Applied Physics B

, 125:13 | Cite as

Experimental assessment of the Tenti S6 model for combustion-relevant gases and filtered Rayleigh scattering applications

  • Thomas A. Mcmanus
  • Ignacio Trueba Monje
  • Jeffrey A. Sutton


Accurate descriptions of Rayleigh–Brillouin scattering (RBS) spectra for gas-phase species are important in light scattering measurement techniques including filtered Rayleigh scattering (FRS). The current manuscript targets evaluation of the well-known Tenti S6 model for calculating the RBS spectra for combustion-relevant species over a broad range of temperatures with relevance towards FRS applications in reacting flows. In this work, testing of the Tenti S6 model was performed by comparing measured FRS signals to synthetic FRS signals generated through the combination of the Tenti S6 model and an experimentally verified I2 absorption model. First, temperature-dependent FRS signals were measured for a number of individual gases including Ar, N2, O2, CH4, H2, CO, and CO2 from 300 to 1400 K. Comparisons between the measurements and synthetic FRS signals show excellent agreement (< 4% average difference) over the full temperature range. For pure CO2, rotational Raman scattering effects must be taken into account when comparing measured and synthetic FRS signals. FRS measurements in binary mixtures were performed to assess the commonly used (but not verified) assumption that the total FRS signal from a mixture can be treated as the mole fraction-weighted average of the FRS signals from each component. Measured FRS signals in mixtures with large variations in both molecular weight and Rayleigh scattering cross section show a linear relationship with constituent mole fraction, indicating that this assumption is valid within the kinetic regime. Finally, FRS measurements were performed in near-adiabatic H2/air and CH4/air flames. Comparisons between measured and synthetic FRS signals show excellent agreement over a broad range of equivalence ratios (\(\phi\)), which includes a temperature range of 1100 < T(K) < 2400 and large relative changes in species mole fractions. Overall, the results indicate that the predicted RBS lineshapes calculated using the Tenti S6 model are sufficiently accurate in the context of FRS measurements for the species and temperatures evaluated.



This work was partially funded by the National Science Foundation (CBET-1055960) and Air Force Office of Scientific Research (FA9550-16-1-0366).


  1. 1.
    J.W. Strutt, On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue of the sky. The London, Edinburgh, and Dublin Philosophical Magazine and. J. Sci. 47, 375–384 (1899)Google Scholar
  2. 2.
    R.W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, Cambridge, 2008)Google Scholar
  3. 3.
    A.T. Young, Rayleigh scattering. Appl. Opt. 20, 533–535 (1981)ADSCrossRefGoogle Scholar
  4. 4.
    C.D. Boley, R.C. Desai, G. Tenti, Kinetic models and Brillouin scattering in a molecular gas. Can. J. Phys. 50, 2158–2173 (1972)ADSCrossRefGoogle Scholar
  5. 5.
    G. Tenti, C.D. Boley, R.C. Desai, On the kinetic model description of Rayleigh–Brillouin scattering from molecular gases. Can. J. Phys. 52, 285–290 (1974)ADSCrossRefGoogle Scholar
  6. 6.
    C.S. Wang Chang, G.E. Uhlenbeck, J. de Boer, The heat conductivity and viscosity of poly-atomic gases. in Studies in Statistical Mechanics, ed. by J. deBoer, G.E. Uhlenbeck (Wiley, New York, 1964)zbMATHGoogle Scholar
  7. 7.
    A. Stoffelen, G.J. Marseille, F. Bouttier, D. Vasiljevic, S. De Haan, C. Cardinali, ADM-aeolus doppler wind lidar observing system simulation experiment. Q. J. R. Meteorol. Soc. 132, 1927–1947 (2006)ADSCrossRefGoogle Scholar
  8. 8.
