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Steady Mach reflection with two incident shock waves

Published online by Cambridge University Press:  21 September 2018

Xiao-Ke Guan
Affiliation:
Department of Engineering Mechanics, School of Aerospace Engineering, Tsinghua University, Beijing 100084, PR China
Chen-Yuan Bai
Affiliation:
Department of Engineering Mechanics, School of Aerospace Engineering, Tsinghua University, Beijing 100084, PR China
Zi-Niu Wu*
Affiliation:
Department of Engineering Mechanics, School of Aerospace Engineering, Tsinghua University, Beijing 100084, PR China
*
Email address for correspondence: ziniuwu@tsinghua.edu.cn

Abstract

Mach reflection in steady supersonic flow with two incident shock waves is studied. The second incident shock wave is produced by an additional deflection of the wedge lower surface, at some point ensuring that the two incident shock waves would intersect at the reflecting surface in case of normal reflection. Both theory and computational fluid dynamics (CFD) are used to study the flow structure and the influence of the second incident shock wave. The overall flow configuration, in case of Mach reflection, is shown to be composed of a triple shock structure, a shock/shock interaction structure and a shock/slipline reflection structure. Similar phenomenon, triggered by a high downstream pressure, has been observed before numerically, but not studied theoretically. The second incident shock wave reflects over the slipline to deflect the slipline more towards the reflecting surface, increasing thus the Mach stem height, advancing the transition of regular reflection to Mach reflection of the first incident shock wave, and causing an inverted Mach reflection below the usual von Neumann condition. A Mach stem height model built for a weak second incident shock wave is used to study the influence of the second incident shock wave on the Mach stem height. Both theory and CFD predict a maximum of the Mach stem height at some additional wedge deflection angle.

Type
JFM Papers
Copyright
© 2018 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, 8390.CrossRefGoogle 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, 116140.CrossRefGoogle Scholar
Ben-Dor, G. 2007 Shock Wave Reflection Phenomena. Springer.Google Scholar
Ben-Dor, G., Elperin, T., Li, H. & Vasiliev, E. 1999 The influence of the downstream pressure on the shock wave reflection phenomenon in steady flows. J. Fluid Mech. 386, 213232.CrossRefGoogle Scholar
Ben-Dor, G., Ivanov, M., Vasilev, E. I. & Elperin, T. 2002 Hysteresis processes in the regular reflection 2 Mach reflection transition in steady flows. Prog. Aerosp. Sci. 38, 347387.CrossRefGoogle 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, 1935.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, 2950.CrossRefGoogle Scholar
Hekiri, H. & Emanuel, G. 2015 Structure and morphology of a triple point. Phys. Fluids 27, 056102.CrossRefGoogle Scholar
Henderson, L. F. & Lozzi, A. 1975 Experiments on transition of Mach reflection. J. Fluid Mech. 68, 139155.CrossRefGoogle Scholar
Henderson, L. F. & Lozzi, A. 1979 Further experiments on transition to Mach reflexon. J. Fluid Mech. 94, 541559.CrossRefGoogle Scholar
Hornung, H. G. 1986 Regular and Mach reflections of shock waves. Annu. Rev. Fluid Mech. 18, 3358.CrossRefGoogle 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. 13841393. AIP Publishing.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, 541560.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, 155164.CrossRefGoogle Scholar
Hu, Z. M., Gao, Y. L., Myong, R. S., Dou, H. S. & Khoo, B. C. 2010 Geometric criterion for transition in hypersonic double-wedge flows. Phys. Fluids 22, 016101.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), 623627.Google 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), 353357.CrossRefGoogle 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, 20792086.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, 157165.CrossRefGoogle 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, 20272037.CrossRefGoogle Scholar
Li, H. & Ben-Dor, G. 1997 A parametric study of Mach reflection in steady flows. J. Fluid Mech. 341, 101125.CrossRefGoogle Scholar
Li, H. & Ben-Dor, G. 1999 Interaction of two Mach reflections over concave double wedges-analytical model. Shock Waves 9, 259268.CrossRefGoogle Scholar
Li, S. G., Gao, B. & Wu, Z. N. 2011 Time history of regular to Mach reflection transition in steady supersonic flow. J. Fluid Mech. 682, 160184.CrossRefGoogle Scholar
Li, J., Zhu, Y. J. & Luo, X. S. 2014 On Type VI–V transition in hypersonic double-wedge flows with thermo-chemical nonequilibrium effects. Phys. Fluids 26, 086104.CrossRefGoogle Scholar
Mach, E. 1878 Uber den verlauf von Funkenwellen in der Ebene und im Raume. Sitzungsbr Akad Wiss Wien 78, 819838.Google Scholar
Mouton, C. A. & Hornung, H. G. 2007 Mach stem height and growth rate predictions. AIAA J. 45, 19771987.CrossRefGoogle Scholar
Roye, L., Henderson, F. & Menikoff, R. 1998 Triple-shock entropy theorem and its consequences. J. Fluid Mech. 366, 179210.Google Scholar
Schmisseur, J. D. & Gaitonde, D. V. 2011 Numerical simulation of Mach reflection in steady flows. Shock Waves 21, 499509.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, 341362.CrossRefGoogle Scholar
Teshukov, V. M. 1989 On stability of RR of shock waves. Prikl. Mekh. Techn. Fiz. 2, 2633.Google Scholar
Von Neumann, J.1943 Oblique reflection of shock. Explos. Res. Rep. 12. Navy Dept., Bureau of Ordinance, Washington, DC.Google Scholar
Von Neumann, J.1945 Refraction, intersection and reflection of shock waves. NAVORD Rep. 203–245. Navy Dept., 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, 3750.CrossRefGoogle Scholar
Xiong, W. T., Zhu, Y. J. & Luo, X. S. 2016 On transition of type V interaction in double-wedge flow with non-equilibrium effects. Theor. Appl. Mech. Lett. 6, 282285.CrossRefGoogle Scholar
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