Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-21T16:46:35.708Z Has data issue: false hasContentIssue false
  • English
  • Français

Propagation of wrinkled turbulent flames in the context of hydrodynamic theory

Published online by Cambridge University Press:  01 June 2011

F. CRETA  and
M. MATALON
F. CRETA*
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
M. MATALON
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the propagation of premixed flames in two-dimensional homogeneous isotropic turbulence using a Navier–Stokes/front-capturing methodology within the context of hydrodynamic theory. The flame is treated as a thin layer separating burnt and unburnt gases, of vanishingly small thickness, smaller than the smallest fluid scales. The method is thus suitable to investigate the flame propagation in the wrinkled flamelet regime of turbulent combustion. A flow-control system regulates the mean position of the flame and the incident turbulence intensity. In this context we study the individual effects of turbulence intensity, turbulence scale, thermal expansion, hydrodynamic strain and hydrodynamic instability on the propagation characteristics of the flame. Results are obtained assuming positive Markstein length, corresponding to lean hydrocarbon–air or rich hydrogen–air mixtures. For stable planar flames we find a quadratic dependence of turbulent speed on turbulence intensity. Upon onset of hydrodynamic instability, corrugated structures replace the planar conformation and we observe a greater resilience to turbulence, the quadratic scaling being replaced by scaling exponents less than one. Such resilience is also confirmed by the observation of a threshold turbulence intensity below which the propagation speed of corrugated flames is indistinguishable from the laminar speed. Turbulent speed is found to increase and later plateau with increasing thermal expansion, this affecting the average flame displacement but not the mean flame curvature. In addition, turbulence integral scale is also observed to affect the propagation of the flame with the existence of an intermediate scale maximizing the turbulent speed. This maximizing scale is smaller for corrugated flames than it is for planar flames, implying that small eddies that will be unable to significantly perturb a planar front could be rather effective in perturbing a corrugated flame. Turbulent planar flames, and more so corrugated flames, were observed to experience a positive mean hydrodynamic strain, which was explained in terms of the overwhelming mean contribution of the normal component of strain. The positive straining causes a decrease in the mean laminar propagation speed which in turn can decrease the turbulent speed. The effect of the flame on the incident turbulent field was examined in terms of loss of isotropy and vorticity destruction by thermal expansion. The latter can be mitigated by a baroclinic vorticity generation which is enhanced for corrugated flames.

JFM classification

Reacting Flows: Flames Reacting Flows: Turbulent reacting flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 680 , 10 August 2011 , pp. 225 - 264
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abdel-Gayed, R. G., Bradley, D. & Lawes, M. 1987 Turbulent burning velocities: a general correlation in terms of straining rates. Proc. R. Soc. Lond. A 414, 389–413.Google Scholar
Aldredge, R. C. & Williams, F. A. 1991 Influence of wrinkled premixed-flame dynamics on large-scale, low intensity turbulent flow. J. Fluid Mech. 228, 487–511.Google Scholar
