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.
Issue Section:
Review Article
References
1.
Watanabe
, Y.
, Suzuki
, S.
, Sugihara
, M.
, and Sueoka
, Y.
, 2002
, “An Experimental Study of Paper Flutter
,” J. Fluids Struct.
, 16
(4
), pp. 529
–542
.2.
Huang
, L.
, 1995
, “Flutter of Cantilevered Plates in Axial Flow
,” J. Fluids Struct.
, 9
(2
), pp. 127
–147
.3.
Tang
, D.
, Yamamoto
, H.
, and Dowell
, E. H.
, 2003
, “Flutter and Limit Cycle Oscillations of Two-Dimensional Panels in Three-Dimensional Axial Flow
,” J. Fluids Struct.
, 17
(2
), pp. 225
–242
.4.
Guo
, C. Q.
, and Paidoussis
, M. P.
, 2000
, “Stability of Rectangular Plates With Free Side-Edges in Two-Dimensional Inviscid Channel Flow
,” ASME J. Appl. Mech.
, 67
(1
), pp. 171
–176
.5.
Yu
, Y.
, and Liu
, Y.
, 2016
, “Energy Harvesting With Two Parallel Pinned Piezoelectric Membranes in Fluid Flow
,” J. Fluids Struct.
, 65
, pp. 381
–397
.6.
Orrego
, S.
, Shoele
, K.
, Ruas
, A.
, Doran
, K.
, Caggiano
, B.
, Mittal
, R.
, and Kang
, S. H.
, 2017
, “Harvesting Ambient Wind Energy With an Inverted Piezoelectric Flag
,” Appl. Energy
, 194
, pp. 212
–222
.7.
Kim
, H.
, Kang
, S.
, and Kim
, D.
, 2017
, “Dynamics of a Flag Behind a Bluff Body
,” J. Fluids Struct.
, 71
, pp. 1
–14
.8.
Allen
, J.
, and Smits
, A.
, 2001
, “Energy Harvesting Eel
,” J. Fluids Struct.
, 15
(3–4
), pp. 629
–640
.9.
Taylor
, G. W.
, Burns
, J. R.
, Kammann
, S.
, Powers
, W. B.
, and Welsh
, T. R.
, 2001
, “The Energy Harvesting Eel: A Small Subsurface Ocean/River Power Generator
,” IEEE J. Oceanic Eng.
, 26
(4
), pp. 539
–547
.10.
Liu
, H.
, Zhang
, S.
, Kathiresan
, R.
, Kobayashi
, T.
, and Lee
, C.
, 2012
, “Development of Piezoelectric Microcantilever Flow Sensor With Wind-Driven Energy Harvesting Capability
,” Appl. Phys. Lett.
, 100
(22
), p. 223905
.11.
Shoele
, K.
, and Mittal
, R.
, 2014
, “Computational Study of Flow-Induced Vibration of a Reed in a Channel and Effect on Convective Heat Transfer
,” Phys. Fluids
, 26
(12
), p. 127103
.12.
Park
, S. G.
, Kim
, B.
, Chang
, C. B.
, Ryu
, J.
, and Sung
, H. J.
, 2016
, “Enhancement of Heat Transfer by a Self-Oscillating Inverted Flag in a Poiseuille Channel Flow
,” Int. J. Heat Mass Transfer
, 96
, pp. 362
–370
.13.
Ali
, S.
, Habchi
, C.
, Menanteau
, S.
, Lemenand
, T.
, and Harion
, J.-L.
, 2015
, “Heat Transfer and Mixing Enhancement by Free Elastic Flaps Oscillation
,” Int. J. Heat Mass Transfer
, 85
, pp. 250
–264
.14.
Müller
, U. K.
, 2003
, “Fish ‘n Flag
,” Science
, 302
(5650
), pp. 1511
–1512
.15.
Liao
, J. C.
, Beal
, D. N.
, Lauder
, G. V.
, and Triantafyllou
, M. S.
, 2003
, “Fish Exploiting Vortices Decrease Muscle Activity
,” Science
, 302
(5650
), pp. 1566
–1569
.16.
Kim
, S.
, Huang
, W.-X.
, and Sung
, H. J.
, 2010
, “Constructive and Destructive Interaction Modes Between Two Tandem Flexible Flags in Viscous Flow
,” J. Fluid Mech.
, 661
, pp. 511
–521
.17.
Naudascher
, E.
, and Rockwell
, D.
, 2012
, Flow-Induced Vibrations: An Engineering Guide
, Dover Publications
, New York.18.
Paidoussis
, M. P.
, 1998
, Fluid-Structure Interactions: Slender Structures and Axial Flow
, Academic Press
, San Diego, CA.19.
Kim
, D.
, Cossé
, J.
, Huertas Cerdeira
, C.
, and Gharib
, M.
, 2013
, “Flapping Dynamics of an Inverted Flag
,” J. Fluid Mech.
, 736
, p. R1
.20.
Sader
, J. E.
