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Localised turbulence in a circular pipe flow with gradual expansion

Published online by Cambridge University Press:  20 April 2015

Kamal Selvam ,
Jorge Peixinho  and
Ashley P. Willis
Kamal Selvam
Affiliation:
Laboratoire Ondes et Milieux Complexes, CNRS & Normandie Université, 53 rue de Prony, 76600 Le Havre, France
Jorge Peixinho*
Affiliation:
Laboratoire Ondes et Milieux Complexes, CNRS & Normandie Université, 53 rue de Prony, 76600 Le Havre, France
Ashley P. Willis
Affiliation:
School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH, UK
*
†Email address for correspondence: [email protected]
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Abstract

We report the results of three-dimensional direct numerical simulations for incompressible viscous fluid in a circular pipe flow with a gradual expansion. At the inlet, a parabolic velocity profile is applied together with a constant finite-amplitude perturbation to represent experimental imperfections. Initially, at low Reynolds number, the solution is steady. As the Reynolds number is increased, the length of the recirculation region near the wall grows linearly. Then, at a critical Reynolds number, a symmetry-breaking bifurcation occurs, where linear growth of asymmetry is observed. Near the point of transition to turbulence, the flow experiences oscillations due to a shear layer instability for a narrow range of Reynolds numbers. At higher Reynolds numbers, the recirculation region breaks into a turbulent state which remains spatially localised and unchanged when the perturbation is removed from the flow. Spatial correlation analysis suggests that the localised turbulence in the gradual expansion possesses a different flow structure from the turbulent puff of uniform pipe flow.

JFM classification

Instability: Instability Instability: Transition to turbulence
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 771 , 25 May 2015 , R2
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Copyright
© 2015 Cambridge University Press 

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