Shock Waves

, Volume 26, Issue 3, pp 287–297 | Cite as

Interaction and coalescence of multiple simultaneous and non-simultaneous blast waves

Original Article


Interaction of multiple blast waves can be used to direct energy toward a target while simultaneously reducing collateral damage away from the target area. In this paper, simulations of multiple point source explosives were performed and the resulting shock interaction and coalescence behavior were explored. Three to ten munitions were placed concentrically around the target, and conditions at the target area were monitored and compared to those obtained using a single munition. For each simulation, the energy summed over all munitions was kept constant, while the radial distances between target and munitions and the munition initiation times were varied. Each munition was modeled as a point source explosion. The resulting blast wave propagation and shock front coalescence were solved using the inviscid Euler equations of gas dynamics on overlapping grids employing a finite difference scheme. Results show that multiple munitions can be beneficial for creating extreme conditions at the intended target area; over 20 times higher peak pressure is obtained for ten simultaneous munitions compared to a single munition. Moreover, peak pressure at a point away from the target area is reduced by more than a factor of three.


Point source explosion Blast wave interaction Shock focusing Multiple munitions 


  1. 1.
    Aki, T., Higashino, F.: A numerical study on implosion of polygonally interacting shocks and consecutive explosion in a box. In: 17th Proceedings of the International Symposium on Shock Waves and Shock Tubes Current topics in shock waves, Bethlehem, PA, July 17–21, (A91–40576 17–34), pp. 167–172. AIP New York (1990)Google Scholar
  2. 2.
    Apazidis, N., Lesser, M.: On generation and convergence of polygonal-shaped shock waves. J. Fluid Mech. 309, 301–319 (1996)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Balasubramanian, K., Eliasson, V.: Numerical investigations of the porosity effect on the shock focusing process. Shock Waves 23(6), 583–594 (2013)CrossRefGoogle Scholar
  4. 4.
    Banks, J.W., Aslam, T.D.: Richardson extrapolation for linearly degenerate discontinuities. J. Sci. Comput. 57(1), 1–18 (2013)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Betelu, S., Aronson, D.: Focusing of noncircular self-similar shock waves. Phys. Rev. Lett. 87(7), 074501 (2001)CrossRefGoogle Scholar
  6. 6.
    Book, D., Löhner, R.: Simulation and theory of the quatrefoil instability of a converging cylindrical shock. In: 17th, Proceedings of the International Symposium on Shock Waves and Shock Tubes Current topics in shock waves, Bethlehem, PA, July 17–21, (A91–40576 17–34), pp. 149–154. AIP New York (1990)Google Scholar
  7. 7.
    Brode, H.L.: Quick estimates of peak overpressure from two simultaneous blast waves. Tech. rep., Tech. Rep. DNA4503T, Defense Nuclear Agency, Aberdeen Proving Ground, MD (1977)Google Scholar
  8. 8.
    Brown, D.L., Henshaw, W.D., Quinlan, D.J.: Overture: An object-oriented framework for solving partial differential equations on overlapping grids. Object Oriented Methods for Interoperable Scientific and Engineering Computing. SIAM pp. 245–255 (1999)Google Scholar
  9. 9.
    Chesshire, G., Henshaw, W.: Composite overlapping meshes for the solution of partial differential equations. J. Comput. Phys. 90(1), 1–64 (1990)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Demmig, F., Hemmsoth, H.H.: Model computation of converging cylindrical shock waves—initial configurations, propagation, and reflection. In: 17th, Proceedings of the International Symposium on Shock Waves and Shock Tubes Current topics in shock waves, Bethlehem, PA, July 17–21, (A91–40576 17–34), pp. 155–160. AIP New York (1990)Google Scholar
  11. 11.
    Dimotakis, P.E., Samtaney, R.: Planar shock cylindrical focusing by a perfect-gas lens. Phys. Fluids 18, 031,705 (2006)CrossRefGoogle Scholar
  12. 12.
    Eliasson, V., Apazidis, N., Tillmark, N.: Shaping converging shock waves by means of obstacles. J. Vis. 9, 240 (2006)CrossRefGoogle Scholar
  13. 13.
    Eliasson, V., Apazidis, N., Tillmark, N.: Controlling the form of strong converging shocks by means of disturbances. Shock Waves 17, 29–42 (2007)CrossRefGoogle Scholar
  14. 14.
    Eliasson, V., Apazidis, N., Tillmark, N., Lesser, M.: Focusing of strong shocks in an annular shock tube. Shock Waves 15, 205–217 (2006)CrossRefGoogle Scholar
  15. 15.
    Glass, I.: Shock Waves and Man. The University Toronto Press, Toronto (1974)Google Scholar
  16. 16.
    Guderley, G.: Starke kugelige und zylindrische Verdichtungsstöße in der Nähe desKugelmittelpunktes bzw. der Zylinderachse. Luftfahrt Forsch. 19, 302–312 (1942)MathSciNetMATHGoogle Scholar
  17. 17.
