SpringerLink
Log in

Statistics and Modelling of Turbulent Kinetic Energy Transport in Different Regimes of Premixed Combustion

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

Abstract

The statistical behaviour of turbulent kinetic energy transport in turbulent premixed flames is analysed using data from three-dimensional Direct Numerical Simulation (DNS) of freely propagating turbulent premixed flames under decaying turbulence. For flames within the corrugated flamelets regime, it is observed that turbulent kinetic energy is generated within the flame brush. By contrast, for flames within the thin reaction zones regime it has been found that the turbulent kinetic energy decays monotonically through the flame brush. Similar trends are observed also for the dissipation rate of turbulent kinetic energy. Within the corrugated flamelets regime, it is demonstrated that the effects of the mean pressure gradient and pressure dilatation within the flame are sufficient to overcome the effects of viscous dissipation and are responsible for the observed augmentation of turbulent kinetic energy in the flame brush. In the thin reaction zones regime, the effects of the mean pressure gradient and pressure dilatation terms are relatively much weaker than those of viscous dissipation, resulting in a monotonic decay of turbulent kinetic energy across the flame brush. The modelling of the various unclosed terms of the turbulent kinetic energy transport equation has been analysed in detail. The predictions of existing models are compared with corresponding quantities extracted from DNS data. Based on this a-priori DNS assessment, either appropriate models are identified or new models are proposed where necessary. It is shown that the turbulent flux of turbulent kinetic energy exhibits counter-gradient (gradient) transport wherever the turbulent scalar flux is counter-gradient (gradient) in nature. A new model has been proposed for the turbulent flux of turbulent kinetic energy, and is found to capture the qualitative and quantitative behaviour obtained from DNS data for both the corrugated flamelets and thin reaction zones regimes without the need to adjust any of the model constants.

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

Similar content being viewed by others

References

  1. Jones, W.P., Launder, B.E.: The calculation of low-Reynolds-number phenomena with a two equation model of turbulence. Int. J. Heat Mass Transfer. 16, 1119–1130 (1973)

    Article  Google Scholar 

  2. Durbin, P.A., Pettersson-Reif, B.A.: Statistical Theory and Modelling of Turbulent Flows, 1st edn. Wiley, Hoboken (2001)

    Google Scholar 

  3. Wilcox, D.C.: Turbulence Modelling for CFD, 2nd edn. D.C.W., La Cañada (2002)

    Google Scholar 

  4. Karlovitz, B., Jr Denniston, D.W., Knapschaefer, D.H., Wells, F.E.: Studies on turbulent flames. Proc. Combust. Inst. 4, 613–620 (1953)

    Google Scholar 

  5. Launder, B.E.: Heat and mass transport by turbulence. In: Bradshaw, P. (ed.) Topics in Applied Physics, vol. 12, pp. 231–287, Springer (1976)

  6. Bray, K.N.C.: Studies of the turbulent burning velocity. Proc. R. Soc. Lond. A 431, 315–355 (1990)

    Article  Google Scholar 

  7. Candel, S., Veynante, D., Lacas, F., Maistret, E., Darabiha, N., Poinsot, T.: Coherent flamelet model: applications and recent extensions. In: Larrouturou, B.E. (ed.) Recent Advances in Combustion Modelling, pp. 19–64. World Scientific, Singapore (1990)

    Google Scholar 

  8. Duclos, J.M., Veynante, D., Poinsot, T.J.: A comparison of flamelet models for premixed turbulent combustion. Combust. Flame. 95, 101–117 (1993)

    Article  Google Scholar 

  9. Mantel, T., Bilger, R.W.: Conditional statistics in a turbulent premixed flame derived from direct numerical simulation. Combust. Sci. Technol. 96(4), 393–417 (1995)

    Article  Google Scholar 

  10. Chakraborty, N., Rogerson, J.W., Swaminathan, N.: A-Priori assessment of closures for scalar dissipation rate transport in turbulent premixed flames using direct numerical simulation. Phys. Fluids. 20, 045106 (2008)

    Article  Google Scholar 

  11. Kolla, H., Rogerson, J.W., Chakraborty, N., Swaminathan, N.: Scalar dissipation rate modelling and its validation. Combust. Sci. Technol. 181, 518–535 (2009)

    Article  Google Scholar 

  12. Bray, K.N.C., Libby, P.A.: Interaction effects in turbulent premixed flames. Phys. Fluids A 19, 1687–1701 (1976)

    Article  MATH  Google Scholar 

  13. Moreau, P., Boutier, A.: Laser velocimeter measurements in a turbulent flame. Proc. Combust. Inst. 16, 1747–1756 (1977)