    B. Witschas, C. Lemmerz, O. Reitebuch, Daytime measurements of atmospheric temperature profiles (2–15 km) by lidar utilizing Rayleigh–Brillouin scatterin. Opt. Lett. 39, 1972–1975 (2014)ADSCrossRefGoogle Scholar
  9. 9.
    M.O. Vieitez, E.J. van Duijn, W. Ubachs, B. Witschas, A. Meijer, A.S. de Wijn, N.J. Dam, W. van de Water, Coherent and spontaneous Rayleigh–Brillouin scattering in atomic and molecular gases and gas mixtures. Phys. Rev. A 82, 043836 (2010)ADSCrossRefGoogle Scholar
  10. 10.
    Y. Ma, H. Li, Z. Gu, W. Ubachs, Y. Yu, J. Huang, B. Zhou, Y. Wang, K. Liang, Analysis of Rayleigh–Brillouin spectral profiles and Brillouin shifts in nitrogen gas and ai. Opt. Express 22, 2092–2104 (2014)ADSCrossRefGoogle Scholar
  11. 11.
    B. Witschas, M.O. Vieitez, E.-J. van Duijn, O. Reitebuch, W. van de Water, W. Ubachs, Spontaneous Rayleigh–Brillouin scattering of ultraviolet light in nitrogen, dry air, and moist ai. Appl. Opt. 49, 4217–4227 (2010)ADSCrossRefGoogle Scholar
  12. 12.
    Z.Y. Gu, W. Ubachs, W. van de Water, Rayleigh–Brillouin scattering of carbon dioxide. Opt. Lett. 39, 3301–3304 (2014)ADSCrossRefGoogle Scholar
  13. 13.
    Z. Gu, W. Ubachs, A systematic study of Rayleigh–Brillouin scattering in air, N2, and O2 gases. J. Chem. Phys. 141, 104320 (2014)ADSCrossRefGoogle Scholar
  14. 14.
    Z. Gu, B. Witschas, W. van de Water, W. Ubachs, Rayleigh–Brillouin scattering profiles of air at different temperatures and pressure. Appl. Opt. 52, 4640–4651 (2013)ADSCrossRefGoogle Scholar
  15. 15.
    J.N. Forkey, W.R. Lempert, R.B. Miles, Accuracy limits for planar measurements of flow field velocity, temperature and pressure using Filtered Rayleigh Scatterin. Exp. Fluids 24, 151–162 (1998)CrossRefGoogle Scholar
  16. 16.
    R.B. Miles, W.R. Lempert, J.N. Forkey, Laser Rayleigh scattering. Meas. Sci. Technol. 12, R33 (2001)ADSCrossRefGoogle Scholar
  17. 17.
    M. Boguszko, G.S. Elliott, On the use of filtered Rayleigh scattering for measurements in compressible flows and thermal field. Exp. Fluids 38, 33–49 (2005)CrossRefGoogle Scholar
  18. 18.
    U. Doll, G. Stockhausen, C. Willert, Pressure, temperature, and three-component velocity fields by filtered Rayleigh scattering velocimetr. Opt. Lett. 42, 3773–3776 (2017)ADSCrossRefGoogle Scholar
  19. 19.
    U. Doll, G. Stockhausen, C. Willert, Endoscopic filtered Rayleigh scattering for the analysis of ducted gas flows. Exp. Fluids 55, 1690 (2014)CrossRefGoogle Scholar
  20. 20.
    F. Benhassen, M.D. Polanka, M.F. Reeder, Trajectory measurements of a horizontally oriented buoyant jet in a coflow using filtered rayleigh scattering. J. Aerosp. Eng. 30, 04016067 (2017)CrossRefGoogle Scholar
  21. 21.
    J. Brübach, J. Zetterberg, A. Omrane, Z.S. Li, M. Aldén, A. Dreizler, Determination of surface normal temperature gradients using thermographic phosphors and filtered Rayleigh scatterin. Appl. Phys. B 84, 537–541 (2006)ADSCrossRefGoogle Scholar
  22. 22.
