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Application of the WSGG Model to Solve the Radiative Transfer in Gaseous Systems with Nongray Boundaries

[+] Author and Article Information
Roberta J C da Fonseca

Department of Mechanical Engineering, Federal University of Rio Grande do Sul, Sarmento Leite Street, 425, 90050-170 - Porto Alegre, RS, Brazil
roberta.fonseca@ufrgs.br

Guilherme C Fraga

Department of Mechanical Engineering, Federal University of Rio Grande do Sul, Sarmento Leite Street, 425, 90050-170 - Porto Alegre, RS, Brazil
guilhermecfraga@ufrgs.br

Rogerio Brittes da Silva

Academic Coordination of Cachoeira do Sul, Federal University of Santa Maria, Ernesto Barros Street, 1345, 96506-322 - Cachoeira do Sul, RS, Brazil
rogerio.silva@ufsm.br

Francis Franca

Department of Mechanical Engineering, Federal University of Rio Grande do Sul, Sarmento Leite Street, 425, 90050-170 - Porto Alegre, RS, Brazil
frfranca@mecanica.ufrgs.br

1Corresponding author.

ASME doi:10.1115/1.4038548 History: Received April 11, 2017; Revised October 16, 2017

Abstract

This paper presents a methodology for the application of the weighted-sum-of-gray-gases (WSGG) model to systems where the medium is bounded by nongray surfaces. The method relies on the assumption that each gray gas absorption coefficient is randomly spread across the entire wavenumber spectrum. It follows that, in the spectral integration of the radiative transfer equation (RTE), the local emission term can be computed by the joint probability of emission from the subsections of the spectrum related to each gray gas coefficient and from each wall emissivity band. One advantage of the proposed methodology is that it allows the use without any modification of WSGG correlations that are available in the literature. The study presents a few test cases considering a one-dimensional, non-uniform medium slab composed of H2O and CO2, bounded by nongray surfaces. The accuracy of the methodology is assessed by direct comparison with line-by-line (LBL) calculations.

Copyright (c) 2017 by ASME
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