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Prandtl number dependence of flow topology in quasi-two-dimensional turbulent Rayleigh–Bénard convection

Published online by Cambridge University Press:  22 August 2024

Ze-Hao Wang ,
Xin Chen Open the ORCID record for Xin Chen [Opens in a new window] ,
Ao Xu Open the ORCID record for Ao Xu [Opens in a new window]  and
Heng-Dong Xi Open the ORCID record for Heng-Dong Xi [Opens in a new window]
Ze-Hao Wang
Affiliation:
School of Aeronautics and Institute of Extreme Mechanics, Northwestern Polytechnical University, Xi'an 710072, PR China
Xin Chen*
Affiliation:
School of Aeronautics and Institute of Extreme Mechanics, Northwestern Polytechnical University, Xi'an 710072, PR China Shanghai Institute of Applied Mathematics and Mechanics and Shanghai Key Laboratory of Mechanics in Energy Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, PR China
Ao Xu
Affiliation:
School of Aeronautics and Institute of Extreme Mechanics, Northwestern Polytechnical University, Xi'an 710072, PR China National Key Laboratory of Aircraft Configuration Design, Northwestern Polytechnical University, Xi'an 710072, PR China
Heng-Dong Xi*
Affiliation:
School of Aeronautics and Institute of Extreme Mechanics, Northwestern Polytechnical University, Xi'an 710072, PR China National Key Laboratory of Aircraft Configuration Design, Northwestern Polytechnical University, Xi'an 710072, PR China
*
†Email addresses for correspondence: xinchen99@shu.edu.cn, hengdongxi@nwpu.edu.cn
†Email addresses for correspondence: xinchen99@shu.edu.cn, hengdongxi@nwpu.edu.cn
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Abstract

To date, a comprehensive understanding of the influence of the Prandtl number ($Pr$) on flow topology in turbulent Rayleigh–Bénard convection (RBC) remains elusive. In this study, we present an experimental investigation into the evolution of flow topology in quasi-two-dimensional turbulent RBC with $7.0 \leq Pr \leq 244.2$ and $2.03\times 10^{8} \leq Ra \leq 2.81\times 10^{9}$. Particle image velocimetry (PIV) measurements reveal the flow transitions from multiple-roll state to single-roll state with increasing $Ra$, and the transition is hindered with increasing $Pr$, i.e. the transitional Rayleigh number $Ra_t$ increases with $Pr$. We mapped out a phase diagram on the flow topology change on $Ra$ and $Pr$, and identified the scaling of $Ra_t$ on $Pr$: $Ra_t \sim Pr^{0.93}$ in the low $Pr$ range, and $Ra_t \sim Pr^{3.3}$ in the high $Pr$ range. The scaling in the low $Pr$ range is consistent with the model of balance of energy dissipation time and plume travel time that we proposed in our previous study, while the scaling in the high $Pr$ range implies a new governing mechanism. For the first time, the scaling of $Re$ on $Ra$ and $Pr$ is acquired through full-field PIV velocity measurement, $Re \sim Ra^{0.63}\,Pr^{-0.87}$. We also propose that increasing horizontal velocity promotes the formation of the large-scale circulation (LSC), especially for the high $Pr$ case. Our proposal was verified by achieving LSC through introducing horizontal driving force $Ra_H$ by tilting the convection cell with a small angle.

JFM classification

Turbulent Flows: Turbulent convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 991 , 25 July 2024 , A14
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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