Spectral Line Weighted-sum-of-gray-gases Research Articles

Comparison and refinement of the various full-spectrum k-distribution and spectral line weighted-sum-of-gray-gases models for nonhomogeneous media

Both the full-spectrum k-distribution (FSK) method and the spectral line weighted-sum-of-gray-gases (SLW) method are global spectral methods, with the former based on a spectral reordering concept, while the latter uses spectral binning. Both can provide excellent accuracy with outstanding numerical efficiency to model radiative heat transfer in combustion gases. In the present paper we aim to complete the development of both methods, and to tie them together, pointing out their commonalities and differences of their nonhomogeneous media extensions, employing either the correlated or scaled absorption coefficient assumption. Results from the complete set of plausible implementations are discussed and compared in detail for several radiative heat transfer calculations carried out in both 1D slabs and a real combustion field. The results show that emission is an important criterion to examine the accuracy of global methods applied to nonhomogeneous media, i.e., those that preserve emission generally give more accurate results than those that do not. It was also found that, while proper choice of the reference temperature required by all methods is important, the recommended methods appear to be only weakly dependent on that choice. Finally, equivalent SLW schemes are generally somewhat less accurate than their FSK counterparts due to their low-order spectral integration scheme; and this may be exacerbated if full-spectrum k-distributions are determined by mixing of values from individual species, as appears to be the preferred approach by SLW users to date.

An Exploration of Advanced SLW Modeling Approaches in Comprehensive Combustion Predictions

ABSTRACT Recent work demonstrated the integration of the Spectral Line Weighted-Sum-of-Gray-Gases (SLW) model for advanced modeling of gas radiation in high temperature gases in a comprehensive combustion modeling prediction scheme. This prior work compared predictions using the Reference Approach SLW model with the Domain Based Weighted-Sum-of-Gray-Gases model used in Fluent. The present work reports on the implementation of the Rank Correlated SLW model and the Locally Correlated SLW model in the combustion scenario studied in the earlier publication, complementing the Reference Approach SLW model predictions reported previously. The predictions confirm the need for such advanced radiation modeling to accurately resolve the radiative flux divergence and temperature fields, particularly in localized regions of the flame zone where very large differences in temperature and radiative heating may be found relative to the more rudimentary modeling approach. Results also reveal the dependence of the predictions for the three SLW model variants on the number of gray gases employed in the simulations. The Reference Approach and Locally Correlated SLW model predictions exhibit rather significant dependence on the number of gray gases used. It is shown that the Rank Correlated SLW model is the most robust of all models, and demonstrates that it can achieve accurate solutions with as few as 3–5 gray gases.

Nongray inverse boundary design problems in enclosures at radiative equilibrium

AbstractIn this paper, an inverse analysis is used to find an appropriate heat flux distribution over the heater surface of radiant enclosures, filled with nongray media at radiative equilibrium from the knowledge of desired (prespecified) temperature and heat flux distributions over the given design surface. Regular and irregular 2D enclosures filled with nongray combustive gas products are considered. Radiation is considered the dominant mode of heat transfer and the medium temperature is obtained from the energy equation. To evaluate the nongray behavior of the participating gases properly, the spectral‐line weighted‐sum‐of‐gray‐gases (SLW) model with updated correlations is used. The dependence of absorption coefficients and the weights of the SLW model on the temperature of the medium makes the inverse problem nonlinear and difficult to handle. Here, the inverse problem is formulated as an optimization problem and the Levenberg‐Marquardt method has been used to solve it. The finite volume method is exploited for the discretization of the energy equation and the spatial discretization of the radiative transfer equation (RTE). The discrete ordinates method (TN quadrature) is used for the angular discretization of RTE. Five test cases, including homogeneous and inhomogeneous media, are investigated to prove the ability of the present methodology for achieving the desired conditions.

SLW modeling of radiation transfer in comprehensive combustion predictions

ABSTRACTThis paper reports on the modeling of turbulent reacting flow using the advanced Spectral Line Weighted-sum-of-gray-gases (SLW) method for prediction of the gas thermal radiative transfer. Predictions using the traditional weighted-sum-of-gray-gases radiation submodel are compared to the more advanced SLW treatment of radiation transfer. For the problem considered, the results reveal little difference in the predicted H2O and CO2 concentrations between the two radiation submodels. Further, the predicted furnace mass-averaged exit temperature for both radiation submodels is unchanged. However, there is considerable difference in the predicted radiative and thermal structure in the flame zone, albeit at considerably higher computational expense. The use of the more rigorous SLW model significantly affects the accurate resolution of the local radiative heating and local temperature in the flame region. It is concluded that the more advanced SLW model should be used when seeking to resolve accurately the detailed flame structure.

