Laboratory experiments were performed to explore the layout effect on multiscale motions of wind turbines that are able to oscillate passively and the impact on power output fluctuations, which is instrumental toward understanding the dynamics of floating turbine arrays. We studied 3 × 3 and 3 × 5 turbine arrays in aligned and staggered configurations with inter-row separations of Sx/dT=5 and ten sharing transverse spacing of Sy/dT=2.5. A three-axis accelerometer characterized turbines' oscillations, whereas the power output was obtained directly. Particle image velocimetry was used to monitor eventual flow irregularities. The standard deviation of pitch angle, Ap(°) about the equilibrium, obtained from direct integration of instantaneous angular velocity, shows that the turbines underwent relatively small-amplitude pitch motions with maximum intensity that monotonically decreasing with increasing row location in the aligned layout. However, this was not the case in the staggered configurations; indeed, the second row of turbines underwent larger pitch amplitude in the Sx/dT=10 case. Flow channeling and larger turbine spacing promote the development and entrainment of large coherent motions producing larger unsteady forcing and triggering enhanced turbine motions. The instantaneous pitching angle density distribution exhibited Gaussian-like distribution irrespective of the units' location. A formulation for turbine pitching motions based on the balance between wind load restoring force and gravity shows that the bulk natural frequency modulates the turbine pitching angular velocity. The variation in turbine pitching amplitudes was similar to those of the mean power output. The power output spectra evidenced modulation of the local turbulence and turbine pitching natural frequency due to the flow-induced turbine pitching motions.

1.
H. E.
Murdock
,
D.
Gibb
,
T.
André
,
J. L.
Sawin
,
A.
Brown
,
F.
Appavou
,
G.
Ellis
,
B.
Epp
,
F.
Guerra
,
F.
Joubert
 et al, “
Renewables 2020-global status report
,” Report No. INIS-FR--20-1110, Reference No. 51070091, France  (
2020
).
2.
S.
Keivanpour
,
A.
Ramudhin
, and
D. A.
Kadi
, “
The sustainable worldwide offshore wind energy potential: A systematic review
,”
J. Renewable Sustainable Energy
9
,
065902
(
2017
).
3.
D.
Song
,
J.
Yang
,
X.
Fan
,
Y.
Liu
,
A.
Liu
,
G.
Chen
, and
Y. H.
Joo
, “
Maximum power extraction for wind turbines through a novel yaw control solution using predicted wind directions
,”
Energy Convers. Manage.
157
,
587
599
(
2018
).
4.
S.-P.
Breton
and
G.
Moe
, “
Status, plans and technologies for offshore wind turbines in Europe and North America
,”
Renewable Energy
34
,
646
654
(
2009
).
5.
T.
Wen
,
K.
Wang
,
Z.
Cheng
, and
M.
Ong
, “
Spar-type vertical-axis wind turbines in moderate water depth: A feasibility study
,”
Energies
11
,
555
(
2018
).
6.
X.
Wang
,
X.
Zeng
,
J.
Li
,
X.
Yang
, and
H.
Wang
, “
A review on recent advancements of substructures for offshore wind turbines
,”
Energy Convers. Manage.
158
,
103
119
(
2018
).
7.
K.-Y.
Oh
,
W.
Nam
,
M. S.
Ryu
,
J.-Y.
Kim
, and
B. I.
Epureanu
, “
A review of foundations of offshore wind energy convertors: Current status and future perspectives
,”
Renewable Sustainable Energy Rev.
88
,
16
36
(
2018
).
8.
X.
Wu
,
Y.
Hu
,
Y.
Li
,
J.
Yang
,
L.
Duan
,
T.
Wang
,
T.
Adcock
,
Z.
Jiang
,
Z.
Gao
,
Z.
Lin
 et al, “
Foundations of offshore wind turbines: A review
,”
Renewable Sustainable Energy Rev.
104
,
379
393
(
2019
).
9.
M.
Leimeister
,
A.
Kolios
, and
M.
Collu
, “
Critical review floating support structures for offshore wind farm deployment
,”
J. Phys.: Conf. Ser.
1104
,
012007
(
2018
).
