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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: [email protected]
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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

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