A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Application to nongray media

DOI: 10.1615/thermopedia.009178


APPLICATION TO NONGRAY MEDIA

Following from: Discrete ordinates and finite volume methods

The application of the discrete ordinates method (DOM) and the finite volume method (FVM) to nongray gaseous media, with or without particles, is described in this article. The formulation depends on the model used to calculate the radiative properties of the gaseous medium. The radiative properties of molecular gases are a strong function of wave number, while the radiative properties of particles, although also being dependent on the wave number, are much smoother. As a consequence, the particles in gas-particle media are often treated as gray within a band, in contrast to the gases. Then, the absorption coefficient of the particles is added to that of the gaseous mixture.

Line-by-Line method

The most accurate method to calculate the radiative properties of gases is the lin ...

You need a subscription to view the full text of the article.

If you already have the subscription, please login here
If you want to subscribe to THERMOPEDIA™ please make your request here.

References

  1. Baek, S. W., Kim, H. S., Yu, M. J., Kang, S. J., and Kim, M. Y., Application of the Extended Weighted Sum of Gray Gases Model to Light Fuel Oil Spray Combustion, Combust. Sci. Technol., vol. 174, no. 7, pp. 37−70, 2002.
  2. Borjini, M. N., Guedri, K., and Saïd, R., Modeling of Radiative Heat Transfer in 3D Complex Boiler with Non-Gray Sooting Media, J. Quant. Spectrosc. Radiat. Transfer, vol. 105, pp. 167−179, 2007.
  3. Bressloff, N. W., The Influence of Soot Loading on Weighted Sum of Grey Gases Solution to the Radiative Transfer Equation Across Mixtures of Gases and Soot, Int. J. Heat Mass Transfer, vol. 42, pp. 3469−3480, 1999.
  4. Byun, D. and Baek, S. W., Numerical Investigation of combustion with Non-Gray Thermal Radiation and Soot Formation Effect in a Liquid Rocket Engine, Int. J. Heat Mass Transfer, vol. 50, pp. 412−422, 2007.
  5. Çayan, F. N. and Selçuk, N., A Comparative Study of Modeling of Radiative Heat Transfer using MOL Solution of DOM with Gray Gas, Wide-Band Correlated-k and Spectral Line-Based Weighted Sum of Gray Gases Model, Numer. Heat Transfer, Part B, vol. 52, pp. 281−296, 2007.
  6. Coelho, P. J., Numerical Simulation of Radiative Heat Transfer from Non-Gray Gases in Three-Dimensional Enclosures, J. Quant. Spectrosc. Radiat. Transfer, vol. 74, pp. 307−328, 2002.
  7. Coelho, P. J., Perez, P., and El-Hafi, M., Benchmark Numerical Solutions for Radiative Heat Transfer in Two-Dimensional Axisymmetric Enclosures with Non-Gray Sooting Media, Numer. Heat Transfer, Part B, vol. 43, no. 5, pp. 425−444, 2003a.
  8. Coelho, P. J., Teerling, O. J., and Roekaerts, D., Spectral Radiative Effects and Turbulence/ Radiation Interaction in a Non-Luminous Turbulent Jet Diffusion Flame, Combust. Flame, vol. 133, pp. 75−91, 2003b.
  9. de Miranda, A. B. and Sacadura, J. F., An Alternative Formulation of the S-N Discrete Ordinates for Predicting Radiative Transfer in Nongray Gases, J. Heat Transfer, vol. 118, pp. 650−653, 1996.
  10. Demarco, R., Consalvi, J. L., Fuentes, A., and Melis, S., Assessment of Radiative Property Models in Non-Gray Sooting Media, Int. J. Thermal Sciences, vol. 50, pp. 1672−1684, 2011.
  11. Denison, M. K. and Fiveland, W. A., A Correlation for the Reordered Wave Number of the Wide Band Absorptance of Radiating Gases, J. Heat Transfer, vol. 119, pp. 853−856, 1997.
  12. Denison, M. K. and Webb, B. W., A Spectral Line-Based Weighted-Sum-of-Gray-Gases Model for Arbitrary RTE Solvers, J. Heat Transfer, vol. 115, pp. 1004−1012, 1993a.