10.
L.
Zhang
,
W.
Shi
,
M.
Karimirad
,
D.
Ning
 et al, “
Performance analysis of a V-shaped semisubmersible floating offshore wind turbine for deep water
,” in
Thirteenth ISOPE Pacific/Asia Offshore Mechanics Symposium
(
International Society of Offshore and Polar Engineers
,
2018
).
11.
L.
Liu
,
H.
Bian
,
Z.
Du
,
C.
Xiao
,
Y.
Guo
, and
W.
Jin
, “
Reliability analysis of blade of the offshore wind turbine supported by the floating foundation
,”
Compos. Struct.
211
,
287
300
(
2019
).
12.
H.
Zuo
,
K.
Bi
,
H.
Hao
, and
C.
Li
, “
Influence of earthquake ground motion modelling on the dynamic responses of offshore wind turbines
,”
Soil Dyn. Earthquake Eng.
121
,
151
167
(
2019
).
13.
E.
Uzunoglu
and
C. G.
Soares
, “
Yaw motion of floating wind turbine platforms induced by pitch actuator fault in storm conditions
,”
Renewable Energy
134
,
1056
1070
(
2019
).
14.
T. T.
Tran
and
D.-H.
Kim
, “
A CFD study into the influence of unsteady aerodynamic interference on wind turbine surge motion
,”
Renewable Energy
90
,
204
228
(
2016
).
15.
I.
Bayati
,
M.
Belloli
,
D.
Ferrari
,
F.
Fossati
, and
H.
Giberti
, “
Design of a 6-DoF robotic platform for wind tunnel tests of floating wind turbines
,”
Energy Procedia
53
,
313
323
(
2014
).
16.
Y.
Liu
,
Q.
Xiao
,
A.
Incecik
, and
C.
Peyrard
, “
Aeroelastic analysis of a floating offshore wind turbine in platform-induced surge motion using a fully coupled CFD-MBD method
,”
Wind Energy
22
,
1
20
(
2019
).
17.
T. T.
Tran
and
D.-H.
Kim
, “
A CFD study of coupled aerodynamic-hydrodynamic loads on a semisubmersible floating offshore wind turbine
,”
Wind Energy
21
,
70
85
(
2018
).
18.
M.
Barooni
,
N. A.
Ali
, and
T.
Ashuri
, “
An open-source comprehensive numerical model for dynamic response and loads analysis of floating offshore wind turbines
,”
Energy
154
,
442
454
(
2018
).
19.
Y.
Kim
and
O. J.
Kwon
, “
Effect of platform motion on aerodynamic performance and aeroelastic behavior of floating offshore wind turbine blades
,”
Energies
12
,
2519
(
2019
).
20.
H.
Lee
and
D.-J.
Lee
, “
Effects of platform motions on aerodynamic performance and unsteady wake evolution of a floating offshore wind turbine
,”
Renewable Energy
143
,
9
23
(
2019
).
21.
C.
Ruzzo
,
N.
Saha
, and
F.
Arena
, “
Experimental study on heave and yaw motions of a 1: 30 spar support for offshore wind turbines
,” in
Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018)
(
Springer
,
2019
), pp.
857
868
.
22.
H.
Lei
,
J.
Su
,
Y.
Bao
,
Y.
Chen
,
Z.
Han
, and
D.
Zhou
, “
Investigation of wake characteristics for the offshore floating vertical axis wind turbines in pitch and surge motions of platforms
,”
Energy
166
,
471
489
(
2019
).
23.
H.
Lei
,
D.
Zhou
,
J.
Lu
,
C.
Chen
,
Z.
Han
, and
Y.
Bao
, “
The impact of pitch motion of a platform on the aerodynamic performance of a floating vertical axis wind turbine
,”
Energy
119
,
369
383
(
2017
).
24.
T.
Tran
,
D.
Kim
, and
J.
Song
, “
Computational fluid dynamic analysis of a floating offshore wind turbine experiencing platform pitching motion
,”
Energies
7
,
5011
5026
(
2014
).
25.
C.-H. K.
Wu
and
V.-T.
