12 results
The dynamics of a rigid inverted flag
- Justin S. Leontini, John E. Sader
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- Journal:
- Journal of Fluid Mechanics / Volume 948 / 10 October 2022
- Published online by Cambridge University Press:
- 16 September 2022, A47
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An ‘inverted flag’ – a flexible plate clamped at its trailing edge – undergoes large-amplitude flow-induced flapping when immersed in a uniform and steady flow. Here, we report direct numerical simulations of a related single degree-of-freedom mechanical system: a rigid plate attached at its trailing edge to a torsional spring. This system is termed a ‘rigid inverted flag’ and exhibits the dynamical states reported for the (flexible) inverted flag, with additional behaviour. This finding shows that the flapping dynamics of inverted flags is not reliant on their continuous flexibility, i.e. many degrees of freedom. The rigid inverted flag exhibits additional, novel states including a heteroclinic-type orbit that results in small-amplitude flapping, and a number of chaotic large-amplitude flapping regimes. We show that the various routes to chaos are driven by a series of periodic states, including at least two which are subharmonic. The instability and competition between these periodic states lead to chaos via type-I intermittency, mode competition and mode locking. The rigid inverted flag allows these periodic states and their subsequent interaction to be explained simply: they arise from an interaction between a preferred vortex shedding frequency and a single natural frequency of the structure. The dynamics of rigid inverted flags is yet to be studied experimentally, and this numerical study provides impetus for such future work.
Flow states and transitions in flows past arrays of tandem cylinders
- Negar Hosseini, Martin D. Griffith, Justin S. Leontini
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- Journal:
- Journal of Fluid Mechanics / Volume 910 / 10 March 2021
- Published online by Cambridge University Press:
- 15 January 2021, A34
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Direct numerical simulations at $Re=200$ have been conducted of the flow past rows of tandem cylinders. It is shown that when the pitch between the two upstream cylinders is large, the wake downstream is characterised by a two-row vortex structure. Placing a third body on the wake centreline in the majority of this two-row structure has basically no impact both upstream and downstream – the third body is cloaked. However, a region is identified where the placement of a body suppresses vortex shedding from the first cylinder and the two-row structure is destroyed, globally broadcasting the presence of the third body. The effect is shown to occur for different third-body shapes. To understand the existence of this broadcasting region, local instability analysis is conducted which shows the majority of the two-row structure to be convectively unstable, with only a small region adjacent to the rear of the second cylinder that is absolutely unstable. This suggests only bodies placed close to the second body will trigger the global change, and this is supported by a global sensitivity analysis and observation from the simulations. However, neither the local analysis nor the global sensitivity analysis explains the presence of a lower limit for the third-body position that will trigger a global change. However the simulation results clearly show that a third body placed very close to the second body does not trigger this change.
Three-dimensional mode selection of the flow past a rotating and inline oscillating cylinder
- David Lo Jacono, Rémi Bourguet, Mark C. Thompson, Justin S. Leontini
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- Journal:
- Journal of Fluid Mechanics / Volume 855 / 25 November 2018
- Published online by Cambridge University Press:
- 19 September 2018, R3
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This paper studies the transition to three-dimensional flow in the wake of a cylinder immersed in a free stream, where the cylinder is externally forced to continuously rotate about its axis and to linearly oscillate in the streamwise direction. Floquet stability analysis is used to assess the stability of the nominal two-dimensional flows at a Reynolds number $Re=100$ and rotation rate $\unicode[STIX]{x1D6FC}=\unicode[STIX]{x1D714}D/U=3$ to three-dimensional perturbations, as a function of the amplitude and frequency of the linear oscillations. Two modes of instability are found, distinguished by their spatial structure, temporal behaviour and apparent mechanism. The first mode has a shorter wavelength in the spanwise direction and appears to be linked to a centrifugal instability in the layer of fluid near the rotating body. The second mode has a longer wavelength and is linked to an instability of the vortex cores in the wake that is subharmonic, leading to a period doubling. Either mode can be stable while the other is unstable, depending primarily on the frequency of the oscillation of the cylinder. This indicates that either mode can control the transition to a three-dimensional flow. The results are compared to the fully three-dimensional simulation results of a rotating cylinder elastically mounted and free to oscillate in the streamwise direction from Bourguet & Lo Jacono (J. Fluid Mech., vol. 781, 2015, pp. 127–165), and appear to be able to explain the surprising switching of the observed spanwise wavelength in that flow as a change in the dominant mode, and therefore mechanism, of instability.
