Skip to main content

Radiation Properties, RTE Solvers, and TRI Models

  • Chapter
  • First Online:
Radiative Heat Transfer in Turbulent Combustion Systems

Part of the book series: SpringerBriefs in Applied Sciences and Technology ((BRIEFSTHERMAL))

Abstract

Radiative heat transfer or thermal radiation is the science of transferring energy in the form of electromagnetic waves. Unlike heat conduction, electromagnetic waves do not require a medium for their propagation. Therefore, because of their ability to travel across vacuum, thermal radiation becomes the dominant mode of heat transfer in low pressure (vacuum) and outer space applications. Another distinguishing characteristic between conduction (and convection, if aided by flow) and thermal radiation is their temperature dependence. While conductive and convective fluxes are more or less linearly dependent on temperature differences, radiative heat fluxes tend to be proportional to differences in the fourth power of temperature (or even higher). For this reason, radiation tends to become the dominant mode of heat transfer in high-temperature applications, such as combustion (fires, furnaces, rocket nozzles), nuclear reactions (solar emission, nuclear weapons), and others. This chapter introduces the fundamentals of thermal radiation, and covers the radiative properties of combustion systems, spectral models and global models, radiative transfer equation solution methods, and turbulence–radiation interactions. Together with the material on combustion and turbulence–chemistry interactions in the previous chapter, this provides the foundation that is needed for the examples that are presented and discussed in subsequent chapters.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. M.F. Modest, Radiative Heat Transfer, 3rd edn. (Academic, New York, 2013)

    Google Scholar 

  2. L.S. Rothman, I.E. Gordon, A. Barbe, D.C. Benner, P.F. Bernath, M. Birk, V. Boudon, L.R. Brown, A. Campargue, J.-P. Champion, K. Chance, L.H. Coudert, V. Dana, V.M. Devi, S. Fally, J.-M. Flaud, R.R. Gamache, A. Goldman, D. Jacquemart, I. Kleiner, N. Lacome, W.J. Lafferty, J.-Y. Mandin, S.T. Massie, S.N. Mikhailenko, C.E. Miller, N. Moazzen-Ahmadi, O.V. Naumenko, A.V. Nikitin, J. Orphal, V.I. Perevalov, A. Perrin, A. Predoi-Cross, C.P. Rinsland, M. Rotger, M. Simeckova, M.A.H. Smith, K. Sung, S.A. Tashkun, J. Tennyson, R.A. Toth, A.C. Vandaele, J.V. Auwera, The HITRAN 2008 molecular spectroscopic database. J. Quant. Spectrosc. Radiat. Transf. 110, 533–572 (2009)

    Google Scholar 

  3. L.S. Rothman, I.E. Gordon, R.J. Barber, H. Dothe, R.R. Gamache, A. Goldman, V.I. Perevalov, S.A. Tashkun, J. Tennyson, HITEMP, the high-temperature molecular spectroscopic database. J. Quant. Spectrosc. Radiat. Transfer 111(15), 2139–2150 (2010)

    Article  Google Scholar 

  4. S.A. Tashkun, V.I. Perevalov, CDSD-4000: high-resolution, high-temperature carbon dioxide spectroscopic databank, J. Quant. Spectrosc. Radiat. Transf. 112(9), 1403–1410 (2011). Available from ftp://ftp.iao.ru/pub/CDSD-4000

    Google Scholar 

  5. J.M. Singer, J. Grumer, Carbon formation in very rich hydrocarbon–air flames—I: studies of chemical content, temperature, ionization and particulate matter, in Seventh Symposium (International) on Combustion (The Combustion Institute, Pittsburg, PA, 1959), pp. 559–572

    Google Scholar 

  6. B.L. Wersborg, J.B. Howard, G.C. Williams, Physical mechanisms in carbon formation in flames, in Fourteenth Symposium (International) on Combustion (The Combustion Institute, Pittsburg, PA, 1972), pp. 929–940

    Google Scholar 

  7. A.F. Sarofim, H.C. Hottel, Radiative transfer in combustion chambers: influence of alternative fuels, in Proceedings of the Sixth International Heat Transfer Conference, vol. 6 (Hemisphere, Washington, DC, 1978), pp. 199–217

