CONDITIONS FOR RIGOROUS USE OF SPECTRAL BAND MODELS IN RADIATIVE TRANSFER CALCULATIONS INVOLVING NON-HOMOGENEOUS MEDIA.
Loading...
Date
1966
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Ohio State University
Abstract
The use of a spectral band model in radiative transfer calculations is equivalent to interchanging the order of integration over frequency and spatial coordinates in the radiative transfer equation and replacing the spectral absorption coefficient by a weighted average value over the frequency interval of interest, i.e., making the transformation. $\int^{\omega_{2}}_{\omega_{1}}\int^{L}_{0}R^{0}_{\omega}(s)k_{\omega}(s)\exp \left[-\int^{L}_{s}k_{\omega}(s')ds'\right]dsd\omega \rightarrow \int^{L}_{0}R^{0}_{\omega_{0}}(s) F(\omega_{1},\omega_{2},s)ds.$[FIGURE] The problem of determining when such a transformation is transformation is rigorously correct has been investigated and two sufficient conditions found: (a) if the spectral system is optically thin over the entire line of sight in the frequency interval of interest, or (2) the spectral absorption coefficient is separable into frequency and spatial parts, ie., $k_{\omega}(s) = f(\omega)g(s)$. In this latter case, the function $F(\omega_{1}, \omega_{2} s)$ has the form $G'(s)\int^{\omega_{2}}_{\omega_{1}}f(\omega)\exp[-f(\omega)G(s)]d\omega$ [FIGURE] where $G(s)\equiv \int^{L}_{s}g(s')ds'.$[FIGURE] It does not appear likely that the transformation is rigorously correct for any other form of the spectral absorption coefficient. The effects of using a spectral band model under conditions where such use is not strictly valid are considered and it is shown that gross errors are possible in such cases. Reduced forms of the radiative transfer equation for cases of isolated Lorentz lines, Elsasser bands, and isolated Doppler lines, in both the optically thick and thin limits have been obtained. Work is continuing on the case of the Doppler analog of the Elsasser band. Work supported in part by the Air Force Avionics Laboratory, Research and Technology Division, Air Force Systems Command, United States Air Force.
Description
Author Institution: Rocketdyne, A Division of North American Aviation Incorporated