Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-26T15:59:20.759Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic calculation of the dynamics of self-sustained detonations in condensed phase explosives

Published online by Cambridge University Press:  31 August 2012

J. A. Saenz ,
B. D. Taylor  and
D. S. Stewart
J. A. Saenz*
Affiliation:
Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia
B. D. Taylor
Affiliation:
Naval Research Laboratory, Washington, DC 20375-5344, USA
D. S. Stewart
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
*
†Email address for correspondence: juan.saenz@anu.edu.au
Get access Rights & Permissions [Opens in a new window]

Abstract

We use the weak-curvature, slow-time asymptotics of detonation shock dynamics (DSD) to calculate an intrinsic relation between the normal acceleration, the normal velocity and the curvature of a lead detonation shock for self-sustained detonation waves in condensed phase explosives. The formulation uses the compressible Euler equations for an explosive that is described by a general equation of state with multiple reaction progress variables. The results extend an earlier asymptotic theory for a polytropic equation of state and a single-step reaction rate model discussed by Kasimov (Theory of instability and nonlinear evolution of self-sustained detonation waves. PhD thesis, University of Illinois Urbana-Champaign, Urbana, Illinois) and by Kasimov & Stewart (Phys. Fluids, vol. 16, 2004, pp. 3566–3578). The asymptotic relation is used to study the dynamics of ignition events in solid explosive PBX-9501 and in porous PETN powders. In the case of porous or powdered explosives, two composition variables are used to represent the extent of exothermic chemical reaction and endothermic compaction. Predictions of the asymptotic formulation are compared against those of alternative DSD calculations and against shock-fitted direct numerical simulations of the reactive Euler equations.

JFM classification

Compressible Flows: Detonation waves Reacting Flows: Detonations
Type
Papers
Information
Journal of Fluid Mechanics , Volume 710 , 10 November 2012 , pp. 166 - 194
Copyright
Copyright © Cambridge University Press 2012

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

1. Bdzil, J. B. & Stewart, D. S. 2007 The dynamics of detonation in explosive systems. Annu. Rev. Fluid Mech. 39 (1), 263–292.CrossRefGoogle Scholar
2. Bdzil, J. B. & Stewart, D. S. 2011 Theory of Detonation Shock Dynamics. Detonation Dynamics (ed. Zhang, F. ). Shock Wave Science and Technology Reference Library , vol. 6, chap. 7. Springer.Google Scholar
3. Davis, W. C. 1985 Equation of state for detonation products. In Proceedings of the 8th (International) Detonation Symposium, pp. 785–795.Google Scholar
4. Davis, W. C. 1993 Equation of state for detonation products. In Proceedings of 10th International Symposium on Detonation, pp. 369–376.Google Scholar
5. Davis, W. C. 1998a Equation of state for detonation products. In Proceedings of 11th International Symposium on Detonation, pp. 303–308.Google Scholar
6. Davis, W. C. 1998b Explosive effects and applications. In Introduction to Explosives, chap. 1. Springer.Google Scholar
7. Davis, W. C. 2000 Complete equation of state for unreacted solid explosive. Combust. Flame 120, 399–403.CrossRefGoogle Scholar
8. Galassi, M., Davies, J., Theiler, J., Gough, B., Jungman, G., Alken, P., Booth, M. & Rossi, F. 2009 GNU Scientific Library Reference Manual, 3rd edn. Network Theory Ltd.Google Scholar
9. Herrmann, W. 1969 Constitutive equation for the dynamic compaction of ductile porous materials. J. Appl. Phys. 40 (6), 2490–2499.CrossRefGoogle Scholar
10. Kasimov, A. R. 2004 Theory of instability and nonlinear evolution of self-sustained detonation waves. PhD thesis, University of Illinois Urbana-Champaign, Urbana, Illinois.Google Scholar
11. 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
12. 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
13. Lambert, D. E., Stewart, D. S., Yoo, S. & Wescott, B. L. 2006 Experimental validation of detonation shock dynamics in condensed explosives. J. Fluid Mech. 546, 227–253.CrossRefGoogle Scholar
14. Menikoff, R. & Plohr, B. J. 1989 The Riemann problem for fluid flow of real materials. Rev. Mod. Phys. 61 (1), 75.CrossRefGoogle Scholar
15. Saenz, J. A. & Stewart, D. S. 2008 Modelling deflagration-to-detonation transition in granular explosive pentaerythritol tetranitrate. J. Appl. Phys. 104 (4), 043519.CrossRefGoogle Scholar
16. Stewart, D. S. 1998 The shock dynamics of multidimensional condensed and gas phase detonations. Proc. Combust. Inst. 27, 2189–2205.CrossRefGoogle Scholar
17. Stewart, D. S., Asay, B. W. & Prasad, K. 1994 Simplified modelling of transition to detonation in porous energetic materials. Phys. Fluids 6, 2515–2534.CrossRefGoogle Scholar
18. Stewart, D. S. & Bdzil, J. B. 1988 The shock dynamics of stable multidimensional detonation. Combust. Flame 72 (3), 311–323.CrossRefGoogle Scholar
19. Stewart, D. S., Davis, W. C. & Yoo, S. 2002 Equation of state for modelling the detonation reaction zone. In Proceedings of 12th Intl Symp. Detonation, pp. 624–631. Office of Naval Research, ONR 333-05-2.Google Scholar
20. Stewart, D. S. & Kasimov, A. R. 2005 Theory of detonation with an embedded sonic locus. SIAM J. Appl. Maths 66 (2), 384–407.CrossRefGoogle Scholar
21. Stewart, D. S. & Yao, J. 1998 The normal detonation shock velocity-curvature relationship for materials with nonideal equation of state and multiple turning points. Combust. Flame 113 (1–2), 224–235.CrossRefGoogle Scholar
22. Stewart, D. S., Yoo, S. & Wescott, B. L. 2007 High order numerical simulation and modelling of the interaction of energetic and inert materials. Combust. Theor. Model. 11 (2), 305–332.CrossRefGoogle Scholar
23. Taylor, B. D. 2010 Instability of steady and quasi-steady detonations. PhD thesis, University of Illinois Urbana-Champaign, Urbana, Illinois.Google Scholar
24. Wescott, B. L., Stewart, D. S. & Davis, W. C. 2005 Equation of state and reaction rate for the condensed-phase explosives. J. Appl. Phys. 98, 053514.CrossRefGoogle Scholar
25. Xu, S. & Stewart, D. S. 1997 Deflagration to detonation transition in porous energetic materials: a model study. J. Engng Maths 31, 143–172.CrossRefGoogle Scholar
26. Yao, J. & Stewart, D. S. 1996 On the dynamics of multi-dimensional detonation. J. Fluid Mech. 309, 225–275.CrossRefGoogle Scholar