| 1. |
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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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| 3. |
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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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| 11. |
- Canton, Jacopo, 1989-
(författare)
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Of Pipes and Bends
- 2018
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 12. |
- Canton, Jacopo, et al.
(författare)
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On Large-Scale Friction Control in Turbulent Wall Flow in Low Reynolds Number Channels
- 2016
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Ingår i: Flow Turbulence and Combustion. - : Springer Netherlands. - 1386-6184 .- 1573-1987. ; 97:3, s. 811-827
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 13. |
- Canton, Jacopo, et al.
(författare)
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On stability and transition in bent pipes
- 2019
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Ingår i: Direct and Large-Eddy Simulation XI. - Cham : Springer. ; , s. 531-536
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Bokkapitel (refereegranskat)abstract
- This work is concerned with the investigation of the instability and transition to turbulence of the viscous, incompressible flow inside curved pipes. For the first time, the impact of the curvature is analysed over the whole parameter space, presenting new results for both the steady flow and the instabilities encountered by this flow.
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| 14. |
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| 15. |
- Canton, Jacopo, et al.
(författare)
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Reynolds number dependence of large-scale friction control in turbulent channel flow
- 2016
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Ingår i: Physical Review Fluids. - : American Physical Society. - 2469-990X. ; 1:8
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 16. |
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| 17. |
- Hufnagel, Lorenz, et al.
(författare)
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The three-dimensional structure of swirl-switching in bent pipe flow
- 2017
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Ingår i: Journal of Fluid Mechanics. - : Cambridge University Press. - 0022-1120 .- 1469-7645. ; 835, s. 86-101
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 18. |
- Lupi, Valerio, et al.
(författare)
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Global stability analysis of a 90°-bend pipe flow
- 2020
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Ingår i: International Journal of Heat and Fluid Flow. - : Elsevier BV. - 0142-727X .- 1879-2278. ; 86
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Tidskriftsartikel (refereegranskat)abstract
- The present work investigates the stability properties of the flow in a 90◦-bend pipe with curvature δ=R/Rc=1/3, with R being the radius of the cross-section of the pipe and Rc the radius of curvature at the pipe centreline. Direct numerical simulations (DNS) for values of the bulk Reynolds number Reb=UbD/ν between 2000 and 3000 are performed. The bulk Reynolds number is based on the bulk velocity Ub, the pipe diameter D, and the ki-nematic viscosity ν. The flow is found to be steady for Reb⩽2500, with two main pairs of symmetric, counter- rotating vortices in the section of the pipe downstream of the bend. The presence of two recirculation regions is detected inside the bend: one on the outer wall and the other on the inner side. For Reb⩾2550, the flow exhibits a periodic behaviour, oscillating with a fundamental non-dimensional frequency St=fD/Ub=0.23. A global stability analysis is performed in order to determine the cause of the transition from the steady to the periodic regime. The spectrum of the linearised Navier-Stokes operator reveals a pair of complex conjugate eigenvalues with positive real part, hence the transition is ascribed to a Hopf bifurcation occurring at Reb,cr≈2531, a value much lower than the critical Reynolds number for the flow in a torus with the same curvature. The velocity components of the unstable direct and adjoint eigenmodes are investigated, and they display a large spatial separation, most likely due to the non-normality of the linearised Navier-Stokes operator. Thus, the core of the instability, also known in the literature as the wavemaker, is sought performing an analysis of the structural sensitivity of the unstable eigenmode to spatially localised feedbacks. The region located 15◦downstream of the bend inlet, on the outer wall, is the most receptive to this kind of perturbations, and thus corresponds to where the instability originates. Since this region coincides with the outer-wall separation bubble, it is concluded that the instability is linked to the strong shear by the backflow phenomena. The present results are relevant for technical applications where bent pipes are frequently used, and their stability properties have hitherto not been studied.
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| 19. |
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| 20. |
- Rinaldi, Enrico, et al.