    Google Scholar 

  8. M. Kunugi, H. Jinno, Determination of size and concentration of soot particles in diffusion flames by a light-scattering technique, in Eleventh Symposium (International) on Combustion (The Combustion Institute, Pittsburg, PA, 1966), pp. 257–266

    Google Scholar 

  9. T. Sato, T. Kunitomo, S. Yoshi, T. Hashimoto, On the monochromatic distribution of the radiation from the luminous flame. Bull. JSME 12, 1135–1143 (1969)

    Article  Google Scholar 

  10. A. Becker, Über die Strahlung und Temperatur der Hefnerlampe. Ann. Phys. 333(5), 1017–1031 (1909)

    Google Scholar 

  11. H. Chang, T.T. Charalampopoulos, Determination of the wavelength dependence of refractive indices of flame soot, Proc. R. Soc. (Lond.) A 430(1880), 577–591 (1990)

    Google Scholar 

  12. M. Frenklach, H. Wang, M. J. Rabinowitz, Optimization and analysis of large chemical kinetic mechanisms using the solution mapping method—combustion of methane. Progr. Energy Combust. Sci. 18, 47–73 (1992)

    Article  Google Scholar 

  13. M. Frenklach, H. Wang, Detailed mechanism and modeling of soot particle formation, in Soot Formation in Combustion (Springer, New York, 1994), pp. 162–192

    Google Scholar 

  14. M. Frenklach, On surface growth mechanism of soot particles, in Twenty-Sixth Symposium (International) on Combustion (The Combustion Institute, Pittsburg, PA, 1996), pp. 2285–2293

    Google Scholar 

  15. H. Wang, M. Frenklach, A detailed kinetic modeling study of aromatics formation in laminar premixed acetylene and ethylene flames. Combust. Flame 110, 173–221 (1997)

    Article  Google Scholar 

  16. M. Frenklach, S.J. Harris, Aerosol dynamics modeling using the method of moments. J. Colloid Interface Sci. 118, 252–261 (1987)

    Article  Google Scholar 

  17. M. Frenklach, S.J. Harris, Aerosol dynamics using the method of moments, J. Colloid Interface Sci. 130, 252–261 (1987)

    Article  Google Scholar 

  18. M. Frenklach, Soot Modeling Home Page, http://www.me.berkeley.edu/soot

  19. R.A. Dobbins, C.M. Megaridis, Morphology of flame-generated soot as determined by thermophoretic sampling. Langmuir 3, 254–259 (1987)

    Article  Google Scholar 

  20. M.F. Iskander, H.Y. Chen, J.E. Penner, Optical scattering and absorption by branched-chains of aerosols. Appl. Opt. 28, 3083–3091 (1989)

    Article  Google Scholar 

  21. Ü.Ö. Köylü, G.M. Faeth, Radiative properties of flame-generated soot. J. Heat Transf. 115(2), 409–417 (1993)

    Article  Google Scholar 

  22. S. Manickavasagam, M.P. Mengüç, Scattering matrix elements of fractal-like soot agglomerates. J. Appl. Phys. 36(6), 1337–1351 (1997)

    Google Scholar 

  23. T.L. Farias, M.G. Carvalho, Ü.Ö. Köylü, G.M. Faeth, Computational evaluation of approximate Rayleigh–Debye–Gans fractal-aggregate theory for the absorption and scattering properties of soot. J. Heat Transf. 117(1), 152–159 (1995)

    Article  Google Scholar 

  24. W. Malkmus, Random Lorentz band model with exponential-tailed S −1 line-intensity distribution function, J. Opt. Soc. Am. 57(3), 323–329 (1967)

    Article  Google Scholar 

  25. A.A. Lacis, V. Oinas, 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), 9027–9063 (1991)

    Article  Google Scholar 

  26. W.L. Grosshandler, RADCAL: a narrow-band model for radiation calculations in a combustion environment. Technical Report NIST Technical Note 1402, National Institute of Standards and Technology (1993)

    Google Scholar 

  27. A. Soufiani, J. Taine, 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 Transf. 40(4), 987–991 (1997)

    Article  Google Scholar 

  28. A. Arking, K. Grossman, The influence of line shape and band structure on temperatures in planetary atmospheres. J. Atmos. Sci. 29, 937–949 (1972)

    Article  Google Scholar 

  29. M.F. Modest, Narrow-band and full-spectrum k-distributions for radiative heat transfer—correlated-k vs. scaling approximation. J. Quant. Spectrosc. Radiat. Transf. 76(1), 69–83 (2003)