    Google Scholar 

  14. Bray, K.N.C., Libby, P.A., Masuya, G., Moss, J.B.: Turbulence production in premixed turbulent flames. Combust. Sci. Technol. 25, 127–140 (1980)

    Article  Google Scholar 

  15. Borghi, R., Escudie, D.: Assessment of a theoretical model of turbulent combustion by comparison with a simple experiment. Combust. Flame. 56, 149–164 (1984)

    Article  Google Scholar 

  16. Chomiak, J., Nisbet, J.: Modelling variable density effects in turbulent flames. Combust. Flame. 102, 371–386 (1995)

    Article  Google Scholar 

  17. Kuznetsov, V.R.: Estimate of the correlation between pressure pulsations and the divergence of the velocity in subsonic flows of variable density. Fluid Dyn. 14(3), 328–334 (1979)

    Article  MATH  Google Scholar 

  18. Strahle, W.C.: Velocity-pressure gradient correlation in turbulent reactive flows. Combust. Sci. Technol. 32, 289–305 (1983)

    Article  Google Scholar 

  19. Rutland, C.J., Cant, R.S.: Turbulent transport in premixed flames, pp.75–94. Proc. of 1994 Summer Program, Centre for Turbulence Research, Stanford University/NASA Ames, Stanford, CA (1994)

  20. Zhang, S., Rutland, C.J.: Premixed flame effects on turbulence and pressure-related terms. Combust. Flame. 102, 447–461 (1995)

    Article  Google Scholar 

  21. Nishiki, S., Hasegawa, T., Borghi, R., Himeno, R.: Modelling of flame generated turbulence based on Direct Numerical Simulation databases. Proc. Combust. Inst. 29, 2017–2022 (2002)

    Article  Google Scholar 

  22. Peters, N.: Turbulent Combustion, 1st edn. Cambridge University Press, UK (2000)

    Book  MATH  Google Scholar 

  23. Vaishnavi, P., Cant, R.S.: Mechanism of induced turbulence through buoyancy suppression in premixed turbulent combustion. Proc. of 2nd European Combustion Meeting, Louvain-la-Neuve, Belgium (2005)

  24. Poinsot, T., Echekki, T., Mungal, M.: A study of the laminar flame tip and implications for turbulent premixed combustion. Combust. Sci. Technol. 81(1–3), 45–73 (1992)

    Article  Google Scholar 

  25. Rutland, C., Trouvé, A.: Direct simulations of premixed turbulent flames with nonunity Lewis numbers. Combust. Flame. 94, 41–57 (1993)

    Article  Google Scholar 

  26. 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 

  27. Chakraborty, N., Cant, R.S.: Influence of Lewis number on curvature effects in turbulent premixed flame propagation in the thin reaction zones regime. Phys. Fluids. 17, 105105 (2005)

    Article  Google Scholar 

  28. Treurniet, T.C., Nieuwstadt, F.T.M., Boersma, B.J.: Direct Numerical Simulation of homogeneous turbulence in combination with premixed combustion at low Mach number modeled by the G-equation. J. Fluid Mech. 565, 25–62 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  29. Chakraborty, N.: Comparison of displacement speed statistics of turbulent premixed flames in the regimes representing combustion in corrugated flamelets and the thin reaction zones. Phys. Fluids 19, 105109 (2007)

    Article  Google Scholar 

  30. Chakraborty, N., Cant, R.S.: Effects of Lewis number on turbulent scalar transport and its modelling in turbulent premixed flames. Combust. Flame. 156, 1427–1444 (2009)

    Article  Google Scholar 

  31. Veynante, D., Trouvé, A., Bray, K.N.C., Mantel, T.: Gradient and counter-gradient scalar transport in turbulent premixed flames. J. Fluid Mech. 332, 263–293 (1997)

    MATH  Google Scholar 

  32. Tullis, S., Cant, R.S.: Scalar transport modeling in large eddy simulation of turbulent premixed flames. Proc. Combust. Inst. 29, 2097–2104 (2002)

    Article  Google Scholar 

  33. Swaminathan, N., Bray, K.N.C.: Effects of dilatation on scalar dissipation in turbulent premixed flames. Combust. Flame. 143, 549–565 (2005)

    Article  Google Scholar 

  34. Bray, K.N.C., Swaminathan, N.: Scalar dissipation rate and flame surface density in premixed turbulent combustion. Comptes Rendus Mechanique. 334, 466–473 (2006)

    Article  MATH  Google Scholar 

  35. Rogerson, J.W., Swaminathan, N.: Correlation between dilatation and scalar dissipation in turbulent premixed flames. Proc. 3rd European Combust. Meeting (2007)

  36. Chakraborty, N., Rogerson, J.W., Swaminathan, N.: A-Priori assessment of closures for scalar dissipation rate transport in turbulent premixed flames using direct numerical simulation. Phys. Fluids 20, 045106 (2008)