    Henshaw, W.D., Schwendeman, D.W.: Parallel computation of three-dimensional flows using overlapping grids with adaptive mesh refinement. J. Comput. Phys. 227(16), 7469–7502 (2008)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Hikida, S., Needham, C.E.: Low amplitude multiple burst (lamb) model. Tech. rep., S-cubed Final Report, S-CUBED-R-81-5067 (1981)Google Scholar
  19. 19.
    Hosseini, S.H.R., Takayama, K.: Implosion of a spherical shock wave reflected from a spherical wall. J. Fluid Mech. 530, 223–239 (2005)CrossRefMATHGoogle Scholar
  20. 20.
    Jiang, Z., Takayama, K., Moosad, K.P.B., Onodera, O., Sun, M.: Numerical and experimental study of a micro-blast wave generated by pulsed-laser beam focusing. Shock waves 8, 337–349 (1998)CrossRefGoogle Scholar
  21. 21.
    Kandula, M., Freeman, R.: On the interaction and coalescence of spherical blast waves. Shock waves 18, 21–33 (2008)CrossRefMATHGoogle Scholar
  22. 22.
    Keefer, J.H., Reisler, R.E.: Simultaneous and non-simultaneous multiple detonations. In: Proceedings of the 14th International Symposium Shock waves and shock tubes, New South Wales, Australia, pp. 543–552 (1984)Google Scholar
  23. 23.
    Kjellander, M.K., Tillmark, N.T., Apazidis, N.: Experimental determination of self-similarity constant for converging cylindrical shocks. Phys. Fluids 23(11), 116103 (2011)CrossRefGoogle Scholar
  24. 24.
    Kjellander, M.K., Tillmark, N.T., Apazidis, N.: Energy concentration by spherical converging shocks generated in a shock tube. Phys. Fluids 24(12), 126103 (2012)CrossRefGoogle Scholar
  25. 25.
    Knystautas, R., Lee, B., Lee, J.: Diagnostic experiments on converging detonations. Phys. Fluids. Suppl. 1, 165–168 (1969)Google Scholar
  26. 26.
    Matsuo, M., Ebihara, K., Ohya, Y.: Spectroscopic study of cylindrically converging shock waves. J. Appl. Phys. 58(7), 2487–2491 (1985)CrossRefGoogle Scholar
  27. 27.
    Needham, C.E.: Blast Waves. Shock Wave and High Pressure Phenomena. Springer, Berlin Heidelberg (2010)Google Scholar
  28. 28.
    Neemeh, R.A., Ahmad, Z.: Stability and collapsing mechanism of strong and weak converging cylindrical shock waves subjected to external perturbation. In: Proceedings of the 15th International Symposium Shock waves and shock tubes, Berkeley, CA, pp. 423–430. Stanford Univ. Press (1986)Google Scholar
  29. 29.
    Perry, R.W., Kantrowitz, A.: The production and stability of converging shock waves. J. Appl. Phys 22, 878–886 (1951)CrossRefGoogle Scholar
  30. 30.
    Roig, R., Glass, I.: Spectroscopic study of combustion-driven implosions. Phys. Fluids 20(10), 1651–1656 (1977)CrossRefGoogle Scholar
  31. 31.
    Roy, C.J.: Review of discretization error estimators in scientific computing. AIAA Paper 2010–0126 (2010)Google Scholar
  32. 32.
    Saito, T., Glass, I.: Temperature measurements at an implosion focus. Proc. R. Soc. Lond. A 384, 217–231 (1982)CrossRefGoogle Scholar
  33. 33.
    Schwendeman, D.W.: On converging shock waves of spherical and polyhedral form. J. Fluid Mech. 454, 365–386 (2002)MathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    Schwendeman, D.W., Whitham, G.B.: On converging shock waves. Proc. R. Soc. Lond. A 413, 297–311 (1987)MathSciNetCrossRefMATHGoogle Scholar
  35. 35.
    Shao-Lin, L.: Cylindrical shock waves produced by instantaneous energy release. J. Appl. Phys. 25(1), 54–57 (1954)CrossRefMATHGoogle Scholar
  36. 36.
    Starkenberg, J.K., Benjamin, K.J.: Predicting coalescence of blast waves from sequentially exploding ammunition stacks. Tech. rep., Army Research Lab Report ARL-TR-645 (1994)Google Scholar
  37. 37.
    Takayama, K., Kleine, H., Grönig, H.: An experimental investigation of the stability of converging cylindrical shock waves in air. Exp. Fluids 5, 315–322 (1987)CrossRefGoogle Scholar
  38. 38.
    Takayama, K., Onodera, O., Hoshizawa, Y.: Experiments on the stability of converging cylindrical shock waves. Theor. Appl. Mech. 32, 305–329 (1984)Google Scholar
  39. 39.
    Taylor, G.: The formation of a blast wave by a very intense explosion. I. Theoretical discussion. In: Proceedings of the Royal Society of London. Series A Mathematical and Physical Sciences pp. 159–174 (1950)Google Scholar
  40. 40.
    Watanabe, M., Onodera, O., Takayama, K.: Shock wave focusing in a vertical annular shock tube. Theor. Appl. Mech 32, 99–104 (1995)Google Scholar
  41. 41.
    Whitham, G.B.: Linear and nonlinear waves. Wiley, New York (1974)MATHGoogle Scholar
  42. 42.
    Wu, J., Neemeh, R., Ostrowski, P.: Experiments on the stability of converging cylindrical shock waves. AIAA J. 19, 257–258 (1981)CrossRefGoogle Scholar
  43. 43.
    Yeghiayan, R.P., Lee, W.N., Walsh, J.P.: Blast and thermal effects of multiple nuclear burst exposure of aircraft in a base-escape mode (ada058301). Tech. rep., No. KA-TR-146. Kaman Avidyne Burlington, MA (1977)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Aerospace and Mechanical EngineeringUniversity of Southern CaliforniaLos AngelesUSA

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