, Cossé
, J.
, Kim
, D.
, Fan
, B.
, and Gharib
, M.
, 2016
, “Large-Amplitude Flapping of an Inverted Flag in a Uniform Steady Flow—A Vortex-Induced Vibration
,” J. Fluid Mech.
, 793
, pp. 524
–555
.21.
Goza
, A.
, Colonius
, T.
, and Sader
, J. E.
, 2018
, “Global Modes and Nonlinear Analysis of Inverted-Flag Flapping
,” J. Fluid Mech.
, 857
, pp. 312
–344
.22.
Ryu
, J.
, Park
, S. G.
, Kim
, B.
, and Sung
, H. J.
, 2015
, “Flapping Dynamics of an Inverted Flag in a Uniform Flow
,” J. Fluids Struct.
, 57
, pp. 159
–169
.23.
Weaver
, D.
, 1976
, “On Flow Induced Vibrations in Hydraulic Structures and Their Alleviation
,” Can. J. Civ. Eng.
, 3
(1
), pp. 126
–137
.24.
Taneda
, S.
, 1968
, “Waving Motions of Flags
,” J. Phys. Soc. Jpn.
, 24
(2
), pp. 392
–401
.25.
Zhang
, J.
, Childress
, S.
, Libchaber
, A.
, and Shelley
, M.
, 2000
, “Flexible Filaments in a Flowing Soap Film as a Model for One-Dimensional Flags in a Two-Dimensional Wind
,” Nature
, 408
(6814
), pp. 835
–839
.26.
Yu
, Y.
, and Liu
, Y.
, 2015
, “Flapping Dynamics of a Piezoelectric Membrane Behind a Circular Cylinder
,” J. Fluids Struct.
, 55
, pp. 347
–363
.27.
Shi
, S.
, New
, T.
, and Liu
, Y.
, 2013
, “Flapping Dynamics of a Low Aspect-Ratio Energy-Harvesting Membrane Immersed in a Square Cylinder Wake
,” Exp. Therm. Fluid Sci.
, 46
, pp. 151
–161
.28.
Pan
, D.
, Shao
, X.
, Deng
, J.
, and Yu
, Z.
, 2014
, “Simulations of Passive Oscillation of a Flexible Plate in the Wake of a Cylinder by Immersed Boundary Method
,” Eur. J. Mech. B
, 46
, pp. 17
–27
.29.
Shelley
, M. J.
, and Zhang
, J.
, 2011
, “Flapping and Bending Bodies Interacting With Fluid Flows
,” Annu. Rev. Fluid Mech.
, 43
(1
), pp. 449
–465
.30.
Gallegos
, R. K. B.
, and Sharma
, R. N.
, 2017
, “Flags as Vortex Generators for Heat Transfer Enhancement: Gaps and Challenges
,” Renewable Sustainable Energy Rev.
, 76
, pp. 950
–962
.31.
Connell
, B. S.
, 2006
, Numerical Investigation of the Flow-Body Interaction of Thin Flexible Foils and Ambient Flow
, Massachusetts Institute of Technology
, Cambridge, MA.32.
Paidoussis
, M. P.
, 2004
, Fluid-Structure Interactions: Slender Structures and Axial Flow
, Vol. 2
, Elsevier Academic Press
, New York
.33.
Connell
, B. S.
, and Yue
, D. K.
, 2007
, “Flapping Dynamics of a Flag in a Uniform Stream
,” J. Fluid Mech.
, 581
, pp. 33
–67
.34.
Tang
, L.
, and Paidoussis
, M. P.
, 2007
, “On the Instability and the Post-Critical Behaviour of Two-Dimensional Cantilevered Flexible Plate's in Axial Flow
,” J. Sound Vib.
, 305
(1–2
), pp. 97
–115
.35.
Alben
, S.
, 2009
, “Simulating the Dynamics of Flexible Bodies and Vortex Sheets
,” J. Comput. Phys.
, 228
(7
), pp. 2587
–2603
.36.
Eloy
, C.
, Lagrange
, R.
, Souilliez
, C.
, and Schouveiler
, L.
, 2008
, “Aeroelastic Instability of Cantilevered Flexible Plates in Uniform Flow
,” J. Fluid Mech.
, 611
, pp. 97
–106
.37.
Huang
, W.-X.
, and Sung
, H. J.
, 2010
, “Three-Dimensional Simulation of a Flapping Flag in a Uniform Flow
,” J. Fluid Mech.
, 653
, pp. 301
–336
.38.
Eloy
, C.
, Kofman
, N.
, and Schouveiler
, L.
, 2012
, “The Origin of Hysteresis in the Flag Instability
,” J. Fluid Mech.
, 691
(1
), pp. 583
–593
.39.
Alben
, S.
, and Shelley
, M. J.
, 2008
, “Flapping States of a Flag in an Inviscid Fluid: Bistability and the Transition to Chaos
,” Phys. Rev. Lett.
, 100
(7
), p. 074301
.40.