(författare)
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The vanishing of strong turbulent fronts in bent pipes
- 2019
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Ingår i: Journal of Fluid Mechanics. - : CAMBRIDGE UNIV PRESS. - 0022-1120 .- 1469-7645. ; 866, s. 487-502
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Tidskriftsartikel (refereegranskat)abstract
- Isolated patches of turbulence in transitional straight pipes are sustained by a strong instability at their upstream front, where the production of turbulent kinetic energy (TKE) is up to five times higher than in the core. Direct numerical simulations presented in this paper show no evidence of such strong fronts if the pipe is bent. We examine the temporal and spatial evolution of puffs and slugs in a toroidal pipe with pipe-to-torus diameter ratio delta = D/d = 0.01 at several subcritical Reynolds numbers. Results show that the upstream overshoot of TKE production is at most one-and-a-half times the value in the core and that the average cross-flow fluctuations at the front are up to three times lower if compared to a straight pipe, while attaining similar values in the core. Localised turbulence can be sustained at smaller energies through a redistribution of turbulent fluctuations and vortical structures by the in-plane Dean motion of the mean flow. This asymmetry determines a strong localisation of TKE production near the outer bend, where linear and nonlinear mechanisms optimally amplify perturbations. We further observe a substantial reduction of the range of Reynolds numbers for long-lived intermittent turbulence, in agreement with experimental data from the literature. Moreover, no occurrence of nucleation of spots through splitting could be detected in the range of parameters considered. Based on the present results, we argue that this mechanism gradually becomes marginal as the curvature of the pipe increases and the transition scenario approaches a dynamical switch from subcritical to supercritical.
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| 21. |
- Schlatter, Philipp, et al.
(författare)
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Swirl Switching in bent pipes studied by numerical simulation
- 2017
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Ingår i: 10th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2017. - : International Symposium on Turbulence and Shear Flow Phenomena, TSFP10. - 9780000000002
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Konferensbidrag (refereegranskat)abstract
- Turbulent flow through pipe bends has been extensively studied, but several phenomena still miss an exhaustive explanation. Due to centrifugal forces, the fluid flowing through a curved pipe forms two symmetric, counter-rotating Dean vortices. It has been observed, experimentally and numerically, that these vortices change their size, intensity and location in a quasi-periodic, oscillatory fashion, a phenomenon known as swirl-switching. These oscillations are responsible for failure due to fatigue in pipes, and their origin has been attributed to a recirculation bubble, disturbances coming from the upstream straight section and others. The present study tackles the problem by direct numerical simulations (DNS) of turbulent pipe flow at moderate Reynolds number, analysed, for the first time, with three-dimensional proper orthogonal decomposition (POD) in an effort to distinguish between the spatial and temporal contributions to the oscillations. The simulations are performed at a friction Reynolds number of about 360 with a divergence-free synthetic turbulence inflow, which is crucial to avoid the interference of low-frequency oscillations generated by a standard recycling method. Two different bends are considered, with curvature 0.1 and 0.3, preceded and followed by straight pipe segments. Our results indicate that a single low-frequency, three-dimensional POD mode is responsible for the swirl-switching. This mode represents a travelling wave, and was previously mistaken by 2D POD for two different modes. Low-order reconstruction clearly shows that the upstream turbulent flow does not play a role for the swirl-switching.
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| 22. |
- Schlatter, Philipp, et al.
(författare)
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Transitional and turbulent bent pipes
- 2017
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Ingår i: Progress in Turbulence VII. - Cham : Springer Science+Business Media B.V.. - 9783319579337 ; , s. 81-87
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Konferensbidrag (refereegranskat)abstract
- We review a number of aspects of the transitional and turbulent flow in bent pipes, obtained at KTH using the spectral-element code Nek5000. This flow, sometimes also called Dean flow, is characterised by the appearance of Dean vortices, which arise due to the action of the centrifugal force in the bend. We start with reviewing recent stability analysis in the toroidal flow, and conclude that for all curvatures δ>0 an exponential instability is present at a bulk Reynolds number of about 4000. Further increasing the Reynolds number lets the flow go through a region with potential sub straight and sublaminar drag. An analysis using proper orthogonal decomposition (POD) reveals that wave-like motions are still present in the otherwise turbulent flow. Upon further increasing Re, the in-plane Dean vortices lead to a modulation of turbulence depending on the azimuthal position. The flow is then dominated by low-frequency so-called swirl-switching motion. This motion is studied in both a periodic and spatially developing framework. Finally, the effect of Dean vortices on Lagrangian inertial particles is studied.
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