Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-12-01T09:03:56.389Z Has data issue: false hasContentIssue false
  • English
  • Français

On regular reflection to Mach reflection transition in inviscid flow for shock reflection on a convex or straight wedge

Published online by Cambridge University Press:  10 December 2019

He Wang  and
Zhigang Zhai Open the ORCID record for Zhigang Zhai [Opens in a new window]
He Wang
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, China
Zhigang Zhai*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The regular reflection to Mach reflection ($\text{RR}\rightarrow \text{MR}$) transition in inviscid perfect air for shock reflection over convex and straight wedges is investigated. Provided that the variation of shock intensity only has a second-order effect on the wave transition, the possible cases for the occurrence of the $\text{RR}\rightarrow \text{MR}$ transition for curved shock reflection over a wedge are discussed. For a planar shock reflecting over a convex wedge, four different flow regions are classified and the mechanism of the disturbance propagation is interpreted. It is found that the flow-induced rarefaction waves exist between disturbances generated from neighbouring positions and isolate them. For a curved shock reflecting over a convex wedge, although the distributions of the flow regions are different from those in planar shock reflection, the analysis for the planar shock case can be extended to curved shock cases as long as the wedge is convex. When a diverging shock reflects off a straight wedge, the flow-induced rarefaction waves are absent. However, the disturbances generated earlier cannot overtake the reflection point before the pseudo-steady criterion is satisfied. In the cases considered, the flow in the vicinity of the reflection point will not be influenced by the unsteady flow caused by the shock intensity and the wedge angle variations. This is clearly a local property of the shock–wall interaction, no matter what the history of the shock trajectory is. For validation, extensive inviscid numerical simulations are performed, and the numerical results show the reliability of the pseudo-steady criterion for predicting the $\text{RR}\rightarrow \text{MR}$ transition on a convex wedge.

JFM classification

Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 884 , 10 February 2020 , A27
Copyright
© 2019 Cambridge University Press