    Google Scholar 

  30. A. Wang, M.F. Modest, High-accuracy, compact database of narrow-band k-distributions for water vapor and carbon dioxide, in Proceedings of the ICHMT 4th International Symposium on Radiative Transfer, Istanbul, Turkey, 2004, ed. by M.P. Mengüç, N. Selçuk

    Google Scholar 

  31. J. Cai, M.F. Modest, Improved full-spectrum k-distribution implementation for inhomogeneous media using a narrow-band database. J. Quant. Spectrosc. Radiat. Transf. 141, 65–72 (2013)

    Article  Google Scholar 

  32. H.C. Hottel, A.F. Sarofim, Radiative Transfer (McGraw-Hill, New York, 1967)

    Google Scholar 

  33. M.F. Modest, The weighted-sum-of-gray-gases model for arbitrary solution methods in radiative transfer. J. Heat Transf. 113(3), 650–656 (1991)

    Article  Google Scholar 

  34. M.K. Denison, B.W. Webb, A spectral line based weighted-sum-of-gray-gases model for arbitrary RTE solvers. J. Heat Transf. 115, 1004–1012 (1993)

    Article  Google Scholar 

  35. M.K. Denison, B.W. Webb, k-Distributions and weighted-sum-of-gray gases: a hybrid model, in Tenth International Heat Transfer Conference (Taylor & Francis, London, 1994), pp. 19–24.

    Google Scholar 

  36. M.K. Denison, B.W. Webb, The spectral-line-based weighted-sum-of-gray-gases model in nonisothermal nonhomogeneous media. J. Heat Transf. 117, 359–365 (1995)

    Article  Google Scholar 

  37. M.K. Denison, B.W. Webb, Development and application of an absorption line blackbody distribution function for CO2. Int. J. Heat Mass Transf. 38, 1813–1821 (1995)

    Article  Google Scholar 

  38. M.K. Denison, B.W. Webb, The spectral-line weighted-sum-of-gray-gases model for H2O/CO2 mixtures. J. Heat Transf. 117, 788–792 (1995)

    Article  Google Scholar 

  39. P. Rivière, A. Soufiani, M.-Y. Perrin, H. Riad, A. Gleizes, Air mixture radiative property modelling in the temperature range 10000–40000 K. J. Quant. Spectrosc. Radiat. Transf.56, 29–45 (1996)

    Article  Google Scholar 

  40. L. Pierrot, A. Soufiani, J. Taine, Accuracy of narrow-band and global models for radiative transfer in H2O, CO2, and H2O–CO2 mixtures at high temperature. J. Quant. Spectrosc. Radiat. Transf. 62, 523–548 (1999)

    Article  Google Scholar 

  41. L. Pierrot, P. Rivière, A. Soufiani, J. Taine, A fictitious-gas-based absorption distribution function global model for radiative transfer in hot gases. J. Quant. Spectrosc. Radiat. Transf. 62, 609–624 (1999)

    Article  Google Scholar 

  42. M.F. Modest, H. Zhang, The full-spectrum correlated-k distribution and its relationship to the weighted-sum-of-gray-gases method, in Proceedings of the IMECE 2000, vol. HTD-366-1 (American Society of Mechanical Engineers, Orlando, FL, 2000), pp. 75–84

    Google Scholar 

  43. H. Zhang, M.F. Modest, A multi-scale full-spectrum correlated-k distribution for radiative heat transfer in inhomogeneous gas mixtures. J. Quant. Spectrosc. Radiat. Transf. 73(2–5), 349–360 (2002)

    Article  Google Scholar 

  44. H. Zhang, M.F. Modest. Scalable multi-group full-spectrum correlated-k distributions for radiative heat transfer. J. Heat Transfer 125(3), 454–461 (2003)

    Article  Google Scholar 

  45. M.F. Modest, R.J. Riazzi, 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. Transf. 90(2), 169–189 (2005)

    Article  Google Scholar 

  46. H.C. Hottel, A.F. Sarofim, Radiative Transfer (McGraw-Hill, New York, 1967)

    Google Scholar 

  47. T.F. Smith, Z.F. Shen, J.N. Friedman, Evaluation of coefficients for the weighted sum of gray gases model. J. Heat Transf. 104, 602–608 (1982)

