Computation of radiative transfer in combustion systems

International Journal of Numerical Methods for Heat and Fluid Flow

Volumn 18, Issue 3-4, 2008, Pages 415-442

  Viskanta, Raymond ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

Combustion chambers; Heat transfer

Indexed keywords

COMBUSTION; COMBUSTION CHAMBERS; NUMERICAL METHODS; PROBLEM SOLVING;

RADIATING COMBUSTION SYSTEMS; TRANSPORT EQUATIONS;

RADIATIVE TRANSFER;

COMBUSTION; COMBUSTION CHAMBERS; NUMERICAL METHODS; PROBLEM SOLVING; RADIATIVE TRANSFER;

EID: 43449138789     PISSN: 09615539     EISSN: None     Source Type: Journal    
DOI: 10.1108/09615530810853664     Document Type: Article

References (96)

1. Abbassi, M.A., Halouani, K., Radhouani, M-S. and Farhat, H. (2005), "A parametric study of radiative heat transfer in an industrial combustor of wood carborization fumes", Numerical Heat Transfer, Part A: Applications, Vol. 47, pp. 825-47.
2. Baek, S.W., Kim, M.Y. and Kim, J.S. (1998), "Nonorthogonal finite volume solutions of radiative heat transfer in three dimensional enclosures", Numerical Heat Transfer, Part B, Vol. 34, pp. 419-37.
3. Balsara, D. (2001), "Fast and accurate discrete ordinates methods for multidimensional radiative transfer. Part I, basic methods", Journal of Quantitative Spectroscopy Radiative Transfer, Vol. 69, pp. 671-707.
4. Baukal, C.E. Jr, Gershtein, V.Y. and Li, X. (Eds) (2001), Computational Fluid Dynamics in Industrial Combustion, CRC Press, Boca Raton, FL.
5. Bialecki, R.A. and Wcel, G. (2004), "Solution of conjugate radiation convection problems by a BEM FVM technique", Journal for Quantitative Spectroscopy and Radiative Transfer, Vol. 84, pp. 539-50.
6. Carlson, B.G. and Lathrop, K.D. (1968), "Transport theory - the method of discrete ordinates", in Greenspan, H., Kelber, C.N. and Okrent, D. (Eds), Computing Methods in Reactor Physics, Chapter 3, Gordon and Breach, New York, NY.
7. Carvalho, M.G. and Farias, T.L. (1998), "Modelling of heat transfer in radiating and combusting systems", Transactions of Institute of Chemical Engineers, Part A, Vol. 76, pp. 175-83.
8. Case, K.M. and Zweifel, P.F. (1967), Linear Transport Theory, Addison-Wesley, Reading, MA.
9. Chai, J.C. and Moder, J.P. (1996), "Spatial-multiblock procedure for radiation heat transfer", in Gopinath, A., Jones, P.D., Seyed-Yagoobi, J. and Woodbury, K.A. (Eds), Proceedings of the ASME Heat Transfer Division, HTD-Vol. 332, Vol. 1, ASME, New York, NY, pp. 119-28.
10. Chai, J.C., Parthasarathy, G., Patankar, S.V. and Lee, H.S. (1994), "A finite-volume radiation heat transfer procedure for irregular geometries", AIAA Paper 94-2095.
11. Chandrasekhar, S. (1960), Radiative Transfer, Dover Publications, New York, NY.
12. Cheong, K.B. and Song, T.H. (1995), "Examination of solution method for second order discrete ordinates method", Numerical Heat Transfer, Part B, Vol. 27, pp. 155-73.
13. Cheong, K.B. and Song, T.H. (1996), "Application of the second order discrete ordinates method to a radiation problem in a square geometry", in Mengüç, M.P. (Ed.), Radiative Transfer - I, Proceedings of the First International Symposium on Radiative Transfer, Begell House, New York, NY, pp. 75-91.
14. Chui, E.H. and Raithby, G.D. (1993), "Computation of radiant heat transfer on a non-orthogonal mesh using the finite-volume method", Numerical Heat Transfer, Part B, Vol. 22, pp. 269-88.
15. Coelho, P.J. (2002), "Numerical simulation of radiative heat transfer in three-dimensional enclosures", Journal of Quantitative Spectroscopy Radiative Transfer, Vol. 74, pp. 307-28.
16. Coelho, P.J. and Carvalho, M.G. (1997), "A conservative formulation of the discrete transfer method", Journal of Heat Transfer, Vol. 119, pp. 118-28.
17. Coelho, P.J., Farias, T. and Carvalho, M.G. (1993), "Multi- dimensional modeling of radiative heat transfer in scattering media", Journal of Heat Transfer, Vol. 115, pp. 486-9.