Eloy
, C.
, Souilliez
, C.
, and Schouveiler
, L.
, 2007
, “Flutter of a Rectangular Plate
,” J. Fluids Struct.
, 23
(6
), pp. 904
–919
.41.
Tang
, L.
, 2008
, “The Influence of the Wake on the Stability of Cantilevered Flexible Plates in Axial Flow
,” J. Sound Vib.
, 310
(3
), pp. 512
–526
.42.
Tang
, C.
, Liu
, N.-S.
, and Lu
, X.-Y.
, 2015
, “Dynamics of an Inverted Flexible Plate in a Uniform Flow
,” Phys. Fluids
, 27
(7
), p. 073601
.43.
Gilmanov
, A.
, Le
, T. B.
, and Sotiropoulos
, F.
, 2015
, “A Numerical Approach for Simulating Fluid Structure Interaction of Flexible Thin Shells Undergoing Arbitrarily Large Deformations in Complex Domains
,” J. Comput. Phys.
, 300
, pp. 814
–843
.44.
Huang
, H.
, Wei
, H.
, and Lu
, X.-Y.
, 2017
, “Coupling Performance of Tandem Flexible Inverted Flags in a Uniform Flow
,” J. Fluid Mech.
, 837
, pp. 461
–476
.45.
Goza
, A.
, and Colonius
, T.
, 2017
, “A Strongly-Coupled Immersed-Boundary Formulation for Thin Elastic Structures
,” J. Comput. Phys.
, 336
, pp. 401–411.46.
Lee
, I.
, and Choi
, H.
, 2015
, “A Discrete-Forcing Immersed Boundary Method for the Fluid–Structure Interaction of an Elastic Slender Body
,” J. Comput. Phys.
, 280
, pp. 529
–546
.47.
Akcabay
, D. T.
, and Young
, Y. L.
, 2012
, “Hydroelastic Response and Energy Harvesting Potential of Flexible Piezoelectric Beams in Viscous Flow
,” Phys. Fluids
, 24
(5
), p. 054106
.48.
Huang
, W.-X.
, Shin
, S. J.
, and Sung
, H. J.
, 2007
, “Simulation of Flexible Filaments in a Uniform Flow by the Immersed Boundary Method
,” J. Comput. Phys.
, 226
(2
), pp. 2206
–2228
.49.
Zhu
, L.
, and Peskin
, C. S.
, 2002
, “Simulation of a Flapping Flexible Filament in a Flowing Soap Film by the Immersed Boundary Method
,” J. Comput. Phys.
, 179
(2
), pp. 452
–468
.50.
Banerjee
, S.
, Connell
, B. S.
, and Yue
, D. K.
, 2015
, “Three-Dimensional Effects on Flag Flapping Dynamics
,” J. Fluid Mech.
, 783
, pp. 103
–136
.51.
Cisonni
, J.
, Lucey
, A. D.
, Elliott
, N. S. J.
, and Heil
, M.
, 2017
, “The Stability of a Flexible Cantilever in Viscous Channel Flow
,” J. Sound Vib.
, 396
, pp. 186
–202
.52.
Balint
, T. S.
, and Lucey
, A. D.
, 2005
, “Instability of a Cantilevered Flexible Plate in Viscous Channel Flow
,” J. Fluids Struct.
, 20
(7
), pp. 893
–912
.53.
Michelin
, S.
, Llewellyn Smith
, S. G.
, and Glover
, B. J.
, 2008
, “Vortex Shedding Model of a Flapping Flag
,” J. Fluid Mech.
, 617
, pp. 1–10.54.
Howell
, R.
, Lucey
, A.
, Carpenter
, P. W.
, and Pitman
, M.
, 2009
, “Interaction Between a Cantilevered-Free Flexible Plate and Ideal Flow
,” J. Fluids Struct.
, 25
(3
), pp. 544
–566
.55.
Wang
, X.
, Alben
, S.
, Li
, C.
, and Young
, Y. L.
, 2016
, “Stability and Scalability of Piezoelectric Flag
,” Phys. Fluids
, 28
(2
), p. 023601.56.
Alben
, S.
, 2015
, “Flag Flutter in Inviscid Channel Flow
,” Phys. Fluids
, 27
(3
), p. 033603
.57.
Shoele
, K.
, and Mittal
, R.
, 2016
, “Flutter Instability of a Thin Flexible Plate in a Channel
,” J. Fluid Mech.
, 786
, pp. 29
–46
.58.
Yamaguchi
, N.
, Yokota
, K.
, and Tsujimoto
, Y.
, 2000
, “Flutter Limits and Behaviors of a Flexible Thin Sheet in High-Speed Flow—I: Analytical Method for Prediction of the Sheet Behavior
,” ASME J. Fluids Eng.
, 122
(1
), pp. 65
–73
.59.
Chen
, M.
, Jia
, L.-B.
, Wu
, Y.-F.
, Yin
, X.-Z.
, and Ma
, Y.-B.
