Flapping of heavy inverted flags: a fluid-elastic instability

Tavallaeinejad, Mohammad; Paı̈doussis, M.P.; Salinas, Manuel Flores; Legrand, Mathias; Kheiri, Mojtaba; Botez, Ruxandra

doi:10.1017/jfm.2020.758

Cited by 19 publications

(12 citation statements)

References 14 publications

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“…This phenomenon was also observed in the experimental study of Tavallaeinejad et al. (2020 c ), which suggests that momentum-induced aerodynamic forces govern the periodic fluttering motion. Also, it has been shown that inverted flags undergo self-sustained periodic fluttering for a wide range of , defined here as the width to length ratio (Sader et al.…”

Section: Introductionsupporting

confidence: 72%

“…The motion of heavy flags with strong inertial forces compared with fluid dynamic forces is governed by fluid elastic instability (Tavallaeinejad et al. 2020 c ), wherein the changes in the geometry and the flow forces are in a dynamically balanced state to promote continuous fluttering motion. We discuss the connection between the deformation-induced vortical structures and fluttering dynamics in the bistable response range by visualizing the Q-criterion (Q), at and , as shown in figure 3.…”

Section: Resultsmentioning

confidence: 99%

“…Later, three additional response modes, the buckled mode, small-amplitude asymmetric flapping mode and chaotic mode, were also identified (Goza, Colonius & Sader 2018; Tavallaeinejad et al. 2020 c ). The first two modes exist between the stationary and flapping modes, while the chaotic mode can occur between the flapping and deflected modes.…”

Section: Introductionmentioning

confidence: 99%

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Aspect ratio-dependent hysteresis response of a heavy inverted flag

et al. 2022

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The bistable fluttering response of heavy inverted flags with different aspect ratios ( $AR$ ) is investigated to determine how the vortical structures affect the intermittent vibration response of the flag. A heavy inverted flag in a uniform flow may exhibit several response modes; amongst them are three major modes that occur over an extended velocity range: stationary, large-scale periodic oscillation and one-sided deflected modes. Significant hysteretic bistability is observed at the transition between these modes for all $AR$ , which is notably different from the conventional flag vibration with a fixed leading edge and free trailing edge where no hysteresis is observed at the lower $AR$ limit ( $AR<1$ ). The difference is associated with the distinct roles of vortices around the flag. Experiments with flags made of spring steel are conducted in a wind tunnel, where the flow speed is steadily increased and later decreased to obtain different oscillatory modes of the heavy inverted flags. The experimental results are used to validate the numerical model of the same problem. It is found that different critical velocities exist for increasing and decreasing flow velocities, and there is a sustained hysteresis for all $AR$ controlled by the initiation threshold and growth of the leading-edge and side-edge vortices. The effect of the vortices in the bistable oscillation regime is quantified by formulating a modal force partitioning approach. It is shown that $AR$ can significantly alter the static and dynamic vortex interaction with the flexible plate, thereby changing the flag's hysteresis behaviour and bistable response.

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Section: Introductionsupporting

confidence: 72%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Aspect ratio-dependent hysteresis response of a heavy inverted flag

et al. 2022

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“…On the other hand, at the highest value of U * = 18.4, the tip oscillations become chaotic, as seen in Figure 11c, while the predominant frequency of vibration becomes almost equal to the structural frequency of the plate, i.e., f ≈ f n . This could indicate that the vibration resembles flutter, i.e., fluid-elastic instability associated with relatively large amplitude oscillations at the structural frequency beyond some critical reduced velocity [59]. It will be very interesting to examine the plate response in more detail in the range of 11.1 < U * < 18.4, which corresponds to the transition between synchronized vortex-induced vibration and chaotic-like flutter vibration, in future work.…”

Section: Discussionmentioning

confidence: 99%

Cross-Flow-Induced Vibration of an Elastic Plate

Konstantinidis

2021

Fluids

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The cross-flow over a surface-mounted elastic plate and its vibratory response are studied as a fundamental two-dimensional configuration to gain physical insight into the interaction of viscous flow with flexible structures. The governing equations are numerically solved on a deforming mesh using an arbitrary Lagrangian-Eulerian finite-element method. The turbulent flow is resolved using the unsteady Reynolds-averaged Navier–Stokes equations at a Reynolds number of 2.5×104 based on the plate height. The material properties of the plate are selected so that the structural frequency is close to the frequency of vortex shedding from the free edge of a rigid plate, which is studied initially as the reference case. The results show that the plate tip oscillates back and forth in response to unsteady fluid loading at twice the frequency of vortex shedding, which is attributable to the sequential formation of a primary vortex from the free edge and a secondary vortex near the base of the plate. The effects of the plate elasticity and density on the structural response are considered, and results are compiled in terms of the reduced velocity U* and the density ratio ρ*. The standard deviation of tip displacement increases with reduced velocity in the range 7.1⩽U*⩽18.4, irrespective of whether the elasticity or the density of the plate is varied. However, the average deflection of the plate in the streamwise direction displays different scaling with U* and ρ*, but scales almost linearly with the Cauchy number ∼U*2/ρ*. Interestingly, the synchronization between plate motion and vortex shedding ceases at U*=18.4, and the excitation mechanism in the latter case resembles flutter instability, rather than vortex-induced vibration found at lower U*.

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“…However, the position of VIV as a governing phenomenon has been challenged in recent work from Tavallaeinejad et al. (2020 a , b ). These authors argue that, at least for heavy flags, the mechanism is not VIV but is instead related to coupled-mode flutter-like instabilities, or a movement-induced excitation (Naudascher & Rockwell 1994; Païdoussis 2014, 2016).…”

Section: Introductionmentioning

confidence: 99%

The dynamics of a rigid inverted flag

Leontini

Sader²

2022

J. Fluid Mech.

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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.

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Flapping of heavy inverted flags: a fluid-elastic instability

Abstract: Abstract

Cited by 19 publications

References 14 publications

Aspect ratio-dependent hysteresis response of a heavy inverted flag

Aspect ratio-dependent hysteresis response of a heavy inverted flag

Cross-Flow-Induced Vibration of an Elastic Plate

The dynamics of a rigid inverted flag

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