    Article  Google Scholar 

  48. I.H. Farag, T.A. Allam, Gray-gas approximation of carbon dioxide standard emissivity. J. Heat Transf. 103, 403–405 (1981)

    Article  Google Scholar 

  49. J.S. Truelove, The zone method for radiative heat transfer calculations in cylindrical geometries. HTFS Design Report DR33 (Part I: AERE-R8167) (Atomic Energy Authority, Harwell, 1975)

    Google Scholar 

  50. T. Kangwanpongpan, F.H.R. França, R.C. da Silva, P.S. Schneider, H.J. Krautz, New correlations for the weighted-sum-of-gray-gases model in oxy-fuel conditions based on HITEMP 2010 database. Int. J. Heat Mass Transf. 55, 7419–7433 (2012)

    Article  Google Scholar 

  51. L.J. Dorigon, G. Duciak, R. Brittes, F. Cassol, M. Galarça, F.H.R. França, WSGG correlations based on HITEMP2010 for computation of thermal radiation in non-isothermal, non-homogeneous H2O/CO2 mixtures. Int. J. Heat Mass Transf. 64, 863–873 (2013)

    Article  Google Scholar 

  52. M.H. Bordbar, G. Wecel, T. Hyppänen, A line by line based weighted sum of gray gases model for inhomogeneous CO2–H2O mixture in oxy-fired combustion. Combust. Flame 161, 2435–2445 (2014)

    Article  Google Scholar 

  53. F. Cassol, R. Brittes, F.H.R. França, O.A. Ezekoye, Application of the weighted-sum-of-gray-gases model for media composed of arbitrary concentrations of H2O, CO2 and soot. Int. J. Heat Mass Transf. 79, 796–806 (2014)

    Article  Google Scholar 

  54. M.K. Denison, B.W. Webb, An absorption-line blackbody distribution function for efficient calculation of total gas radiative transfer. J. Quant. Spectrosc. Radiat. Transf. 50, 499–510 (1993)

    Article  Google Scholar 

  55. M.F. Modest, R.S. Mehta, Full spectrum k-distribution correlations for CO2 from the CDSD-1000 spectroscopic databank. Int. J. Heat Mass Transf.47, 2487–2491 (2004)

    Article  Google Scholar 

  56. M.F. Modest, V. Singh, Engineering correlations for full spectrum k-distribution of H2O from the HITEMP spectroscopic databank. J. Quant. Spectrosc. Radiat. Transf. 93, 263–271 (2005)

    Article  Google Scholar 

  57. F. Liu, H. Chu, H. Zhou, G.J. Smallwood. Evaluation of the absorption line blackbody distribution function of CO2 and H2O using the proper orthogonal decomposition and hyperbolic correlations. J. Quant. Spectrosc. Radiat. Transf. 128, 27–33 (2013)

    Article  Google Scholar 

  58. J.T. Pearson, B.W. Webb, V.P. Solovjov, J. Ma, Efficient representation of the absorption line blackbody distribution function for H2O, CO2, and CO at variable temperature, mole fraction, and total pressure. J. Quant. Spectrosc. Radiat. Transf. 138, 82–96 (2014)

    Article  Google Scholar 

  59. C. Wang, W. Ge, M.F. Modest, J. Cai, A full-spectrum k-distribution look-up table for radiative transfer in nonhomogeneous gaseous media, in CHT-15: Advances in Computational Heat Transfer (Begell House, Redding, CT, 2015)

    Google Scholar 

  60. V.P. Solovjov, B.W. Webb, SLW modeling of radiative transfer in multicomponent gas mixtures. J. Quant. Spectrosc. Radiat. Transf. 65, 655–672 (2000)

    Article  Google Scholar 

  61. M.F. Modest, J. Yang, Elliptic PDE formulation and boundary conditions of the spherical harmonics method of arbitrary order for general three-dimensional geometries. J. Quant. Spectrosc. Radiat. Transf. 109, 1641–1666 (2008)

    Article  Google Scholar 

  62. J. Yang, M.F. Modest, High-order P-N approximation for radiative transfer in arbitrary geometries. J. Quant. Spectrosc. Radiat. Transf. 104(2), 217–227 (2007)

    Article  Google Scholar 

  63. M.F. Modest, Further developments of the elliptic P N -approximation formulation and its Marshak boundary conditions. Numer. Heat Transfer B 62(2–3), 181–202 (2012)

