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The persistence of large-scale circulation in Rayleigh–Bénard convection

Published online by Cambridge University Press:  12 August 2021

Ping Wei Open the ORCID record for Ping Wei [Opens in a new window]
Ping Wei*
Affiliation:
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, PR China
*
†Email address for correspondence: [email protected]
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Abstract

The time-averaged strength $\langle \delta \rangle /\varDelta$ of a convective cellular pattern and large-scale circulation (LSC) in the turbulence regime of turbulent Rayleigh–Bénard convection exhibits a sequence of sharp changes with the Rayleigh number $Ra$. Changes occur when $Ra$ reaches transition values between the conduction, convection, chaotic, transition, soft turbulence and hard turbulence regimes. Measurements were taken from two cylindrical cells with Plexiglas walls and nitrogen gas as the working fluid. The data cover the range $10^{3} \lesssim Ra \lesssim 10^{9}$ at $Pr = 0.72$, where $Pr$ is the Prandtl number and $\varGamma \equiv D/H=1.00$ is the aspect ratio (diameter over height). The cellular pattern strength $\delta$ grows continuously as $Ra$ exceeds the critical value $Ra_c=7300$ for the wall admittance $C=2.02$ in the convection regime. In the oscillation regime, the temperature power spectra at the sidewall show an oscillatory frequency peak. In the chaotic regime, δ is diminished as $Ra$ increases. In the transition regime, $\langle \delta \rangle /\varDelta$ continues to decrease, nearly to 0. Under soft turbulence where the LSC is formed, $\langle \delta \rangle$ grows with $Ra$ as a cellular pattern in the convection regime, suggesting that LSC reflects a cellular pattern. Under hard turbulence, the LSC flow strength decreases as $Ra$ increases. The Reynolds number $Re$ was also measured based on the LSC turnover time, and it was found that two power laws, $\langle \delta \rangle /\varDelta \times Ra/Pr = 0.007Re^{3.0}$ and $\langle \delta \rangle /\varDelta \times Ra/Pr = 15.4Re^{1.76}$, fit the data for $Re<400$ and $Re>400$, respectively.

JFM classification

Convection: Buoyancy-driven instability Turbulent Flows: Turbulent convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 924 , 10 October 2021 , A28
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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