Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-12-01T12:04:45.701Z Has data issue: false hasContentIssue false
  • English
  • Français

Shock wave interaction with convex circular cylindrical surfaces

Published online by Cambridge University Press:  16 April 2010

BERIC W. SKEWS  and
HARALD KLEINE
BERIC W. SKEWS*
Affiliation:
School of Mechanical, Industrial, and Aeronautical Engineering, University of the Witwatersrand, Johannesburg 2050, South Africa
HARALD KLEINE
Affiliation:
School of Engineering and Information Technology, University of New South Wales, Australian Defence Force Academy, Canberra, ACT 2600, Australia
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The reflection of shock waves off cylindrical surfaces of different radii is examined with the help of time-resolved flow visualization. The primary diagnostic is a newly developed technique based on the tracking of deliberately introduced small perturbations in the flow. The main focus of the investigation is to determine at which position the shock wave receives information about the shape of the wall that it reflects off. In the pseudo-steady shock reflection off a plane wall, it is commonly accepted that the reflection changes from regular to irregular as soon as sonic signals generated behind the reflection point catch up with the reflection point, and the common interpretation is that this corresponds to the transition from regular to Mach reflection (the so-called sonic criterion). The results obtained here for convex circular surfaces show that this ‘catch-up’ condition occurs at wall angles considerably higher than in the plane wall case, while a visible Mach stem occurs only further along the surface at wall angles distinctively lower than those for plane walls. Tests are also conducted on a surface where a cylindrical portion is followed by a fixed angle plane section. The Mach numbers are chosen to be on either side of the plane wall transition condition so as to examine the adjustment from reflection on the cylindrical portion to that on the plane wall. These tests confirm that the wall angle at which sonic ‘catch-up’ to the reflection point occurs on the cylindrical surface is much higher than the corresponding wall angle predicted by the sonic criterion for a plane wall. While the transition from regular to irregular reflection is not the main concern of this contribution, the present results show that the transition criteria developed for steady and pseudo-steady flows are only of limited use in the fully unsteady flows such as the one investigated here.

JFM classification

Compressible Flows: Shock waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 654 , 10 July 2010 , pp. 195 - 205
Copyright
Copyright © Cambridge University Press 2010

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

REFERENCES

Ben-Dor, G. 2007 Shock Wave Reflection Phenomena. Springer.Google Scholar
Ben-Dor, G., Mazor, G., Takayama, K. & Igra, O. 1987 Influence of surface roughness on the transition from regular to Mach reflection in pseudo-steady flows. J. Fluid Mech. 176, 336–356.CrossRefGoogle Scholar
Hakkaki-Fard, A. & Timofeev, E. 2009 High resolution determination of sonic and detachment angles at shock wave reflection from a circular cylinder. In Proceedings of 17th Annual Conference of the CFD Society of Canada. Paper CFDSC2009-4D3.Google Scholar
Hornung, H. G., Oertel, H. & Sandeman, R. J. 1979 Transition to Mach reflexion of shock waves in steady and pseudosteady flow with and without relaxation. J. Fluid Mech. 90, 541–560.CrossRefGoogle Scholar
Lock, G. D. & Dewey, J. M. 1989 An experimental investigation of the sonic criterion for transition from regular to Mach reflection of weak shock waves. Exp. Fluids 7, 289–292.CrossRefGoogle Scholar
von Neumann, J. 1943 Oblique reflection of shocks. Tech. Rep. 12. Bur. Ord. Explosives Research.Google Scholar
Skews, B. W. & Kleine, H. 2009 Unsteady flow diagnostics using weak perturbations. Exp. Fluids 46, 65–76.CrossRefGoogle Scholar
Smith, L. G. 1945 Photographic investigation of the reflection of plane shocks in air. Tech. Rep. 6271. Office of Scientific Research and Development.Google Scholar
Takayama, K. & Sasaki, M. 1983 Effects of radius of curvature and initial angle on the shock transition over concave and convex walls. Tech. Rep. 46. Institute of High Speed Mechanics, Tohoku University, Sendai, Japan.Google Scholar
Timofeev, E., Skews, B. W., Voinovich, P. A. & Takayama, K. 1999 The influence of unsteadiness and three-dimensionality on the regular-to-Mach reflection transitions: a high-resolution study. In Proceedings of the 22nd International Symposium on Shock Waves (ed. Ball, G. J., Hillier, R. & Roberts, G. T.), pp. 1231–1236. University of Southampton, UK.Google Scholar

Skews and Kleine supplementary movie

Movie 1. A Mach number 1.324 incident shock reflecting off a 75 mm radius cylinder showing the development of the perturbation signals. The number at the bottom right-hand corner of each frame is the elapsed time in microseconds.

Download Skews and Kleine supplementary movie(Video)
Video 677.9 KB

Skews and Kleine supplementary movie

Movie 2. Propagation of a Mach 1.230 shock along a 300 mm radius surface fitted with two perturbation sources, one on either side of the catch-up condition.

Download Skews and Kleine supplementary movie(Video)
Video 716.8 KB

Skews and Kleine supplementary movie

Movie 3. Propagation of a Mach 1.230 incident wave over a compound wall consisting of a 75 mm circular cylinder followed by a plane wall at 45 degrees inclination. A new corner signal appears along the upper portion of the plane wall.

Download Skews and Kleine supplementary movie(Video)
Video 235.5 KB