Sound Wave Structures Downstream of Incident Propagating Oblique Shock Waves

  • J. J. Liu
Conference paper

Abstract

Graphical illustration for the sound wave structure downstream of a moving incident oblique shock is presented for weak and strong Mach reflections (MR). For experimentally observed MR-like phenomena, where the classical three-shock theory requires a forward facing reflected shock solution, it is found that the downstream flow velocity is almost sonic relative to the triple point and the path of sound generation centers of the triple point becomes essentially identical to the observed slipstream line. The observed reflected shock emanating from the triple point is shown to degenerate to a normal Mach wave for very small reflecting wedge angle, or be replaced by a backward-facing compression wave for not very small edge angles. Furthermore, forward facing reflected shocks, which were never observed before, are unphysical from the consideration of sound wave structures downstream of incident propagating oblique shocks. When the three-shock theory does provide a backward-facing reflected shock solution, it is shown that the trajectory of sound generation centers of the triple point is no longer along the same line as the observed slipstream. The existence of a non-negligible angle between these two lines explains why a reflected shock is required to turn the downstream flow parallel to the slipstream; thereby a reflected shock solution can be found from the theory.

Key words

Mach reflection Sound wave structure von Neumann paradox 

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References

  1. Ben-Dor G (1992) Shock Wave Reflection Phenomena. Springer-Verlag, New York Berl in HeidelbergMATHGoogle Scholar
  2. Bleakney W, Taub AH (1949) Interaction of shock waves. Rev. Mod. Phys. 21: 584–605CrossRefMATHADSMathSciNetGoogle Scholar
  3. Colella P, Henderson LF (1990) The von Neumann paradox for the diffraction of weak shock waves. J. Fluid Mech. 213: 71–94CrossRefADSMathSciNetGoogle Scholar
  4. Deschambault RL (1984) Nonstationary oblique-shock-wave reflections in air. UTIAS Rep No. 270Google Scholar
  5. Dewey JM, Ohm M, Van Netten AA, Walker DK (1989) The properties of curved oblique shocks associated with the reflection of weak shock waves. In: Kim YW (ed) 17th Intl. Symp. on Shock Waves and Shock Tubes. Bethlehem, USAGoogle Scholar
  6. Griffith WE (1981) Shock waves. J. Fluid Mech. 106: 81–101MATHADSGoogle Scholar
  7. Henderson LF, Siegenthaler A (1980) Experiments on the diffraction of weak blast waves: the von Neumann paradox. Proc. R. Soc. Lond. A 369, 537–555CrossRefADSGoogle Scholar
  8. Henderson LF (1987) Regions and boundaries for diffracting shock wave systems. Z. Ang. Math. and Mech. 67: 1–14CrossRefGoogle Scholar
  9. Hornung HG (1986) Regular and Mach reflections of shock waves. Ann. Rev. Fluid Mech. 18: 33–58CrossRefADSGoogle Scholar
  10. Kawamura R, Saito H (1956) Reflection of shock waves - 1. Pseudo-stationary case. J. Phys. Soc. Japan, 11: 584–692CrossRefADSGoogle Scholar
  11. Mach E (1878) Uber den Verlauf der Funkenwellen in der Ebene and in Raume. Vienna Academy Sitzungsberichte 78: 819–538Google Scholar
  12. von Neumann J (1943) Oblique reflection of shocks. Explosive Research Report No. 12. Navy Dept, Bureau of Ordnance, Washington, DC, USAGoogle Scholar
  13. Ohm M, Dewey JM (1992) A revised three-shock solution for the Mach reflection of weak shocks. Shock Waves 2: 167–176CrossRefADSGoogle Scholar
  14. Sakurai A, Henderson LF, Takayama K, Walenta Z, Colella P (1989) On the von Neumann paradox of weak Mach reflection. Fluid Dynamics Res. 4: 333–345CrossRefADSGoogle Scholar
  15. Smith LG (1945) Photographic investigation of the reflection of plane shocks in air. Office of Scientific Research and Development, Rep No. 6271, USAGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • J. J. Liu
    • 1
  1. 1.Department of Engineering ScienceNational Cheng Kung UniversityTainanTaiwan, R.O.C.

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