Journal of Thermal Science

, Volume 29, Issue 1, pp 58–68 | Cite as

Influence of Turbulence Schmidt Number on Exit Temperature Distribution of an Annular Gas Turbine Combustor using Flamelet Generated Manifold

  • Weihao WangEmail author
  • Songlin Yang
  • Chuang GaoEmail author
  • Weiguang Huang


The Reynolds analogy concept has been used in almost all turbulent reacting flow RANS (Reynolds-averaged Navier-Stokes) simulations, where the turbulence scalar transfers in flow fields are calculated based on the modeled turbulence momentum transfer. This concept, applied to a lean premixed combustion system, was assessed in this paper in terms of exit temperature distribution. Because of the isotropic assumption involved in this analogy, the prediction in some flow condition, such as jet cross flow mixing, would be inaccurate. In this study, using Flamelet Generated Manifold as reaction model, some of the numerical results, obtained from an annular combustor configuration with the turbulent Schmidt number varying from 0.85 to 0.2, were presented and compared with a benchmark atmospheric test results. It was found that the Schmidt number σt in mean mass fraction f transport equation had significant effect on dilution air mixing process. The mixing between dilution air and reaction products from the primary zone obviously improved as σt decreased on the combustor exit surface. Meanwhile, the sensitivity of σt in three turbulence models including Realizable k-ε, SST (Shear Stress Transport) and RSM (Reynolds Stress Model) has been compared as well. Since the calculation method of eddy viscosity was different within these three models, RSM was proved to be less sensitive than another two models and can guarantee the best prediction of mixing process condition. On the other hand, the results of dilution air mixing were almost independent of Schmidt number Sct in progress variable c transport equation. This study suggested that for accurate prediction of combustor exit temperature distribution in steady state reacting flow simulation, the turbulent Schmidt number in steady state simulation should be modified to cater to dilution air mixing process.


gas turbine combustor flamelet-generated manifold turbulent Schmidt Number Reynolds Stress Model Reynolds analogy 


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This work is funded by the Key Programs of Chinese Academy of Sciences (Project No. ZDRW-CN-2017-2).


