Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-10T06:03:36.027Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite-amplitude thresholds for transition in pipe flow

Published online by Cambridge University Press:  14 June 2007

J. PEIXINHO  and
T. MULLIN
J. PEIXINHO
Affiliation:
Manchester Centre for Nonlinear Dynamics, The University of Manchester, M13 9PL, UK
T. MULLIN
Affiliation:
Manchester Centre for Nonlinear Dynamics, The University of Manchester, M13 9PL, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

We report the results of an experimental study of the finite-amplitude thresholds for transition to turbulence in a constant mass flux pipe flow. The flow was perturbed using small impulsive jets and push–pull disturbances from holes in the pipe wall. The flux of the disturbance is used to define an amplitude for the perturbation and the critical value required to cause transition scales in proportion to Re−1 for jets. In this case, the transition is catastrophic and the scaling suggests a simple balance between inertia and viscosity. On the other hand, the threshold scales as Re−1.3 or Re−1.5 for push–pull disturbances with the precise value depending on the orientation of the perturbation. Further, the amplitudes required to cause transition are typically an order of magnitude smaller than for jets. When the push–pull perturbation was applied in the oblique direction, streaks and hairpin vortices appeared during the growth phase of the disturbance. The scaling of the threshold and the growth of structures are both consistent with ideas associated with temporary algebraic growth.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 582 , 10 July 2007 , pp. 169 - 178
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Acarlar, M. S. & Smith, C. R. 1987 A study of hairpin vortices in a laminar boundary layer. Part 2. Hairpin vortices generated by fluid injection. J. Fluid Mech. 175, 43–83.CrossRefGoogle Scholar
Binnie, A. M. & Fowler, J. S. 1948 A study by double-refraction method of the development of turbulence in a long circular tube. Proc. R. Soc. Lond. 192, 32–44.Google Scholar
Brandt, L. 2007 Numerical studies of the instability and breakdown of a boundary-layer low-speed streak. Eur. J. Mech. B Fluids 26, 64–82.CrossRefGoogle Scholar
Darbyshire, A. G. & Mullin, T. 1995 Transition to turbulence in constant-mass-flux pipe flow. J. Fluid Mech. 289, 83–114.CrossRefGoogle Scholar
van Doorne, C. W. H. 2004 Stereoscopic PIV on transition in pipe flow. PhD thesis, Technische Universiteit Delft.Google Scholar
Draad, A. A., Kuiken, G. D. C. & Nieuwstadt, F. T. M. 1998 Laminar–turbulent transition in pipe flow for Newtonian and non-Newtonian fluids. J. Fluid Mech. 377, 267–312.CrossRefGoogle Scholar
Drazin, P. G. & Reid, W. H. 1980 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Eckhardt, B. & Mersmann, A. 1999 Transition to turbulence in a shear flow. Phys. Rev. E 60, 509–517.Google Scholar
Faisst, H. & Eckhardt, B. 2003 Travelling waves in pipe flow. Phys. Rev. Lett. 91 (224502).CrossRefGoogle ScholarPubMed
Govindarajan, R. & Narasimha, R. 1991 The role of residual nonturbulent disturbances on transition onset in two-dimensional boundary layers. Trans. ASME} I: J. Fluids Engng. 113, 147–149.Google Scholar
Grossmann, S. 2000 The onset of shear flow turbulence. Rev. Mod. Phys. 72, 603–618.CrossRefGoogle Scholar
Han, G., Tumin, A. & Wygnanski, I. J. 2000 Laminar–turbulent transition in Poiseuille pipe flow subjected to periodic perturbation emanating from the wall. J. Fluid Mech. 419, 1–27.CrossRefGoogle Scholar
