Comparative analysis of reduced-order spectral models and grouping strategies for non-equilibrium radiation

Abstract

Radiative transfer calculations in complex three-dimensional domains are plagued by computational bottlenecks due to the combined cost of resolving spectral, angular, and spatial dependence. The current work presents a systematic study into the efficacy of three commonly used reduced-order wide-band models, Planck-averaging, and statistics-based k-distribution and theory of homogenization, for modeling non-equilibrium radiation. A reinterpretation of Planck-averaging based on the maximum entropy principle combined with the commonly used multi-band opacity binning allows a direct equivalence to be drawn with the two statistics-based approaches. Additionally, the three seemingly distinct methods are shown to be strictly derived only for local thermodynamic equilibrium conditions which limits their accuracy when simulating non-equilibrium radiation. This shortcoming is addressed through the development of a novel grouping strategy for defining larger groups of individual frequencies from detailed radiation databases (based on line-by-line or narrow-band models) while accounting for variation in all radiative properties under non-equilibrium. Radiative transfer calculations for different Earth and Jupiter entry problems are performed using the different spectral models. Conventional reduced-order wide-band approaches converge slowly to the solution obtained using detailed spectral models. However, the new non-equilibrium grouping strategy allows both total quantities-of-interest and their detailed spectral variation to be predicted accurately while employing fewer reduced-order groups. The current model-reduction methodology provides nearly two orders-of-magnitude decrease in required spectral evaluations along a given line-of-sight with respect to narrow-band methods (and three to four orders with respect to original LBL databases) and is ideal for coupled flow-radiation calculations.