This study investigates energy harvesting of a two-dimensional foil in the wake downstream of a cylinder. The foil is passively mobile in the transverse direction. An immersed boundary (IB) method with a fluid–structure interaction (FSI) model is validated and employed to carry out the numerical simulation. For improving numerical stability, this study incorporates a modified low-storage first-order Runge–Kutta scheme for time integration and demonstrates the performance of this temporal scheme on reducing spurious pressure oscillations of the IB method. The simulation shows the foil emerged in a vortical wake achieves better energy harvesting performance than that in a uniform flow. The types of the dynamic response of the energy harvester are identified, and the periodic response is desired for optimal energy harvesting performance. Last, the properties of vortical wakes are found to be of pivotal importance in obtaining this desired periodic response.

References

1.
Wu
,
T. Y.
,
1972
, “
Extraction of Flow Energy by a Wing Oscillating in Waves
,”
J. Ship Res.
,
14
(
1
), pp.
66
78
.http://www.sname.org/HigherLogic/System/DownloadDocumentFile.ashx?DocumentFileKey=a3ebee7f-1619-4089-a781-d03ffeb0ba22
2.
Anderson
,
J. M.
,
Streitlien
,
K.
,
Barrett
,
D. S.
, and
Triantafyllou
,
M. S.
,
1998
, “
Oscillating Foils of High Propulsive Efficiency
,”
J. Fluid Mech.
,
360
, pp.
41
72
.
3.
Schouveiler
,
L.
,
Hover
,
F. S.
, and
Triantafyllou
,
M. S.
,
2005
, “
Performance of Flapping Foil Propulsion
,”
J. Fluid Struct.
,
20
(
7
), pp.
949
959
.
4.
Peng
,
Z.
, and
Zhu
,
Q.
,
2009
, “
Energy Harvesting Through Flow-Induced Oscillations of a Foil
,”
Phys. Fluids
,
21
(
12
), p.
123602
.
5.
Simpson
,
B. J.
,
Hover
,
F. S.
, and
Triantafyllou
,
M. S.
,
2008
, “
Experiments in Direct Energy Extraction Through Flapping Foils
,”
18th International Offshore and Polar Engineering Conference
, Vancouver, BC, Canada, July 6-11,
SPE
Paper No. ISOPE-I-08-040.https://www.onepetro.org/conference-paper/ISOPE-I-08-040
6.
Zhu
,
Q.
, and
Peng
,
Z.
,
2009
, “
Mode Coupling and Flow Energy Harvesting by a Flapping Foil
,”
Phys. Fluids
,
21
(
3
), p.
033601
.
7.
Zhu
,
Q.
,
2012
, “
Energy Harvesting by a Purely Passive Flapping Foil From Shear Flows
,”
J. Fluid Struct.
,
34
, pp.
157
169
.
8.
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
.
9.
Taylor
,
G. K.
,
Nudds
,
R. L.
, and
Thomas
,
A. L. R.
,
2003
, “
Flying and Swimming Animals Cruise at a Strouhal Number Tuned for High Power Efficiency
,”
Nature
,
425
(
6959
), pp.
707
711
.
10.
Liao
,
J. C.
,
Beal
,
D. N.
,
Lauder
,
G. V.
, and
Triantafyllou
,
M. S.
,
2003
, “
The Karman Gait: Novel Body Kinematics of Rainbow Trout Swimming in a Vortex Street
,”
J. Exp. Biol.
,
206
(
6
), pp.
1059
1073
.
11.
Beal
,
D. N.
,
Hover
,
F. S.
,
Triantafyllou
,
M. S.
,
Liao
,
J. C.
, and
Lauder
,
G. V.
,
2006
, “
Passive Propulsion in Vortex Wakes
,”
J. Fluid Mech.
,
549
, pp.
385
402
.
12.
Allen
,
J. J.
, and
Smits
,
A. J.
,
2001
, “
Energy Harvesting Eel
,”
J. Fluid Struct.
,
15
(
3–4
), pp.
