Large-eddy simulation and deduced scaling analysis of Rayleigh–Bénard convection up to Ra = 10⁹

Abstract

Large-eddy simulation of turbulent Rayleigh–Bénard (RB) convection has been performed for a 6:1:6 open-ended domain for Rayleigh numbers ranging from 6.3 × 10⁵ to 10⁹ at Prandtl number of Pr = 0.71. The scaling analysis based on the LES data shows that the heat transfer follows a single relation of Nu = 0.162 Ra ^0.286, which is consistent with the scaling law for the hard turbulence regime reported in several earlier experimental and DNS studies. The present LES also supports some earlier experimental and DNS findings that most of characteristic parameters can be scaled reasonably well with Ra number in the considered Ra number range using a single relation. Nonetheless, it is found that the scaling of several quantities shows a sensible offset from a single relation, and could be fitted better with the separate scaling relations for the soft and hard convective turbulence transitioned at about Ra = 4 × 10⁷. It has been argued that the transition, reflected in the scaling relation, may be attributed to the increasing ‘containing effect’ of the plume leaving the horizontal wall on the plume approaching the wall at large Ra numbers in the near-wall region.

**This paper is a modified version from the paper presented at the Forth International Symposium of Turbulence and Shear Flow Phenomena (Williamsburg, Virginia, 27–29 June 2005).

Acknowledgments

The authors are grateful for the enlightening comments from the anonymous referees.

Notes

**This paper is a modified version from the paper presented at the Forth International Symposium of Turbulence and Shear Flow Phenomena (Williamsburg, Virginia, 27–29 June 2005).