, 2014
, “Bifurcation and Chaos of a Flag in an Inviscid Flow
,” J. Fluids Struct.
, 45
, pp. 124
–137
.60.
Attar
, P.
, Dowell
, E.
, and Tang
, D.
, 2003
, “Modeling Aerodynamic Nonlinearities for Two Aeroelastic Configurations: Delta Wing and Flapping Flag
,” AIAA
Paper No. 2003-1402.61.
Zhao
, W.
, Païdoussis
, M. P.
, Tang
, L.
, Liu
, M.
, and Jiang
, J.
, 2012
, “Theoretical and Experimental Investigations of the Dynamics of Cantilevered Flexible Plates Subjected to Axial Flow
,” J. Sound Vib.
, 331
(3
), pp. 575
–587
.62.
Dunnmon
, J.
, Stanton
, S.
, Mann
, B.
, and Dowell
, E.
, 2011
, “Power Extraction From Aeroelastic Limit Cycle Oscillations
,” J. Fluids Struct.
, 27
(8
), pp. 1182
–1198
.63.
Gibbs
, S. C.
, Wang
, I.
, and Dowell
, E.
, 2012
, “Theory and Experiment for Flutter of a Rectangular Plate With a Fixed Leading Edge in Three-Dimensional Axial Flow
,” J. Fluids Struct.
, 34
, pp. 68
–83
.64.
Goza
, A.
, and Colonius
, T.
, 2017, “A Global Mode Analysis of Flapping Flags
,” 10th International Symposium on Turbulence and Shear Flow Phenomena (TSFP10
), Chicago, IL, July 6–9.http://tsfp10.org/TSFP10_program/s333.html65.
Kornecki
, A.
, Dowell
, E.
, and O'Brien
, J.
, 1976
, “On the Aeroelastic Instability of Two-Dimensional Panels in Uniform Incompressible Flow
,” J. Sound Vib.
, 47
(2
), pp. 163
–178
.66.
Jia
, L.-B.
, Li
, F.
, Yin
, X.-Z.
, and Yin
, X.-Y.
, 2007
, “Coupling Modes Between Two Flapping Filaments
,” J. Fluid Mech.
, 581
(1
), pp. 199
–220
.67.
Argentina
, M.
, and Mahadevan
, L.
, 2005
, “Fluid-Flow-Induced Flutter of a Flag
,” Proc. Natl. Acad. Sci. U. S. A.
, 102
(6
), pp. 1829
–1834
.68.
Lemaitre
, C.
, Hémon
, P.
, and de Langre
, E.
, 2005
, “Instability of a Long Ribbon Hanging in Axial Air Flow
,” J. Fluids Struct.
, 20
(7
), pp. 913
–925
.69.
Datta
, S. K.
, and Gottenberg
, W. G.
, 1975
, “Instability of an Elastic Strip Hanging in an Airstream
,” ASME J. Appl. Mech.
, 42
(1
), pp. 195
–198
.70.
De Nayer
, G.
, Kalmbach
, A.
, Breuer
, M.
, Sicklinger
, S.
, and Wüchner
, R.
, 2014
, “Flow Past a Cylinder With a Flexible Splitter Plate: A Complementary Experimental–Numerical Investigation and a New FSI Test Case (FSI-PfS-1a)
,” Comput. Fluids
, 99
, pp. 18
–43
.71.
Hübner
, B.
, Walhorn
, E.
, and Dinkler
, D.
, 2004
, “A Monolithic Approach to Fluid–Structure Interaction Using Space–Time Finite Elements
,” Comput. Methods Appl. Mech. Eng.
, 193
(23–26
), pp. 2087
–2104
.72.
Manela
, A.
, and Howe
, M.
, 2009
, “The Forced Motion of a Flag
,” J. Fluid Mech.
, 635
, pp. 439
–454
.73.
Gibbs
, S. C.
, Fichera
, S.
, Zanotti
, A.
, Ricci
, S.
, and Dowell
, E. H.
, 2014
, “Flow Field Around the Flapping Flag
,” J. Fluids Struct.
, 48
, pp. 507
–513
.74.
Shang-Rou
, H.
, Shaw
, S. W.
, and Pierre
, C.
, 1994
, “Normal Modes for Large Amplitude Vibration of a Cantilever Beam
,” Int. J. Solids Struct.
, 31
(14
), pp. 1981
–2014
.75.
Gurugubelli
, P. S.
, and Jaiman
, R. K.
, 2015
, “Self-Induced Flapping Dynamics of a Flexible Inverted Foil in a Uniform Flow
,” J. Fluid Mech.
, 781
, pp. 657
–694
.76.
Souilliez
, C.
, Eloy
, C.
, and Schouveiler
, L.
, 2006
, “An Experimental Study of Flag Flutter
,” ASME
Paper No. PVP2006-ICPVT-11-93864.77.
Shelley
, M.
, Vandenberghe
, N.
, and Zhang
, J.
