0
Research Papers: Heat Exchangers

The Treatment of Nongray Properties in Radiative Heat Transfer: From Past to Present

[+] Author and Article Information
Michael F. Modest

Life Fellow ASME
University of California at Merced,
Merced, CA 95343
e-mail: MModest@ucmerced.edu

Manuscript received October 19, 2012; final manuscript received December 17, 2012; published online May 16, 2013. Assoc. Editor: Leslie Phinney.

J. Heat Transfer 135(6), 061801 (May 16, 2013) (12 pages) Paper No: HT-12-1582; doi: 10.1115/1.4023596 History: Received October 19, 2012; Revised December 17, 2012

Radiative heat transfer in high-temperature participating media displays very strong spectral, or “nongray,” behavior, which is both very difficult to characterize and to evaluate. This has led to very gradual development of nongray models, starting with primitive semigray and box models based on old experimental property data, to today's state-of-the-art k-distribution approaches with properties obtained from high-resolution spectroscopic databases. In this paper a brief review of the historical development of nongray models and property databases is given, culminating with a more detailed description of the most modern spectral tools.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Edwards, D. K., 1976, “Molecular Gas Band Radiation,” Advances in Heat Transfer, Vol. 12, Academic, New York, pp. 115–193.
Wang, L., Modest, M. F., Haworth, D. C., and Turns, S. R., 2005, “Modeling Nongray Soot and Gas-Phase Radiation in Luminous Turbulent Nonpremixed Jet Flames,” Combust. Theory Model., 9(3), pp. 479–498. [CrossRef]
Modest, M. F., 2013, Radiative Heat Transfer, 3rd ed., Academic, New York.
Herzberg, G., 1944, Atomic Spectra and Atomic Structure, 2nd ed., Van Nostrand, New York.
Herzberg, G., 1945, Molecular Spectra and Molecular Structure, Vol. II: Infrared and Raman Spectra of Polyatomic Molecules, Van Nostrand, Princeton, NJ.
Herzberg, G., 1950, Molecular Spectra and Molecular Structure, Vol. I: Spectra of Diatomic Molecules, 2nd ed., Van Nostrand, Princeton, NJ.
Penner, S. S., 1960, Quantitative Molecular Spectroscopy and Gas Emissivities, Addison-Wesley, Reading, MA.
Lorenz, L., 1890, Videnskab Selskab Skrifter, Vol. 6, Kongelige Danske Videnskabernes Selskab, Copenhagen, Denmark.
Mie, G., 1908, “Beiträge zur Optik Trüber Medien, Speziell Kolloidaler Metallösungen,” Ann. Phys., 330, pp. 377–445. [CrossRef]
Debye, P., 1909, “Der Lichtdruck auf Kugeln von Beliebigem Material,” Ann. Phys., 335(11), pp. 57–136. [CrossRef]
Rayleigh, Lord, 1871, “On the Light From the Sky, Its Polarization and Colour,” Philos. Mag., 41, pp. 107–120, 274–279 (Reprinted in Scientific Papers by Lord Rayleigh, Vol. I: 1869–1881, No. 8, Dover, New York, 1964).
Howell, J. R., Siegel, R., and Mengüç, M. P., 2002, Thermal Radiation Heat Transfer, 4th ed., Taylor and Francis, New York.
van de Hulst, H. C., 1957, Light Scattering by Small Particles, John Wiley, New York.
Kerker, M., 1969, The Scattering of Light and Other Electromagnetic Radiation, Academic, New York.
Goody, R. M., and Yung, Y. L., 1989, Atmospheric Radiation: Theoretical Basis, 2nd ed., Oxford University Press, New York.
Hottel, H. C., and Mangelsdorf, H. G., 1935, “Heat Transmission by Radiation From Non-Luminous Gases II. Experimental Study of Carbon Dioxide and Water Vapor,” Trans. AIChE, 31, pp. 517–549.
