HYBRID NONGRAY RADIATIVE TRANSFER EQUATION SOLVER USING FULL SPECTRUM CORRELATED K-DISTRIBUTION (FSCK) METHOD FOR COMBUSTION GASES

The Full Spectrum Correlated k-Distribution (FSK) method is a state-of-the-art popular method for the treatment of the extremely oscillatory spectral absorption coefficient of combustion gases. It offers high accuracy while requiring the RTE to be solved for only a few quadrature points in reordered spectral (or g) space. However, solution of the RTE for even a few quadrature points can be expensive for multidimensional problems. To further improve computational efficiency, the current study proposes a Hybrid nongray RTE solver. The Discrete Ordinates Method (DOM) or its variant, the Finite Angle Method (FAM), yields accurate solutions when used with sufficient angular resolution, especially when the medium is optically thin. However, this can be computationally expensive. On the other hand, the lowest order spherical harmonics approximation (P1) yields a single elliptic partial differential equation and is relatively efficient to solve. However, the P1 approximation is accurate only when the intensity field is fairly isotropic, as is the case in optically thick media. The new Hybrid solver utilizes the P1 method for optically thick parts of the spectrum (quadrature points), while using FAM for the remaining quadrature points. Another variation of the proposed approach where the FAM is used within a spectral window is also explored. Several test cases, both one-dimensional and two-dimensional, are considered to assess the Hybrid solver. The proposed Hybrid solver was found to offer a 2-3 times speed-up from FAM while offering comparable accuracy to FAM solutions.