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On non-Oberbeck–Boussinesq effects in Rayleigh–Bénard convection of air for large temperature differences

Published online by Cambridge University Press:  21 February 2020

Zhen-Hua Wan Open the ORCID record for Zhen-Hua Wan [Opens in a new window] ,
Qi Wang Open the ORCID record for Qi Wang [Opens in a new window] ,
Ben Wang ,
Shu-Ning Xia ,
Quan Zhou Open the ORCID record for Quan Zhou [Opens in a new window]  and
De-Jun Sun
Zhen-Hua Wan
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei230027, PR China
Qi Wang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei230027, PR China
Ben Wang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei230027, PR China
Shu-Ning Xia
Affiliation:
Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai200072, PR China
Quan Zhou
Affiliation:
Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai200072, PR China
De-Jun Sun*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei230027, PR China
*
†Email address for correspondence: [email protected]
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Abstract

We present direct numerical simulations of non-Oberbeck–Boussinesq (NOB) Rayleigh–Bénard (RB) convection due to large temperature differences in two-dimensional (2-D) and three-dimensional (3-D) cells. Perfect air is chosen as the operating fluid and the Prandtl number ($Pr$) is fixed to 0.71 for the reference state $\hat{T}_{0}=300~\text{K}$. In the present system, we consider large temperature differences ranging from 60 K to 240 K, and relatively strong NOB effects are induced at moderate Rayleigh numbers ($Ra$) in the range $3\times 10^{6}\leqslant Ra\leqslant 5\times 10^{9}$. The large temperature difference also induces the turbulence system with large density variation. Due to top-down symmetry breaking under NOB conditions, an increase of the centre temperature $T_{c}$ is found compared to the arithmetic mean temperature $T_{m}$ of the top and bottom plates, and the shift of $T_{c}$ is strongly dependent on Rayleigh number $Ra$ and temperature differential $\unicode[STIX]{x1D716}$. The NOB effects on the Nusselt number ($Nu$) are quite small (${\lesssim}2\,\%$). The power-law scalings of $Nu$ versus $Ra$ are robust against NOB effects, even for the extremely large temperature difference 240 K, which has never been reached in previous experiments and simulations. The Reynolds numbers $Re$, as well as the scalings of $Re$ versus $Ra$, are also insensitive to NOB effects. It is noteworthy that the influence of NOB effects on $Nu$ and $Re$ in 3-D RB flow are weaker than its 2-D counterpart. Furthermore, the extended laminar boundary layer (BL) equations are developed based on the low-Mach-number Navier–Stokes equations, which qualitatively predicts the NOB effects on velocity profiles. Direct numerical simulation results indicate that the top and bottom thermal BLs can compensate each other much better than the velocity BLs under NOB conditions, which contribute to the robustness of $Nu$.

JFM classification

Convection: Convection in cavities
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 889 , 25 April 2020 , A10
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Wan et al. supplementary movie 1

The distribution of temperature and velocity vectors at Ra=5e8 for OB case

Download Wan et al. supplementary movie 1(Video)
Video 4.2 MB

Wan et al. supplementary movie 2

The distribution of temperature and velocity vectors at Ra=5e8 for ε=0.2

Download Wan et al. supplementary movie 2(Video)
Video 3.6 MB

Wan et al. supplementary movie 3

The distribution of temperature and velocity vectors at Ra=8e8 for OB case

Download Wan et al. supplementary movie 3(Video)
Video 12 MB

Wan et al. supplementary movie 4

The distribution of temperature and velocity vectors at Ra=8e8 for ε=0.2

Download Wan et al. supplementary movie 4(Video)
Video 12.5 MB