Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-10T08:48:29.326Z Has data issue: false hasContentIssue false
  • English
  • Français

Exploring the severely confined regime in Rayleigh–Bénard convection

Published online by Cambridge University Press:  23 September 2016

Kai Leong Chong  and
Ke-Qing Xia
Kai Leong Chong
Affiliation:
Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China
Ke-Qing Xia*
Affiliation:
Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China
*
†Email address for correspondence: kxia@cuhk.edu.hk
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the effect of severe geometrical confinement in Rayleigh–Bénard convection with a wide range of width-to-height aspect ratio $\unicode[STIX]{x1D6E4}$, $1/128\leqslant \unicode[STIX]{x1D6E4}\leqslant 1$, and Rayleigh number $Ra$, $3\times 10^{4}\leqslant Ra\leqslant 1\times 10^{11}$, at a fixed Prandtl number of $Pr=4.38$ by means of direct numerical simulations in Cartesian geometry with no-slip walls. For convection under geometrical confinement (decreasing $\unicode[STIX]{x1D6E4}$ from 1), three regimes can be recognized (Chong et al., Phys. Rev. Lett., vol. 115, 2015, 264503) based on the global and local properties in terms of heat transport, plume morphology and flow structures. These are Regime I: classical boundary-layer-controlled regime; Regime II: plume-controlled regime; and Regime III: severely confined regime. The study reveals that the transition into Regime III leads to totally different heat and momentum transport scalings and flow topology from the classical regime. The convective heat transfer scaling, in terms of the Nusselt number $Nu$, exhibits the scaling $Nu-1\sim Ra^{0.61}$ over three decades of $Ra$ at $\unicode[STIX]{x1D6E4}=1/128$, which contrasts sharply with the classical scaling $Nu-1\sim Ra^{0.31}$ found at $\unicode[STIX]{x1D6E4}=1$. The flow in Regime III is found to be dominated by finger-like, long-lived plume columns, again in sharp contrast with the mushroom-like, fragmented thermal plumes typically observed in the classical regime. Moreover, we identify a Rayleigh number for regime transition, $Ra^{\ast }=(29.37/\unicode[STIX]{x1D6E4})^{3.23}$, such that the scaling transition in $Nu$ and $Re$ can be clearly demonstrated when plotted against $Ra/Ra^{\ast }$.

