Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-16T13:21:30.463Z Has data issue: false hasContentIssue false
  • English
  • Français

Formation and decay of coherent structures in pipe flow

Published online by Cambridge University Press:  14 May 2010

JIMMY PHILIP  and
JACOB COHEN
JIMMY PHILIP*
Affiliation:
Faculty of Aerospace Engineering, Technion-I.I.T., Haifa 32000, Israel
JACOB COHEN
Affiliation:
Faculty of Aerospace Engineering, Technion-I.I.T., Haifa 32000, Israel
*
†Present Address: Laboratoire d'Hydrodynamique (LadHyX), École Polytechnique, 91128 Palaiseau, France. Email address for correspondence: jimmyp@aerodyne.technion.ac.il
Get access Rights & Permissions [Opens in a new window]

Abstract

Experimental investigation of the generation and decay of coherent structures, namely, streaks (accompanied by a counter-rotating vortex pair) and hairpin vortices in pipe flow, is carried out by artificial injection of continuous disturbances. Flow visualization and velocity measurements show that for small amplitudes of disturbances (v0) streaks are produced, and increasing v0 produces instability waves on the streaks, which further break down into an array of hairpin vortices. However, the streaks and hairpins decay along the downstream direction (X). In fact, the critical value of v0 required for the initiation of hairpins at a given Re (Reynolds number) varies with the streamwise distance (in contrast to the previously found scaling of v0 ~ Re−1, valid only close to the location of injection, i.e. smaller X). This is a consequence of the decay of the coherent structures in the pipe. Moreover, the hairpins have been found to decay more slowly with increasing Re. Measurements of energy in the cross-sectional plane of the pipe, and maps of disturbance velocity at various X-locations show the transient growth and decay of energy for relatively low v0. For higher v0 and Re the energy has been seen to increase continuously along the length of the pipe under observation. Owing to the increase in the cross-sectional area occupied by the disturbance along the X-direction, it is observed that energy can transiently increase even when the total disturbance magnitude is decreasing. Observing the similarity of the present work and other investigations wherein decay of turbulence in pipe flow is found, a schematic illustration of the transition surface for pipe flow on a v0−Re−X, three-dimensional coordinate system is presented.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 655 , 25 July 2010 , pp. 258 - 279
Copyright
Copyright © Cambridge University Press 2010