    P.M. Allison, T.A. McManus, J.A. Sutton, Quantitative fuel vapor/air mixing imaging in droplet/gas regions of an evaporating spray flow using filtered Rayleigh scattering. Opt. Lett. 41, 1074–1077 (2016)ADSCrossRefGoogle Scholar
  23. 23.
    D. Hoffman, K.U. Münch, A. Leipertz, Two-dimensional temperature determination in sooting flames by filtered Rayleigh scattering. Opt. Lett. 21, 525–527 (1996)ADSCrossRefGoogle Scholar
  24. 24.
    G. Elliott, N. Glumac, C. Carter, Molecular filtered Rayleigh scattering applied to combustion. Meas. Sci. Technol. 12, 452 (2001)ADSCrossRefGoogle Scholar
  25. 25.
    D. Most, A. Leipertz, Simultaneous two-dimensional flow velocity and gas temperature measurements by use of a combined particle image velocimetry and filtered Rayleigh scattering technique. Appl. Opt. 40, 5379–5387 (2001)ADSCrossRefGoogle Scholar
  26. 26.
    D. Most, F. Dinkelacker, A. Leipertz, Direct determination of the turbulent flux by simultaneous application of filtered rayleigh scattering thermometry and particle image velocimetry. Proc. Comb. Inst. 29, 2669–2677 (2002)CrossRefGoogle Scholar
  27. 27.
    A.P. Yalin, Y.Z. Ionikh, R.B. Miles, Gas temperature measurements in weakly ionized glow discharges with filtered Rayleigh scattering. Appl. Opt. 41, 3753–3762 (2002)ADSCrossRefGoogle Scholar
  28. 28.
    S.P. Kearney, R.W. Schefer, S.J. Beresh, T.W. Grasser, Temperature imaging in nonpremixed flames by joint filtered Rayleigh and Raman scattering. Appl. Opt. 44, 1548–1558 (2005)ADSCrossRefGoogle Scholar
  29. 29.
    J.R. Bonatto, W. Marques Jr., Kinetic model analysis of light scattering in binary mixtures of monatomic ideal gases. J. Stat. Mech. 2005, P09014–P09014 (2005)CrossRefGoogle Scholar
  30. 30.
    A.S. Fernandes, W. Marques, Sound propagation in binary gas mixtures from a kinetic model of the Boltzmann equation. Phys. A 332, 29–46 (2004)CrossRefGoogle Scholar
  31. 31.
    W. Marques, Coherent Rayleigh–Brillouin scattering in binary gas mixtures. J. Stat. Mech. 2007, 03013–03013 (2007)CrossRefGoogle Scholar
  32. 32.
    L. Letamendia, Light-scattering studies of moderately dense gas mixtures: Hydrodynamic regime. Phys. Rev. A Gen. Phys. 24, 1574–1590 (1981)ADSCrossRefGoogle Scholar
  33. 33.
    L. Letamendia, P. Joubert, J.P. Chabrat, J. Rouch, C. Vaucamps, C.D. Boley, S. Yip, S.H. Chen, Light-scattering studies of moderately dense gases. II. Nonhydrodynamic regime. Phys. Rev. A 25, 481–488 (1982)ADSCrossRefGoogle Scholar
  34. 34.
    J.N. Forkey, W.R. Lempert, R.B. Miles, Corrected and calibrated I 2 absorption model at frequency-doubled Nd:YAG laser wavelengths. Appl. Opt. 36, 6729–6738 (1997)ADSCrossRefGoogle Scholar
  35. 35.
    T.L. Labus, E.P. Symons, Experimental investigation of an axisymmetric free jet with an initially uniform velocity profile, NASA Technical Report NASA-TN-D-6783, E-6801 (1972)Google Scholar
  36. 36.
    J. Gauntner, P. Hrycak, D. Lee, J. Livingood, Experimental flow characteristics of a single turbulent jet impinging on a flat plate, NASA Technical Report NASA-TN D-5690 (1970)Google Scholar
  37. 37.
