Skip to main content Accessibility help

Influence of flame geometry on turbulent premixed flame propagation: a DNS investigation

  • T. D. Dunstan (a1), N. Swaminathan (a1) and K. N. C. Bray (a1)


The sensitivity of the turbulent flame speed to the geometry of the flame is investigated using direct numerical simulations of turbulent premixed flames in three canonical configurations: freely propagating statistically planar flames, planar flames stabilized in stagnating flows, and rod-stabilized V-flames. We consider both the consumption speed, which measures the integrated rate of burning, and the propagation speed, which measures the speed of an isosurface within the flame brush. An algebraic model for the propagation speed of the leading edge of the flame brush, which is blind to flame geometry, is also applied to the data for the purposes of establishing its range of validity and the causes of its failure. The turbulent consumption speed is found to be strongly geometry dependent, primarily due to the continuous growth of the flame brush thickness. Changes in the structure and consumption speed of instantaneous flame fronts are found to be only weakly sensitive to flame geometry. The turbulent propagation speed is analysed in terms of its reactive, diffusive and turbulent flux components. All three terms are shown to be significant, both through the flame brush and along the leading edge. The leading-edge propagation speed is found to be sensitive to flame geometry only in the V-flames under certain conditions. It is suggested that this apparent geometry dependence, which the model cannot capture, results from the relation between the turbulence and mean flow time scales in these particular cases, and is not intrinsic to the flame geometry itself.


Corresponding author

Email address for correspondence:


Hide All
1. Batchelor, G. K. & Townsend, A. A. 1948 Decay of turbulence in the final period. Proc. R. Soc. Lond. A 194, 527543.
2. Bell, J. B., Day, M. S. & Grcar, J. F. 2002 Numerical simulation of premixed turbulent methane combustion. Proc. Combust. Inst. 29, 19871993.
3. Bell, J. B., Day, M. S., Shepherd, I. G., Johnson, M. R., Cheng, R. K., Grcar, J. F., Beckner, V. E. & Lijewski, M. J. 2005 Numerical simulation of a laboratory-scale turbulent V-flame. Proc. Natl Acad. Sci. USA 102 (29), 1000610011.
4. Bradley, D., Lawes, M. & Mansour, M. S. 2011 The problems of the turbulent burning velocity. Flow Turbul. Combust. 87 (2–3), 191204.
5. Bray, K. N. C. 1980 Turbulent flows with premixed reactants. In Turbulent Reacting Flows (ed. Libby, P. A. & Williams, F. A. ), pp. 115183. Springer.
6. Bray, K. N. C. 1990 Studies of the turbulent burning velocity. Proc. R. Soc. Lond. A 431, 315335.
7. Bray, K. N. C., Champion, M. & Libby, P. A. 1989 The interaction between turbulence and chemistry in premixed turbulent flames. In Turbulent Reacting Flows (ed. Borghi, R. & Murthy, S. N. B. ), pp. 541563. Springer.
8. Bray, K. N. C., Champion, M. & Libby, P. A. 1998 Premixed flames in stagnating turbulence. Part II. The mean velocity and pressure and the damköhler number. Combust. Flame 112, 635654.
9. Bray, K. N. C., Champion, M. & Libby, P. A. 2000 Premixed flames in stagnating turbulence. Part IV. A new theory for the Reynolds stresses and Reynolds fluxes applied to impinging flows. Combust. Flame 120, 118.
10. Cant, R. S., Bray, K. N. C., Kostiuk, L. W. & Rogg, B. 1994 Flow divergence effects in strained laminar flamelets for premixed turbulent combustion. Combust. Sci. Technol. 95, 261276.
11. Chakraborty, N. & Cant, R. S. 2011 Effects of Lewis number on flame surface density transport in turbulent premixed combustion. Combust. Flame 158, 17681787.
12. Chakraborty, N., Katragadda, M. & Cant, R. S. 2011 Statistics and modelling of turbulent kinetic energy transport in different regimes of premixed combustion. Flow Turbul. Combust. 87 (2–3), 205235.
13. Chakraborty, N., Rogerson, J. W. & Swaminathan, N. 2008 A priori assessment of closures for scalar dissipation rate transport in turbulent premixed flames using direct numerical simulation. Phys. Fluids 20, 045106.
14. Chen, Y.-C. & Bilger, R. W. 2002 Experimental investigation of three-dimensional flame-front structure in premixed turbulent combustion I: hydrocarbon/air bunsen flames. Combust. Flame 131, 400435.
15. Chen, Y. C., Kim, M., Han, J., Yun, S. & Yoon, Y. 2008 Measurements of the heat release rate integral in turbulent premixed stagnation flames with particle image velocimetry. Combust. Flame 154, 434447.
16. Cheng, R. K. & Shepherd, I. G. 1991 The influence of burner geometry on premixed turbulent flame propagation. Combust. Flame 85, 726.
17. Cho, P., Law, C. K., Cheng, R. K. & Shepherd, I. G. 1988 Velocity and scalar fields of turbulent premixed flames in stagnation flow. Proc. Combust. Inst. 22, 739745.
18. Clavin, P. & Williams, F. A. 1982 Effects of molecular diffusion and of thermal expansion on the structure and dynamics of premixed flames in turbulent flows of large-scale and intensity. J. Fluid Mech. 116, 251282.
19. Dinkelacker, F., Manickam, B. & Muppala, S. P. R. 2011 Modelling and simulation of lean premixed turbulent methane/hydrogen/air flames with an effective Lewis number approach. Combust. Flame 158 (9), 17421749.
20. Domingo, P., Vervisch, L., Payet, S. & Hauguel, R. 2005 DNS of a premixed turbulent V flame and LES of a ducted flame using a fsd-pdf subgrid scale closure with fpi-tabulated chemistry. Combust. Flame 143, 566586.
21. Driscoll, J. F. 2008 Turbulent premixed combustion: flamelet structure and its effect on turbulent burning velocities. Prog. Energy Combust. Sci. 34, 91134.
22. Dunstan, T. D. & Jenkins, K. W. 2009 The effects of hydrogen substitution on turbulent premixed methane–air kernels using direct numerical simulation. Intl J. Hydrogen Energ. 34, 83898404.
23. Dunstan, T. D., Swaminathan, N. & Bray, K. N. C. 2011 Geometrical properties and turbulent flame speed measurements in stationary premixed V-flames using direct numerical simulations. Flow Turbul. Combust. 87, 237259.
24. Gamard, S. & George, W. K. 1999 Reynolds number dependence of energy spectra in the overlap region of isotropic turbulence. Flow Turbul. Combust. 63, 443477.
25. Gouldin, F. C. 1996 Combustion intensity and burning rate integral of premixed flames. Proc. Combust. Inst. 26, 381388.
26. Gülder, Ö. L. & Smallwood, G. J. 2007 Flame surface densities in premixed flames at medium to high turbulence intensities. Combust. Sci. Technol. 179 (1), 191206.
27. Hawkes, E. R. & Chen, J. H. 2006 Comparison of direct numerical simulation of lean premixed methane–air flames with strained laminar flame calculations. Combust. Flame 144, 112125.
28. Hemchandra, S. & Lieuwen, T. 2010 Local consumption speed of turbulent premixed flames: an analysis of ‘memory effects’. Combust. Flame 157, 955965.
29. Im, H. G. & Chen, J. H. 2002 Preferential diffusion effects on the burning rate of interacting turbulent premixed hydrogen–air flames. Combust. Flame 131, 246258.
30. Jenkins, K. W. & Cant, R. S. 1999 DNS of turbulent flame kernels. In Proceedings of the Second AFOSR Conference on DNS and LES, pp. 192202. Kluwer Academic.
31. Kolla, H., Rogerson, J. W., Chakraborty, N. & Swaminathan, N. 2009 Scalar dissipation rate modeling and its validation. Combust. Sci. Technol. 181 (3), 518535.
32. Kolla, H., Rogerson, J. W. & Swaminathan, N. 2010 Validation of a turbulent flame speed model across combustion regimes. Combust. Sci. Technol. 182 (3), 284308.
33. Kolla, H. & Swaminathan, N. 2011 Influence of turbulent scalar mixing physics on premixed flame propagation. J. Combust. 2011, 451351.
34. Kollmann, W. & Chen, J. H. 1998 Pocket formation and the flame surface density equation. Proc. Combust. Inst. 27, 927934.
35. Kostiuk, L. W., Shepherd, I. G. & Bray, K. N. C. 1999 Experimental study of premixed turbulent combustion in opposed streams. Part iii. Spatial structure of flames. Combust. Flame 118, 129139.
36. Law, C. K. 2006 Combustion Physics. Cambridge University Press.
37. Lee, D. & Huh, K. Y. 2011 DNS analysis of propagation speed and conditional statistics of turbulent premixed flame in a planar impinging jet. Proc. Combust. Inst. 33, 13011307.
38. Libby, P. A. 1989 Characteristics of laminar lifted flames in a partially premixed jet. Combust. Sci. Technol. 68, 1533.
39. Libby, P. A. 2005 Recent research on premixed flames in stagnating turbulence. Combust. Sci. Technol. 177, 10731094.
40. Lipatnikov, A. N. & Chomiak, J. 2002 Turbulent flame speed and thickness: phenomenology, evaluation, and application in multi-dimensional simulations. Prog. Energy Combust. Sci. 28, 174.
41. Lipatnikov, A. N. & Chomiak, J. 2005a Molecular transport effects on turbulent flame propagation and structure. Prog. Energy Combust. Sci. 31, 173.
42. Lipatnikov, A. N. & Chomiak, J. 2005b A theoretical study of premixed turbulent flame development. Proc. Combust. Inst. 30, 843850.
43. Lipatnikov, A. N. & Chomiak, J. 2007 Global stretch effects in premixed turbulent combustion. Proc. Combust. Inst. 31, 13611368.
44. Minamoto, Y., Fukushima, N., Tanahashi, M., Miyauchi, T., Dunstan, T. D. & Swaminathan, N. 2011 Effect of flow-geometry on turbulence-scalar interaction in premixed flames. Phys. Fluids 23 (12), 125107.
45. Mura, A. & Borghi, R. 2003 Towards an extended scalar dissipation equation for turbulent premixed combustion. Combust. Flame 133, 193196.
46. O’Young, F. & Bilger, R. W. 1997 Scalar gradient and related quantities in turbulent premixed flames. Combust. Flame 109, 683700.
47. Peters, N. 1999 The turbulent burning velocity for large-scale and small-scale turbulence. J. Fluid Mech. 384, 107132.
48. Peters, N. 2000 Turbulent Combustion. Cambridge University Press.
49. Poinsot, T. & Lele, S. 1992 Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101, 104129.
50. Pope, S. B. 1988 The evolution of surfaces in turbulence. Intl J. Engng Sci. 26, 445469.
51. Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
52. Rogallo, R. S. 1981 Numerical experiments in homogeneous turbulence. NASA Tech. Mem. 81835.
53. Sankaran, R., Hawkes, E. R., Chen, J. H., Lu, T. & Law, C. K. 2007 Structure of a spatially developing turbulent lean methane–air bunsen flame. Proc. Combust. Inst. 31, 12911298.
54. Shepherd, I. G., Cheng, R. K., Plessing, T., Kortschik, C. & Peters, N. 2002 Premixed flame front structure in intense turbulence. Proc. Combust. Inst. 29, 18331840.
55. Shepherd, I. G. & Kostiuk, L. W. 1994 The burning rate of premixed turbulent flames in divergent flows. Combust. Flame 96, 371380.
56. Smith, K. O. & Gouldin, F. C. 1978 Experimental investigation of flow turbulence effects on premixed methane–air flames. Prog. Astro. Aero. 58, 3754.
57. Soika, A., Dinkelacker, F. & Leipertz, A. 1998 Measurement of the resolved flame structure of turbulent premixed flames with constant Reynolds number and varied stoichiometry. Proc. Combust. Inst. 27, 785.
58. Spalding, D. B. 1976 Development of the eddy-break-up model of turbulent combustion. Proc. Combust. Inst. 16, 16571663.
59. Swaminathan, N. & Bray, K. N. C. 2005 Effect of dilatation on scalar dissipation in turbulent premixed flames. Combust. Flame 143, 549565.
60. Tanahashi, M., Nada, Y., Ito, Y. & Miyauchi, T. 2002 Local flame structure in the well-stirred reactor regime. Proc. Combust. Inst. 29, 20412049.
61. Venkateswaran, P., Marshall, A., Shin, D. H., Noble, D., Seitzman, J. & Lieuwen, T. 2011 Measurements and analysis of turbulent consumption speeds of H2/CO mixtures. Combust. Flame 158, 16021614.
62. Zeldovich, Y. 1980 Flame propagation in a substance reacting at initial temperature. Combust. Flame 39, 219224.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Influence of flame geometry on turbulent premixed flame propagation: a DNS investigation

  • T. D. Dunstan (a1), N. Swaminathan (a1) and K. N. C. Bray (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed