Skip to main content Accessibility help

Direct and indirect thermal expansion effects in turbulent premixed flames

  • Vincent Robin (a1), Arnaud Mura (a1) and Michel Champion (a1)


The thermal expansion induced by the exothermic chemical reactions taking place in a turbulent reactive flow affects the velocity field so strongly that the large-scale velocity fluctuations as well as the small-scale velocity gradients can be governed by chemistry rather than by turbulence. Moreover, thermal expansion is well known to be responsible for counter-gradient turbulent diffusion and flame-generated turbulence phenomena. In the present study, by making use of an original splitting procedure applied to the velocity field, we establish the occurrence of two distinct thermal expansion effects in the flamelet regime of turbulent premixed combustion. The first is referred to as the direct thermal expansion effect. It is associated with a local flamelet crossing contribution as previously considered in early analyses of turbulent transport in premixed flames. The second, denoted herein as the indirect thermal expansion effect, is an outcome of the turbulent wrinkling processes that increases the flame surface area. Based on a splitting procedure applied to the velocity field, the respective influences of the two effects are identified and analysed. Furthermore, the theoretical analysis shows that the thermal expansion induced through the local flames can be treated separately in the usual continuity and momentum equations. This description of the turbulent reactive velocity field, leads also to relate all of the usual turbulent quantities to the reactive scalar field. Finally, algebraic closures for the turbulent transport terms of mass and momentum are proposed and successfully validated through comparison with direct numerical simulation data.


Corresponding author

Email address for correspondence:


Hide All
1. Bailly, P., Champion, M. & Garréton, D. 1997 Counter-gradient diffusion in a confined turbulent premixed flame. Phys. Fluids 9, 766775.
2. Bigot, P., Champion, M. & Garréton-Bruguières, D. 1999 Modelling a turbulent reactive flow with variable equivalence ratio: application to a flame stabilized by a two-dimensional sudden expansion. Combust. Sci. Technol. 158, 299320.
3. Borghi, R. 1985 On the structure and morphology of turbulent premixed flames. In Recent Advances in the Aerospace Science (ed. Casci, C. ), pp. 117138. Plenum Publishing Corporation.
4. Borghi, R. & Escudié, D. 1984 Assessment of a theoretical model of turbulent combustion by comparison with a simple experiment. Combust. Flame 56, 149164.
5. Bray, K. N. C. 1980 Turbulent flows with premixed reactants. In Turbulent Reacting Flows (ed. Libby, P.A. & Williams, F.A. ), pp. 115184. Springer.
6. Bray, K. N. C. 1995 Turbulent transport in flames. Proc. R. Soc. Lond. A 451, 231256.
7. Bray, K. N. C., Champion, M. & Libby, P. A. 1998 Premixed flames in stagnating turbulence part II: the mean velocities and pressure and the Damköhler number. Combust. Flame 112, 635653.
8. Bray, K. N. C., Champion, M. & Libby, P. A. 2000 Premixed flames in stagnating turbulence. Part IV: a new theory for Reynolds stresses and Reynolds fluxes applied to impinging flows. Combust. Flame 120, 118.
9. Bray, K. N. C., Libby, P. A., Masuya, G. J. & Moss, B. 1981 Turbulence production in premixed turbulent flames. Combust. Sci. Technol. 25, 127140.
10. Candel, S. M. & Poinsot, T. J. 1990 Flame stretch and the balance equation for the flame area. Combust. Sci. Technol. 70, 115.
11. Chakraborty, N. & Cant, R. A. 2009 Effects of Lewis number on scalar transport in turbulent premixed flames. Phys. Fluids 21, 035110.
12. Chakraborty, N., Champion, M., Mura, A. & Swaminathan, N. 2011 Scalar dissipation rate approach. In Turbulent Premixed Flames (ed. Swaminathan, N. & Bray, K. N. C. ), pp. 74102. Cambridge University Press.
13. Chakraborty, N. & Swaminathan, N. 2007 Influence of the Damköhler number on turbulence–scalar interaction in premixed flames, part II: model developement. Phys. Fluids 19, 045104.1045104.11.
14. Champion, M. 1989 Modelling the effects of combustion on a premixed turbulent flow: a review. In Turbulent Reactive Flows (ed. Murthy, S.N.B. & Borghi, R. ), pp. 731753. Springer.
15. Chomiak, J. & Nisbet, J. R. 1995 Modelling variable density effects in turbulent flames. Some basic considerations. Combust. Flame 102, 371386.
16. Clavin, P. & Joulin, G. 1983 Premixed flames in large scale and high intensity turbulent flows. J. Phys. Lett. 44, L1L12.
17. Clavin, P. & Williams, F. A. 1979 Theory of premixed-flame propagation in large-scale turbulence. J. Fluid Mech. 90 (3), 589604.
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 low intensity. J. Fluid Mech. 116, 251282.
19. Creta, F., Fogla, N. & Matalon, M. 2011 Turbulent propagation of premixed flames in the presence of Darrieus–Landau instability. Combust. Theor. Model. 15 (2), 267298.
20. Creta, F. & Matalon, M. 2011 Propagation of wrinkled turbulent flames in the context of hydrodynamic theory. J. Fluid Mech. 680, 225264.
21. Domingo, P. & Bray, K. N. C. 2000 Laminar flamelet expressions for pressure fluctuation terms in second moment models of premixed turbulent combustion. Combust. Flame 121, 555574.
22. Frank, J. H., Kalt, P. A. M. & Bilger, R. W. 1999 Measurements of conditional velocities in turbulent premixed flames by simultaneous OH PLIF and PIV. Combust. Flame 116, 220232.
23. Furakawa, J., Nogushi, Y., Hirano, T. & Williams, F. A. 2002 Anisotropic enhancement of turbulence in large-scale, low-intensity turbulent premixed propane-air flames. J. Fluid Mech. 462, 209243.
24. Heitor, M. V., Taylor, A. M. K. P. & Whitelaw, J. H. 1987 The interaction of turbulence and pressure gradients in a baffle-stabilized premixed flame. J. Fluid Mech. 181, 387413.
25. Im, Y. H., Huh, K. Y., Nishiki, S. & Hasegawa, T. 2004 Zone conditional assessment of flame-generated turbulence with DNS database of a turbulent premixed flame. Combust. Flame 137 (4), 478488.
26. Joulin, G. & Vidal, P. 1998 Flames, shocks and detonation. In Hydrodynamics and Nonlinear Instabilities (ed. Godrèche, C. & Manneville, P. ), pp. 546568. Cambridge University Press.
27. Kalt, P. A. M., Chen, Y. C. & Bilger, R. W. 2002 Experimental investigation of turbulent scalar flux in premixed stagnation type flames. Combust. Flame 129, 401415.
28. Kataoka, I. 1986 Local instant formulation of two-phase flows. Intl J. Multiphase Flow 12 (5), 745758.
29. Kuznetsov, V. R. 1978 Estimate of the correlation between pressure pulsations and the divergence of the velocity in subsonic flows of variable density. Combust. Flame 14, 328334.
30. Libby, P. A. & Bray, K. N. C. 1981 Counter gradient diffusion in premixed turbulent flames. AIAA J. 19, 205213.
31. Lindstedt, R. P. & Vaos, E. M. 1999 Modelling of premixed turbulent flames with second moment methods. Combust. Flame 116, 461485.
32. Lipatnikov, A. N. & Chomiak, J. 2010 Effects of premixed flames on turbulence and turbulent scalar transport. Prog. Energy Combust. Sci. 36, 1102.
33. Louch, D. S. & Bray, K. N. C. 1998 Vorticity and scalar transport in premixed turbulent combustion. Proc. Combust. Inst. 27, 801810.
34. Mantel, T. & Borghi, R. 1994 A new model of premixed wrinkled flame propagation based on a scalar dissipation equation. Combust. Flame 96, 443457.
35. Marble, F. E. & Broadwell, J. E. 1977 The Coherent Flame Model for Turbulent Chemical Reactions. Techincal Report TRW-9-PU, Project Squid Headquarters, Chaffee Hall, Purdu University (USA).
36. Matalon, M. & Matkowsky, B. J. 1982 Flames as hydrodynamics discontinuities. J. Fluid Mech. 124, 239259.
37. Mura, A. & Champion, M. 2009 Relevance of the Bray number in the small-scale modelling of turbulent premixed flames. Combust. Flame 156, 729733.
38. Mura, A., Robin, V., Champion, M. & Hasegawa, T. 2009 Small scales features of velocity and scalar fields in turbulent premixed flames. Flow Turbul. Combust. 82, 339358.
39. Mura, A., Tsuboi, K. & Hasegawa, T. 2008 Modelling of the correlation between velocity and reactive scalar gradients in turbulent premixed flames based on DNS data. Combust. Theor. Model. 12, 671698.
40. Nishiki, S., Hasegawa, T., Borghi, R. & Himeno, R. 2002 Modelling of flame-generated turbulence based on direct numerical simulation databases. Proc. Combust. Inst. 29, 20172022.
41. Nishiki, S., Hasegawa, T., Borghi, R. & Himeno, R. 2006 Modelling of turbulent scalar flux in turbulent premixed flames based on DNS databases. Combust. Theor. Model. 10, 3955.
42. Pelcé, P. & Clavin, P. 1982 Influence of hydrodynamics and diffusion upon the stability limits of laminar premixed flames. J. Fluid Mech. 124, 219237.
43. Peters, N. 1986 Laminar flamelet concepts in turbulent combustion. Proc. Combust. Inst. 21, 12311250.
44. Peters, N. 1992 A spectral closure for premixed turbulent combustion in the flamelet regime. J. Fluid Mech. 242, 611629.
45. Peters, N. 1999 The turbulent burning velocity for large scale and small scale turbulence. J. Fluid Mech. 384, 107132.
46. Pfadler, S., Leipertz, A. & Dinkelacker, F. 2008 Systematic experiments on turbulent premixed Bunsen flames including turbulent flux measurements. Combust. Flame 152, 616631.
47. Pope, S. B. 1987 Turbulent premixed flames. Annu. Rev. Fluid Mech. 19, 237270.
48. Pope, S. B. 1988 The evolution of surface in turbulence. Intl J. Engng. Sci. 26, 445469.
49. Robin, V., Champion, M. & Mura, A. 2008a A second-order model for turbulent reactive flows with variable equivalence ratio. Combust. Sci. Technol. 180, 17071732.
50. Robin, V., Mura, A., Champion, M. & Hasegawa, T. 2008b A new analysis of the modelling of pressure fluctuations effects on premixed turbulent flames and its validation based on DNS data. Combust. Sci. Technol. 180, 9961009.
51. Robin, V., Mura, A., Champion, M. & Hasegawa, T. 2010 Modelling the effects of thermal expansion on scalar fluxes in turbulent flames. Combust. Sci. Technol. 182, 449464.
52. Rutland, C. J. & Cant, R. S. 1994 Turbulent transport in premixed flames. In Proceedings of the Summer Program. Center for Turbulence Research, NASA Ames/Stanford University.
53. Shepherd, I. G., Moss, J. B. & Bray, K. N. C. 1982 Turbulent transport in confined premixed flame. Proc. Combust. Inst. 20, 423431.
54. Spalding, D. B. 1985 Two-fluids Models of Turbulence. Report CFD/85/4, Computational Fluid Dynamics Unit, Imperial College, London, UK.
55. Spalding, D. B. 1986 The two-fluids model of turbulence applied to combustion phenomena. AIAA J. 24 (6), 876884.
56. Veynante, D. & Poinsot, T. 1997 Effects of pressure gradients on turbulent premixed flames. J. Fluid Mech. 353, 83114.
57. Veynante, D., Trouvé, A., Bray, K. N. C. & Mantel, T. 1997 Gradient and counter-gradient scalar transport in turbulent premixed flames. J. Fluid Mech. 332, 263293.
58. Weller, H. G. 1993 The Development of a New Flame Area Combustion Model using Conditional Averaging. Thermo-Fluids Section Report TF/9307, Imperial College, London, UK.
59. Weller, H. G., Marooney, C. J. & Gosman, A. D. 1990 A new spectral method for calculation of the time-varying area of a laminar flame in homogeneous turbulence. Proc. Combust. Inst. 23, 629636.
60. Williams, F. A. 1985a Combustion Theory, 2nd edn. Benjamin Cummings.
61. Williams, F. A. 1985b Turbulent combustion. In The Mathematics of Combustion (ed. Buckmaster, J. ), pp. 115147. SIAM.
62. Zimont, V. L. & Biagoli, F. 2002 Gradient, counter-gradient transport and their transition in turbulent premixed flames. Combust. Theor. Model. 6, 79101.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification


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