Hostname: page-component-77c89778f8-7drxs Total loading time: 0 Render date: 2024-07-24T06:04:20.969Z Has data issue: false hasContentIssue false
  • English
  • Français

Shock-wave/expansion-wave interactions and the transition between regular and Mach reflection

Published online by Cambridge University Press:  07 March 2007

R. HILLIER
R. HILLIER*
Affiliation:
Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper presents numerical simulations for the interaction of an expansion wave with an incident shock wave of the opposite family, the specific aim being to study the resultant reflection of the now-perturbed shock wave from a solid surface. This problem is considered in the context of an incident flow entering a parallel duct, a situation that commonly arises in a range of flow-turning problems including supersonic intake flows. Once the incident shock conditions are such that Mach reflection must occur, it is shown that stabilization of a simple Mach reflection is only possible for a narrow range of Mach numbers and that this depends sensitively on the relative streamwise positioning of the origins of the shock wave and the expansion wave.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 575 , March 2007 , pp. 399 - 424
Copyright
Copyright © Cambridge University Press 2007

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

Azevedo, D. J. & Liu, C. S. 1989 Engineering approach to the prediction of shock patterns in bounded high-speed flows. AIAA J. 31, 83–90.CrossRefGoogle Scholar
Ben-Artzi, M. & Falcovitz, J. 1984 A second-order Godunov-type scheme for compressible fluid dynamics. J. Comput. Phys. 55, 1–32.CrossRefGoogle Scholar
Ben-Dor, G., Elperin, T., Li, H. & Vasiliev, E. I. 1999 The influence of downstream pressure on the shock wave reflection process in steady flows. J. Fluid Mech. 386, 213–232.CrossRefGoogle Scholar
Ben-Dor, G., Ivanov, M., Vasiliev, E. I. & Elperin, T. 2002 Hysteresis processes in the regular reflection ← Mach reflection transition in steady flows. Prog. Aerospace Sci. 38, Nos 4–5, 347–387.CrossRefGoogle Scholar
Chpoun, A., Passerel, D., Li, H. & Ben-Dor, G. 1995 Reconsideration of oblique shock wave reflection in steady flows. Part 1. Experimental investigation. J. Fluid Mech. 301, 19–50.CrossRefGoogle Scholar
Henderson, L. F. & Lozzi, A. 1975 Experiments on transition of Mach reflection. J. Fluid Mech. 68, 139–155.CrossRefGoogle Scholar
Henderson, L. F. & Lozzi, A. 1979 Further experiments on transition of Mach reflection. J. Fluid Mech. 94, 541–549.CrossRefGoogle Scholar
Hillier, R. 1991 Numerical modelling of shock wave diffraction at a ninety degrees convex edge. Shock Wave J. 1, 89–98.CrossRefGoogle Scholar
Hornung, H. G., Oertel, H. & Sandeman, R. J. 1979 Transition Mach reflexion of shock waves in steady and pseudosteady 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., Markelov, G. N., Kudryavtsev, A. N. & Gimelshein, S. F. 1998 Numerical analysis of shock wave reflection in steady flows. AIAA J. 36, 2079–2086.CrossRefGoogle Scholar
Li, H. & Ben-Dor, G. 1995 Oblique-shock/expansion interaction –analytical solution. AIAA J. 34, 418–421.CrossRefGoogle Scholar
Li, H. & Ben-Dor, G. 1997 A parametric study of Mach reflection in steady flows. J. Fluid Mech. 341, 101–125.CrossRefGoogle Scholar
Liepmann, H. W. & Roshko, A. 1957 Elements of Gas Dynamics. Wiley.Google Scholar
Molder, S. 1979 Particular conditions for the termination of regular reflection of shock waves. CASI Trans. 25, 44–49.Google Scholar
vonNeumann, J. Neumann, J. 1943 Oblique reflection of shock. Collected Works, vol. 6, pp. 238–299. Pergamon.Google Scholar