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Research Papers: Radiative Heat Transfer

Hybrid Full-Spectrum Correlated k-Distribution Method for Radiative Transfer in Nonhomogeneous Gas Mixtures

[+] Author and Article Information
Gopalendu Pal, Liangyu Wang

Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA 16802

Michael F. Modest1

Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA 16802mfmodest@psu.edu

1

Corresponding author.

J. Heat Transfer 130(8), 082701 (Jun 03, 2008) (8 pages) doi:10.1115/1.2909612 History: Received May 29, 2007; Revised October 16, 2007; Published June 03, 2008

The full-spectrum k-distribution (FSK) approach is a promising model for radiative transfer calculations in participating media. FSK achieves line-by-line (LBL) accuracy for homogeneous media at a tiny fraction of LBL’s high computational cost. However, inhomogeneities in gas temperature, total pressure, and component-gas mole fractions change the spectral distribution of the absorption coefficient and can cause inaccuracies in the FSK approach. In this paper, a new hybrid FSK method is proposed that combines the advantages of the multigroup FSK (MGFSK) method for temperature inhomogeneities in a single gas species and the multiscale FSK (MSFSCK) method for concentration inhomogeneities in gas mixtures. In this new hybrid method, the absorption coefficients of each gas species in the mixture are divided into M spectral groups depending on their temperature dependence. Accurate MGFSK databases are constructed for combustion gases, such as CO2 and H2O. This paper includes a detailed mathematical development of the new method, method of database construction, and sample heat transfer calculations for 1D inhomogeneous gas mixtures with step changes in temperature and species mole fractions. Performance and accuracy are compared to LBL and plain FSK calculations. The new method achieves high accuracy in radiative heat transfer calculations in participating media containing extreme inhomogeneities in both temperature and mole fractions using as few as M=2 spectral groups for each gas species, accompanied by several orders of magnitude lower computational expense as compared to LBL solutions.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Grouping of several spectral locations across 4.3μm band of CO2 in a CO2–air mixture containing 10% CO2

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Figure 2

Grouping of several spectral locations across 2.7μm band of H2O in a H2O–air mixture containing 10% H2O

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Figure 3

Original and smoothed weight function a and cumulative k-distributions of Group 2 for 10% H2O in H2O–air mixture

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Figure 4

Nondimensional heat flux leaving an inhomogeneous slab of 10% CO2 and 20% H2O at a total pressure of 1bar with a step change in temperature: The hot left layer is at 1500K and the cold right layer is at 300K

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Figure 5

Nondimensional heat flux leaving an inhomogeneous slab at a total pressure of 1bar with step changes in temperature and mole fraction: The hot left layer contains 20% CO2 and 10% H2O at 1500K and the cold right layer contains 10% CO2 and 20% H2O

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Figure 6

Nondimensional heat flux leaving an inhomogeneous slab at a total pressure of 10bar with step changes in temperature and mole fraction: The hot left layer contains 20% CO2 and 10% H2O at 1500K and the cold right layer contains 10% CO2 and 20% H2O

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