    Article  Google Scholar 

  37. Kolla, H., Rogerson, J.W., Chakraborty, N., Swaminathan, N.: Scalar dissipation rate modelling and its validation. Combust. Sci. Technol. 181, 518–535 (2009)

    Article  Google Scholar 

  38. Chakraborty, N., Klein, M.: A Priori direct numerical simulation assessment of algebraic flame surface density models for turbulent premixed flames in the context of large eddy simulation. Phys. Fluids 20, 085108 (2008)

    Article  Google Scholar 

  39. Wray, A.A.: Minimal storage time advancement schemes for spectral methods, Report No. MS 202 A-1, NASA Ames Research Center, California (1990)

  40. Poinsot, T., Lele, S.K.: Boundary conditions for direct simulation of compressible viscous flows. J. Comp. Physiol. 101, 104–129 (1992)

    MathSciNet  MATH  Google Scholar 

  41. Jenkins, K.W., Cant, R.S.: DNS of turbulent flame kernels. In: Liu, C., Sakell, L., Beautner, T. (eds.) Proc. Second AFOSR Conf. on DNS and LES, pp. 192–202. Kluwer Academic Publishers (1999)

  42. Rogallo, R.S.: Numerical experiments in homogeneous turbulence. NASA TM81315, NASA Ames Research Center, California (1981)

  43. Batchelor, G.K., Townsend, A.A.: Decay of turbulence in final period. Proc. R. Soc. Lond. A 194, 527–542 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  44. Poinsot, T., Veynante, D.: Theoretical and Numerical Combustion. R.T. Edwards, Philadelphia, USA (2001)

  45. Haworth, D.C., Poinsot, T.J.: Numerical simulations of Lewis number effects in turbulent premixed flames. J. Fluid Mech. 244, 405–436 (1992)

    Article  Google Scholar 

  46. Peters, N., Terhoeven, P., Chen, J.H., Echekki, T.: Statistics of flame displacement speeds from computations of 2-D unsteady methane-air flames. Proc. Combust. Inst. 27, 833–839 (1998)

    Google Scholar 

  47. Boger, M., Veynante, D., Boughanem, H., Trouvé, A.: Direct numerical simulation analysis of flame surface density concept for Large Eddy Simulation of turbulent premixed combustion. Proc. Combust. Inst. 27, 917–925 (1998)

    Google Scholar 

  48. Bray, K.N.C., Libby, P.A., Moss, J.B.: Unified modelling approach for premixed turbulent combustion – Part I: general formulation. Combust. Flame. 61, 87–102 (1985)

    Article  Google Scholar 

  49. Veynante, D., Poinsot, T.J.: Effects of pressure gradients on turbulent premixed flames. J. Fluid Mech. 353, 83–114 (1997)

    Article  MATH  Google Scholar 

  50. Chakraborty, N., Cant, R.S.: Effects of Lewis number on scalar transport in turbulent premixed flames. Phys. Fluids 21, 035110 (2009)

    Article  Google Scholar 

  51. Chakraborty, N., Cant, R.S.: Physical insight and modelling for Lewis number effects on turbulent heat and mass transport in turbulent premixed flames. Numer. Heat Transf. A 55(8), 762–779 (2009)

    Article  Google Scholar 

  52. Launder, B.L., Reece, G.J., Rodi, W.J.: Progress in the development of a Reynolds stress turbulence closure. J. Fluid Mech. 68, 537–566 (1975)

    Article  MATH  Google Scholar 

  53. Bray, K.N.C., Champion, M., Libby, P.A.: Premixed flames in stagnating turbulence part IV: a new theory for the Reynolds stresses and Reynolds fluxes applied to im**ing flows. Combust. Flame 120, 1–18 (2000)

    Article  Google Scholar 

  54. Domingo, P., Bray, K.N.C.: Laminar flamelet expressions for pressure fluctuation terms in second moment models of premixed turbulent combustion. Combust. Flame 121, 555–574 (2000)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering, University of Liverpool, Brownlow Hill, Liverpool, L69 3GH, UK

    Nilanjan Chakraborty & Mohit Katragadda

  2. Engineering Department, Cambridge University, Trum**ton Street, Cambridge, CB2 1PZ, UK

    R. Stewart Cant

Authors
  1. Nilanjan Chakraborty
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohit Katragadda
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. Stewart Cant
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Stewart Cant.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chakraborty, N., Katragadda, M. & Cant, R.S. Statistics and Modelling of Turbulent Kinetic Energy Transport in Different Regimes of Premixed Combustion. Flow Turbulence Combust 87, 205–235 (2011). https://doi.org/10.1007/s10494-010-9312-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10494-010-9312-1

Keywords

Search

Navigation