629
640
.
13.
Dabiri
,
J. O.
,
2007
, “
Renewable Fluid Dynamic Energy Derived From Aquatic Animal Locomotion
,”
Bioinspiration Biomimetics
,
2
(
3
), pp.
L1
L3
.
14.
Pan
,
D. Y.
,
Shao
,
X. M.
,
Deng
,
J.
, and
Yu
,
Z. S.
,
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
.
15.
Yu
,
Y. L.
, and
Liu
,
Y. Z.
,
2015
, “
Flapping Dynamics of a Piezoelectric Membrane Behind a Circular Cylinder
,”
J. Fluid Struct.
,
55
, pp.
347
363
.
16.
Zhu
,
X. J.
,
He
,
G. W.
, and
Zhang
,
X.
,
2014
, “
Flow-Mediated Interactions Between Two Self-Propelled Flapping Filaments in Tandem Configuration
,”
Phys. Rev. Lett.
,
113
(
23
), p. 238105.https://www.ncbi.nlm.nih.gov/pubmed/25526164
17.
Xiao
,
Q.
, and
Liao
,
W.
,
2010
, “
Numerical Investigation of Angle of Attack Profile on Propulsion Performance of an Oscillating Foil
,”
Comput. Fluids
,
39
(
8
), pp.
1366
1380
.
18.
Xiao
,
Q.
,
Sun
,
K.
,
Liu
,
H.
, and
Hu
,
J. X.
,
2011
, “
Computational Study on Near Wake Interaction Between Undulation Body and a D-Section Cylinder
,”
Ocean Eng.
,
38
(
4
), pp.
673
683
.
19.
Liao
,
Q.
,
Dong
,
G.-J.
, and
Lu
,
X.-Y.
,
2004
, “
Vortex Formation and Force Characteristics of a Foil in the Wake of a Circular Cylinder
,”
J. Fluid Struct.
,
19
(
4
), pp.
491
510
.
20.
Gopalkrishnan
,
R.
,
Triantafyllou
,
M. S.
,
Triantafyllou
,
G. S.
, and
Barrett
,
D.
,
1994
, “
Active Vorticity Control in a Shear Flow Using a Flapping Foil
,”
J. Fluid Mech.
,
274
, pp.
1
21
.
21.
Streitlien
,
K.
,
Triantafyllou
,
G. S.
, and
Triantafyllou
,
M. S.
,
1996
, “
Efficient Foil Propulsion Through Vortex Control
,”
AIAA J.
,
34
(
11
), pp.
2315
2319
.
22.
Shao
,
X. M.
, and
Pan
,
D. Y.
,
2011
, “
Hydrodynamics of a Flapping Foil in the Wake of a D-Section Cylinder
,”
J. Hydrodyn.
,
23
(
4
), pp.
422
430
.
23.
Yang
,
X.
, and
Zheng
,
Z.
,
2010
, “
Nonlinear Spacing and Frequency Effects of an Oscillating Cylinder in the Wake of a Stationary Cylinder
,”
Phys. Fluids
,
22
(4),
p
. 043601.
24.
Zheng
,
Z. C.
, and
Wei
,
Z.
,
2012
, “
Study of Mechanisms and Factors That Influence the Formation of Vortical Wake of a Heaving Airfoil
,”
Phys. Fluids
,
24
(
10
), p. 103601.http://dx.doi.org/10.1063/1.4760258
25.
Wei
,
Z.
, and
Zheng
,
Z. C.
,
2014
, “
Mechanisms of Wake Deflection Angle Change Behind a Heaving Airfoil
,”
J. Fluids Struct.
,
48
, pp.
1
13
.
26.
Tang
,
E.
,
Wei
,
Z. A.
,
Whitehead
,
K. K.
,
Khiabani
,
R. H.
,
Restrepo
,
M.
,
Mirabella
,
L.
,
Bethel
,
J.
