Investigation of Reactive Scalar Mixing in Transported PDF Simulations of Turbulent Premixed Methane-Air Bunsen Flames

  • Hua Zhou
  • Zhuyin RenEmail author
  • Michael Kuron
  • Tianfeng Lu
  • Jacqueline H. Chen


Transported probability density function (TPDF) simulations have been performed in conjunction with DNS data to investigate the mixing characteristics of reactive scalars in two turbulent lean premixed methane-air Bunsen flames with Case A being close to the corrugated flamelet regime and Case C being close to the broken reaction zones regime. The study shows that with an accurate mixing timescale of progress variable being provided, TPDF simulations using the EMST mixing model predict scalar mixing and flame characteristics reasonably well. Modeling reactive scalar mixing rate remains one key challenge. For turbulent flames close to the flamelet regime, i.e. Case A, the turbulent flame structure represented by the scatter of OH, as well as the resemblance of the flame induced dissipation rate to the actual dissipation rate, highlights the necessity to account for flame structure when modeling reactive scalar mixing in flamelet region. A posteriori tests show that the hybrid mixing timescale model, which accounts for both turbulence and flame structure effects on the scalar mixing timescale, yields better performance than the constant mechanical-to-scalar timescale model for turbulent premixed flames close to the flamelet regime. Moreover, the hybrid model shows potential for modeling differential mixing rates of intermediate species featuring their own characteristic timescales. The effects of progress variable definition and turbulence modeling on the computed flame characteristics are investigated, and the significance of turbulence modeling in RANS-TPDF simulation is illustrated.


Turbulent premixed flames Reactive scalar mixing Transported PDF methods Mixing models 



The work at Tsinghua is supported by National Natural Science Foundation of China 91841302 and 51476087. Simulations are performed with the computational resources of the Tsinghua National Laboratory for Information Science and Technology. The work at Sandia is supported by the Division of Chemical Sciences, Geosciences and Biosciences, the Office of Basic Energy Sciences, the US Department of Energy (DOE). Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525.

Compliance with Ethical Standards

Conflict of Interests

The authors declare that they have no conflict of interest.


