Skip to main content
SpringerLink
Log in

Analysis of pipe flow transition. Part II. Energy transfer

  • Published:
Theoretical and Computational Fluid Dynamics Aims and scope Submit manuscript

Abstract

The present article describes the results from a study of nonlinear mechanisms at work during the process of transition to turbulence in pipe flows. Using an accurate hybrid finite-difference code for the simulation of unsteady incompressible pipe flow, we have performed a direct numerical simulation designed to model experiments performed by Han, Tumin and Wygnanski [12]. Based on these numerical data, we have conducted a meticulous investigation of the dynamic interactions of the structures and flow modes that can be observed during this process. Based on this study, we can paint a detailed picture of the dynamical interactions of flow structures during both the linear and nonlinear stages of pipe flow transition. While this picture does have some similarities to earlier proposed mechanisms, we find that even for the simple cases considered here the structure of the pertinent interactions is much richer than suggested by these earlier models.

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

Similar content being viewed by others

References

  1. Alfredsson, P.H., Matsubara, M.: Streaky structures in transition. In: Henkes, R.A.W.M., van Ingen, J.L. (eds.) Transitional Boundary Layers in Aeronautics, vol. 46 of Verhandelingen der Koninklijke Nederlandse Akademie van Wetenschappen, Afdeling Natuurkunde. North-Holland Amsterdam, pp. 373–386 (1996).

  2. Baggett, J.S., Driscoll, T.A., Trefethen, L.N.: A mostly linear model of transition to turbulence. Phys. Fluids 7(4), 833–838 (1995)

  3. Baggett, J.S., Trefethen, L.N.: Low-dimensional models of subcritical transition to turbulence. Phys. Fluids 9(4), 1043–1053 (1997)

  4. Bergström, L.: Initial algebraic growth of small angular dependent disturbances in pipe Poiseuille flow. Stud. Appl. Math. 87(1), 61–79 (1992)

  5. Bergström, L.: Optimal growth of small disturbances in pipe Poiseuille flow. Phys. Fluids A 5(11), 2710–2720 (1993)

  6. Boberg, L., Brosa, U.: Onset of turbulence in a pipe. Zeitschrift für Naturforschung, Teil A 43(8–9), 697–726 (1988)

  7. Butler, K.M., Farrell, B.F.: Three-dimensional optimal perturbations in viscous shear flows. Phys. Fluids A 4(8), 1637–1650 (1992)

  8. Ellingsen, T., Palm, E.: Stability of linear flow. Phys. Fluids 18(4), 487–488 (1975)

  9. Farrell, B.F.: Optimal excitation of perturbations in viscous shear flow. Phys. Fluids 31(8), 2093–2102 (1988)

  10. Gustavsson, L.H., Hultgren, L.S.: A resonance mechanism in plane Couette flow. J. Fluid Mech. 98(1), 149–159 (1980)

  11. Hamilton, J.M., Kim, J., Waleffe, F.: Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317–348 (1995)

  12. Han, G., Tumin, A., Wygnanski, I.: Laminar-turbulent transition in Poiseuille pipe flow subjected to periodic perturbation emanating from the wall. Part 2. Late stage of transition. J. Fluid Mech. 419, 1–27 (2000)

  13. Henningson, D.S., Schmid, P.S.: A note on measures of disturbance size for spatially evolving flows. Phys. Fluids 6(8), 2862–2864 (1994)

  14. Jeong, J., Hussain, F.: On the identification of a vortex. J. Fluid Mech. 285, 69–94 (1995)

  15. Jimenez, J., Moin, P.: The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–40 (1991)

  16. Klebanoff, P.S., Tidstrom, K.D., Sargent, L.M.: The tree-dimensional nature of boundary-layer instability. J. Fluid Mech. 12(1), 1–34 (1962)

  17. Kline, S.J., Reynolds, W.C., Schraub, F.A., Runstadler, P.W.: The structure of turbulent boundary layers. J. Fluid Mech. 30(4), 741–773 (1967)

  18. Landahl, M.T.: Wave breakdown and turbulence. SIAM J. on Appl. Math. 28(4), 735–756 (1975a)

  19. Landahl, M.T.: Wave mechanics of boundary layer turbulence and noise. J. Acoust. Soc. Am. 57(4), 824–31 (1975b)

  20. Landahl, M.T.: A note on algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98(2), 243–251 (1980)

  21. Ma, B., van Doorne, C.W.H., Zhang, Z., Nieuwstadt, F.T.M.: On the spatial evolution of a wall-imposed periodic disturbance in pipe Poiseuille flow at Re=3000. Part 1. subcritical disturbance. J. Fluid Mech. 398, 181–224 (1999)

