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| 2. |
- Canton, Jacopo, 1989-
(författare)
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Approaching zero curvature: modal instability in a bent pipe
- 2018
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 4. |
- Canton, Jacopo, et al.
(författare)
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Characterisation of the steady, laminar incompressible flow in toroidal pipes covering the entire curvature range
- 2017
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Ingår i: International Journal of Heat and Fluid Flow. - : Elsevier. - 0142-727X .- 1879-2278. ; 66, s. 95-107
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 5. |
- Canton, Jacopo, et al.
(författare)
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Critical Point for Bifurcation Cascades and Featureless Turbulence
- 2020
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Ingår i: Physical Review Letters. - : AMER PHYSICAL SOC. - 0031-9007 .- 1079-7114. ; 124:1
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Tidskriftsartikel (refereegranskat)abstract
- In this Letter we show that a bifurcation cascade and fully sustained turbulence can share the phase space of a fluid flow system, resulting in the presence of competing stable attractors. We analyze the toroidal pipe flow, which undergoes subcritical transition to turbulence at low pipe curvatures (pipe-to-torus diameter ratio) and supercritical transition at high curvatures, as was previously documented. We unveil an additional step in the bifurcation cascade and provide evidence that, in a narrow range of intermediate curvatures, its dynamics competes with that of sustained turbulence emerging through subcritical transition mechanisms.
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| 6. |
- Canton, Jacopo, et al.
(författare)
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Linear global stability of two incompressible coaxial jets
- 2017
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Ingår i: Journal of Fluid Mechanics. - : Cambridge University Press. - 0022-1120 .- 1469-7645. ; 824, s. 886-911
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Tidskriftsartikel (refereegranskat)abstract
- The linear stability of two incompressible coaxial jets, separated by a thick duct wall, is investigated by means of both a modal and a non-modal approach within a global framework. The attention is focused on the range of unitary velocity ratios for which an alternate vortex shedding from the duct wall is known to dominate the flow. In spite of the inherent convective nature of jet flow instabilities, such behaviour is shown to originate from an unstable global mode of the dynamics linearised around the axisymmetric base flow. The corresponding wavemaker is located in the recirculating-flow region formed behind the duct wall. At the same time, the transient-growth analysis reveals that huge amplifications (up to 20 orders of magnitude) of small flow perturbations at the nozzle exit can occur in the subcritical regime, especially for high ratios between the outer and the inner velocities.
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| 7. |
- Canton, Jacopo, et al.
(författare)
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Linear stability of the flow in a toroidal pipe
- 2015
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Ingår i: 9th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2015. - : TSFP-9. - 9780000000002
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Konferensbidrag (refereegranskat)abstract
- While hydrodynamic stability and transition to turbulence in straight pipes - being one of the most fundamental problems in fluid mechanics - has been studied extensively, the stability of curved pipes has received less attention. In the present work, the first (linear) instability of the canonical flow inside a toroidal pipe is investigated as a first step in the study of the related laminar-turbulent transition process. The impact of the curvature of the pipe, in the range 8 e [0.002,1], on the stability properties of the flow is studied in the framework of linear stability analysis. Results show that the flow is indeed modally unstable for all curvatures investigated and that the wave number corresponding to the critical mode depends on the curvature, as do several other features of this problem. The critical modes are mainly located in the region of the Dean vortices, and are characterised by oscillations which are symmetric or antisymmetric as a function of the curvature. The neutral curve associated with the first bifurcation is the result of a complex interaction between isolated modes and branches composed by several modes characterised by a common structure. This behaviour is in obvious contrast to that of straight pipes, which are linearly stable for all Reynolds numbers.
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| 8. |
- Canton, Jacopo, et al.
(författare)
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Modal instability of the flow in a toroidal pipe
- 2016
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Ingår i: Journal of Fluid Mechanics. - : Cambridge University Press. - 0022-1120 .- 1469-7645. ; 792, s. 894-909
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 9. |
- Canton, Jacopo, et al.
(författare)
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Neutral stability of the flow in a toroidal pipe
- 2015
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Ingår i: Proceedings - 15th European Turbulence Conference, ETC 2015. - : TU Delft.
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Konferensbidrag (refereegranskat)abstract
- This work is concerned with the numerical investigation of the linear stability properties of the viscous, incompressible flow inside a toroidal pipe. A Hopf bifurcation is found and tracked in phase space, showing that the flow is modally unstable even at extremely low curvatures. The bifurcation and the eigenfunctions associated with it are analysed as a function of the two parameters governing the flow, i.e. the Reynolds number, Re, and the curvature, δ. For all curvatures, the critical Reynolds number is found to be about 3000.
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| 10. |
- Canton, Jacopo, 1989-
(författare)
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Numerical studies on flows with secondary motion
- 2016
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This work is concerned with the study of flow stability and turbulence control - two old but still open problems of fluid mechanics. The topics are distinct and are (currently) approached from different directions and with different strategies. This thesis reflects this diversity in subject with a difference in geometry and, consequently, flow structure: the first problem is approached in the study of the flow in a toroidal pipe, the second one in an attempt to reduce the drag in a turbulent channel flow.The flow in a toroidal pipe is chosen as it represents the common asymptotic limit between spatially developing and helical pipes. Furthermore, the torus represents the smallest departure from the canonical straight pipe flow, at least for small curvatures. The interest in this geometry is twofold: it allows us to isolate the effect of the curvature on the flow and to approach straight as well as helical pipes. The analysis features a characterisation of the steady solution as a function of curvature and the Reynolds number. The problem of forcing fluid in the pipe is addressed, and the so-called Dean number is shown to be of little use, except for infinitesimally low curvatures. It is found that the flow is modally unstable and undergoes a Hopf bifurcation that leads to a limit cycle. The bifurcation and the corresponding eigenmodes are studied in detail, providing a complete picture of the instability.The second part of the thesis approaches fluid mechanics from a different perspective: the Reynolds number is too high for a deterministic description and the flow is analysed with statistical tools. The objective is to reduce the friction exerted by a turbulent flow on the walls of a channel, and the idea is to employ a control strategy independent of the small, and Reynolds number-dependent, turbulent scales. The method of choice was proposed by Schoppa & Hussain [Phys. Fluids 10:1049-1051 (1998)] and consists in the imposition of streamwise invariant, large-scale vortices. The vortices are re-implemented as a volume force, validated and analysed. Results show that the original method only gave rise to transient drag reduction while the forcing version is capable of sustained drag reduction of up to 18%. An analysis of the method, though, reveals that its effectiveness decreases rapidly as the Reynolds number is increased.
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