Interaction of compressible turbulence and radiation of heat using large-eddy simulation

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Direct numerical simulations of turbulent flows that are affected by radiation of heat are not possible at the present time (except in strongly simplified settings) due to the enormous computational effort needed. Presently available high-performance computers are, however, powerful enough to allow for large-eddy simulations (LES) of turbulence-radiation interaction (TRI). With very few exceptions TRI has, up to now, been treated on a statistical level, i.e. the mean product of spectral absorption coefficient and spectral radiation intensity (which is just one specific term appearing in the radiative transfer equation) was modelled using statistically averaged quantities. When the radiative transfer equation (RTE) is low-pass filtered to perform an LES, unknown terms appear that need modelling to close the equation. First attempts in this direction, found in the literature, are however incomplete.It is the aim of this project to develop a modelling strategy for all unclosed terms in the lowpass filtered RTE for a non-scattering medium, i.e. for the subgrid-scale contributions to spectral emission and absorption. To this end a transport equation for the filtered density function (PDF) involving temperature and species mass fractions (or the mixture fraction) is modelled and solved. The PDF allows the evaluation of all unknown filtered terms. A priori tests of this ansatz will be made by performing a DNS of supersonic turbulent flow (without radiation) In a minimal channel using water vapour at a temperature level of 1200 K. When the wall temperatures are of the order of 1000 K the core flow will at least reach 1200 K as a result of kinetic energy dissipation. This flow field contains fluctuations of temperature and species mass fraction and allows the computation of radiation properties and radiation intensities without computing the full coupling between radiation and turbulence. A comparison of filtered DNS data and modelled terms in the radiative transfer equation (a priori test) will show the validity of the approach and allow for LES of TRI.