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Slug genesis in cylindrical pipe flow

Published online by Cambridge University Press:  05 October 2010

Y. DUGUET ,
A. P. WILLIS  and
R. R. KERSWELL
Y. DUGUET*
Affiliation:
School of Mathematics, University of Bristol, BS8 1TW Bristol, UK Linné Flow Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden LIMSI-CNRS, UPR 3251, 91403 Orsay, France
A. P. WILLIS
Affiliation:
School of Mathematics, University of Bristol, BS8 1TW Bristol, UK Laboratoire d'Hydrodynamique, Ecole Polytechnique, 91128 Palaiseau, France
R. R. KERSWELL
Affiliation:
School of Mathematics, University of Bristol, BS8 1TW Bristol, UK
*
†Email address for correspondence: duguet@mech.kth.se
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Abstract

Transition to uniform turbulence in cylindrical pipe flow occurs experimentally via the spatial expansion of isolated coherent structures called ‘slugs’, triggered by localized finite-amplitude disturbances. We study this process numerically by examining the preferred route in phase space through which a critical disturbance initiates a ‘slug’. This entails first identifying the relative attractor – ‘edge state’ – on the laminar–turbulent boundary in a long pipe and then studying the dynamics along its low-dimensional unstable manifold, leading to the turbulent state. Even though the fully turbulent state delocalizes at Re ≈ 2300, the edge state is found to be localized over the range Re = 2000–6000, and progressively reduces in both energy and spatial extent as Re is increased. A key process in the genesis of a slug is found to be vortex shedding via a Kelvin–Helmholtz mechanism from wall-attached shear layers quickly formed at the edge state's upstream boundary. Whether these shedded vortices travel on average faster or slower downstream than the developing turbulence determines whether a puff or a slug (respectively) is formed. This observation suggests that slugs are out-of-equilibrium puffs which therefore do not co-exist with stable puffs.

JFM classification

Instability: Transition to turbulence Turbulent Flows: Turbulence simulation

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Papers
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Journal of Fluid Mechanics , Volume 663 , 25 November 2010 , pp. 180 - 208
Copyright
Copyright © Cambridge University Press 2010

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References

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Duguet et al. supplementary movie

Movie 1: Genesis of a turbulent puff starting from the edge state at Re=2000. Azimuthal vorticity perturbation in a plane containing the axis. Scale is logarithmic, from -5 (white) to -1 (black). The length of the pipe is 33.51 diameters, with periodic boundary conditions.

Download Duguet et al. supplementary movie(Video)
Video 6.6 MB

Duguet et al. supplementary movie

Movie 1: Genesis of a turbulent puff starting from the edge state at Re=2000. Azimuthal vorticity perturbation in a plane containing the axis. Scale is logarithmic, from -5 (white) to -1 (black). The length of the pipe is 33.51 diameters, with periodic boundary conditions.

Download Duguet et al. supplementary movie(Video)
Video 6.4 MB

Duguet et al. supplementary movie

Movie 2: Genesis of a turbulent slug starting from the edge state at Re=3000. Azimuthal vorticity perturbation in a plane containing the axis. Scale is logarithmic, from -5 (white) to -1 (black).The length of the pipe is 33.51 diameters, with periodic boundary conditions.

Download Duguet et al. supplementary movie(Video)
Video 11.3 MB

Duguet et al. supplementary movie

Movie 2: Genesis of a turbulent slug starting from the edge state at Re=3000. Azimuthal vorticity perturbation in a plane containing the axis. Scale is logarithmic, from -5 (white) to -1 (black).The length of the pipe is 33.51 diameters, with periodic boundary conditions.

Download Duguet et al. supplementary movie(Video)
Video 6.4 MB

Duguet et al. supplementary movie

Movie 3: Genesis of a turbulent slug starting from the edge state at Re=4500. Azimuthal vorticity perturbation in a plane containing the axis. Scale is logarithmic, from -5 (white) to -1 (black).The length of the pipe is 33.51 diameters, with periodic boundary conditions.

Download Duguet et al. supplementary movie(Video)
Video 7.7 MB

Duguet et al. supplementary movie

Movie 3: Genesis of a turbulent slug starting from the edge state at Re=4500. Azimuthal vorticity perturbation in a plane containing the axis. Scale is logarithmic, from -5 (white) to -1 (black).The length of the pipe is 33.51 diameters, with periodic boundary conditions.

Download Duguet et al. supplementary movie(Video)
Video 4.8 MB

Duguet et al. supplementary movie

Movie 4: Genesis of a turbulent slug starting from the edge state at Re=6000. Azimuthal vorticity perturbation in a plane containing the axis. Scale is logarithmic, from -5 (white) to -1 (black).The length of the pipe is 33.51 diameters, with periodic boundary conditions.

Download Duguet et al. supplementary movie(Video)
Video 15.6 MB

Duguet et al. supplementary movie

Movie 4: Genesis of a turbulent slug starting from the edge state at Re=6000. Azimuthal vorticity perturbation in a plane containing the axis. Scale is logarithmic, from -5 (white) to -1 (black).The length of the pipe is 33.51 diameters, with periodic boundary conditions.

Download Duguet et al. supplementary movie(Video)
Video 6.4 MB