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

Bagheri, S., Schlatter, P., Schmid, P. J. & Henningson, D. S. 2009 Global stability of a jet in crossflow. J. Fluid Mech. 624, 33–44.CrossRefGoogle Scholar
Ben-Dov, G., Levinski, V. & Cohen, J. 2003 On the mechanism of optimal disturbances: The role of a pair of nearly parallel modes. Phys. Fluids 15 (7), 1961–1972.CrossRefGoogle Scholar
Brosa, T. 1989 Turbulence without strange attractor. J. Stat. Phys. 55, 1303–1312.CrossRefGoogle Scholar
Cohen, J., Philip, J. & Ben-Dov, G. 2009 Aspects of linear and nonlinear instabilities leading to transition in pipe and channel flows. Phil. Trans. R. Soc. A 367, 509–527.CrossRefGoogle ScholarPubMed
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. & Westerweel, J. 2009 The flow structure of puff. Phil. Trans. R. Soc. A 367, 489–507.CrossRefGoogle ScholarPubMed
Eckhardt, B. (Ed.) 2009 Turbulence Transition in Pipe Flow: 125th Anniversary of the Publication of Reynolds' paper, 1888. In Phil. Trans. R. Soc. A, vol. 367.Google Scholar
Eckhardt, B., Schneider, T. M., Hof, B. & Westerweel, J. 2007 Turbulence transition in pipe flow. Annu. Rev. Fluid Mech. 39, 447–468.CrossRefGoogle Scholar
Elofsson, P. A. & Alfredsson, P. H. 1998 An experimental study of oblique transition in plane poiseuille flow. J. Fluid Mech. 358, 177–202.CrossRefGoogle Scholar
Faisst, H. & Eckhardt, B. 2004 Sensitive dependence of initial conditions in transition to turbulence in pipe flow. J. Fluid Mech. 504, 343–352.CrossRefGoogle Scholar
Fric, T. F. & Roshko, A. 1994 Vortical structure in the wake of a transverse jet. J. Fluid Mech. 279, 1–47.Google Scholar
Guala, M., Hommema, S. E. & Adrian, R. J. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521–542.CrossRefGoogle Scholar
Hof, B., van Doorne, C. W. H., Westerweel, J., Nieuwstadt, F. T. M., Faisst, H., Eckhardt, B., Wedin, H., Kerswell, R. R. & Waleffe, F. 2004 Experimental observations of nonlinear travelling waves in turbulent pipe flow. Science 305, 1594–1598.CrossRefGoogle ScholarPubMed
Hof, B., Juel, A. & Mullin, T. 2003 Scaling of the turbulent transition threshold in a pipe. Phys. Rev. Lett. 91 (24), 2445021–4.CrossRefGoogle Scholar
Hof, B., Westerweel, J., Schneider, T. M. & Eckhardt, B. 2006 Finite lifetime of turbulence in shear flows. Nature 443, 59–62.CrossRefGoogle ScholarPubMed
Joseph, D. D. 1976 Stability of Fluid Motions I. Springer-Verlag.Google Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773.CrossRefGoogle Scholar
de Lozar, A. & Hof, B. 2009 An experimental study of the decay of turbulent puffs in pipe flow. Phil. Trans. R. Soc. A 367, 589–599.CrossRefGoogle ScholarPubMed
Matsubara, M. & Alfredsson, P. H. 2001 Disturbance growth in boundary layers subjected to free-stream turbulence. J. Fluid Mech. 430, 149–168.CrossRefGoogle Scholar
Mellibovsky, F. & Meseguer, A. 2007 Pipe flow transition threshold following localized impulsive perturbations. Phys. Fluids 19, 044102.CrossRefGoogle Scholar
Meseguer, A. 2003 Streak breakdown instability in pipe poiseuille flow. Phys. Fluids 15, 1203–1213.CrossRefGoogle Scholar
Meseguer, A. & Trefethen, L. N. 2003 Linearized pipe flow to Reynolds number 107. J. Comp. Phys. 186, 178–197.CrossRefGoogle Scholar
Peixinho, J. & Mullin, T. 2006 Decay of turbulence in pipe flow. Phys. Rev. Lett. 96, 094501.CrossRefGoogle ScholarPubMed
Peixinho, J. & Mullin, T. 2007 Finite-amplitude thresholds for transition in pipe flow. J. Fluid Mech. 582, 169–178.CrossRefGoogle Scholar
Pfenniger, W. 1961 Boundary layer suction experiments with laminar flow at high Reynolds numbers in the inlet length of a tube by various suction methods. In Boundary Layer and Flow Control (ed. Lachman, G. V.), pp. 961–980. Pergamon.CrossRefGoogle Scholar
Philip, J., Svizher, A. & Cohen, J. 2007 Scaling law for subcritical transition in plane poiseuille flow. Phys. Rev. Lett. 98, 154502.CrossRefGoogle ScholarPubMed
Reshotko, E. & Tumin, A. 2001 Spatial theory of optimal disturbances in a circular pipe flow. Phys. Fluids 13 (4), 991–996.CrossRefGoogle Scholar
Reynolds, O. 1883 An experimental investigation of the circumstances which determine whether motion of water shall be direct or sinous and of the law of resistance in parallel channels. Phil. Trans. R. Soc. Lond. 174, 935–982.Google Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layers. Annu. Rev. Fluid Mech. 23, 601–639.CrossRefGoogle Scholar
Sau, R. & Mahesh, K. 2008 Dynamics and mixing of vortex rings in crossflow. J. Fluid Mech. 604, 329–354.CrossRefGoogle Scholar
Schlatter, P., Brandt, L., de Lange, H. C. & Henningson, D. S. 2008 On streak breakdown in bypass transition. Phys. Fluids 20, 101505.CrossRefGoogle Scholar
Schmid, P. J. 2007 Nonmodal stability theory. Annu. Rev. Fluid Mech. 39, 219–268.CrossRefGoogle Scholar
Schmid, P. J. & Henningson, D. S. 1994 Optimal energy density growth in Hagen–Poiseuille flow. J. Fluid Mech. 277, 197–225.CrossRefGoogle Scholar
Suponitsky, V., Cohen, J. & Bar-Yoseph, P. Z. 2005 The generation of streaks and hairpin vortices from a localized vortex embedded in unbounded uniform shear flow. J. Fluid Mech. 535, 65–100.CrossRefGoogle Scholar
Svizher, A. & Cohen, J. 2006 Holographic particle image velocimetry measurements of hairpin vortices in a subcritical air channel flow. Phys. Fluids 18, 014105.CrossRefGoogle Scholar
Wedin, H. & Kerswell, R. R. 2004 Exact coherent structures in pipe flow: Travelling wave solutions. J. Fluid Mech. 508, 333–371.CrossRefGoogle Scholar
Wygnanski, I. J. & Champagne, F. H. 1973 On transition in a pipe. 1. The origin of puffs and slugs and the flow in a turbulent slug. J. Fluid Mech. 59, 281–335.CrossRefGoogle Scholar
Zikanov, O. Y. 1996 On the stability of pipe poiseuille flow. Phys. Fluids 8, 2923–2932.CrossRefGoogle Scholar