TY - JOUR

T1 - Aspect Ratio Dependence of Heat Transfer in a Cylindrical Rayleigh-Bénard Cell

AU - Ahlers, Guenter

AU - Bodenschatz, Eberhard

AU - Hartmann, Robert

AU - He, Xiaozhou

AU - Lohse, Detlef

AU - Reiter, Philipp

AU - Stevens, Richard J.A.M.

AU - Verzicco, Roberto

AU - Wedi, Marcel

AU - Weiss, Stephan

AU - Zhang, Xuan

AU - Zwirner, Lukas

AU - Shishkina, Olga

N1 - Funding Information:
The authors acknowledge the Deutsche Forschungsgemeinschaft (SPP1881 “Turbulent Superstructures” and Grants No. Sh405/7, No. Sh405/8, and No. Sh405/10), the Twente Max-Planck Center, the European Research Council (ERC Starting Grant No. 804283 UltimateRB), the National Natural Science Foundation of China (Grant No. 91952101), PRACE (Projects No. 2020235589 and No. 2020225335), and the Gauss Centre for Supercomputing e.V. for providing computing time in the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre.
Publisher Copyright:
© 2022 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

PY - 2022/2/24

Y1 - 2022/2/24

N2 - While the heat transfer and the flow dynamics in a cylindrical Rayleigh-Bénard (RB) cell are rather independent of the aspect ratio Γ (diameter/height) for large Γ, a small-Γ cell considerably stabilizes the flow and thus affects the heat transfer. Here, we first theoretically and numerically show that the critical Rayleigh number for the onset of convection at given Γ follows Rac,Γ∼Rac,∞(1+CΓ-2)2, with C ≲ 1.49 for Oberbeck-Boussinesq (OB) conditions. We then show that, in a broad aspect ratio range (1/32)≤Γ≤32, the rescaling Ra→RaℓRa[Γ2/(C+Γ2)]3/2 collapses various OB numerical and almost-OB experimental heat transport data Nu(Ra,Γ). Our findings predict the Γ dependence of the onset of the ultimate regime Rau,Γ∼[Γ2/(C+Γ2)]-3/2 in the OB case. This prediction is consistent with almost-OB experimental results (which only exist for Γ=1, 1/2, and 1/3) for the transition in OB RB convection and explains why, in small-Γ cells, much larger Ra (namely, by a factor Γ-3) must be achieved to observe the ultimate regime.

AB - While the heat transfer and the flow dynamics in a cylindrical Rayleigh-Bénard (RB) cell are rather independent of the aspect ratio Γ (diameter/height) for large Γ, a small-Γ cell considerably stabilizes the flow and thus affects the heat transfer. Here, we first theoretically and numerically show that the critical Rayleigh number for the onset of convection at given Γ follows Rac,Γ∼Rac,∞(1+CΓ-2)2, with C ≲ 1.49 for Oberbeck-Boussinesq (OB) conditions. We then show that, in a broad aspect ratio range (1/32)≤Γ≤32, the rescaling Ra→RaℓRa[Γ2/(C+Γ2)]3/2 collapses various OB numerical and almost-OB experimental heat transport data Nu(Ra,Γ). Our findings predict the Γ dependence of the onset of the ultimate regime Rau,Γ∼[Γ2/(C+Γ2)]-3/2 in the OB case. This prediction is consistent with almost-OB experimental results (which only exist for Γ=1, 1/2, and 1/3) for the transition in OB RB convection and explains why, in small-Γ cells, much larger Ra (namely, by a factor Γ-3) must be achieved to observe the ultimate regime.

KW - fluid mechanics

KW - fluid dynamics

KW - turbulence

KW - heat transfer

KW - theory

KW - Rayleigh-Benard convection

KW - convection

UR - http://www.scopus.com/inward/record.url?scp=85125557928&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.128.084501

DO - 10.1103/PhysRevLett.128.084501

M3 - Article

C2 - 35275677

AN - SCOPUS:85125557928

SN - 0031-9007

VL - 128

JO - Physical review letters

JF - Physical review letters

IS - 8

M1 - 084501

ER -