Henningson, D. S. & Kreiss, G. 2005 Threshold amplitudes in subcritical shear flows. In Proc. IUTAM Symposium Laminar–Turbulent Transition and Finite Amplitude Solutions (ed. Mullin, T. & Kerswell, R.), pp. 232–245. Springer.Google Scholar
Hof, B. 2005 Transition to turbulence in pipe flow. In Proc. IUTAM Symposium Laminar–Turbulent Transition and Finite Amplitude Solutions (ed. Mullin, T. & Kerswell, R.), pp. 221–231. Springer.CrossRefGoogle Scholar
Hof, B., Juel, A. & Mullin, T. 2003 Scaling of the turbulence transition threshold in a pipe. Phys. Rev. Lett. 91 (244502).CrossRefGoogle Scholar
Kachanov, Y. S. 1994 Physical mechanisms of laminar–boundary-layer transition. Annu. Rev. Fluid Mech. 26, 411–82.CrossRefGoogle Scholar
Kerswell, R. R. 2005 Recent progress in understanding the transition to turbulence in a pipe. Nonlinearity 18, 17–44.CrossRefGoogle Scholar
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 The three-dimensional nature of boundary-layer instability. J. Fluid Mech. 12, 1–34.CrossRefGoogle Scholar
Leite, R. J. 1959 An experimental investigation of the stability of Poiseuille flow. J. Fluid Mech. 5, 81–96.CrossRefGoogle Scholar
Levin, O. 2005 Numerical studies of transition in wall-bounded flows. PhD thesis, KTH Mechanics.Google Scholar
Levin, O., Davidsson, E. N. & Henningson, D. S. 2005 Transition thresholds in the asymptotic suction boundary layer. Phys. Fluids 17 (114104).CrossRefGoogle Scholar
Mellibvosky, F. & Meseguer, A. 2006 The role of streamwise perturbations in pipe flow transition. Phys. Fluids 18 (074104-9).Google Scholar
Meseguer, A. 2003 Streak breakdown instability in pipe Poiseuille flow. Phys. Fluids 6 (5), 1203–1213.CrossRefGoogle Scholar
Mullin, T. & Peixinho, J. 2005 Recent observations of the transition to turbulence in a pipe. In Proc. Sixth IUTAM Symposium on Laminar-Turbulent Transition (ed. Govindarajan, R.), pp. 45–55. Springer.Google Scholar
O'Sullivan, P. L. & Breuer, K. S. 1994 Transient growth in circular pipe flow. II Nonlinear development. Phys. Fluids 6 (11), 3652–64.CrossRefGoogle Scholar
Peixinho, J. & Mullin, T. 2006 Decay of turbulence in pipe flow. Phys. Rev. Lett. 96 (094501).CrossRefGoogle ScholarPubMed
Pfenniger, W. 1961 Transition in the inlet length of tubes at high Reynolds numbers. In Boundary Layer and Flow Control (ed. Lachman, G. V.), pp. 970–980.Google Scholar
Reynolds, O. 1883 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. Proc. R. Soc. Lond. A 35, 84–99.Google Scholar
Schmid, P. J. 2007 Nonmodal stability theory. Annu. Rev. Fluid. Mech. 39, 129–162.CrossRefGoogle Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.CrossRefGoogle Scholar
Seidel, J. & Fasel, H. F. 2001 Numerical investigations of heat transfer mechanisms in the forced laminar wall jet. J. Fluid Mech. 442, 191–215.CrossRefGoogle Scholar
Shan, H., Zhang, Z. & Nieuwstadt, F. T. M. 1998 Direct numerical simulation of transition in pipe flow under the influence of wall disturbances. Intl. J. Heat Fluid Flow 19, 320–325.CrossRefGoogle Scholar
Trefethen, L. N., Trefethen, A. E., Reddy, S. C. & Driscoll, T. A. 1993 Hydrodynamic stability without eigenvalues. Science 261, 578–583.CrossRefGoogle ScholarPubMed
Wedin, H. & Kerswell, R. R. 2004 Exact coherent structures in pipe flow: travelling wave solutions. J. Fluid Mech. 508, 333–371.CrossRefGoogle Scholar
Williams, S. D. 2001 An investigation of the stability of developing pipe flow. PhD thesis, University of Manchester.Google Scholar
Willis, A. P. & Kerswell, R. R. 2007 Critical behavior in the relaminarization of localized turbulence in pipe flow. Phys. Rev. Lett. 98, 014501.CrossRefGoogle ScholarPubMed
Wygnanski, I. J. & Champagne, F. H. 1973 On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug. J. Fluid Mech. 59, 281–351.CrossRefGoogle Scholar