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

Ben-Dor, G. 2007 Shock Wave Reflection Phenomena. Springer.Google Scholar
Ben-Dor, G., Dewey, J., McMillin, D. & Takayama, K. 1988 Experimental investigation of the asymptotically approached Mach reflection over the second surface in a double wedge reflection. Exp. Fluids 6, 429–434.CrossRefGoogle Scholar
Ben-Dor, G., Dewey, J. M. & Takayama, K. 1987 The reflection of a plane shock wave over a double wedge. J. Fluid Mech. 176, 483–520.CrossRefGoogle Scholar
Chester, W. 1954 The quasi-cylindrical shock tube. Phil. Mag. 45, 1293–1301.CrossRefGoogle Scholar
Chisnell, R. F. 1957 The motion of a shock wave in a channel, with applications to cylindrical and spherical shock waves. J. Fluid Mech. 2, 286–298.CrossRefGoogle Scholar
Colella, P. & Henderson, L. F. 1990 The von Neumann paradox for the diffraction of weak shock waves. J. Fluid Mech. 213, 71–94.CrossRefGoogle Scholar
Geva, M., Ram, O. & Sadot, O. 2013 The non-stationary hysteresis phenomenon in shock wave reflections. J. Fluid Mech. 732, R1.CrossRefGoogle Scholar
Geva, M., Ram, O. & Sadot, O. 2018 The regular reflection → Mach reflection transition in unsteady flow over convex surfaces. J. Fluid Mech. 837, 48–79.CrossRefGoogle Scholar
Gray, B. & Skews, B. 2017 Reflection of a converging cylindrical shock wave segment by a straight wedge. Shock Waves 27, 551–563.CrossRefGoogle Scholar
Hakkaki-Fard, A. & Timofeev, E. 2012 On numerical techniques for determination of the sonic point in unsteady inviscid shock reflections. Intl J. Aerosp. Innovations 4, 41–52.CrossRefGoogle Scholar
Heilig, W. H. 1969 Diffraction of a shock wave by a cylinder. Phys. Fluids 12, I154–I157.CrossRefGoogle Scholar
Henderson, L. F. 1982 Exact expressions for shock reflexion transition criteria in a perfect gas. Z. Angew. Math. Mech. 62, 258–261.CrossRefGoogle Scholar
Hornung, H. G., Oertel, H. & Sandeman, R. J. 1979 Transition to Mach reflection of shock waves in steady and pseudo-steady flow with and without relaxation. J. Fluid Mech. 90, 541–560.CrossRefGoogle Scholar
Itoh, S., Okazaki, N. & Itaya, M. 1981 On the transition between regular and Mach reflection in truly non-stationary flows. J. Fluid Mech. 108, 383–400.CrossRefGoogle Scholar
Kleine, H., Timofeev, E., Hakkaki-Fard, A. & Skews, B. W. 2014 The influence of Reynolds number on the triple point trajectories at shock reflection off cylindrical surfaces. J. Fluid Mech. 740, 47–60.CrossRefGoogle Scholar
Li, H. & Ben-Dor, G. 1995 Reconsideration of pseudo-steady shock wave reflections and the transition criteria between them. Shock Waves 5, 59–73.CrossRefGoogle Scholar
Li, H. & Ben-Dor, G. 1999 Interaction of two Mach reflections over concave double wedges-analytical model. Shock Waves 9, 259–268.CrossRefGoogle Scholar
Lock, G. D. & Dewey, J. M. 1989 An experimental investigation of the sonic criterion for transition from regular to Mach reflection of weak shock waves. Exp. Fluids 7, 289–292.CrossRefGoogle 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
von Neumann, J.1943a Oblique reflection of shock. Explos. Res. Rep. 12, Navy Dept., Bureau of Ordinance, Washington, DC, USA.Google Scholar
von Neumann, J.1943b Refraction, intersection and reflection of shock waves. NAVORD Rep. 203-45, Navy Dept., Bureau of Ordinance, Washington, DC, USA.Google Scholar
Ram, O., Geva, M. & Sadot, O. 2015 High spatial and temporal resolution study of shock wave reflection over a coupled convex–concave cylindrical surface. J. Fluid Mech. 768, 219–239.CrossRefGoogle Scholar
Skews, B. & Kleine, H. 2009 Unsteady flow diagnostics using weak perturbations. Exp. Fluids 46, 65–76.CrossRefGoogle Scholar
Skews, B. W. & Blitteswijk, A. 2011 Shock wave reflection off coupled surfaces. Shock Waves 21, 491–498.CrossRefGoogle Scholar
Skews, B. W. & Kleine, H. 2010 Shock wave interaction with convex circular cylindrical surfaces. J. Fluid Mech. 654, 195–205.CrossRefGoogle Scholar
Skews, B. W., Li, G. & Paton, R. 2009 Experiments on Guderley Mach reflection. Shock Waves 19, 95–102.CrossRefGoogle Scholar
Smith, L. G.1945 Photographic investigation of the reflection of plane shocks in air. OSRD Rep. no. 6271.Google Scholar
Soni, V., Hadjadj, A., Chaudhuri, A. & Ben-Dor, G. 2017 Shock-wave reflections over double-concave cylindrical reflectors. J. Fluid Mech. 813, 70–84.CrossRefGoogle Scholar
Sun, M. & Takayama, K. 1999 Conservative smoothing on an adaptive quadrilateral grid. J. Comput. Phys. 150, 143–180.CrossRefGoogle Scholar
Suzuki, T., Adachi, T. & Kobayashi, S. 1997 Nonstationary shock reflection over nonstraight surfaces: an approach with a method of multiple steps. Shock Waves 7, 55–62.CrossRefGoogle Scholar
Takayama, K. & Sasaki, M. 1983 Effects of radius of curvature and initial angle on the shock transition over concave and convex walls. Rep. Inst. High-Speed Mech. 46, 1–30.Google Scholar
Vasilev, E. I., Elperin, T. & Ben-Dor, G. 2008 Analytical reconsideration of the von Neumann paradox in the reflection of a shock wave over a wedge. Phys. Fluids 20, 046101.CrossRefGoogle Scholar
Vignati, F. & Guardone, A. 2017 Transition from regular to irregular reflection of cylindrical converging shock waves over convex obstacles. Phys. Fluids 29, 116104.CrossRefGoogle Scholar
Wang, H., Zhai, Z., Luo, X., Yang, J. & Lu, X. 2017 A specially curved wedge for eliminating wedge angle effect in unsteady shock reflection. Phys. Fluids 29, 086103.CrossRefGoogle Scholar
Whitham, G. B. 1957 A new approach to problems of shock dynamics. Part I. Two-dimensional problems. J. Fluid Mech. 2, 145–171.CrossRefGoogle Scholar
Xie, P., Han, Z. Y. & Takayama, K. 2005 A study of the interaction between two triple points. Shock Waves 14, 29–36.CrossRefGoogle Scholar
Yin, J., Ding, J. & Luo, X. 2018 Numerical study on dusty shock reflection over a double wedge. Phys. Fluids 30, 013304.CrossRefGoogle Scholar
Zhai, Z., Si, T., Luo, X. & Yang, J. 2011 On the evolution of spherical gas interfaces accelerated by a planar shock wave. Phys. Fluids 23, 084104.CrossRefGoogle Scholar
Zhai, Z., Wang, M., Si, T. & Luo, X. 2014 On the interaction of a planar shock with a light polygonal interface. J. Fluid Mech. 757, 800–816.CrossRefGoogle Scholar
Zhang, F., Si, T., Zhai, Z., Luo, X., Yang, J. & Lu, X. 2016 Reflection of cylindrical converging shock wave over a plane wedge. Phys. Fluids 28, 086101.CrossRefGoogle Scholar