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Axially homogeneous Rayleigh–Bénard convection in a cylindrical cell

Published online by Cambridge University Press:  01 December 2011

Laura E. Schmidt ,
Enrico Calzavarini ,
Detlef Lohse ,
Federico Toschi  and
Roberto Verzicco
Laura E. Schmidt
Affiliation:
Physics of Fluids, Department of Science and Technology, Impact and Mesa+ Institutes, and J. M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Enrico Calzavarini*
Affiliation:
Laboratoire de Mécanique de Lille, CNRS/UMR 8107, Université Lille 1, and Polytech’Lille, Cité Scientifique, Avenue P. Langevin, 59650 Villeneuve d’Ascq, France
Detlef Lohse
Affiliation:
Physics of Fluids, Department of Science and Technology, Impact and Mesa+ Institutes, and J. M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Federico Toschi
Affiliation:
Department of Physics, and Department of Mathematics and Computer Science, and J. M. Burgers Center for Fluid Dynamics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands CNR-IAC, Via dei Taurini 19, 00185 Rome, Italy
Roberto Verzicco
Affiliation:
Physics of Fluids, Department of Science and Technology, Impact and Mesa+ Institutes, and J. M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands Department of Mechanical Engineering, University of Rome ‘Tor Vergata’, Via del Politecnico 1, 00133 Rome, Italy
*
†Email address for correspondence: enrico.calzavarini@polytech-lille.fr
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Abstract

Previous numerical studies have shown that the ‘ultimate regime of thermal convection’ can be attained in a Rayleigh–Bénard cell when the kinetic and thermal boundary layers are eliminated by replacing both lateral and horizontal walls with periodic boundary conditions (homogeneous Rayleigh–Bénard convection). Then, the heat transfer scales like and turbulence intensity as , where the Rayleigh number indicates the strength of the driving force (for fixed values of , which is the ratio between kinematic viscosity and thermal diffusivity). However, experiments never operate in unbounded domains and it is important to understand how confinement might alter the approach to this ultimate regime. Here we consider homogeneous Rayleigh–Bénard convection in a laterally confined geometry – a small-aspect-ratio vertical cylindrical cell – and show evidence of the ultimate regime as is increased: in spite of the lateral confinement and the resulting kinetic boundary layers, we still find at . Further, it is shown that the system supports solutions composed of modes of exponentially growing vertical velocity and temperature fields, with as the critical parameter determining the properties of these modes. Counter-intuitively, in the low- regime, or for very narrow cylinders, the numerical simulations are susceptible to these solutions, which can dominate the dynamics and lead to very high and unsteady heat transfer. As is increased, interaction between modes stabilizes the system, evidenced by the increasing homogeneity and reduced fluctuations in the root-mean-square velocity and temperature fields. We also test that physical results become independent of the periodicity length of the cylinder, a purely numerical parameter, as the aspect ratio is increased.

JFM classification

Convection: Buoyancy-driven instability Turbulent Flows: Turbulent convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 691 , 25 January 2012 , pp. 52 - 68
Copyright
Copyright © Cambridge University Press 2011

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Schmidt et al. supplementary material

Destabilization of the growing dipolar mode: Instantaneous contour plots of the dimensionless vertical velocity w through a vertical cross-section of the cell, for Rayleigh $Ra=7.66 \cdot 10^{3}$, Prandtl Pr = 1 and Aspect-ratio $\Gamma = 1/2$. The color scale is varied according to the flow so that the structures can be seen at all times.

Download Schmidt et al. supplementary material(Video)
Video 1.2 MB

Schmidt et al. supplementary material

Destabilization of the growing dipolar mode: Instantaneous contour plots of the dimensionless vertical velocity w through a vertical cross-section of the cell, for Rayleigh $Ra=7.66 \cdot 10^{3}$, Prandtl Pr = 1 and Aspect-ratio $\Gamma = 1/2$. The color scale is varied according to the flow so that the structures can be seen at all times.

Download Schmidt et al. supplementary material(Video)
Video 1.7 MB