Nguyen
, “
Aerodynamic simulations of offshore floating wind turbine in platform-induced pitching motion
,”
Wind Energy
20
,
835
858
(
2017
).
26.
T.-T.
Tran
and
D.-H.
Kim
, “
The platform pitching motion of floating offshore wind turbine: A preliminary unsteady aerodynamic analysis
,”
J. Wind Eng. Ind. Aerodyn.
142
,
65
81
(
2015
).
27.
Z.
Li
,
G.
Dong
, and
X.
Yang
, “
Onset of wake meandering for a floating offshore wind turbine under side-to-side motion
,”
J. Fluid Mech.
934
,
A29
(
2022
).
28.
S.
Fu
,
Y.
Jin
,
Y.
Zheng
, and
L. P.
Chamorro
, “
Wake and power fluctuations of a model wind turbine subjected to pitch and roll oscillations
,”
Appl. Energy
253
,
113605
(
2019
).
29.
B.
Zhang
,
Y.
Jin
,
S.
Cheng
,
Y.
Zheng
, and
L. P.
Chamorro
, “
On the dynamics of a model wind turbine under passive tower oscillations
,”
Appl. Energy
311
,
118608
(
2022
).
30.
H.
Lei
,
D.
Zhou
,
Y.
Bao
,
C.
Chen
,
N.
Ma
, and
Z.
Han
, “
Numerical simulations of the unsteady aerodynamics of a floating vertical axis wind turbine in surge motion
,”
Energy
127
,
1
17
(
2017
).
31.
B.
Wen
,
X.
Tian
,
X.
Dong
,
Z.
Peng
, and
W.
Zhang
, “
Influences of surge motion on the power and thrust characteristics of an offshore floating wind turbine
,”
Energy
141
,
2054
2068
(
2017
).
32.
B.
Wen
,
X.
Tian
,
X.
Dong
,
Z.
Peng
, and
W.
Zhang
, “
On the power coefficient overshoot of an offshore floating wind turbine in surge oscillations
,”
Wind Energy
21
,
1076
1091
(
2018
).
33.
K.
Sivalingam
,
S.
Martin
, and
A.
Singapore Wala
, “
Numerical validation of floating offshore wind turbine scaled rotors for surge motion
,”
Energies
11
,
2578
(
2018
).
34.
T. T.
Tran
and
D. H.
Kim
, “
The aerodynamic interference effects of a floating offshore wind turbine experiencing platform pitching and yawing motions
,”
J. Mech. Sci. Technol.
29
,
549
561
(
2015
).
35.
X.
Shen
,
J.
Chen
,
P.
Hu
,
X.
Zhu
, and
Z.
Du
, “
Study of the unsteady aerodynamics of floating wind turbines
,”
Energy
145
,
793
809
(
2018
).
36.
S.
Rockel
,
E.
Camp
,
J.
Schmidt
,
J.
Peinke
,
R.
Cal
, and
M.
Hölling
, “
Experimental study on influence of pitch motion on the wake of a floating wind turbine model
,”
Energies
7
,
1954
1985
(
2014
).
37.
S.
Ke
,
T.
Wang
,
Y.
Ge
, and
Y.
Tamura
, “
Aerodynamic loads and aeroelastic responses of large wind turbine tower-blade coupled structure in yaw condition
,”
Struct. Eng. Mech.
56
,
1021
1040
(
2015
).
38.
Z.
Li
,
B.
Wen
,
X.
Dong
,
Z.
Peng
,
Y.
Qu
, and
W.
Zhang
, “
Aerodynamic and aeroelastic characteristics of flexible wind turbine blades under periodic unsteady inflows
,”
J. Wind Eng. Ind. Aerodyn.
197
,
104057
(
2020
).
39.
D.
Hu
,
L.
Deng
, and
L.
Zeng
, “
Study on the aerodynamic performance of floating offshore wind turbine considering the tower shadow effect
,”
Processes
9
,
1047
(
2021
).
40.
B.
Pérez
,
R.
Mínguez
, and
R.
Guanche
, “
Offshore wind farm layout optimization using mathematical programming techniques
,”
Renewable Energy
53
,
389
399
(
2013
).