    Article  Google Scholar 

  64. R.E. Marshak, Note on the spherical harmonics method as applied to the Milne problem for a sphere. Phys. Rev. 71, 443–446 (1947)

    Article  MathSciNet  MATH  Google Scholar 

  65. H. Jasak, A. Jemcov, Z. Tukovic, OpenFOAM: A C++ library for complex physics simulations, in International Workshop on Coupled Methods in Numerical Dynamics (Inter-University Centre, Dubrovnik, 2007), pp. 1–20

    Google Scholar 

  66. A. Wang, M.F. Modest, Importance of combined Lorentz–Doppler broadening in high-temperature radiative heat transfer applications. J. Heat Transf. 126(5), 858–861 (2004)

    Article  Google Scholar 

  67. A. Wang, M.F. Modest, Spectral Monte Carlo models for nongray radiation analyses in inhomogeneous participating media. Int. J. Heat Mass Transf. 50, 3877–3889 (2007)

    Article  MATH  Google Scholar 

  68. A.M. Feldick, M.F. Modest, An improved wavelength selection scheme for Monte Carlo solvers applied to hypersonic plasmas. J. Quant. Spectrosc. Radiat. Transf. 112, 1394–1401 (2011)

    Article  Google Scholar 

  69. T. Ren, M.F. Modest. Hybrid wavenumber selection scheme for line-by-line photon Monte Carlo simulations in high-temperature gases. J. Heat Transfer 135(8), 084501 (2013)

    Google Scholar 

  70. M.F. Modest, S.C. Poon, Determination of three-dimensional radiative exchange factors for the space shuttle by Monte Carlo. ASME paper no. 77-HT-49 (1977)

    Google Scholar 

  71. M.F. Modest, Determination of radiative exchange factors for three dimensional geometries with nonideal surface properties. Numer. Heat Transf. 1, 403–416 (1978)

    Google Scholar 

  72. A. Wang, M.F. Modest, Photon Monte Carlo simulation for radiative transfer in gaseous media represented by discrete particle fields. J. Heat Transf. 128, 1041–1049 (2006)

    Article  Google Scholar 

  73. A. Wang, M.F. Modest, An adaptive emission model for Monte Carlo ray-tracing in participating media represented by statistical particle fields. J. Quant. Spectrosc. Radiat. Transf. 104(2), 288–296 (2007)

    Article  Google Scholar 

  74. P.J. Coelho, A theoretical analysis of the influence of turbulence on radiative emission in turbulent diffusion flames of methane. Combust. Flame 160, 610–617 (2013)

    Article  Google Scholar 

  75. G.P. Smith, D.M. Golden, M. Frenklach, N.W. Moriarty, B. Eiteneer, M. Goldenberg, C.T. Bowman, R. Hanson, S. Song, W.C. Gardiner, V. Lissianski, Z. Qin, GRI-Mech 3.0 (1999). Available at http://www.me.berkeley.edu/gri_mech

  76. H. Pitsch, FlameMaster v3.3.10, A C++ Computer Program for 0D Combustion and 1D Laminar Flame Calculations (2015). Available at http://www.itv.rwth-aachen.de/index.php?id=128

  77. V.P. Kabashinikov, G. I. Myasnikova, Thermal radiation in turbulent flows—temperature and concentration fluctuations. Heat Transf.-Sov. Res. 17(6), 116–125 (1985)

    Google Scholar 

  78. T.-H. Song, R. Viskanta, Interaction of radiation with turbulence: application to a combustion system. J. Thermophys. Heat Transf. 1(1), 56–62 (1987)

    Article  Google Scholar 

  79. J.W. Hartick, M. Tacke, G. Fruchtel, E.P. Hassel, J. Janicka, Interaction of turbulence and radiation in confined diffusion flames, in Twenty-Sixth Symposium (International) on Combustion (The Combustion Institute, Pittsburg, PA, 1996), pp. 75–82

    Google Scholar 

  80. P.J. Coelho, Detailed numerical simulation of radiative transfer in a nonluminous turbulent jet diffusion flame. Combust. Flame 136, 481–492 (2004)

