Similarity parameters for radiative energy transfer in isothermal and non-isothermal gas mixtures

Abstract

The similarity groups for multicomponent, reacting gas mixtures with radiative energy transport are derived (Section I). The resulting relations are used to consider the feasibility if scaling for flow processes with radiative energy transport under highly simplified conditions (Sections 2 and 3). Next the scaling parameters are derived for radiant energy emission from isobaric and isothermal gases for arbitrary opacities and various spectral line and molecular band models (Section 4). Scaling parameters for radiant energy emission from isobaric but non-isothermal systems are discussed for arbitrary opacities and various spectral line and molecular band models under the restrictions imposed on the allowed temperature profiles for dispersion and Doppler lines by the Eddington-Barbier approximation (Section 5). Finally, we consider the radiative scaling properties for representative temperature profiles for both collision-broadened and Doppler-broadened line profiles on the basis if exact numerical calculations that we have performed for a rotational spectral line belonging to a molecular vibration-rotation band. (Section 6). It appears that simple scaling rules generally constitute a fair approximation for dispersion lines in non-isothermal systems but that corresponding relations apply to lines with Doppler contour only in the transparent gas regime.