In the evolution of floating-point absorber wave energy conversion systems, multiple-body systems are gaining more attention than single-body systems. Meanwhile, the design and operation factors affecting the performance of multiple-body systems are much greater than those of single-body systems. However, no systematic study has yet been presented. In this article, a theoretical model is proposed by using a coupled oscillator system consisting of a damper-spring system to represent a two-body system (the floating body and the reacting body). Dimensionless expressions for the motion response and wave power absorption efficiency are derived. With the newly developed model, we prove that an appropriately tuned two-body system can obtain a limiting power absorption width of (L is the incident wavelength) as much as a single-body system. The generic case of a two-body system is presented with numerical simulations as an example. The results show that increasing the damping coefficient can reduce the wave frequency at which the peak of power absorption efficiency occurs. Increasing stiffness can make the wave frequencies for high power absorption efficiency move to a higher frequency region and can also make the spectrum bandwidth for high power absorption efficiency become narrower. Further, we show that the two-body system can absorb more wave energy at low wave frequencies than the single-body system.
REFERENCES
1.
Arbic
,
B. K.
and
Garrett
,
C.
, “
A coupled oscillator model of shelf and ocean tides
,” Cont. Shelf Res.
30
, 564
–574
(2010
).2.
Beatty
,
S. J.
,
Hall
,
M.
,
Buckham
,
B. J.
,
Wild
,
P.
, and
Bocking
,
B.
, “
Experimental and numerical comparisons of self-reacting point absorber wave energy converters in regular waves
,” Ocean Eng.
104
, 370
–386
(2015
).3.
Budal
,
K.
, “
Theory for absorption of wave power by a system of interacting bodies
,” J. Ship Res.
21
, 248
–254
(1977
).4.
Budar
,
K.
, and
Falnes
,
J.
, “
A resonant point absorber of ocean-wave power
,” Nature
256
, 478
–479
(1975
).5.
Chen
,
X.
,
Jiang
,
Z.
,
Li
,
Q.
,
Li
,
Y.
, and
Ren
,
N.
, “
Extended environmental contour methods for long-term extreme response analysis of offshore wind turbines
,” J. Offshore Mech. Arct. Eng.
142
, 052003
(2020
).6.
Chen
,
H.
,
Xu
,
Q.
,
Zheng
,
X.
,
Bennetts
,
L. G.
,
Xie
,
B.
,
Lin
,
Z.
,
Lin
,
Z.
, and
Li
,
Y.
, “
Viscous effects on the added mass and damping forces during free heave decay of a floating cylinder with a hemispherical bottom
,” Eur. J. Mech. /B Fluids
98
, 8
–20
(2023
).7.
8.
Drew
,
B.
,
Plummer
,
A. R.
, and
Sahinkaya
,
M. N.
, “
A review of wave energy converter technology
,” Proc. Inst. Mech. Eng., Part A
223
, 887
–902
(2009
).9.
Evans
,
D. V.
, “
A theory for wave-power absorption by oscillating bodies
,” J. Fluid Mech.
77
, 1
–25
(1976
).10.
Evans
,
D. V.
, “
Power from water waves
,” Annu. Rev. Fluid Mech.
13
, 157
–187
(1981
).11.
Falcão
,
A.
, “
Wave energy utilization: A review of the technologies
,” Renewable Sustainable Energy Rev.
14
, 899
–918
(2010
).12.
Falnes
,
J.
, “
A review of wave-energy extraction
,” Mar. Struct.
20
, 185
–201
(2007
).13.
Falnes
,
J.
, “
Radiation impedance matrix and optimum power absorption for interacting oscillators in surface waves
,” Appl. Ocean Res.
2
, 75
–80
(1980
).14.
Falnes
,
J.
, “
Wave-energy conversion through relative motion between two single-mode oscillating bodies
,” J. Offshore Mech. Arct. Eng.
121
, 32
–38
(1999
).15.
Gao
,
Z.
,
Feng
,
X.
,
Zhang
,
Z.
,
Liu
,
Z.
,
Gao
,
X.
,
Zhang
,
L.
,
Li
,
S.
, and
Li
,
Y.
, “
A brief discussion on offshore wind turbine hydrodynamics problem
,” J. Hydrodyn.
34
, 15
–30
(2022
).16.
He
,
F.
,
Lin
,
Y.
,
Pan
,
J.
, and
Wei
,
M.
, “
Experimental investigation of vortex evolution around oscillating water column wave energy converter using particle image velocimetry
,” Phys. Fluids
35
, 015151
(2023
).17.
Hu
,
Q.
