SpringerLink
Log in

A Comparison of Strategies for Direct Numerical Simulation of Turbulence Chemistry Interaction in Generic Planar Turbulent Premixed Flames

  • Published:
Flow, Turbulence and Combustion Aims and scope Submit manuscript

Abstract

Three different methods to introduce turbulence in the computational domain of Direct Numerical Simulations (DNS) of statistically planar turbulent premixed flame configurations have been reviewed and their advantages and disadvantages in terms of run time, natural flame development, control of turbulence parameters and convergence of statistics extracted from the simulations have been discussed in detail. It has been found that there is no method, which is clearly superior to the other two alternative methods. An analysis has been performed to explain why Lundgren’s physical space linear forcing results in an integral length scale which is, independent of the Reynolds number, a constant fraction of the domain size. Furthermore, an evolution equation for the integral length scale has been derived, and a scaling analysis of its terms has been performed to explain the evolution of the integral length scale in the context of Lundgren’s physical space linear forcing. Finally, a modification to Lundgren’s forcing approach has been suggested which ensures that the integral length scale settles to a predetermined value so that DNS of statistically planar turbulent premixed flames with physical space forcing can be conducted for prescribed values of Damköhler and Karlovitz numbers.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Trouvé, A.: The production of premixed flame surface area in turbulent shear flow. Combust. Flame 99, 687–696 (1994)

    Article  Google Scholar 

  2. Chakraborty, N., Klein, M., Cant, R.S.: Effects of turbulent reynolds number on the displacement speed statistics in the thin reaction zones regime of turbulent premixed combustion. J. Combust. 2011, Article ID 473679 (2011)

    Google Scholar 

  3. Han, I., Huh, K.Y.: Roles of displacement speed on evolution of flame surface density for different turbulent intensities and Lewis numbers in turbulent premixed combustion. Combust. Flame 152, 194–205 (2008)

    Article  Google Scholar 

  4. Kim, S.H., Pitsch, H.: Scalar gradient and small-scale structure in turbulent premixed combustion. Phys. Fluids 19, 115114 (2007)

    MATH  Google Scholar 

  5. Rogallo, R.S.: Numerical Experiments in Homogeneous Turbulence, NASA Technical Memorandum, vol. 81315. NASA Ames Research Center, California (1981)

    Google Scholar 

  6. Rutland, C.J., Cant, R.S.: Turbulent transport in premixed flames.. In: Proceedings of Summer Program, Center for Turbulence Research, pp. 75–94 (1994)

  7. Nishiki, S., Hasegawa, T., Borghi, R., Himeno, R.: Modelling of turbulent scalar flux in turbulent premixed flames based on DNS databases. Combust. Theor. Model. 10(1), 39–55 (2006)

    Article  MATH  Google Scholar 

  8. Chakraborty, N., Cant, S.: Unsteady effects of strain rate and curvature on turbulent premixed flames in an inflow–outflow configuration. Combust. Flame 137, 129–147 (2004)

    Article  Google Scholar 

  9. Aspden, A.J., Day, M. S., Bell, J.B.: Turbulence-flame interactions in lean premixed hydrogen: transition to the distributed burning regime. J. Fluid Mech. 680, 287–320 (2011)

    Article  MATH  Google Scholar 

  10. Poludnenko, A.Y., Oran, E.S: The interaction of high-speed turbulence with flames: global properties and internal flame structure. Combust. Flame 157, 995–1011 (2010)

    Article  Google Scholar 

  11. Savard, B., Blanquart, G.: Broken reaction zone and differential diffusion effects in high Karlovitz n-C7H16 premixed turbulent flames. Combust. Flame 162, 2020–2033 (2015)

    Article  Google Scholar 

  12. Lundgren, T.: Linear Forced Isotropic Turbulence in Annual Research Briefs. Center for Turbulence Research, Stanford, pp. 461–473 (2003)

  13. Rosales, C, Meneveau, C.: Linear forcing in numerical simulations of isotropic turbulence: physical space implementations and convergence properties. Phys. Fluids 17, 095106 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  14. Carroll, P.L., Blanquart, G.: A proposed modification to Lundgren’s physical space velocity forcing method for isotropic turbulence. Phys. Fluids 25, 105114 (2013)

    Article  Google Scholar 

  15. Carroll, P.L., Blanquart, G.: The effect of velocity field forcing techniques on the Karman–Howarth equation. J. Turbul. 15, 429–448 (2014)

    Article  MathSciNet  Google Scholar 

  16. Jenkins, K.W., Klein, M., Chakraborty, N., Cant, R.S: Effects of strain rate and curvature on the propagation of a spherical flame kernel in the thin-reaction-zones regime. Combust. Flame 145, 415–434 (2006)

    Article  Google Scholar 

  17. Chakraborty, N., Klein, M., Cant, R.S.: Stretch rate effects on displacement speed in turbulent premixed flame kernels in the thin reaction zones regime. Proc. Combust. Inst. 31, 1385–1392 (2007)