18. Coelho, P.J., Goncalves, J.M. and Carvalho, M.G. (1995), "Comparative study of radiation models for coupled fluid flow/heat transfer problems", in Lewis, R.W. and Dubotaki, P. (Eds), Proceedings of the 9th International Conference on Numerical Methods in Thermal Problems, Pineridge Press, Swansea, Vol. IX, Part 1, pp. 378-89.
19. Coelho, P.J., Perez, P. and El Hafi, M. (2003a), "Benchmark numerical solutions for radiative heat transfer in two-dimensional axisymmetric enclosures with nongray sooting media", Numerical Heat Transfer, Part B, Vol. 43, pp. 425-44.
20. Coelho, P.J., Perez, P. and El Hafi, M. (2003b), "Radiative accurate numerical solutions in two-dimensional axisymmetric enclosures for a gas-particles mixture with varying soot volumetric fraction", in Lybaert, P., Feldheim, V., Lemonnier, D. and Selçuk, N. (Eds), Proceedings of the Eurotherm Seminar 73 on Computational Thermal Radiation in Participating Media, Elsevier, Paris, pp. 161-70.
21. Crosbie, A.L. and Farrell, J.B. (1984), "Exact formulation of multiple scattering in a three-dimensional cylindrical geometry", Journal of Quantitative Spectroscopy Radiative Transfer, Vol. 131, pp. 397-416.
22. Crosbie, A.L. and Schenker, R.G. (1982), "Exact expressions for radiative transfer in a three-dimensional rectangular geometry", Journal of Quantitative Spectroscopy Radiative Transfer, Vol. 28, pp. 507-26.
23. Davidson, B. (1958), Neutron Transport Theory, Clarendon, Oxford.
24. Denison, M.K. and Webb, B.W. (1993), "The spectral line-based weighted-sum-of-gray-gases model for arbitrary RTE solvers", Journal of Heat Transfer, Vol. 115, pp. 1004-12.
25. Dua, S.S. and Cheng, P. (1975), "Multi-dimensional radiative transfer in a cylindrical geometry with anisotropic scattering", Journal of Quantitative Spectroscopy Radiative Transfer, Vol. 18, pp. 245-59.
26. Fiveland, W.A. (1984), "Discrete ordinates solutions of the radiative transport equation for rectangular enclosures", Journal of Heat Transfer, Vol. 106, pp. 699-706.
27. Fiveland, W.A. (1988), "Three-dimensional radiative heat transfer solutions by the discrete-ordinate method", Journal of Thermophysics and Heat Transfer, Vol. 2, pp. 309-16.
28. Fiveland, W.A. and Jamaludin, A.S. (1991), "Three-dimensional spectral radiative heat transfer by the discrete-ordinates method", Journal of Thermophysics and Heat Transfer, Vol. 5, pp. 335-9.
29. Fiveland, W.A. and Jessee, J.P. (1995), "Comparison of discrete ordinates formulations for radiative heat transfer in multidimensional geometries", Journal of Thermophysics and Heat Transfer, Vol. 9 No. 1, pp. 47-54.
30. Floyd, J.E., Baum, H.R. and McGratten, K.B. (2001), "A mixture fraction combustion model for fire simulation using CFD", Proceedings of the International Conference on Engineered Fire Protection Design, Society of Fire Protection Engineers, Bethesda, MD, pp. 279-90.
31. Grosshandler, W.L. (1980), "Radiative heat transfer in nonhomogeneous gases: a simplified approach", International Journal of Heat and Mass Transfer, Vol. 23, pp. 1447-59.
32. Harmandr, S. and Selçuk, N. (2004), "The method of lines solution of discrete ordinates method for radiative transfer in cylindrical enclosures", Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 84, pp. 395-407.
33. Helbig, K-P., Coelho, P., Chamiço, J., Marakis, J., Mbiock, A., Weber, R. and Pasini, S. (2001), "Comparison of radiative heat transfer methods using benchmark test cases", in Mengüç, M.P. and Selçuk, N. (Eds), Radiative Transfer - III, Begell House, Inc., New York, NY, pp. 102-10.
34. Hottel, H.C. and Sarofim, A.F. (1967), Radiative Transfer, McGraw-Hill, New York, NY.
35. Howell, L.H., Pember, R.B., Coella, P., Jesse, J.P. and Fiveland, W.A. (1999), "A conservative adaptive-mesh algorithm for unsteady, combined-mode heat transfer using the discrete ordinates method", Numerical Heat Transfer, Part B, Vol. 35, pp. 407-30.
36. Iyer, R.K. and Mengüç, M.P. (1989), "Quadruple spherical harmonics approximations for radiative transfer in two-dimensional rectangular enclosures", Journal of Thermophysics and Heat Transfer, Vol. 3, pp. 266-74.
37. Jamaluddin, A.S. and Smith, P.J. (1988), "Predicting radiative transfer in rectangular enclosures using the discrete ordinates method", Combustion Science and Technology, Vol. 59, pp. 321-40.
38. Jesse, J.P. and Fiveland, W.A. (1997), "Bounded, high-resolution differencing schemes applied to the discrete ordinates method", Journal of Thermophysics and Heat Transfer, Vol. 11, pp. 540-8.
39. Jesse, J.P., Fiveland, W.A., Howell, L.H., Colella, P. and Pember, R.B. (1998), "An adaptive mesh refinement algorithm for the radiative algorithm for the radiative transfer equation", Journal of Computational Physics, Vol. 139, pp. 380-98.
40. Joseph, D., Coelho, P.J., Cuenot, B. and El Hafi, M. (2003), "Application of the discrete ordinates method to grey media in complex geometries using unstructured meshes", in Lybaert, P., Feldheim, V., Lemonnier, D. and Selçuk, N. (Eds), Proceedings of the Eurotherm Seminar 73 on Computational Thermal Radiation in Participating Media, Elsevier, Paris, pp. 97-106.
41. Khalil, E.E. (1982), Modeling of Furnaces and Combustors, Abacus Press, Turnbridge Wells.
42. Khosla, P.K. and Rubin, S.G. (1974), "A diagonally dominant second order accurate implicit scheme", Computers & Fluids, Vol. 2, pp. 207-9.
43. Kim, M.Y., Baek, S.W. and Park, J.H. (2001), "Unstructured finite-volume method for radiative heat transfer in a complex two-dimensional geometry with obstacles", Numerical Heat Transfer, Part B, Vol. 39, pp. 617-35.
44. Kim, T.K. and Lee, H.S. (1990), "Scaled isotropic results for two-dimensional anisotropic scattering media", Journal of Heat Transfer, Vol. 112, pp. 721-7.
45. Kim, T.K., Park, W.H. and Lee, C.H. (2001), "Radiative transfer solutions for purely absorbing gray and nongray gases within a cubical enclosure", KSME International Journal, Vol. 15, pp. 752-63.
46. Koch, R. and Becker, R. (2004), "Evaluation of quadrature schemes for the discrete ordinates method", Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 84, pp. 423-35.
47. Koch, R., Krebs, W., Wittig, S. and Viskanta, R. (1996), "A parabolic formulation of the discrete ordinates method for treatment of complex geometries", in Mengüç, M.P. (Ed.), Radiative Transfer-I, Begell House, Inc., New York, NY, pp. 43-61.
48. Koo, H-M., Cheong, K-B. and Song, T-H. (1997), "Schemes and applications of first and second-order discrete ordinates interpolation methods to irregular two-dimensional geometries", Journal of Heat Transfer, Vol. 119, pp. 730-7.
49. Krishnamoorthy, G., Rawat, R. and Smith, P.J. (2005), "Parallel computations of radiativeheat transfer using the discrete ordinates method", Numerical Heat Transfer, Part B, Vol. 46, pp. 19-38.
50. Lallemant, N., Sayre, A. and Weber, R. (1996), "Evaluation of emissivity correlations for H2O-CO2 N2/air mixtures and coupling with solution methods of the radiative transfer equation", Progress in Energy and Combustion Science, Vol. 22, pp. 543-74.
51. Lewis, E.E. and Miller, W.F. Jr (1984), Computational Methods in Neutron Transport, Wiley, New York, NY.
52. Li, G. and Modest, M.F. (2003), "Importance of turbulence-radiation interactions in turbulent diffusion flames", Journal of Heat Transfer, Vol. 125, pp. 831-8.
53. Liu, F. (1999), "Numerical solutions of three-dimension non-gray gas radiative transfer using the statistical narrow-band model", Journal of Heat Transfer, Vol. 121, pp. 200-3.
54. Liu, F. and Smallwood, G. (2004), "An efficient approach for the implementation of the SNB based correlated-k method and its evaluation", Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 84, pp. 465-75.
55. Liu, F., Becker, H.A. and Bindar, Y. (1998), "A comparative study of radiative transfer modelling in gas-fired furnaces using simple gray gas and the weighted-sum of gray gases models", International Journal of Heat and Mass Transfer, Vol. 41, pp. 3357-71.
56. Liu, F., Garbett, E.S. and Swithenbank, J. (1992), "Effects of anisotropic scattering on radiative heat transfer using the P1- approximation", International Journal of Heat and Mass Transfer, Vol. 35, pp. 2491-9.
