Approximate solutions of the filtered radiative transfer equation in large eddy simulations of turbulent reactive flows

An analysis of the relevance of turbulence–radiation interaction in the numerical simulation of turbulent reactive flows is presented. A semi-causal stochastic model was used to generate a time-series of turbulent scalar fluctuations along optical paths of Sandia flame D, a widely studied piloted turbulent jet nonpremixed flame. The radiative transfer equation was integrated along these paths for every realization using a grid resolution typical of a direct numerical simulation. The correlated k-distribution method was employed to compute the radiative properties of the medium. The results were used to determine the ensemble average, as well as the extreme values, of quantities that indicate the importance of the turbulence–radiation interaction. Several approximate methods are then proposed to solve the filtered radiative transfer equation in the framework of large eddy simulations. The proposed methods are applicable along with combustion models that either assume the filtered probability density function of a conserved scalar or solve a transport equation for a joint scalar or joint scalar/velocity filtered density function. It is concluded that the errors resulting from neglecting the turbulence–radiation interaction in large eddy simulations are much lower than those found in Reynolds-averaged Navier–Stokes calculations. The optically thin fluctuation approximation may be extended to large eddy simulations yielding predictions in excellent agreement with the reference solution. If the turbulence–radiation interaction is accounted for using this approximation, the average relative error of the filtered total radiation intensity is generally below 0.3% for the studied flame.