Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-01-07T19:44:55.818Z Has data issue: false hasContentIssue false
  • English
  • Français

On transition to cellularity in expanding spherical flames

Published online by Cambridge University Press:  04 July 2007

G. JOMAAS ,
C. K. LAW  and
J. K. BECHTOLD
G. JOMAAS
Affiliation:
Princeton University, Princeton, NJ 08544, USA
C. K. LAW
Affiliation:
Princeton University, Princeton, NJ 08544, USA
J. K. BECHTOLD
Affiliation:
New Jersey Institute of Technology, Newark, NJ 07102, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The instant of transition to cellularity of centrally ignited, outwardly propagating spherical flames in a reactive environment of fuelx–oxidizer mixture, at atmospheric and elevated pressures, was experimentally determined using high-speed schlieren imaging and subsequently interpreted on the basis of hydrodynamic and diffusional–thermal instabilities. Experimental results show that the transition Péclet number, Pec = RcℓL, assumes an almost constant value for the near-equidiffusive acetylene flames with wide ranges in the mixture stoichiometry, oxygen concentration and pressure, where Rc is the flame radius at transition and ℓL the laminar flame thickness. However, for the non-equidiffusive hydrogen and propane flames, Pec respectively increases and decreases somewhat linearly with the mixture equivalence ratio. Evaluation of Pec using previous theory shows complete qualitative agreement and satisfactory quantitative agreement, demonstrating the insensitivity of Pec to all system parameters for equidiffusive mixtures, and the dominance of the Markstein number, Ze(Le – 1), in destabilization for non-equidiffusive mixtures, where Ze is the Zel'dovich number and Le the Lewis number. The importance of using locally evaluated values of ℓL, Ze and Le, extracted from either computationally simulated one-dimensional flame structure with detailed chemistry and transport, or experimentally determined response of stretched flames, in the evaluation of Pec is emphasized.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 583 , 25 July 2007 , pp. 1 - 26
Copyright
Copyright © Cambridge University Press 2007

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

Addabbo, R., Bechtold, J. K. & Matalon, M. 2002 Wrinkling of spherically expanding flames. Proc. Combust. Inst. 29, 1527–1535.Google Scholar
Bechtold, J. K. & Matalon, M. 1987 Hydrodynamic and diffusion effects on the stability of spherically expanding flames. Combust. Flame 67, 77–90.Google Scholar
Bechtold, J. K. & Matalon, M. 2001 The dependence of the Markstein length on stoichiometry. Combust. Flame 127, 1906–1913.Google Scholar
Bradley, D. 1999 Instabilities and flame speeds in large-scale premixed gaseous explosions. Phil. Trans. R. Soc. Lond. A 357, 3567–3581.CrossRefGoogle Scholar
Bradley, D. & Harper, C. M. 1994 The development of instabilities in laminar explosion flames. Combust. Flame 99, 562–572.CrossRefGoogle Scholar
Bradley, D., Sheppard, C. G. W., Woolley, R., Greenhalgh, D. A. & Lockett, R. D. 2000 The development and structure of flame instabilities and cellularity at low Markstein numbers in explosions. Combust. Flame 122, 195–209.Google Scholar
Clavin, P. 1985 Dynamic behavior of premixed flame fronts in laminar and turbulent flows. Prog. Energy Combust. Sci. 11, 1–59.Google Scholar
D'Angelo, G., Joulin, G. & Boury, G. 2000 On model evolution equations for the whole surface of three-dimensional expanding wrinkled premixed flames. Combust. Theory Modelling 4, 317–338.Google Scholar
Darrieus, G. 1938 Propagation d'un front de flamme. La Technique Moderne 30, no. 18.Google Scholar
Dowdy, D. R., Smith, D. B., Taylor, S. C. & Williams, A. 1990 The use of expanding spherical flames to determine burning velocities and stretch effects in hydrogen/air mixtures. Proc. Combust. Instit. 23, 325–333.Google Scholar
Egolfopoulos, F. N. & Law, C. K. 1990 Chain mechanisms in the overall reaction orders in laminar flame propagation. Combust. Flame 80, 7–16.Google Scholar
Groff, E. G. 1982 The cellular nature of confined spherical propane-air flames. Combust. Flame 48, 51–62.Google Scholar
Gu, X. J., Haq, M. Z., Lawes, M. & Woolley, R. 2000 Laminar burning velocity and Markstein lengths of methane-air mixtures. Combust. Flame 121, 41–58.Google Scholar
Jomaas, G. 2005 An experimental study on the laminar burning velocities and stability boundaries of outwardly propagating spherical flames. MSE thesis, Princeton University.Google Scholar
Jomaas, G., Zheng, X., Zhu, D. L., & Law, C. K. 2005 Experimental determination of counterflow ignition temperatures and laminar flame speeds of C2–C3 hydrocarbons at atmospheric and elevated pressures. Proc. Combust. Inst. 30, 193–200.Google Scholar
Karlin, V. & Sivashinsky, G. 2006 The rate of expansion of spherical flames. Combust. Theory Modelling 10, 625–637.Google Scholar
Kee, R. J., Grcar, J. F., Smooke, M. D. & Miller, J. A. 1985 A Fortran program for modeling steady laminar one-dimensional premixed flames. Sandia. Rep. SAND85-8240.Google Scholar
Kwon, O. C. & Faeth, G. M. 2001 Flame/stretch interactions of premixed hydrogen-fueled flames: measurements and predictions. Combust. Flame 124, 590–610.CrossRefGoogle Scholar
Kwon, O. C., Rozenchan, G. & Law, C. K. 2002 Cellular instabilities and self-acceleration of outwardly propagating spherical flames. Proc. Combust. Instit. 29, 1775–1784.Google Scholar
Landau, L. D. 1944 On the theory of slow combustion. Acta Physicochim. URSS 19, 77–85.Google Scholar
Law, C. K. 2006 Combustion Physics. Cambridge University Press.Google Scholar
Law, C. K. & Sung, C. J. 2000 Structure, aerodynamics, and geometry of premixed flamelets. Prog. Energy Combust. Sci. 26, 459–505.Google Scholar
Law, C. K., Cho, P., Mizomoto, M. & Yoshida, H. 1988 Flame curvature and preferential diffusion in the burning intensity of Bunsen flames. Proc. Combust. Instit. 21, 1803–1809.Google Scholar
Law, C. K., Jomaas, G. & Bechtold, J. K. 2005 Cellular instabilities of expanding hydrogen/propane spherical flames at elevated pressure: theory and experiment. Proc. Combust. Instit. 30, 159–167.CrossRefGoogle Scholar
Markstein, G. H. (ed.) 1964 Non-steady Flame Propagation. Pergamon.Google Scholar
Mueller, M. A., Kim, T. J., Yetter, R. A. & Dryer, F. L. 1999 Flow reactor studies and kinetic modeling of the H2/O2 reaction. Intl J. Chem. Kinet. 31, 113–125.3.0.CO;2-0>CrossRefGoogle Scholar
Poinsot, T. & Veynante, D. 2005 Theoretical and Numerical Combustion. R. T. Edwards, Flourtown.Google Scholar
Qin, Z., Lissianski, V., Yang, H., Gardiner, W. C., Davis, S. G. & Wang, H. 2000 Combustion chemistry of propane: a case study of detailed reaction mechanism optimization. Proc. Combust. Inst. 28, 1663–1669.Google Scholar
Rastigejev, Y. & Matalon, M. 2006 Nonlinear evolution of hydrodynamically unstable premixed flames. J. Fluid Mech. 554, 371–392.Google Scholar
Sivashinsky, G. I. 1977 Diffusional-thermal theory of cellular flames. Combust. Sci. Tech. 15, 137–146.Google Scholar
Sivashinsky, G. I. 1983 Instabilities, pattern formation, and turbulence in flames. Annu. Rev. Fluid Mech. 15, 179–199.CrossRefGoogle Scholar
Sivashinsky, G. I., Law, C. K. & Joulin, G. 1982 On stability of premixed flames in stagnation-point flow. Combust. Sci. Tech. 28, 155–159.Google Scholar
Sun, C. J., Sung, C. J., He, L. & Law, C. K. 1999 Dynamics of weakly stretched flames: quantitative description and extraction of global parameters. Combust. Flame 118, 108–128.Google Scholar
Tse, S. D., Zhu, D. L. & Law, C. K. 2000 Morphology and burning rates of expanding spherical flames in H2 O2 inert mixtures up to 60 atmospheres. Proc. Combust. Inst. 28, 1793–1799.Google Scholar
Tse, S. D., Zhu, D. L. & Law, C. K. 2004 An optically accessible high-pressure combustion apparatus. Rev. Sci. Instrum. 75, 233–239.CrossRefGoogle Scholar
Williams, F. A. 1985 Combustion Theory. Benjamin-Cummins.Google Scholar