Thermal radiation transfer calculations in combustion fields using the SLW model coupled with a modified reference approach

The spectral-line weighted-sum-of-gray-gases (SLW) model is considered as a modern global model, which can be used in predicting the thermal radiation heat transfer within the combustion fields. The past SLW model users have mostly employed the reference approach to calculate the local values of gray gases’ absorption coefficient. This classical reference approach assumes that the absorption spectra of gases at different thermodynamic conditions are scalable with the absorption spectrum of gas at a reference thermodynamic state in the domain. However, this assumption cannot be reasonable in combustion fields, where the gas temperature is very different from the reference temperature. Consequently, the results of SLW model incorporated with the classical reference approach, say the classical SLW method, are highly sensitive to the reference temperature magnitude in non-isothermal combustion fields. To lessen this sensitivity, the current work combines the SLW model with a modified reference approach, which is a particular one among the eight possible reference approach forms reported recently by Solovjov, et al. [DOI: 10.1016/j.jqsrt.2017.01.034, 2017]. The combination is called “modified SLW method”. This work shows that the modified reference approach can provide more accurate total emissivity calculation than the classical reference approach if it is coupled with the SLW method. This would be particularly helpful for more accurate calculation of radiation transfer in highly non-isothermal combustion fields. To approve this, we use both the classical and modified SLW methods and calculate the radiation transfer in such fields. It is shown that the modified SLW method can almost eliminate the sensitivity of achieved results to the chosen reference temperature in treating highly non-isothermal combustion fields.

Interaction of radiation with double-diffusive natural convection in a three-dimensional cubic cavity filled with a non-gray gas mixture in cooperating cases

ABSTRACTA three-dimensional (3D) numerical study has been performed to investigate the effects of non-gray gas radiation on double-diffusive natural convection in a cubic enclosure filled with either air–H2O or air–CO2 mixtures in cooperating situations. Gas radiation was taken into account by the discrete ordinates method (DOM) associated with the spectral line weighted-sum-of-gray-gases (SLW) spectral model. Results obtained for two average concentrations of H2O and CO2 (10% and 20%) show that radiation modifies the temperature and concentration structures by creating oblique stratifications. The heat transfer rate is decreased, whereas mass transfer is not much modified. In addition, a comparison between 2D and 3D results is presented.

Extension of the exact SLW model to non-isothermal gaseous media

Absract The exact limit of the spectral line weighted-sum-of-gray-gases (SLW) model in isothermal media is extended to the case of non-isothermal media following the reference approach. The problem is thus expressed in terms of a continuously varying absorption cross-section in the limit as the number of gray gases tends to infinity. The limiting case of the SLW reference approach is developed for spectral integration of the RTE in non-isothermal environments. Analytical solutions of the Exact SLW model are obtained for a multilayer system of isothermal layers, and the analytical solutions for a non-isothermal medium are obtained in the limit when the number of sublayers approaches infinity. The Exact SLW model is applied also for construction of the optimized efficient SLW-1 model consisting of a single gray gas and a single clear gas. The Exact SLW model is a theoretical approach which is useful for better understanding of the possibilities and limitations of the SLW method, but it also has implications for practical applications.

SLW-1 Modeling of Radiative Heat Transfer in Nonisothermal Nonhomogeneous Gas Mixtures With Soot

The spectral line weighted-sum-of-gray-gases (SLW) model consisting only of a single gray gas and of one clear gas is developed as an efficient spectral method for modeling radiation transfer in gaseous medium. The model is applied here in prediction of radiative transfer in nonisothermal and nonhomogeneous gas mixtures with nongray soot. The absorption spectrum of the gas mixture and soot particles is treated as a spectrum of a single effective gas, reducing the problem to the simplest case of the SLW model with a single gray gas and a clear gas. Good accuracy can be achieved by the optimal choice of the model’s gray gas absorption coefficient and its weight by application of the absorption-line blackbody distribution functions of individual species in the mixture calculated with a high-resolution spectral database. The SLW-1 model is validated by comparison with benchmark solutions using the line-by-line method, the SLW method with a large number of gray gases, and the SNB model.

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

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.

An Efficient Method for Modeling Radiative Transfer in Multicomponent Gas Mixtures With Soot

An efficient approach for predicting radiative transfer in high temperature multicomponent gas mixtures with soot particles is presented. The method draws on the previously published multiplication approach for handling gas mixtures in the spectral line weighted-sum-of-gray-gases (SLW) model. In this method, the gas mixture is treated as a single gas whose absorption blackbody distribution function is calculated through the distribution functions of the individual species in the mixture. The soot is, in effect, treated as another gas in the mixture. Validation of the method is performed by comparison with line-by-line solutions for radiative transfer with mixtures of water vapor, carbon dioxide, and carbon monoxide with a range of soot loadings (volume fractions). Comparison is performed also with previously published statistical narrow band and classical weighted-sum-of-gray-gases solutions.

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

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.