Abstract
The onset of Mach reflection or regular reflection at the vertices of a converging polygonal shock wave was investigated experimentally in a horizontal annular shock tube. The converging shock waves were visualized by schlieren optics. Two different types of polygonal shock convergence patterns were observed. We compared the behavior during the focusing process for triangular and square-shaped shocks. It is shown that once a triangular shaped shock is formed, the corners in the converging shock will undergo regular reflection and consequently the shape will remain unaltered during the focusing process. A square-shaped shock suffers Mach reflections at the corners and hence a reconfiguring process takes place; the converging shock wave alternates between a square and an octagon formation during the focusing process.
Similar content being viewed by others
References
Apazidis N. and Lesser M.B. (1996). On generation and convergence of polygonal-shaped shock waves. J. Fluid Mech. 309: 301–319
Apazidis N., Lesser M.B., Tillmark N. and Johansson B. (2002). An experimental and theoretical study of converging polygonal shock waves. Shock waves 12: 39–58
Barbosa F.J. and Skews B.W. (2002). Experimental confirmation of the von Neumann theory of shock wave reflection transition. J. Fluid Mech. 472: 263–282
Ben-Dor G. (1992). Shock wave reflection phenomena. Springer, New York
Ben-Dor G. (2006). A state-of-the-knowledge review on pseudo-steady shock-wave reflections and their transition criteria. Shock waves 15: 277–294
Betelu, S.I., Aronson, D.G.: Focusing of noncircular self-similar shock waves. Phys. Rev. Lett. 87(7), 074,501 (2001). doi:10.1103/ PhysRevLett.87.074501
Eliasson, V., Apazidis, N., Tillmark, N.: Controlling the form of strong converging shocks by means of disturbances. Shock Waves (in press) (2006)
Eliasson V., Apazidis N., Tillmark N. and Lesser M.B. (2006). Focusing of strong shocks in an annular shock tube. Shock Waves 15: 205–217
Guderley G. (1942). Starke kugelige und zylindrische verdichtungsstöß e in der nähe des kugelmittelpunktes bzw. der zylinderachse. Luftfahrt Forsch 19: 302–312
Hornung H.G., Oertal H.J. and Sandeman R.J. (1979). Transitions to Mach reflection of shock waves in steady and pseudo steady flow with and without relaxation. J. Fluid Mech. 90: 541–560
von Neumann J. (1943). Collected Works VI. Pergamon, New York
Schwendeman D.W. (2002). On converging shock waves of spherical and polyhedral form. J. Fluid Mech. 454: 365–386
Schwendeman D.W. and Whitham G.B. (1987). On converging shock waves. Proc. R. Soc. Lond. A A413: 297–311
Takayama K., Kleine H. and Grönig H. (1987). An experimental investigation of the stability of converging cylindrical shock waves in air. Exp. Fluids 5: 315–322
Takayama K., Onodera O. and Hoshizawa Y. (1984). Experiments on the stability of converging cylindrical shock waves. Theor. Appl. Mech. 32: 305–329
Watanabe M. and Takayama K. (1991). Stability of converging cylindrical shock waves. Shock Waves 5: 149–160
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by B.W. Skews.
Rights and permissions
About this article
Cite this article
Eliasson, V., Kjellander, M. & Apazidis, N. Regular versus Mach reflection for converging polygonal shocks. Shock Waves 17, 43–50 (2007). https://doi.org/10.1007/s00193-007-0091-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00193-007-0091-0