Shock Waves

, Volume 29, Issue 1, pp 193–219 | Cite as

Numerical study of multiscale compaction-initiated detonation

  • J. R. Gambino
  • D. W. SchwendemanEmail author
  • A. K. Kapila
Original Article


A multiscale model of heterogeneous condensed-phase explosives is examined computationally to determine the course of transient events following the application of a piston-driven stimulus. The model is a modified version of that introduced by Gonthier (Combust Sci Technol 175(9):1679–1709, 2003. in which the explosive is treated as a porous, compacting medium at the macro-scale and a collection of closely packed spherical grains capable of undergoing reaction and diffusive heat transfer at the meso-scale. A separate continuum description is ascribed to each scale, and the two scales are coupled together in an energetically consistent manner. Following piston-induced compaction, localized energy deposition at the sites of intergranular contact creates hot spots where reaction begins preferentially. Reaction progress at the macro-scale is determined by the spatial average of that at the grain scale. A parametric study shows that combustion at the macro-scale produces an unsteady detonation with a cyclical character, in which the lead shock loses strength and is overtaken by a stronger secondary shock generated in the partially reacted material behind it. The secondary shock in turn becomes the new lead shock and the process repeats itself.


Reactive flow Detonation Multiphase flow Multiscale modeling Godunov methods 



Research support was provided by Los Alamos National Laboratory under Contract 336767. The work of JRG was performed under the auspices of the US Department of Energy (DOE) by LLNL under Contract DE-AC52-07NA27344. LLNL Report LLNL-JRNL-735470.