  13. Denison, M. K. and Webb, B. W., An Absorption-Line Blackbody Distribution Function for Efficient Calculation of Total Gas Radiative Transfer, J. Quantitative Spectroscopy Radiative Transfer, vol. 50, pp. 499−510, 1993b.
  14. Denison, M. K. and Webb, B. W., Development and Application of an Absorption-Line Blackbody Distribution Function for CO2, Int. J. Heat Mass Transfer, vol. 38, pp. 1813−1821, 1995a.
  15. Denison, M. K. and Webb, B. W., The Spectral Line-Based Weighted-Sum-of-Gray-Gases Model in Nonisothermal Nonhomogeneous Media, J. Heat Transfer, vol. 117, pp. 359−365, 1995b.
  16. Denison, M. K. and Webb, B. W., The Spectral-Line Weighted-Sum-of-Gray-Gases Model for H2O/CO2 Mixtures, J. Heat Transfer, vol. 117, pp. 788−792, 1995c.
  17. Edwards, D. K., Molecular Gas Band Radiation, Advances in Heat Transfer, T. F. Irvine. Jr., and J.P. Hartnett, Eds., New York: Academic Press, vol. 12, p. 115−193, 1976.
  18. Edwards, D. K. and Balakrishnan, A., Thermal Radiation by Combustion Gases, Int. J. Heat Mass Transfer, vol. 16, pp. 25−40, 1973.
  19. Elsasser, W. M., Heat Transfer by Infrared Radiation in the Atmosphere, Cambridge, MA: Harvard University Press, 1943.
  20. Goody, R. M., A Statistical Model for Water-Vapour Absorption, Quart. J. R. Meteorol. Soc., vol. 78, pp. 165−169, 1952.
  21. Goody, R. M., West, R., Chen, L., and Crisp, D., The Correlated k Method for Radiation Calculations in Non-Homogeneous Atmospheres, J. Quant. Spectrosc. Radiat. Transfer, vol. 42, pp. 539−550, 1989.
  22. Gosman, A. D. and Lockwood, F. C., Incorporation of a Flux Model for Radiation into a Finite Difference Procedure for Furnace Calculations, Proc. Combust. Inst., vol. 14, pp. 661−671, 1973.
  23. Goutiere, V., Liu, F., and Charette, A., An Assessment of Real-Gas Modelling in 2D Enclosures, J. Quant. Spectrosc. Radiat. Transfer, vol. 64, pp. 299−326, 2000.
  24. Goutiere, V., Charette, A., and Kiss, L., Comparative Performance of Nongray Gas Modeling Techniques, Numer. Heat Transfer, Part B, vol. 41, pp. 361−381, 2002.
  25. Hottel, H. C. and Sarofim, A. F., Radiative Transfer, New York: McGraw-Hill, 1967.
  26. Ismail, K. A. R. and Salinas, C. T., Application of a Local-Spectrum Correlated Model to Modeling Radiative Transfer in a Mixture of Real Gas Media in Bidimensional Enclosures, Numer. Heat Transfer, Part A, vol. 47, pp. 183−207, 2005.
  27. Joseph, D., El-Hafi, M., Fournier, R., and Cuenot, B., Comparison of Three Spatial Differencing Schemes in Discrete Ordinates Method using Three-Dimensional Unstructured Meshes, Int. J. Thermal Sci., vol. 44, no. 9, pp. 851−864, 2004.
  28. Joseph, D., Perez, P., El-Hafi, M., and Cuenot, B., Discrete Ordinates and Monte Carlo Methods for Radiative Transfer Simulation Applied to Computational Fluid Dynamics Combustion Modeling, J. Heat Transfer, vol. 131, no. 5, pp. 052701, 2009.
  29. Kim, O. J. and Song, T.-H., Implementation of the Weighted Sum of Gray Gases Model to a Narrow Band: Application and Validity, Numer. Heat Transfer, Part B, vol. 30, pp. 453−468, 1996.
  30. Kim, T. K., Menart, J. A., and Lee, H. S., Nongray Radiative Gas Analyses using the S-N Discrete Ordinates Method, J. Heat Transfer, vol. 113, pp. 946−952, 1991.
  31. Lacis, A. A. and Oinas, V. A., Description of the Correlated k-Distribution Method for Modelling Nongray Gaseous Absorption, Thermal Emission, and Multiple Scattering in Vertically Inhomogeneous Atmospheres, J. Geophys. Res., vol. 96, pp. 9027−9063, 1991.
