The Spectral Line-Based Weighted-Sum-of-Gray-Gases Model in Nonisothermal Nonhomogeneous Media

1995 ◽  
Vol 117 (2) ◽  
pp. 359-365 ◽  
Author(s):  
M. K. Denison ◽  
B. W. Webb
Keyword(s):  
Spectral Line ◽  
Cross Sections ◽  
Spatial Dependence ◽  
Radiative Transfer Equation ◽  
Gas Absorption ◽  
Weighted Sum ◽  
Absorption Cross ◽  
Arbitrary Solution ◽  
Nonhomogeneous Media ◽  
Solution Methods

An approach is developed to extend the previously developed spectral-line weighted-sum-of-gray-gases (SLW) model to nonisothermal, nonhomogeneous media. The distinguishing feature of the SLW gas property model is that it has been developed for use in arbitrary solution methods of the radiative transfer equation (RTE). A spatial dependence of the gray gas absorption cross sections on local temperature, pressure, and mole fraction is introduced through the absorption-line blackbody distribution function. Incorporating this spatial dependence results in significant improvement over the use of spatially uniform gray gas absorption cross sections in comparisons with line-byline benchmarks.

A Spectral Line-Based Weighted-Sum-of-Gray-Gases Model for Arbitrary RTE Solvers

1993 ◽  
Vol 115 (4) ◽  
pp. 1004-1012 ◽  
Author(s):  
M. K. Denison ◽  
B. W. Webb
Keyword(s):  
Spectral Line ◽  
Absorption Coefficient ◽  
Cross Section ◽  
Solution Method ◽  
Radiative Transfer Equation ◽  
Weighted Sum ◽  
Absorption Cross ◽  
Arbitrary Solution ◽  
Nonhomogeneous Media ◽  
Cross Section Spectrum

This paper presents an approach for generating weighted-sum-of-gray gases (WSGG) models directly from the line-by-line spectra of H2O. Emphasis is placed on obtaining detailed spectral division among the gray gases. Thus, for a given model spectrum, the gray gas weights are determined as blackbody fractional functions for specific subline spectral regions at all temperatures. The model allows the absorption coefficient to be the basic radiative property rather than a transmissivity or band absorptance, etc., and can be used with any arbitrary solution method for the Radiative Transfer Equation (RTE). A single absorption cross section spectrum is assumed over the entire spatial domain in order to fix the subline spectral regions associated with a single spectral calculation. The error associated with this assumption is evaluated by comparison with line-by-line benchmarks for problems of nonisothermal and nonhomogeneous media.

Inverse Estimation of Main Parameters of Spectral Line-Based Weighted Sum of Gray Gases Model With Few Gray Gases to Simulate the Radiation in Nongray Media

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
A. Dehghanian ◽  
S. M. Hosseini Sarvari
Keyword(s):  
Heat Transfer ◽  
Spectral Line ◽  
Cross Sections ◽  
Radiation Heat Transfer ◽  
Noisy Data ◽  
Extreme Case ◽  
Least Square ◽  
Weighted Sum ◽  
Absorption Cross ◽  
Radiation Heat

The aim of this study is to present a reduced spectral line-based weighted sum of gray gases (SLW) model to simulate the radiation heat transfer in nongray media at high temperatures. Inverse approach is used to divide the absorption cross section band into a clear gas with one gray gas and two gray gases, which are called the S-1 and S-2 approaches, respectively. The unknown absorption cross sections are determined from the knowledge of measured total incident intensities received by wall surfaces. In order to simulate the exact solution of radiation heat transfer in nongray gaseous media, the discrete transfer method (DTM) in combination with S-20 model is used, where the nongray medium is replaced with a set of a clear gas and 20 gray gases. The inverse problem is formulated as an optimization problem to minimize a least square objective function, which is solved by the conjugate gradient method (CGM). The accuracy of the present method is verified by comparing with previous researches and the S-20 approach with a large number of gray gases. The effects of noisy data on the inverse solution are investigated by considering an extreme case with large measurement error. The results show that the unknown absorption cross sections are retrieved well, even for noisy data.

