Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-19T02:54:18.450Z Has data issue: false hasContentIssue false
  • English
  • Français

Characterization of disturbance propagation in weak shock-wave reflections

Published online by Cambridge University Press:  26 April 2006

Akihiro Sasoh  and
Kazuyoshi Takayama
Akihiro Sasoh
Affiliation:
Shock Wave Research Center, Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba, Sendai 980, Japan
Kazuyoshi Takayama
Affiliation:
Shock Wave Research Center, Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba, Sendai 980, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

Reflections of weak shock waves over wedges are investigated mainly by considering disturbance propagation which leads to a flow non-uniformity immediately behind a Mach stem. The flow non-uniformity is estimated by the local curvature of a smoothly curved Mach stem, and is characterized not only by a pressure increase immediately behind the Mach stem on the wedge but also by a propagation speed. In the case of a smoothly curved Mach stem as is observed in a von Neumann Mach reflection, the pressure increase behind the Mach stem is approximately determined by Whitham's ray-shock theory. The propagation speed of the flow non-uniformity is approximated by Whitham's shock-shock relation. If the shock-shock does not catch up with a point where a curvature of the Mach stem vanishes, a von Neumann Mach reflection appears. The boundary on which the above-mentioned condition breaks results in the transition from a von Neumann Mach reflection to a simple Mach reflection. This idea leads to a transition criterion for a von Neumann Mach reflection, which is algebraically expressed by χ1 = χs where χ1 is the trajectory angle of the point on the Mach stem where the local curvature vanishes and is approximately replaced by χg—θw (χg is the angle of glancing incidence, and θw is the apex angle of the wedge) and χs is the trajectory angle of Whitham's shock-shock, measured from the surface of the wedge. For shock Mach numbers of 1.02 to 2.2 and a wedge angle from 0° to 30°, the domains of a von Neumann Mach reflection, simple Mach reflection and regular reflection are determined by experiment, numerical simulation and theory. The present transition criterion agrees well with experiments and numerical simulations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 277 , 25 October 1994 , pp. 331 - 345
Copyright
© 1994 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ames 1953 Equations, tables and charts for compressible flow. Ames Aeronautical Laboratory Rep. 1135.
Ben-Dor, G. 1991 Shock Wave Reflection Phenomena. Springer.
Ben-Dor, G. & Takayama, K. 1992 The phenomena of shock reflection - a review of unsolved problems and future research needs. Shock Waves Intl J. 2, 211–223.Google Scholar
Birkhoff, G. 1950 Hydrodynamics, a Study in Logic, Fact and Similitude. Princeton University Press, NJ.
Brown, L. (ed.) 1992 Book of Abstracts, the 10th Mach Reflection Symposium, Denver.
Chester, W. 1954 The quasi cylindrical shock tube. Phil. Mag. 45, 1293–1301.Google Scholar
Chisnell, R. F. 1957 The motion of a shock wave in a channel with applications to cylindrical and spherical shock waves. J. Fluid Mech. 2, 286–298.Google Scholar
Colella, P. & Henderson, L. F. 1990 The von Neumann paradox for the diffraction of weak shock waves. J. Fluid Mech. 213, 71–94.Google Scholar
Glass, I. I. 1987 Some aspects of shock-wave research. AIAA J. 25, 214–229.Google Scholar
Harten, A. 1983 High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49, 357–393.Google Scholar
Henderson, L. F. 1987 Z. angew. Math. Mech. 67, 73–86.
Jahn, R. G. 1957 Transition processes in shock wave interactions. J. Fluid Mech. 2, 33–52.Google Scholar
Jones, D. M., Martin, P. M. E. & Thornhill, C. K. 1951 A note on the pseudo-stationary flow behind a strong shock diffracted or reflected at a corner. Proc. R. Soc. Lond. A 209, 238–248.Google Scholar
Lighthill, M. J. 1949 They diffraction of blast. I. Proc. R. Soc. Lond. A 198, 454–470.Google Scholar
Neumann, J. von 1945 Refraction, intersection and reflection of shock waves. NAVORD Rep. 203-45, Navy Dept, Bureau of Ordinance, Washington, DC.
Olim, M. & Dewey, J. M. 1992 A revised three-shock solution for the Mach reflection of weak shocks (1.1 < Mt < 1.5). Shock Waves Intl J. 2, 167–176.Google Scholar
Reichenbach, H. (ed.) 1990 Book of Abstracts, the 9th Mach Reflection Symposium, Freiburg.
Sakurai, A. 1964 On the problem of weak Mach reflection. J. Phys. Soc. Japan 19, 1440–1450.Google Scholar
Sakurai, A., Henderson, L. F., Takayama, K., Walenta, Z. & Colella, P. 1989 On the von Neumann paradox of weak Mach reflection. Fluid Dyn. Res. 4, 333–345.Google Scholar
Sasoh, A., Takayama, K. & Saito, T. 1992 A weak shock wave reflection over wedges. Shock Waves Intl J. 2, 277–281.Google Scholar
Sternberg, J. 1959 Triple-shock-wave intersections. J. Fluid Mech. 2, 179–206.Google Scholar
Takayama, K. 1983 Application of holographic interferometry to shock wave research. Proc. SPIE 398, 174–181.Google Scholar
Tanno, H. 1991 Study on weak shock wave reflections. Master dissertation, Tohoku University (in Japanese).
Whitham, G. B. 1957 A new approach to problems of shock dynamics. Part 1. Two-dimensional problems. J. Fluid Mech. 2, 145–171.Google Scholar
Yang, J., Onodera, O. & Takayama, K. 1994 Design and performance of a quick opening shock tube using a rubber membrane for weak shock wave generation. JSME J. (in Japanese) 60, 473–478.Google Scholar
Yee, H. C. 1987 Upwind and symmetric shock-capturing schemes. NASA Tech. Mem. 89464.Google Scholar