  32. Lallemant, N., Sayre, A., and Weber, R., Evaluation of Emissivity Correlations for H2O-CO2-N2/Air Mixtures and Coupling with Solution Methods of the Radiative Transfer Equation, Prog. Energy Combust. Sci., vol. 22, pp. 543−574, 1996.
  33. Lallemant, N. and Weber, R., A Computationally Efficient Procedure for Calculating Gas Radiative Properties using the Exponential Wide Band Model, Int. J. Heat Mass Transfer, vol. 39, pp. 3273−3286, 1996.
  34. Lee, P. Y. C., Hollands, K. G. T., and Raithby, G. D., Reordering the Absorption Coefficient within the Wide Band for Predicting Gaseous Radiant Exchange, J. Heat Transfer, vol. 118, pp. 394−400, 1996.
  35. Liu, F., Becker, H. A., and Bindar, Y., A Comparative Study of Radiative Heat Transfer Modelling in Gas-Fired Furnaces using the Simple Grey Gas and the Weighted-Sum-of Grey-Gases Models, Int. J. Heat Mass Transfer, vol. 41, pp. 3357−3371, 1998a.
  36. Liu, F., Gülder, Ö. L., and Smallwood, G. J., Three-Dimensional Non-Grey Gas Radiative Transfer Analyses using the Statistical Narrow-Band Model, Rev. Gén. Thermique, vol. 37, pp. 759−768, 1998b.
  37. Liu, F., Gülder, Ö. L., and Smallwood, G. J., Non-Grey Gas Radiative Transfer Analyses using the Statistical Narrow-Band Model, Int. J. Heat Mass Transfer, vol. 41, pp. 2227−2236, 1998c.
  38. Liu, F., Smallwood, G. J., and Gülder, Ö. L., Application of the Statistical Narrow-Band Correlated-k Method to Low-Resolution Spectral Intensity and Radiative Heat Transfer Calculations — Effects of the Quadrature Scheme, Int. J. Heat Mass Transfer, vol. 43, pp. 3119−3135, 2000a.
  39. Liu, F., Smallwood, G. J., and Gülder, Ö. L., Band Lumping Strategy for Radiation Heat Transfer Calculations using a Narrowband Model, J. Thermophys. Heat Transfer, vol. 14, no. 2, pp. 278−281, 2000b.
  40. Liu, F., Smallwood, G. J., and Gülder, Ö. L., Application of the Statistical Narrow-Band Correlated-k Method to Non-Grey Gas Radiation in CO2-H2O Mixtures: Approximate Treatments of Overlapping Bands, J. Quant. Spectrosc. Radiat. Transfer, vol. 68, pp. 401−417, 2001.
  41. Ludwig, C. B., Malkmus, W., Reardon, J. E., and Thompson, J. A. L., Handbook of Infrared Radiation from Combustion Gases, Technical Report NASA SP−3080, Washington, DC, 1973.
  42. Malkmus W., Random Lorentz Band Model with Exponential-Tailed S−1 Line-Intensity Distribution Function, J. Opt. Soc. Am., vol. 57, no. 3, pp. 323−329, 1967.
  43. Marakis, J. G., Application of Narrow and Wide Band Models for Radiative Transfer in Planar Media, Int. J. Heat Mass Transfer, vol. 44, pp. 131−142, 2001.
  44. Marin, O. and Buckius, R. O., Wideband Correlated-k Method Applied to Absorbing, Emitting, and Scattering Media, J. Thermophys. Heat Transfer, vol. 10, no. 2, pp. 364−371, 1996.
  45. Marin, O. and Buckius, R. O., Wideband Correlated-k Approach to Thermal Radiative Transport in Nonhomogeneous Media, J. Heat Transfer, vol. 1119, pp. 719−729, 1997.
  46. Marin, O. and Buckius, R. O., A Simplified Wide Band Model of the Cumulative Distribution Function for Water Vapor, Int. J. Heat Mass Transfer, vol. 41, pp. 2877−2892, 1998a.
  47. Marin, O. and Buckius, R. O., A Simplified Wide Band Model of the Cumulative Distribution Function for Carbon Dioxide, Int. J. Heat Mass Transfer, vol. 41, pp. 3881−3897, 1998b.
  48. Mazumder, S. and Modest, M. F., Application of the Full-Spectrum Correlated-k Distribution Approach to Modeling Non-Gray Radiation in Combustion Gases, Combust. Flame, vol. 129, pp. 416−438, 2002.
  49. Menart, J., Radiative Transport in a Two-Dimensional Axisymmetric Thermal Plasma Using the S-N Discrete Ordinates Method on a Line-By-Line Basis, J. Quant. Spectrosc. Radiat. Transfer, vol. 67, pp. 273−291, 2000.
