Absorption line black body distribution function evaluated with proper orthogonal decomposition for mixture of CO₂ and H₂O

Abstract

Purpose

The purpose of this paper is to present a new approach of evaluation of the absorption line black body distribution function (ALBDF) for a mixture of gases. Currently published correlations, which are used to reproduce the ALBDF, treat only single gases.

Design/methodology/approach

A discrete form of the ALBDF is generated using line by line (LBL) calculations. The latest spectroscopic database HITEMP 2010 is used for the generation of the absorption coefficient histogram, which is cumulated later in order to produce a tabulated form of the ALBDF. The proper orthogonal decomposition (POD) statistical method is employed for the reproduction of the ALBDF. Interpolation property of the POD allows to reproduce the ALBDF for arbitrary gas mixture parameters.

Findings

POD proved to possess optimal interpolation properties. Results obtained by using POD are in very good agreement with LBL integration.

Research limitations/implications

One have to be aware that the model generated with the POD method can be used only within the range of parameters used to build the model. The POD does not perform any property extrapolation. The model is limited to a mixture of two gases, namely CO₂ and H₂O. Expanding the number of gases used in the mixture may lead to a relatively large matrix system, which is difficult to process with the POD approach.

Practical implications

The presented approach can be used to produce absorption coefficients values and their weights, which can be applied in the gas radiative properties description using the weighted sum of gray gas (WSGG) concept. The proposed model can be used with any radiative transfer equation solver which employs the WSGG approach.

Originality/value

For the first time, radiative properties of gas mixtures are reproduced using the POD approach.

Citation

Węcel, G., Ostrowski, Z. and Kozołub, P. (2014), "Absorption line black body distribution function evaluated with proper orthogonal decomposition for mixture of CO₂ and H₂O", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 24 No. 4, pp. 932-948. https://doi.org/10.1108/HFF-04-2013-0142