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RELATIONSHIP BETWEEN THE SPECTRAL LINE BASED WEIGHTED-SUM-OF-GRAY-GASES MODEL AND THE FULL SPECTRUM K-DISTRIBUTION MODEL

DOI: 10.1615/ICHMT.2013.IntSympRadTransf.300
pages 389-401

Fengshan Liu
National Research Council, Combustion Technology Group, Institute for Chemical Process & Environmental Technology, National Research Council Building M-9, 1200 Montreal Road, Ottawa, Ontario, Canada K1 A 0R6

Huaqiang Chu
State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, P. R. China; School of Energy and environment, Anhui University of Technology, Ma’anshan 243002, Anhui, China

Jean-Louis Consalvi
Aix-Marseille Université, IUSTI/ UMR CNRS 7343, 5 rue E. Fermi, 13453 Marseille Cedex 13, France

Abstrakt

The relationship between the spectral line based weighted-sum-of-gray-gases (SLW) model and the full-spectrum k-distribution (FSK) model in isothermal and homogeneous media is investigated in this paper. The SLW transfer equation can be derived from the FSK transfer equation expressed in the k-distribution function without approximation. It confirms that the SLW model is equivalent to the FSK model in the k-distribution form. The numerical implementation of the SLW relies on a discretization of the absorption cross section where as the FSK model finds the spectrally integrated intensity by integration over the smoothly-varying cumulative-k distribution function using a Gaussian quadrature scheme. The latter is therefore in general more efficient as fewer gray gases are required to achieve a prescribed accuracy. Sample numerical calculations were conducted to demonstrate the different efficiency of these two methods. The FSK model is more efficient than the SLW model in radiation transfer in H2O; however, the two models perform similarly in CO2.

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