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Effects of Prandtl number in quasi-two-dimensional Rayleigh–Bénard convection

Published online by Cambridge University Press:  16 March 2021

Xiao-Ming Li
Affiliation:
Center for Complex Flows and Soft Matter Research, and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Southern University of Science and Technology, Shenzhen518055, PR China
Ji-Dong He
Affiliation:
Center for Complex Flows and Soft Matter Research, and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China
Ye Tian
Affiliation:
Center for Complex Flows and Soft Matter Research, and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Southern University of Science and Technology, Shenzhen518055, PR China
Peng Hao
Affiliation:
Center for Complex Flows and Soft Matter Research, and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China
Shi-Di Huang*
Affiliation:
Center for Complex Flows and Soft Matter Research, and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China
*
Email address for correspondence: huangsd@sustech.edu.cn

Abstract

We report an experimental study of the Prandtl-number effects in quasi-two-dimensional (quasi-2-D) Rayleigh–Bénard convection. The experiments were conducted in four rectangular convection cells over the Prandtl-number range of $11.7 \leqslant Pr \leqslant 650.7$ and over the Rayleigh-number range of $6.0\times 10^8 \leqslant Ra \leqslant 3.0\times 10^{10}$. Flow visualization reveals that, as $Pr$ increases from 11.7 to 145.7, thermal plumes pass through the central region much less frequently and their self-organized large-scale motion is more confined along the periphery of the convection cell. The large-scale flow is found to break down for higher $Pr$, resulting in a regime transition in the Reynolds number $Re$. For the $Pr$ range with a large-scale flow of system size, the $Re$ number, Nusselt number $Nu$ and local temperature fluctuations were investigated systematically. It is found that $Re$ scales as $Re \sim Ra^{0.58}Pr^{-0.82}$ in the present geometry, which suggests that it is in line with the behaviour in the 2-D configuration. On the other hand, the measured $Nu(Ra, Pr)$ relation $Nu \sim Ra^{0.289}Pr^{-0.02}$ tends to be compatible with the finding in a three-dimensional (3-D) system. For the temperature fluctuations in the cell centre and near the sidewall, they exhibit distinct $Ra$-dependent scalings that could not be accounted for with existing theories, but their $Pr$ dependences for $Pr \lesssim 50$ are in agreement with the predictions by Grossmann & Lohse (Phys. Fluids, vol. 16, 2004, pp. 4462–4472). These results enrich our understanding of quasi-2-D thermal convection, and its similarities and differences compared to 2-D and 3-D systems.

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

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References

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