Response of Heat Release Rate to Flame Straining in Swirling Hydrogen-Air Premixed Flames


The main objective of this study is to clarify effects of flame straining on flame structures and heat release rate (HRR) of swirling flames. This is achieved by analyzing results of direct numerical simulations (DNS) of hydrogen—air turbulent swirling premixed flames considering two swirl number and two equivalence ratio cases. Statistical characteristics of HRR are investigated by examining the mean HRR conditioned on a reaction progress variable and the total HRR in the computational domain. Conditional means of the HRR show that the magnitude of the HRR in reaction zones is smaller for higher swirl number cases than that for lower swirl number cases. A direct comparison between strained laminar and swirling flames shows the influence of the strain rate on the flame structure and the progress of elementary reactions. As strain rate increases in a laminar flame, the peak of the HRR by an exothermic reaction H2 + OH → H2O + H shifts toward the burnt side, implying active production of H in the burnt side. The HRR of the above reaction also shows an increasing tendency in a laminar flame under the strain rates greater than 106 s− 1. The strain–flame interaction with this tendency affects the HRR on highly strained flame surfaces of the swirling flames. It is also clarified that the local HRR intensity is dominated not only by strain rate but also by diffusion of H from the burnt to unburnt side.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19


  1. 1.

    Davis, D.W., Therkelsen, P.L., Littlejohn, D., Cheng, R.K.: Proc. Combust. Inst. 34, 3135 (2013)

    Article  Google Scholar 

  2. 2.

    Day, M., Tachibana, S., Bell, J., Lijewski, M., Beckner, V., Cheng, R.K.: Combust. Flame 162(5), 2148 (2015)

    Article  Google Scholar 

  3. 3.

    Rayleigh, J.: The Theory of Sound. Dover (1945)

  4. 4.

    Chu, B.T.: Acta Mech., 215–234 (1965)

  5. 5.

    Nicoud, F., Poinsot, T.: Combust. Flame 142, 153 (2005)

    Article  Google Scholar 

  6. 6.

    Crighton, D., Dowling, A., Williams, J., Heckl, M., Leppington, F.: Modern Methods in Analytical Acoustics: Lecture Notes. Springer (1992)

  7. 7.

    Dawling, A., Mahmoudi, Y.: Proc. Combust. Inst. 35(1), 65 (2015)

    Article  Google Scholar 

  8. 8.

    Aspden, A.J., Day, M.S., Bell, J.B.: Proc. Combust. Inst. 35(2), 1321 (2015)

    Article  Google Scholar 

  9. 9.

    Aspden, A.J.: Proc. Combust. Inst. 36(2), 1997 (2017)

    Article  Google Scholar 

  10. 10.

    Dasgupta, D., Sun, W., Day, M., Lieuwen, T.: Combust. Flame 176, 191 (2017)

    Article  Google Scholar 

  11. 11.

    Trisjono, P., Kleinheinz, K., Hawkes, E.R., Pitsch, H.: Combust. Flame 174, 194 (2016)

    Article  Google Scholar 

  12. 12.

    Sankaran, R., Hawkes, E.R., Chen, J.H., Lu, T., Law, C.K.: Proc. Combust. Inst. 31, 1291 (2007)

    Article  Google Scholar 

  13. 13.

    Wang, H., Hawkes, E.R., Chen, J.H., Zhou, B., Li, Z., Aldén, M.: J. Fluid Mech. 815, 511 (2017)

    Article  Google Scholar 

  14. 14.

    Wang, H., Luo, K., Qiu, K., Lu, S., Fan, J.: Int. J. Hydrogen Energ. 37(6), 5246 (2012)

    Article  Google Scholar 

  15. 15.

    Chen, J.H., Im, H.G.: Proc. Combust. Inst. 28, 211 (2000)

    Article  Google Scholar 

  16. 16.

    Barlow, R.S., Dunn, M.J., Sweeney, M.S., Hochgreb, S.: Combust. Flame 159(8), 2563 (2012)

    Article  Google Scholar 

  17. 17.

    Tanaka, S., Shimura, M., Fukushima, N., Tanahashi, M., Miyauchi, T.: Proc. Combust. Inst. 33, 3293 (2011)

    Article  Google Scholar 

  18. 18.

