Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-30T23:04:59.290Z Has data issue: false hasContentIssue false
  • English
  • Français

Detonation propagation in a circular arc: reactive burn modelling

Published online by Cambridge University Press:  28 November 2017

Mark Short Open the ORCID record for Mark Short [Opens in a new window] ,
James J. Quirk ,
Carlos Chiquete  and
Chad D. Meyer
Mark Short*
Affiliation:
Los Alamos National Laboratory, Los Alamos, New Mexico, NM 87545, USA
James J. Quirk
Affiliation:
Los Alamos National Laboratory, Los Alamos, New Mexico, NM 87545, USA
Carlos Chiquete
Affiliation:
Los Alamos National Laboratory, Los Alamos, New Mexico, NM 87545, USA
Chad D. Meyer
Affiliation:
Los Alamos National Laboratory, Los Alamos, New Mexico, NM 87545, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The dynamics of steady detonation propagation in a two-dimensional, high explosive circular arc geometry are examined computationally using a reactive flow model approach. The arc is surrounded by a low impedance material confiner on its inner surface, while its outer surface is surrounded either by the low impedance confiner or by a high impedance confiner. The angular speed of the detonation and properties of the steady detonation driving zone structure, i.e. the region between the detonation shock and sonic flow locus, are examined as a function of increasing arc thickness for a fixed inner arc radius. For low impedance material confinement on the inner and outer arc surfaces, the angular speed increases monotonically with increasing arc thickness, before limiting to a constant. The limiting behaviour is found to occur when the detonation driving zone detaches from the outer arc surface, leaving a region of supersonic flow on the outer surface. Consequently, the angular speed of the detonation becomes insensitive to further increases in the arc thickness. For high impedance material confinement on the outer arc surface, the observed flow structures are significantly more complex. As the arc thickness increases, we sequentially observe regions of negative shock curvature on the detonation front, reflected shock formation downstream of the reaction zone, and eventually Mach stem formation on the detonation front. Subsequently, a region of supersonic flow develops between the detonation driving zone and the Mach stem structure. For sufficiently wide arcs, the Mach stem structure disappears. For the high impedance material confinement, the angular speed of the detonation first increases with increasing arc thickness, reaches a maximum, decreases, and then limits to a constant for sufficiently large arc thickness. The limiting angular speed is the same as that found for the low impedance confiner on the outer arc surface.

JFM classification

Compressible Flows: Compressible Flows Compressible Flows: Detonation waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 835 , 25 January 2018 , pp. 970 - 998
Check for updates
Copyright
© 2017 Cambridge University Press 