Flow-induced vibration of two cylinders in tandem and staggered arrangements
- Martin D. Griffith, David Lo Jacono, John Sheridan, Justin S. Leontini
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- Journal:
- Journal of Fluid Mechanics / Volume 833 / 25 December 2017
- Published online by Cambridge University Press:
- 02 November 2017, pp. 98-130
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A numerical study of the flow-induced vibration of two elastically mounted cylinders in tandem and staggered arrangements at Reynolds number $Re=200$ is presented. The cylinder centres are set at a streamwise distance of 1.5 cylinder diameters, placing the rear cylinder in the near-wake region of the front cylinder for the tandem arrangement. The cross-stream or lateral offset is varied between 0 and 5 cylinder diameters. The two cylinders are identical, with the same elastic mounting, and constrained to oscillate only in the cross-flow direction. The variation of flow behaviours is examined for static cylinders and for elastic mountings of a range of spring stiffnesses, or reduced velocity. At least seven major modes of flow response are identified, delineated by whether the oscillation is effectively symmetric, and the strength of the influence of the flow through the gap between the two cylinders. Submodes of these are also identified based on whether or not the flow remains periodic. More subtle temporal behaviours, such as period doubling, quasi-periodicity and chaos, are also identified and mapped. Across all of these regimes, the amplitudes of vibration and the magnitude of the fluid forces are quantified. The modes identified span the parameter space between two important limiting cases: two static bodies at varying lateral offset; and two elastically mounted bodies in a tandem configuration at varying spring stiffnesses. Some similarity in the response of extremely stiff or static bodies and extremely slack bodies is shown. This is explained by the fact that the slack bodies are free to move to an equilibrium position and stop, effectively becoming a static system. However, the most complex behaviour appears between these limits, when the bodies are in reasonably close proximity, and the natural structural frequency is close to the vortex shedding frequency of a single cylinder. This appears to be driven by the interplay between a series of time scales, including the vortex formation time, the advection time across the gap between the cylinders and the oscillation period of both bodies. This points out an important difference between this multi-body system and the classic single-cylinder vortex-induced vibration: two bodies in close proximity will not oscillate in a synchronised, periodic manner when their natural structural frequencies are close to the nominal vortex shedding frequency of a single cylinder.
Three-dimensionality of elliptical cylinder wakes at low angles of incidence
- Anirudh Rao, Justin S. Leontini, Mark C. Thompson, Kerry Hourigan
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- Journal:
- Journal of Fluid Mechanics / Volume 825 / 25 August 2017
- Published online by Cambridge University Press:
- 20 July 2017, pp. 245-283
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The wake of an elliptical cylinder at low incident angles is investigated for different aspect ratio ($\unicode[STIX]{x1D6E4}=\text{major:minor axis ratio}$) cylinders using stability analysis and direct simulations. In particular, two- and three-dimensional transitions are mapped for cylinders of aspect ratios between 1 and 4 using Floquet stability analysis. The transition scenario for near-unity aspect ratio cylinders resembles that for a circular cylinder wake as Reynolds number is increased to $Re\lesssim 400$; first, with the transition from steady two-dimensional flow to unsteady two-dimensional flow, followed by the onset of three-dimensional flow via a long-wavelength instability (mode A), then, a short-wavelength instability (mode B) and, finally, an intermediary wavelength instability which is quasi-periodic in nature (mode QP). The effect of the incident angle on this transition scenario for the low-aspect-ratio cylinders is minimal. As the aspect ratio is increased towards 2, two synchronous modes, modes $\widehat{\text{A}}$ and $\widehat{\text{B}}$, become unstable; these modes have spatio-temporal symmetries similar to their circular cylinder wake counterparts, modes A and mode B, respectively. While mode $\widehat{\text{A}}$ persists for all incident angles investigated here, mode $\widehat{\text{B}}$ is found only to be unstable for incident angles up to $10^{\circ }$. Surprisingly, for $1.8\lesssim \unicode[STIX]{x1D6E4}\lesssim 2.9$, the mode A instability observed at zero incident angle emerges as a quasi-periodic mode as the incident angle is increased even slightly. At higher incident angles, this quasi-periodic mode once again transforms to a real mode on increasing the Reynolds number. The parameter space maps for the various aspect ratios are presented in the Reynolds number–incident angle plane, and the three-dimensional modes are discussed in terms of similarities to and differences from existing modes. A key aim of the work is to map the different modes and various transition sequences as a simple body geometry is systematically changed and as the flow symmetry is systematically broken; thus, insight is provided on the overall path towards fully turbulent flow.
