Transient analysis of Rayleigh–Bénard convection with a RANS model

Abstract

Abstract Rayleigh–Benard (RB) convection at high Rayleigh numbers was studied by transient Reynolds-averaged-Navier–Stokes (TRANS) approach. The aim of the study was to assess the RANS method in reproducing the coherent structure and large-scale unsteadiness in buoyancy-driven turbulent flows. The method can be regarded as a very large eddy simulation (VLES) combining the rationale of the LES and of RANS modelling. Following the experimental and DNS evidence that the RB convection is characterised by a coherent cellular motion with scales which are much larger than the scales of the rest of turbulent fluctuations, the instantaneous flow properties are decomposed into time-mean, periodic and random (triple decomposition). A conventional single-point closure (here an algebraic low-Re-number k−e− θ 2 stress/flux model), used for the unresolved motion, was found to reproduce well the near-wall turbulent heat flux and wall heat transfer. The large scale motion, believed to be the major mode of heat and momentum transfer in the bulk central region, is fully resolved by time solutions. In contrast to LES, the contribution of both modes to the turbulent fluctuations are of the same order of magnitude. In the horizontal wall boundary layers the model accounts almost fully for the turbulence statistics, with a marginal contribution of resolved scales. The approach was assessed by comparison with the available direct numerical simulations (DNS) and experimental data using several criteria: visual observation of the large structure morphology, different structure identification techniques, and long-term averaged mean flow and turbulence properties. A visible similarity with large structures in DNS was observed. The mean flow variables, second-moments and wall heat transfer show good agreement with most DNS and experimental results for different flow cases considered.