Hybrid Solver for the Radiative Transport Equation in Nongray Combustion Gases

Abstract

The absorption coefficient of molecular gases exhibits strong oscillations with wavelength. Thus, solution of the Radiative Transfer Equation (RTE) in a medium comprised of combustion gases require repeated solution of the gray RTE, rendering such calculations computationally very expensive. Popular methods to solve the RTE include the Finite Angle Method (FAM) and the Spherical Harmonics Method (PN). FAM, the finite-angle variant of the discrete ordinates method, produces accurate solutions when used with sufficient angular resolution. However, it has high computational cost. The lowest order Spherical Harmonics Method (P1) requires solution of a single elliptic partial differential equation and is very efficient in comparison to FAM. It yields accurate solutions for fairly isotropic intensity fields. In this study, a Hybrid solver for the nongray RTE is proposed that capitalizes upon the efficiency of the P1 method and the accuracy of the FAM. Depending on the spectral (or band) optical thickness, an appropriate solution method is chosen. The objective is to determine optimal parameters for selecting the solution method that can provide the best compromise between accuracy and computational cost. Using the statistical narrow band (SNB) model for carbon dioxide and water vapor, the nongray radiative transfer equation is solved in inhomogeneous media enclosed in multidimensional enclosures. Two different approaches — cut-off and filter optical thickness — are investigated for selecting the solution method. Several problems, both two-dimensional and three-dimensional, and with and without coupling to other modes of heat transfer are considered. The filter approach was found to be the best choice for prediction of the radiative source, while the cut-off approach was found to be the best for prediction of wall radiative heat fluxes.