    M.W. Thring, M.P. Newby, Combustion length of enclosed turbulent jet flames. Sym. (Int.) Combust. 4, 789–796 (1953)CrossRefGoogle Scholar
  38. 38.
    K.M. Tacina, W.J. Dahm, Effects of heat release on turbulent shear flows. Part 1. A general equivalence principle for non-buoyant flows and its application to turbulent jet flames. J. Fluid Mech. 415, 23–44 (2000)ADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    R.D. Hancock, K.E. Bertagnolli, R.P. Lucht, Nitrogen and hydrogen CARS temperature measurements in a hydrogen/air flame using a near-adiabatic flat-flame burner. Combust. Flame 109, 323–331 (1997)CrossRefGoogle Scholar
  40. 40.
    M.J. Papageorge, C. Arndt, F. Fuest, W. Meier, J.A. Sutton, High-speed mixture fraction and temperature imaging of pulsed, turbulent fuel jets auto-igniting in high-temperature, vitiated co-flows. Exp. Fluids 55, 1763 (2014)CrossRefGoogle Scholar
  41. 41.
    J.A. Sutton, J.F. Driscoll, Rayleigh scattering cross sections of combustion species at 266, 355, and 532 nm for thermometry application. Opt. Lett. 29, 2620–2622 (2004)ADSCrossRefGoogle Scholar
  42. 42.
    C. Carter, Laser-based Rayleigh and Mie scattering methods (Wiley, New York, 1996), pp. 1078–1093Google Scholar
  43. 43.
    R.L. McKenzie, Measurement capabilities of planar Doppler velocimetry using pulsed lasers. Appl. Opt. 35, 948–964 (1996)ADSCrossRefGoogle Scholar
  44. 44.
    R. Patton, J. Sutton, Seed laser power effects on the spectral purity of Q-switched Nd:YAG lasers and the implications for filtered rayleigh scattering measurements. Appl. Phys. B Lasers Opt. 111, 457–468 (2013)ADSCrossRefGoogle Scholar
  45. 45.
    J.A. Sutton, R.A. Patton, Improvements in filtered Rayleigh scattering measurements using Fabry–Perot etalons for spectral filtering of pulsed, 532-nm Nd:YAG output. Appl. Phys. B 116, 681–698 (2014)ADSCrossRefGoogle Scholar
  46. 46.
    P. Linstrom, W. Mallard, Nist standard reference database number 69 (2003), 2018Google Scholar
  47. 47.
    B.J. McBride, S. Gordon, M.A. Reno, Coefficients for calculating thermodynamic and transport properties of individual species, NASA Technical Report NASA-TM-4513, E-7981 (1993)Google Scholar
  48. 48.
    X. Pan, M.N. Shneider, R.B. Miles, Coherent Rayleigh–Brillouin scattering in molecular gases. Phys. Rev. A 69, 033814 (2004)ADSCrossRefGoogle Scholar
  49. 49.
    J.D. Lambert, Vibrational and rotational relaxation in gases (Oxford University Press, Oxford, 1977)Google Scholar
  50. 50.
    H.E. Bass, J.R. Olson, R.C. Amme, Vibrational relaxation in H2O vapor in the temperature range 373–946 K. J. Acoust. Soc. Am. 56, 1455–1460 (1974)ADSCrossRefGoogle Scholar
  51. 51.
    R. Kung, R. Center, High temperature vibrational relaxation of H2O by H2O, He, Ar, and N2. J. Chem. Phys. 62, 2187–2194 (1975)ADSCrossRefGoogle Scholar
  52. 52.
    Q. Lao, P. Schoen, B. Chu, Rayleigh–Brillouin scattering of gases with internal relaxation. J. Chem. Phys. 64, 3547–3555 (1976)ADSCrossRefGoogle Scholar
  53. 53.
