A narrow band model based on the absorption coefficient and its application to the calculation of radiative transfer in one-dimensional enclosures

Abstract

A narrow band model (NBM) with the absorption coefficient as the fundamental radiative property is investigated so that numerical solution methods compatible with the differential form of the radiative transfer equation (RTE) may be employed. The advantage of a NBM based on the absorption coefficient rather than the transmissivity is that the expression for the mean absorption coefficient is independent of the functional form of the probability density function for spectral line intensities, P(S). Accordingly, it is seen that the narrow-band mean absorption coefficient κ¯η=S¯d, where S¯ and d are the mean line intensity and mean line spacing, respectively, of a narrow band. The mean absorption coefficient κ¯η may be directly used in solving the differential RTE without having to specify a path length. Two approaches were considered for obtaining the ratio of S¯ and d. The first, referred to here as NBM with EM2C data, involves using S¯d values tabulated in the EM2C narrow-band property database (Riviere and Soufiani, Int J. Heat Mass Transf., Vol. 55, 2012). In the second approach, denoted as NBM with spectral averaging, κ¯η is evaluated by directly averaging the line-by-line absorption coefficients over the narrow band. Accuracy of the two NBM approaches is investigated through comparison with three other methods for calculating spectral radiative properties: (1) line-by-line (LBL) calculations that serve as the benchmark, with the spectral absorption coefficients obtained from the HITEMP 2010 database, (2) spectral line-based weighted sum of gray gasses (SLW) method, and (3) wavenumber-selective line-by-line (WS-LBL) calculations wherein the absorption coefficients are directly picked from the LBL spectrum at discrete wavenumbers separated by an interval equal to the width of the narrow band. The five spectral approaches — NBM with EM2C data, NBM with spectral averaging, LBL, SLW, and WS-LBL — are applied to compute the radiative fluxes and flux divergences in a number of 1-D, non-gray enclosures. The enclosure cases were chosen to study the effects of medium optical depth, as well as inhomogeneities in medium temperature and species concentrations, on the accuracy of the narrow band models.