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Research Papers: Radiative Heat Transfer

Global Spectral Methods in Gas Radiation: The Exact Limit of the SLW Model and Its Relationship to the ADF and FSK Methods

[+] Author and Article Information
V. P. Solovjov, B. W. Webb

Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602

J. Heat Transfer 133(4), 042701 (Jan 10, 2011) (9 pages) doi:10.1115/1.4002775 History: Received February 05, 2010; Revised September 28, 2010; Published January 10, 2011; Online January 10, 2011

The exact form of the spectral line weighted-sum-of-gray-gases (SLW) model is developed as a limiting case of the classical SLW method when the number of gray gases in the classical model approaches infinity. Solutions of the exact SLW radiative transfer equation are obtained in the case of isothermal media. It is demonstrated that the accuracy of the exact SLW method is limited only by the accuracy of the absorption-line blackbody distribution function (ALBDF) correlations used for the characterization of the absorption spectrum. This work also theoretically and rigorously demonstrates for the first time the relationship among the SLW, absorption distribution function (ADF), and full spectrum k-distribution (FSK) models. The theoretical foundation is laid for the extension of the exact method in the case of nonisothermal media.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

SLW histogram spectral model and geometrical meaning of the gray gas absorption coefficient and associated gray gas weight

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Figure 2

Partition of the absorption cross section

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Figure 3

Generation of the classical SLW model supplemental cross sections C̃j and the absorption cross sections Cj by the integral quadrature’s nodes Fj and weights wj applied in the FSK method

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Figure 4

Comparison of predicted forward-directed total radiative flux from SLW solution methods for Example 1

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Figure 5

Divergence of the total net radiative flux in an isothermal layer of CO2 for Example 2

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Figure 6

Divergence of the total net radiative flux in an isothermal layer of H2O for Example 3

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Figure 7

The ideal gas assumption of the SLW reference approach

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