    Article  Google Scholar 

  18. Klein, M., Sadiki, A., Janicka, J.: A digital filter based generation of inflow data for spatially develo** direct numerical or large eddy simulations. J. Comp. Physics 186, 652–665 (2003)

    Article  MATH  Google Scholar 

  19. Chakraborty, N., Cant, R.S.: Effects of Lewis number on flame surface density transport in turbulent premixed combustion. Combust. Flame 158, 1768–1787 (2011)

    Article  Google Scholar 

  20. Chakraborty, N., Wang, L., Klein M.: Streamline segment statistics of premixed flames with nonunity Lewis numbers. Phys. Rev. E 89, 033015 (2014)

    Article  Google Scholar 

  21. Matalon, M., Matkowsky, B.J.: Flames as gasdynamic discontinuities. J. Fluid Mech. 124, 239–259 (1982)

    Article  MATH  Google Scholar 

  22. Chaudhuri, S., Akkerman, V., Law, C.K.: Spectral formulation of turbulent flame speed with consideration of hydrodynamic instability. Phys. Rev. E 84, 026322 (2011)

    Article  Google Scholar 

  23. Denet, B., Haldenwang, P.: A numerical study of premixed flames Darrieus-landau instability. Combust. Sci. Tech. 104, 143–167 (1995)

    Article  Google Scholar 

  24. Tennekes, H, Lumley, J.L.: A First Course in Turbulence, 1st edn. MIT Press, Cambridge (1972)

  25. Corless, R.M., Gonnet, G.H., Hare, D.E.G., Jeffrey, D.J., Knuth, D.E.: On the Lambert W function. Adv. Compos. Mater. 5, 329–359 (1996)

    MathSciNet  MATH  Google Scholar 

  26. Pope, S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2000)

    Book  MATH  Google Scholar 

  27. Wacks, D.H., Chakraborty, N., Klein, M., Arias, P.G., Im, H.G.: Flow topologies in different regimes of premixed turbulent combustion: A direct numerical simulation analysis. Phys. Rev. Fluids 1, 083401 (2016)

    Article  Google Scholar 

  28. Ashurst, W., Kerstein, A., Kerr, R.M., Gibson, C.H.: Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence. Phys. Fluids A 30, 2343 (1987)

    Article  Google Scholar 

  29. Majda, A.J.: Vorticity, turbulence, and acoustics in fluid flow. SIAM Rev. 33, 349 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  30. Jimenez, J.: Kinematic alignment effects in turbulent flows. Phys. Fluids A 4, 652 (1992)

    Article  Google Scholar 

  31. Batchelor, G., Townsend, A.: The nature of turbulent motion at large wave-numbers. In: Proceedings of the Royal Society of London A: Mathematical, 240 Physical and Engineering Sciences, volume 199, The Royal Society, pp. 238–255 (1949)

  32. Monin, A.S., Yaglom, A.M.: Statistical Fluid mechanics, volume II: Mechanics of turbulence, volume 2. Courier Corporation (2013)

  33. She, Z.-S., Jackson, E., Orszag, S.A.: Scale-dependent intermittency and coherence in turbulence. J. Sci. Comput. 3, 407–434 (1988)

    Article  MATH  Google Scholar 

  34. Yamamoto, K., Kambe, T.: Gaussian and near-exponential probability distributions of turbulence obtained from a numerical simulation. Fluid Dyn. Res. 8, 65–72 (1991)

    Article  Google Scholar 

  35. Mallouppas, G., George, W.K., van Wachem, B.G.M.: New forcing scheme to sustain particle-laden homogeneous and isotropic turbulence. Phys. Fluids 25, 083304 (2013)

    Article  Google Scholar 

  36. Eswaran, V., Pope, S.B.: An examination of forcing in direct numerical simulations of turbulence. Comput. Fluids 16, 257–278 (1988)

    Article  MATH  Google Scholar 

Download references

Acknowledgments

Support by the German Research Foundation (Deutsche Forschungsgemeinschaft - DFG, GS: KL1456/1-1) is gratefully acknowledged. The authors are grateful to N8, ARCHER and grant number (EP/K025163/1) EPSRC for computational support.

Author information

Authors and Affiliations

  1. Department of Aerospace Engineering, Universität der Bundeswehr München, Neubiberg, 85577, Germany

    Markus Klein & Sebastian Ketterl

  2. School of Mechanical & Systems Engineering, Newcastle University, Newcastle-Upon-Tyne, NE1 7RU, UK

    Nilanjan Chakraborty

Authors
  1. Markus Klein
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nilanjan Chakraborty
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sebastian Ketterl
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Markus Klein.

Ethics declarations

Conflict of interests

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Klein, M., Chakraborty, N. & Ketterl, S. A Comparison of Strategies for Direct Numerical Simulation of Turbulence Chemistry Interaction in Generic Planar Turbulent Premixed Flames. Flow Turbulence Combust 99, 955–971 (2017). https://doi.org/10.1007/s10494-017-9843-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10494-017-9843-9

Keywords

Search

Navigation