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 - 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 - 2022/2/25
Y1 - 2022/2/25
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.
UR - https://www.scopus.com/pages/publications/85125557928
U2 - 10.1103/PhysRevLett.128.084501
DO - 10.1103/PhysRevLett.128.084501
M3 - 文章
C2 - 35275677
AN - SCOPUS:85125557928
SN - 0031-9007
VL - 128
JO - Physical Review Letters
JF - Physical Review Letters
IS - 8
M1 - 084501
ER -