Computation of a turbulent Rayleigh–Benard convection with the elliptic-blending second-moment closure

Abstract

This communication reports briefly on the computational results of a turbulent Rayleigh–Benard convection with the elliptic-blending second-moment closure (EBM). The primary emphasis of the study is placed on an investigation of accuracy and numerical stability of the elliptic-blending second-moment closure for the turbulent Rayleigh–Benard convection. The turbulent heat fluxes in this study are treated by the algebraic flux model where the molecular dissipation rate of turbulent heat flux is included. The model is applied to the prediction of the turbulent Rayleigh–Benard convection for Rayleigh numbers ranging from Ra = 2 × 10 6 to Ra = 10 9, and the computed results are compared with the previous experimental correlations, T-RANS and LES results. The predicted cell-averaged Nusselt number follows the correlation by Peng et al. [S.H. Peng, K. Hanjalic, L. Davidson, Large-eddy simulation and deduced scaling analysis of Rayleigh–Benard convection up to Ra = 10 9, J. Turbulence 7 (2006) 1–29.] ( Nu = 0.162 Ra 0.286) in the ‘soft’ convective turbulence region (2 × 10 6 ≤ Ra ≤ 4 × 10 7) and it follows the experimental correlation by Niemela et al. [J.J. Niemela, L. Skrbek, K.R., Sreenivasan, R.J. Donnelly, Turbulent convection at very high Rayleigh numbers, Nature 404 (2000) 837–840.] ( Nu = 0.124 Ra 0.309) in the ‘hard’ convective turbulence region (10 8 ≤ Ra ≤ 10 9) within 5% accuracy. This result shows that the elliptic-blending second-moment closure with an algebraic flux model predicts very accurately the Rayleigh–Benard convection.