The ω-absorption line distribution function for rank correlated SLW model prediction of radiative transfer in non-uniform gases

Abstract

Unlike previous global methods, the recently developed Rank Correlated Spectral Line Weighted-sum-of-gray-gases (RC-SLW) model does not require specification of a reference gas thermodynamic state from which all other states are corrected using a correlated spectrum assumption. However, the RC-SLW approach still requires specification of an arbitrary blackbody source temperature to generate the Absorption Line Blackbody Distribution Function (ALBDF) used in construction of the spectral model. This paper reports on the development of a universal RC-SLW model that eliminates the need for the specification of a blackbody source temperature. The approach replaces the ALBDF with a new spectral distribution function, herein termed the ω-Absorption Line Distribution Function (ω-ALDF), and is based on a new spectral weighting function instead of the Planck blackbody distribution function. The ω-ALDF presented here depends only on the local gas thermodynamic state, and does not involve the blackbody source temperature used in the ALBDF. The new weighting function is determined using the well-established ALBDF, avoiding the need to generate a radically new distribution function database from the detailed gas absorption cross-section data. The ω-ALDF based RC-SLW model thus requires no user-specified parameters (no reference thermodynamic state and no blackbody source temperature). Further, only minor modification of the conventional RC-SLW model is needed to implement the new approach. Development of this new distribution function is only possible within the theoretical framework of the Rank Correlated SLW model. This work presents the theoretical development of the ω-ALDF, and demonstrates the use and accuracy of this new universal RC-SLW model.