On Stability and Transition in Bent Pipes

  • J. CantonEmail author
  • R. Örlü
  • P. Schlatter
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 25)


This work is concerned with the investigation of the instability and transition to turbulence of the viscous, incompressible flow inside curved pipes. For the first time, the impact of the curvature is analysed over the whole parameter space, presenting new results for both the steady flow and the instabilities encountered by this flow.



This work is funded by The Swedish Research Council Grant No. 621-2013-5788. Computer time was provided by the Swedish National Infrastructure for Computing (SNIC). We acknowledge PRACE for awarding us access to resource Sisu based in Finland at CSC.


  1. 1.
    Kalpakli Vester, A., Örlü, R., Alfredsson, P.H.: Turbulent flows in curved pipes: recent advances in experiments and simulations. Appl. Mech. Rev. 68, 050802 (2016)CrossRefGoogle Scholar
  2. 2.
    Vashisth, S., Kumar, V., Nigam, K.D.P.: A review on the potential applications of curved geometries in process industry. Ind. Eng. Chem. Res. 47, 3291–3337 (2008)CrossRefGoogle Scholar
  3. 3.
    Berger, S.A., Talbot, L., Yao, L.-S.: Flow in curved pipes. Annu. Rev. Fluid Mech. 15, 461–512 (1983)CrossRefGoogle Scholar
  4. 4.
    Bulusu, K.V., Hussain, S., Plesniak, M.W.: Determination of secondary flow morphologies by wavelet analysis in a curved artery model with physiological inflow. Exp. Fluids 55, 1832 (2014)CrossRefGoogle Scholar
  5. 5.
    Canton, J.: Global linear stability of axisymmetric coaxial jets. Master’s thesis, Politecnico di Milano, Italy (2013)Google Scholar
  6. 6.
    Fischer, P.F., Lottes, J.W., Kerkemeier, S.G.: Nek5000 Web page (2008)Google Scholar
  7. 7.
    Boussinesq, M.J.: Mémoire sur l’influence des frottements dans les mouvements réguliers des fluides. J. Math. Pure Appl. 13, 377–424 (1868)zbMATHGoogle Scholar
  8. 8.
    Eustice, J.: Flow of water in curved pipes. Proc. R. Soc. Lond. Ser. A 84, 107–118 (1910)CrossRefGoogle Scholar
  9. 9.
    Eustice, J.: Experiments on stream-line motion in curved pipes. Proc. R. Soc. A Math. Phys. Eng. Sci. 85, 119–131 (1911)CrossRefGoogle Scholar
  10. 10.
    Dean, W.R.: XVI. Note on the motion of fluid in a curved pipe. Lond. Edinb. Dublin Philos. Mag. J. Sci. 4, 208–223 (1927)CrossRefGoogle Scholar
  11. 11.
    Dean, W.R.: The streamline motion of fluid in a curved pipe. Phil. Mag. 5, 673–693 (1928)CrossRefGoogle Scholar
  12. 12.
    Ito, H.: Friction factors for turbulent flow in curved pipes. J. Basic Eng. 81, 123–134 (1959)Google Scholar
  13. 13.
    Cieślicki, K., Piechna, A.: Can the Dean number alone characterize flow similarity in differently bent tubes? J. Fluids Eng. 134(5), 051205 (2012)CrossRefGoogle Scholar
  14. 14.
    Canton, J., Örlü, R., Schlatter, P.: Characterisation of the steady, laminar incompressible flow in toroidal pipes covering the entire curvature range. Int. J. Heat Fluid Flow 66, 95–107 (2017)CrossRefGoogle Scholar
  15. 15.
    Noorani, A., Schlatter, P.: Swirl-switching phenomenon in turbulent flow through toroidal pipes. Int. J. Heat Fluid Flow 61, 108–116 (2016)CrossRefGoogle Scholar
  16. 16.
    Canton, J., Schlatter, P., Örlü, R.: Modal instability of the flow in a toroidal pipe. J. Fluid Mech. 792, 894–909 (2016)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Kühnen, J., Braunshier, P., Schwegel, M., Kuhlmann, H.C., Hof, B.: Subcritical versus supercritical transition to turbulence in curved pipes. J. Fluid Mech. 770, R3 (2015)CrossRefGoogle Scholar
  18. 18.
    Avila, K., Moxey, D., de Lozar, A., Avila, M., Barkley, D., Hof, B.: The onset of turbulence in pipe flow. Science 333, 192–196 (2011)CrossRefGoogle Scholar
  19. 19.
    Sreenivasan, K.R., Strykowski, P.J.: Stabilization effects in flow through helically coiled pipes. Exp. Fluids 1, 31–36 (1983)CrossRefGoogle Scholar
  20. 20.
    Noorani, A., Schlatter, P.: Evidence of sublaminar drag naturally occurring in a curved pipe. Phys. Fluids 27, 035105 (2015)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Linné FLOW Centre, KTH Mechanics, Royal Institute of TechnologyStockholmSweden

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