Eckert, E. R. G., 1937, “Messung der Gesamtstrahlung von Wasserdampf und Kohlensäure in Mischung mit Nichtstrahlenden Gasen bei Temperaturen bis 1300 °C,” VDI Forschungshefte, 387, pp. 1–20.
Hottel, H. C., 1954, “Radiant Heat Transmission,” Heat Transmission, 3rd ed., W. H. McAdams, ed., McGraw-Hill, New York, Chap. 4.
Hottel, H. C., and Sarofim, A. F., 1967, Radiative Transfer, McGraw-Hill, New York.
Leckner, B., 1972, “Spectral and Total Emissivity of Water Vapor and Carbon Dioxide,” Combust. Flame, 19, pp. 33–48. [CrossRef]
Tingwaldt, C., 1938, “The Absorbtion of Carbonic Acid in the Range of Lambda=4.3 mu Between 300 Degrees and 1000 Degrees Absolute,” Phys. Z., 39, pp. 1–6 (in German).
Howard, D. N., Burch, D. E., and Williams, D., 1956, “Infrared Transmission of Synthetic Atmospheres—1: Instrumentation,” J. Opt. Soc. Am., 46(3), pp. 186–190. [CrossRef]
Bevans, J. T., Dunkle, R. V., Edwards, D. K., Gier, J. T., Levenson, L. L., and Oppenheim, A. K., 1960, “Apparatus for the Determination of the Band Absorption of Gases at Elevated Pressures and Temperatures,” J. Opt. Soc. Am., 50, pp. 130–136. [CrossRef]
Tien, C. L., and Giedt, W. H., 1965, “Experimental Determination of Infrared Absorption of High-Temperature Gases,” Advances in Thermophysical Properties at Extreme Temperatures and Pressures, ASME, New York, pp. 167–173.
Grosshandler, W. L., 1993, “RADCAL: A Narrow-Band Model for Radiation Calculations in a Combustion Environment,” NIST Technical Note 1402, National Institute of Standards and Technology.
Edwards, D. K., and Menard, W. A., 1964, “Comparison of Models for Correlation of Total Band Absorption,” Appl. Opt., 3, pp. 621–625. [CrossRef]
Soufiani, A., and Taine, J., 1997, “High Temperature Gas Radiative Property Parameters of Statistical Narrow-Band Model for H2O, CO2, and CO, and Correlated-k Model for H2O and CO2,” Int. J. Heat Mass Transfer, 40(4), pp. 987–991. [CrossRef]
McClatchey, R. A., Benedict, W. S., Clough, S. A., Burch, D. E., Fox, K., Rothman, L. S., and Garing, J. S., 1973, “AFCRL Atmospheric Absorption Line Parameters Compilation,” Technical Report No. AFCRL-TR-0096.
Rothman, L. S., Gamache, R. R., Goldman, A., Brown, L. R., Toth, R. A., Pickett, H. M., Poynter, R. L., Flaud, J.-M., Camy-Peyret, C., Barbe, A., Husson, N., Rinsland, C. P., and Smith, M. A. H., 1987, “The HITRAN Database: 1986 Edition,” Appl. Opt., 26(19), pp. 4058–4097. [CrossRef] [PubMed]
Rothman, L. S., Gordon, I. E., Barbe, A., Benner, D. C., Bernath, P. F., Birk, M., Boudon, V., Brown, L. R., Campargue, A., Champion, J.-P., Chance, K., Coudert, L. H., Dana, V., Devi, V. M., Fally, S., Flaud, J.-M., Gamache, R. R., Goldman, A., Jacquemart, D., Kleiner, I., Lacome, N., Lafferty, W. J., Mandin, J.-Y., Massie, S. T., Mikhailenko, S. N., Miller, C. E., Moazzen-Ahmadi, N., Naumenko, O. V., Nikitin, A. V., Orphal, J., Perevalov, V. I., Perrin, A., Predoi-Cross, A., Rinsland, C. P., Rotger, M., Simeckova, M., Smith, M. A. H., Sung, K., Tashkun, S. A., Tennyson, J., Toth, R. A., Vandaele, A. C., and Auwera, J. V., 2009, “The HITRAN 2008 Molecular Spectroscopic Database,” J. Quant. Spectrosc. Radiat. Transfer, 110, pp. 533–572. [CrossRef]
Scutaru, D., Rosenmann, L., and Taine, J., 1994, “Approximate Band Intensities of CO2 Hot Bands at 2.7, 4.3 and 12 μm for High Temperature and Medium Resolution Applications,” J. Quant. Spectrosc. Radiat. Transfer, 52, pp. 765–781. [CrossRef]
