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Dynamic effects on the transition between two-dimensional regular and Mach reflection of shock waves in an ideal, steady supersonic free stream

Published online by Cambridge University Press:  15 April 2011

K. NAIDOO  and
B. W. SKEWS
K. NAIDOO*
Affiliation:
School of Mechanical, Aeronautical and Industrial Engineering, University of the Witwatersrand, Johannesburg, 2050, South Africa
B. W. SKEWS
Affiliation:
School of Mechanical, Aeronautical and Industrial Engineering, University of the Witwatersrand, Johannesburg, 2050, South Africa
*
†Council for Scientific and Industrial Research, Defence Peace Safety and Security, Aeronautics Systems Competency, Pretoria, South Africa, 0001. Email address for correspondence: [email protected]
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Abstract

There have been numerous studies on the steady-state transition criteria between regular and Mach reflection of shock waves generated by a stationary, two-dimensional wedge in a steady supersonic flow, since the original shock-wave reflection research by Ernst Mach in 1878. The steady, two-dimensional transition criteria between regular and Mach reflection are well established. There has been little done to consider the dynamic effect of a rapidly rotating wedge on the transition between regular and Mach reflection. This paper presents the results of an investigation on the effect of rapid wedge rotation on regular to Mach reflection transition in the weak- and strong-reflection ranges with the aid of experiment and computational fluid dynamics. The experimental set-up includes a novel facility to rotate a pair of large aspect ratio wedges in a 450 mm × 450 mm supersonic wind tunnel at wedge rotation speeds up to 11000 deg s−1. High-speed images and measurements are presented. A numerical solution of the inviscid governing flow equations was used to mimic the experimental motion and to extend the investigation beyond the limits of the current facility to explore the influence of variables in the parameter space. There is good agreement between experimental measurements and numerical simulation. This paper includes the first experimental evidence of the regular to Mach reflection transition beyond the steady-state detachment condition in the weak- and strong-reflection ranges. It also presents results of simulations for the dynamic regular to the Mach reflection transition which show a difference between the sonic, length-scale and detachment conditions. This paper includes experimental evidence of the Mach to regular reflection transition below the steady-state von Neumann condition.