  50. Menart, J. A., Lee, H. S., and Kim, T. K., Discrete Ordinates Solutions of Nongray Radiative Transfer with Diffusely Reflecting Walls, J. Heat Transfer, vol. 115, pp. 184−193, 1993.
  51. Modest, M. F., The Weighted-Sum-of-Grey-Gases Model for Arbitrary Solution Methods in Radiative Transfer, J. Heat Transfer, vol. 113, pp. 650−656, 1991.
  52. Modest, M. F., Radiative Heat Transfer, New York: Academic Press, 2003a.
  53. Modest, M. F., Narrow-Band and Full-Spectrum k-Distributions for Radiative Heat Transfer — Correlated-k vs. Scaling Approximation, J. Quant. Spectrosc. Radiat. Transfer, vol. 76, pp. 69−83, 2003b.
  54. Modest, M. F. and Riazzi, R. J., 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, vol. 90, pp. 169−189, 2005.
  55. Modest, M. F. and Zhang, H., The Full-Spectrum Correlated-k Distribution for Thermal Radiation from Molecular Gas-Particulate Mixtures, J. Heat Transfer, vol. 124, pp. 30−38, 2002.
  56. Parthasarathy, G., Chai, J. C., and Patankar, S. V., A Simple Approach to Non-Gray Gas Modeling, Numer. Heat Transfer, Part B, vol. 29, pp. 113−123, 1996.
  57. Perez, P., El-Hafi, M., Coelho, P. J., and Fournier, R., Accurate Solutions for Radiative Heat Transfer in Two-Dimensional Axisymmetric Enclosures with Gas Radiation and Reflective Surfaces, Numer. Heat Transfer, Part B, vol. 47, no. 1, pp. 39−63, 2005.
  58. Pierrot, L., Soufiani, A., and Taine, J., 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, vol. 62, pp. 523−548, 1999a.
  59. Pierrot, L., Soufiani, A., and Taine, J., A Fictitious-Gas-Based Absorption Distribution Function Global Model for Radiative Transfer in Hot Gases, J. Quant. Spectrosc. Radiat. Transfer, vol. 62, pp. 609−624, 1999b.
  60. Porter, R., Liu, F., Pourkashanian, M., Williams, A., and Smith, D., Evaluation of Solution Methods for Radiative Heat Transfer in Gaseous Oxy-Fuel Combustion Environments, J. Quant. Spectrosc. Radiat. Transfer, vol. 111, pp. 2084−2094, 2010.
  61. Rivière, Ph., Soufiani, A., Perrin, M.-Y., Riad, H., and Gleizes, A., Air Mixture Radiative Property Modelling in the Temperature Range 10000–40000 K, J. Quant. Spectrosc. Radiat. Transfer, vol. 56, pp. 29−45, 1996.
  62. Rivière, Ph., Soufiani, A., and Taine, J., Correlated-k and Fictitious Gas Methods for H2O near 2.7 μm, J. Quant. Spectrosc. Radiat. Transfer, vol. 48, pp. 187−203, 1992.
  63. Runstedtler, A. and Hollands, K. G. T., Modeling of Gaseous Radiant Exchange with the Smooth Reordered Band Model, Int. J. Heat Mass Transfer, vol. 45, pp. 1653−1660, 2002.
  64. Selçuk, N and Doner, N., A 3-D Radiation Model for Non-Grey Gases, J. Quant. Spectrosc. Radiat. Transfer, vol. 110, pp. 184−191, 2009.
  65. Shi, G., Xu, N., Wang, B., Dai, T., and Zhao, J., An Improved Treatment of Overlapping Absorption Bands Based on the Correlated k Distribution Model for Thermal Infrared Radiative Transfer Calculations, J. Quant. Spectrosc. Radiat. Transfer, vol. 110, pp. 435−451, 2009.
  66. Smith, T. F. , Shenand, Z. F,., and Friedman, J. N., Evaluation of Coefficients for the Weighted Sum of Gray Gases Model, J. Heat Transfer, vol. 104, pp. 602−608, 1982.
  67. Solovjov, V. P. and Webb, B. W., SLW Modeling of Radiative Transfer in Multicomponent Gas Mixtures, J. Quant. Spectrosc. Radiat. Transfer, vol. 65, pp. 655−672, 2000.
  68. Solovjov, V. P. and Webb, B. W., An Efficient Method for Modeling Radiative Transfer in Multicomponent Gas Mixtures with Soot, J. Heat Transfer, vol. 123, pp. 450−457, 2001.
  69. Solovjov, V. P. and Webb, B. W., A Local-Spectrum Correlated Model for Radiative Transfer in Non-Uniform Gas Media, J. Quant. Spectrosc. Radiat. Transfer, vol. 73, pp. 361−373, 2002.