,
Paridon
,
S. M.
,
Marino
,
B. S.
,
Fogel
,
M. A.
, and
Yoganathan
,
A. P.
,
2017
, “
Effect of Fontan Geometry on Exercise Haemodynamics and Its Potential Implications
,”
Heart
, epub.http://dx.doi.org/10.1136/heartjnl-2016-310855
27.
Trusty
,
P. M.
,
Wei
,
Z.
,
Tree
,
M.
, and
Kanter
,
K.
,
2017
, “
Local Hemodynamic Differences Between Commercially Available Y-Grafts and Traditional Fontan Baffles Under Simulated Exercise Conditions: Implications for Exercise Tolerance
,”
Cardiovasc. Eng. Technol.
, epub
.
https://doi.org/10.1007/s13239-017-0310-5
28.
Wei
,
Z.
, and
Zheng
,
Z. C.
,
2017
, “
Energy-Harvesting Mechanism of a Heaving Airfoil in a Vortical Wake
,”
AIAA J.
, epub.
29.
Wei
,
Z.
,
Zheng
,
Z. C.
, and
Yang
,
X.
,
2014
, “
Computation of Flow Through a Three-Dimensional Periodic Array of Porous Structures by a Parallel Immersed-Boundary Method
,”
ASME J. Fluids Eng.
,
136
(
4
), p.
040905
.
30.
Wei
,
Z. L.
,
Trusty
,
P. M.
,
Tree
,
M.
,
Haggerty
,
C. M.
,
Tang
,
E.
,
Fogel
,
M.
, and
Yoganathan
,
A. P.
,
2017
, “
Can Time-Averaged Flow Boundary Conditions Be Used to Meet the Clinical Timeline for Fontan Surgical Planning?
,”
J. Biomech.
,
50
, pp.
172
179
.
31.
Zhang
,
N.
, and
Zheng
,
Z. C.
,
2007
, “
An Improved Direct-Forcing Immersed Boundary Method for Finite Difference Applications
,”
J. Comput. Phys.
,
221
(
1
), pp.
250
268
.
32.
Hou
,
G. N.
,
Wang
,
J.
, and
Layton
,
A.
,
2012
, “
Numerical Methods for Fluid-Structure Interaction—A Review
,”
Commun. Comput. Phys.
,
12
(
2
), pp.
337
377
.
33.
Gibou
,
F.
, and
Min
,
C. H.
,
2012
, “
Efficient Symmetric Positive Definite Second-Order Accurate Monolithic Solver for Fluid/Solid Interactions
,”
J. Comput. Phys.
,
231
(
8
), pp.
3246
3263
.
34.
Robinson-Mosher
,
A.
,
Shinar
,
T.
,
Gretarsson
,
J.
,
Su
,
J.
, and
Fedkiw
,
R.
,
2008
, “
Two-Way Coupling of Fluids to Rigid and Deformable Solids and Shells
,”
ACM Trans. Graphics
,
27
(
3
), p. 46.
35.
Borazjani
,
I.
,
Ge
,
L.
, and
Sotiropoulos
,
F.
,
2008
, “
Curvilinear Immersed Boundary Method for Simulating Fluid Structure Interaction With Complex 3D Rigid Bodies
,”
J. Comput. Phys.
,
227
(
16
), pp.
7587
7620
.
36.
Yang
,
J. M.
, and
Balaras
,
E.
,
2006
, “
An Embedded-Boundary Formulation for Large-Eddy Simulation of Turbulent Flows Interacting With Moving Boundaries
,”
J. Comput. Phys.
,
215
(
1
), pp.
12
40
.
37.
Balaras
,
E.
, and
Yang
,
J. M.
,
2005
, “
Nonboundary Conforming Methods for Large-Eddy Simulations of Biological Flows
,”
ASME J. Fluids Eng.
,
127
(
5
), pp.
851
857
.
38.
Lee
,
J.
,
Kim
,
J.
,
Choi
,
H.
