Theoretical analysis and experimental investigations have shown that the mean heat fluxes in turbulent gaseous flows are influenced not only by the mean scalar fields (temperature and molar fraction of the species), but also by the scalar fluctuations. It is widely recognized that the increase of radiative fluxes in comparison with laminar flows may exceed 100%. This interaction between turbulence and radiation is mainly due to the non-linearity between radiative emission and temperature. It is particularly important in reactive flows, since temperature fluctuations are typically higher in these flows than in non-reactive ones. In this article, a survey of the theory concerning turbulence-radiation interaction (TRI) is presented, along with applications in numerical simulations. We firstly present experimental and theoretical fundamentals on TRI. Then, direct numerical simulation and stochastic methods are addressed. Although they provide reliable information on TRI, they are too computationally demanding for practical applications. We will then focus on methods based on the solution of the time-averaged form of the conservation equations. Although many different approaches are available, we will concentrate on two methods. One is based on the solution of the time-averaged form of the radiative transfer equation using the optically thin fluctuation approximation, and a combustion model based on a prescribed probability density function (pdf) approach. The second one is based on the photon Monte Carlo method for radiative transfer calculations in media represented by discrete particle fields, and a combustion model based on the Monte Carlo solution of the transport equation for the joint pdf of scalars. Finally, the role of TRI in large eddy simulation is discussed, and the main consequences of TRI in combustion systems are summarized.

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