Rivière, P., Langlois, S., Soufiani, A., and Taine, J., 1995, “An Approximate Data Base of H2O Infrared Lines for High Temperature Applications at Low Resolution. Statistical Narrow-Band Model Parameters,” J. Quant. Spectrosc. Radiat. Transfer, 53, pp. 221–234. [CrossRef]
Rothman, L. S., Wattson, R. B., Gamache, R. R., Schroeder, J., and McCann, A., 1995, “HITRAN HAWKS and HITEMP: High-Temperature Molecular Database,” Proc. SPIE, 2471, pp. 105–111. [CrossRef]
Fleckl, T., Jäger, H., and Obernberger, I., 2002, “Experimental Verification of Gas Spectra Calculated for High Temperatures Using the HITRAN/HITEMP Database,” J. Phys. D: Appl. Phys., 35(23), pp. 3138–3144. [CrossRef]
Bharadwaj, S. P., and Modest, M. F., 2007, “Medium Resolution Transmission Measurements of CO2 at High Temperature—An Update,” J. Quant. Spectrosc. Radiat. Transfer, 103, pp. 146–155. [CrossRef]
Tashkun, S. A., and Perevalov, V. I., 2008, “Carbon Dioxide Spectroscopic Databank (CDSD): Updated and Enlarged Version for Atmospheric Applications,” 10th HITRAN Conference, Cambridge, MA, Paper T2.3. Available at ftp://ftp.iao.ru/pub/CDSD-2008
Tashkun, S. A., and Perevalov, V. I., 2011, “CDSD-4000: High-Resolution, High-Temperature Carbon Dioxide Spectroscopic Databank,” J. Quant. Spectrosc. Radiat. Transfer, 112(9), pp. 1403–1410. [CrossRef]
Partridge, H., and Schwenke, D. W., 1997, “The Determination of an Accurate Isotope Dependent Potential Energy Surface for Water From Extensive Ab Initio Calculations and Experimental Data,” J. Chem. Phys., 106(11), pp. 4618–4639. [CrossRef]
Barber, R. J., Tennyson, J., Harris, G. J., and Tolchenov, R. N., 2006, “A High-Accuracy Computed Water Line List,” Mon. Not. R. Astron. Soc., 368, pp. 1087–1094. [CrossRef]
Rothman, L. S., Gordon, I. E., Barber, R. J., Dothe, H., Gamache, R. R., Goldman, A., Perevalov, V. I., Tashkun, S. A., and Tennyson, J., 2010, “HITEMP, the High-Temperature Molecular Spectroscopic Database,” J. Quant. Spectrosc. Radiat. Transfer, 111(15), pp. 2139–2150. [CrossRef]
Truelove, J. S., 1975, “The Zone Method for Radiative Heat Transfer Calculations in Cylindrical Geometries,” HTFS Design Report DR33 (Part I: AERE-R8167), Atomic Energy Authority, Harwell, UK.
Smith, T. F., Shen, Z. F., and Friedman, J. N., 1982, “Evaluation of Coefficients for the Weighted Sum of Gray Gases Model,” ASME J. Heat Transfer, 104(4), pp. 602–608. [CrossRef]
Modest, M. F., 1991, “The Weighted-Sum-of-Gray-Gases Model for Arbitrary Solution Methods in Radiative Transfer,” ASME J. Heat Transfer, 113(3), pp. 650–656. [CrossRef]
Denison, M. K., and Webb, B. W., 1993, “A Spectral Line-Based Weighted-Sum-of-Gray-Gases Model for Arbitrary RTE Solvers,” ASME J. Heat Transfer, 115(4), pp. 1004–1012. [CrossRef]
Modest, M. F., and Zhang, H., 2002, “The Full-Spectrum Correlated-k Distribution for Thermal Radiation From Molecular Gas–Particulate Mixtures,” ASME J. Heat Transfer, 124(1), pp. 30–38. [CrossRef]
Elsasser, W. M., 1943, Heat Transfer by Infrared Radiation in the Atmosphere, Harvard University Press, Cambridge, MA.
Goody, R. M., 1952, “A Statistical Model for Water-Vapour Absorption,” Q. J. R. Meteorol. Soc., 78, pp. 165–169. [CrossRef]
Godson, W. L., 1955, “The Computation of Infrared Transmission by Atmospheric Water Vapour,” J. Meteor., 12, pp. 272–284. [CrossRef]
Godson, W. L., 1955, “The Computation of Infrared Transmission by Atmospheric Water Vapour, Part II,” J. Meteor., 12, pp. 533–535. [CrossRef]
Malkmus, W., 1967, “Random Lorentz Band Model With Exponential-Tailed S1 Line-Intensity Distribution Function,” J. Opt. Soc. Am., 57(3), pp. 323–329. [CrossRef]