,
Li
,
Y.
,
Di
,
Y.
, and
Chen
,
J.
, “
A large-eddy simulation study of horizontal axis tidal turbine in different inflow conditions
,” J. Renewable Sustainable Energy
9
, 064501
(2017
).18.
Ishaq
,
M.
,
Chen
,
Z.
, and
Zhao
,
Q.
, “
Analysis of nonlinear water wave interaction solutions and energy exchange between different wave modes
,” Phys. Fluids
35
, 021907
(2023
).19.
Jungrungruengtaworn
,
S.
and
Hyun
,
B.
, “
Influence of slot width on the performance of multi-stage overtopping wave energy converters
,” Int. J. Naval Archit. Ocean Eng.
9
, 668
–676
(2017
).20.
Li
,
Y.
,
Lence
,
B.
, and
Calisal
,
S.
, “
Modeling tidal turbine farm with vertical axis tidal current turbines
,” in IEEE International Conference on Systems, Man and Cybernetics
(
IEEE
, 2007
), pp. 697
–702
.21.
Li
,
Y.
and
Yu
,
Y. H.
, “
A synthesis of numerical methods for modeling wave energy converter-point absorbers
,” Renewable Sustainable Energy Rev.
16
, 4352
–4364
(2012
).22.
Liang
,
C.
and
Zuo
,
L.
, “
On the dynamics and design of a two-body wave energy converter
,” Renewable Energy
101
, 265
–274
(2017
).23.
Liu
,
Y.
,
Mizutani
,
N.
,
Cho
,
Y.
, and
Nakamura
,
T.
, “
Performance enhancement of a bottom-hinged oscillating wave surge converter via resonant adjustment
,” Renewable Energy
201
, 624
–635
(2022a
).24.
Liu
,
Y.
,
Zheng
,
S.
,
Liang
,
H.
, and
Cong
,
P.
, “
Wave interaction and energy absorption from arrays of complex-shaped point absorbers
,” Phys. Fluids
34
, 097107
(2022b
).25.
Liu
,
Z.
,
Han
,
Z.
,
Shi
,
H.
, and
Yang
,
W.
, “
Experimental study on multi-level overtopping wave energy convertor under regular wave conditions
,” Int. J. Naval Archit. Ocean Eng.
10
, 651
–659
(2018
).26.
Ma
,
Y.
,
Zhang
,
A.
,
Yang
,
L.
,
Li
,
H.
, and
Zhou
,
H.
, “
Motion simulation and performance analysis of two-body floating point absorber wave energy converter
,” Renewable Energy
157
, 353
–367
(2020
).27.
Mei
,
C.
, “
Power extraction from water waves
,” J. Ship Res.
20
, 63
–66
(1976
).28.
Meng
,
F.
,
Ding
,
B.
,
Sergiienko
,
N.
,
Chen
,
H.
,
Xu
,
H.
, and
Li
,
Y.
, “
Power set-point tracking of a wave energy converter with multiple power take-off units in irregular waves
,” IEEE Trans. Sustainable Energy
13
(2), 767
–777
(2021
).29.
Mia
,
M. R.
,
Zhao
,
M.
, and
Wu
,
H.
, “
Effects of heave motion of an elastically supported floating oscillating water column device on wave energy harvesting efficiency
,” Phys. Fluids
35
, 017115
(2023
).30.
Micallef
,
D.
and
Rezaeiha
,
A.
, “
Floating offshore wind turbine aerodynamics: Trends and future challenges
,” Renewable Sustainable Energy Rev.
152
, 111696
(2021
).31.
Naik
,
N.
,
Zheng
,
S.
, and
Behera
,
H.
, “
Role of dual breakwaters and trenches on efficiency of an oscillating water column
,” Phys. Fluids
35
, 047115
(2023
).32.
Newman
,
J.
, “
The interaction of stationary vessels with regular waves
,” in Proceedings of the 11th Symposium on Naval Hydrodynamics
(University College, London, 1976
), pp. 491
–501
.33.
34.
Newman
,
J. N.
, “
The exciting forces on fixed bodies in waves
,” J. Ship Res.
6
, 10
–17
(1962
).35.
Nihous
,
G.
, and
Gauthier
,
M.
, Ocean Thermal Energy Conversion: A Historical Perspective
(
John Wiley & Sons, Ltd
, 2013
), pp. 367
–404
.36.
OPT
, see http://www.oceanpowertechnologies.com for “information about PB3 PowerBuoy wave energy deice. (2023
).”37.
Rhinefrank
,
K.
