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Influence of the inlet velocity profile on the flow stability in a symmetric channel expansion

Published online by Cambridge University Press:  22 December 2020

Robin Debuysschère Open the ORCID record for Robin Debuysschère [Opens in a new window] ,
Lorenzo Siconolfi ,
Bart Rimez ,
François Gallaire Open the ORCID record for François Gallaire [Opens in a new window]  and
Benoit Scheid Open the ORCID record for Benoit Scheid [Opens in a new window]
Robin Debuysschère
Affiliation:
Transfers, Interfaces and Processes (TIPs), ULB, 1050Brussels, Belgium
Lorenzo Siconolfi
Affiliation:
Laboratory of Fluid Mechanics and Instabilities (LFMI), EPFL, 1015Lausanne, Switzerland
Bart Rimez
Affiliation:
Transfers, Interfaces and Processes (TIPs), ULB, 1050Brussels, Belgium
François Gallaire
Affiliation:
Laboratory of Fluid Mechanics and Instabilities (LFMI), EPFL, 1015Lausanne, Switzerland
Benoit Scheid*
Affiliation:
Transfers, Interfaces and Processes (TIPs), ULB, 1050Brussels, Belgium
*
†Email address for correspondence: [email protected]
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Abstract

In a channel flow with a sudden expansion, whether for three-dimensional (3-D) pipe and channel flows, or for two-dimensional (2-D) channel flow, it is known that increasing the Reynolds number beyond a critical value $Re_c$ induces a symmetry breaking Pitchfork bifurcation. The linear stability analysis of the symmetric steady solution enables the $Re_c$ to be determined efficiently and thus the influence of the expansion ratio ($ER$), defined as the ratio between upstream and downstream diameter regarding the expansion, to be explored. In this study, we investigate the behaviour of the flow after 2-D sudden expansions while varying the $ER$ and the inlet flow profile, e.g. corresponding to a transition profile between a plug and a Poiseuille flow that could be reached for a flow after a sudden constriction upstream. Results demonstrate that imposing a plug flow at the inlet gives a higher $Re_c$ than any other profile and that the concomitant recirculation zones are shorter. We show that these results can be rationalized using basic convection–diffusion arguments.

JFM classification

Mathematical Foundations: Computational methods Nonlinear Dynamical Systems: Bifurcation Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 909 , 25 February 2021 , A13
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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