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.

References

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.html
65.
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-02-109
82.
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/I12/124701
87.
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/1711.01065
96.
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
.
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