    A. Meijer, A. de Wijn, M. Peters, N. Dam, W. van de Water, Coherent Rayleigh–Brillouin scattering measurements of bulk viscosity of polar and nonpolar gases, and kinetic theory. J. Chem. Phys. 133, 164315 (2010)ADSCrossRefGoogle Scholar
  54. 54.
    M.S. Cramer, Numerical estimates for the bulk viscosity of ideal gases. Phys. Fluids 24, 066102 (2012)ADSCrossRefGoogle Scholar
  55. 55.
    S.P. Kearney, S.J. Beresh, T.W. Grasser, R.W. Schefer, P.E. Schrader, R.L. Farrow, A filtered rayleigh scattering apparatus for gas-phase and combustion temperature imaging. Paper AIAA 2003 – 584, 41st Aerospace Sciences Meeting, Reno, NV, January 2003Google Scholar
  56. 56.
    G.K. Wertheim, M.A. Butler, K. West, D.N.E. Buchanan, Determination of the Gaussian and Lorentzian content of experimental line shapes. Rev. Sci. Instrum. 45(11), 1369–1371 (1974)ADSCrossRefGoogle Scholar
  57. 57.
    T. Ida, M. Ando, H. Toraya, Extended pseudo-Voigt function for approximating the Voigt profile. J. Appl. Crystallogr. 33(6), 1311–1316 (2000)CrossRefGoogle Scholar
  58. 58.
    C.M. Penney, R.L. St. Peters, M. Lapp, Absolute rotational Raman cross sections for N2, O2, and CO2. J. Opt. Soc. Am. 64(5), 712–716 (1974)ADSCrossRefGoogle Scholar
  59. 59.
    A. Weber, in The Raman Effect, vol 2: Applications, ed. by A. Anderson (Dekker, New York, 1973) (Ch. 9) Google Scholar
  60. 60.
    G. Herzberg, Molecular Spectra and Molecular Structure I. Spectra of Diatomic Molecules (Van Nostrand, Princeton, 1950)Google Scholar
  61. 61.
    M.P. Bogaard, A.D. Buckingham, R.K. Pierens, A.H. White, Rayleigh scattering depolarization ratio and molecular polarizability anisotropy for gases. J. Chem. Soc. Faraday Trans. 1 Phys. Chem. Condensed Phases 74, 3008–3015 (1978)Google Scholar
  62. 62.
    K.S. Jammu, G.E. St. John, H.L. Welsh, Pressure broadening of the rotational raman lines of some simple gases. Can. J. Phys. 44(4), 797–814 (1966)ADSCrossRefGoogle Scholar
  63. 63.
    J.W. Gallagher, R.D. Johnson, in NIST Chemistry WebBook, NIST Standard Reference Database Number 69, ed. by P.J. Linstrom, W.G. Mallard. Constants of Diatomics Molecules (National Institute of Standards and Technology, Gaithersburg). Accessed 6 Nov 2018CrossRefGoogle Scholar
  64. 64.
    R. Kee, F. Rupley, J. Miller, M. Coltrin, J. Grcar, E. Meeks, H. Moffat, A. Lutz, G. Dixon-Lewis, M. Smooke, CHEMKIN Collection, Release 3.6 (Reaction Design, Inc, San Diego, 2000)Google Scholar
  65. 65.
    G. Prangsma, A. Alberga, J. Beenakker, Ultrasonic determination of the volume viscosity of N2, CO, CH4 and CD4 between 77 and 300 K. Physica 64, 278–288 (1973)ADSCrossRefGoogle Scholar
  66. 66.
    B. Annis, A. Malinauskas, Temperature dependence of rotational collision numbers from thermal transpiration. J. Chem. Phys. 54, 4763–4768 (1971)ADSCrossRefGoogle Scholar
  67. 67.
    T.G. Winter, G.L. Hill, High-temperature ultrasonic measurements of rotational relaxation in hydrogen, deuterium, nitrogen, and oxygen. J. Acoust. Soc. Am. 42, 848–858 (1967)ADSCrossRefGoogle Scholar
  68. 68.