, and
Yang
,
K. S.
,
2011
, “
Sources of Spurious Force Oscillations From an Immersed Boundary Method for Moving-Body Problems
,”
J. Comput. Phys.
,
230
(
7
), pp.
2677
2695
.
39.
Breugem
,
W. P.
,
2012
, “
A Second-Order Accurate Immersed Boundary Method for Fully Resolved Simulations of Particle-Laden Flows
,”
J. Comput. Phys.
,
231
(
13
), pp.
4469
4498
.
40.
Kim
,
J.
,
Kim
,
D.
, and
Choi
,
H.
,
2001
, “
An Immersed-Boundary Finite Volume Method for Simulations of Flow in Complex Geometries
,”
J. Comput. Phys.
,
171
(
1
), pp.
132
150
.
41.
Uhlmann
,
M.
,
2005
, “
An Immersed Boundary Method With Direct Forcing for the Simulation of Particulate Flows
,”
J. Comput. Phys.
,
209
(
2
), pp.
448
476
.
42.
Le
,
H.
, and
Moin
,
P.
,
1991
, “
An Improvement of Fractional Step Methods for the Incompressible Navier–Stokes Equations
,”
J. Comput. Phys.
,
92
(
2
), pp.
369
379
.
43.
Wei
,
Z.
,
2014
, “
Numerical and Theoretical Study of Flapping Airfoil Aerodynamics Using a Parallelized Immersed-Boundary Method
,”
Ph.D. thesis
, University of Kansas, Lawrence, KS.http://hdl.handle.net/1808/19600
44.
Zheng
,
Z.
, and
Zhang
,
N.
,
2008
, “
Frequency Effect on Lift and Drag of an Oscillating Cylinder in Flow
,”
J. Fluid Struct.
,
24
(
3
), pp.
382
399
.
45.
Yang
,
X.
,
Zhang
,
X.
,
Li
,
Z.
, and
He
,
G.
,
2009
, “
A Smoothing Technique for Discrete Delta Functions With Application to Immersed Boundary Method in Moving Boundary Simulations
,”
J. Comput. Phys.
,
228
(
20
), pp.
7821
7836
.
46.
Zhao
,
M.
,
2013
, “
Flow Induced Vibration of Two Rigidly Coupled Circular Cylinders in Tandem and Side-by-Side Arrangements at a Low Reynolds Number of 150
,”
Phys. Fluids
,
25
(
12
), p. 123601.http://dx.doi.org/10.1063/1.4832956
47.
Ahn
,
H. T.
, and
Kallinderis
,
Y.
,
2006
, “
Strongly Coupled Flow/Structure Interactions With a Geometrically Conservative ALE Scheme on General Hybrid Meshes
,”
J. Comput. Phys.
,
219
(
2
), pp.
671
696
.
48.
Zhu
,
Q.
,
2011
, “
Optimal Frequency for Flow Energy Harvesting of a Flapping Foil
,”
J. Fluid Mech.
,
675
(1), pp.
495
517
.
49.
Zhang
,
H.
, and
Ma
,
T. W.
,
2015
, “
Roles of the Excitation in Harvesting Energy From Vibrations
,”
PloS One
,
10
(
10
), pp. 1–10.http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0141299
50.
Shen
,
W. N.
, and
Zhu
,
S. Y.
,
2015
, “
Harvesting Energy Via Electromagnetic Damper: Application to Bridge Stay Cables
,”
J. Intell. Mater. Syst. Struct.
,
26
(
1
), pp.
3
19
.
51.
Eldredge
,
J. D.
, and
Pisani
,
D.
,
2008
, “
Passive Locomotion of a Simple Articulated Fish-Like System in the Wake of an Obstacle
,”
J. Fluid Mech.
,
607
, pp.
279
288
.
52.
Zhang
,
N.
, and
Zheng
,
Z. C.
,
2009
, “
Flow/Pressure Characteristics for Flow Over Two Tandem Swimming Fish
,”
Comput. Fluids
,
38
(
5
), pp.
1059
1064
.
You do not currently have access to this content.