Radiation statistics in homogeneous isotropic turbulence

Abstract

An analysis of the interaction between turbulence and radiation in homogeneous and isotropic turbulence has been carried out. A direct numerical simulation code was used to generate instantaneous turbulent scalar fields, and the radiative transfer equation was solved to provide statistical data of the radiation intensity and absorption coefficient, as well as correlations related to radiative emission and absorption. In addition, the time averaged radiative transfer equation was solved and the mean radiation intensity, mean absorption coefficient, and mean emission and absorption terms were computed and compared with those derived from the statistical data. An analysis of the number of samples required to achieve statistically meaningful results is presented. The influence of the optical thickness of the medium, mean and variance of the temperature, and variance of the mean molar fraction of the absorbing species were studied. The moments of the radiation intensity, Planck and incident mean absorption coefficient and emission and absorption correlations relevant to the turbulence – radiation interaction were calculated. It was found that in all cases the correlation between fluctuations of the absorption coefficient and fluctuations of the radiation intensity is small, which supports the optically thin fluctuation approximation, and justifies the good predictions achieved using the time averaged radiative transfer equation.