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Numerical investigations of the porosity effect on the shock focusing process

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Abstract

The effect of cylindrical obstacles and the porosity in between them along the path of a converging cylindrical shock is studied through numerical simulations. An initially cylindrical converging shock wave is perturbed by cylindrical obstacles placed radially in its path. High pressures and temperatures are achieved as the shock wave is focused. Results show that the shape of the shock wave close to the point of convergence as well as the porosity and type of shock wave reflection the converging shock undergoes influence the peak values. Various configurations of the obstacle size and number are considered. The Guderley constant for each case is compared with previous reported experimental values.

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References

  1. Apazidis, N., Lesser, M.: On generation and convergence of polygonal-shaped shock waves. J. Fluid Mech. 309, 301–319 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  2. Apazidis, N., Lesser, M., Tillmark, N., Johansson, B.: An experimental and theoretical study of converging polygonal shock waves. Shock Waves 12, 39–58 (2002)

    Article  MATH  Google Scholar 

  3. Berger, S., Sadot, O., Ben-Dor, G.: Experimental investigation on the shock-wave load attenuation by geometrical means. Shock Waves 20, 29–40 (2010)

    Article  Google Scholar 

  4. Betelu, S., Aronson, D.: Focusing of noncircular self-similar shock waves. Phys. Rev. Lett. 87, 074501 (2001)

    Article  Google Scholar 

  5. Britan, A., Igra, O., Ben-Dor, G., Shapiro, H.: Shock wave attenuation by grids and orifice plates. Shock Waves 16, 1–15 (2006)

    Article  Google Scholar 

  6. Britan, A., Karpov, A.V., Vasilev, E.I., Igra, O., Ben-Dor, G., Shapiro, E.: Experimental and numerical study of shock wave interaction with perforated plates. J. Fluids Eng. 126(3), 399–409 (2004)

    Article  Google Scholar 

  7. Butler, D.S.: Converging spherical and cylindrical shocks. Rep. No 54/54, Armament Research and Development Establishment, Ministry of Supply, Fort Halstead, Kent, GB (1954)

  8. Chaudhuri, A., Hadjadj, A., Sadot, O., Ben-Dor, G.: Numerical study of shock-wave mitigation through matrices of solid obstacles. Shock Waves 23(1), 91–101 (2013)

    Article  Google Scholar 

  9. Chaudhuri, A., Hadjadj, A., Sadot, O., Glazer, E.: Computational study of shock-wave interaction with solid obstacles using immersed boundary methods. Int. J. Numer. Methods Eng. 89(8), 975–990 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Chesshire, G., Henshaw, W.D.: Composite overlapping meshes for the solution of partial differential equations. J. Comput. Phys. 90(1), 1–64 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  11. Chester, W.: The quasi-cylindrical shock tube. Phil. Mag. 45(7), 1239–1301 (1954)

    MathSciNet  Google Scholar 

  12. Chisnell, R.F.: The motion of a shock wave in a channel, with applications to cylindrical and spherical shocks. J. Fluid Mech. 2(3), 286–298 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  13. Chisnell, R.F.: An analytic description of converging shock waves. J. Fluid Mech. 354, 357–375 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  14. Dimotakis, P.E., Samtaney, R.: Planar shock cylindrical focusing by a perfect-gas lens. Phys. Fluids 18(3), 031705 (2006)

    Article  Google Scholar 

  15. Dosanjh, D.S.: Interaction of Grids with Traveling Shock Waves. In: NASA Technical Note TN 3680 (1956)

  16. Eliasson, V., Apazidis, N., Tillmark, N.: Controlling the form of strong converging shocks by means of disturbances. Shock Waves 17, 29–42 (2007)

    Article  Google Scholar 

  17. Eliasson, V., Henshaw, W., Appelö, D.: On cylindrically converging shock waves shaped by obstacles. Physica D Nonlinear Phenomena 237, 2203–2209 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Eliasson, V., Tillmark, N., Szeri, A.J., Apazidis, N.: Light emission during shock wave focusing in air and argon. Phys. Fluids 19, 106106 (2007)

    Article  Google Scholar 

  19. Fong, K., Ahlborn, B.: Stability of converging shock waves. Phys. Fluids 22(3), 416–421 (1979)

    Article  Google Scholar 

  20. Gardner, J.H., Book, D.L., Bernstein, I.B.: Stability of imploding shocks in the CCW approximation. J. Fluid Mech. 114, 41–58 (1982)

    Article  MATH  Google Scholar 

  21. Guderley, G.: Starke kugelige und zylindrische Verdichtungsstöße in der Nähe des Kugelmittelpunktes bzw. der Zylinderachse. Luftfahrt Forsch. 19, 302–312 (1942)

    Google Scholar 

  22. 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)

    Article  MathSciNet  MATH  Google Scholar 

  23. Henshaw, W.D., Schwendeman, D.W.: Moving overlapping grids with adaptive mesh refinement for high-speed reactive and non-reactive flow. J. Comput. Phys. 216(2), 744–779 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  24. Hornung, H., Pullin, D., Ponchaut, N.: On the question of universality of imploding shock waves. Acta Mech. 201, 31–35 (2008)

