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Detonation in supersonic radial outflow

  • Aslan R. Kasimov (a1) and Svyatoslav V. Korneev (a1)

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.

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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. 373453. Springer.
Bykovskii, F. A., Mitrofanov, V. V. & Vedernikov, E. F. 1997 Continuous detonation combustion of fuel–air mixtures. Combust. Explos. Shock Waves 33 (3), 344353.
Bykovskii, F. A., Zhdan, S. A. & Vedernikov, E. F. 2006 Continuous spin detonations. J. Propul. Power 22 (6), 12041216.
Dadone, A. 1998 Symmetry techniques for the numerical solution of the 2D Euler equations at impermeable boundaries. Intl J. Numer. Meth. Fluids 28 (7), 10931108.
Döring, W. 1943 Uber den Detonationvorgang in Gasen. Ann. Phys. 43 (6–7), 421428.
Fickett, W. & Davis, W. C. 2011 Detonation: Theory and Experiment. Dover.
Gottlieb, S. & Shu, C.-W. 1998 Total variation diminishing Runge–Kutta schemes. Maths Comput. 67 (221), 7385.
Hu, X. Y., Adams, N. A. & Shu, C.-W.2012 Positivity-preserving flux limiters for high-order conservative schemes. Preprint arXiv:1203.1540.
Jones, J. 1991 The spherical detonation. Adv. Appl. Maths 12 (2), 147186.
Kailasanath, K. 2000 Review of propulsion applications of detonation waves. AIAA J. 38 (9), 16981708.
Kasimov, A. R. & Stewart, D. S. 2005 Asymptotic theory of evolution and failure of self-sustained detonations. J. Fluid Mech. 525, 161192.
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.
Klein, R. & Stewart, D. S. 1993 The relation between curvature, rate state-dependence, and detonation velocity. SIAM J. Appl. Maths 53 (5), 14011435.
Landau, L. D. & Lifshits, E. M. 1960 Course of Theoretical Physics: Mechanics. Pergamon.
Lee, J. H. S. 2008 The Detonation Phenomenon. Cambridge University Press.
Liu, X.-D., Osher, S. & Chan, T. 1994 Weighted essentially non-oscillatory schemes. J. Comput. Phys. 115 (1), 200212.
von Neumann, J.1942 Theory of detonation waves. Office of Scientific Research and Development Rep. 549. National Defense Research Committee Div. B.
Nicholls, J. A. & Dabora, E. K. 1961 Recent results on standing detonation waves. In Symposium (International) on Combustion, vol. 8, pp. 644655. Elsevier.
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), 545672.
Rubins, P. M. & Bauer, R. C. 1994 Review of shock-induced supersonic combustion research and hypersonic applications. J. Propul. Power 10 (5), 593601.
Soloukhin, R. I. 1966 Shock Waves and Detonations in Gases. Mono Book Corporation.
Stewart, D. S. & Kasimov, A. R. 2006 State of detonation stability theory and its application to propulsion. J. Propul. Power 22 (6), 12301244.
Taylor, B. D., Kasimov, A. R. & Stewart, D. S. 2009 Mode selection in unstable two-dimensional detonations. Combust. Theor. Model. 13 (6), 973992.
Vasil’ev, A. A., Zvegintsev, V. I. & Nalivaichenko, D. G. 2006 Detonation waves in a reactive supersonic flow. Combust. Explos. Shock Waves 42 (5), 568581.
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).
Wintenberger, E.2004 Application of steady and unsteady detonation waves to propulsion. PhD thesis, California Institute of Technology.
Wintenberger, E. & Shepherd, J. E.2003 The performance of steady detonation engines. AIAA Paper 2003–0714, 41st Aerospace Sciences Meeting and Exhibit, Reno, Nevada.
Wolański, P. 2013 Detonative propulsion. Proc. Combust. Inst. 34 (1), 125158.
Zel’dovich, Y. B. 1940 On the theory of propagation of detonation in gaseous systems. J. Expl Theor. Phys. 10 (5), 542569.
Zel’dovich, Y. B. & Kompaneets, A. S. 1960 Theory of Detonation. Academic.
Zhang, F.(Ed.) 2012 Shock Waves Science and Technology Library, Vol. 6: Detonation Dynamics. Springer.
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), 3149.
Zhuravskaya, T. A. & Levin, V. A. 2012 Investigation of certain techniques for stabilizing detonation waves in a supersonic flow. Fluid Dyn. 47 (6), 793801.
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