  1. 1.
    Gonthier, K.A.: Modeling and analysis of reactive compaction for granular energetic solids. Combust. Sci. Technol. 175(9), 1679–1709 (2003). CrossRefGoogle Scholar
  2. 2.
    Lee, E.L., Tarver, C.M.: Phenomenological model of shock initiation in heterogeneous explosives. Phys. Fluids 23(12), 2362–2372 (1980). CrossRefGoogle Scholar
  3. 3.
    Tarver, C.M., McGuire, E.M.: Reactive flow modeling of the interaction of TATB detonation waves with inert materials. In: The Twelfth Symposium (International) on Detonation, pp. 641–649 (2002)Google Scholar
  4. 4.
    Tarver, C.M.: Ignition and growth modeling of LX-17 hockey puck experiments. Propellants Explos Pyrotech. 30, 109–117 (2005). CrossRefGoogle Scholar
  5. 5.
    Baer, M.R., Nunziato, J.W.: A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials. Int. J. Multiph. Flow 12, 861–889 (1986). CrossRefzbMATHGoogle Scholar
  6. 6.
    Butler, P.B., Krier, H.: Analysis of deflagration to detonation transition in high-energy solid propellants. Combust. Flame 63(1–2), 31–48 (1986). CrossRefGoogle Scholar
  7. 7.
    Powers, J.M., Stewart, D.S., Krier, H.: Theory of two-phase detonation, part I: modeling. Combust. Flame 80(3–4), 264–279 (1990). CrossRefGoogle Scholar
  8. 8.
    Powers, J.M., Stewart, D.S., Krier, H.: Theory of two-phase detonation, part II: structure. Combust. Flame 80(3–4), 280–303 (1990). CrossRefGoogle Scholar
  9. 9.
    Gonthier, K.A., Powers, J.M.: A numerical investigation of transient detonation in granulated material. Shock Waves 6, 183–195 (1996). CrossRefzbMATHGoogle Scholar
  10. 10.
    Bdzil, J.B., Menikoff, R., Son, S.F., Kapila, A.K., Stewart, D.S.: Two-phase modeling of deflagration-to-detonation transition in granular materials: a critical examination of modeling issues. Phys. Fluids 11(2), 378–402 (1999). CrossRefzbMATHGoogle Scholar
  11. 11.
    Gonthier, K.A., Powers, J.M.: A high-resolution numerical method for a two-phase model of deflagration-to-detonation transition. J. Comput. Phys. 163, 376–433 (2000). CrossRefzbMATHGoogle Scholar
  12. 12.
    Saurel, R., Abgrall, R.: A simple method for compressible multifluid flows. SIAM J. Sci. Comput. 21(3), 1115–1145 (1999). MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Saurel, R., Lemetayer, O.: A multiphase model for compressible flows with interfaces, shocks, detonation waves and cavitation. J. Fluid Mech. 431, 239–271 (2001). CrossRefzbMATHGoogle Scholar
  14. 14.
    Schwendeman, D.W., Wahle, C.W., Kapila, A.K.: The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow. J. Comput. Phys. 212, 490–526 (2006). MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Schwendeman, D.W., Wahle, C.W., Kapila, A.K.: A study of detonation evolution and structure for a model of compressible two-phase reactive flow. Combust. Theory Model. 12, 159–204 (2008). CrossRefzbMATHGoogle Scholar
  16. 16.
    Michael, L., Nikiforakis, N.: A hybrid formulation for the numerical simulation of condensed phase explosives. J. Comput. Phys. 316, 193–217 (2016). MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Baer, M.R.: Mesoscale Modeling of Shocks in Heterogeneous Reactive Materials. In: Shock Wave Science and Technology Reference Library, pp. 321–356. Springer, Berlin (2007).
  18. 18.
    Zhang, J., Jackson, T.L., Buckmaster, J., Freund, J.B.: Numerical modeling of shock-to-detonation transition in energetic materials. Combust. Flame 159, 1769–1778 (2012). CrossRefGoogle Scholar
  19. 19.
    Jackson, T.L., Buckmaster, J.D., Zhang, J., Anderson, J.: Pore collapse in an energetic material from the micro-scale to the macro-scale. Combust. Theory Model. 19, 347–381 (2015).
  20. 20.
    Zhang, J., Jackson, T.L.: Direct detonation initiation with thermal deposition due to pore collapse in energetic materials—towards the coupling between micro- and macro scales. Combust. Theory Model. 21, 248–273 (2017). MathSciNetCrossRefGoogle Scholar
  21. 21.
    Menikoff, R.: Deflagration wave profiles. Tech. Rep. LA-UR-12-20353, Los Alamos National Laboratory (2012)Google Scholar
  22. 22.
    Ozlem, M., Schwendeman, D.W., Kapila, A.K., Henshaw, W.D.: A numerical study of shock-induced cavity collapse. Shock Waves 22, 89–117 (2012). CrossRefGoogle Scholar
  23. 24.
    Henshaw, W.D., Schwendeman, D.W.: An adaptive numerical scheme for high-speed reactive flow on overlapping grids. J. Comput. Phys. 191(2), 420–447 (2003). MathSciNetCrossRefzbMATHGoogle Scholar
  24. 25.
    Banks, J.B., Schwendeman, D.W., Kapila, A.K., Henshaw, W.D.: A high-resolution Godunov method for multi-material flows on overlapping grids. J. Comput. Phys. 223, 262–297 (2007). MathSciNetCrossRefzbMATHGoogle Scholar
  25. 26.
    Henshaw, W.D., Schwendeman, D.W.: Parallel computation of three-dimensional flows using overlapping grids with adaptive mesh refinement. J. Comput. Phys. 227, 7469–7502 (2008). MathSciNetCrossRefzbMATHGoogle Scholar
  26. 27.
    Schwendeman, D.W., Kapila, A.K., Henshaw, W.D.: A study of detonation diffraction and failure for a model of compressible two-phase reactive flow. Combust. Theory Model. 14, 331–366 (2010). CrossRefzbMATHGoogle Scholar
  27. 28.
    Gambino, J., Kapila, A.K., Schwendeman, D.W.: Sensitivity of run-to-detonation distance in practical explosives. Combust. Theory Model. 20, 1088–1117 (2016). MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Lawrence Livermore National LaboratoryLivermoreUSA
  2. 2.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroyUSA

Personalised recommendations