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Of Pipes and Bends
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0003-3211-4347
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 [en]
nonlinear instability, bifurcation, flow control
National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-228225ISBN: 978-91-7729-823-6 (print)OAI: oai:DiVA.org:kth-228225DiVA, id: diva2:1208739
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
List of papers
1. Characterisation of the steady, laminar incompressible flow in toroidal pipes covering the entire curvature range
Open this publication in new window or tab >>Characterisation of the steady, laminar incompressible flow in toroidal pipes covering the entire curvature range
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
Keywords
Bent pipes, Dean number, Friction factor
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-209516 (URN)10.1016/j.ijheatfluidflow.2017.05.014 (DOI)000407524500009 ()2-s2.0-85020316303 (Scopus ID)
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
2. Modal instability of the flow in a toroidal pipe
Open this publication in new window or tab >>Modal instability of the flow in a toroidal pipe
2016 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 792, p. 894-909Article in journal (Refereed) Published
Abstract [en]

The modal instability encountered by the incompressible flow inside a toroidal pipe is studied, for the first time, by means of linear stability analysis and direct numerical simulation (DNS). In addition to the unquestionable aesthetic appeal, the torus represents the smallest departure from the canonical straight pipe flow, at least for low curvatures. The flow is governed by only two parameters: the Reynolds number (Formula presented.) and the curvature of the torus (Formula presented.), i.e. the ratio between pipe radius and torus radius. The absence of additional features, such as torsion in the case of a helical pipe, allows us to isolate the effect that the curvature has on the onset of the instability. Results show that the flow is linearly unstable for all curvatures investigated between 0.002 and unity, and undergoes a Hopf bifurcation at (Formula presented.) of about 4000. The bifurcation is followed by the onset of a periodic regime, characterised by travelling waves with wavelength (Formula presented.) pipe diameters. The neutral curve associated with the instability is traced in parameter space by means of a novel continuation algorithm. Tracking the bifurcation provides a complete description of the modal onset of instability as a function of the two governing parameters, and allows a precise calculation of the critical values of (Formula presented.) and (Formula presented.). Several different modes are found, with differing properties and eigenfunction shapes. Some eigenmodes are observed to belong to groups with a set of common characteristics, deemed ‘families’, while others appear as ‘isolated’. Comparison with nonlinear DNS shows excellent agreement, confirming every aspect of the linear analysis, its accuracy, and proving its significance for the nonlinear flow. Experimental data from the literature are also shown to be in considerable agreement with the present results.

Place, publisher, year, edition, pages
Cambridge University Press, 2016
Keywords
bifurcation, instability, nonlinear dynamical systems
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-187267 (URN)10.1017/jfm.2016.104 (DOI)000379218400003 ()2-s2.0-84960155237 (Scopus ID)
Note

QC 20160519

Available from: 2016-05-19 Created: 2016-05-19 Last updated: 2018-05-21Bibliographically approved
3. Approaching zero curvature: modal instability in a bent pipe
Open this publication in new window or tab >>Approaching zero curvature: modal instability in a bent pipe
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.

National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-228221 (URN)
Note

QC 20180521

Available from: 2018-05-18 Created: 2018-05-18 Last updated: 2018-05-21Bibliographically approved
4. The collapse of strong turbulent fronts in bent pipes
Open this publication in new window or tab >>The collapse of strong turbulent fronts in bent pipes
(English)In: Article in journal (Other academic) Submitted
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-228222 (URN)
Note

QC 20180521

Available from: 2018-05-18 Created: 2018-05-18 Last updated: 2018-05-21Bibliographically approved
5. A critical point for bifurcation cascades and intermittency
Open this publication in new window or tab >>A critical point for bifurcation cascades and intermittency
2018 (English)Report (Other academic)
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-228224 (URN)
Note

QC 20180521

Available from: 2018-05-18 Created: 2018-05-18 Last updated: 2018-05-21Bibliographically approved
6. The three-dimensional structure of swirl-switching in bent pipe flow
Open this publication in new window or tab >>The three-dimensional structure of swirl-switching in bent pipe flow
Show others...
2017 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 835, p. 86-101Article in journal (Refereed) Published
Abstract [en]

Swirl-switching is a low-frequency oscillatory phenomenon which affects the Dean vortices in bent pipes and may cause fatigue in piping systems. Despite thirty years worth of research, the mechanism that causes these oscillations and the frequencies that characterise them remain unclear. Here we show that a three-dimensional wave-like structure is responsible for the low-frequency switching of the dominant Dean vortex. The present study, performed via direct numerical simulation, focuses on the turbulent flow through a 90 degrees pipe bend preceded and followed by straight pipe segments. A pipe with curvature 0.3 (defined as ratio between pipe radius and bend radius) is studied for a bulk Reynolds number Re = 11 700, corresponding to a friction Reynolds number Re-tau approximate to 360. Synthetic turbulence is generated at the inflow section and used instead of the classical recycling method in order to avoid the interference between recycling and swirl-switching frequencies. The flow field is analysed by three-dimensional proper orthogonal decomposition (POD) which for the first time allows the identification of the source of swirl-switching: a wave-like structure that originates in the pipe bend. Contrary to some previous studies, the flow in the upstream pipe does not show any direct influence on the swirl-switching modes. Our analysis further shows that a three-dimensional characterisation of the modes is crucial to understand the mechanism, and that reconstructions based on two-dimensional POD modes are incomplete.

