Direct numerical simulation of Nusselt number scaling in rotating Rayleigh-Bénard convection

G.L. Kooij; M.A. Botchev; B.J. Geurts

doi:10.1016/j.ijheatfluidflow.2015.05.016

Direct numerical simulation of Nusselt number scaling in rotating Rayleigh-Bénard convection

G.L. Kooij^*, M.A. Botchev, B.J. Geurts

^*Corresponding author for this work

Multiscale Modeling and Simulation

Research output: Contribution to journal › Article › Academic › peer-review

19 Citations (Scopus)

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Abstract

We report results from Direct Numerical Simulation (DNS) of rotating Rayleigh-Bénard convection, regarding the scaling of heat transfer with the Rayleigh number for rotating systems at a fixed rate of rotation. The Prandtl number, Pr=6.4, is kept constant. We perform simulations, using a spectral element method, for Rayleigh numbers Ra from 10⁶ to 10⁹, and Rossby numbers Ro from 0.09 to ∞. We find that the Nusselt number Nu scales approximately with a power 2/7 of Ra at sufficiently high Ra for all Ro. The value of Ra beyond which this Nusselt scaling is well established increases with decreasing Ro. Depending on the rotation rate, the Nusselt number can increase up to 18% with respect to the non-rotating case.

Original language	English
Pages (from-to)	26-33
Number of pages	8
Journal	International journal of heat and fluid flow
Volume	55
DOIs	https://doi.org/10.1016/j.ijheatfluidflow.2015.05.016
Publication status	Published - 1 Oct 2015

Keywords

Direct numerical simulation
Heat transfer
Rayleigh-Bénard convection
Rotation
Turbulence
2023 OA procedure

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10.1016/j.ijheatfluidflow.2015.05.016

ArticleFinal published version, 2.6 MBLicence: Taverne

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title = "Direct numerical simulation of Nusselt number scaling in rotating Rayleigh-B{\'e}nard convection",

abstract = "We report results from Direct Numerical Simulation (DNS) of rotating Rayleigh-B{\'e}nard convection, regarding the scaling of heat transfer with the Rayleigh number for rotating systems at a fixed rate of rotation. The Prandtl number, Pr=6.4, is kept constant. We perform simulations, using a spectral element method, for Rayleigh numbers Ra from 106 to 109, and Rossby numbers Ro from 0.09 to ∞. We find that the Nusselt number Nu scales approximately with a power 2/7 of Ra at sufficiently high Ra for all Ro. The value of Ra beyond which this Nusselt scaling is well established increases with decreasing Ro. Depending on the rotation rate, the Nusselt number can increase up to 18% with respect to the non-rotating case.",

keywords = "Direct numerical simulation, Heat transfer, Rayleigh-B{\'e}nard convection, Rotation, Turbulence, 2023 OA procedure",

author = "G.L. Kooij and M.A. Botchev and B.J. Geurts",

note = "Funding Information: This project is supported financially by NWO , the Netherlands Organisation for Scientific Research, through FOM, Foundation for Fundamental Research on Matter, as part of the “Ultimate Turbulence” program. The simulations were made possible through Grant SH-061 of the Computational Science Board of NWO, and executed on the supercomputers of SURFsara in Amsterdam. The work of the second author is supported in part by the Institute of Numerical Mathematics , Russian Academy of Sciences , Moscow through the Russian Science Foundation Grant 14-11-00659 . Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

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doi = "10.1016/j.ijheatfluidflow.2015.05.016",

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AU - Kooij, G.L.

AU - Botchev, M.A.

AU - Geurts, B.J.

N1 - Funding Information: This project is supported financially by NWO , the Netherlands Organisation for Scientific Research, through FOM, Foundation for Fundamental Research on Matter, as part of the “Ultimate Turbulence” program. The simulations were made possible through Grant SH-061 of the Computational Science Board of NWO, and executed on the supercomputers of SURFsara in Amsterdam. The work of the second author is supported in part by the Institute of Numerical Mathematics , Russian Academy of Sciences , Moscow through the Russian Science Foundation Grant 14-11-00659 . Publisher Copyright: © 2015 Elsevier Inc.

PY - 2015/10/1

Y1 - 2015/10/1

N2 - We report results from Direct Numerical Simulation (DNS) of rotating Rayleigh-Bénard convection, regarding the scaling of heat transfer with the Rayleigh number for rotating systems at a fixed rate of rotation. The Prandtl number, Pr=6.4, is kept constant. We perform simulations, using a spectral element method, for Rayleigh numbers Ra from 106 to 109, and Rossby numbers Ro from 0.09 to ∞. We find that the Nusselt number Nu scales approximately with a power 2/7 of Ra at sufficiently high Ra for all Ro. The value of Ra beyond which this Nusselt scaling is well established increases with decreasing Ro. Depending on the rotation rate, the Nusselt number can increase up to 18% with respect to the non-rotating case.

AB - We report results from Direct Numerical Simulation (DNS) of rotating Rayleigh-Bénard convection, regarding the scaling of heat transfer with the Rayleigh number for rotating systems at a fixed rate of rotation. The Prandtl number, Pr=6.4, is kept constant. We perform simulations, using a spectral element method, for Rayleigh numbers Ra from 106 to 109, and Rossby numbers Ro from 0.09 to ∞. We find that the Nusselt number Nu scales approximately with a power 2/7 of Ra at sufficiently high Ra for all Ro. The value of Ra beyond which this Nusselt scaling is well established increases with decreasing Ro. Depending on the rotation rate, the Nusselt number can increase up to 18% with respect to the non-rotating case.

KW - Direct numerical simulation

KW - Heat transfer

KW - Rayleigh-Bénard convection

KW - Rotation

KW - Turbulence

KW - 2023 OA procedure

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U2 - 10.1016/j.ijheatfluidflow.2015.05.016

DO - 10.1016/j.ijheatfluidflow.2015.05.016

M3 - Article

SN - 0142-727X

VL - 55

SP - 26

EP - 33

JO - International journal of heat and fluid flow

JF - International journal of heat and fluid flow

ER -

Direct numerical simulation of Nusselt number scaling in rotating Rayleigh-Bénard convection

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