Advertisement

Shock Waves

, Volume 6, Issue 1, pp 29–39 | Cite as

Conical Mach reflection of moving shock waves

Part 1: Analytical considerations
  • B. E. Milton
  • R. D. Archer
Article

Abstract

Conical Mach reflections differ from those of the equivalent plane, two-dimensional Mach reflection because in axisymmetry, the disturbances generated at the reflecting surface are modified by their more rapidly increasing or decreasing area as they move towards or away from the centerline. Equations for conical Mach reflection cases have now been developed using a simplified ray-shock theory formulation based on the initial assumption that the stem is straight and normal to the wall. These are in a form that applies generally. Their simple structure provides an easy conceptual understanding of self-similarity and non-self-similarity as well as a clear mathematical approach for the development of the curved triple-point locus of the latter by integration. They provide a quick and direct solution in all cases and can easily incorporate the Mach stem curvature by progressively calculating the new ray direction. A range of cases has been considered and results are presented for converging and diverging, self-similar and non-self-similar cases.

Key words

Conical Mach reflection Axisymmetric shocks Triple-point locus curvature 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ben-Dor G (1992) Phenomena of shock reflections, Heidelberg, NY: SpringerGoogle Scholar
  2. Bryson AE, Gross RWF (1961) Diffraction of strong shocks by cones, cylinders and spheres. J Fluid Mech 10:1–16MATHMathSciNetCrossRefADSGoogle Scholar
  3. Chester W (1954) The quasi-cylindrical shock tube, Phil. Mag., 45:1293–1301MATHMathSciNetGoogle Scholar
  4. Duong DQ, Milton BE (1985) The Mach reflection of shock waves in converging cylindrical channels. Expts Fluids 3:161–168CrossRefADSGoogle Scholar
  5. Han ZY, Yin X (1993) Shock dynamics. Kluwer Academic Publishers Group, The NetherlandsMATHGoogle Scholar
  6. Han ZY, Milton BE, Takayama K (1992) The Mach reflection triple-point locus for internal and external conical diffraction of a moving shock wave. Shock Waves 2:5–12MATHCrossRefADSGoogle Scholar
  7. Itoh S, Okazaki N, Itaya M (1981) On the transition between regular and Mach reflection in truly non-stationary flows. J Fluid Mech 108:384–400CrossRefADSGoogle Scholar
  8. Laporte O (1954) On the interaction of a shock wave with a constriction. Los Alamos Scientific Lab. Rept., LA-1740, Univ. of CaliforniaGoogle Scholar
  9. Milton BE (1975) Mach reflection using ray-shock theory. AIAA J 13:1531–1533ADSCrossRefGoogle Scholar
  10. Milton BE, Archer RD (1969) Generation of implosions by area change in a shock tube. AIAA J 7(4):779–780ADSGoogle Scholar
  11. Milton BE, Archer RD (1993) Generalised concepts for the internal and external conical Mach reflection of moving shock waves. Proc. 19th Int. Shock Wave Symp., Marseille, IV, 157–162Google Scholar
  12. Milton BE, Duong DQ, Takayama K (1985) Multiple internal conical Mach reflections. In Proc. 15th Int Symp on Shock Waves and Shock Tubes, Standord, pp 113–119Google Scholar
  13. Obermeier, F, Steinoff C (1994), Von Neumann's Paradox Revisited. 11th International Mach reflection Symposium University of Victoria, BC, CanadaGoogle Scholar
  14. Setchell RE, Storm E, Sturtevant B (1972) An investigation of shock strengthening in a conical convergent channel. J Fluid Mech 56:505–522MATHCrossRefADSGoogle Scholar
  15. Smith LG (1945) Photographic investigation of the reflection of plane shocks in air. Rept no 6271 Office of Sci Res and Dev, USAGoogle Scholar
  16. Takayama K, Sekiguchi H (1976) Shock wave reflection by cones. Rept Inst High Speed Mech Tohoku Univ, JapanGoogle Scholar
  17. Whitham GB (1957) A new approach to problems of shock dynamics, Part 1: Two dimensional problems. J Fluid Mech 2:145–171MATHMathSciNetCrossRefADSGoogle Scholar
  18. Whitham GB (1958) On the propagation of shock waves through regions of non-uniform area or flow. J Fluid Mech 4:337–360MATHMathSciNetCrossRefADSGoogle Scholar
  19. Whitham GB (1959) A new approach to problems of shock dynamics Part 2: Three dimensional problems. J Fluid Mech 5:369–386MATHMathSciNetCrossRefADSGoogle Scholar

Copyright information

© Springer Verlag 1996

Authors and Affiliations

  • B. E. Milton
    • 1
  • R. D. Archer
    • 1
  1. 1.School of Mechanical and Manufacturing EngineeringUniversity of New South WalesSydneyAustralia

Personalised recommendations