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Characterisation of the steady, laminar incompressible flow in toroidal pipes covering the entire curvature range
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.ORCID iD: 0000-0003-3211-4347
KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-1663-3553
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.ORCID iD: 0000-0001-9627-5903
2017 (English)In: International Journal of Heat and Fluid Flow, ISSN 0142-727X, E-ISSN 1879-2278, Vol. 66, p. 95-107Article in journal (Refereed) Published
Abstract [en]

This work is concerned with a detailed investigation of the steady (laminar), incompressible flow inside bent pipes. In particular, a toroidal pipe is considered in an effort to isolate the effect of the curvature, δ, on the flow features, and to compare the present results to available correlations in the literature. More than 110 000 numerical solutions are computed, without any approximation, spanning the entire curvature range, 0 ≤ δ ≤ 1, and for bulk Reynolds numbers Re up to 7 000, where the flow is known to be unsteady. Results show that the Dean number De provides a meaningful non-dimensional group only below very strict limits on the curvature and the Dean number itself. For δ>10−6 and De > 10, in fact, not a single flow feature is found to scale well with the Dean number. These considerations are also valid for quantities, such as the Fanning friction factor, that were previously considered Dean-number dependent only. The flow is therefore studied as a function of two equally important, independent parameters: the curvature of the pipe and the Reynolds number. The analysis shows that by increasing the curvature the flow is fundamentally changed. Moderate to high curvatures are not only quantitatively, but also qualitatively different from low δ cases. A complete description of some of the most relevant flow quantities is provided. Most notably the friction factor f for laminar flow in curved pipes by Ito [J. Basic Eng. 81:123–134 (1959)] is reproduced, the influence of the curvature on f is quantified and the scaling is discussed. A complete database including all the computed solutions is available at www.flow.kth.se.

Place, publisher, year, edition, pages
Elsevier, 2017. Vol. 66, p. 95-107
Keywords [en]
Bent pipes, Dean number, Friction factor
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-209516DOI: 10.1016/j.ijheatfluidflow.2017.05.014ISI: 000407524500009Scopus ID: 2-s2.0-85020316303OAI: oai:DiVA.org:kth-209516DiVA, id: diva2:1112646
Funder
Swedish Research Council, 621-2013-5788Knut and Alice Wallenberg FoundationSwedish e‐Science Research Center
Note

QC 20170620

Available from: 2017-06-20 Created: 2017-06-20 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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