  1. 1.
    Bradley, T., Fadok, J.: Advanced hydrogen turbine development update. ASME Turbo Expo 2009: Power for Land, Sea, and Air. Orlando, Florida, USA (2009)Google Scholar
  2. 2.
    York, W.D., Ziminsky, W.S., Yilmaz, E.: Development and testing of a low NOx hydrogen combustion system for heavy-duty gas turbines. J. Eng. Gas Turbines Power. 135(1–8), 022001 (2013)CrossRefGoogle Scholar
  3. 3.
    Yuri, M., Masada, J., Tsukagoshi, K., Ito, E., Hada, S.: Development of 1600 C-class high-efficiency gas turbine for power generation applying J-type technology. Mitsubishi heavy Ind. Technol. Rev. 50, 1–10 (2013)Google Scholar
  4. 4.
    Pope, S.B.: PDF methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11, 119–192 (1985)CrossRefGoogle Scholar
  5. 5.
    Haworth, D.: Progress in probability density function methods for turbulent reacting flows. Prog. Energy Combust. Sci. 36, 168–259 (2010)CrossRefGoogle Scholar
  6. 6.
    Pope, S.B.: Small scales, many species and the manifold challenges of turbulent combustion. Proc. Combust. Inst. 34, 1–31 (2013)CrossRefGoogle Scholar
  7. 7.
    Celis, C., da Silva, L.F.F.: Lagrangian mixing models for turbulent combustion: review and prospects. Flow. Turbul. Combust. 94, 643–689 (2015)CrossRefGoogle Scholar
  8. 8.
    Tang, Q., Xu, J., Pope, S.B.: Probability density function calculations of local extinction and NO production in piloted-jet turbulent methane/air flames. Proc. Combust. Inst. 28, 133–139 (2000)CrossRefGoogle Scholar
  9. 9.
    Xu, J., Pope, S.B.: PDF calculations of turbulent nonpremixed flames with local extinction. Combust. Flame. 123, 281–307 (2000)CrossRefGoogle Scholar
  10. 10.
    Muradoglu, M., Liu, K., Pope, S.B.: PDF modeling of a bluff-body stabilized turbulent flame. Combust. Flame. 132, 115–137 (2003)Google Scholar
  11. 11.
    Ren, Z., Pope, S.B.: An investigation of the performance of turbulent mixing models. Combust. Flame. 136, 208–216 (2004)CrossRefGoogle Scholar
  12. 12.
    Gordon, R.L., Masri, A.R., Pope, S.B., Goldin, G.M.: A numerical study of auto-ignition in turbulent lifted flames issuing into a vitiated co-flow. Combust. Theor. Model. 11, 351–376 (2007)CrossRefzbMATHGoogle Scholar
  13. 13.
    Wang, H., Pope, S.B.: Large eddy simulation/probability density function modeling of a turbulent CH4/H2/N2 jet flame. Proc. Combust. Inst. 33, 1319–1330 (2011)CrossRefGoogle Scholar
  14. 14.
    Yang, Y., Wang, H., Pope, S.B., Chen, J.H.: Large-eddy simulation/probability density function modeling of a non-premixed CO/H2 temporally evolving jet flame. Proc. Combust. Inst. 34, 1241–1249 (2013)CrossRefGoogle Scholar
  15. 15.
    Lindstedt, R., Vaos, E.: Transported PDF modeling of high-Reynolds-number premixed turbulent flames. Combust. Flame. 145, 495–511 (2006)CrossRefGoogle Scholar
  16. 16.
    Stöllinger, M., Heinz, S.: Evaluation of scalar mixing and time scale models in PDF simulations of a turbulent premixed flame. Combust. Flame. 157, 1671–1685 (2010)CrossRefGoogle Scholar
  17. 17.
    Rowinski, D.H., Pope, S.B.: Computational study of lean premixed turbulent flames using RANS-PDF and LES-PDF methods. Combust. Theor. Model. 17, 610–656 (2013)CrossRefGoogle Scholar
  18. 18.
    Tirunagari, R.R., Pope, S.B.: An investigation of turbulent premixed counterflow flames using large-eddy simulations and probability density function methods. Combust. Flame. 166, 229–242 (2016)CrossRefGoogle Scholar
  19. 19.
    Bray, K.N.C.: Turbulent flows with premixed reactants. Top. Appl. Phys. 44, 115–183 (1980)CrossRefGoogle Scholar
  20. 20.
    Anand, M., Pope, S.B.: Calculations of premixed turbulent flames by PDF methods. Combust. Flame. 67, 127–142 (1987)Google Scholar
  21. 21.
    Bray, K., Champion, M., Libby, P.A., Swaminathan, N.: Scalar dissipation and mean reaction rates in premixed turbulent combustion. Combust. Flame. 158, 2017–2022 (2011)CrossRefGoogle Scholar
  22. 22.
    Villermaux, J., Devillon, J.C.: Représentation de la coalescence et de la redispersion des domaines de ségrégation dans un fluide par un modele d'interaction phénoménologique. Proceedings of the 2nd International Symposium on Chemical Reaction Engineering. New York (1972)Google Scholar
  23. 23.
    Dopazo, C., O'Brien, E.E.: An approach to the autoignition of a turbulent mixture. Acta Astronautica. 1, 1239–1266 (1974)CrossRefzbMATHGoogle Scholar
  24. 24.
    Curl, R.L.: Dispersed phase mixing: I. theory and effects in simple reactors. AICHE J. 9, 175–181 (1963)CrossRefGoogle Scholar
  25. 25.
    Janicka, J., Kolbe, W., Kollmann, W.: Closure of the transport equation for the probability density Funcfion of turbulent scalar fields. J. Non-equil. Thermody. 4, 47–66 (1979)CrossRefzbMATHGoogle Scholar
  26. 26.
    Subramaniam, S., Pope, S.B.: A mixing model for turbulent reactive flows based on Euclidean minimum spanning trees. Combust. Flame. 115, 487–514 (1998)CrossRefGoogle Scholar
  27. 27.
    Ren, Z., Subramaniam, S., Pope, S.B.: Implementation of the EMST Mixing Model. Available from:
  28. 28.
    Valiño, L., Dopazo, C.: A binomial Langevin model for turbulent mixing. Phys. Fluids. 3, 3034–3037 (1991)CrossRefzbMATHGoogle Scholar
  29. 29.
