Assessing turbulence-radiation interactions in turbulent flows of non-gray media. (August 2019) - Silvestri, S.; Roekaerts, D.J.E.M.; Pecnik, R.
Highlights: We investigated the effect of a temperature and wavelength dependent absorption coefficient on the temperature radiation interactions in a turbulent flow of participating media. Approximations for radiative field fluctuations were analytically derived. Gray gas cases showed that absorption coefficient fluctuations can be neglected independently on the optical thickness. A diagnostic quantity to compare non-grey gas cases was introduced. Wavelength dependent absorption coefficient results in a increase of "effective" optical thickness in terms of temperature radiation interaction effects. A different spectral averaging procedure, which takes into account turbulence, results in a spectrally mean optical thickness which is good predictor for TRI. Abstract: The present work investigates gray and non-gray gas turbulence-radiation interactions (TRI) in a turbulent channel flow bounded by two isothermal hot and cold walls. Cases of various optical thicknesses are examined using Direct Numerical Simulations (DNS), coupled with a computationally efficient Monte Carlo radiative transfer solver. Several novel concepts are presented which not only allow to uniquely characterize but also to accurately model TRI for a wide range optical properties in non-reacting flows. First, we propose linear relations between fluctuations in radiative quantities (emission, incident radiation and absorption coefficient) and temperature fluctuations, where the coefficients of proportionality are solely functions of averaged quantities (e.g. emission fluctuations E ′ can be related with temperature θ in the following way, E ′ = f E ( θ ¯ ) θ ′ ). The validity of these linear relations is supported by an excellent agreement with DNS for all considered gray gas cases. Using these linear relations it is possible to show that gray gas TRI can be fully characterized without accounting for fluctuations in absorption coefficient. Second, TRI for non-gray gases is investigated and the developed concepts are extended to account for the spectrally varying absorption coefficient. In particular, the derived linear relations are used to show that the influence of a wavelength dependent κ manifests itself in an increase of the "effective" optical thickness of the flow. A new turbulence based spectral averaging is proposed that results in a mean κ, which uniquely characterizes TRI of non-gray participating media. Finally, we apply our models to estimate classical TRI (impact of fluctuations in radiative quantities on the mean radiative source) and a perfect agreement with DNS is observed. We anticipate that the proposed formulations also have the potential to allow for a better characterization in TRI, where strong temperature fluctuations are present, such as in combustion applications. Yet, this needs to be explored in future studies.