    R. Healy, T. Storvick, Rotational collision number and Eucken factors from thermal transpiration measurements. J. Chem. Phys. 50, 1419–1427 (1969)ADSCrossRefGoogle Scholar
  69. 69.
    M. Camac, Avco Everett Research Laboratory. Research Report 172 (1963)Google Scholar
  70. 70.
    R.J. Gallagher, J.B. Fenn, Rotational relaxation of molecular hydrogen. J. Chem. Phys. 60, 3492–3499 (1974)ADSCrossRefGoogle Scholar
  71. 71.
    A.D. Gupta, T. Storvick, Analysis of the heat conductivity data for polar and nonpolar gases using thermal transpiration measurements. J. Chem. Phys. 52, 742–749 (1970)ADSCrossRefGoogle Scholar
  72. 72.
    J. Tao, G. Ganzi, S. Sandler, Determination of thermal transport properties from thermal transpiration measurements. II. J. Chem. Phys. 56, 3789–3793 (1972)ADSCrossRefGoogle Scholar
  73. 73.
    J. Tao, W. Revelt, S. Sandler, Determination of thermal transport properties from thermal transpiration measurements. III. Polar gases. J. Chem. Phys. 60, 4475–4482 (1974)ADSCrossRefGoogle Scholar
  74. 74.
    M.J. Assael, W.A. Wakeham, Thermal conductivity of four polyatomic gases. J. Chem. Soc. Faraday Trans. 1 Phys. Chem. Condensed Phases 77, 697–707 (1981)Google Scholar
  75. 75.
    G. Hill, T. Winter, Effect of temperature on the rotational and vibrational relaxation times of some hydrocarbons. J. Chem. Phys. 49, 440–444 (1968)ADSCrossRefGoogle Scholar
  76. 76.
    P. Kistemaker, M. Hanna, A. Tom, A. De Vries, Rotational relaxation in mixtures of methane with helium, argon and xenon. Physica 60, 459–471 (1972)ADSCrossRefGoogle Scholar
  77. 77.
    R. Holmes, G. Jones, N. Pusat, Combined viscothermal and thermal relaxation in polyatomic gases. Trans. Faraday Soc. 60, 1220–1229 (1964)CrossRefGoogle Scholar
  78. 78.
    A. Malinauskas, Thermal transpiration. rotational relaxation numbers for nitrogen and carbon dioxide. J. Chem. Phys. 44, 1196–1202 (1966)ADSCrossRefGoogle Scholar
  79. 79.
    A. Tip, J. Los, A. De Vries, Rotational relaxation numbers from thermal transpiration measurements. Physica 35, 489–498 (1967)ADSCrossRefGoogle Scholar
  80. 80.
    C. O’Neal Jr., R.S. Brokaw, Relation between thermal conductivity and viscosity for nonpolar gases. II. Rotational relaxation of polyatomic molecules. Phys. Fluids 6, 1675–1682 (1963)ADSCrossRefGoogle Scholar
  81. 81.
    E. Mason, Molecular relaxation times from thermal transpiration measurements. J. Chem. Phys. 39, 522–526 (1963)ADSCrossRefGoogle Scholar
  82. 82.
    R.G. Keeton, H. Bass, Vibrational and rotational relaxation of water vapor by water vapor, nitrogen, and argon at 500 K. J. Acoust. Soc. Am. 60, 78–82 (1976)ADSCrossRefGoogle Scholar
  83. 83.
    H. Roesler, K.F. Sahm, Vibrational and rotational relaxation in water vapor. J. Acoust. Soc. Am. 37, 386–387 (1965)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Thomas A. Mcmanus
    • 1
  • Ignacio Trueba Monje
    • 1
  • Jeffrey A. Sutton
    • 1
  1. 1.Mechanical and Aerospace Engineering DepartmentOhio State UniversityColumbusUSA

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