    Pope, S.B.: A model for turbulent mixing based on shadow-position conditioning. Phys. Fluids. 25, 110803 (2013)CrossRefGoogle Scholar
  30. 30.
    Fox, R.O.: The Fokker–Planck closure for turbulent molecular mixing: passive scalars. Phys. Fluids A. 4, 1230–1244 (1992)CrossRefzbMATHGoogle Scholar
  31. 31.
    Meyer, D.W., Jenny, P.: A mixing model for turbulent flows based on parameterized scalar profiles. Phys. Fluids. 18, 035105 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Rowinski, D.H., Pope, S.B.: PDF calculations of piloted premixed jet flames. Combust. Theor. Model. 15, 245–266 (2011)CrossRefzbMATHGoogle Scholar
  33. 33.
    Zhou, H., Li, S., Ren, Z., Rowinski, D.H.: Investigation of mixing model performance in transported PDF calculations of turbulent lean premixed jet flames through Lagrangian statistics and sensitivity analysis. Combust. Flame. 181, 136–148 (2017)CrossRefGoogle Scholar
  34. 34.
    Kuron, M., Hawkes, E.R., Ren, Z., Tang, J.C.K., Zhou, H., Chen, J.H., Lu, T.: Performance of transported PDF mixing models in a turbulent premixed flame. Proc. Combust. Inst. 36, 1987–1995 (2017)CrossRefGoogle Scholar
  35. 35.
    Hawkes, E.R., Chatakonda, O., Kolla, H., Kerstein, A.R., Chen, J.H.: A petascale direct numerical simulation study of the modelling of flame wrinkling for large-eddy simulations in intense turbulence. Combust. Flame. 159, 2690–2703 (2012)CrossRefGoogle Scholar
  36. 36.
    Swaminathan, N., Bray, K.: Effect of dilatation on scalar dissipation in turbulent premixed flames. Combust. Flame. 143, 549–565 (2005)CrossRefGoogle Scholar
  37. 37.
    Kolla, H., Rogerson, J., Chakraborty, N., Swaminathan, N.: Scalar dissipation rate modeling and its validation. Combust. Sci. Technol. 181, 518–535 (2009)CrossRefGoogle Scholar
  38. 38.
    Mantel, T., Borghi, R.: A new model of premixed wrinkled flame propagation based on a scalar dissipation equation. Combust. Flame. 96, 443–457 (1994)CrossRefGoogle Scholar
  39. 39.
    Kuan, T., Lindstedt, R., Vaos, E.: Higher moment based modeling of turbulence enhanced explosion kernels in confined fuel-air mixtures. Moscow (2003)Google Scholar
  40. 40.
    Lindstedt, R.P., Milosavljevic, V.D., Persson, M.: Turbulent burning velocity predictions using transported PDF methods. Proc. Combust. Inst. 33, 1277–1284 (2011)CrossRefGoogle Scholar
  41. 41.
    Kuron, M., Ren, Z., Hawkes, E.R., Zhou, H., Kolla, H., Chen, J.H., Lu, T.: A mixing timescale model for TPDF simulations of turbulent premixed flames. Combust. Flame. 177, 171–183 (2017)CrossRefGoogle Scholar
  42. 42.
    Mura, A., Robin, V., Champion, M.: Modeling of scalar dissipation in partially premixed turbulent flames. Combust. Flame. 149, 217–224 (2007)CrossRefGoogle Scholar
  43. 43.
    Sankaran, R., Hawkes, E.R., Chen, J.H., Lu, T., Law, C.K.: Structure of a spatially developing turbulent lean methane–air Bunsen flame. Proc. Combust. Inst. 31, 1291–1298 (2007)CrossRefGoogle Scholar
  44. 44.
    Chen, J.H., Choudhary, A., Supinski, B.D., DeVries, M., Hawkes, E.R., Klasky, S., Liao, W.K., Ma, K.L., Mellor-Crummey, J., Podhorszki, N., Sankaran, R., Shende, S., Yoo, C.S.: Terascale direct numerical simulations of turbulent combustion using S3D. Comput. Sci. Discov. 2, 1–31 (2009)CrossRefGoogle Scholar
  45. 45.
    Sankaran, R., Hawkes, E.R., Yoo, C.S., Chen, J.H.: Response of flame thickness and propagation speed under intense turbulence in spatially developing lean premixed methane–air jet flames. Combust. Flame. 162, 3294–3306 (2015)CrossRefGoogle Scholar
  46. 46.
    Merci, B., Roekaerts, D., Naud, B., Pope, S.B.: Comparative study of micromixing models in transported scalar PDF simulations of turbulent nonpremixed bluff body flames. Combust. Flame. 146, 109–130 (2006)CrossRefGoogle Scholar
  47. 47.
    Dunn, M.J., Masri, A.R., Bilger, R.W., Barlow, R.S.: Finite rate chemistry effects in highly sheared turbulent premixed flames. Flow. Turbul. Combust. 85, 621–648 (2010)CrossRefzbMATHGoogle Scholar
  48. 48.
    Pope, S.B.: Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation. Combust. Theor. Model. 1, 41–63 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  49. 49.
    Lu, L., Pope, S.B.: An improved algorithm for in situ adaptive tabulation. J. Comput. Phys. 228, 361–386 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  50. 50.
    Richardson, E.S., Sankaran, R., Grout, R.W., Chen, J.H.: Numerical analysis of reaction–diffusion effects on species mixing rates in turbulent premixed methane–air combustion. Combust. Flame. 157, 506–515 (2010)CrossRefGoogle Scholar
  51. 51.
    Richardson, E.S., Chen, J.H.: Application of PDF mixing models to premixed flames with differential diffusion. Combust. Flame. 159, 2398–2414 (2012)CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Hua Zhou
    • 1
  • Zhuyin Ren
    • 1
    • 2
    Email author
  • Michael Kuron
    • 3
    • 4
  • Tianfeng Lu
    • 4
  • Jacqueline H. Chen
    • 5
  1. 1.Center for Combustion EnergyTsinghua UniversityBeijingChina
  2. 2.School of Aerospace EngineeringTsinghua UniversityBeijingChina
  3. 3.ANSYS, Inc.CanonsburgUSA
  4. 4.Department of Mechanical EngineeringUniversity of ConnecticutStorrsUSA
  5. 5.Combustion Research Facility, Sandia National LaboratoriesLivermoreUSA

Personalised recommendations