Turbulence-Radiation Interactions in Flames: A Chaotic-Map Based Formulation

In this paper we report initial efforts in developing large-eddy simulation (LES) subgrid-scale (SGS) models capable of treating turbulence-radiation interactions in sufficient detail to permit calculation of radiation intensity fluctuations on small scales. These models are constructed with a fluctuating component consisting of a discrete dynamical system (chaotic map) and are thus completely deterministic. We present an outline of the development of this formulation and then employ experimental data to generate large-scale behavior permitting what might be viewed as part of an a priori test of the SGS model. We display spatially extensive instantaneous fluctuating temperatures produced by the model as well as time series of fluctuating intensity calculated from the radiative transfer equation at several heights in a pool fire. We conclude that such results are physically realistic (and very efficiently computed) and warrant continued investigations, but we have at this time not yet completely validated the approach due to lack of detailed laboratory data.