Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-02-05T07:35:43.052Z Has data issue: false hasContentIssue false
  • English
  • Français

The hydrodynamic structure of unstable cellular detonations

Published online by Cambridge University Press:  21 May 2007

MATEI I. RADULESCU ,
GARY J. SHARPE ,
CHUNG K. LAW  and
JOHN H. S. LEE
MATEI I. RADULESCU*
Affiliation:
Princeton University, Princeton, NJ, USA
GARY J. SHARPE
Affiliation:
School of Mechanical Engineering, University of Leeds, Leeds, UK
CHUNG K. LAW
Affiliation:
Princeton University, Princeton, NJ, USA
JOHN H. S. LEE
Affiliation:
McGill University, Canada
*
†Author to whom correspondence should be addressed.
Get access Rights & Permissions [Opens in a new window]

Abstract

The study analyses the cellular reaction zone structure of unstable methane–oxygen detonations, which are characterized by large hydrodynamic fluctuations and unreacted pockets with a fine structure. Complementary series of experiments and numerical simulations are presented, which illustrate the important role of hydrodynamic instabilities and diffusive phenomena in dictating the global reaction rate in detonations. The quantitative comparison between experiment and numerics also permits identification of the current limitations of numerical simulations in capturing these effects. Simulations are also performed for parameters corresponding to weakly unstable cellular detonations, which are used for comparison and validation. The numerical and experimental results are used to guide the formulation of a stochastic steady one-dimensional representation for such detonation waves. The numerically obtained flow fields were Favre-averaged in time and space. The resulting one-dimensional profiles for the mean values and fluctuations reveal the two important length scales, the first being associated with the chemical exothermicity and the second (the ‘hydrodynamic thickness’) with the slower dissipation of the hydrodynamic fluctuations, which govern the location of the average sonic surface. This second length scale is found to be much longer than that predicted by one-dimensional reaction zone calculations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 580 , 10 June 2007 , pp. 31 - 81
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.)

Footnotes

Present address: Mechanical Engineering, University of Ottawa, 161 Louis Pasteur, Ottawa, Ontario, K1N 6N5, Canada, [email protected]

References

REFERENCES

Arienti, M. & Shepherd, J. E. 2005 The role of diffusion in irregular detonations. The 4th Joint Meeting of the US Sections of the Combustion Institute, Philadelphia, PA, March 20–23. Google Scholar
Austin, J. 2003 The role of instability in gaseous detonation. PhD thesis, California Institute of Technology, Pasadena, California.Google Scholar
Austin, J. M., Pintgen, F. & Shepherd, J. E. 2005 Reaction zones in highly unstable detonations. Proc. Combust. Inst. 30, 1849–1857.CrossRefGoogle Scholar
Bourlioux, A. & Majda, A. J. 1992 Theoretical and numerical structure for unstable two dimensional detonations. Combust. Flame 90, 211–229.CrossRefGoogle Scholar
Deiterding, R. 2003 Parallel adaptive simulation of multi-dimensional detonation structures. PhD thesis, Brandenburgischen Technischen Universität Cottbus.Google Scholar
Deledicque, V. & Papalexandris, M. V. 2006 Computational study of three-dimensional gaseous detonation structures. Combust. Flame 144, 821–837.CrossRefGoogle Scholar
Edwards, D. H., Hooper, G., Job, E. M. & Parry, D. J. 1970 The behavior of the frontal and transverse shocks in gaseous detonation waves. Astronaut. Acta 15, 323–333.Google Scholar
Edwards, D. H., Jones, A. J. & Phillips, D. E. 1976 Location of Chapman – Jouguet surface in a multiheaded detonation-wave. J. Phys. D 9, 1331–1342.CrossRefGoogle Scholar
Edwards, D. H., Jones, T. G. & Price, B. 1963 Observations on oblique shock waves in gaseous detonations. J. Fluid Mech. 17, 21–34.CrossRefGoogle Scholar
Eto, K., Tsuboi, N. & Hayashi, A. K. 2005 Numerical study on three-dimensional C-J detonation waves: detailed propagating mechanism and existence of OH radical. Proc. Combust. Inst. 30, 1907–1913.CrossRefGoogle Scholar
Falle, S. A. E. G. 1991 Self-similar jets. Mon. Not. R. Astron. Soc. 250, 581–596.CrossRefGoogle Scholar
Falle, S. A. E. G. & Giddings, J. R. 1993 Body capturing. In Numerical Methods for Fluid Dynamics (ed. Morton, K. W. & Baines, M. J.), vol. 4, pp. 337–343. Clarendon.Google Scholar
Falle, S. A. E. G. & Komissarov, S. S. 1996 An upwind scheme for relativistic hydrodynamics with a general equation of state. Mon. Not. R. Astron. Soc. 278, 586–602.CrossRefGoogle Scholar
Favre, A. 1965 Equations des gas turbulents compressibles. J. Méc. 4, 361–421.Google Scholar
Fickett, W. & Davis, W. C. 1979 Detonation. University of California Press.Google Scholar
Frisch, U. 1995 Turbulence. Cambridge University Press.CrossRefGoogle Scholar
Gamezo, V. N., Desbordes, D. & Oran, E. S. 1999 Formation and evolution of two-dimensional cellular detonations. Combust. Flame 116, 154–165.CrossRefGoogle Scholar
Gordon, S. & McBride, B. J. 1994 Computer program for calculation of complex chemical equilibrium compositions and applications. NASA RP-1311.Google Scholar
Henrick, A. K., Aslam, T. D. & Powers, J. M. 2006 Simulations of pulsating one-dimensional detonations with true fifth order accuracy. J. Comput. Phys. 213, 311–329.CrossRefGoogle Scholar
Hu, X. Y., Zhang, D. L., Khoo, B. C. & Jiang, Z. L. 2005 The structure and evolution of a two-dimensional H-2/O-2/Ar cellular detonation. Shock Waves 14, 37–44.CrossRefGoogle Scholar
Inaba, K., Matsuo, A. & Tanaka, K. 2005 Numerical investigation on acoustic coupling of transverse waves in two-dimensional H-2-O-2-diluent detonations. Trans. Japan Soc. Aero. Space Sci. 47 (158), 249–255.CrossRefGoogle Scholar
Kasimov, A. R. & Stewart, D. S. 2004 On the dynamics of self-sustained one-dimensional detonations: a numerical study in the shock-attached frame. Phys. Fluids 16, 3566–3578.CrossRefGoogle Scholar
Khokhlov, A. M., Oran, E. S. & Thomas, G. O. 1999 Numerical simulation of deflagration-to-detonation transition: the role of shock–flame interactions in turbulent flames. Combust. Flame 117, 323–339.CrossRefGoogle Scholar
Kistiakowsky, G. B. & Kydd, P. H. 1956 Gaseous detonations. IX. A study of the reaction zone by gas density measurements. J. Chem. Phys. 25, 824–835.CrossRefGoogle Scholar
Kiyanda, C. B. 2005 Photographic study of the structure of irregular detonation waves. Master's thesis, McGill University, Montreal, Canada.Google Scholar
Kiyanda, C. B., Higgins, A. J. & Lee, J. H. S. 2005 Photographic study of the two-Dimensional dynamics of irregular detonation waves. Paper presented at the 20th Intl Colloquium on the Dynamics of Explosions and Reactive Systems, Montreal, Canada, July 31–August 5 (on CD-ROM).Google Scholar
Laberge, S., Knystautas, R. & Lee, J. H. S. 1993 Propagation and extinction of detonation waves in tube bundles. Prog. Astro. Aero. 153, 381–396.Google Scholar
Lee, J. H. 1984 Dynamic parameters of gaseous detonations. Annu. Rev. Fluid. Mech. 16, 311–336.CrossRefGoogle Scholar
Lee, J. H. S. & Radulescu, M. I. 2005 On the hydrodynamic thickness of cellular detonations. Fizika Goreniya i Vzryva, 41 (6), 157–180 (in Russian), translated in Combust. Explo. Shock Waves 41 (6), 745–765.Google Scholar
Lutz, A. E., Kee, R. J., Miller, J. A., Dwyer, H. A. & Oppenheim, A. K. 1988 Dynamic effects of autoignition centers for hydrogen and C1,2-hydrocarbon fuels. Proc. Combust. Inst. 22, 1683–1693.CrossRefGoogle Scholar
Manzhalei, V. I. 1977 Fine structure of the leading front of a gas detonation. Fizika Goreniya I Vzryva 13, 470–472 (in Russian). Translated in Combust. Explo. Shock Waves 13(3), 402–404.Google Scholar
Ng, H. D., Higgins, A. J., Kiyanda, C. B., Radulescu, M. I., Lee, J.H. S., Bates, K. R. & Nikiforakis, N. 2005 a Nonlinear dynamics and chaos analysis of one-dimensional pulsating detonations. Combust. Theory Modell. 9, 159–170.CrossRefGoogle Scholar
Ng, H. D., Radulescu, M. I., Higgins, A. J., Nikiforakis, N. & Lee, J. H. S. 2005 b Numerical investigation of the instability for one-dimensional Chapman-Jouguet detonations with chain-branching kinetics. Combust. Theory Modell. 9, 385–401.CrossRefGoogle Scholar
Nikolaev, Yu. A. & Zak, D. V. 1989 Quasi-one-dimensional model of self-sustaining multifront gas detonation with losses and turbulence taken into account. Combust. Explo. Shock Waves 25, 103–112.CrossRefGoogle Scholar
Oran, E. S., Weber, J. W., Stefaniw, E. I., Lefebvre, M. H. & Anderson, J. D. 1998 A numerical study of a two-dimensional H-2-O-2-Ar detonation using a detailed chemical reaction model. Combust. Flame 113, 147–163.CrossRefGoogle Scholar
Oran, E. S., Young, T. R., Boris, J. P., Picone, J. M. & Edwards, D. H. 1982 A study of detonation structure: the formation of unreacted pockets. In Nineteenth Symp. (Intl) on Combustion, pp. 573–582. Pittsburgh: the Combustion Institute.Google Scholar
Panton, R. 1971 Effects of structure on average properties of two-dimensional detonations. Combust. Flame 16, 75–82.CrossRefGoogle Scholar
Peters, N. 2000 Turbulent Combustion. Cambridge University Press.CrossRefGoogle Scholar
Pintgen, F., Eckett, C. A., Austin, J. M. & Shepherd, J. E. 2003 Direct observations of reaction zone structure in propagating detonations. Combust. Flame 133, 211–229.CrossRefGoogle Scholar
Quirk, J. J. 1994 Godunov-type schemes applied to detonation flows. In Combustion in High Speed Flows (ed. Buckmaster, J., Jackson, T. L. & Kumar, A.), pp. 575–596. Kluwer.CrossRefGoogle Scholar
Radulescu, M. I. 2003 The propagation and failure mechanism of gaseous detonations: experiments in porous-walled tubes. PhD thesis, McGill University, Montreal, Canada.Google Scholar
Radulescu, M. I. & Lee, J. H. S. 2002 The failure mechanism of gaseous detonations: experiments in porous wall tubes. Combust. Flame 131, 29–46.CrossRefGoogle Scholar
Radulescu, M. I., Sharpe, G. J., Lee, J. H. S., Kiyanda, C., Higgins, A. J. & Hanson, R. K. 2005 The ignition mechanism in irregular structure gaseous detonations. Proc. Combust. Inst. 30, 1859–1867.CrossRefGoogle Scholar
Rybanin, S. S. 1966 Turbulence in detonations. Combust. Explo. Shock Waves 2, 29–35.Google Scholar
Sharpe, G. J. 2001 Transverse waves in numerical simulations of cellular detonations. J. Fluid Mech. 447, 31–51.CrossRefGoogle Scholar
Sharpe, G. J. & Falle, S. A. E. G. 2000. Two-dimensional numerical simulations of idealized detonations. Proc. R. Soc. Lond. A 456, 2081–2100.CrossRefGoogle Scholar
Shepherd, J. E. 1986 Chemical kinetics of hydrogen-air-diluent mixtures. Prog. Astro. Aero. 106, 263–293.Google Scholar
Soloukhin, R. I. 1966 Multiheaded structure of gaseous detonation. Combust. Flame 10, 51–58.CrossRefGoogle Scholar
Strehlow, R. A. 1971 Detonation structure and gross properties. Combust. Sci. Tech. 4, 65–71.CrossRefGoogle Scholar
Subbotin, V. 1975 a Two kinds of transverse wave structures in multi-front detonation. Combust. Explo. Shock Waves 11, 96–102.Google Scholar
Subbotin, V. 1975 b Collision of transverse detonation waves in gases. Combust. Explo. Shock Waves 11, 411–414.CrossRefGoogle Scholar
Svehla, R. A. 1995 Transport coefficients for the NASA chemical equilibrium program. NASA TM 4647.Google Scholar
Taylor, G. I. 1950 The dynamics of the combustion products behind plane and spherical detonation fronts in explosives. Proc. R. Soc. Lond. A 200, 235–247.Google Scholar
Thomas, G. O. & Edwards, D. H. 1983 Simulation of detonation cell kinematics using two-dimensional reactive blast waves. J. Phys. D 16, 1881–1892.CrossRefGoogle Scholar
Voitsekhovskii, B. V., Mitrofanov, V. V. & Topchian, M. E. 1963 Structure of a detonation front in gases. Izd. Akad. Nauk SSSR, Novosibirsk.Google Scholar
White, D. R. 1961 Turbulent structure of gaseous detonation. Phys. Fluids 4, 465–480.CrossRefGoogle Scholar
Williams, F. A. 1985 Combustion Theory, 2nd Edn. Perseus Books Publishing.Google Scholar