A Narrow Band-Based Multiscale Multigroup Full-Spectrum $k$-Distribution Method for Radiative Transfer in Nonhomogeneous Gas-Soot Mixtures

The full-spectrum $k$-distribution (FSK) approach has become a promising method for radiative heat transfer calculations in strongly nongray participating media, due to its ability to achieve high accuracy at a tiny fraction of the line-by-line (LBL) computational cost. However, inhomogeneities in temperature, total pressure, and component mole fractions severely challenge the accuracy of the FSK approach. The objective of this paper is to develop a narrow band-based hybrid FSK model that is accurate for radiation calculations in combustion systems containing both molecular gases and nongray particles such as soot with strong temperature and mole fraction inhomogeneities. This method combines the advantages of the multigroup FSK method for temperature inhomogeneities in a single species, and the modified multiscale FSK method for concentration inhomogeneities in gas-soot mixtures. In this new method, each species is considered as one scale; the absorption coefficients within each narrow band of every gas scale are divided into $M$ exclusive spectral groups, depending on their temperature dependence. Accurate and compact narrow band multigroup databases are constructed for combustion gases such as $CO2$ and $H2O$⁠. Sample calculations are performed for a 1D medium and also for a 2D axisymmetric combustion flame. The narrow band-based hybrid method is observed to accurately predict heat transfer from extremely inhomogeneous gas-soot mixtures with/without wall emission, yielding close-to-LBL accuracy.