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Radial boundary layer structure and Nusselt number in Rayleigh–Bénard convection

Published online by Cambridge University Press:  15 January 2010

RICHARD J. A. M. STEVENS ,
ROBERTO VERZICCO  and
DETLEF LOHSE
RICHARD J. A. M. STEVENS*
Affiliation:
Department of Science and Technology and J. M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
ROBERTO VERZICCO
Affiliation:
Department of Mechanical Engineering, Universitá di Roma ‘Tor Vergata’, Via del Politecnico 1, 00133 Roma, Italy
DETLEF LOHSE
Affiliation:
Department of Science and Technology and J. M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
*
†Email address for correspondence: r.j.a.m.stevens@tnw.utwente.nl
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Abstract

Results from direct numerical simulation (DNS) for three-dimensional Rayleigh–Bénard convection in a cylindrical cell of aspect ratio 1/2 and Prandtl number Pr=0.7 are presented. They span five decades of Rayleigh number Ra from 2 × 106 to 2 × 1011. The results are in good agreement with the experimental data of Niemela et al. (Nature, vol. 404, 2000, p. 837). Previous DNS results from Amati et al. (Phys. Fluids, vol. 17, 2005, paper no. 121701) showed a heat transfer that was up to 30% higher than the experimental values. The simulations presented in this paper are performed with a much higher resolution to properly resolve the plume dynamics. We find that in under-resolved simulations the hot (cold) plumes travel further from the bottom (top) plate than in the better-resolved ones, because of insufficient thermal dissipation mainly close to the sidewall (where the grid cells are largest), and therefore the Nusselt number in under-resolved simulations is overestimated. Furthermore, we compare the best resolved thermal boundary layer profile with the Prandtl–Blasius profile. We find that the boundary layer profile is closer to the Prandtl–Blasius profile at the cylinder axis than close to the sidewall, because of rising plumes close to the sidewall.

JFM classification

Turbulent Flows: Turbulent convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 643 , 25 January 2010 , pp. 495 - 507
Copyright
Copyright © Cambridge University Press 2010

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References

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Stevens et al. supplementary movie

Temperature field close to the bottom plate for the simulations at Ra = 2 x 109, Pr = 0.7, and G = 0.5, with grid resolution 129 x 65 x 257 (heights: 0.0021L, 0.0049L, 0.0079L, 0.0111L, and here lqsl=0.0056L). The dimensionless time is indicated in the top of the movie. Note that in this low resolution simulation the smoothness of the solution is insufficient to represent all flow dynamics observed in a high resolution simulation.

Download Stevens et al. supplementary movie(Video)
Video 4.5 MB

Stevens et al. supplementary movie

Temperature field close to the bottom plate for the simulations at Ra = 2 x 109, Pr = 0.7, and G = 0.5, with grid resolution 193 x 65 x 257 (heights: 0.0021L, 0.0049L, 0.0079L, 0.0111L, and here lqsl=0.0059L). The dimensionless time is indicated in the top of the movie.

Download Stevens et al. supplementary movie(Video)
Video 4.5 MB

Stevens et al. supplementary movie

Temperature field close to the bottom plate for the simulations at Ra = 2 x 109, Pr = 0.7, and G = 0.5, with grid resolution 385 x 97 x 385 (heights: 0.0020L, 0.0044L, 0.0077L, 0.0112L, and here lqsl=0.0059L). The dimensionless time is indicated in the top of the movie.

Download Stevens et al. supplementary movie(Video)
Video 4 MB

Stevens et al. supplementary movie

Temperature field at mid height for the simulations at Ra = 2 x 109, Pr = 0.7, and G = 0.5 with grid resolution 129 x 65 x 257. The dimensionless time is indicated in the top of the movie. Note that in this low resolution simulation the smoothness of the solution is insufficient to represent all flow dynamics observed in a high resolution simulation.

Download Stevens et al. supplementary movie(Video)
Video 3.9 MB

Stevens et al. supplementary movie

Temperature field at mid height for the simulations at Ra = 2 x 109, Pr = 0.7, and G = 0.5 with grid resolution 193 x 65 x 257. The dimensionless time is indicated in the top of the movie.

Download Stevens et al. supplementary movie(Video)
Video 3.9 MB

Stevens et al. supplementary movie

Temperature field at mid height for the simulations at Ra = 2 x 109, Pr = 0.7, and G = 0.5 with grid resolution 385 x 97 x 385. The dimensionless time is indicated in the top of the movie.

Download Stevens et al. supplementary movie(Video)
Video 3.9 MB