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Reflection of a converging cylindrical shock wave segment by a straight wedge

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Abstract

As a converging cylindrical shock wave propagates over a wedge, the shock wave accelerates and the angle between the shock wave and the wedge decreases. This causes the conditions at the reflection point to move from what would be the irregular reflection domain for a straight shock wave into the regular reflection domain. This paper covers a largely qualitative study of the reflection of converging shock wave segments with Mach numbers between 1.2 and 2.1 by wedges inclined at angles between \(15^\circ \) and \(60^\circ \) from experimental and numerical results. The sonic condition conventionally used for predicting the type of reflection of straight shock waves was found to also be suitable for predicting the initial reflection of a curved shock wave. Initially regular reflections persisted until the shock was completely reflected by the wedge, whereas the triple point of initially irregular reflections was observed to return to the wedge surface, forming transitioned regular reflection. After the incident shock wave was completely reflected by the wedge, a shock wave focusing mechanism was observed to amplify the pressure on the surface of the wedge by a factor of up to 100 for low wedge angles.

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References

  1. Ben-Dor, G.: Shock Wave Reflection Phenomena, 2nd edn. Springer, Berlin (2007)

    MATH  Google Scholar 

  2. Hornung, H., Oertel, H., Sandeman, R.: Transition to Mach reflection of shock waves in steady and pseudosteady flow with and without relaxation. J. Fluid Mech. 90, 541–560 (1979)

    Article  Google Scholar 

  3. Guderley, G.: Starke kugelige und zylindrische Verdichtungsstösse in der Nähe des Kugelmittelpunktes bzw. der Zylinderachse. Luftfahrtforschung 199, 302 (1942)

    MathSciNet  MATH  Google Scholar 

  4. Ben-Dor, G., Dewey, J., Takayama, K.: The reflection of a planar shock wave over a double wedge. J. Fluid Mech. 176, 483–520 (1987)

    Article  Google Scholar 

  5. Ben-Dor, G., Takayama, K.: The dynamics of the transition from Mach to regular reflection over concave cylinders. Israel J. Tech. 23, 71–74 (1986/7)

  6. Ben-Dor, G., Elperin, T.: Analysis of the wave configuration resulting from the termination of an inverse Mach reflection. Shock Waves 1(3), 237–241 (1991)

    Article  MATH  Google Scholar 

  7. Dewey, J., Classen, D., McMillin, D.: Photogrammetry of the shock front trajectory on dipole west shots 8, 9, 10 and 11. Technical Report UVIC-PF-1-75, University of Victoria, British Columbia, Canada (1975)

  8. Dewey, J., McMillin, D., Classen, D.: Photogrammetry of spherical shocks reflected from real and ideal surfaces. J. Fluid Mech. 81, 701–717 (1977)

    Article  Google Scholar 

  9. Takayama, K., Sekiguchi, H.: Formation and diffraction of spherical shock waves in shock tube. Reports of the Institute of High Speed Mechanics, Tokuhoku University, Sendai, Japan, vol. 43, pp. 89–119 (1981)

  10. Takayama, K., Sekiguchi, H.: Triple-point trajectory of a strong spherical shock wave. AIAA J. 19, 815–817 (1981)

    Article  Google Scholar 

  11. Liang, S., Hsu, J., Wang, J.: Numerical study of cylindrical blast-wave propagation and reflection. AIAA J. 399(6), 1152–1158 (2001)

    Article  Google Scholar 

  12. Liang, S., Wang, J., Chen, H.: Numerical study of spherical blast-wave propagation and reflection. Shock Waves 12(1), 59–68 (2002)

  13. Hu, T., Glass, I.: Blast wave reflection trajectories from a height of burst. AIAA J. 24, 607–610 (1986)

    Article  Google Scholar 

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

    Article  Google Scholar 

  15. Schwendeman, D., Whitham, G.: On converging shock waves. Proc. R. Soc. A. 413(1845), 297 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  16. Watanabe, M., Takayama, K.: Stability of converging cylindrical shock waves. Shock Waves 1(2), 149 (1991)

    Article  Google Scholar 

  17. Gray, B., Skews, B.: Reflection transition of converging cylindrical shock wave segments. In: Kontis, K. (ed.) Proceedings 28th International Symposium on Shock Waves, pp. 995–1000 (2012)

  18. Gray, B., Skews, B.: Experimental investigation into converging cylindrical shock wave reflection. In: Bonazza, R., Ranjan, D. (eds.) Proceedings 29th International Symposium on Shock Waves, pp. 1309–1314 (2015)

  19. Skews, B., Gray, B., Paton, R.: Experimental production of two-dimensional shock waves of arbitrary profile. Shock Waves 25, 1–10 (2015)

    Article  Google Scholar 

  20. ANSYS\({}^{\textregistered }\) Fluent, Release 14.0. Dec 2011. ANSYS, Inc (2011)

  21. van Leer, B.: Towards the ultimate conservative difference scheme, V. A second order sequel to Godunov’s method. J. Comput. Phys. 32, 101–136 (1979)

    Article  MATH  Google Scholar 

  22. Roe, P.: The use of the Riemann problem in finite difference schemes. Lect. Notes Phys. 141, 354–359 (1980)

    Article  Google Scholar 

  23. Gray, B., Skews, B.: The Mach reflection of a converging cylindrical shock wave segment encountering a straight wedge. In: Ben-Dor, G., Igra, O., Sadot, O. (eds.) Proceedings 30th International Symposium on Shock Waves (in press)

  24. Sturtevant, B., Kulkarny, V.: The focusing of weak shock waves. J. Fluid Mech. 73, 651–671 (1976)

    Article  Google Scholar 

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Correspondence to B. Skews.

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Communicated by M. Brouillette.

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Gray, B., Skews, B. Reflection of a converging cylindrical shock wave segment by a straight wedge. Shock Waves 27, 551–563 (2017). https://doi.org/10.1007/s00193-017-0708-x

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  • DOI: https://doi.org/10.1007/s00193-017-0708-x

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