The influence of a small upstream wire on transition in a rotating cylinder wake
- Anirudh Rao, Alexander Radi, Justin S. Leontini, Mark C. Thompson, John Sheridan, Kerry Hourigan
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- Journal:
- Journal of Fluid Mechanics / Volume 769 / 25 April 2015
- Published online by Cambridge University Press:
- 25 March 2015, R2
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Recent experimental research on rotating cylinder wakes has found that a previously numerically predicted subharmonic instability mode, mode C, occurs for considerably lower rotation rates than predicted through stability analysis, yet other mode transitions occur closer to the predicted onset. One difference between the theoretical and experimental set-ups is the use of a small-diameter hydrogen bubble visualisation wire placed upstream of the rotating cylinder. The current paper tests the hypothesis that a wire, of only $1/100$th of the cylinder diameter, placed five diameters upstream of the cylinder, sufficiently perturbs the flow to substantially affect certain wake transitions, including the onset of mode C. This is achieved using stability analysis of a flow that includes the upstream wire. The results indeed show that the wire of a tiny diameter induces a non-negligible asymmetry in the flow, triggering the subharmonic mode at substantially lower rotation rates. Furthermore, at higher rotation rates, the onset of two other three-dimensional modes are delayed to higher Reynolds numbers. These results make the point that even seemingly minute perturbations caused by minimally intrusive methods may result in substantially altered experimental flow behaviour.
Stability analysis of the elliptic cylinder wake
- Justin S. Leontini, David Lo Jacono, Mark C. Thompson
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- Journal:
- Journal of Fluid Mechanics / Volume 763 / 25 January 2015
- Published online by Cambridge University Press:
- 16 December 2014, pp. 302-321
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This paper presents the results of numerical stability analysis of the wake of an elliptical cylinder. Aspect ratios where the ellipse is longer in the streamwise direction than in the transverse direction are considered. The focus is on the dependence on the aspect ratio of the ellipse of the various bifurcations to three-dimensional flow from the two-dimensional Kármán vortex street. It is shown that the three modes present in the wake of a circular cylinder (modes A, B and QP) are present in the ellipse wake, and that in general they are all stabilized by increasing the aspect ratio of the ellipse. Two new pertinent modes are found: one long-wavelength mode with similarities to mode A, and a second that is only unstable for aspect ratios greater than approximately 1.75, which has similar spatiotemporal symmetries to mode B but has a distinct spatial structure. Results from fully three-dimensional simulations are also presented confirming the existence and growth of these two new modes in the saturated wakes.
Fluid–structure interaction of a square cylinder at different angles of attack
- Jisheng Zhao, Justin S. Leontini, David Lo Jacono, John Sheridan
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- Journal:
- Journal of Fluid Mechanics / Volume 747 / 25 May 2014
- Published online by Cambridge University Press:
- 23 April 2014, pp. 688-721
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This study investigates the free transverse flow-induced vibration (FIV) of an elastically mounted low-mass-ratio square cylinder in a free stream, at three different incidence angles: ${{\alpha }}=0^\circ $, $20^\circ $ and $45^\circ $. This geometric setup presents a body with an angle of attack, sharp corners and some afterbody, and therefore is a generic body that can be used to investigate a wide range of FIV phenomena. A recent study by Nemes et al. (J. Fluid Mech., vol. 710, 2012, pp. 102–130) provided a broad overview of the flow regimes present as a function of both the angle of attack ${{\alpha }}$ and reduced flow velocity ${U^{*}}$. Here, the focus is on the three aforementioned representative angles of attack: ${{\alpha }}=0^\circ $, where the FIV is dominated by transverse galloping; ${{\alpha }}=45^\circ $, where the FIV is dominated by vortex-induced vibration (VIV); and an intermediate value of ${{\alpha }}=20^\circ $, where the underlying FIV phenomenon has previously been difficult to determine. For the ${{\alpha }}=0^\circ $ case, the amplitude of oscillation increases linearly with the flow speed except for a series of regimes that occur when the vortex shedding frequency is in the vicinity of an odd-integer multiple of the galloping oscillation frequency, and the vortex shedding synchronizes to this multiple of the oscillation frequency. It is shown that only odd-integer multiple synchronizations should occur. These synchronizations explain the ‘kinks’ in the galloping amplitude response for light bodies first observed by Bearman et al. (J. Fluids Struct., vol. 1, 1987, pp. 19–34). For the ${{\alpha }}=45^\circ $ case, the VIV response consists of a number of subtle, but distinctly different regimes, with five regimes of high-amplitude oscillations, compared to two found in the classic VIV studies of a circular cylinder. For the intermediate ${{\alpha }}=20^\circ $ case, a typical VIV ‘upper branch’ occurs followed by a ‘higher branch’ of very large-amplitude response. The higher branch is caused by a subharmonic synchronization between the vortex shedding and the body oscillation frequency, where two cycles of vortex shedding occur over one cycle of oscillation. It appears that this subharmonic synchronization is a direct result of the asymmetric body. Overall, the FIV of the square cylinder is shown to be very rich, with a number of distinct regimes, controlled by both ${{\alpha }}$ and ${U^{*}}$. Importantly, ${{\alpha }}$ controls the underlying FIV phenomenon, as well as controlling the types of possible synchronization between the oscillation and vortex shedding.