  70. Solovjov, V. P. and Webb, B. W., Application of CW Local Correction Approach to SLW Modeling of Radiative Transfer in non-Isothermal Gaseous Media, J. Quant. Spectrosc. Radiat. Transfer, vol. 111, pp. 318−324, 2010.
  71. Soufiani, A. and Taine, J., 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, vol. 40, pp. 987−991, 1997.
  72. Ströhle, J., Assessment of the Re-ordered Wide Band Model for Non-Grey Radiative Transfer Calculations in 3D Enclosures, J. Quant. Spectrosc. Radiat. Transfer, vol. 109, pp. 1622−1640, 2008.
  73. Ströhle, J. and Coelho, P. J., On the Application of the Exponential Wide Band Model to the Calculation of Radiative Heat Transfer in One- and Two-Dimensional Enclosures, Int. J. Heat Mass Transfer, vol. 45, pp. 2129−2139, 2002.
  74. Taine, J., A Line-by-Line Calculation of Low-Resolution Radiative Properties of CO2-CO-Transparent Nonisothermal Gases Mixtures up to 3000 K, J. Quant. Spectrosc. Radiat. Transfer, vol. 30, no. 4, pp. 371−379, 1983.
  75. Taine, J. and Soufiani, A., Gas IR Radiative Properties: from Spectroscopic Data to Approximate Models, Advances in Heat Transfer, San Diego: Academic Press, J. P. Hartnett and T. Irvine, Eds., vol. 33, pp. 295−414, 1999.
  76. Taine, J., Soufiani, A., Rivière, P., and Perrin, M.-Y., Recent Developments in Modeling the Infrared Radiative Properties of Hot Gases, Proc. of 11th Int. Heat Transfer Conference, vol. 1, J. S. Lee, Ed., Boca Raton: CRC Press, pp. 175−187, 1998.
  77. Tang, K. C. and Brewster, M. Q., k-Distribution Analysis of Gas Radiation with Nongray, Emitting, Absorbing, and Anisotropic Scattering Particles, J. Heat Transfer, vol. 116, pp. 980−985, 1994.
  78. Taylor, P. B. and Foster, P. J., The Total Emissivities of Luminous and Non-Luminous Flames, Int. J. Heat Mass Transfer, vol. 17, pp. 1591−1605, 1974.
  79. Taylor, P. B. and Foster, P. J., Some Gray Gas Weighting Coefficients for CO2-H2O-Soot Mixtures, Int. J. Heat Mass Transfer, vol. 18, pp. 1331−1332, 1975.
  80. Trivic, D. N., Modeling of 3-D Non-Gray Gases Radiation by Coupling the Finite Volume Method with Weighted Sum of Gray Gases Model, Int. J. Heat Mass Transfer, vol. 47, pp. 1367−1382, 2004.
  81. Truelove, J. S., A Mixed Grey Gas Model for Flame Radiation, Harwell Report No. AERE−R8494, 1976.
  82. Young, S. J., Nonisothermal Band Model Theory, J. Quantit. Spectrosc. Radiat. Transfer, vol. 18, pp. 1−28, 1977.
  83. Yu, M. J., Baek, S. W., and Park, J. H., An Extension of the Weighted Sum of Gray Gases Non-Gray Gas Radiation Model to a Two Phase Mixture of Non-Gray Gas with Particles, Int. J. Heat Mass Transfer, vol. 43, pp. 1699−1713, 2000.
  84. Yu, M. J., Baek, S. W., and Kang, S. J., Modeling of Pulverized Coal Combustion with Non-Gray Gas Radiation Effects, Combust. Sci. Technol., vol. 166, pp. 151−174, 2001.
  85. Zhang, H. and Modest, M. F., A Multi-Scale Full-Spectrum Correlated k-Distribution for Radiative Heat Transfer in Inhomogeneous Gas Mixtures, J. Quant. Spectrosc. Radiat. Transfer, vol. 73, pp. 349−360, 2002.
  86. Zhang, H. and Modest, M. F., Multi-Group Full-Spectrum k-Distribution Database for Water Vapor Mixtures in Radiative Transfer Calculations, Int. J. Heat Mass Transfer, vol. 46, pp. 3593−3603, 2003.
  87. Zhang, L., Soufiani, A., and Taine, J., Spectral Correlated and Non-Correlated Radiative Transfer in a Finite Axisymmetric System Containing an Absorbing and Emitting Real Gas-Particle Mixture, Int. J. Heat Mass Transfer, vol. 31, pp. 2261−2272, 1988.
Number of views: 21215 Article added: 24 September 2012 Article last modified: 24 September 2012 © Copyright 2010-2019 Back to top