JFM classification

Compressible Flows: Shock waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 676 , 10 June 2011 , pp. 432 - 460
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Azevedo, D. J. & Liu, C. S. 1993 Engineering approach to the prediction of shock patterns in bounded high-speed flows. AIAA J. 31, 83–90.CrossRefGoogle Scholar
Ben-Dor, G. 1999 Hysteresis phenomena in shock wave reflections in steady flows. In Proc. 22nd Intl Symp. on Shock Waves (ed. Ball, G. J., Hillier, R. & Roberts, G. T.), paper 6000. University of Southampton Press.Google Scholar
Ben-Dor, G. 2007 Shock Wave Reflection Phenomena. Springer.Google Scholar
Ben-Dor, G., Ivanov, M., Vasilev, E. I. & Elperin, T. 2002 Hysteresis processes in the regular reflection ↔ Mach reflection transition in steady flows. Prog. Aerosp. Sci. 38, 347–387.CrossRefGoogle Scholar
Chpoun, A. & Ben-Dor, G. 1995 Numerical confirmation of the hysteresis phenomenon in the regular to Mach reflection transition in steady flows. Shock Waves 5, 199–203.CrossRefGoogle Scholar
Felthun, L. T. & Skews, B. W. 2004 Dynamic shock wave reflection. AIAA J. 42, 1633–1639.CrossRefGoogle Scholar
Henderson, L. F. & Lozzi, A. 1979 Further experiments on transition to Mach reflexion. J. Fluid Mech. 94, 541–559.CrossRefGoogle Scholar
Hornung, H. G. 1986 Regular and Mach reflection of shock waves. Annu. Rev. Fluid Mech. 18, 33–58.CrossRefGoogle Scholar
Hornung, H. G. 1997 On the stability of steady-flow regular and Mach reflection. Shock Waves 7, 123–125.CrossRefGoogle Scholar
Hornung, H. G., Oertel, H. & Sandeman, R. J 1979 Transition to Mach reflection of shock-waves in steady and pseudo-steady flow with and without relaxation. J. Fluid Mech. 90, 541–560.CrossRefGoogle Scholar
Hornung, H. G. & Robinson, M. L. 1982 Transition from regular to Mach reflection of shock waves. Part 2. The steady flow criterion. J. Fluid Mech. 123, 155–164.CrossRefGoogle Scholar
Ivanov, M. S., Gimelshein, S. F. & Beylich, A. E. 1995 Hysteresis effect in stationary reflection of shock-waves. Phys. Fluids 7, 685–687.CrossRefGoogle Scholar
Ivanov, M. S., Kudryavtsev, A. N., Nikiforov, S. B., Khotyanovsky, D. V. & Pavlov, A. A. 2003 Experiments on shock-wave reflection transition and hysteresis in a low-noise wind tunnel. Phys. Fluids 15, 1807–1810.CrossRefGoogle Scholar
Ivanov, M. S., Markelov, G. N., Kudryavtsev, A. N. & Gimelshein, S. F. 1998 Numerical analysis of shock wave reflection transition in steady flows. AIAA J. 36, 2079–2086.CrossRefGoogle Scholar
Ivanov, M. S., Vandromme, D., Fomin, V. M., Kudryavtsev, A. N., Hadjadj, A. & Khotyanovsky, D. V. 2001 Transition between regular and Mach reflection of shock waves: new numerical and experimental results. Shock Waves 11, 199–207.CrossRefGoogle Scholar
Ivanov, M. S., Zeitoun, D., Vuillon, J., Gimelshein, S. F. & Markelov, G. N. 1996 Investigation of the hysteresis phenomena in steady shock reflection using kinetic and continuum methods. Shock Waves 5, 341–346.CrossRefGoogle Scholar
Khotyanovsky, D. V., Kudryavtsev, A. N. & Ivanov, M. S. 1999 Numerical study of transition between steady regular and Mach reflection caused by free-stream perturbations. In Proc. 22nd Intl Symp. on Shock Waves (ed. Ball, G. J., Hillier, R. & Roberts, G. T.). University of Southampton Press.Google Scholar
Kudryavtsev, A. N., Khotyanovsky, D. V., Ivanov, M. S., Hadjadj, A. & Vandromme, D. 2002 Numerical investigations of transition between regular and Mach reflections caused by free-stream disturbances. Shock Waves 12, 157–165.CrossRefGoogle Scholar
Li, H., Chpoun, A. & Ben-Dor, G. 1999 Analytical and experimental investigations of the reflection of asymmetric shock waves in steady flows. J. Fluid Mech. 390, 25–43.CrossRefGoogle Scholar
Liou, M. 1996 A sequel to AUSM: AUSM+. J. Comput. Phys. 129, 364–382.CrossRefGoogle Scholar
Markelov, G. N., Pivkin, I. V. & Ivanov, M. S. 1999 Impulsive wedge rotation effects on transition from regular to Mach reflection. In Proc. 22nd Intl Symp. on Shock Waves (ed. Ball, G. J., Hillier, R. & Roberts, G. T.). University of Southampton Press.Google Scholar
Mouton, C. A. & Hornung, H. G. 2007 Mach stem height and growth rate predictions. AIAA J. 45, 1977–1987.CrossRefGoogle Scholar
Mouton, C. A. & Hornung, H. G. 2008 Experiments on the mechanism of inducing transition between regular and Mach reflection. Phys. Fluids 20, 126103:1–11.CrossRefGoogle Scholar
Settles, G. S. 2001 Schlieren and Shadowgraph Techniques:Visualising Phenomena in Transparent Media. Springer.CrossRefGoogle Scholar
Skews, B. W 1997 Aspect ratio effects in wind tunnel studies of shock wave reflection transition. Shock Waves 7, 373–383.CrossRefGoogle Scholar
Skews, B. W. 2000 Three dimensional effects in wind tunnel studies of shock wave reflection. J. Fluid Mech. 407, 85–104.CrossRefGoogle Scholar
Sudani, N., Sato, M., Karasawa, T., Noda, J., Tate, A. & Watanabe, M. 2002 Irregular effects on the transition from regular to Mach reflection of shock waves in wind tunnel flows. J. Fluid Mech. 459, 167–185.CrossRefGoogle Scholar
Vuillon, J., Zeitoun, D. & Ben-Dor, G. 1995 Reconsideration of oblique shock wave reflection in steady flows. Part 2. Numerical investigation. J. Fluid Mech. 301, 37–50.CrossRefGoogle Scholar