JFM classification

Low-Reynolds-number flows: Hele-Shaw flows Low-Reynolds-number flows: Low-Reynolds-number flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 805 , 25 October 2016 , R4
Check for updates
Copyright
© 2016 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer & large-scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81 (2), 503–537.CrossRefGoogle Scholar
Bailon-Cuba, J., Emran, M. S. & Schumacher, J. 2010 Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection. J. Fluid Mech. 655, 152–173.CrossRefGoogle Scholar
Bizon, C., Werne, J., Predtechensky, A. A., Julien, K., McCormick, W. D., Swift, J. B. & Swinney, H. L. 1997 Plume dynamics in quasi-2D turbulent convection. Chaos 7 (1), 107–124.CrossRefGoogle ScholarPubMed
Brown, E., Nikolaenko, A. & Ahlers, G. 2005 Reorientation of the large-scale circulation in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 95, 084503.CrossRefGoogle ScholarPubMed
Cheng, J. S., Stellmach, S., Ribeiro, A., Grannan, A., King, E. M. & Aurnou, J. M. 2015 Laboratory-numerical models of rapidly rotating convection in planetary cores. Geophys. J. Intl 201 (1), 1–17.CrossRefGoogle Scholar
Chillà, F. & Schumacher, J. 2012 New perspectives in turbulent Rayleigh–Bénard convection. Eur. Phys. J. E 35, 1–25.Google ScholarPubMed
Ching, E. S. C. & Tam, W. S. 2006 Aspect-ratio dependence of heat transport by turbulent Rayleigh–Bénard convection. J. Turbul. 7, 1–10.Google Scholar
Chong, K. L., Huang, S. D., Kaczorowski, M. & Xia, K. Q. 2015 Condensation of coherent structures in turbulent flows. Phys. Rev. Lett. 115, 264503.CrossRefGoogle ScholarPubMed
Cioni, S., Ciliberto, S. & Sommeria, J. 1997 Strongly turbulent Rayleigh–Bénard convection in mercury: comparison with results at moderate Prandtl number. J. Fluid Mech. 335, 111–140.CrossRefGoogle Scholar
Funfschilling, D., Brown, E., Nikolaenko, A. & Ahlers, G. 2005 Heat transport by turbulent Rayleigh–Bénard convection in cylindrical cells with aspect ratio one and larger. J. Fluid Mech. 536, 145–154.CrossRefGoogle Scholar
Grooms, I., Julien, K., Weiss, J. B. & Knobloch, E. 2010 Model of convective Taylor columns in rotating Rayleigh–Bénard convection. Phys. Rev. Lett. 104, 224501.CrossRefGoogle ScholarPubMed
Grossmann, S. & Lohse, D. 2000 Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 27–56.CrossRefGoogle Scholar
Grossmann, S. & Lohse, D. 2001 Thermal convection for large Prandtl numbers. Phys. Rev. Lett. 86 (15), 3316.CrossRefGoogle ScholarPubMed
Grossmann, S. & Lohse, D. 2003 On geometry effects in Rayleigh–Bénard convection. J. Fluid Mech. 486, 105–114.CrossRefGoogle Scholar
Hewitt, D. R., Neufeld, J. A. & Lister, J. R. 2012 Ultimate regime of high Rayleigh number convection in a porous medium. Phys. Rev. Lett. 108, 224503.CrossRefGoogle Scholar
Huang, S.-D., Kaczorowski, M., Ni, R. & Xia, K.-Q. 2013 Confinement-induced heat-transport enhancement in turbulent thermal convection. Phys. Rev. Lett. 111, 104501.CrossRefGoogle ScholarPubMed
Huang, S.-D. & Xia, K.-Q. 2016 Effects of geometric confinement in quasi-2-D turbulent Rayleigh–Bénard convection. J. Fluid Mech. 794, 639–654.CrossRefGoogle Scholar
Kaczorowski, M., Chong, K.-L. & Xia, K.-Q. 2014 Turbulent flow in the bulk of Rayleigh–Bénard convection: aspect-ratio dependence of the small-scale properties. J. Fluid Mech. 747, 73–102.CrossRefGoogle Scholar
Kaczorowski, M., Shishkin, A., Shishkina, O. & Wagner, C 2008 Development of a numerical procedure for direction simulations of turbulent convection in a closed rectangular cell. New Results Numerical Exp. Fluids Mech. VI 96, 381–388.CrossRefGoogle Scholar
Kaczorowski, M. & Xia, K.-Q. 2013 Turbulent flow in the bulk of Rayleigh–Bénard convection: small-scale properties in a cubic cell. J. Fluid Mech. 722, 596–617.CrossRefGoogle Scholar
