Subgrid-scale model for radiative transfer in turbulent participating media

The simulation of turbulent flows of radiating gases, taking into account all turbulence length scales with an accurate radiation transport solver, is computationally prohibitive for high Reynolds or Rayleigh numbers. This is particularly the case when the small structures are not optically thin. We develop in this paper a radiative transfer subgrid model suitable for the coupling with direct numerical simulations of turbulent radiating fluid flows. Owing to the linearity of the Radiative Transfer Equation (RTE), the emission source term is spatially filtered to define large-scale and subgrid-scale radiation intensities. The large-scale or filtered intensity is computed with a standard ray tracing method on a coarse grid, and the subgrid intensity is obtained analytically (in Fourier space) from the Fourier transform of the subgrid emission source term. A huge saving of computational time is obtained in comparison with direct ray tracing applied on the fine mesh. Model accuracy is checked for three 3D fluctuating temperature fields. The first field is stochastically generated and allows us to discuss the effects of the filtering level and of the optical thicknesses of the whole medium, of the integral length scale, and of the cutoff wave length. The second and third cases correspond respectively to turbulent natural convection of humid air in a cubical box, and to the flow of hot combustion products inside a channel. In all cases, the achieved accuracy on radiative powers and wall fluxes is about a few percents.