)^2{\sim} Ra^{1/2}$, which is in remarkable agreement with our simulation. We found that the settling and preferential concentration of particles are strongly correlated with the coupling mechanisms.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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