Young, S. J., 1977, “Nonisothermal Band Model Theory,” J. Quant. Spectrosc. Radiat. Transfer, 18, pp. 1–28. [CrossRef]
Soufiani, A., Hartmann, J.-M., and Taine, J., 1985, “Validity of Band-Model Calculations for CO2 and H2O Applied to Radiative Properties and Conductive–Radiative Transfer,” J. Quant. Spectrosc. Radiat. Transfer, 33, pp. 243–257. [CrossRef]
Menart, J. A., Lee, H. S., and Kim, T. K., 1993, “Discrete Ordinates Solutions of Nongray Radiative Transfer With Diffusely Reflecting Walls,” ASME J. Heat Transfer, 115(1), pp. 184–193. [CrossRef]
Cherkaoui, M., Dufresne, J.-L., Fournier, R.Grandpeix, J.-Y., and Lahellec, A., 1998, “Radiative Net Exchange Formulation Within One-Dimensional Gas Enclosures With Reflective Surfaces,” ASME J. Heat Transfer, 120(1), pp. 275–278. [CrossRef]
Liu, F., 1999, “Numerical Solutions of Three-Dimensional Non-Grey Gas Radiative Transfer Using the Statistical Narrow-Band Model,” ASME J. Heat Transfer, 121(1), pp. 200–203. [CrossRef]
Edwards, D. K., and Balakrishnan, A., 1973, “Thermal Radiation by Combustion Gases,” Int. J. Heat Mass Transfer, 16, pp. 25–40. [CrossRef]
Felske, J. D., and Tien, C. L., 1974, “A Theoretical Closed Form Expression for the Total Band Absorptance of Infrared-Radiating Gases,” ASME J. Heat Transfer, 96, pp. 155–158.
Wang, W. C., 1983, “An Analytical Expression for the Total Band Absorptance of Infrared-Radiating Gases,” J. Quant. Spectrosc. Radiat. Transfer, 29, pp. 279–281. [CrossRef]
Cumber, P. S., Fairweather, M., and Ledin, H. S., 1998, “Application of Wide Band Radiation Models to Non-Homogeneous Combustion Systems,” Int. J. Heat Mass Transfer, 41(11), pp. 1573–1584. [CrossRef]
Liu, F., Smallwood, G. J., and Gülder, Ö. L., 1999, “Application of Statistical Narrowband Model to Three-Dimensional Absorbing–Emitting–Scattering Media,” J. Thermophys. Heat Transfer, 13(3), pp. 285–291. [CrossRef]
Maruyama, S., and Guo, Z., 1999, “Radiative Heat Transfer in Arbitrary Configurations With Nongray Absorbing, Emitting, and Anisotropic Scattering Media,” ASME J. Heat Transfer, 121(3), pp. 722–726. [CrossRef]
Arking, A., and Grossman, K., 1972, “The Influence of Line Shape and Band Structure on Temperatures in Planetary Atmospheres,” J. Atmos. Sci., 29, pp. 937–949. [CrossRef]
Kondratyev, K. Y., 1969, Radiation in the Atmosphere, Academic, New York.
Goody, R. M., West, R., Chen, L., and Crisp, D., 1989, “The Correlated k Method for Radiation Calculations in Nonhomogeneous Atmospheres,” J. Quant. Spectrosc. Radiat. Transfer, 42, pp. 539–550. [CrossRef]
Lacis, A. A., and Oinas, V., 1991, “A Description of the Correlated-k Distribution Method for Modeling Nongray Gaseous Absorption, Thermal Emission, and Multiple Scattering in Vertically Inhomogeneous Atmospheres,” J. Geophys. Res., 96(D5), pp. 9027–9063. [CrossRef]
Fu, Q., and Liou, K. N., 1992, “On the Correlated k-Distribution Method for Radiative Transfer in Nonhomogeneous Atmospheres,” J. Atmos. Sci., 49(22), pp. 2139–2156. [CrossRef]
Rivière, P., Scutaru, D., Soufiani, A., and Taine, J., 1994, “A New c–k Data Base Suitable From 300 to 2500 K for Spectrally Correlated Radiative Transfer in CO2–H2O Transparent Gas Mixtures,” 10th International Heat Transfer Conference, Taylor & Francis, London, pp. 129–134.
Wang, A., and Modest, M. F., 2005, “High-Accuracy, Compact Database of Narrow-Band k-Distributions for Water Vapor and Carbon Dioxide,” J. Quant. Spectrosc. Radiat. Transfer, 93, pp. 245–261. [CrossRef]