Kadanoff, L. P. 2001 Turbulent heat flow: structures and scaling. Phys. Today 54 (8), 34–39.CrossRefGoogle Scholar
King, E. M., Stellmach, S. & Aurnou, J. M. 2012 Heat transfer by rapidly rotating Rayleigh–Bénard convection. J. Fluid Mech. 691, 568–582.CrossRefGoogle Scholar
Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42, 335–364.CrossRefGoogle Scholar
Ni, R., Huang, S.-D. & Xia, K.-Q. 2015 Reversals of the large-scale circulation in quasi-2D Rayleigh–Bénard convection. J. Fluid Mech. 778, R5.CrossRefGoogle Scholar
Nikolaenko, A., Brown, E., Funfschilling, D. & Ahlers, G. 2005 Heat transport by turbulent Rayleigh–Bénard convection in cylindrical cells with aspect ratio one and less. J. Fluid Mech. 523, 251–260.CrossRefGoogle Scholar
van der Poel, E. P., Stevens, R. J. A. M. & Lohse, D. 2011 Connecting flow structures and heat flux in turbulent Rayleigh–Bénard convection. Phys. Rev. E 84 (4), 045303.Google ScholarPubMed
van der Poel, E. P., Stevens, R. J. A. M., Sugiyama, K. & Lohse, D. 2012 Flow states in two-dimensional Rayleigh–Bénard convection as a function of aspect-ratio and Rayleigh number. Phys. Fluids 24, 085104.CrossRefGoogle Scholar
Shang, X.-D., Qiu, X.-L., Tong, P. & Xia, K.-Q. 2003 Measured local heat transport in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 90, 074501.CrossRefGoogle ScholarPubMed
Shishkina, O., Stevens, R. J. A. M, Grossmann, S. & Lohse, D. 2010 Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution. New J. Phys. 12, 075022.CrossRefGoogle Scholar
Stevens, R. J. A. M., Zhong, J. Q., Clercx, H. J. H., Ahlers, G. & Lohse, D. 2009 Transitions between turbulent states in rotating Rayleigh–Bénard convection. Phys. Rev. Lett. 103, 024503.CrossRefGoogle ScholarPubMed
Sun, C., Ren, L.-Y., Song, H. & Xia, K.-Q. 2005a Heat transport by turbulent Rayleigh–Bénard convection in cylindrical cells of widely varying aspect ratios. J. Fluid Mech. 542, 165–174.CrossRefGoogle Scholar
Sun, C., Xi, H.-D. & Xia, K.-Q. 2005b Azimuthal symmetry, flowdynamics, and heat transport in turbulent thermal convection in a cylinder with an aspect ratio of 0.5. Phys. Rev. Lett. 95, 074502.CrossRefGoogle Scholar
Wagner, S. & Shishkina, O. 2013 Aspect-ratio dependency of Rayleigh–Bénard convection in box-shaped containers. Phys. Fluids 25, 085110.CrossRefGoogle Scholar
Wei, P., Weiss, S. & Ahlers, G. 2015 Multiple transitions in rotating turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 114, 114506.CrossRefGoogle ScholarPubMed
Wu, X.-Z. & Libchaber, A. 1992 Scaling relations in thermal turbulence: the aspect-ratio dependence. Phys. Rev. A 45 (2), 842–845.CrossRefGoogle ScholarPubMed
Xi, H.-D., Lam, S. & Xia, K.-Q. 2004 From laminar plumes to organized flows: the onset of large-scale circulation in turbulent thermal convection. J. Fluid Mech. 503 (47), 47–56.CrossRefGoogle Scholar
Xi, H.-D., Zhou, Q. & Xia, K.-Q. 2006 Azimuthal motion of the mean wind in turbulent thermal convection. Phys. Rev. E 73 (5), 056312.Google ScholarPubMed
Xia, K.-Q. 2013 Current trends and future directions in turbulent thermal convection. Theor. Appl. Mech. Lett. 3, 052001.CrossRefGoogle Scholar
Xia, K.-Q. & Lui, S.-L. 1997 Turbulent thermal convection with an obstructed sidewall. Phys. Rev. Lett. 79, 5006–5009.CrossRefGoogle Scholar
Yang, Y., Verzicco, R. & Lohse, D. 2016 From convection rolls to finger convection in double-diffusive turbulence. Proc. Natl Acad. Sci. USA 113, 69–73.CrossRefGoogle ScholarPubMed
Zhou, Q., Liu, B.-F., Li, C.-M. & Zhong, B.-C. 2012 Aspect ratio dependence of heat transport by turbulent Rayleigh–Bénard convection in rectangular cells. J. Fluid Mech. 710, 260–276.CrossRefGoogle Scholar
Zhou, Q. & Xia, K.-Q. 2010 Physical and geometrical properties of thermal plumes in turbulent Rayleigh–Bénard convection. New J. Phys. 12, 075006.Google Scholar