Assessment of the spectral vanishing viscosity LES model for the simulation of coupled molecular radiation and Rayleigh–Bénard convection in a cubic cavity

Abstract

Large-eddy simulations (LES) of coupled turbulent convection and radiative transfer in a cubic Rayleigh–Bénard cell are performed up to a Rayleigh number of $\mathrm{Ra}=10^{10}$, for an air mixture containing small amounts of water vapor and carbon dioxide. The Spectral Vanishing Viscosity (SVV) model is used to account for the unresolved subgrid scales. The accuracy of the LES-SVV model with respect to the model parameters is assessed against Direct Numerical Simulations (DNS) at Rayleigh numbers $10^8$ and $10^9$. Comparisons between LES-SVV and DNS calculations are given in terms of first order and second order statistics, spatial auto-correlation functions, and POD eigenmodes. Simulation results at $\mathrm{Ra}=10^{10}$ show a significant increase of the kinetic energy of the mean flow and of the convective flux when radiative transfer is taken into account. On the other hand, radiation has little influence on the wall radiative and conductive fluxes, on the turbulent kinetic energy and on the variance of temperature fluctuations. In the Rayleigh number range $10^6\le Ra\le 10^{10}$, the simulations show that radiative transfer effects decrease when the Rayleigh number increases at fixed cavity size.