New Findings on the Shock Reflection from Wedges with Small Concave Tips

  • F. Alzamora Previtali
  • H. Kleine
  • E. Timofeev
Conference paper


Planar shock reflection from straight wedges and wedges with small concave tips is considered. It is demonstrated that, in shock tube experiments for a certain wedge angle and incident shock Mach number, the resulting reflection is of irregular type in the presence of a small concave tip with an arc radius as small as 4 mm while a straight wedge with the same wedge angle produces a regular reflection. In the numerical experiments, corner signal tracking is used to demonstrate that in the case of a concave tip wedge the corner signal is always merged with the Mach stem and never detaches. It is concluded that for the prediction of the Mach-to-regular reflection transition angle for wedges with concave tips, it is essential to predict as accurately as possible the strength of the Mach stem. An initial development of an analytical method to predict the transition angle is then provided.



The present research is supported by the Fonds de recherche du Quèbec—Nature et technologies (FRQNT) via the Team Research Project program and the National Science and Engineering Research Council (NSERC) via the Discovery Grant program. F.A.P. gratefully acknowledges the McGill Engineering Undergraduate Student Masters Award (MEUSMA) funded in part by the Faculty of Engineering, McGill University. Rabi Tahir’s support regarding Masterix code is greatly appreciated.


  1. 1.
    Alzamora Previtali, F., Timofeev, E., Kleine, H.: On unsteady shock wave reflections from wedges with straight and concave tips. AIAA Paper 2015–2642 (2015).
  2. 2.
    Lau-Chapdelaine, S.S., Radulescu, M.I.: Non-uniqueness of solutions in asymptotically self-similar shock reflections. Shock Waves 23(6), 595–602 (2013)Google Scholar
  3. 3.
    Kleine, H., Timofeev, E., Hakkaki-Fard, A., Skews, B.: The influence of Reynolds number on the triple point trajectories at shock reflection off cylindrical surfaces. J. Fluid Mech. 740, 47–60 (2014)CrossRefGoogle Scholar
  4. 4.
    Masterix: Ver. 3.40, RBT Consultants, Toronto, Ontario (2003–2015)Google Scholar
  5. 5.
    Saito, T., Voinovich, P., Timofeev, E., Takayama, K.: Development and application of high-resolution adaptive numerical techniques in shock wave research center. In: Toro, E.F. (ed.) Godunov Methods: Theory and Applications, pp. 763–784. Kluwer Academic/Plenum Publishers, New York, USA (2001)CrossRefGoogle Scholar
  6. 6.
    Hakkaki-Fard, A., Timofeev, E.: On numerical techniques for determination of the sonic point in unsteady inviscid shock reflections. Int. J. Aerosp. Innovations 4, 41–52 (2012)CrossRefGoogle Scholar
  7. 7.
    Itoh, S., Okazaki, N., Itaya, M.: On the transition between regular and Mach reflection in truly non-stationary flows. J. Fluid Mech. 108, 383–400 (1981)CrossRefGoogle Scholar
  8. 8.
    Milton, B.E.: Mach reflection using ray-shock theory. AIAA J. 13(11), 1531–1533 (1975)CrossRefzbMATHGoogle Scholar
  9. 9.
    Ben-Dor, G., Takayama, K.: Analytical prediction of the transition from Mach to regular reflection over cylindrical concave wedges. J. Fluid Mech. 158, 365–380 (1985)CrossRefGoogle Scholar
  10. 10.
    Takayama, K., Ben-Dor, G.: A reconsideration of the transition criterion from Mach to regular reflection over cylindrical concave surface. Korean Soc. Mech. Eng. 3, 6–9 (1989)Google Scholar
  11. 11.
    Ben-Dor, G.: Shock Wave Reflection Phenomena, 2nd edn. Springer (2007)Google Scholar
  12. 12.
    Timofeev, E., Alzamora Previtali, F., Kleine, H.: On unsteady shock wave reflection from a concave cylindrical surface. In: Proceedings of Present ISIS22 (2016)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringMcGill UniversityMontrealCanada
  2. 2.School of Engineering and Information TechnologyUniversity of New South WalesCanberraAustralia

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