Modest, M. F., and Riazzi, R. J., 2005, “Assembly of Full-Spectrum k-Distributions From a Narrow-Band Database; Effects of Mixing Gases, Gases and Nongray Absorbing Particles, and Mixtures With Nongray Scatterers in Nongray Enclosures,” J. Quant. Spectrosc. Radiat. Transfer, 90(2), pp. 169–189. [CrossRef]
Marin, O., and Buckius, R. O., 1997, “Wide Band Correlated-k Approach to Thermal Radiative Transport in Nonhomogeneous Media,” ASME J. Heat Transfer, 119(4), pp. 719–729. [CrossRef]
Dembele, S., Delmas, A., and Sacadura, J.-F., 1997, “A Method for Modeling the Mitigation of Hazardous Fire Thermal Radiation by Water Spray Curtains,” ASME J. Heat Transfer, 119(4), pp. 746–753. [CrossRef]
Dembele, S., and Wen, J. X., 2000, “Investigation of a Spectral Formulation for Radiative Heat Transfer in a One-Dimensional Fires and Combustion System,” Int. J. Heat Mass Transfer, 43, pp. 4019–4030. [CrossRef]
Tang, K. C., and Brewster, M. Q., 1998, “Analysis of Molecular Gas Radiation: Real Gas Property Effects,” 7th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, ASME, Vol. HTD-357-1, pp. 23–32.
Pierrot, L., Soufiani, A., and Taine, J., 1999, “Accuracy of Narrow-Band and Global Models for Radiative Transfer in H2O, CO2, and H2O–CO2 Mixtures at High Temperature,” J. Quant. Spectrosc. Radiat. Transfer, 62, pp. 523–548. [CrossRef]
Pierrot, L., Rivière, P., Soufiani, A., and Taine, J., 1999, “A Fictitious-Gas-Based Absorption Distribution Function Global Model for Radiative Transfer in Hot Gases,” J. Quant. Spectrosc. Radiat. Transfer, 62, pp. 609–624. [CrossRef]
Liu, F., Smallwood, G. J., and Gülder, Ö. L., 2000, “Application of the Statistical Narrow-Band Correlated-k Method to Low-Resolution Spectral Intensity and Radiative Heat Transfer Calculations—Effects of the Quadrature,” Int. J. Heat Mass Transfer, 43, pp. 3119–3135. [CrossRef]
Liu, F., and Smallwood, G. J., 2004, “An Efficient Approach for the Implementation of the SNB Based Correlated-k Method and Its Evaluation,” J. Quant. Spectrosc. Radiat. Transfer, 84, pp. 465–475. [CrossRef]
Tessé, L., Dupoirieux, F., Zamuner, B., and Taine, J., 2002, “Radiative Transfer in Real Gases Using Reciprocal and Forward Monte Carlo Methods and a Correlated-k Approach,” Int. J. Heat Mass Transfer, 45, pp. 2797–2814. [CrossRef]
Denison, M. K., and Webb, B. W., 1993, “An Absorption-Line Blackbody Distribution Function for Efficient Calculation of Total Gas Radiative Transfer,” J. Quant. Spectrosc. Radiat. Transfer, 50, pp. 499–510. [CrossRef]
Denison, M. K., and Webb, B. W., 1995, “The Spectral Line-Based Weighted-Sum-of-Gray-Gases Model in Nonisothermal Nonhomogeneous Media,” ASME J. Heat Transfer, 117(2), pp. 359–365. [CrossRef]
Modest, M. F., and Mehta, R. S., 2004, “Full Spectrum k-Distribution Correlations for CO2 From the CDSD-1000 Spectroscopic Databank,” Int. J. Heat Mass Transfer, 47, pp. 2487–2491. [CrossRef]
Modest, M. F., 2003, “Narrow-Band and Full-Spectrum k-Distributions for Radiative Heat Transfer—Correlated-k vs. Scaling Approximation,” J. Quant. Spectrosc. Radiat. Transfer, 76(1), pp. 69–83. [CrossRef]
Zhang, H., and Modest, M. F., 2003, “Full-Spectrum k-Distribution Correlations for Carbon Dioxide Mixtures,” J. Thermophys. Heat Transfer, 17(2), pp. 259–263. [CrossRef]
Modest, M. F., and Singh, V., 2005, “Engineering Correlations for Full Spectrum k-Distribution of H2O From the HITEMP Spectroscopic Databank,” J. Quant. Spectrosc. Radiat. Transfer, 93, pp. 263–271. [CrossRef]
