Vladimir P. Solovjov Brent W. Webb Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602 An Efficient Method for Modeling Radiative Transfer in Multicomponent Gas Mixtures With Soot An efficient approach for predicting radiative transfer in high temperature multicompo- nent 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. DOI: 10.1115/1.1350824 Keywords: Gaseous, Heat Transfer, Participating Media, Particulate, Radiation Introduction In a combustion environment yielding luminous flames, the combustion products are comprised not only of the mixture of combustion gases mainly water vapor, carbon dioxide, and car- bon monoxide but also soot. Soot consists of very small carbon particles which, when unagglomerated, are primarily absorbing/ emitting and non-scattering. When soot is present in the flame, the radiation transfer is significantly increased because of high values of its spectral absorption coefficient relative to that of the sur- rounding gases. While the prediction of radiative transfer in high temperature gas mixtures is already an imposing challenge, the added presence of soot renders the problem even more difficult because of the superposition of band radiation from the gases and the continuum radiation from the soot particles. Historically, the simplest approach for the prediction of radia- tive transfer in gas/soot mixtures are simple gray models, which are computationally efficient but yield very poor accuracy 1. The most accurate method is the line-by-line LBL method, in which the Radiative Transfer Equation is integrated over the detailed molecular spectrum for the gases and soot 2. Because of the computational requirements of the line-by-line method, it is gen- erally used only for benchmark solutions. The statistical narrow band model SNB provides good accu- racy in the prediction of radiative transfer in high temperature gases, but it requires a large number of bands and, therefore, is computationally expensive 3. Often this method is used for ob- taining benchmark solutions in lieu of the line-by-line approach e.g., 4. The wide band model WBM is a simplification of the SNB method but the accuracy of this method is limited 5. It also requires the specification of the path length in the model and spectral parameters associated with the path length. Komornicki and Tomeczek have demonstrated the use of a modified WBM for luminous flame calculation in nonhomogeneous media 6. Modak developed a generalized code for calculating the absorptivity/ emissivity of combustion gases with soot using the wide band model 7. Taylor et al. present total emissivities of mixtures of high temperature gases and soot calculated from band models 8,9. The Weighted-Sum-of-Gray-Gases WSGG model can be used with arbitrary solvers of the RTE 10. It requires specification of the gray gas weights and absorption coefficients for any combina- tion of gas species and soot over their expected range of concen- trations, temperatures, etc. Bressloff studied the influence of soot loading on WSGG solutions to the radiative transfer equation through mixtures of gases and soot 4. WSGG solutions were compared to SNB model predictions. In the Spectral Line Weighted-sum-of-gray-gases SLW model, the weights in the classical WSGG model are determined with the help of the absorption-line blackbody distribution func- tion, which is calculated directly from the high resolution molecu- lar spectrum of gases 11,12. The integration of the RTE over wavenumber wavelength is then replaced by an integration over absorption cross-section. The presence of soot particles in the flame has been handled previously by the hybrid SLW and k-distribution model in which the absorption line blackbody dis- tribution function of the gas mixture was calculated using the convolution or the double integration approaches 13. The spec- tral dependence of the soot absorption coefficient was accommo- dated by the additional subdivision of wavenumber on subinter- vals where the spectral properties of the soot are assumed to be constant. This approach renders the model significantly more complicated and computationally burdensome, and the SLW method loses some of its advantage for engineering radiative transfer predictions. Using this approach, Denison and Webb cal- culated the radiative dissipation source in water vapor with soot 13, and Denison reported predictions of the radiative dissipation source for the mixture of water vapor and carbon dioxide with soot 14. In the present work, a new approach is proposed where the multicomponent gas mixture with soot is treated as a single gas in the SLW model. The absorption line blackbody distribution func- tion of this single gas is calculated using the distribution functions of the individual species included in the mixture 15. The devel- opment for the addition of soot presented here treats soot simply as another gas whose absorption distribution function is calculated from the absorption spectrum of the soot. This approach can be Contributed by the Heat Transfer Division for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received by the Heat Transfer Division September 28, 1999; revision received November 3, 2000. Associate Editor: M. P. Mengu ¨c ¸. 450 Õ Vol. 123, JUNE 2001 Copyright © 2001 by ASME Transactions of the ASME Downloaded 20 Sep 2009 to 128.187.72.10. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm