The “turbulent flame speed” of wrinkled premixed flames

Moshe Matalon; Francesco Creta

doi:10.1016/j.crme.2012.10.031

The “turbulent flame speed” of wrinkled premixed flames

Moshe Matalon ¹ ; Francesco Creta ²

¹ University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
² University of Rome La Sapienza, 00185 Roma, Italy

Comptes Rendus. Mécanique, Out of Equilibrium Dynamics, Volume 340 (2012) no. 11-12, pp. 845-858.

Abstract

The determination of the turbulent flame speed is a central problem in combustion theory. Early studies by Damköhler and Shelkin resorted to geometrical and scaling arguments to deduce expressions for the turbulent flame speed and its dependence on turbulence intensity. A more rigorous approach was undertaken by Clavin and Williams who, based on a multi-scale asymptotic approach valid for weakly wrinkled flames, derived an expression that apart from a numerical factor recaptures the early result by Damköhler and Shelkin. The common denominator of the phenomenological and the more rigorous propositions is an increase in turbulent flame speed due solely to an increase in flame surface area. Various suggestions based on physical and/or experimental arguments have been also proposed, incorporating other functional parameters into the flame speed relation. The objective of this work is to extend the asymptotic results to a fully nonlinear regime that permits to systematically extract scaling laws for the turbulent flame speed that depend on turbulence intensity and scale, mixture composition and thermal expansion, flow conditions including effects of curvature and strain, and flame instabilities. To this end, we use a hybrid Navier–Stokes/front-capturing methodology, which consistently with the asymptotic model, treats the flame as a surface of density discontinuity separating burned and unburned gases. The present results are limited to positive Markstein length, corresponding to lean hydrocarbon–air or rich hydrogen–air mixtures, and to wrinkled flames of vanishingly small thickness, smaller that the smallest fluid scales. For simplicity we have considered here two-dimensional turbulence, which although lacks some features of real three-dimensional turbulence, is not detrimental when using the hydrodynamic model under consideration, because the turbulent flame retains its laminar structure and its interaction with turbulence is primarily advective/kinematic in nature.

Published online: 2012-11-01

DOI: 10.1016/j.crme.2012.10.031

Keywords: Turbulent flame speed, Darrieus–Landau instability, Premixed flames, Wrinkled flames, Flamelets, Markstein length, Flame stretch

Author's affiliations:

Moshe Matalon ¹; Francesco Creta ²

¹ University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
² University of Rome La Sapienza, 00185 Roma, Italy

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Moshe Matalon; Francesco Creta. The “turbulent flame speed” of wrinkled premixed flames. Comptes Rendus. Mécanique, Out of Equilibrium Dynamics, Volume 340 (2012) no. 11-12, pp. 845-858. doi : 10.1016/j.crme.2012.10.031. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.10.031/

References
Cited by

[1] D. Bradley How fast can we burn, Proceedings of the Combustion Institute, Volume 24 (1992), pp. 247-262

[2] G. Damköhler Der Einfluss der Turbulenz auf die Flammengeschwindigkeit in Gasgemischen, Zeitschrift Für Elektrochemie, Volume 46 (1940), pp. 601-652

[3] K.I. Shelkin On combustion in a turbulent flow, NACA TM, Volume 1110 (1947)

[4] F.A. Williams Combustion Theory, Benjamin/Cummings, Menlo Park, 1985

[5] N. Peters Turbulent Combustion, Cambridge University Press, 2000

[6] K.N.C. Bray Studies of the turbulent burning velocity, Proceedings of the Royal Society A: Mathematical and Physical Sciences, Volume 431 (1990), pp. 315-335

[7] A.N. Lipatnikov; J. Chomiak Turbulent flame speed and thickness: Phenomenology evaluation and application in multi-dimensional simulations, Progress in Energy and Combustion Science, Volume 28 (2002), pp. 1-74

[8] J.F. Driscoll Turbulent premixed combustion: Flamelet structure and its effect on turbulent burning velocities, Progress in Energy and Combustion Science, Volume 34 (2008) no. 1, pp. 91-134

[9] P. Clavin; F.A. Williams Theory of premixed flame propagation in large-scale turbulence, Journal of Fluid Mechanics, Volume 90 (1979), pp. 589-604

[10] P. Clavin; F.A. Williams Effects of molecular diffusion and thermal expansion on the structure and dynamics of premixed flames in turbulent flows of large scales and low intensity, Journal of Fluid Mechanics, Volume 116 (1982), p. 251

[11] R.C. Aldredge; F.A. Williams Influence of wrinkled premixed-flame dynamics on large-scale, low intensity turbulent flow, Journal of Fluid Mechanics, Volume 228 (1991), pp. 487-511

[12] M. Matalon; B.J. Matkowsky Flames as gasdynamic discontinuities, Journal of Fluid Mechanics, Volume 124 (1982), pp. 239-259

[13] M. Matalon; C. Cui; J.K. Bechtold Hydrodynamic theory of premixed flames: Effects of stoichiometry, variable transport coefficients and arbitrary reaction orders, Journal of Fluid Mechanics, Volume 487 (2003), pp. 179-210

[14] Y. Rastigejev; M. Matalon Numerical simulation of flames as gas-dynamic discontinuities, Combustion Theory and Modelling, Volume 10 (2006) no. 3, pp. 459-481

[15] F. Creta; M. Matalon Strain rate effects on nonlinear development of hydrodynamically unstable flames, Proceedings of the Combustion Institute, Volume 33 (2011), pp. 1087-1094

[16] F. Creta; M. Matalon Propagation of wrinkled turbulent flames in the context of hydrodynamic theory, Journal of Fluid Mechanics, Volume 680 (2011), pp. 225-264

[17] C. Altantzis; C. Frouzakis; A. Tomboulides; M. Matalon; K. Boulouchos Hydrodynamic and thermodiffusive instability effects on the evolution of laminar planar lean premixed hydrogen flames, Journal of Fluid Mechanics, Volume 700 (2012), pp. 329-361

[18] M.L. Frankel; G.I. Sivashinsky The effect of viscosity on hydrodynamic stability of a plane flame front, Combustion Science and Technology, Volume 29 (1982), pp. 207-224

[19] P. Pelce; P. Clavin Influence of hydrodynamics and diffusion upon the stability limits of laminar premixed flames, Journal of Fluid Mechanics, Volume 124 (1982), pp. 219-237

[20] Y. Rastigejev; M. Matalon Nonlinear evolution of hydrodynamically unstable premixed flames, Journal of Fluid Mechanics, Volume 554 (2006), pp. 371-392

[21] F. Creta; N. Fogla; M. Matalon Turbulent propagation of premixed fames in the presence of Darrieus–Landau instability, Combustion Theory and Modelling, Volume 15 (2011), pp. 267-298

[22] D. Vaynblat; M. Matalon Stability of pole solutions for planar propagating flames: I. Exact eigenvalues and eigenfunctions, SIAM Journal on Applied Mathematics, Volume 60 (2000) no. 2, pp. 679-702

[23] D. Vaynblat; M. Matalon Stability of pole solutions for planar propagating flames: II. properties of eigenvalues/eigenfunctions and implications to stability, SIAM Journal on Applied Mathematics, Volume 60 (2000) no. 2, pp. 703-728

[24] D. Garrido-Lopez; S. Sarkar Effects of imperfect premixing coupled with hydrodynamic instability on flame propagation, Proceedings of the Combustion Institute, Volume 30 (2005) no. 1, pp. 621-628

[25] V. Akkerman; V. Bychkov; L. Eriksson Numerical study of turbulent flame velocity, Combustion and Flame, Volume 151 (2007) no. 3, pp. 452-471

[26] N. Peters; H. Wenzel; F.A. Williams Modification of the turbulent burning velocity by gas expansion, Proceedings of the Combustion Institute, Volume 28 (2000) no. 1, pp. 235-243

[27] T.C. Treurniet; F.T.M. Nieuwstadt; B.J. Boersma Direct numerical simulation of homogeneous turbulence in combination with premixed combustion at low Mach number modelled by the G-equation, Journal of Fluid Mechanics, Volume 565 (2006), pp. 25-62

[28] H. Kobayashi; T. Tamura; K. Maruta; T. Niioka Burning velocity of turbulent premixed flames in a high pressure environment, Proceedings of the Combustion Institute, Volume 26 (1996), pp. 389-396

[29] R.N. Paul; K.N.C. Bray Study of premixed turbulent combustion including Landau–Darrieus instability effects, Proceedings of the Combustion Institute, Volume 26 (1996) no. 1, pp. 259-266

[30] H. Kobayashi; Y. Kawabata; K. Maruta Experimental study on general correlation of turbulent burning velocity at high pressure, Proceedings of the Combustion Institute, Volume 27 (1998), pp. 941-948

[31] Jean-Marie Truffaut; Geoff Searby Experimental study of the Darrieus–Landau instability on an inverted flame, and measurement of the Markstein number, Combustion Science and Technology, Volume 149 (1999) no. 1–6, pp. 35-52

[32] D. Bradley Instabilities and flame speeds in large-scale premixed gaseous explosions, Proceedings of the Royal Society A: Mathematical and Physical Sciences, Volume 357 (1999), pp. 3567-3581

[33] H. Kobayashi; H. Kawakoe Flame instability effects on the smallest wrinkling scale and burning velocity of high-pressure turbulent premixed flames, Proceedings of the Combustion Institute, Volume 28 (2000), pp. 375-382

[34] D. Bradley, M. Lawes, K. Liu, M.S. Mansour, Measurements and correlations of turbulent burning velocities over wide ranges of fuels and elevated pressures, Proceedings of the Combustion Institute (2012), in press, . | DOI

[35] A. Soika; F. Dinkelacker; A. Liepertz Pressure influence on the flame front curvature of turbulent premixed flames: Comparison between experiment and theory, Combustion and Flame, Volume 132 (2003), pp. 451-462

[36] G. Troiani, private communication, Agenzia Nazionale per le Nuove Tecnologie, Rome, Italy, 2012.

[37] N. Fogla, F. Creta, M. Matalon, Influence of the Darrieus–Landau instability on the propagation of planar turbulent flames, Proceedings of the Combustion Institute (2012), in press, . | DOI

[38] H. Kobayashi; K. Seyama; H. Hagiwara; Y. Ogami Burning velocity correlation of methane/air turbulent premixed flames at high pressure and high temperature, Proceedings of the Combustion Institute, Volume 30 (2005), pp. 827-834

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^☆ This article is dedicated to Paul Clavin for his distinctive contributions to flame theory, on the occasion of his 70th birthday.

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