Simulation of Rayleigh-Benárd convection at up to Ra=1016 by generalized elliptic-relaxation hybrid RANS-LES model

Abstract We performed simulations of Rayleigh-Benard convection (RBC) for very high Ra number, 10 9 , 10 12 , 10 13 , 10 14 and 10 16 , thus beyond the reach of classical LES, by using an elliptic-relaxation hybrid RANS-LES (ER-HRL) model paired with a compound wall treatment that allows much coarser mesh resolution in the near wall region. The standard switching criterion used in the hybrid RANS-LES modeling based on wall distance is modified and linked to the local turbulence properties in order to sustain the modeled turbulence production in the RBC configuration. The proposed hybrid model successfully predicts the main integral and mean flow features at Ra = 10 9 for which experimental and LES data exists. The Nusselt number obtained is closely following the power law correlation based on 0.307 exponent up to Ra = 10 13 . For higher Ra number, the Nusselt number displays a Ra -scaling behaviour that is consistent with the so-called ultimate regime, where Nu ≈ Ra 1 / 2 . Furthermore, unlike LES, the ER-HRL model provides generally good results even when using a very coarse mesh at high Ra number. The instantaneous three-dimensional fields reveal interesting features of the Rayleigh-Benard convection at very high Ra number such as a strong correlation between instantaneous pressure and temperature fields, a major similarity of the flow structures in the near-wall region to those present in the impinging jet, existence of the superstructures and their tendency to cluster and localise with increasing Ra number. The simulations are performed with an in–house unstructured finite-volume code T-Flows, using second-order-accuracy discretisation schemes for space and time.