Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-01-09T21:14:41.307Z Has data issue: false hasContentIssue false
  • English
  • Français

Time history of regular to Mach reflection transition in steady supersonic flow

Published online by Cambridge University Press:  11 July 2011

S. G. LI ,
B. GAO  and
Z. N. WU
S. G. LI
Affiliation:
School of Aerospace Science, Tsinghua University, Beijing 100084, P R China
B. GAO
Affiliation:
School of Aerospace Science, Tsinghua University, Beijing 100084, P R China
Z. N. WU*
Affiliation:
School of Aerospace Science, Tsinghua University, Beijing 100084, P R China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we study the transition from regular to Mach reflection (RR → MR) in the dual solution domain due to the influence of an upstream disturbance, by considering the transition as an evolutionary rather than an abrupt process. From numerical simulation, we observe for the early stage of transition a multiple interaction structure, composed of a triple-shock structure, a type VI shock interaction and a shock/slipline interaction. In the end, we observe a pure unsteady MR structure. Under self-similar assumption of the triple point for the first stage and including additional Mach waves over the slipline for the last stage, we develop an idealized unsteady model to obtain the evolution of the Mach stem height and the time taken for the Mach stem to stabilize. The triple point is found to move at a nearly constant speed in the multiple interaction stage which occupies about one quarter of the transition time. In the pure unsteady MR stage, which occupies the rest of transition, the speed of the triple point drops nonlinearly until the Mach stem stabilizes.

JFM classification

Compressible Flows: Gas dynamics Aerodynamics: High-speed flow Compressible Flows: Shock waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 682 , 10 September 2011 , pp. 160 - 184
Copyright
Copyright © Cambridge University Press 2011

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., Igra, O., & Elperin, T. 2001 Handbook of Shock Waves. Academic.Google Scholar
Edney, B. 1968 Effects of shock-impingement on the heat transfer around blunt bodies. AIAA J. 6 (1), 15–21.CrossRefGoogle Scholar
Gao, B. & Wu, Z. N. 2010 A study of the flow structure for Mach reflection in steady supersonic flow. J. Fluid Mech. 656, 29–50.CrossRefGoogle Scholar
Gottlieb, J. J. & Groth, C. P. T. 1988 Assessment of Riemann solvers for unsteady one-dimensional inviscid flows of perfect gases. J. Comput. Phys. 78, 437–458.CrossRefGoogle Scholar
Ivanov, M. S., Klemenkov, G. P., Kudryavtsev, A. N., Fomin, V. M. & Kharitonov, A. M. 1997 Experimental investigation of transition to Mach reflection of steady shock waves. Dokl. Akad. Nauk 357 (5), 623–627.Google Scholar
Ivanov, M. S., Markelov, G. N., Kudryavtsev, A. N. & Gimelshein, S. E. 1998 Numerical analysis of shock wave reflection transition in steady flows. AIAA J. 36, 2079–2086.CrossRefGoogle Scholar
Ivanov, M. S., Kudryavtsev, A. N. & Khotyanovskii, D. V. 2000 Numerical simulation of the transition between the regular and Mach reflection of shock waves under the action of local perturbations. Dokl. Phys. 45 (7), 353–357.CrossRefGoogle Scholar
Kudryavtsev, A. N., Khotyanovsky, D. V., Ivanov, M. S. & Vandromme, D. 2002 Numerical investigations of transition between regular and Mach reflections caused by free-stream disturbances. Shock Waves 12, 157–165.CrossRefGoogle Scholar
Landau, L. D., & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon.Google Scholar
Li, H. & Ben-Dor, G. 1996 Application of the principle of minimum entropy production to shock wave reflections. I. Steady flows. J. Appl. Phys. 80, 2027–2037.CrossRefGoogle Scholar
Mouton, C. A. & Hornung, H. G. 2007 Mach stem height and growth rate predictions. AIAA J. 45, 1977–1987.CrossRefGoogle Scholar
Ren, Y. X. 2003 A robust shock-capturing scheme based on rotated Riemann solvers. Comput. Fluids 32, 1379–1403.CrossRefGoogle Scholar
Semenov, A. N., Berezkina, M. K., & Krasovskaya, I. V. 2009 Classification of shock wave reflections from a wedge. Part II. Experimental and numerical simulations of different types of Mach reflections. Tech. Phys., 54 (4), 497–503.CrossRefGoogle Scholar
Tan, L. H., Ren, Y. X. & Wu, Z. N. 2006 Analytical and numerical study of the near flow field and shape of the Mach stem in steady flows. J. Fluid Mech. 546, 341–362.CrossRefGoogle Scholar
Teshukov, V. M. 1989 On stability of RR of shock waves. Prikl. Mekh. Tekh. Fiz. 2, 26–33.Google Scholar
Von Neumann, J. 1943 Oblique reflection of shock. Explosive Research Report 12. Navy Department, Bureau of Ordnance, Washington, DC.Google Scholar
Von Neumann, J. 1945 Refraction, intersection and reflection of shock waves. NAVORD Report 203–245. Navy Department, Bureau of Ordnance, Washington, DC.Google Scholar