Wake states and frequency selection of a streamwise oscillating cylinder
- Justin S. Leontini, David Lo Jacono, Mark C. Thompson
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- Journal:
- Journal of Fluid Mechanics / Volume 730 / 10 September 2013
- Published online by Cambridge University Press:
- 30 July 2013, pp. 162-192
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This paper presents the results of an in-depth study of the flow past a streamwise oscillating cylinder, examining the impact of varying the amplitude and frequency of the oscillation, and the Reynolds number of the incoming flow. These findings are presented in a framework that shows that the relationship between the frequency of vortex shedding ${f}_{s} $ and the amplitude of oscillation ${A}^{\ast } $ is governed by two primary factors: the first is a reduction of ${f}_{s} $ proportional to a series in ${A}^{\ast 2} $ over a wide range of driving frequencies and Reynolds numbers; the second is nonlinear synchronization when this adjusted ${f}_{s} $ is in the vicinity of $N= {(1- {f}_{s} / {f}_{d} )}^{- 1} $, where $N$ is an integer. Typically, the influence of higher-order terms is small, and truncation to the first term of the series (${A}^{\ast 2} $) well represents the overall trend of vortex shedding frequency as a function of amplitude. However, discontinuous steps are overlaid on this trend due to the nonlinear synchronization. When ${f}_{s} $ is normalized by the Strouhal frequency ${f}_{St} $ (the frequency of vortex shedding from an unperturbed cylinder), the rate at which ${f}_{s} / {f}_{St} $ decreases with amplitude, at least for ${f}_{d} / {f}_{St} = 1$, shows a linear dependence on the Reynolds number. For a fixed $\mathit{Re}= 175$, the truncated series shows that the rate of decrease of ${f}_{s} / {f}_{St} $ with amplitude varies as ${(2- {f}_{d} / {f}_{St} )}^{- 1/ 2} $ for $1\leqslant {f}_{d} / {f}_{St} \leqslant 2$, but is essentially independent of ${f}_{d} / {f}_{St} $ for ${f}_{d} / {f}_{St} \lt 1$. These trends of the rate of decrease of ${f}_{s} $ with respect to amplitude are also used to predict the amplitudes of oscillation around which synchronization occurs. These predicted amplitudes are shown to fall in regions of the parameter space where synchronized modes occur. Further, for the case of varying ${f}_{d} / {f}_{St} $, a very reasonable prediction of the amplitude of oscillation required for the onset of synchronization to the mode where ${f}_{s} = 0. 5{f}_{d} $ is given. In a similar manner, amplitudes at which ${f}_{s} = 0$ are calculated, predicting where the natural vortex shedding is completely supplanted by the forcing. These amplitudes are found to coincide approximately with those at which the onset of a symmetric vortex shedding mode is observed. This result is interpreted as meaning that the symmetric shedding mode occurs when the dynamics crosses over from being dominated by the vortex shedding to being dominated by the forcing.