,
Schacher
,
A.
,
Prudell
,
J.
,
Stillinger
,
C.
,
Naviaux
,
D.
,
Brekken
,
T.
,
von Jouanne
,
A.
,
Newborn
,
D.
,
Yim
,
S.
, and
Cox
,
D.
, “
High resolution wave tank testing of scaled wave energy devices
,” in 29th International Conference on Ocean, Offshore and Arctic Engineering
, 2010
.38.
Salter
,
S.
, “
Wave power
,” Nature
249
, 720
–724
(1974
).39.
Soleimani
,
K.
,
Ketabdari
,
M. J.
, and
Gharechae
,
A.
, “
Smoothed particle hydrodynamics study of a heaving point absorber in various waves using wave tank and calm-water models
,” Phys. Fluids
35
, 033116
(2023
).40.
Stansby
,
P.
,
Moreno
,
E.
, and
Stallard
,
T.
, “
Large capacity multi-float configurations for the wave energy converter M4 using a time-domain linear diffraction model
,” Appl. Ocean Res.
68
, 53
–64
(2017
).41.
Sricharan
,
V. V. S.
and
Chandrasekaran
,
S.
, “
Time-domain analysis of a bean-shaped multi-body floating wave energy converter with a hydraulic power take-off using WEC-Sim
,” Energy
223
, 119985
(2021
).42.
Temiz
,
I.
,
Ekweoba
,
C.
,
Thomas
,
S.
,
Kramer
,
M.
, and
Savin
,
A.
, “
Wave absorber ballast optimization based on the analytical model for a pitching wave energy converter
,” Ocean Eng.
240
, 109906
(2021
).43.
Windt
,
C.
,
Davidson
,
J.
, and
Ringwood
,
J.
, “
Numerical analysis of the hydrodynamic scaling effects for the wavestar wave energy converter
,” J. Fluids Struct.
105
, 103328
(2021
).44.
Xu
,
Q.
,
Li
,
Y.
, and
Lin
,
Z.
, “
An improved boundary element method for modelling a self-reacting point absorber wave energy converter
,” Acta Mech. Sin.
34
, 1015
–1034
(2018
).45.
Xu
,
Q.
,
Li
,
Y.
,
Ding
,
B.
,
Lin
,
Z.
, and
Cazzolato
,
B.
, “
A study of reactively controlled floating point absorber in wave tank experiments
,” in Proceedings of 34th International Workshop on Water Waves and Floating Bodies
, 2019a
.46.
Xu
,
Q.
,
Li
,
Y.
,
Yu
,
Y. H.
,
Ding
,
B.
,
Jiang
,
Z.
,
Lin
,
Z.
, and
Cazzolato
,
B.
, “
Experimental and numerical investigations of a two-body floating-point absorber wave energy converter in regular waves
,” J. Fluids Struct.
91
, 102613
(2019b
).47.
Yu
,
D.
,
Wang
,
K.
,
Liu
,
H.
,
Kong
,
F.
,
Yang
,
C.
,
Duan
,
Y.
, and
Chen
,
H.
, “
Investigation on motion characteristics of an anti-pitching generating wec considering the viscous effect
,” Ocean Eng.
246
, 110619
(2022
).48.
Yu
,
Y. H.
and
Li
,
Y.
, “
Reynolds-averaged Navier-Stokes simulation of the heave performance of a two-body floating-point absorber wave energy system
,” Comput. Fluids
73
, 104
–114
(2013
).49.
Zang
,
W.
,
Zhang
,
Y.
,
Zheng
,
Y.
,
Zhang
,
J.
,
Guan
,
D.
, and
Fernandez-Rodriguez
,
E.
, “
On the impact of waves and turbulence on the power fluctuations and wake structure of a tidal-stream turbine
,” Phys. Fluids
35
, 055115
(2023
).50.
Zhang
,
W.
,
Li
,
Y.
,
Wu
,
X.
, and
Guo
,
S.
, “
Review of the applied mechanical problems in ocean thermal energy conversion
,” Renewable Sustainable Energy Rev.
93
, 231
–244
(2018
).51.
Zheng
,
X.
,
Chen
,
G.
,
Cao
,
W.
,
Xu
,
H.
,
Zhao
,
R.
,
Xu
,
Q.
,
Kramer
,
M.
,
Touzé
,
D. L.
,
Borthwick
,
A. G.
, and
Li
,
Y.
, “
On the energy conversion characteristics of a top-mounted pitching absorber by using smoothed particle hydrodynamics
,” Energy Convers. Manage.
250
, 114893
(2021
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.