  1. [1]
    Widener S., Improving the development process for main combustor exit temperature distribution. International Journal of Turbo & Jet Engines, 1990, 7(3–4): 339–347.ADSGoogle Scholar
  2. [2]
    Dejoan A., Leschziner M.A., Large eddy simulation of a plane turbulent wall jet. Physics of Fluids, 2005, 17(2): 025102. DOI: Scholar
  3. [3]
    Bogey C., Bailly C., Juvé D., Noise investigation of a high subsonic, moderate Reynolds number jet using a compressible large eddy simulation. Theoretical & Computational Fluid Dynamics, 2003, 16(4): 273–297.ADSCrossRefGoogle Scholar
  4. [4]
    Dianat M., Yang Z., Jiang D., Mcguirk J.J., Large eddy simulation of scalar mixing in a coaxial confined jet. Flow Turbulence & Combustion, 2006, 77(1–4): 205–227.CrossRefGoogle Scholar
  5. [5]
    Koupper C., Gicquel L., Duchaine F., Bonneau G., Advanced combustor exit plane temperature diagnostics based on large eddy simulations. Flow Turbulence & Combustion, 2015, 95(1): 1–18.CrossRefGoogle Scholar
  6. [6]
    Bacci A., Facchini B., Turbulence modeling for the numerical simulation of film and effusion cooling flows. ASME Turbo Expo 2007: Power for Land, Sea, and Air, May 14–17, 2007, Montreal, Canada, Paper No.: GT2007-27182, pp. 247–257.Google Scholar
  7. [7]
    Jiang L.Y., Campbell I., Prandtl/Schmidt number effect on temperature distribution in a generic combustor. International Journal of Thermal Sciences, 2009, 48(2): 322–330.CrossRefGoogle Scholar
  8. [8]
    Kays W.M., Turbulent Prandtl number—where are we? Journal of Heat Transfer, 1994, 116(2): 284–295.ADSCrossRefGoogle Scholar
  9. [9]
    Reynolds A.J., The variation of turbulent Prandtl and Schmidt numbers in wakes and jets. International Journal of Heat Mass Transfer, 1976, 19(7): 757–764.ADSCrossRefGoogle Scholar
  10. [10]
    Ivanova E.M., Noll B.E., Aigner M., A numerical study on the turbulent Schmidt numbers in a jet in cross-flow. In Proceedings of ASME Turbo Expo 2012: Turbine Technical Conference and Exposition. June 11–15, 2012. Copenhagen, Denmark, Paper No: GT2012-69294, pp. 949–960. DOI:
  11. [11]
    Galeazzo F.C.C., Donnert G., Habisreuther P., et al., Measurement and simulation of turbulent mixing in a jet in crossflow. Journal of Engineering for Gas Turbines and Power, 2011, 133(6): 061504. DOI: Scholar
  12. [12]
    Galeazzo F.C.C., Donnert G., Cárdenas C., et al., Computational modeling of turbulent mixing in a jet in crossflow. International Journal of Heat and Fluid Flow, 2013, 41: 55–65.CrossRefGoogle Scholar
  13. [13]
    Ingenito A., Bruno C., LES of a supersonic combustor with variable turbulent Prandtl and Schmidt numbers. 46th AIAA Aerospace Sciences Meeting and Exhibit, Jan 7–10, Reno, Nevada. DOI:
  14. [14]
    Wang W.H., Huang W.G., Cao Y., et al., Atmospheric test and numerical models assessment of annular combustor on ZK2000 gas turbine. Journal of Thermal Science, 2018, 27(06): 516–526.ADSCrossRefGoogle Scholar
  15. [15]
    Pope S.B., Turbulent flows. Cambridge University Press, UK, 2000. DOI: Scholar
  16. [16]
    Pope S.B., An explanation of the turbulent round-jet/plane-jet anomaly. AIAA Journal, 1978, 16(3): 279–281.ADSCrossRefGoogle Scholar
  17. [17]
    Bardino J., Improved turbulence models based on large eddy simulation of homogeneous, incompressible, turbulent flows. Stanford University, 1983.Google Scholar
  18. [18]
    Alvarez J., Jones W.P., Seoud R., Predictions of momentum and scalar fields in a jet in cross-flow using first and second order turbulence closures. AGARD Conference Proceedings, April 19–22, 1993, Winchester, UK, Paper No. 24.Google Scholar
  19. [19]
    He G., Guo Y., Hsu A.T., The effect of Schmidt number on turbulent scalar mixing in a jet-in-crossflow. International Journal of Heat and Mass Transfer, 1999, 42(20): 3727–3738.CrossRefGoogle Scholar
  20. [20]
    Innocenti A., Andreini A., Giusti A., et al., Numerical investigations of NOx emissions of a partially premixed burner for natural gas operations in industrial gas turbine. Asme Turbo Expo. June 16–20, 2014, Düsseldorf, Germany, Paper No: GT2014-26906. DOI:
  21. [21]
    Chen R.H., Kothawala A., Chaos M., et al., Schmidt number effects on laminar jet diffusion flame lift off. Combustion and Flame, 2005, 141(4): 469–472.CrossRefGoogle Scholar
  22. [22]
    Keistler P., Simulation of supersonic combustion using variable turbulent Prandtl/Schmidt numbers formulation. Aiaa Fluid Dynamics Conference and Exhibit, 2006, June 5–8, Paper No. AIAA2006-3733. DOI:
  23. [23]
    Jiang L.Y., Campbell I., Prandtl/Schmidt number effect on temperature distribution in a generic combustor. International Journal of Thermal Sciences, 2009, 48(2): 322–330.CrossRefGoogle Scholar
  24. [24]
    Chornyi A.D., Zhdanov V.L., Verification of chemical reaction rate models in turbulent reacting flows at Schmidt number considerably exceeding 1. Journal of Engineering Physics and Thermophysics, 2010, 83(3): 513–524.ADSCrossRefGoogle Scholar
  25. [25]
    Tian R., Dai X.Y., Wang D.B., Shi L., Study of variable Turbulent Prandtl number model for heat transfer to supercritical fluids in vertical tubes. Journal of Thermal Science, 2018, 27(3): 213–222.ADSCrossRefGoogle Scholar
  26. [26]
    Oijen J.A.V., Goey L.P.H.D., Modelling of premixed laminar flames using Flamelet-Generated Manifolds. Combustion Science and Technology. 2000, 161(1): 113–137.CrossRefGoogle Scholar
  27. [27]
    Mu Y., Wang C.D., Liu C.X., et al., Numerical study of effect of compressor swirling flow on combustor design in a MTE. Journal of Thermal Science, 2017, 26(4): 349–354.ADSCrossRefGoogle Scholar
  28. [28]
    Mattingly J.D., Elements of propulsion: gas turbines and rockets. American Institute of Aeronautics and Astronautics, Reston, VA, US, 2006, ISBN No. 1563477793.CrossRefGoogle Scholar
  29. [29]
    Menter F.R., Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal, 1994, 32(8): 1598–1605.ADSCrossRefGoogle Scholar
  30. [30]
    Sarkar S., Lakshmanan B., Application of a Reynolds stress turbulence model to the compressible shear layer. AIAA Journal, 1991, 29(5): 743–749.ADSCrossRefGoogle Scholar

Copyright information

© Science Press, Institute of Engineering Thermophysics, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Shanghai Advanced Research InstituteChinese Academy of SciencesShanghaiChina
  2. 2.University of Chinese Academy of SciencesBeijingChina
  3. 3.School of Physical Science and TechnologyShanghaiTech UniversityShanghaiChina
  4. 4.Helan Turbines Co., LtdShanghaiChina

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