A numerical study of an inline oscillating cylinder in a free stream
- Justin S. Leontini, David Lo Jacono, Mark C. Thompson
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- Journal:
- Journal of Fluid Mechanics / Volume 688 / 10 December 2011
- Published online by Cambridge University Press:
- 03 November 2011, pp. 551-568
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Simulations of a cylinder undergoing externally controlled sinusoidal oscillations in the free stream direction have been performed. The frequency of oscillation was kept equal to the vortex shedding frequency from a fixed cylinder, while the amplitude of oscillation was varied, and the response of the flow measured. With varying amplitude, a rich series of dynamic responses was recorded. With increasing amplitude, these states included wakes similar to the Kármán vortex street, quasiperiodic oscillations interleaved with regions of synchronized periodicity (periodic on multiple oscillation cycles), a period-doubled state and chaotic oscillations. It is hypothesized that, for low to moderate amplitudes, the wake dynamics are controlled by vortex shedding at a global frequency, modified by the oscillation. This vortex shedding is frequency modulated by the driven oscillation and amplitude modulated by vortex interaction. Data are presented to support this hypothesis.
Modification of three-dimensional transition in the wake of a rotationally oscillating cylinder
- DAVID LO JACONO, JUSTIN S. LEONTINI, MARK C. THOMPSON, JOHN SHERIDAN
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- Journal:
- Journal of Fluid Mechanics / Volume 643 / 25 January 2010
- Published online by Cambridge University Press:
- 24 December 2009, pp. 349-362
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A study of the flow past an oscillatory rotating cylinder has been conducted, where the frequency of oscillation has been matched to the natural frequency of the vortex street generated in the wake of a stationary cylinder, at Reynolds number 300. The focus is on the wake transition to three-dimensional flow and, in particular, the changes induced in this transition by the addition of the oscillatory rotation. Using Floquet stability analysis, it is found that the fine-scale three-dimensional mode that typically dominates the wake at a Reynolds number beyond that at the second transition to three-dimensional flow (referred to as mode B) is suppressed for amplitudes of rotation beyond a critical amplitude, in agreement with past studies. However, the rotation does not suppress the development of three-dimensionality completely, as other modes are discovered that would lead to three-dimensional flow. In particular, the longer-wavelength mode that leads the three-dimensional transition in the wake of a stationary cylinder (referred to as mode A) is left essentially unaffected at low amplitudes of rotation. At higher amplitudes of oscillation, mode A is also suppressed as the two-dimensional near wake changes in character from a single- to a double-row wake; however, another mode is predicted to render the flow three-dimensional, dubbed mode D (for double row). This mode has the same spatio-temporal symmetries as mode A.
Three-dimensional transition in the wake of a transversely oscillating cylinder
- JUSTIN S. LEONTINI, M. C. THOMPSON, K. HOURIGAN
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- Journal:
- Journal of Fluid Mechanics / Volume 577 / 25 April 2007
- Published online by Cambridge University Press:
- 19 April 2007, pp. 79-104
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A Floquet stability analysis of the transition to three-dimensionality in the wake of a cylinder forced to oscillate transversely to the free stream has been undertaken. The effect of varying the oscillation amplitude is determined for a frequency of oscillation close to the natural shedding frequency. The three-dimensional modes that arise are identified, and the effect of the oscillation amplitude on their structure and growth rate quantified.
It is shown that when the two-dimensional wake is in the 2S configuration (which is similar to the Kármán vortex street), the three-dimensional modes that arise are similar in nature and symmetry structure to the modes in the wake of a fixed cylinder. These modes are known as modes A, B and QP and occur in this order with increasing Re. However, increasing the amplitude of oscillation causes the critical Reynolds number for mode A to increase significantly, to the point where mode B becomes critical before mode A. The critical wavelength for mode A is also affected by the oscillation, becoming smaller with increasing amplitude. Elliptic instability theory is shown also to predict this trend, providing further support that mode A primarily arises as a result of an elliptic instability.
At higher oscillation amplitudes, the spatio-temporal symmetry of the two-dimensional wake changes and it takes on the P + S configuration, with a pair of vortices on one side of the wake and a single vortex on the other side, for each oscillation cycle. With the onset of this configuration, modes A, B and QP cease to exist. It is shown that two new three-dimensional modes arise from this base flow, which we call modes SL and SS. Both of these modes are subharmonic, repeating over two base-flow periods. Also, either mode can be the first to become critical, depending on the amplitude of oscillation of the cylinder.
The emergence of these two new modes, as well as the reversal of the order of inception of the three-dimensional modes A and B, leads to the observation that for an oscillating cylinder wake there are four different modes that can lead the transition to three-dimensionality, depending on the amplitude of oscillation. Therefore this type of flow provides a good example for studying the effect of mode-order inception on the path taken to turbulence in bluff-body wakes.
For the range of amplitudes studied, the maximum Re value for which the flow remains two-dimensional is 280.