    Article  Google Scholar 

  81. A. Wang, M.F. Modest, D.C. Haworth, L. Wang, Monte Carlo simulation of radiative heat transfer and turbulence interactions in methane/air jet flames. J. Quant. Spectrosc. Radiat. Transf. 109(2), 269–279 (2008)

    Article  Google Scholar 

  82. L. Tessé, F. Dupoirieux, J. Taine, Monte Carlo modeling of radiative transfer in a turbulent sooty flame. Int. J. Heat Mass Transf. 47, 555–572 (2004)

    Article  MATH  Google Scholar 

  83. B. Zamuner, F. Dupoirieux, Numerical simulation of soot formation in a turbulent flame with a Monte-Carlo PDF approach and detailed chemistry. Combust. Sci. Technol. 158, 407–438 (2000)

    Article  Google Scholar 

  84. R.S. Mehta, M.F. Modest, Modeling absorption TRI in optically thick eddies, in Proceedings of Eurotherm Seminar 78, April (Elsevier, Poitiers, 2006)

    Google Scholar 

  85. P.J. Coelho, Assessment of a presumed joint pdf for the simulation of turbulence–radiation interaction in turbulent reactive flows. Appl. Therm. Eng. 49, 22–30 (2012)

    Article  Google Scholar 

  86. R.S. Mehta, A. Wang, M.F. Modest, D.C. Haworth, Modeling of a turbulent ethylene/air flame using hybrid finite volume/Monte Carlo methods. Comput. Therm. Sci. 1, 37–53 (2009)

    Article  Google Scholar 

  87. R.S. Mehta, D.C. Haworth, M.F. Modest, Composition PDF/photon Monte Carlo modeling of moderately sooting turbulent jet flames. Combust. Flame 157, 982–994 (2010)

    Article  Google Scholar 

  88. R.S. Mehta, M.F. Modest, D.C. Haworth, Radiation characteristics and turbulence–radiation interactions in sooting turbulent jet flames. Combust. Theor. Model. 14(1), 105–124 (2010)

    Article  MATH  Google Scholar 

  89. A. Coppalle, D. Joyeux, Temperature and soot volume fraction in turbulent diffusion flames: measurements of mean and fluctuating values. Combust. Flame 96, 275–285 (1994)

    Article  Google Scholar 

  90. J.H. Kent, D. Honnery, Modeling sooting turbulent jet flames using an extended flamelet technique. Combust. Sci. Technol. 54, 383–397 (1987)

    Article  Google Scholar 

  91. N.E. Endrud. Soot, radiation and pollutant emissions in oxygen-enhanced turbulent jet flames. Master’s thesis, The Pennsylvania State University, University Park, PA, 2000

    Google Scholar 

  92. R.S. Mehta, D.C. Haworth, M.F. Modest, An assessment of gas-phase thermochemistry and soot models for laminar atmospheric-pressure ethylene–air flames. Proc. Combust. Inst. 32, 1327–1334 (2009)

    Article  Google Scholar 

  93. M. Roger, C.B.D. Silva, P.J. Coelho, Analysis of the turbulence–radiation interactions for large eddy simulations of turbulent flows. Int. J. Heat Mass Transf. 52, 2243–2254 (2009)

    Article  MATH  Google Scholar 

  94. C.B. da Silva, I. Malico, P.J. Coelho, Radiation statistics in homogeneous isotropic turbulence. New J. Phys. 11, 093001–1–34 (2009)

    Google Scholar 

  95. M. Roger, P.J. Coelho, C.B. da Silva, The influence of the non-resolved scales of thermal radiation in large eddy simulation of turbulent flows: a fundamental study. Int. J. Heat Mass Transf. 53, 2897–2907 (2010)

    Article  MATH  Google Scholar 

  96. M. Roger, P.J. Coelho, C.B. da Silva, Relevance of the subgrid-scales for large eddy simulations of turbulence-radiation interactions in a turbulent plane jet. J. Quant. Spectrosc. Radiat. Transf. 112, 1250–1256 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2016 The Author(s)

About this chapter

Cite this chapter

Modest, M.F., Haworth, D.C. (2016). Radiation Properties, RTE Solvers, and TRI Models. In: Radiative Heat Transfer in Turbulent Combustion Systems. SpringerBriefs in Applied Sciences and Technology(). Springer, Cham. https://doi.org/10.1007/978-3-319-27291-7_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-27291-7_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27289-4

  • Online ISBN: 978-3-319-27291-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics