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Detonation in supersonic radial outflow

Published online by Cambridge University Press:  07 November 2014

Aslan R. Kasimov  and
Svyatoslav V. Korneev
Aslan R. Kasimov*
Affiliation:
Applied Mathematics and Computational Science, King Abdullah University of Science and Technology, Room 4-2226, 4700 KAUST, Thuwal 23955-6900, Saudi Arabia
Svyatoslav V. Korneev
Affiliation:
Applied Mathematics and Computational Science, King Abdullah University of Science and Technology, Room 4-2226, 4700 KAUST, Thuwal 23955-6900, Saudi Arabia
*
†Email address for correspondence: aslan.kasimov@kaust.edu.sa
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Abstract

We report on the structure and dynamics of gaseous detonation stabilized in a supersonic flow emanating radially from a central source. The steady-state solutions are computed and their range of existence is investigated. Two-dimensional simulations are carried out in order to explore the stability of the steady-state solutions. It is found that both collapsing and expanding two-dimensional cellular detonations exist. The latter can be stabilized by putting several rigid obstacles in the flow downstream of the steady-state sonic locus. The problem of initiation of standing detonation stabilized in the radial flow is also investigated numerically.

JFM classification

Compressible Flows: Detonation waves Reacting Flows: Detonations Reacting Flows: Reacting Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 760 , 10 December 2014 , pp. 313 - 341
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Copyright
© 2014 Cambridge University Press 

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References

Bdzil, J. B. & Stewart, D. S. 2012 Theory of detonation shock dynamics. In Shock Waves Science and Technology Library (ed. Zhang, F.), vol. 6, pp. 373–453. Springer.Google Scholar
Bykovskii, F. A., Mitrofanov, V. V. & Vedernikov, E. F. 1997 Continuous detonation combustion of fuel–air mixtures. Combust. Explos. Shock Waves 33 (3), 344–353.Google Scholar
Bykovskii, F. A., Zhdan, S. A. & Vedernikov, E. F. 2006 Continuous spin detonations. J. Propul. Power 22 (6), 1204–1216.Google Scholar
Dadone, A. 1998 Symmetry techniques for the numerical solution of the 2D Euler equations at impermeable boundaries. Intl J. Numer. Meth. Fluids 28 (7), 1093–1108.Google Scholar
Döring, W. 1943 Uber den Detonationvorgang in Gasen. Ann. Phys. 43 (6–7), 421–428.Google Scholar
Fickett, W. & Davis, W. C. 2011 Detonation: Theory and Experiment. Dover.Google Scholar
Gottlieb, S. & Shu, C.-W. 1998 Total variation diminishing Runge–Kutta schemes. Maths Comput. 67 (221), 73–85.Google Scholar
Hu, X. Y., Adams, N. A. & Shu, C.-W.2012 Positivity-preserving flux limiters for high-order conservative schemes. Preprint arXiv:1203.1540.Google Scholar
Jones, J. 1991 The spherical detonation. Adv. Appl. Maths 12 (2), 147–186.Google Scholar
Kailasanath, K. 2000 Review of propulsion applications of detonation waves. AIAA J. 38 (9), 1698–1708.Google Scholar
Kasimov, A. R. & Stewart, D. S. 2005 Asymptotic theory of evolution and failure of self-sustained detonations. J. Fluid Mech. 525, 161–192.CrossRefGoogle Scholar
Khasainov, B. A. & Veyssiere, B.2013 Standard mathematical model of detonation and physical reality. In 24th International Colloquium on the Dynamics of Explosions and Reactive Systems, Taipei, Taiwan.Google Scholar
Klein, R. & Stewart, D. S. 1993 The relation between curvature, rate state-dependence, and detonation velocity. SIAM J. Appl. Maths 53 (5), 1401–1435.Google Scholar
Landau, L. D. & Lifshits, E. M. 1960 Course of Theoretical Physics: Mechanics. Pergamon.Google Scholar
Lee, J. H. S. 2008 The Detonation Phenomenon. Cambridge University Press.CrossRefGoogle Scholar
Liu, X.-D., Osher, S. & Chan, T. 1994 Weighted essentially non-oscillatory schemes. J. Comput. Phys. 115 (1), 200–212.Google Scholar
von Neumann, J.1942 Theory of detonation waves. Office of Scientific Research and Development Rep. 549. National Defense Research Committee Div. B.Google Scholar
Nicholls, J. A. & Dabora, E. K. 1961 Recent results on standing detonation waves. In Symposium (International) on Combustion, vol. 8, pp. 644–655. Elsevier.Google Scholar
Roy, G. D., Frolov, S. M., Borisov, A. A. & Netzer, D. W. 2004 Pulse detonation propulsion: challenges, current status, and future prospects. Prog. Energy Combust. Sci. 30 (6), 545–672.Google Scholar
Rubins, P. M. & Bauer, R. C. 1994 Review of shock-induced supersonic combustion research and hypersonic applications. J. Propul. Power 10 (5), 593–601.Google Scholar
Soloukhin, R. I. 1966 Shock Waves and Detonations in Gases. Mono Book Corporation.Google Scholar
Stewart, D. S. & Kasimov, A. R. 2006 State of detonation stability theory and its application to propulsion. J. Propul. Power 22 (6), 1230–1244.CrossRefGoogle Scholar
Taylor, B. D., Kasimov, A. R. & Stewart, D. S. 2009 Mode selection in unstable two-dimensional detonations. Combust. Theor. Model. 13 (6), 973–992.Google Scholar
Vasil’ev, A. A., Zvegintsev, V. I. & Nalivaichenko, D. G. 2006 Detonation waves in a reactive supersonic flow. Combust. Explos. Shock Waves 42 (5), 568–581.CrossRefGoogle Scholar
Voitsekhovskii, B. V., Mitrofanov, V. V. & Topchian, M. Y.1966 The structure of detonation front in gases. Rep. FTD-MTD-64-527. Foreign Technology Division, Wright Patterson Air Force Base, OH (AD 633-821).Google Scholar
Wintenberger, E.2004 Application of steady and unsteady detonation waves to propulsion. PhD thesis, California Institute of Technology.Google Scholar
Wintenberger, E. & Shepherd, J. E.2003 The performance of steady detonation engines. AIAA Paper 2003–0714, 41st Aerospace Sciences Meeting and Exhibit, Reno, Nevada.Google Scholar
Wolański, P. 2013 Detonative propulsion. Proc. Combust. Inst. 34 (1), 125–158.Google Scholar
Zel’dovich, Y. B. 1940 On the theory of propagation of detonation in gaseous systems. J. Expl Theor. Phys. 10 (5), 542–569.Google Scholar
Zel’dovich, Y. B. & Kompaneets, A. S. 1960 Theory of Detonation. Academic.Google Scholar
Zhang, F.(Ed.) 2012 Shock Waves Science and Technology Library, Vol. 6: Detonation Dynamics. Springer.Google Scholar
Zhang, F., Chue, R. S., Frost, D. L., Lee, J. H. S., Thibault, P. & Yee, C. 1995 Effects of area change and friction on detonation stability in supersonic ducts. Proc. R. Soc. Lond. A 449 (1935), 31–49.Google Scholar
Zhuravskaya, T. A. & Levin, V. A. 2012 Investigation of certain techniques for stabilizing detonation waves in a supersonic flow. Fluid Dyn. 47 (6), 793–801.Google Scholar