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Shock reflection in the presence of an upstream expansion wave and a downstream shock wave

Published online by Cambridge University Press:  22 October 2013

Y. Yao ,
S. G. Li  and
Z. N. Wu
Y. Yao
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
S. G. Li
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
Z. N. 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

In this paper, we consider shock reflection problems, occurring in supersonic and hypersonic intake flow under off-design conditions, in which the incident shock wave is disturbed by the lip-generated upstream expansion wave and the reflected shock wave intersects with a downstream cowl-turning deflected shock wave. The expansion wave and deflected shock wave are here generated with the same magnitude of flow deflection angle or turning angle. With the help of shock interaction theory and numerical simulation, the influence of the turning angle of the lip and cowl on the flow structure and the critical conditions for transition between regular reflection and Mach reflection are analysed. It is found that the dual-solution domain is significantly altered by the interference between the expansion wave and shock waves. The flow structure in the condition of Mach reflection is then analysed with a model updated from a previous study. It is shown that the Mach stem height is an increasing function of the turning angle, while the horizontal position of the Mach stem is shifted in the downstream direction for small turning angle and in the upstream direction for large turning angle.

JFM classification

Aerodynamics: High-speed flow Compressible Flows: Shock waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 735 , 25 November 2013 , pp. 61 - 90
Copyright
©2013 Cambridge University Press 

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References

Anderson, & John, D. 2004 Modern Compressible Flow. McGraw-Hill.Google Scholar
Azevedo, D. J. 1989 Analytical prediction of shock patterns in a high-speed wedge bounded duct. PhD thesis, Department of Aerospace and Mechanical Engineering, State University NY, Buffalo.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.Google 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.Google Scholar
Ben-Dor, G., Ivanov, M., Vasiliev, E. I. & Elperin, T. 2002 Hysteresis processes in the regular reflection $\leftrightarrow $ Mach reflection transition in steady flows. Prog. Aerosp. Sci. 38, 347–387.Google Scholar
Bloor, M. I. G. 1965 Determination of the sonic line in hypersonic flow past a blunt body. J. Fluid Mech. 21, 495–501.Google Scholar
Chen, S. X. 2006 Stability of a Mach configuration. Commun. Pure Appl. Maths 59, 1–35.Google Scholar
Chen, S. X. 2009 Study on Mach reflection and Mach configuration. Hyperbol. Problems: Theory, Numerics Applics 1 67, 53–71.Google Scholar
Chen, S. X. 2012 E–H type Mach configuration and its stability. Commun. Math. Phys. 315, 563–602.Google Scholar
Chow, W. L. & Chang, I. S. 1974 Mach reflection associated with over-expanded nozzle free jet flows. AIAA J. 13, 762–766.Google 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. Mecanique des Fluides 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.Google Scholar
Dalle, D. J., Fotia, M. L. & Driscoll, J. F. 2010 Reduced-order modelling of two-dimensional supersonic flows with applications to scramjet inlets. J. Propul. Power 26, 545–555.Google Scholar
Dalle, D. J., Torrez, S. M., Driscoll, J. F. & Bolender, M. A. 2011 Flight envelope calculation of a hypersonic vehicle using first principles-derived model. 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference. San Francisco, California.Google Scholar
Dewey, J. M. & Barss, T. 1996 The shape of the Mach stem. In Proc. 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
Emami, S., Trexler, C. A., Auslender, A. H. & Weidner, J. P. 1995 Experimental investigation of inlet-combustor isolators for a dual-mode scramjet at a Mach number of 4. NASA Tech. Pub. 3502.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
Henderson, L. F. & Lozzi, A. 1975 Experiments on transition of Mach reflection. J. Fluid Mech. 68, 139–155.Google Scholar
Henderson, L. F. & Lozzi, A. 1979 Further experiments on transition of Mach reflection. J. Fluid Mech. 94, 541–559.Google Scholar
Hillier, R. 2007 Shock-wave/expansion-wave interactions and the transition between regular and Mach reflection. J. Fluid Mech. 575, 399–424.Google Scholar
Hornung, H. G. 1997 Technical note on the stability of steady-flow regular and Mach reflection. Shock Waves 7 (2), 123–125.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 MR of shock waves. Part 2. The steady flow criterion. J. Fluid Mech. 123, 155–164.Google Scholar
Hornung, H. G. & Smith, G. H. 1979 The influence of relaxation on shock detachment. J. Fluid Mech. 93 (2), 225–239.Google Scholar
Irving Brown, Y. A. & Skews, B. W. 2004 Three-dimensional effects on regular reflection in steady supersonic flows. Shock Waves 13, 339–349.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. 469, 71–87.Google Scholar
Ivanov, M. S., Gimelshein, S. F. & Beylich, A. E. 1995 Hysteresis effect in stationary reflection of shock waves. Phys. Fluids 7, 685–687.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), 353–357.Google Scholar
Kawamura, R. & Saito, H. 1956 Reflection of shock waves-1. Pseudo-stationary cases. J. Phys. 11, 584–592.Google Scholar
Kolluru, R. & Gopal, V. 2012 Comparative numerical studies of scramjet inlet performance using $k{{\unicode{x2013}}}\varepsilon $ turbulence model with adaptive grids. Excerpt from the Proceedings of the 2012 COMSOL Conference in Bangalore.Google Scholar
Kovachevich, A., Paull, A. & McIntyre, T. 2004 Investigation of an intake injected hot-wall scramjet. AIAA J. 2004-1037.Google 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 (2), 157–165.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1987 Course of Theoretical Physics, Vol. 6. 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.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 analysing the reflection of weak shock waves over small wedge angles. Shock Waves 4, 41–45.Google 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, 160–184.Google Scholar
Mach, E. 1878 Uber den verlauf von Funkenwellen in der Ebene und im Raume. Sitz.ber. 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.Google Scholar
Olim, M. & Dewey, J. M. 1992 A revised three-shock solution for the Mach reflection of weak shocks ( $1. 1\lt {M}_{i} \lt 1. 5$ ). Shock Waves 2, 167–176.Google Scholar
Pasha, A. A, Vadivelan, C. & Sinha, K. 2012 Simulation of a practical scramjet inlet using shock-unsteadiness model. In 28th International Symposium on Shock Waves, pp. 477–482. Springer.Google Scholar
Samtaney, R. & Pullin, D. I. 1996 On initial value and self-similar solutions of the compressible Euler equations. Phys. Fluids 8, 2650–2655.Google Scholar
Sauer, R. 1947 General characteristics of the flow through nozzles at near critical speeds. NACA Tech. Mem. 1147.Google Scholar
Shirozu, T. & Nishida, M. 1995 Numerical studies of oblique shock reflection in steady two-dimensional flows. Mem. Faculty Engng Kyushu Univ. 55, 193–204.Google Scholar
Siddiqui, A. M. & Ahmed, G. M. S. 2013 Design and analysis on scramjet engine inlet. Intl J. Sci. Res. Pub. 3 (1), 192–203.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
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 Deptartment, Bureau of Ordinance, Washington, DC.Google Scholar
von Neumann, J. 1945 Refraction, intersection and reflection of shock waves. NAVORD Report 203–245. Navy Deptartment, 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.Google Scholar