    Minamoto, Y., Aoki, K., Tanahashi, M., Swaminathan, N.: Int. J. Hydrogen Energ. 40, 13604 (2015)

    Article  Google Scholar 

  19. 19.

    Aoki, K., Shimura, M., Ogawa, S., Fukushima, N., Naka, Y., Nada, Y., Tanahashi, M., Miyauchi, T.: Proc. Combust. Inst. 35, 3209 (2015)

    Article  Google Scholar 

  20. 20.

    Aoki, K., Shimura, M., Naka, Y., Tanahashi, M.: Proc. Combust. Inst. 36(3), 3809 (2017)

    Article  Google Scholar 

  21. 21.

    Miller, J., Bowman, C.: Prog. Energy Combust. Sci. 15, 287 (1989)

    Article  Google Scholar 

  22. 22.

    Smooke, M., Giovangigli, V.: Reduced Kinetic Mechanisms and Asymptotic Approximations for Methane–Air Flames, pp. 1–28. Springer (1991)

  23. 23.

    Kee, R., Rupley, F., Miller, J.: Chemkin-II: A Fortran Chemical Kinetics Package for the Analysis of Gas-Phase Chemical Kinetics, Sandia Report, Sandia Report No SAND89-8009B (Sandia National Laboratories (1989)

  24. 24.

    Kee, R., Dixon-Lewis, G., Warnatz, J., Coltrin, M., Miller, J.: A Fortran Computer Code Package for the Evaluation of Gas-Phase, Multicomponent Trans- port Properties, SandiaNo SAND86-8246. Sandia National Laboratories (1986)

  25. 25.

    Peter, N., George, D., Alan, C.: SIAM. J. Sci. Stat. Comput. 10, 1038 (1989)

    Article  Google Scholar 

  26. 26.

    Baum, M., Poinsot, T., Thévenin, D.: J. Comput. Phys. 116, 247 (1995)

    Article  Google Scholar 

  27. 27.

    Poinsot, T., Lele, S.: J. Comput. Phys. 101, 104 (1992)

    MathSciNet  Article  Google Scholar 

  28. 28.

    Wang, Y., Tanahashi, M., Miyauchi, T.: Int. J. Heat Fluid Flow 28, 1280 (2007)

    Article  Google Scholar 

  29. 29.

    Peters, N.: Turbulent Combustion. Cambridge University Press (2000)

  30. 30.

    Candel, S.M., Poinsot, T.J.: Combust. Sci. Technol. 70, 1 (1990)

    Article  Google Scholar 

  31. 31.

    Gicquel, O., Darabiha, N., Thévenin, D., Emc, L., Cha, F.: Proc. Combust. Inst. 28(2), 1901 (2000)

    Article  Google Scholar 

  32. 32.

    Lutz, A., Kee, R., Grcar, J., Rupley, F.: OPPDIF: A Fortran Program for Computing Opposed-Flow Diffusion Flames, Sandia Report No SAND96-8243. Sandia National Laboratories (1997)

  33. 33.

    Baum, M., Poinst, T., Haworth, D., Darabiha, N.: J. Fluid Mech. 281, 1 (1994)

    Article  Google Scholar 

  34. 34.

    Hawkes, E.R., Chen, J.H.: Combust. Flame 144(1-2), 112 (2006)

    Article  Google Scholar 

  35. 35.

    Law, C.K.: Combustion Physics. Cambridge University Press (2006)

  36. 36.

    Chakraborty, N., Cant, S.: Combust. Flame 137, 129 (2004)

    Article  Google Scholar 

Download references


The authors gratefully acknowledge supports by Japan Society for the Promotion of Science.


This work is partially supported by Grant-in-Aid for JSPS Research Fellow (No. 16J10835) of Japan Society for the Promotion of Science.

Author information



Corresponding author

Correspondence to Masayasu Shimura.

Ethics declarations

Conflict of interests

The authors declare that they have no conflict of interest.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Aoki, K., Shimura, M., Park, J. et al. Response of Heat Release Rate to Flame Straining in Swirling Hydrogen-Air Premixed Flames. Flow Turbulence Combust 104, 451–478 (2020).

Download citation


  • Swirling flame
  • Direct numerical simulation
  • Heat release rate
  • Strain rate
  • Elementary reaction
  • Flame structure