, 2005
, “Heavy Flags Undergo Spontaneous Oscillations in Flowing Water
,” Phys. Rev. Lett.
, 94
(9
), p. 094302
.78.
Doaré
, O.
, and Michelin
, S.
, 2011
, “Piezoelectric Coupling in Energy-Harvesting Fluttering Flexible Plates: Linear Stability Analysis and Conversion Efficiency
,” J. Fluids Struct.
, 27
(8
), pp. 1357
–1375
.79.
Yu
, Y.
, Liu
, Y.
, and Chen
, Y.
, 2018
, “Vortex Dynamics and Heat Transfer Behind Self-Oscillating Inverted Flags of Various Lengths in Channel Flow
,” Phys. Fluids
, 30
(4
), p. 045104
.80.
Akaydin
, H. D.
, Elvin
, N.
, and Andreopoulos
, Y.
, 2010
, “Energy Harvesting From Highly Unsteady Fluid Flows Using Piezoelectric Materials
,” J. Intell. Mater. Syst. Struct.
, 21
(13
), pp. 1263
–1278
.81.
Techet
, A. H.
, Allen
, J. J.
, and Smits
, A. J.
, 2002
, “Piezoelectric Eels for Energy Harvesting in the Ocean
,” 12th International Offshore and Polar Engineering Conference
, Kitakyushu, Japan, May 26–31, pp. 713
–718
.https://www.onepetro.org/conference-paper/ISOPE-I-02-10982.
Shi
, S.
, New
, T. H.
, and Liu
, Y.
, 2014
, “Effects of Aspect-Ratio on the Flapping Behaviour of Energy-Harvesting Membrane
,” Exp. Therm. Fluid Sci.
, 52
, pp. 339
–346
.83.
De Nayer
, G.
, and Breuer
, M.
, 2014
, “Numerical FSI Investigation Based on LES: Flow Past a Cylinder With a Flexible Splitter Plate Involving Large Deformations (FSI-PfS-2a)
,” Int. J. Heat Fluid Flow
, 50
, pp. 300
–315
.84.
Bao
, C.-Y.
, Chao
, T.
, Xie-Zhen
, Y.
, and Xi-Yun
, L.
, 2010
, “Flutter of Finite-Span Flexible Plates in Uniform Flow
,” Chin. Phys. Lett.
, 27
(6
), p. 064601
.85.
Virot
, E.
, Amandolese
, X.
, and Hémon
, P.
, 2013
, “Fluttering Flags: An Experimental Study of Fluid Forces
,” J. Fluids Struct.
, 43
, pp. 385
–401
.86.
Bai
, Y.
, Jia
, Y. X.
, Lee
, C.
, and Zhu
, Y.
, 2016
, “Experimental Study of a Periodical Flapping Flag
,” Acta Phys. Sin.
, 65
(12
), p. 124701
.http://wulixb.iphy.ac.cn/EN/Y2016/V65/I12/12470187.
Abderrahmane
, H. A.
, Paidoussis
, M. P.
, Fayed
, M.
, and Ng
, H. D.
, 2011
, “Flapping Dynamics of a Flexible Filament
,” Phys. Rev. E
, 84
(6
), p. 066604
.88.
Virot
, E.
, Faranda
, D.
, Amandolese
, X.
, and Hémon
, P.
, 2017
, “Chaotic Dynamics of Flags From Recurring Values of Flapping Moment
,” Int. J. Bifurcation Chaos
, 27
(2
), p. 1750020
.89.
Abderrahmane
, H. A.
, Païdoussis
, M. P.
, Fayed
, M.
, and Ng
, H. D.
, 2012
, “Nonlinear Dynamics of Silk and Mylar Flags Flapping in Axial Flow
,” J. Wind Eng. Ind. Aerodyn.
, 107
, pp. 225
–236
.90.
Roshko
, A.
, 1961
, “Experiments on the Flow Past a Circular Cylinder at Very High Reynolds Number
,” J. Fluid Mech.
, 10
(3
), pp. 345
–356
.91.
Knisely
, C. W.
, 1990
, “Strouhal Numbers of Rectangular Cylinders at Incidence: A Review and New Data
,” J. Fluids Struct.
, 4
(4
), pp. 371
–393
.92.
Shukla
, S.
, Govardhan
, R.
, and Arakeri
, J.
, 2013
, “Dynamics of a Flexible Splitter Plate in the Wake of a Circular Cylinder
,” J. Fluids Struct.
, 41
, pp. 127
–134
.93.
Shoele
, K.
, and Mittal
, R.
, 2016
, “Energy Harvesting by Flow-Induced Flutter in a Simple Model of an Inverted Piezoelectric Flag
,” J. Fluid Mech.
, 790
, pp. 582
–606
.94.
Yu
, Y.
, Liu
, Y.
, and Chen
, Y.
, 2017
, “Vortex Dynamics Behind a Self-Oscillating Inverted Flag Placed in a Channel Flow: Time-Resolved Particle Image Velocimetry Measurements
,” Phys. Fluids
, 29
(12
), p. 125104
.95.