Place, publisher, year, edition, pages
Cambridge University Press, 2017
Keywords
pipe flow boundary layer, turbulence simulation, turbulent flows
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-220487 (URN)10.1017/jfm.2017.749 (DOI)000416940800003 ()2-s2.0-85038601971 (Scopus ID)
Funder
Swedish Research CouncilSwedish e‐Science Research Center
Note

QC 20180103

Available from: 2018-01-03 Created: 2018-01-03 Last updated: 2018-05-21Bibliographically approved
7. On Large-Scale Friction Control in Turbulent Wall Flow in Low Reynolds Number Channels
Open this publication in new window or tab >>On Large-Scale Friction Control in Turbulent Wall Flow in Low Reynolds Number Channels
Show others...
2016 (English)In: Flow Turbulence and Combustion, ISSN 1386-6184, E-ISSN 1573-1987, Vol. 97, no 3, p. 811-827Article in journal (Refereed) Published
Abstract [en]

The present study reconsiders the control scheme proposed by Schoppa & Hussain (Phys. Fluids 10, 1049–1051 1998), using a new set of numerical simulations. The computations are performed in a turbulent channel at friction Reynolds numbers of 104 (the value employed in the original study) and 180. In particular, the aim is to better characterise the physics of the control as well as to investigate the optimal parameters. The former purpose lead to a re-design of the control strategy: moving from a numerical imposition of the mean flow to the application of a volume force. A comparison between the two is presented. Results show that the original method only gave rise to transient drag reduction. The forcing method, on the other hand, leads to sustained drag reduction, and thus shows the superiority of the forcing approach for all wavelengths investigated. A clear maximum efficiency in drag reduction is reached for the case with a viscous-scaled spanwise wavelength of the vortices of 1200, which yields a drag reduction of 18 %, as compared to the smaller wavelength of 400 suggested as the most efficient vortex in Schoppa & Hussain. Various turbulence statistics are considered, in an effort to elucidate the causes of the drag-reducing effect. For instance, a region of negative production was found, which is quite unusual for developed turbulent channel flow.

Place, publisher, year, edition, pages
Springer Netherlands, 2016
Keywords
Direct numerical simulation, Flow control, Skin-friction reduction, Turbulent channel flow
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-187264 (URN)10.1007/s10494-016-9723-8 (DOI)000388171600007 ()2-s2.0-84960409466 (Scopus ID)
Note

QC 20161004

Available from: 2016-05-19 Created: 2016-05-19 Last updated: 2018-05-21Bibliographically approved
8. Reynolds number dependence of large-scale friction control in turbulent channel flow
Open this publication in new window or tab >>Reynolds number dependence of large-scale friction control in turbulent channel flow
2016 (English)In: Physical Review Fluids, E-ISSN 2469-990X, Vol. 1, no 8, article id 081501Article in journal (Refereed) Published
Abstract [en]

The present work investigates the effectiveness of the control strategy introduced by Schoppa and Hussain [Phys. Fluids 10, 1049 (1998)] as a function of Reynolds number (Re). The skin-friction drag reduction method proposed by these authors, consisting of streamwise-invariant, counter-rotating vortices, was analyzed by Canton et al. [Flow, Turbul. Combust. 97, 811 (2016)] in turbulent channel flows for friction Reynolds numbers (Re t) corresponding to the value of the original study (i.e., 104) and 180. For these Re, a slightly modified version of the method proved to be successful and was capable of providing a drag reduction of up to 18%. The present study analyzes the Reynolds number dependence of this drag-reducing strategy by performing two sets of direct numerical simulations (DNS) for Re-tau = 360 and 550. A detailed analysis of the method as a function of the control parameters (amplitude and wavelength) and Re confirms, on the one hand, the effectiveness of the large-scale vortices at low Re and, on the other hand, the decreasing and finally vanishing effectiveness of this method for higher Re. In particular, no drag reduction can be achieved for Re t = 550 for any combination of the parameters controlling the vortices. For low Reynolds numbers, the large-scale vortices are able to affect the near-wall cycle and alter the wall-shear-stress distribution to cause an overall drag reduction effect, in accordance with most control strategies. For higher Re, instead, the present method fails to penetrate the near-wall region and cannot induce the spanwise velocity variation observed in other more established control strategies, which focus on the near-wall cycle. Despite the negative outcome, the present results demonstrate the shortcomings of the control strategy and show that future focus should be on methods that directly target the near-wall region or other suitable alternatives.

Place, publisher, year, edition, pages
American Physical Society, 2016
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-202448 (URN)10.1103/PhysRevFluids.1.081501 (DOI)000391943600001 ()2-s2.0-85032142744 (Scopus ID)
Funder
Swedish Research Council
Note

QC 20170306

Available from: 2017-03-06 Created: 2017-03-06 Last updated: 2019-04-04Bibliographically approved

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