Shock Waves

, Volume 29, Issue 2, pp 285–296 | Cite as

Experimental and numerical investigations of shock wave propagation through a bifurcation

  • A. MartyEmail author
  • E. Daniel
  • J. Massoni
  • L. Biamino
  • L. Houas
  • D. Leriche
  • G. Jourdan
Original Article


The propagation of a planar shock wave through a split channel is both experimentally and numerically studied. Experiments were conducted in a square cross-sectional shock tube having a main channel which splits into two symmetric secondary channels, for three different shock wave Mach numbers ranging from about 1.1 to 1.7. High-speed schlieren visualizations were used along with pressure measurements to analyze the main physical mechanisms that govern shock wave diffraction. It is shown that the flow behind the transmitted shock wave through the bifurcation resulted in a highly two-dimensional unsteady and non-uniform flow accompanied with significant pressure loss. In parallel, numerical simulations based on the solution of the Euler equations with a second-order Godunov scheme confirmed the experimental results with good agreement. Finally, a parametric study was carried out using numerical analysis where the angular displacement of the two channels that define the bifurcation was changed from \(90^{\circ }\), \(45^{\circ }\), \(20^{\circ }\), and \(0^{\circ }\). We found that the angular displacement does not significantly affect the overpressure experience in either of the two channels and that the area of the expansion region is the important variable affecting overpressure, the effect being, in the present case, a decrease of almost one half.


Shock wave Shock tube environment Shock wave propagation Reflection Attenuation 



The project leading to this publication has received funding from Excellence Initiative of Aix-Marseille University—\(\hbox {A}*\)MIDEX, a French Investissements d’Avenir program. It has been carried out in the framework of the Labex MEC.


  1. 1.
    Ben-Dor, G., Igra, O., Elperin, T.: Handbook of Shock Waves. Academic Press, New York (2000). zbMATHGoogle Scholar
  2. 2.
    Igra, O., Wu, X., Falcovitz, J., Meguro, T., Takayama, K., Heilig, W.: Experimental and theoretical studies of shock wave propagation through double-bend ducts. J. Fluid Mech. 437, 255–282 (2001). CrossRefzbMATHGoogle Scholar
  3. 3.
    Chester, W.: The propagation of shock waves in a channel of non-uniform width. Q. J. Mech. Appl. Math. 6, 440 (1953). MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Laporte, O.: On Interaction of a Shock with Constriction. Los Alamos Scientific Laboratory Technical Report No. LA-1740 (1954)Google Scholar
  5. 5.
    Chisnell, F.: The normal motion of a shock wave through a non-uniform one-dimensional medium. Proc. R. Soc. Lond. 223, 350–370 (1955). MathSciNetzbMATHGoogle Scholar
  6. 6.
    Whitham, B.: On the propagation of shock waves through regions of non-uniform area or flow. J. Fluid Mech. 4, 337–360 (1958). MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Nettleton, M.A.: Shock attenuation in a ‘gradual’ area expansion. J. Fluid Mech. 60(part 2), 209–223 (1973). CrossRefGoogle Scholar
  8. 8.
    Salas, M.D.: Shock wave interaction with an abrupt area change. Appl. Numer. Math. 12, 239–256 (1993). CrossRefzbMATHGoogle Scholar
  9. 9.
    Igra, O., Elperin, T., Falcovitz, J., Zmiri, B.: Shock wave interaction with area changes in ducts. Shock Waves 3, 233–238 (1994). CrossRefzbMATHGoogle Scholar
  10. 10.
    Heilig, W.H.: Propagation of shock waves in various branched ducts. In: Kamimoto, G. (ed.) Modern Developments in Shock Tube Research, pp. 273–283. Shock Tube Research Society, Kyoto (1975)Google Scholar
  11. 11.
    Skews, B.W.: The propagation of shock waves in a complex tunnel system. J. S. Afr. Inst. Min. Met. 91(4), 137–144 (1991)Google Scholar
  12. 12.
    Igra, O., Falcovitz, J., Reichenbach, H., Heilig, W.: Experimental and numerical study of the interaction between a planar shock wave and a square cavity. J. Fluid Mech. 313, 105–130 (1996). CrossRefGoogle Scholar
  13. 13.
    Igra, O., Wang, L., Falcovitz, J., Heilig, W.: Shock wave propagation in a branched duct. Shock Waves 8, 375–381 (1998). CrossRefzbMATHGoogle Scholar
  14. 14.
    Jourdan, G., Houas, L., Schwaederle, L., Layes, G., Carrey, R., Diaz, F.: A new variable inclination shock tube for multiple investigations. Shock Waves 13, 501–504 (2004). CrossRefGoogle Scholar
  15. 15.
    Thevand, N., Daniel, E., Loraud, J.C.: On high resolution schemes for compressible viscous two-phase dilute flows. Int. J. Numer. Methods Fluids 31, 681–702 (1999).;2-K CrossRefzbMATHGoogle Scholar
  16. 16.
    Ben-Dor, G.: Shock Wave Reflection Phenomena, pp. 46–52. Springer, Berlin (1992). CrossRefzbMATHGoogle Scholar
  17. 17.
    Skews, B.W.: The perturbed region behind a diffracting shock wave. J. Fluid Mech. 29(4), 705–719 (1967). CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • A. Marty
    • 1
    Email author
  • E. Daniel
    • 1
  • J. Massoni
    • 1
  • L. Biamino
    • 1
  • L. Houas
    • 1
  • D. Leriche
    • 2
  • G. Jourdan
    • 1
  1. 1.Aix Marseille Univ, CNRS, IUSTIMarseilleFrance
  2. 2.DGA/Techniques NavalesToulon CedexFrance

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