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Study on the Mach and regular reflections of shock wave

  • Kexin Wu
  • Guang Zhang
  • Heuy Dong KimEmail author
Regular Paper
  • 22 Downloads

Abstract

While a moving incident shock wave moves through a sharp compression ramp with the fixed angle, θr, the incident shock wave is reflected by the ramp surface and the induced pseudo-steady flow behind it is deflected by the ramp corner. It is known that four basic shock reflection patterns can be obtained, including regular reflection, single-Mach reflection, transitional-Mach reflection, and double-Mach reflection. Previously, the shock reflections were mainly studied by various experimental methods with different test gases in the shock tubes, which include air, nitrogen, helium, and argon. In this paper, in order to clearly illustrate the transitional properties between Mach and regular reflections, theoretical and numerical analyses were carried out. Detachment and mechanical equilibrium criteria were established by the theoretical analysis based on the two- and three-shock theories. Further, which criterion is more suitable and accurate to explain the transitional processes between the Mach and regular reflections was illustrated. The generation and variation of the reflected shock waves were clearly captured based on the total variation diminishing scheme within Fluidyn software. A series of 2D (two-dimensional) models were simulated at different operating conditions that the incident Mach numbers (1.1, 1.5, 2.03, 3, 4 and 5) and compression ramp angles (27°, 50°, and 60°) were changed, respectively. The detailed properties on Mach and regular reflections were illustrated in the present studies. In addition, some new and constructive conclusions for transitional processes between the Mach and regular reflections of shock wave were obtained.

Graphical abstract

Keywords

Unsteady Inviscid Shock reflection Detachment criterion Mechanical equilibrium criterion 

Notes

Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. NRF-2016R1A2B3016436).

References

  1. Barbosa FJ, Skews BW (2002) Experimental confirmation of the von Neumann theory of shock wave reflection transition. J Fluid Mech 472:541–559.  https://doi.org/10.1017/S0022112002002343 MathSciNetCrossRefzbMATHGoogle Scholar
  2. Ben-Dor G (2007) Shock wave reflection phenomenon. Springer, Berlin, Heidelbery.  https://doi.org/10.1007/978-3-540-71382-1 zbMATHGoogle Scholar
  3. Ben-Dor G, Glass II (1979) Domains and boundaries of non-stationary oblique shock-wave reflections. 1. Diatomic gas. J Fluid Mech 92:459–496.  https://doi.org/10.1017/S0022112079000732 CrossRefGoogle Scholar
  4. Ben-Dor G, Glass II (1980) Domains and boundaries of non-stationary oblique shock-wave reflections. 2. Monatomic gas. J Fluid Mech 96:735–756.  https://doi.org/10.1017/S0022112080002339 CrossRefGoogle Scholar
  5. Bleakney W, Taub AH (1949) Interaction of shock waves. Rev Mod Phys 21:584–605.  https://doi.org/10.1007/978-94-011-1086-0 MathSciNetCrossRefzbMATHGoogle Scholar
  6. Deschambault RL, Glass II (1983) An update on non-stationary oblique shock-wave reflections: actual isopycnics and numerical experiments. J Fluid Mech 131:27–57.  https://doi.org/10.1017/S0022112083001226 CrossRefGoogle Scholar
  7. Geva M, Ram O, Sadot O (2017) The regular reflection → Mach reflection transition in unsteady flow over convex surfaces. J Fluid Mech 837:48–79.  https://doi.org/10.1017/jfm.2017.835 MathSciNetCrossRefGoogle Scholar
  8. Glass II, Sislian JP (1994) Nonstationary flows and shock waves. Oxford University Press, New York, United StatesGoogle Scholar
  9. Henderson LF, Lozzi A (1975) Experiments on transition of Mach reflection. J Fluid Mech 68:139–155.  https://doi.org/10.1017/S0022112079001178 CrossRefGoogle Scholar
  10. Henderson LF, Lozzi A (1979) Further experiments on transition to Mach reflexion. J Fluid Mech 94:541–559.  https://doi.org/10.1017/S0022112079001178 CrossRefGoogle Scholar
  11. Henderson LF, Siegenthaler A (1980) Experiments on the diffraction of weak blast waves: the von Neumann paradox. Proc R Soc A Math Phys 369:537–555CrossRefGoogle Scholar
  12. Herron T, Skews BW (2011) On the persistence of regular reflection. Shock Waves 21:573–578.  https://doi.org/10.1007/s00193-011-0341-z CrossRefGoogle Scholar
  13. Hryniewicki MK, Gottlieb JJ, Groth CPT (2016) Transition boundary between regular and Mach reflections for a moving shock interacting with a wedge in inviscid and polytropic air. Shock Waves.  https://doi.org/10.1007/S00193-016-0697-1 Google Scholar
  14. Kawamura R, Saito H (1956) Reflection of shock waves: 1. Pseudo-stationary case. J Phys Soc Jpn 11:584–592.  https://doi.org/10.1143/JPSJ.11.584 CrossRefGoogle Scholar
  15. Kobayashi S, Adachi T, Suzuki T (2000) On the unsteady transition phenomenon of weak shock waves. Theor Appl Mech 49:271–278Google Scholar
  16. Lock GD, Dewey JM (1989) An experimental investigation of the sonic criterion for transition from regular to Mach reflection of weak shock waves. Exp Fluids 7:289–292.  https://doi.org/10.1007/BF00198446 CrossRefGoogle Scholar
  17. Previtali FA, Timofeev E, Kleine H (2015) On unsteady shock wave reflections from wedges with straight and concave tips. In: 45th AIAA fluid dynamics conference. Dallas, United StatesGoogle Scholar
  18. Semenov AN, Berezkina MK, Krassovskaya IV (2012) Classification of pseudo-steady shock wave reflection types. Shock Waves 22:307–316.  https://doi.org/10.1007/S00193-012-0373-z CrossRefGoogle Scholar
  19. Smith LG (1945) Photographic investigation of the reflection of plane shocks in air. National defense research committee of the office of scientific research and development, United StatesGoogle Scholar
  20. Smith WR (1959) Mutual reflection of two shock waves of arbitrary strengths. Phys Fluids 2:533–541.  https://doi.org/10.1063/1.1705945 MathSciNetCrossRefzbMATHGoogle Scholar
  21. von Neumann J (1943a) Oblique reflection of shocks. Explosive research report, United StatesGoogle Scholar
  22. von Neumann J (1943b) Theory of shock waves. National defense research committee of the office of scientific research and development, United StatesGoogle Scholar
  23. von Neumann J (1945) Refraction, intersection and reflection of shock waves. In: Conference on shock waves and supersonic flow. Princeton University, United StatesGoogle Scholar
  24. Walker DK, Dewey JM, Scotten LN (1982) Observation of density discontinuities behind reflected shocks close to the transition from regular to Mach reflection. J Appl Phys 53:1398–1400.  https://doi.org/10.1063/1.329871 CrossRefGoogle Scholar
  25. White DR (1952) An experimental survey of the Mach reflection of shock waves. In: Proceedings of the second midwestern conference on fluid mechanics. Ohio State University, United StatesGoogle Scholar
  26. Zhang Q, Chen X, He LM, Rong K, Deiterding R (2016) Investigation of shock focusing in a cavity with incident shock diffracted by an obstacle. Shock Waves.  https://doi.org/10.1007/S00193-016-0653-10 Google Scholar

Copyright information

© The Visualization Society of Japan 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringAndong National UniversityAndongRepublic of Korea
  2. 2.College of Mechanical Engineering & AutomationZhejiang Sci-Tech UniversityHangzhouChina

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