Almgren, A. S., Bell, J. B., Colella, P., Howell, L. H. & Welcome, M. L. 1998 A conservative adaptive projection method for the variable density incompressible Navier–Stokes equations. J. Comput. Phys. 142, 1–46.CrossRefGoogle Scholar
Ballal, D. R. & Lefebvre, A. H. 1974 Turbulence effects on enclosed flames. Acta Astron. 1, 471–483.CrossRefGoogle Scholar
Baum, M., Poinsot, T. J., Haworth, D. C. & Darabiha, N. 1994 Direct numerical simulation of H2/O2/N2 flames with complex chemistry in two-dimensional turbulent flows. J. Fluid Mech. 281, 1–32.CrossRefGoogle Scholar
Borghi, R. 1985 On the structure and morphology of turbulent premixed flames. In Recent Advances in the Aerospace Sciences, pp. 117–138. Plenum.CrossRefGoogle Scholar
Bradley, D., Gaskell, P. H. & Gu, X. J. 1994 Application of a Reynolds stress, stretched flamelet, mathematical model to computations of turbulent burning velocities and comparison with experiments. Combust. Flame 96, 221–248.CrossRefGoogle Scholar
Bray, K. N. C. 1980 Turbulent flows with premixed reactants. In Turbulent Reacting Flows (ed. Williams, F. A. & Libby, P. A.), chapter 4, pp. 115–138. Springer.CrossRefGoogle Scholar
Bray, K. N. C. 1996 The challenge of turbulent combustion. Proc. Combust. Inst. 26, 1–26.CrossRefGoogle Scholar
Cambray, P. & Joulin, G. 1992 On moderately-forced premixed flames. Proc. Combust. Inst. 24, 61–67.CrossRefGoogle Scholar
Chen, J. H., Hawkes, E. R., Sankaran, R., Mason, S. D. & Im, H. G. 2006 Direct numerical simulation of ignition front propagation in a constant volume with temperature inhomogeneities. I. Fundamental analysis and diagnostics. Combust. Flame 145, 128–144.CrossRefGoogle Scholar
Chen, J. H. & Im, H. G. 2000 Stretch effects on the burning velocity of turbulent premixed hydrogen/air flames. Proc. Combust. Inst. 28, 211–218.CrossRefGoogle Scholar
Clavin, P. & Williams, F. A. 1979 Theory of premixed-flame propagation in large-scale turbulence. J. Fluid Mech. 90, 589–604.CrossRefGoogle Scholar
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 scales and low intensity. J. Fluid Mech. 116, 251–282.CrossRefGoogle Scholar
Creta, F., Fogla, N. & Matalon, M. 2011 Turbulent propagation of premixed flames in the presence of Darrieus–Landau instability. Combust. Theory Model. 15 (2), 267–298.Google Scholar
Creta, F. & Matalon, M. 2011 Strain rate effects on the nonlinear development of hydrodynamically unstable flames. Proc. Combust. Inst. 33, 1087–1094.CrossRefGoogle Scholar
Damköhler, G. 1940 Der Einfluss der Turbulenz auf die Flammengeschwindigkeit in Gasgemischen. Z. Elektrochem. 46, 601–652.Google Scholar
Darrieus, G. 1938 Propagation d'un front de flamme. Unpublished work, presented at La Technique Moderne (Paris), and in 1945 at Congrès de Mećanique Appliqueé (Paris).Google Scholar
Driscoll, J. F. 2008 Turbulent premixed combustion: Flamelet structure and its effect on turbulent burning velocities. Prog. Energy Combust. Sci. 34, 91–134.CrossRefGoogle Scholar
Filatyev, S. A., Driscoll, J. F., Carter, C. D. & Donbar, J. M. 2005 Measured properties of turbulent premixed flames for model assessment, including burning velocities, stretch rates, and surface densities. Combust. Flame 141, 1–21.CrossRefGoogle Scholar
Ghenai, G., Gouldin, F. C. & Gökalp, I. 1998 Mass flux measurements for burning rate determination of premixed turbulent flames. Proc. Combust. Inst. 27, 979–987.CrossRefGoogle Scholar
Girimaji, S. S. & Pope, S. B. 1992 Propagating surfaces in isotropic turbulence. J. Fluid Mech. 234, 247–277.CrossRefGoogle Scholar
Haworth, D. C. & Poinsot, T. J. 1992 Numerical simulations of Lewis number effects in turbulent premixed flames. J. Fluid Mech. 244, 405–436.CrossRefGoogle Scholar
Hinze, J. O. 1975 Turbulence, 2nd edn. McGraw-Hill.Google Scholar
Im, H. G. & Chen, J. H. 2002 Preferential diffusion effects on the burning rate of interacting turbulent premixed hydrogen–air flames. Combust. Flame 131, 246–258.CrossRefGoogle Scholar
Kardar, M., Parisi, G. & Zhang, Y. 1986 Dynamic scaling of growing interfaces. Phys. Rev. Lett. 56 (9), 889–892.CrossRefGoogle ScholarPubMed
Karlin, V. 2006 Pseudoresonant interaction between flame and upstream velocity fluctuations. Phys. Rev. E 73, 016305.Google ScholarPubMed
Kerstein, A. R., Ashurst, W. T. & Williams, F. A. 1988 Field equations for interface propagation in an unsteady homogeneous flowfield. Phys. Rev. A 37, 2728–2731.CrossRefGoogle Scholar
Klimenko, A. Y. & Bilger, R. W. 1999 Conditional moment closure for turbulent combustion. Prog. Energy Combust. Sci. 25, 597–687.CrossRefGoogle Scholar
Kobayashi, H., Kawabata, Y. & Maruta, K. 1998 Experimental study on general correlation of turbulent burning velocity at high pressure. Proc. Combust. Inst. 27, 941–948.CrossRefGoogle Scholar
Kobayashi, H., Seyama, K., Hagiwara, H. & Ogami, Y. 2005 Burning velocity correlation of methane/air turbulent premixed flames at high pressure and high temperature. Proc. Combust. Inst. 30, 827–834.CrossRefGoogle Scholar
Kobayashi, H., Tamura, T., Maruta, K. & Niioka, T. 1996 Burning velocity of turbulent premixed flames in a high pressure environment. Proc. Combust. Inst. 26, 389–396.CrossRefGoogle Scholar
Landau, L. D. 1944 On the theory of slow combustion. Acta Physicochim. USSR 19, 77–85.Google Scholar
Launder, B. E., Reece, G. J. & Rodi, W. 1975 Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech. 68, 537–566.CrossRefGoogle Scholar
Lee, T.-W., North, G. L. & Santavicca, D. A. 1992 Curvature and orientation statistics of turbulent premixed flame fronts. Combust. Sci. Tech. 84, 121–132.CrossRefGoogle Scholar
Lipatnikov, A. N. & Chomiak, J. 2002 Turbulent flame speed and thickness: phenomenology, evaluation, and application in multi-dimensional simulations. Prog. Energy Combust. Sci. 28, 1–74.Google Scholar
Markstein, G. H. 1964 Nonsteady Flame Propagation. Macmillan.Google Scholar
Matalon, M., Cui, C. & Bechtold, J. K. 2003 Hydrodynamic theory of premixed flames: effects of stoichiometry, variable transport coefficients and arbitrary reaction orders. J. Fluid Mech. 487, 179–210.CrossRefGoogle Scholar
Matalon, M. & Matkowsky, B. J. 1982 Flames as gasdynamic discontinuities. J. Fluid Mech. 128, 239–259.CrossRefGoogle Scholar
Meneveau, C. & Poinsot, T. 1991 Stretching and quenching of flamelets in premixed turbulent combustion. Combust. Flame 86, 311–332.CrossRefGoogle Scholar
Michelson, D. M. & Sivashinsky, G. I. 1977 Nonlinear analysis of hydrodynamic instability in laminar flames. II. Numerical experiments. Acta Astron. 4, 1207–1221.CrossRefGoogle Scholar
Mueller, C. J., Driscoll, J. F., Reuss, D. L., Drake, M. C. & Rosalik, M. E. 1998 Vorticity generation and attenuation as vortices convect through a premixed flame. Combust. Flame 112, 342–358.CrossRefGoogle Scholar
Orszag, S. A. & Patterson, G. S. 1972 Numerical simulation of three-dimensional homogeneous isotropic turbulence. Phys. Rev. Lett. 28 (2), 251–282.CrossRefGoogle Scholar
Peters, N. 1986 Laminar flamelet concepts in turbulent combustion. Proc. Combust. Inst. 21, 1231–1250.CrossRefGoogle Scholar
Peters, N. 1992 A spectral closure for premixed turbulent combustion in the flamelet regime. J. Fluid Mech. 242, 611–629.CrossRefGoogle Scholar
Peters, N. 1999 The turbulent burning velocity for large-scale and small-scale turbulence. J. Fluid Mech. 384, 107–132.CrossRefGoogle Scholar
Peters, N. 2000 Turbulent Combustion. Cambridge University Press.CrossRefGoogle Scholar
Peters, N., Wenzel, H. & Williams, F. A. 2000 Modification of the turbulent burning velocity by gas expansion. Proc. Combust. Inst. 28, 235–243.CrossRefGoogle Scholar
Pitsch, H. & Duchamp De Lageneste, L. 2002 Large-eddy simulation of premixed turbulent combustion using a level-set approach. Proc. Combust. Inst. 29, 2001–2008.CrossRefGoogle Scholar
Plessing, T., Kortschik, C., Peters, N., Mansour, M. S. & Cheng, R. K. 2000 Measurements of the turbulent burning velocity and the structure of premixed flames on a low-swirl burner. Proc. Combust. Inst. 28, 359–366.CrossRefGoogle Scholar
Poinsot, T. J., Veynante, D. & Candel, S. 1991 Quenching processes and premixed turbulent combustion diagrams. J. Fluid Mech. 228, 561–606.Google Scholar
Poludnenko, A. Y. & Oran, E. S. The interaction of high-speed turbulence with flames: Global 2010 properties and internal flame structure. Combust. Flame 157, 995–1011.CrossRefGoogle Scholar
Pope, S. B. 1985 Pdf methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11 (2), 119–192.CrossRefGoogle Scholar
Pope, S. B. 1987 Turbulent premixed flames. Annu. Rev. Fluid Mech. 19, 237–270.CrossRefGoogle Scholar
Rastigejev, Y. & Matalon, M. 2006 a Numerical simulation of flames as gas-dynamic discontinuities. Combust. Theory Model. 10 (3), 459–481.CrossRefGoogle Scholar
Rastigejev, Y. & Matalon, M. 2006 b Nonlinear evolution of hydrodynamically unstable premixed flames. J. Fluid Mech. 554, 371–392.CrossRefGoogle Scholar
Ronney, P. D. 1994 In Modeling in Combustion Science (ed. Takeno, T. & Buckmaster, J.), p. 3. Springer.Google Scholar
Shelkin, K. I. 1947 On combustion in a turbulent flow. NACA TM, 1110.Google Scholar
Shepherd, I. G., Cheng, R. K., Plessing, T., Kortschik, C. & Peters, N. 2002 Premixed flame front structure in intense turbulence. Proc. Combust. Inst. 29, 1833–1840.CrossRefGoogle Scholar
Sivashinsky, G. I. 1977 Nonlinear analysis of hydrodynamic instability in laminar flames. I. derivation of basic equations. Acta Astron. 4, 1177–1206.CrossRefGoogle Scholar
Thual, O., Frisch, U. & Heńon, M. 1985 Application of pole decomposition to an equation governing the dynamics of wrinkled flame fronts. J. Phys. 46, 1485–1494.CrossRefGoogle Scholar
Vaynblat, D. & Matalon, M. 2000 a Stability of pole solutions for planar propagating flames. I. Exact eigenvalues and eigenfinctions. SIAM J. Appl. Maths 60 (2), 679–702.CrossRefGoogle Scholar
Vaynblat, D. & Matalon, M. 2000 b Stability of pole solutions for planar propagating flames. II. Properties of eigenvalues/eigenfunctions and implications to stability. SIAM J. Appl. Maths 60 (2), 703–728.CrossRefGoogle Scholar
Vervisch, L., Bidaux, E., Bray, K. N. C. & Kollmann, W. 1995 Surface density function in premixed turbulent combustion modeling, similarities between probability density function and flame surface approaches. Phys. Fluids 7 (10), 2496–2503.CrossRefGoogle Scholar
Williams, F. A. 1985 Combustion Theory, 2nd ed. Benjamin/Cummings.Google Scholar
Yoo, C. S., Sankaran, R. & Chen, J. H. 2009 Three-dimensional direct numerical simulation of a turbulent lifted hydrogen jet flame in heated coflow: flame stabilization and structure. J. Fluid Mech. 640, 453–481.CrossRefGoogle Scholar