Quadrature Point Selection in the Full-Spectrum K-Distribution Method for Nongray Radiation in Combustion Gases

Abstract

Abstract Radiation is the dominant mode of heat transfer in combustion environments. Combustion gases, such as carbon dioxide and water vapor, have oscillatory spectral properties. Solving the Radiative Transfer Equation (RTE) is challenging in such scenarios and requires a nongray model. The Full-Spectrum k-distribution (FSK) model is a popular state-of-the-art model that offers high accuracy while requiring the RTE to be solved for only a few quadrature points in reordered spectral (or g) space. The selection of optimal quadrature points has been investigated in the literature, broadly suggesting that 8 to 10-point schemes, with more points for larger g-values, work best. In this study, a new split scheme is tested for quadrature point distributions wherein the g-space is first split into two zones prior selecting quadrature points for each zone. The split scheme is tested for one-dimensional gas slabs with uniform properties of carbon dioxide, water vapor and a mixture for different temperatures. Slab thicknesses are varied to vary the optical thicknesses. Errors for radiative heat source and radiative wall flux are computed against benchmark line-by-line (LBL) solutions. Results are compared with existing quadrature schemes. Overall, the split scheme resulted in an improvement in accuracy compared to existing quadrature schemes more consistently across different length scales for the same number of quadrature points.