Gurugubelli
, P.
, and Jaiman
, R.
, 2017
, “On the Mechanism of Large Amplitude Flapping of Inverted Foil in a Uniform Flow
,” epub, arXiv:1711.01065.
https://arxiv.org/abs/1711.0106596.
Lee
, J. H.
, Huang
, W.-X.
, and Sung
, H. J.
, 2014
, “Flapping Dynamics of a Flexible Flag in a Uniform Flow
,” Fluid Dyn. Res.
, 46
(5
), p. 055517
.97.
Giacomello
, A.
, and Porfiri
, M.
, 2011
, “Underwater Energy Harvesting From a Heavy Flag Hosting Ionic Polymer Metal Composites
,” J. Appl. Phys.
, 109
(8
), p. 084903
.98.
Jia
, L.
, 2014
, The Interaction Between Flexible Plates and Fluid in Two-Dimensional Flow
, Springer
, Berlin, Germany.99.
Portaro
, R.
, Fayed
, M.
, Gunter
, A.-L.
, Abderrahmane
, H. A.
, and Ng
, H. D.
, 2011
, “Fractal Geometry of the Wake Shed by a Flapping Filament in Flowing Soap-Film
,” Fractals
, 19
(3
), pp. 311
–316
.100.
Perez
, M.
, Boisseau
, S.
, Gasnier
, P.
, Willemin
, J.
, and Reboud
, J. L.
, 2015
, “An Electret-Based Aeroelastic Flutter Energy Harvester
,” Smart Mater. Struct.
, 24
(3
), p. 035004
.101.
Perez
, M.
, Boisseau
, S.
, Geisler
, M.
, Gasnier
, P.
, Willemin
, J.
, Despesse
, G.
, and Reboud
, J. L.
, 2018
, “Aeroelastic Flutter Energy Harvesters Self-Polarized by Triboelectric Effects
,” Smart Mater. Struct.
, 27
(1
), p. 014003
.102.
Doaré
, O.
, Mano
, D.
, and Carlos Bilbao Ludena
, J.
, 2011
, “Effect of Spanwise Confinement on Flag Flutter: Experimental Measurements
,” Phys. Fluids
, 23
(11
), p. 111704
.103.
Doaré
, O.
, Sauzade
, M.
, and Eloy
, C.
, 2011
, “Flutter of an Elastic Plate in a Channel Flow: Confinement and Finite-Size Effects
,” J. Fluids Struct.
, 27
(1
), pp. 76
–88
.104.
Hoepffner
, J.
, and Naka
, Y.
, 2011
, “Oblique Waves Lift the Flapping Flag
,” Phys. Rev. Lett.
, 107
(19
), p. 194502
.105.
Sader
, J. E.
, Huertas-Cerdeira
, C.
, and Gharib
, M.
, 2016
, “Stability of Slender Inverted Flags and Rods in Uniform Steady Flow
,” J. Fluid Mech.
, 809
, pp. 873
–894
.106.
Alben
, S.
, 2009
, “Wake-Mediated Synchronization and Drafting in Coupled Flags
,” J. Fluid Mech.
, 641
, pp. 489
–496
.107.
Ristroph
, L.
, and Zhang
, J.
, 2008
, “Anomalous Hydrodynamic Drafting of Interacting Flapping Flags
,” Phys. Rev. Lett.
, 101
(19
), p. 194502
.108.
Huertas-Cerdeira
, C.
, Fan
, B.
, and Gharib
, M.
, 2018
, “Coupled Motion of Two Side-by-Side Inverted Flags
,” J. Fluids Struct.
, 76
, pp. 527
–535
.109.
Ryu
, J.
, Park
, S. G.
, and Sung
, H. J.
, 2018
, “Flapping Dynamics of Inverted Flags in a Side-by-Side Arrangement
,” Int. J. Heat Fluid Flow
, 70
, pp. 131
–140
.110.
Farnell
, D. J. J.
, David
, T.
, and Barton
, D. C.
, 2004
, “Coupled States of Flapping Flags
,” J. Fluids Struct.
, 19
(1
), pp. 29
–36
.111.
Zhu
, L.
, and Peskin
, C. S.
, 2003
, “Interaction of Two Flapping Filaments in a Flowing Soap Film
,” Phys. Fluids
, 15
(7
), pp. 1954
–1960
.112.
Tang
, L.
, and Païdoussis
, M. P.
, 2009
, “The Coupled Dynamics of Two Cantilevered Flexible Plates in Axial Flow
,” J. Sound Vib.
, 323
(3–5
), pp. 790
–801
.113.
Sun
, C. B.
, Wang
, S. Y.
, Jia
, L. B.
, and Yin
, X. Z.
, 2016
, “Force Measurement on Coupled Flapping Flags in Uniform Flow
,” J. Fluids Struct.
, 61
, pp. 339
–346
.114.
Wang
, S.-Y.
, Duan
, W.-G.