57. Liu, L.H., Zhao, L. and Li, B.X. (2005), "A concept of equivalent absorption and emission coefficients for gray analysis of radiative heat transfer", Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 90, pp. 253-8.
58. Lockwood, F.C. and Shah, N.G. (1981), "A new radiation solution method for incorporation in general combustion prediction procedures", paper presented at Eighteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, pp. 1405-14.
59. Lowes, T.M., Bartelds, H., Heap, M.P., Michelfelder, S. and Pai, B.R. (1973), "Prediction of radiant heat flux distributions", in Afgan, N.H. and Beer, J.M. (Eds), Heat Transfer in Flames, Scripta Book Co., New York, NY, pp. 179-90.
60. Marin, O. and Buckius, R.O. (1996), "Wideband correlated-k method applied to absorbing, emitting, and scattering media", Journal of Thermophysics and Heat Transfer, Vol. 10, pp. 364-71.
61. Mathur, S.R. and Murthy, J.Y. (1999), "Coupled ordinates method for multigrid acceleration of radiation calculations", Journal of Thermophysics and Heat Transfer, Vol. 13, pp. 467-73.
62. Mbiock, A. and Weber, R. (2000), Radiation in Enclosures, Springer, Berlin.
63. Mengüç, M.P. and Viskanta, R. (1985), "Radiative transfer in three-dimensional rectangular enclosures containing inhomogeneous aisotropically scattering media", Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 33, pp. 321-40.
64. Mihalas, D. and Klein, R.E. (1982), "On the solution of the time-dependent inertial-frame equation of radiating transfer in moving media to o(v/c)", Journal of Computational Physics, Vol. 46, pp. 97-137.
65. Modak, A.T. (1979), "Radiation from products of combustion", Fire Research, Vol. 1, pp. 339-61.
66. Modest, M.F. (1991), "The weighted-sum-of-gray-gases model for arbitrary solution methods in radiative transfer", Journal of Heat Transfer, Vol. 113, pp. 650-6.
67. Modest, M.F. (2003), Radiative Heat Transfer, 2nd ed., Academic Press, New York, NY.
68. Murthy, J.Y. and Mathur, S.R. (1998), "A finite volume method for radiative heat transfer using unstructured meshes", Journal of Thermophysics and Heat Transfer, Vol. 12, pp. 313-21.
69. Murthy, J.Y. and Mathur, S.R. (2001), "Unstructured mesh methods for combustion problems", in Baukal, C.E. Jr, Gershtein, V.Y. and Li, X. (Eds), Computational Fluid Dynamics in Industrial Combustion, Chapter 3, CRC Press, Boca Raton, FL.
70. Park, H.M., Lee, J.H. and Park, J.H. (1999), "Analysis of spectral radiative heat transfer in furnaces using an efficient computational technique", Journal of Quantitative Spectroscopy Radiative Transfer, Vol. 62, pp. 459-75.
71. Park, W.H. and Kim, T.K. (2002), "Narrow band solutions of radiative transfer for purely absorbing nongray gases within a 3-dimensional cylindrical enclosure", Heat Transfer 2002, Vol. 1, Elsevier, Paris, pp. 675-80.
72. Patankar, S.V. and Spalding, D.B. (1973), "Simultaneous predictions of flow pattern and radiation for three-dimensional flow in flames", paper presented at Fourteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, pp. 605-14.
73. Pierrot, L., Soufiani, A. and Taine, J. (1999a), "Accuracy of narrow-band and global models for radiative transfer in H2O-CO2, and H2O-CO2 mixtures at high temperature", Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 62, pp. 523-48.
74. Pierrot, L., Rivière, P., Soufiani, A. and Taine, J. (1999b), "A fictitious-gas-based absorption distribution function global model for radiative transfer in hot gases", Journal of Quantitative Spectroscopy Radiative Transfer, Vol. 62, pp. 609-24.
75. Raithby, G.D. and Chui, E.H. (1990), "A finite-volume method for predicting a radiant heat transfer in enclosures with participating media", Journal of Heat Transfer, Vol. 112, pp. 415-23.
76. Richter, W. and Quack, R. (1973), "A mathematical model of a low-volatile pulverized fuel flame", in Afgan, N.H. and Beer, J.M. (Eds), Heat Transfer in Flames, Scripta Book Co., New York, NY, pp. 95-109.
77. Rivière, P., Scuturu, D., Soufiani, T. and Taine, J. (1994), "A new CK basic suitable from 300 to 2500 K for spectrally correlated radiative transfer in CO2-H2O-transparent gas mixtures", in Hewith, G.F. (Ed.), Heat Transfer 1994, Vol. 2, Institute of Chemical Engineers, Rugby, pp. 129-34.