41.
X.
Gao
,
H.
Yang
, and
L.
Lu
, “
Study on offshore wind power potential and wind farm optimization in Hong Kong
,”
Appl. Energy
130
,
519
531
(
2014
).
42.
X.
Yin
,
W.
Zhang
,
Z.
Jiang
, and
L.
Pan
, “
Data-driven multi-objective predictive control of offshore wind farm based on evolutionary optimization
,”
Renewable Energy
160
,
974
986
(
2020
).
43.
M.
Fischetti
and
D.
Pisinger
, “
Mathematical optimization and algorithms for offshore wind farm design: An overview
,”
Bus. Inf. Syst. Eng.
61
,
469
485
(
2019
).
44.
S.
Tao
,
S.
Kuenzel
,
Q.
Xu
, and
Z.
Chen
, “
Optimal micro-siting of wind turbines in an offshore wind farm using Frandsen–Gaussian wake model
,”
IEEE Trans. Power Syst.
34
,
4944
4954
(
2019
).
45.
N.
Mittelmeier
,
T.
Blodau
, and
M.
Kühn
, “
Monitoring offshore wind farm power performance with SCADA data and an advanced wake model
,”
Wind Energy Sci.
2
,
175
187
(
2017
).
46.
R. J.
Adrian
,
C. D.
Meinhart
, and
C. D.
Tomkins
, “
Vortex organization in the outer region of the turbulent boundary layer
,”
J. Fluid Mech.
422
,
1
54
(
2000
).
47.
H.
Shiu
,
E.
Johnson
,
M.
Barone
,
R.
Phillips
,
W.
Straka
,
A.
Fontaine
,
M.
Jonson
 et al, “
A design of a hydrofoil family for current-driven marine-hydrokinetic turbines
,” in
2012 20th International Conference on Nuclear Engineering and the ASME 2012 Power Conference
(
American Society of Mechanical Engineers
,
2012
), pp.
839
847
.
48.
E.
Johnson
,
A.
Fontaine
,
M.
Jonson
,
R.
Meyer
,
W.
Straka
,
S.
Young
,
C.
van Dam
,
H.
Shiu
, and
M.
Barone
, “
A1: 8.7 scale water tunnel test of an axial flow water turbine
,” in
Proceedings of the 1st Marine Energy Technology Symposium, METS13
USDOE National Nuclear Security Administration (NNSA)
,
2013
, pp.
10
11
.
49.
N.
Tobin
,
H.
Zhu
, and
L.
Chamorro
, “
Spectral behaviour of the turbulence-driven power fluctuations of wind turbines
,”
J. Turbul.
16
,
832
846
(
2015
).
50.
N.
Tobin
,
A.
Hamed
, and
L.
Chamorro
, “
An experimental study on the effects of winglets on the wake and performance of a modelwind turbine
,”
Energies
8
,
11955
11972
(
2015
).
51.
N.
Tobin
,
A. M.
Hamed
, and
L. P.
Chamorro
, “
Fractional flow speed-up from porous windbreaks for enhanced wind-turbine power
,”
Boundary-Layer Meteorol.
163
,
253
271
(
2017
).
52.
A. M.
Hamed
,
Y.
Jin
, and
L. P.
Chamorro
, “
On the transient dynamics of the wake and trajectory of free falling cones with various apex angles
,”
Exp. Fluids
56
,
207
(
2015
).
53.
Y.
Jin
,
S.
Ji
,
B.
Liu
, and
L.
Chamorro
, “
On the role of thickness ratio and location of axis of rotation in the flat plate motions
,”
J. Fluids Struct.
64
,
127
137
(
2016
).
54.
T.
Von Karman
, “
Progress in the statistical theory of turbulence
,”
Proc. Natl. Acad. Sci. U. S. A.
34
,
530
(
1948
).
55.
H.
Liu
,
Y.
Jin
,
N.
Tobin
, and
L. P.
Chamorro
, “
Towards uncovering the structure of power fluctuations of wind farms
,”
Phys. Rev. E
96
,
063117
(
2017
).
You do not currently have access to this content.