, and Yin
, X.-Z.
, 2013
, “Transition Mode of Two Parallel Flags in Uniform Flow
,” Chin. Phys. Lett.
, 30
(11
), p. 110502
.115.
Schouveiler
, L.
, and Eloy
, C.
, 2009
, “Coupled Flutter of Parallel Plates
,” Phys. Fluids
, 21
(8
), p. 081703
.116.
Michelin
, S.
, and Llewellyn Smith
, S. G.
, 2009
, “Linear Stability Analysis of Coupled Parallel Flexible Plates in an Axial Flow
,” J. Fluids Struct.
, 25
(7
), pp. 1136
–1157
.117.
Jeong
, Y. D.
, and Lee
, J. H.
, 2017
, “Passive Control of a Single Flexible Flag Using Two Side-by-Side Flags
,” Int. J. Heat Fluid Flow
, 65
, pp. 90
–104
.118.
Tian
, F.-B.
, Luo
, H.
, Zhu
, L.
, and Lu
, X.-Y.
, 2011
, “Coupling Modes of Three Filaments in Side-by-Side Arrangement
,” Phys. Fluids
, 23
(11
), p. 111903
.119.
Tian
, F. B.
, Luo
, H.
, Zhu
, L.
, Liao
, J. C.
, and Lu
, X. Y.
, 2011
, “An Efficient Immersed Boundary-Lattice Boltzmann Method for the Hydrodynamic Interaction of Elastic Filaments
,” J. Comput. Phys.
, 230
(19
), pp. 7266
–7283
.120.
Uddin
, E.
, Huang
, W.-X.
, and Sung
, H. J.
, 2013
, “Interaction Modes of Multiple Flexible Flags in a Uniform Flow
,” J. Fluid Mech.
, 729
, pp. 563
–583
.121.
Son
, Y.
, and Lee
, J. H.
, 2017
, “Flapping Dynamics of Coupled Flexible Flags in a Uniform Viscous Flow
,” J. Fluids Struct.
, 68
, pp. 339
–355
.122.
Zhang
, W.
, Liu
, X.
, Zhai
, J.
, and Ye
, Z.
, 2012
, “Experimental Study on Side Force Alleviation of Conical Forebody With a Fluttering Flag
,” Phys. Fluids
, 24
(12
), p. 124105
.123.
Zhai
, J.
, Zhang
, W.
, Gao
, C.
, Zhang
, Y.
, Ye
, Z.
, and Wang
, H.
, 2016
, “Side Force Control on Slender Body by Self-Excited Oscillation Flag
,” Theor. Appl. Mech. Lett.
, 6
(5
), pp. 230
–232
.124.
Sudevalayam
, S.
, and Kulkarni
, P.
, 2011
, “Energy Harvesting Sensor Nodes: Survey and Implications
,” IEEE Commun. Surv. Tutorials
, 13
(3
), pp. 443
–461
.125.
Xia
, Y.
, Michelin
, S.
, and Doaré
, O.
, 2015
, “Fluid-Solid-Electric Lock-In of Energy-Harvesting Piezoelectric Flags
,” Phys. Rev. Appl.
, 3
(1
), p. 014009
.126.
Ottman
, G. K.
, Hofmann
, H. F.
, Bhatt
, A. C.
, and Lesieutre
, G. A.
, 2002
, “Adaptive Piezoelectric Energy Harvesting Circuit for Wireless Remote Power Supply
,” IEEE Trans. Power Electron.
, 17
(5
), pp. 669
–676
.127.
Robbins
, W. P.
, Morris
, D.
, Marusic
, I.
, and Novak
, T. O.
, 2006
, “Wind-Generated Electrical Energy Using Flexible Piezoelectric Materials
,” ASME
Paper No. IMECE2006-14050.128.
Michelin
, S.
, and Doaré
, O.
, 2013
, “Energy Harvesting Efficiency of Piezoelectric Flags in Axial Flows
,” J. Fluid Mech.
, 714
, pp. 489
–504
.129.
Tang
, L.
, Païdoussis
, M. P.
, and Jiang
, J.
, 2009
, “Cantilevered Flexible Plates in Axial Flow: Energy Transfer and the Concept of Flutter-Mill
,” J. Sound Vib.
, 326
(1–2
), pp. 263
–276
.130.
Virot
, E.
, Amandolese
, X.
, and Hémon
, P.
, 2016
, “Coupling Between a Flag and a Spring-Mass Oscillator
,” J. Fluids Struct.
, 65
, pp. 447
–454
.131.
Chen
, M.
, Jia
, L. B.
, Wang
, S. Y.
, and Yin
, X. Z.
, 2014
, “Effects of Material Damping on Flag Flutter
,” Sci. China Technol. Sci.
, 57
(1
), pp. 117
–127
.132.
Invernizzi
, F.
, Dulio
, S.
, Patrini
, M.
, Guizzetti
, G.
, and Mustarelli
, P.
, 2016
, “Energy Harvesting From Human Motion: Materials and Techniques
,” Chem. Soc. Rev.
