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Study of asymmetrical shock wave reflection in steady supersonic flow

Published online by Cambridge University Press:  13 February 2019

Jing Lin ,
Chen-Yuan Bai  and
Zi-Niu Wu Open the ORCID record for Zi-Niu Wu [Opens in a new window]
Jing Lin
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
Chen-Yuan Bai
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
Zi-Niu Wu*
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
*
†Email address for correspondence: ziniuwu@tsinghua.edu.cn
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Abstract

The asymmetrical Mach reflection configuration is studied analytically in this paper, using an asymmetrical model extended from a recent symmetrical model and accounting for the new features related to asymmetry of the two wedges. It is found that the two sliplines do not turn parallel to the incoming flow at the same horizontal location and the sonic throat locates at the position where the difference of slopes of the two sliplines vanishes. This allows us to define a new sonic throat compatibility condition essential to determine the size of the Mach stem. The present model gives the height of the Mach stem, declined angle of the Mach stem from vertical axis, sonic throat location and shape of all shock waves and sliplines. The accuracy of the model is checked by computational fluid dynamics (CFD) simulation. It is found that the Mach stem height is strongly dependent on asymmetry of the wedge angles and almost linearly dependent on the asymmetry of the wedge lower surface lengths. The Mach stem height is shown to be insensitive to the asymmetry of the horizontal positions of the two wedges. The mechanisms for these observations are explained. For instance, it is demonstrated that the Mach reflection configuration remains closely similar when there is horizontal shift of either wedge.

JFM classification

Aerodynamics: High-speed flow Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 864 , 10 April 2019 , pp. 848 - 875
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Copyright
© 2019 Cambridge University Press 

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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.Google Scholar
Bai, C. Y. & Wu, Z. N. 2017 Size and shape of shock waves and slipline for Mach reflection in steady flow. J. Fluid Mech. 818, 116–140.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.Google Scholar
Chpoun, A. & Lengrand, J. C. 1997 Confirmation experimentale d’un phenomene d’hysteresis lors de l’interaction de deux chocs obliques de familles differentes. C. R. Acad. Sci. Paris 324 (1), 1–8.Google Scholar
Courant, R. & Friedrichs, K. O. 1948 Supersonic Flow and Shock Waves. Wiley-Interscience.Google 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. 1985a Observation and analysis of the Mach reflection of weak uniform plane shock waves. Part 1. Observations. J. Fluid Mech. 152, 49–66.Google Scholar
Dewey, J. M. & McMillin, D. J. 1985b Observation and analysis of the Mach reflection of weak uniform plane shock waves. Part 2. Analysis. J. Fluid Mech. 152, 67–81.Google 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.Google Scholar
Guan, X. K, Bai, C. Y. & Wu, Z. N. 2018 Steady Mach reflection with two incident shock waves. J. Fluid Mech. 855, 882–909.Google Scholar
Henderson, L. F. & Lozzi, A. 1975 Experiments on transition of Mach reflection. J. Fluid Mech. 68, 139–155.Google Scholar
Hornung, H. G. 2014 Mach reflection in steady flow. I. Mikhail Ivanov’s contributions, II. Caltech stability experiments. In AIP Conference Proceedings, vol. 1628, pp. 1384–1393. AIP Publishing.Google Scholar
Hornung, H. G. & Mouton, C. A. 2008 Some more on transition between regular and Mach reflection of shock waves. In 38th Fluid Dynamics Conference and Exhibit, Washington, USA, AIAA.Google 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.Google 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.Google 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. 496, 71–87.Google Scholar
Kudryavstsev, A. N., Khotyanosky, D. V. & Ivanov, M. S 2000 Numerical simulation of asymmetrical steady shock wave interactions. In European Congress on Computational Methods in Applied Science and Engineering, Barcelona, Spain.Google Scholar
Li, H. & Ben-Dor, G. 1996 Oblique-shock/expansion–fan interaction – analytical solution. AIAA J. 34, 418–421.Google Scholar
Li, H. & Ben-Dor, G. 1997 A parametric study of Mach reflection in steady flows. J. Fluid Mech. 341, 101–125.Google Scholar
Li, H., Ben-Dor, G. & Han, Z. Y. 1994 Modification on the Whitham theory for analyzing the reflection of weak shock waves over small wedge angles. Shock Waves 4, 41–45.Google 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.Google Scholar
Mouton, C. A.2008 Transition between regular reflection and Mach reflection in the dual-solution domain. PhD thesis, California Institute of Technology.Google Scholar
Mouton, C. A. & Hornung, H. G. 2007 Mach stem height and growth rate predictions. AIAA J. 45, 1977–1987.Google Scholar
Mouton, C. A. & Hornung, H. G. 2008 Experiments on the mechanism of inducing transition between regular and Mach reflection. Phys. Fluids 20, 126103.Google Scholar
Olim, M. & Dewey, J. M. 1992 A revised three-shock solution for the Mach reflection of weak shocks (1. 1 < Mi < 1. 5). Shock Waves 2, 167–176.Google Scholar
Roe, P. L. 1986 Characteristic based schemes for the Euler equations. Annu. Rev. Fluid Mech. 18, 337–365.Google Scholar
Roy, S. & Rajesh, G. 2017 Analytical prediction of Mach stem height for asymmetric wedge reflection in 2-D steady flows. In 31st International Symposium on Shock Waves, Nagoya, Japan.Google Scholar
Schmisseur, J. D. & Gaitonde, D. V. 2011 Numerical simulation of Mach reflection in steady flows. Shock Waves 21, 499–509.Google 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.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.Google Scholar
Tao, Y., Liu, W., Fan, X., Xiong, B., Yu, J. & Sun, M. 2017 A study of the asymmetric shock reflection configurations in steady flows. J. Fluid Mech. 825, 1–15.Google Scholar
von Neumann, J.1943 Oblique reflection of shock. Explos. Res. Rep. 12. Navy Dept., Bureau of Ordinance, Washington, DC.Google Scholar