A Review on Fluid-Induced Flag Vibrations

Abstract

Fluid-induced flag vibrations provide unattended, efficient, low-cost, and scalable solutions for energy harvesting to power distributed wireless sensor nodes, heat transfer enhancement in channel flow, and mixing enhancement in process industries. This review surveys three generic configurations, the inverted flag, the standard flag, and the forced flag, i.e., an inverted or standard flag located downstream of a bluff body. Their instability boundaries, vibration dynamics, and vortex dynamics are compared in a unified framework to elucidate their common and distinct features and provide insights into the design of vibrating flags for various applications. Some common features are also identified and analyzed for describing the interaction between multiple flags, three-dimensional (3D) effects, and Reynolds number effects. The suggestions are intended to guide future research directions.

Dynamics of flags over wide ranges of mass and bending stiffness

“…If we imagine that the finite flag is modeled by the infinite periodic flag with a range of allowed |k| down to a prescribed nonzero minimum value that is comparable to the finite flag length (k = 2π corresponds to a half-period of a sine function on a flag of length 2, and k = 1 a smaller fraction of a period), the stability boundary would have the same form as the dashed lines. These stability boundaries show qualitative agreement with the shape of the stability boundary seen in large amplitude viscous and inviscid simulations and in experiments [9,39,45]. In these studies, the threshold value of R 2 for instability increases with R 1 at small R 1 and reaches a plateau for R 1 1.…”

“…There have been many experimental and theoretical studies of the flutter of flexible plates or flags in recent years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], following earlier work in the field of aeroelasticity [19][20][21]. Recent extensions include multiple-flag or flagboundary interactions [22][23][24][25][26][27], three-dimensional effects [11,[28][29][30], inverted flags [31][32][33], and applications to energy harvesting [34][35][36][37][38] and heat transfer [39][40][41][42][43][44]. Many of these studies addressed the stability problem: determining the region in parameter space where a flag in a uniform flow becomes unstable to transverse oscillations.…”

Fluid-structure interaction of multi-body systems: Methodology and applications

“…Motivated by this problem, we present here a fundamental study of the flow around a deformable filament of length L attached to a sphere of diameter D. In particular, the objective of the study is to determine what is the effect of the filament on the flow around the sphere, as well as the fluid forces acting upon it. From the point of view of the filament, this problem can be classified as an extraneously induced excitation (EIE) fluid-induced vibration problem [61,62].…”

Aspect ratio-dependent hysteresis response of a heavy inverted flag

“…They identified three distinct response modes of the structure due to its interaction with the flow: a stationary mode at low flow velocities, a two-sided flapping mode at intermediate flow velocities and a one-sided flapping or deflected mode at high flow velocities (Kim et al 2013;Sader et al 2016a;Gurugubelli & Jaiman 2019;Ojo et al 2019Ojo et al , 2021Park, Ryu & Sung 2019). These modes emerge from the balance between vortex-generated forces and the elastic restoring force in the flag (Yu et al 2019), resulting in self-sustained vibrations at relatively low flow speeds. 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 2020c).…”

“…The bending stiffness of the flag then becomes dominant and restores the flag toward its undeflected state. The sequence of vortex separation and bending restoration effects enable symmetric fluttering motion(Gurugubelli & Jaiman 2019;Park et al 2019;Yu et al 2019). In figure3(a), for a slender flag (AR = 0.25), during upsweep at initial…”