, 45
(20
), pp. 5455
–5473
.133.
Shan
, X.
, Song
, R.
, Fan
, M.
, Deng
, J.
, and Xie
, T.
, 2016
, “A Novel Method for Improving the Energy Harvesting Performance of Piezoelectric Flag in a Uniform Flow
,” Ferroelectrics
, 500
(1
), pp. 283
–290
.134.
Piñeirua
, M.
, Doaré
, O.
, and Michelin
, S.
, 2015
, “Influence and Optimization of the Electrodes Position in a Piezoelectric Energy Harvesting Flag
,” J. Sound Vib.
, 346
, pp. 200
–215
.135.
Pobering
, S.
, Ebermeyer
, S.
, and Schwesinger
, N.
, 2009, “Generation of Electrical Energy Using Short Piezoelectric Cantilevers in Flowing Media
,” Proc. SPIE
7288
, p. 728807
.136.
Lee
, H. J.
, Sherrit
, S.
, Tosi
, L. P.
, and Colonius
, T.
, 2016, “Design and Experimental Evaluation of Flextensional-Cantilever Based Piezoelectric Transducers for Flow Energy Harvesting
,” Proc. SPIE
9806
, p. 980610
.137.
Lee
, H. J.
, Sherrit
, S.
, Tosi
, L. P.
, Walkemeyer
, P.
, and Colonius
, T.
, 2015
, “Piezoelectric Energy Harvesting in Internal Fluid Flow
,” Sensors
, 15
(10
), pp. 26039
–26062
.138.
Pobering
, S.
, and Schwesinger
, N.
, 2004, “A Novel Hydropower Harvesting Device
,” International Conference on MEMS, NANO and Smart Systems
, (ICMENS'04
), Banff, AB, Canada, Aug. 25–27, pp. 480
–485
.139.
Dewan
, A.
, Mahanta
, P.
, Raju
, K. S.
, and Kumar
, P. S.
, 2004
, “Review of Passive Heat Transfer Augmentation Techniques
,” Proc. Inst. Mech. Eng., Part A
, 218
(7
), pp. 509
–527
.140.
Promvonge
, P.
, and Eiamsa-ard
, S.
, 2007
, “Heat Transfer Augmentation in a Circular Tube Using V-Nozzle Turbulator Inserts and Snail Entry
,” Exp. Therm. Fluid Sci.
, 32
(1
), pp. 332
–340
.141.
Bhagoria
, J.
, Saini
, J.
, and Solanki
, S.
, 2002
, “Heat Transfer Coefficient and Friction Factor Correlations for Rectangular Solar Air Heater Duct Having Transverse Wedge Shaped Rib Roughness on the Absorber Plate
,” Renewable Energy
, 25
(3
), pp. 341
–369
.142.
Promvonge
, P.
, and Thianpong
, C.
, 2008
, “Thermal Performance Assessment of Turbulent Channel Flows Over Different Shaped Ribs
,” Int. Commun. Heat Mass Transfer
, 35
(10
), pp. 1327
–1334
.143.
Wang
, L.
, and Sunden
, B.
, 2002
, “Performance Comparison of Some Tube Inserts
,” Int. Commun. Heat Mass Transfer
, 29
(1
), pp. 45
–56
.144.
Jha
, S.
, Crittenden
, T.
, and Glezer
, A.
, 2017
, “Enhancement of Forced Convection Heat Transfer Using Aero-Elastically Fluttering Reeds
,” 23rd IEEE International Workshop on Thermal Investigations of ICs and Systems
(THERMINIC
), Amsterdam, The Netherlands, Sept. 27–29.145.
Crittenden
, T.
, Jha
, S.
, and Glezer
, A.
, 2017
, “Forced Convection Heat Transfer Enhancement in Heat Sink Channels Using Aeroelastically Fluttering Reeds
,” 16th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm
), Orlando, FL, May 30–June 2, pp. 114
–121
.146.
Anxionnaz
, Z.
, Cabassud
, M.
, Gourdon
, C.
, and Tochon
, P.
, 2008
, “Heat Exchanger/Reactors (HEX Reactors): Concepts, Technologies: State-of-the-Art
,” Chem. Eng. Process.: Process Intensif.
, 47
(12
), pp. 2029
–2050
.147.
Ghanem
, A.
, Lemenand
, T.
, Della Valle
, D.
, and Peerhossaini
, H.
, 2014
, “Static Mixers: Mechanisms, Applications, and Characterization Methods—A Review
,” Chem. Eng. Res. Des.
, 92
(2
), pp. 205
–228
.148.
Habchi
, C.
, Lemenand
, T.
, Della Valle
, D.
, and Peerhossaini
, H.
, 2016
, “Turbulence Statistics Downstream of a Vorticity Generator at Low Reynolds Numbers
,” Phys. Fluids
, 28
(10
), p. 105106
.Copyright © 2019 by ASME
You do not currently have access to this content.
