Assessment of a presumed joint pdf for the simulation of turbulence–radiation interaction in turbulent reactive flows

Turbulent reactive flows are an important problem in engineering, with a major impact on combustion efficiency, pollutant emissions and climate change. The numerical simulation of these flows is difficult, not only due to the need to address different physical phenomena, but also due to the interaction between them. The interaction between turbulence and radiation, due to the strong non-linearity between temperature and radiative emission, is the subject of the present work. To account for this interaction, the time-averaged form of the radiative transfer equation may be solved. The correlation between the absorption coefficient of the medium and the radiation intensity is often neglected in simulations, because the radiation intensity depends on the temperature and chemical composition along an optical path, and therefore it may be argued that it is relatively independent of local turbulent fluctuations. However, this approximation may introduce errors that are not negligible. A model has recently been proposed to determine that correlation, which relies on the assumption that the joint probability density function of mixture fraction and radiation intensity is a two-dimensional clipped Gaussian. This assumption is investigated here using experimental data for the mean and variance of mixture fraction for a turbulent free jet flame. It is shown that the presumed joint pdf accurately allows the evaluation of the mean radiation emission and absorption, but the prediction of the correlation between fluctuations of the absorption coefficient and fluctuations of the radiation intensity is not so good near the end of radial optical paths.

► A model for turbulence–radiation interaction in turbulent flames is assessed.
► The shape of the joint pdf of mixture fraction and radiation intensity is presumed.
► The joint pdf shape assumption in a free turbulent jet flame is reasonable.
► However, the accuracy of this assumption is not so good at the flame edge.
► The mean radiative emission and absorption terms are accurately estimated.