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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: beric.skews@wits.ac.za
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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

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References

REFERENCES

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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.

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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.

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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.

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Video 235.5 KB