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Approaching zero curvature: modal instability in a bent pipe
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0003-3211-4347
2018 (English)Report (Other academic)
Abstract [en]

Canton et al. [J. Fluid Mech. 792:894–909 (2016)] showed that the flow in a toroidal pipe is linearly unstable for any pipe curvature δ greater than 0.002. The same authors later provided a detailed characterisation of the laminar steady flow, reporting lower limits for the influence of the pipe curvature [Canton et al. Int. J. Heat Fluid Fl. 66:95-107 (2017)]. The objective of the present work is to investigate the behaviour of the linear instability as the curvature of the pipe tends to zero. Results indicate that the toroidal pipe remains linearly unstable for curvatures as low as 10−7. While the critical Reynolds number Re necessary for the instability grows with an approximately algebraic trend below δ = 0.002, the neutral curve also closes in onto the limit of negligible curvature. It therefore appears that there could be values of δ and Re where a linearly unstable toroidal flow could be connected to the linearly stable straight pipe flow.

Place, publisher, year, edition, pages
2018.
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-228221OAI: oai:DiVA.org:kth-228221DiVA, id: diva2:1208736
Note

QC 20180521

Available from: 2018-05-18 Created: 2018-05-18 Last updated: 2018-05-21Bibliographically approved
In thesis
1. Of Pipes and Bends
Open this publication in new window or tab >>Of Pipes and Bends
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This work is concerned with the transition to turbulence of the flow in bent pipes, but it also includes an analysis of large-scale turbulent structures and their use for flow control.

The flow in a toroidal pipe is selected as it represents the common asymptotic limit between spatially developing and helical pipes. The study starts with a characterisation of the laminar flow as a function of curvature and the Reynolds number Re, since the so-called Dean number is found to be of little use except for infinitesimally low curvatures. It is found that the flow is modally unstable and undergoes a Hopf bifurcation for any curvature greater than zero. The bifurcation is studied in detail, and an effort to connect this modal instability with the linearly stable straight pipe is also presented.

This flow is not only modally unstable, but undergoes subcritical transition at low curvatures. This scenario is found to bear similarities to straight pipes, but also fundamental differences such as weaker turbulent structures and the apparent absence of puff splitting. Toroidal pipe flow is peculiar, in that it is one of the few fluid flows presenting both sub- and supercritical transition to turbulence; the critical point where the two scenarios meet is therefore of utmost interest. It is found that a bifurcation cascade and featureless turbulence actually coexist for a range of curvature and Re, and the attractors of the respective structures have a small but finite basin of attraction.

In 90◦ bent pipes at higher Re large-scale flow structures cause an oscilla- tory motion known as swirl-switching. Three-dimensional proper orthogonal decomposition is used to determine the cause of this phenomenon: a wave-like structure which is generated in the bent section, and is possibly a remnant of a low-Re instability.

The final part of the thesis has a different objective: to reduce the turbulent frictional drag on the walls of a channel by employing a control strategy independent of Re-dependent turbulent scales, initially proposed by Schoppa & Hussain [Phys. Fluids 10:1049–1051 (1998)]. Results show that the original method only gives rise to transient drag reduction while a revised version is capable of sustained drag reduction of up to 18%. However, the effectiveness of this control decreases rapidly as the Reynolds number is increased, and the only possibility for high-Re applications is to use impractically small actuators.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2018. p. 51
Series
TRITA-SCI-FOU ; 2018:25
Keywords
nonlinear instability, bifurcation, flow control
National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-228225 (URN)978-91-7729-823-6 (ISBN)
Public defence
2018-06-15, F2, Lindstedtsvägen 26, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20180521

Available from: 2018-05-21 Created: 2018-05-18 Last updated: 2018-05-21Bibliographically approved

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