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

Aslam, T. D. & Bdzil, J. B. 2002 Numerical and theoretical investigations on detonation-inert confinement interactions. In Twelfth International Symposium on Detonation, ONR 333-05-2, pp. 483–488. Office of Naval Research.Google Scholar
Aslam, T. D. & Bdzil, J. B. 2006 Numerical and theoretical investigations on detonation confinement sandwich tests. In Thirteenth International Detonation Symposium, ONR 351-07-01, pp. 761–769. Office of Naval Research.Google Scholar
Aslam, T. D. & Stewart, D. S. 1999 Detonation shock dynamics and comparisons with direct numerical simulation. Combust. Theor. Model. 3, 77–101.CrossRefGoogle Scholar
Bdzil, J. B. 1981 Steady-state two-dimensional detonation. J. Fluid Mech. 108, 195–226.CrossRefGoogle Scholar
Bdzil, J. B., Aslam, T. D., Henninger, R. & Quirk, J. J. 2003 High-explosives performance: understanding the effects of a finite-length reaction zone. Los Alamos Sci. 28, 96–110.Google Scholar
Bdzil, J. B., Fickett, W. & Stewart, D. S. 1989 Detonation shock dynamics: a new approach to modeling multi-dimensional detonation waves. In Ninth Symposium (International) on Detonation, OCNR 113291-7, pp. 730–742. Office of Naval Research.Google Scholar
Bdzil, J. B. & Short, M. 2017 Theory of Mach reflection of detonation at glancing incidence. J. Fluid Mech. 811, 269–314.Google Scholar
Bdzil, J. B. & Stewart, D. S. 2007 The dynamics of detonation in explosive systems. Annu. Rev. Fluid Mech. 39, 263–292.CrossRefGoogle Scholar
Bdzil, J. B. & Stewart, D. S. 2011 Theory of detonation shock dynamics. In Detonation Dynamics (ed. Zhang, F.), Shock Waves Science and Technology Library, vol. 6, pp. 373–453. Springer.Google Scholar
Fedkiw, R. P., Aslam, T. D., Merriman, B. & Osher, S. 1999 A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J. Comput. Phys. 152, 457–492.Google Scholar
Gustavsen, R. L., Sheffield, S. A. & Alcon, R. R. 1998 Progress in measuring detonation wave profiles in PBX 9501. In Eleventh International Detonation Symposium, ONR 333000-5, pp. 821–827. Office of Naval Research.Google Scholar
Jackson, S. I. & Short, M. 2015 Scaling of detonation velocity in cylinder and slab geometries for ideal, insensitive and non-ideal explosives. J. Fluid Mech. 773, 224–266.Google Scholar
Kailasanath, K 2017 Recent developments in the research on rotating-detonation-wave engines. In 55th AIAA Aerospace Sciences Meeting, art. 0784. AIAA.Google Scholar
Kapila, A. K., Schwendeman, D. W., Bdzil, J. B. & Henshaw, W. D. 2007 A study of detonation diffraction in the Ignition-and-Growth model. Combust. Theor. Model. 11 (5), 781–822.Google Scholar
Li, J., Mi, X. & Higgins, A. J. 2015 Geometric scaling for a detonation wave governed by a pressure-dependent reaction rate and yielding confinement. Phys. Fluids 27, 027102.Google Scholar
Lieberthal, B., Bdzil, J. B. & Stewart, D. S. 2014 Modelling detonation of heterogeneous explosives with embedded inert particles using detonation shock dynamics: normal and divergent propagation in regular and simplified microstructure. Combust. Theor. Model. 18, 204–241.Google Scholar
Lubyatinsky, S. N., Batalov, S. V., Garmashev, A. Yu., Israelyan, V. G., Kostitsyn, O. V., Loboiko, B. G, Pashentsev, V. A., Sibilev, V. A., Smirnov, E. B. & Filin, V. P. 2003 Detonation propagation in 180° ribs of an insensitive high explosive. In Shock Compression of Condensed Matter (ed. Furnish, M. D., Gupta, Y. M. & Forbes, J. W.), CP 706, pp. 859–862. American Institute of Physics.Google Scholar
Marsh, S. P.(Ed.) 1980 LASL Shock Hugoniot Data. University of California Press.Google Scholar
Menikoff, R. 2007 Empirical equations of state for solids. In Solids I (ed. Horie, Y.), Shock Wave Science and Technology Reference Library, vol. 2, pp. 143–188. Springer.Google Scholar
Menikoff, R. & Plohr, B. J. 1989 The Riemann problem for fluid flow of real materials. Rev. Mod. Phys. 61 (1), 75–130.Google Scholar
Nakayama, H., Kasahara, J., Matsuo, A. & Funaki, I. 2013 Front shock behavior of stable curved detonation waves in rectangular-cross-section curved channels. Proc. Combust. Inst. 34, 1939–1947.Google Scholar
Nakayama, H., Moriya, T., Kasahara, J., Matsuo, A., Sasamoto, Y. & Funaki, I. 2012 Stable detonation wave propagation in rectangular-cross-section curved channels. Combust. Flame 159, 859–869.CrossRefGoogle Scholar
Quirk, J. J.1991 An adaptive grid algorithm for computational shock hydrodynamics. PhD thesis, Cranfield Institute of Technology, UK.Google Scholar
Quirk, J. J. 1998a AMRITA: a computational facility (for CFD modelling). In 29th Computational Fluid Dynamics (ed. Deconinck, H.), VKI LS 1998-03. Von Karman Institute for Fluid Dynamics.Google Scholar
Quirk, J. J. 1998b Amr_sol: design principles and practice. In 29th Computational Fluid Dynamics (ed. Deconinck, H.), VKI LS 1998-03. Von Karman Institute for Fluid Dynamics.Google Scholar
Quirk, J. J.2007 amr_sol::multimat. Tech. Rep. LA-UR-07-0539. Los Alamos National Laboratory.Google Scholar
Sharpe, G. J. & Braithwaite, M. 2005 Steady non-ideal detonations in cylindrical sticks of explosives. J. Engng Maths 53 (1), 39–58.CrossRefGoogle Scholar
Short, M., Anguelova, I. I., Aslam, T. D., Bdzil, J. B., Henrick, A. K. & Sharpe, G. J. 2008 Stability of detonations for an idealized condensed-phase model. J. Fluid Mech. 595, 45–82.CrossRefGoogle Scholar
Short, M., Bdzil, J. B. & Anguelova, I. I. 2006 Stability of Chapman–Jouguet detonations for a stiffened-gas model of condensed-phase explosives. J. Fluid Mech. 552, 299–309.CrossRefGoogle Scholar
Short, M., Quirk, J. J., Meyer, C. D. & Chiquete, C. 2016 Steady detonation propagation in a circular arc: a detonation shock dynamics model. J. Fluid Mech. 807, 87–134.Google Scholar
Tarver, C. M. & Chidester, S. K. 2007 Ignition and growth modeling of detonating TATB cones and arcs. In Shock Compression of Condensed Matter (ed. Elert, M., Furnish, M. D., Chau, R., Holmes, N. & Nguyen, J.), CP 955, pp. 429–432. American Institute of Physics.Google Scholar
Wescott, B. L., Stewart, D. S. & Davis, W. C. 2005 Equation of state and reaction rate for condensed-phase explosives. J. Appl. Phys. 98 (5), 053514.Google Scholar
Zhao, T., Li, Q., Zhao, F., Sun, C., Han, L., He, Z. & Gao, W. 1998 An experimental study of detonation propagation in the arc: insensitive high explosive initiated on the basal plane. In Eleventh International Detonation Symposium, ONR 333000-5, pp. 1023–1028. Office of Naval Research.Google Scholar