Evaluation of Coefficients for the Weighted Sum of Gray Gases Model

TLDR

The weighted sum of gray gases model represents total emissivity and absorptivity as a temperature‑dependent weighted sum of gray‑gas emissivity, with the weighting factors expressed as polynomials in gas temperature and the gray‑gas emissivity defined by a temperature‑independent absorption coefficient, gas partial pressure, and path length. The authors introduce a second polynomial for irradiation temperature in absorptivity and use a regression scheme to fit the model to total emissivity and absorptivity values from an exponential wide‑band model. Reported absorption and polynomial coefficients for CO₂, H₂O, and their mixtures yield a model that more accurately captures total properties across a broader range of temperatures and partial‑pressure‑path‑length products than previously available coefficients.

Abstract

The weighted sum of gray gases model postulates that total emissivity and absorptivity may be represented by the sum of a gray gas emissivity weighted with a temperature dependent factor. The gray gas emissivity is expressed in terms of a temperature-independent absorption coefficient, absorbing gas partial pressure, and path length. The weighting factors are given by polynomials in gas temperature with associated polynomial coefficients. For absorptivity, a second polynomial for the irradiation temperature is introduced. A regression scheme is employed to fit the model to total emissivity and absorptivity values obtained from the exponential wide-band model. Absorption and polynomial coefficients are reported for carbon dioxide, water vapor, and mixtures of these gases. The model with these coefficients more accurately represents the total properties over a wider range of temperatures and partial pressure-path length products than previously available coefficients.