The Weighted-Sum-of-Gray-Gases Model for Arbitrary Solution Methods in Radiative Transfer

1991 ◽  
Vol 113 (3) ◽  
pp. 650-656 ◽  
Author(s):  
M. F. Modest
Keyword(s):  
Radiative Transfer ◽  
Integral Equations ◽  
Solution Method ◽  
Weighted Sum ◽  
Arbitrary Solution ◽  
Absorption Coefficients ◽  
Zonal Method ◽  
Radiation Problem ◽  
Participating Media ◽  
Solution Methods

The weighted-sum-of-gray-gases approach for radiative transfer in nongray participating media, first developed by Hottel in the context of the zonal method, has been shown to be applicable to the general radiative equation of transfer. Within the limits of the weighted-sum-of-gray-gases model (nonscattering media within a black-walled enclosure), any nongray radiation problem can be solved by any desired solution method after replacing the medium by an equivalent small number of gray media with constant absorption coefficients. Some examples are presented for isothermal media and media at radiative equilibrium, using the exact integral equations as well as the popular P-I approximation for the equivalent gray media solutions. The results demonstrate the equivalency of the method with the quadrature of spectral results, as well as the tremendous computer times savings (by a minimum of 95 percent) that are achieved.

A Novel WSGG Model Based on Weighted Absorption-Emission Coefficients

2015 ◽  
Author(s):  
Rogério Brittes ◽  
Fabiano Cassol ◽  
Felipe Roman Centeno ◽  
Francis H. R. França
Keyword(s):  
Spectral Line ◽  
Radiative Transfer Equation ◽  
Computational Effort ◽  
Spectral Lines ◽  
Weighted Sum ◽  
Global Models ◽  
Spectral Integration ◽  
Constant Coefficients ◽  
Computationally Expensive ◽  
Wsgg Model

The absorption coefficient of participating species, such as CO2 and H2O, shows very irregular dependence with the wavenumber, which makes it difficult the spectral integration of the radiative transfer equation (RTE). This task can be performed with the line-by-line (LBL) integration, which is very computationally expensive due to the vast amount of spectral lines that span the spectrum. As alternatives to the LBL integration, there are global models, such as the weighted-sum-of-gray-gases (WSGG) and the spectral line weighted-sum-of-gray gases (SLW). These models replace the integration with respect to the wavenumber by the summation over a certain number of gray gases, thus reducing the computational effort. This paper shows a modification of the WSGG model, in which the absorption and emission coefficients of each gray gas are considered to be function of the temperature. The model, named WSGG with non-constant coefficients (NCC-WSGG), is applied to solve a few non-isothermal and non-homogeneous problems. The results show very satisfactory agreement with the LBL integration.

Spectroscopy Fundamentals

2017 ◽  
Author(s):  
Kelly Chance ◽  
Randall V. Martin
Keyword(s):  
Vibrational Spectroscopy ◽  
Cross Sections ◽  
Nuclear Spin ◽  
Electronic Spectroscopy ◽  
Rotational Spectroscopy ◽  
Absorption Cross ◽  
Transfer Processes ◽  
Atmospheric Spectroscopy ◽  
Quantitative Spectroscopy ◽  
Broad Overview

This chapter provides a broad overview of the spectroscopic principles required in order to perform quantitative spectroscopy of atmospheres. It couples the details of atmospheric spectroscopy with the radiative transfer processes and also with the assessment of rotational, vibrational, and electronic spectroscopic measurements of atmospheres. The principles apply from line-resolved measurements (chiefly microwave through infrared) through ultraviolet and visible measurements employing absorption cross sections developed from individual transitions. The chapter introduces Einstein coefficients before in turn discussing rotational spectroscopy, vibrational spectroscopy, nuclear spin, and electronic spectroscopy.

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