78. Siddall, R.G. and Selcuk, N. (1979), "Evaluation of new six-flux model for radiative transfer in enclosure", Transactions of the Institute of Chemical Engineers, Vol. 57, pp. 163-9.
79. Siegel, R. and Howell, J.R. (2002), Thermal Radiation Heat Transfer, 4th ed., Taylor & Francis, New York, NY.
80. Song, T.H. (1993), "Comparison of engineering models of nongray behavior of combustion products", International Journal of Heat and Mass Transfer, Vol. 36, pp. 3975-82.
81. Song, T.H. and Park, C.W. (1992), "Formulation and application of the second order discrete ordinate method", in Wang, B-X. (Ed.), Transport Phenomena Science and Technology 1992, Higher Education Press, Beijing, pp. 833-41.
82. Soufiani, A. and Taine, J. (1997), "High temperature gas radiation property parameters of statistical narrow-band model for H2O, CO2 and CO and correlated-k (ck) model for H2O and CO2", International Journal of Heat and Mass Transfer, Vol. 40, pp. 987-91.
83. Ströhle, J. and Coelho, P.J. (2002), "On the application of the exponential wide band model to the calculation of radiative heat transfer in one- and two-dimensionless enclosures", International Journal of Heat and Mass Transfer, Vol. 45, pp. 2129-39.
84. Ströhle, J., Schnell, U. and Klein, K.R.G. (2003), "Optimization of the wide band correlated-k method for non-gray radiative transfer calculations in multidimensional enclosures", in Lybaert, P., Feldheim, V., Lemonnier, D. and Selçuk, N. (Eds), Proceedings of the Eurotherm Seminar 73 on Computational Thermal Radiation in Participating Media, Elsevier, Paris, pp. 119-28.
85. Taine, J. and Soufiani, A. (1999), "Gas IR radiative properties: from spectroscopic data to approximate models", in Hartnett, J.P. et al. (Eds), Advances in Heat Transfer, Vol. 33, Academic Press, San Diego, CA, pp. 295-414.
86. Tang, K.C. and Brewster, M.Q. (1994), "K-distribution analysis of gas radiation with non-gray, emitting, and anisotropic scattering particles", Journal of Heat Transfer, Vol. 116, pp. 980-5.
87. Tessé, L., Dupoirieux, F. and Taine, J. (2004), "Monte Carlo modeling of radiative transfer in turbulent sooty flame", International Journal of Heat and Mass Transfer, Vol. 47, pp. 555-72.
88. 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", International Journal of Heat and Mass Transfer, Vol. 45, pp. 2797-814.
89. Tong, T.W. and Skocypec, R.D. (1992), "Summary on comparison of radiative heat transfer solutions for a specified problem", in Thynell, S.T., Modest, M.F., Burmeister, L.C. et al. (Eds), Developments in Radiative Heat Transfer, HTD-Vol. 203, ASME, New York, NY, pp. 253-64.
90. Tsuji, H., Gupta, A.K., Hasegawa, T., Katsuki, M., Kishimoto, K. and Morita, M. (2003), High Temperature Air Combustion, CRC Press, Boca Raton, FL.
91. van Leer, B. (1974), "Towards ultimate conservation difference scheme: II monoticity and conservation combined in a second-order-scheme", Journal of Computational Physics, Vol. 11, pp. 361-70.
92. Versteeg, H.K., Henson, J.C. and Malalasekera, W. (2001), "A comparison of convergence and error estimates for the Monte Carlo and discrete transfer methods", in Mengüç, M.P. and Selçuk, N. (Eds), Radiative Transfer - III, Begell House, Inc., New York, NY, pp. 92-101.
93. Viskanta, R. (1964), "Concerning the definition of the mean absorption coefficient", International Journal of Heat and Mass Transfer, Vol. 7, pp. 1047-9.
94. Viskanta, R. and Mengüç, M.P. (1987), "Radiation heat transfer in combustion systems", Progress in Energy and Combustion Science, Vol. 13, pp. 97-160.
95. Wcel, G. and Bialecki, R.A. (2006), "BEM solution of the radiative heat transfer within natural gas fired combustion chamber", Combustion Science and Technology, Vol. 178 No. 8, pp. 1413-40.
96. Wilson, S.J. and Sen, K.K. (1986), "Generalized Eddington approximation method for radiation transfer in slab medium", Journal of Quantitative Spectroscopy Radiative Transfer, Vol. 35, pp. 467-72.