Liu, F., Chu, H., Zhou, H., and Smallwood, G. J., 2012, “Evaluation of the Absorption Line Blackbody Distribution Function of CO2 and H2O Using the Proper Orthogonal Decomposition and Hyperbolic Correlations,” Proceedings of Eurotherm Seminar 95, Elsevier, Nancy, France.
Solovjov, V. P., and Webb, B. W., 2000, “SLW Modeling of Radiative Transfer in Multicomponent Gas Mixtures,” J. Quant. Spectrosc. Radiat. Transfer, 65, pp. 655–672. [CrossRef]
Wang, L., and Modest, M. F., 2005, “Narrow-Band Based Multiscale Full-Spectrum k-Distribution Method for Radiative Transfer in Inhomogeneous Gas Mixtures,” ASME J. Heat Transfer, 127(7), pp. 740–748. [CrossRef]
Pal, G., and Modest, M. F., 2009, “A Multi-Scale Full-Spectrum k-Distribution Method for Radiative Transfer in Nonhomogeneous Gas–Soot Mixture With Wall Emission,” Comput. Thermal Sci., 1, pp. 137–158. [CrossRef]
Zhang, H., and Modest, M. F., 2003, “Scalable Multi-Group Full-Spectrum Correlated-k Distributions for Radiative Heat Transfer,” ASME J. Heat Transfer, 125(3), pp. 454–461. [CrossRef]
Pal, G., and Modest, M. F., 2010, “A Narrow Band-Based Multiscale Multi-group Full-Spectrum k-Distribution Method for Radiative Transfer in Nonhomogeneous Gas–Soot Mixture,” ASME J. Heat Transfer, 132(2), p. 023307. [CrossRef]
Kent, J. H., and Honnery, D., 1987, “Modeling Sooting Turbulent Jet Flames Using an Extended Flamelet Technique,” Combust. Sci. Technol., 54, pp. 383–397. [CrossRef]
Mehta, R. S., Haworth, D. C., and Modest, M. F., 2010, “Composition PDF/Photon Monte Carlo Modeling of Moderately Sooting Turbulent Jet Flames,” Combust. Flame, 157, pp. 982–994. [CrossRef]
Mazumder, S., and Modest, M. F., 2002, “Application of the Full Spectrum Correlated-k Distribution Approach to Modeling Non-Gray Radiation in Combustion Gases,” Combust. Flame, 129(4), pp. 416–438. [CrossRef]
Sun, X., and Smith, P. J., 2010, “A Parametric Case Study in Radiative Heat Transfer Using the Reverse Monte-Carlo Ray-Tracing With Full-Spectrum k-Distribution Method,” ASME J. Heat Transfer, 132(2), p. 024501. [CrossRef]
Porter, R., Liu, F., Pourkashanian, M., Williams, A., and Smith, D., 2010, “Evaluation of Solution Methods for Radiative Heat Transfer in Gaseous Oxy-Fuel Combustion Environments,” J. Quant. Spectrosc. Radiati. Transfer, 111(14), pp. 2084–2094. [CrossRef]
Demarco, R., Consalvi, J. L., Fuentes, A., and Melis, S., 2011, “Assessment of Radiative Property Models in Non-Gray Sooting Media,” Int. J. Thermal Sci., 50, pp. 1672–1684. [CrossRef]
Pawlak, D. T., Clothiaux, E. E., Modest, M. F., and Cole, J. N. S., 2004, “Full Spectrum Correlated-k for Shortwave Atmospheric Radiative Transfer,” J. Atmos. Sci., 61, pp. 2588–2601. [CrossRef]
Hogan, R. J., 2010, “The Full-Spectrum Correlated-k Method for Longwave Atmospheric Radiative Transfer Using an Effective Planck Function,” J. Atmos. Sci., 67, pp. 2086–2100.
Bansal, A., Modest, M. F., and Levin, D. A., 2011, “Multi-Scale k-Distribution Model for Gas Mixtures in Hypersonic Nonequilibrium Flows,” J. Quant. Spectrosc. Radiat. Transfer, 112(7), pp. 1213–1221. [CrossRef]
Bansal, A., and Modest, M. F., 2011, “Multiscale Part-Spectrum k-Distribution Database for Atomic Radiation in Hypersonic Nonequilibrium Flows,” ASME J. Heat Transfer, 133(12), p. 122701. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Absorption coefficient of water vapor at 1000 K, 1 bar, and a mole fraction of 25% in nitrogen

