Skip to main content
SpringerLink
Log in

Experimental and numerical investigations of shock wave propagation through a bifurcation

  • Original Article
  • Published:
Shock Waves Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

References

  1. Ben-Dor, G., Igra, O., Elperin, T.: Handbook of Shock Waves. Academic Press, New York (2000). https://doi.org/10.1016/B978-0-12-086430-0.50045-2

    MATH  Google Scholar 

  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). https://doi.org/10.1017/S0022112001004098

    Article  MATH  Google Scholar 

  3. Chester, W.: The propagation of shock waves in a channel of non-uniform width. Q. J. Mech. Appl. Math. 6, 440 (1953). https://doi.org/10.1093/qjmam/6.4.440

    Article  MathSciNet  MATH  Google Scholar 

  4. Laporte, O.: On Interaction of a Shock with Constriction. Los Alamos Scientific Laboratory Technical Report No. LA-1740 (1954)

  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). https://doi.org/10.1098/rspa.1955.0223

    MathSciNet  MATH  Google Scholar 

  6. Whitham, B.: On the propagation of shock waves through regions of non-uniform area or flow. J. Fluid Mech. 4, 337–360 (1958). https://doi.org/10.1017/S0022112058000495

    Article  MathSciNet  MATH  Google Scholar 

  7. Nettleton, M.A.: Shock attenuation in a ‘gradual’ area expansion. J. Fluid Mech. 60(part 2), 209–223 (1973). https://doi.org/10.1017/S0022112073000121

    Article  Google Scholar 

  8. Salas, M.D.: Shock wave interaction with an abrupt area change. Appl. Numer. Math. 12, 239–256 (1993). https://doi.org/10.1016/0168-9274(93)90121-7

    Article  MATH  Google Scholar 

  9. Igra, O., Elperin, T., Falcovitz, J., Zmiri, B.: Shock wave interaction with area changes in ducts. Shock Waves 3, 233–238 (1994). https://doi.org/10.1007/BF01414717

    Article  MATH  Google Scholar 

  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. 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. 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). https://doi.org/10.1017/S0022112096002145

    Article  Google Scholar 

  13. Igra, O., Wang, L., Falcovitz, J., Heilig, W.: Shock wave propagation in a branched duct. Shock Waves 8, 375–381 (1998). https://doi.org/10.1007/s001930050130

    Article  MATH  Google Scholar 

  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). https://doi.org/10.1007/s00193-004-0232-7

    Article  Google Scholar 

  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). https://doi.org/10.1002/(SICI)1097-0363(19991030)31:4%3c681::AID-FLD893%3e3.0.CO;2-K

    Article  MATH  Google Scholar 

  16. Ben-Dor, G.: Shock Wave Reflection Phenomena, pp. 46–52. Springer, Berlin (1992). https://doi.org/10.1007/978-3-540-71382-1

    Book  MATH  Google Scholar 

  17. Skews, B.W.: The perturbed region behind a diffracting shock wave. J. Fluid Mech. 29(4), 705–719 (1967). https://doi.org/10.1017/S0022112067001132

    Article  Google Scholar 

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

  1. Aix Marseille Univ, CNRS, IUSTI, Marseille, France

    A. Marty, E. Daniel, J. Massoni, L. Biamino, L. Houas & G. Jourdan

  2. DGA/Techniques Navales, Avenue de la Tour Royale, 83050, Toulon Cedex, France

    D. Leriche

Authors
  1. A. Marty
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Daniel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Massoni
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. L. Biamino
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. L. Houas
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. D. Leriche
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. G. Jourdan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Marty.

Additional information

Communicated by R. Bonazza and A. Higgins.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Marty, A., Daniel, E., Massoni, J. et al. Experimental and numerical investigations of shock wave propagation through a bifurcation. Shock Waves 29, 285–296 (2019). https://doi.org/10.1007/s00193-017-0797-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00193-017-0797-6

Keywords

Search

Navigation