Rayleigh–Bénard convection in a cubic cell under the effects of gas radiation up to [formula omitted

Abstract

This paper investigates radiative transfer effects on Rayleigh–Bénard convection in a cubic cell over a large range of Rayleigh numbers, from Ra=103 (below the onset of convection) to Ra=109 in the turbulent regime. Coupled direct numerical simulations are carried out for a radiating air/H2O/CO2 mixture at room temperature, using a Chebyshev spectral method for the flow and a ray-tracing method for the radiation field. For the highest Rayleigh numbers, a subgrid model is used to account for the radiation of the smallest, non-optically thin, turbulent scales. Symmetry and time-averaging (for unsteady solutions) are applied to compare coupled and uncoupled results, regardless of the multiple flow configurations that may be obtained. At low Rayleigh number, the potential energy decreases, and the onset of convection is delayed when radiation is taken into account. However, once convection settles, the potential energy increases with radiation, leading to a higher convective flux in the core and a higher kinetic energy. Specific contributions of radiative transfer to the potential energy balance and to the thermal energy balance are highlighted. It is also shown that the ratio of radiative and convective source terms in the energy balance roughly scales as Ra−1/2 and that radiative transfer effects weaken at high Rayleigh numbers. Finally, radiative transfer effects on turbulence budgets of mechanical and thermal fluctuations are analysed in the range 107≤Ra≤109. The magnitude of each term of these budgets is stronger when radiation is taken into account. However, radiative dissipation has little influence on the temperature fluctuation budget.