Skip to main content
SpringerLink
Log in

Shock wave bifurcation in channels with a bend

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

The study addresses 2D and 3D turbulent transonic flows in divergent channels with a bend, where a shock wave is formed upstream of the sonic line/surface arisen over an expansion corner of the lower wall. Solutions of the Reynolds-averaged Navier–Stokes equations are obtained with a finite-volume solver of the second-order accuracy on fine meshes. Numerical simulations reveal a considerable hysteresis in the shock wave position versus the supersonic Mach number given at the inlet. A dependence of the hysteresis on the slopes of walls and length of channel is analyzed. The bifurcation band persists when unsteady perturbations are imposed at the inlet. A physical interpretation of the shock wave instability is suggested.

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

Similar content being viewed by others

References

  1. Anand, P., Lakshmanan, D., Saravanan, R.: Computational analysis of flow behaviour in curved section of the serpentine intake. Glob. J. Eng. Des. Technol. 3(4), 46–51 (2014)

    Google Scholar 

  2. Blazek, J.: Computational Fluid Dynamics: Principles and Applications. Elsevier, Amsterdam (2001)

    MATH  Google Scholar 

  3. Bur, R., Benay, R., Galli, A., Berthouze, P.: Experimental and numerical study of forced shock-wave oscillations. Aerosp. Sci. Technol. 10, 265–278 (2006)

    Article  Google Scholar 

  4. Chung, K.-M.: Unsteadiness of transonic convex-corner flows. Exp. Fluids 37, 917–922 (2004)

    Article  Google Scholar 

  5. Délery, J.M.: The different facets of an old but always present concern: shock-wave/boundary layer interaction. In: Sobieczky, H. (ed.) IUTAM Symposium Transsonicum IV, pp. 91–98. Kluwer, Dordrecht (2003)

  6. Hsieh, T., Coakley, T.J.: Downstream boundary effects on the frequency of self-excited oscillations in diffuser flows. In: AIAA Paper, no. 87-0161 (1987)

  7. Kuzmin, A.G.: Interaction of a shock wave with the sonic line. In: Sobieczky, H. (ed.) IUTAM Symposium Transsonicum IV, pp. 13–18. Kluwer, Dordrecht (2003)

  8. Kuzmin, A.G.: Aerodynamic surfaces admitting jumps of the lift coefficient in transonic flight. In: Hafez, M.M., Oshima, K., Kwak, D. (eds.) Computational Fluid Dynamics Review 2010, pp. 543–562. World Scientific Publishing, Singapore (2010). (Chapter 22)

    Chapter  Google Scholar 

  9. Kuzmin, A.: Shock wave instability in a channel with an expansion corner. Int. J. App. Mech. 7(2), 1550019: 1–9 (2015). (World Scientific Publishing)

    Google Scholar 

  10. Kuzmin, A.: Sensitivity analysis of transonic flow over J-78 wings. Int. J. Aerosp. Eng. 2015, 579343 (2015). (Hindawi: 1–7)

    Article  Google Scholar 

  11. Liu, H., Wang, B., Guo, Y., Zhang, H., Lin, W.: Effects of inflow Mach number and step height on supersonic flows over a backward-facing step. Adv. Mech. Eng. 2013, 147916: 1–11 (2013)

    Google Scholar 

  12. Matsuo, K., Kim, H.-D.: Normal shock wave oscillations in supersonic diffusers. Shock Waves 3, 25–33 (1993)

    Article  Google Scholar 

  13. Menter, F.R.: Review of the shear-stress transport turbulence model experience from an industrial perspective. Int. J. Comput. Fluid Dyn. 23, 305–316 (2009)

    Article  MATH  Google Scholar 

  14. Moerel, J.-L., Veraar, R.G., Halswijk, W.H.C., Pimentel, R., Corriveau, D., Hamel, N., Lesage, F., Vos, J.B.: Internal flow characteristics of a rectangular ramjet air intake. In: AIAA Paper, no. 2009–5076. pp. 1–26 (2009)

  15. Nguyen, T.T.Q., Behr, M., Reinartz, B.U.: Numerical investigation of compressible turbulent boundary layer over expansion corner. In: AIAA Paper, no. 2009–7371. pp. 1–20 (2009)

  16. Sajben, M., Bogar, T.J., Kroutil, J.C.: Characteristic frequency and length scales in transonic diffuser flow oscillations. In: AIAA Paper, no. 81-1291 (1981)

  17. Sharcnet: Computing Tomorrow’s Solutions. https://www.sharcnet.ca/Software/Fluent14/help/cfx_thry/i1303039.html (2013)

  18. Shifrin, E.G.: Plane vortex flow in the vicinity of the point of orthogonality of the sonic line to the velocity vector. In: Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, no. 6. pp. 144–146 (1966)

  19. Sung, H.-G., Kim, S.-J., Yeom, H.-W., Heo, J.-Y.: On the assessment of compressibility effects of two-equation turbulence models for supersonic transition flow with flow separation. Int. J. Aeronaut. Space Sci. 14(4), 387–397 (2013)

    Google Scholar 

  20. Szumowski, A.P., Obermeier, F., Meier, G.E.A.: Oscillation modes of laval nozzle flow. Exp. Fluids 18, 145–152 (1995)

    Article  Google Scholar 

  21. Xiao, Q., Tsai, H.M.: Computation of transonic diffuser flows by a lagged \(k\)-\(\omega \) turbulence model. J. Propuls. Power 19(3), 473–483 (2003)

    Article  Google Scholar 

Download references

Acknowledgments

This research was performed using computational resources provided by the Computational Center of St. Petersburg State University (http://cc.spbu.ru). The work was supported by the Russian Foundation for Basic Research under grant no. 13-08-00288.

Author information

Authors and Affiliations

  1. Department of Fluid Dynamics, St. Petersburg State University, St. Petersburg, Russia

    Alexander Kuzmin

Authors
  1. Alexander Kuzmin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexander Kuzmin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kuzmin, A. Shock wave bifurcation in channels with a bend. Arch Appl Mech 86, 787–795 (2016). https://doi.org/10.1007/s00419-015-1062-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-015-1062-z

Keywords

Search

Navigation