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A study of the flow structure for Mach reflection in steady supersonic flow

Published online by Cambridge University Press:  21 May 2010

B. GAO  and
Z. N. WU
B. GAO
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R. China
Z. N. WU*
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R. China
*
†Email address for correspondence: [email protected]
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Abstract

In this paper we study the waves generated over the slipline and their interactions with other waves for Mach reflection in steady two-dimensional supersonic flow. We find that a series of expansion and compression waves exist over the slip line, even in the region immediately behind the leading part of the reflected shock wave, previously regarded as a uniform flow. These waves make the leading part of the slipline, previously regarded as straight, deviate nonlinearly towards the reflecting surface. When the transmitted expansion waves from the upper corner first intersect the slipline, an inflexion point is produced. Downstream of this inflexion point, compression waves are produced over the slipline. By considering the interaction between the various expansion or compression waves, we obtain a Mach stem height, the shape and position of the slipline and reflected shock wave, compared well to computational fluid dynamics (CFD) results. We also briefly consider the case with a subsonic portion behind the reflected shock wave. The global flow pattern is obtained through CFD and the starting point of the sonic line is identified through a simple analysis. The sonic line appears to coincide with the first Mach wave from the upper corner expansion fan after transmitted from the reflected shock wave.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 656 , 10 August 2010 , pp. 29 - 50
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Azevedo, D. J. 1989 Analytical prediction of shock patterns in a high-speed wedge bounded duct. PhD thesis, Department of Mechanical and Aeronautical Engineering, State University, Buffalo, NY.Google Scholar
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. 2007 Shock Wave Reflection Phenomena. Springer.Google Scholar
Ben-Dor, G., Elperin, T. & Vasiliev, E. I. 2003 Flow Mach number induced hysteresis phenomena in the interaction of conical shock waves – a numerical investigation. J. Fluid Mech. 496, 335–354.CrossRefGoogle Scholar
Bloor, M. I. G. 1965 Determination of the sonic line in hypersonic flow past a blunt body. J. Fluid Mech. 21, 495–501.CrossRefGoogle Scholar
Chow, W. L. & Chang, I. S. 1974 Mach reflection associated with over-expanded nozzle free jet flows. AIAA J. 13, 762–766.CrossRefGoogle Scholar
Chpoun, A., Passerel, D., Lengrand, J. C., Li, H. & Ben-Dor, G. 1994 Mise en evidence experimentale et numerique d'un phenomane d'hysteresis lors de la transition reflexion de Mach-reflexion reguliere. Mec. Fluides/Fluid Mech., C. R. Acad. Sci. Paris 319 (II), 1447–1453.Google Scholar
Chpoun, A., Passerel, D., Li, H. & Ben-Dor, G. 1995 Reconsideration of the oblique shock wave reflection in steady flows. Part 1. Experimental investigation J. Fluid Mech. 301, 19–35.CrossRefGoogle Scholar
Dewey, J. M. & Barss, T. 1996 The shape of the Mach stem. In Proceedings of 12th International Mach Reflection Symposium, Pilanesberg, South Africa, pp. 263–274.Google Scholar
Dewey, J. M. & McMillin, D. J. 1985 a Observation and analysis of the Mach reflection of weak uniform plane shock waves. Part 1. Observations. J. Fluid Mech. 152, 49–66.CrossRefGoogle Scholar
Dewey, J. M. & McMillin, D. J. 1985 b Observation and analysis of the Mach reflection of weak uniform plane shock waves. Part 2. Analysis. J. Fluid Mech. 152, 67–81.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, 541–559.CrossRefGoogle Scholar
Hornung, H. G., Oertel, H. & Sandeman, R. J. 1979 Transition to Mach reflection of shock waves in steady and pseudo-steady flows with and without relaxation. J. Fluid Mech. 90, 541–560.CrossRefGoogle Scholar
Hornung, H. G. & Robinson, M. L. 1982 Transition from regular to MR of shock waves. Part 2. The steady flow criterion. J. Fluid Mech. 123, 155–164.CrossRefGoogle Scholar
Ivanov, M. S., Ben-Dor, G., Elperin, T., Kudryavtsev, A. N. & Khotyanovsky, D. V. 2002 The reflection of asymmetric shock waves in steady flows: a numerical investigation. J. Fluid Mech. 469, 71–87.CrossRefGoogle Scholar
Irving Brown, Y. A. & Skews, B. W. 2004 Three-dimensional effects on regular reflection in steady supersonic flows. Shock Waves 13, 339–349.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
Landau, L. D. & Lifshitz, E. M. 1987 Course of Theoretical Physics Vol. 06 Fluid mechanics. Butterworth-Heinemann.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
Li, H. & Ben-Dor, G. 1997 A parametric study of Mach reflection in steady flows. J. Fluid Mech. 341, 101–125.CrossRefGoogle Scholar
Li, H., Ben-Dor, G. & Han, Z. Y. 1994 Modification on the Whitham theory for analysing the reflection of weak shock waves over small wedge angles. Shock Waves J. 4, 41–45.CrossRefGoogle Scholar
Mach, E. 1878 Uber den verlauf von Funkenwellen in der Ebene und im Raume. Sitzungsbr. Akad. Wiss. Wien. 78, 819–838.Google Scholar
Mouton, C. A. & Hornung, H. G. 2007 Mach stem height and growth rate predictions. AIAA J. 45, 1977–1987.CrossRefGoogle Scholar
Olim, M. & Dewey, J. M. 1992 A revised three-shock solution for the Mach reflection of weak shocks (1.1 < M i < 1.5). Shock Waves J. 2, 167–176.CrossRefGoogle Scholar
Ren, Y. X. 2003 A robust shock-capturing scheme based on rotated Riemann solvers. Comput. Fluids 32, 1379–1403.CrossRefGoogle Scholar
Samtaney, R. & Pullin, D. I. 1996 On initial value and self-similar solutions of the compressible Euler equations. Phys. Fluids 8, 2650–2655.CrossRefGoogle Scholar
Shirozu, T. & Nishida, M. 1995 Numerical studies of oblique shock reflection in steady two-dimensional flows. Mem. Fac. Engng Kyushu Univ. 55, 193–204.Google Scholar
Sauer, R. 1947 General characteristics of the flow through nozzles at near critical speeds. Tech Rep. TM-1147. NACA.Google 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. Techn. Fiz. 2, 26–33.Google Scholar
Von Neumann, J. 1943 Oblique reflection of shock. Explos. Res. Rep. 12. Navy Depatment, Bureau of Ordinance, Washington, DC.Google Scholar
Von Neumann, J. 1945 Refraction, intersection and reflection of shock waves. NAVORD Rep. 203–245. Navy Department, Bureau of Ordinance, Washington, DC.Google Scholar
Vuillon, J., Zeitoun, D. & Ben-Dor, G. 1995 Reconstruction of oblique shock wave reflection in steady flows. Part 2. Numerical investigation. J. Fluid Mech. 301, 37–50.CrossRefGoogle Scholar