    Article  MATH  Google Scholar 

  25. Hosseini, S.H.R., Takayama, K.: Implosion of a spherical shock wave reflected from a spherical wall. J. Fluid Mech. 530, 223–239 (2005)

    Article  MATH  Google Scholar 

  26. Kjellander, M., Tillmark, N., Apazidis, N.: Experimental determination of self-similarity constant for converging cylindrical shocks. Phys. Fluids 23(11), 116103 (2011)

    Article  Google Scholar 

  27. Kleine, H.: Time resolved shadowgraphs of focusing cylindrical shock waves. In: Study Treatise at the Stoßenwellenlabor, RWTH Achen, FRG (1985)

  28. Mishkin, E.A., Fujimoto, Y.: Analysis of a cylindrical imploding shock wave. J. Fluid Mech. 89(1), 61–78 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  29. Naiman, H., Knight, D.: The effect of porosity on shock interaction with a rigid, porous barrier. Shock Waves 16, 321–337 (2007)

    Article  MATH  Google Scholar 

  30. Nakamura, Y.: Analysis of self-similar problems of imploding shock waves by the method of characteristics. Phys. Fluids 26(5), 1234–1239 (1983)

    Article  MATH  Google Scholar 

  31. de Neef, T., Nechtman, C.: Numerical study of the flow due to a cylindrical implosion. Comput. Fluids 6(3), 185–202 (1978)

    Article  MATH  Google Scholar 

  32. Perry, R.W., Kantrowitz, A.: The production and stability of converging shock waves. J. Appl. Phys. 22(7), 878–886 (1951)

    Article  Google Scholar 

  33. Ponchaut, N.F., Hornung, H.G., Pullin, D.I., Mouton, C.A.: On imploding cylindrical and spherical shock waves in a perfect gas. J. Fluid Mech. 560, 103–122 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  34. Ramsey, S.D., Kammb, J.R., Bolstad, J.H.: The Guderley problem revisited. Int. J. Comput. Fluid Dyn. 26(2), 79–99 (2012)

    Article  MathSciNet  Google Scholar 

  35. Schwendeman, D.: On converging shock waves of spherical and polyhedral form. J. Fluid Mech. 454, 365–386 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  36. Schwendeman, D., Whitham, D.: On converging shock waves. Proc. R. Soc. Lond. A413, 297–311 (1987)

    Article  MathSciNet  Google Scholar 

  37. Seeraj, S., Skews, B.W.: Dual-element directional shock wave attenuators. Exp. Therm. Fluid Sci. 33(3), 503–516 (2009)

    Article  Google Scholar 

  38. Shi, H., Yamamura, K.: The interaction between shock waves and solid spheres arrays in a shock tube. Acta Mech. Sin. 20(3), 219–227 (2004)

    Article  Google Scholar 

  39. Skews, B.W., Kleine, H.: Flow features resulting from shock wave impact on a cylindrical cavity. J. Fluid Mech. 580, 481–493 (2007)

    Article  MATH  Google Scholar 

  40. Stanyukovich, K.P.: Unsteady motion of continuous media. Pergamon Press, Oxford (1960)

    Google Scholar 

  41. Taieb, D., Ribert, G., Hadjadj, A.: Numerical simulations of shock focusing over concave surfaces. AIAA J. 48(8), 1739–1747 (2010)

    Google Scholar 

  42. 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)

    Google Scholar 

  43. Takayama, K., Onodera, O., Hoshizawa, Y.: Experiments on the stability of converging cylindrical shock waves. Theor. Appl. Mech. 32, 117–127 (1984)

    Google Scholar 

  44. Vandenboomgaerde, M., Aymard, C.: Analytical theory for planar shock focusing through perfect gas lens and shock tube experiment designs. Phys. Fluids 23, 016101 (2011)

    Article  Google Scholar 

  45. Watanabe, M., Takayama, K.: Stability of converging cylindrical shock waves. Shock Waves 5, 149–160 (1991)

    Article  Google Scholar 

  46. Welsh, R.L.: Imploding shocks and detonations. J. Fluid Mech. 29, 61–79 (1967)

    Article  MATH  Google Scholar 

  47. Whitham, G.: Linear and nonlinear waves. Wiley, New York (1974)

    MATH  Google Scholar 

  48. Zel’dovich, Y., Raizer, Y.: Physics of shock waves and high-temperature hydrodynamic phenomena. Dover Publications, New York (2002)

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Acknowledgments

The authors would sincerely like to thank the anonymous reviewers for their insightful and generous comments.

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  1. University of Southern California, Los Angeles, CA, 90089-1189, USA

    K. Balasubramanian & V. Eliasson

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  1. K. Balasubramanian
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  2. V. Eliasson
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Correspondence to V. Eliasson.

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Communicated by O. Igra.

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Balasubramanian, K., Eliasson, V. Numerical investigations of the porosity effect on the shock focusing process. Shock Waves 23, 583–594 (2013). https://doi.org/10.1007/s00193-013-0470-7

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  • DOI: https://doi.org/10.1007/s00193-013-0470-7

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