Modeling in-depth transfer of thermal radiation in non-gray condensed materials

Abstract

In-depth radiation absorption is a key mechanism in the flammability and decomposition of materials. This mechanism is commonly modeled by Beer's law or by solving the radiative transfer equation (RTE) by applying a mean value of the material's absorption coefficient. The mentioned approaches cannot be accurate because they neglect the spectral nature of the absorption coefficient and the real directional distribution of the thermal radiation inside the condensed materials. This research aims to efficiently address thermal radiation's spectral and directional details when modeling in-depth radiation absorption and emission for fire simulations. To handle the spectral aspect, a full spectrum k-distribution (FSK) method was developed for the condensed materials. This method greatly improved accuracy compared to the gray method (constant absorption coefficient). However, due to the weakness of the FSK method in estimating medium emission, the separated FSK (SFSK) method was developed to solve the issue by separately treating the irradiation of the source and medium emission. An ordinate weighting method (OWM) was developed for the finite volume method (FVM) to consider interface refraction in the directional distribution of the radiation. This method relates the angular distributions of the radiative heat fluxes at both sides of the interface by assigning a weighting parameter to each pair of control angles. The spectroscopy technique was used to extract the absorption coefficient spectrum and optical constants of black poly (methyl methacrylate) (PMMA). Then, an efficient level of thermal radiation details was proposed by applying different combinations of the developed methods and simplified approaches to the PMMA pyrolysis modeling problem. The proposed thermal radiation details are the two-flux method for RTE solution, the gray method with source temperature- and depth-dependent absorption coefficient, and the diffuse interface with equivalent reflectivities.