Grahic Jump Location
Fig. 2

Nondimensional heat loss from an isothermal N2, H2O, CO2 mixture with and without soot [3]

Grahic Jump Location
Fig. 3

Extraction of k-distributions from spectral absorption coefficient data: (a) simplified absorption coefficient across a small portion of the CO2 15 μm band (p = 1.0 bar, T = 296 K); (b) corresponding k-distribution f (k) and cumulative k-distribution k (g) [3]

Grahic Jump Location
Fig. 4

Planck function weighted cumulative k-distributions for 10% CO2 in nitrogen for gas and Planck function temperatures of 1000 K, as evaluated from the HITEMP database and the correlation by Modest [3]

Grahic Jump Location
Fig. 5

Heat loss from an isothermal slab of 10% CO2 in nitrogen at T=1000 K, as evaluated from the LBL, FSK, and SLW models [3]

Grahic Jump Location
Fig. 6

Relative errors of the FSCK, FSSK, MSFSKdir, and MSFSKnb calculations for heat fluxes leaving from the right side of a two-layer slab with step changes in temperature and mole fraction. Left layer (50 cm width): 1500 K, 2% CO2 and 20% H2O; right layer (varying width): 500 K, 20% CO2 and 2% H2O [87].

Grahic Jump Location
Fig. 7

(a) Local radiative heat source using LBL method and relative error (compared to LBL) for heat source calculations using (b) the single-scale FSK method; (c) the MSFSK method; and (d) the 2 group MSMGFSK method [90]

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In