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Off-center blast in a shocked medium

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Abstract

When multiple blasts occur at different times, the situation arises in which a blast wave is propagating into a medium that has already been shocked. Determining the evolution in the shape of the second shock is not trivial, as it is propagating into air that is not only non-uniform, but also non-stationary. To accomplish this task, we employ the method of Kompaneets to determine the shape of a shock in a non-uniform media. We also draw from the work of Korycansky (Astrophys J 398:184–189. https://doi.org/10.1086/171847, 1992) on an off-center explosion in a medium with radially varying density. Extending this to treat non-stationary flow, and making use of approximations to the Sedov solution for the point blast problem, we are able to determine an analytic expression for the evolving shape of the second shock. In particular, we consider the case of a shock in air at standard ambient temperature and pressure, with the second shock occurring shortly after the original blast wave reaches it, as in a sympathetic detonation.

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Notes

  1. Note that it is not necessary that the sources be equal. The results of changing the source sizes will be similar to those seen by changing the time of detonation for the second source, with a larger second source being similar to a smaller \(t_0\).

References

  1. Bethe, H., Fuchs, K., Hirschfelder, J., Magee, J., Peieris, R., von Neumann, J.: Blast wave. Technical report, Los Alamos Scientific Lab., N. Mex. (1947)

  2. Taylor, G.: The formation of a blast wave by a very intense explosion I. Theoretical discussion. Proc. R. Soc. Lond. A 201(1065), 159–174 (1950). https://doi.org/10.1098/rspa.1950.0049

  3. Sedov, L.I.: Similarity and Dimensional Methods in Mechanics. CRC Press, Boca Raton (1993)

    Google Scholar 

  4. Petruk, O.: Approximations of the self-similar solution for blastwave in a medium with power-law density variation. Astron. Astrophys. 357, 686–696 (2000)

    Google Scholar 

  5. Ostriker, J.P., McKee, C.F.: Astrophysical blastwaves. Rev. Mod. Phys. 60(1), 1–68 (1988). https://doi.org/10.1103/RevModPhys.60.1

    Article  Google Scholar 

  6. Bisnovatyi-Kogan, G., Silich, S.: Shock-wave propagation in the nonuniform interstellar medium. Rev. Mod. Phys. 67(3), 661–712 (1995). https://doi.org/10.1103/RevModPhys.67.661

    Article  Google Scholar 

  7. Bannikova, E.Y., Karnaushenko, A., Kontorovich, V., Shulga, V.: A new exact solution of Kompaneets equation for a shock front. Astron. Rep. 56(7), 496–503 (2012). https://doi.org/10.1134/S1063772912060017

  8. Korycansky, D.: An off-center point explosion in a radially stratified medium-Kompaneets approximation. Astrophys. J. 398, 184–189 (1992). https://doi.org/10.1086/171847

    Article  Google Scholar 

  9. Zel’dovich, Y.B., Raizer, Y.P.: Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, vol. II. Academic Press, New York (1967)

    Google Scholar 

  10. Kontorovich, V., Pimenov, S.: An exact solution of the Kompaneets equations for a strong point explosion in a medium with quadratic density decrease. Radiophys. Quantum Electron. 41(6), 457–468 (1998). https://doi.org/10.1007/BF02676679

    Article  Google Scholar 

  11. Kandula, M., Freeman, R.: On the interaction and coalescence of spherical blast waves. Shock Waves 18(1), 21–33 (2008). https://doi.org/10.1007/s00193-008-0134-1

    Article  MATH  Google Scholar 

  12. Needham, C.: Blast loads and propagation around and over a building. In: Hannemann, K., Seiler, F. (eds.) Shock Waves. 26th International Symposium on Shock Waves, Volume 2. Springer, Berlin (2009). https://doi.org/10.1007/978-3-540-85181-3_91

  13. Needham, C.: Blast Waves. Springer, Berlin (2010). https://doi.org/10.1007/978-3-642-05288-0

    Book  Google Scholar 

  14. Whitham, G.: Linear and Nonlinear Waves. Wiley, New York (1974)

    MATH  Google Scholar 

  15. McGlaun, J.M., Thompson, S., Elrick, M.: CTH: A three-dimensional shock wave physics code. Int. J. Impact Eng. 10(1–4), 351–360 (1990). https://doi.org/10.1016/0734-743X(90)90071-3

    Article  Google Scholar 

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Acknowledgements

This work was funded in part by Sandia National Laboratories.

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Authors and Affiliations

  1. Mathematics Department, New Mexico Tech, 801 Leroy Place, Socorro, NM, 87801, USA

    G. C. Duncan-Miller & W. D. Stone

  2. Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM, 87185–0840, USA

    G. C. Duncan-Miller

Authors
  1. G. C. Duncan-Miller
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  2. W. D. Stone
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Correspondence to G. C. Duncan-Miller.

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Communicated by F. Zhang and G. Ciccarelli.

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Duncan-Miller, G.C., Stone, W.D. Off-center blast in a shocked medium. Shock Waves 28, 631–640 (2018). https://doi.org/10.1007/s00193-017-0747-3

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  • DOI: https://doi.org/10.1007/s00193-017-0747-3

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