  22. O’Sullivan, P.L., Breuer, K.S.: Transient growth in circular pipe flow. I. Linear disturbances. Phys. Fluids 6(11), 3643–3651 (1994a)

  23. O’Sullivan, P.L., Breuer, K.S.: Transient growth in circular pipe flow. II. Nonlinear development. Phys. Fluids 6(11), 3652–3664 (1994b)

  24. Rayleigh, L.: On the stability, or instability, of certain fluid motions. Proceedings of the London Mathematical Society 11, 57–70 (1880)

  25. Reddy, S.C., Henningson, D.S.: Energy growth in viscous channel flows. J. Fluid Mech. 252, 209–238 (1993)

  26. Reddy, S.C., Schmid, P.J., Baggett, J.S., Henningson, D.S.: On stability of streamwise streaks and transition thresholds in plane channel flows. J. Fluid Mech. 365, 269–303 (1998)

  27. Reddy, S.C., Schmid, P.J., Henningson, D.S.: Pseudospectra of the Orr-Sommerfeld operator. SIAM J. Appl. Math. 53(1), 15–47 (1993)

  28. Rempfer, D.: Low-dimensional modeling and numerical simulation of transition in simple shear flows. Annu. Rev. Fluid Mech. 35, 229–265 (2003)

  29. Reshotko, E., Tumin, A.: Spatial theory of optimal disturbances in a circular pipe flow. Phys. Fluids 13(4), 991–996 (2001)

  30. Reuter, J., Rempfer, D.: Analysis of pipe flow transition. Part I. Direct numerical simulation. Theor. Comput. Fluid Dynamics 17(4), 273–292 (2004)

  31. Reynolds, O.: An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Phil. Trans. R. Soc. London 174, 935–982 (1883)

  32. Salwen, H., Cotton, F.W., Grosch, C.E.: Linear stability of Poiseuille flow in a circular pipe. J. Fluid Mech. 98(2), 273–284 (1980)

  33. Schmid, P.J., Henningson, D.S.: Optimal energy density growth in Hagen-Poiseuille flow. J. Fluid Mech. 277, 197–225 (1994)

  34. Schubauer, G.B., Skramstad, H.K.: Laminar boundary-layer oscillations and transition on a flat plate. J. Res. Nat. Bureau Standards 38, 251–292 (1947)

  35. Stuart, J.T.: The production of intense shear layers by vortex stretching and convection. AGARD Report 514, AGARD (1965)

  36. Taneda, S.: A visual study of the structures in turbulent pipe flow. J. Phys. Soc. Japan 58(3), 771–774 (1989)

  37. Trefethen, L.N.: Pseudospectra of matrices. In: Griffith, D.F., Watson, G.A. (eds.) Numerical Analysis 1991. Longman pp. 234–266 (1992)

  38. Trefethen, L.N., Trefethen, A.E., Reddy, S.C., Driscoll, T.A.: Hydrodynamic stability without eigenvalues. Science 261(5121), 578–584 (1993)

  39. Waleffe, F.: Hydrodymanic stability and turbulence: Beyond transients to a self-sustaining process. Stud. Appl. Math. 95(3), 319–343 (1995)

  40. Waleffe, F.: On a self-sustaining process in shear flows. Phys. Fluids 9(4), 883–900 (1997)

  41. Waleffe, F., Kim, J., Hamilton, J.: On the origin of streaks in turbulent shear flows. In: Durst, F., Friedrichs, R., Launder, B.E., Schmidt, F.W. Schumann, U., Whitelaw, J.H. (eds.) Turbulent Shear Flows 8. Springer Berlin Heidelberg, pp. 37–49 (1993)

  42. Zikanov, O.Y.: On the instability of pipe Poiseuille flow. Phys. Fluids 8(11), 2923–2932 (1996)

Download references

Author information

Author notes

  1. Jörg Reuter

    Present address: Voith Paper GmbH & Co. KG, Heidenheim, Germany

Authors and Affiliations

  1. Institut für Aerodynamik und Gasdynamik, Universität Stuttgart, Germany

    Jörg Reuter

  2. Department of Mechanical, Materials and Aerospace Engineering, Illinois Institute of Technology, USA

    Dietmar Rempfer

Authors
  1. Jörg Reuter
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dietmar Rempfer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dietmar Rempfer.

Additional information

Communicated by

R. Moser

Rights and permissions

Reprints and permissions

About this article

Cite this article

Reuter, J., Rempfer, D. Analysis of pipe flow transition. Part II. Energy transfer. Theor. Comput. Fluid Dyn. 19, 39–64 (2005). https://doi.org/10.1007/s00162-004-0158-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00162-004-0158-9

Keywords

Search

Navigation