Graphical Abstract Figure
Graphical Abstract Figure
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Abstract

The wake of wind turbines is a main concern for offshore wind farms, in which the wake width is a key index and needs to be accurately predicted. However, the existing wake width models have shortcomings in predicting the wake of wind turbines in different offshore environments. In view of this, large eddy simulation (LES) is adopted to simulate offshore wind turbines under various environmental conditions. The analyses show that there are evident differences in wake widths between horizontal and vertical directions. The variations in turbulence intensity and wind speed in the environment have significant effects on the wake width. By fitting the simulation results, a three-dimensional (3D) wake width model is proposed to predict the wake widths in horizontal and vertical directions, which considers the effects of lateral and vertical turbulence intensities on the wake width in different directions, and uses the thrust coefficient to reflect the effect of wind speed. The proposed 3D model is then compared with existing models through test cases, indicating that it is more accurate in predicting wake widths in horizontal and vertical directions under different environmental conditions, meanwhile showing good applicability in complex offshore environments.

References

1.
Barthelmie
,
R. J.
,
Pryor
,
S. C.
,
Frandsen
,
S. T.
,
Hansen
,
K. S.
,
Schepers
,
J. G.
,
Rados
,
K.
,
Schlez
,
W.
,
Neubert
,
A.
,
Jensen
,
L. E.
, and
Neckelmann
,
S.
,
2010
, “
Quantifying the Impact of Wind Turbine Wakes on Power Output at Offshore Wind Farms
,”
J. Atmos. Ocean. Technol.
,
27
(
8
), pp.
1302
1317
.
2.
Jensen
,
N. O.
,
1983
, “
A Note on Wind Generator Interaction
,” Technical Report No. Risø-M-2411, Risø National Laboratory, Roskilde, Denmark.
3.
Bastankhah
,
M.
, and
Porté-Agel
,
F.
,
2014
, “
A new Analytical Model for Wind-Turbine Wakes
,”
Renew. Energy
,
70
, pp.
116
123
.
4.
Cheng
,
Y.
,
Zhang
,
M. M.
,
Zhang
,
Z. L.
, and
Xu
,
J. Z.
,
2019
, “
A New Analytical Model for Wind Turbine Wakes Based on Monin-Obukhov Similarity Theory
,”
Appl. Energy
,
239
, pp.
96
106
.
5.
Frandsen
,
S.
,
Barthelmie
,
R.
,
Pryor
,
S.
,
Rathmann
,
O.
,
Larsen
,
S.
,
Højstrup
,
J.
, and
Thøgersen
,
M.
,
2006
, “
Analytical Modelling of Wind Speed Deficit in Large Offshore Wind Farms
,”
Wind Energy
,
9
(
1–2
), pp.
39
53
.
6.
He
,
R.
,
Yang
,
H.
,
Sun
,
H.
, and
Gao
,
X.
,
2021
, “
A Novel Three-Dimensional Wake Model Based on Anisotropic Gaussian Distribution for Wind Turbine Wakes
,”
Appl. Energy
,
296
, p.
117059
.
7.
Ishihara
,
T.
, and
Qian
,
G.-W.
,
2018
, “
A New Gaussian-Based Analytical Wake Model for Wind Turbines Considering Ambient Turbulence Intensities and Thrust Coefficient Effects
,”
J. Wind Eng. Ind. Aerodyn.
,
177
, pp.
275
292
.
8.
Tian
,
L. L.
,
Song
,
Y. L.
,
Xiao
,
P. C.
,
Zhao
,
N.
,
Shen
,
W. Z.
, and
Zhu
,
C. L.
,
2022
, “
A New Three-Dimensional Analytical Model for Wind Turbine Wake Turbulence Intensity Predictions
,”
Renew. Energy
,
189
, pp.
762
776
.
9.
Tian
,
L. L.
,
Zhu
,
W. J.
,
Shen
,
W. Z.
,
Zhao
,
N.
, and
Shen
,
Z. W.
,
2015
, “
Development and Validation of a New Two-Dimensional Wake Model for Wind Turbine Wakes
,”
J. Wind Eng. Ind. Aerodyn.
,
137
, pp.
90
99
.
10.
Cheng
,
W. C.
, and
Porté-Agel
,
F.
,
2018
, “
A Simple Physically-Based Model for Wind-Turbine Wake Growth in a Turbulent Boundary Layer
,”
Boundary Layer Meteorol.
,
169
(
1
), pp.
1
10
.
11.
Du
,
B. W.
,
Ge
,
M. W.
, and
Liu
,
Y. Q.
,
2022
, “
A Physical Wind-Turbine Wake Growth Model Under Different Stratified Atmospheric Conditions
,”
Wind Energy
,
25
(
10
), pp.
1812
1836
.
12.
Vahidi
,
D.
, and
Porté-Agel
,
F.
,
2022
, “
A Physics-Based Model for Wind Turbine Wake Expansion in the Atmospheric Boundary Layer
,”
J. Fluid Mech.
,
943
, p.
A49
.
13.
Liu
,
M. Q.
,
Liang
,
Z. C.
, and
Liu
,
H. X.
,
2022
, “
Numerical Investigations of Wake Expansion in the Offshore Wind Farm Using a Large Eddy Simulation
,”
Energies
,
15
(
6
), p.
2022
.
14.
Abkar
,
M.
, and
Porté-Agel
,
F.
,
2015
, “
Influence of Atmospheric Stability on Wind-Turbine Wakes: A Large-Eddy Simulation Study
,”
Phys. Fluids
,
27
(
3
), p.
035104
.
15.
Xie
,
S. B.
, and
Archer
,
C.
,
2015
, “
Self-Similarity and Turbulence Characteristics of Wind Turbine Wakes via Large-Eddy Simulation
,”
Wind Energy
,
18
(
10
), pp.
1815
1838
.
16.
Frandsen
,
S.
,
1992
, “
On the Wind Speed Reduction in the Center of Large Clusters of Wind Turbines
,”
J. Wind Eng. Ind. Aerodyn.
,
39
(
1–3
), pp.
251
265
.
17.
Niayifar
,
A.
, and
Porté-Agel
,
F.
,
2016
, “
Analytical Modeling of Wind Farms: A New Approach for Power Prediction
,”
Energies
,
9
(
9
), p.
741
.
18.
Carbajo Fuertes
,
F.
,
Markfort
,
C. D.
, and
Porté-Agel
,
F.
,
2018
, “
Wind Turbine Wake Characterization With Nacelle-Mounted Wind Lidars for Analytical Wake Model Validation
,”
Remote Sens.
,
10
(
5
), p.
668
.
19.
Aitken
,
M. L.
,
Banta
,
R. M.
,
Pichugina
,
Y. L.
, and
Lundquist
,
J. K.
,
2014
, “
Quantifying Wind Turbine Wake Characteristics From Scanning Remote Sensor Data
,”
J. Atmos. Ocean. Technol.
,
31
(
4
), pp.
765
787
.
20.
Wu
,
Y. T.
, and
Porté-Agel
,
F.
,
2013
, “
Simulation of Turbulent Flow Inside and Above Wind Farms: Model Validation and Layout Effects
,”
Boundary Layer Meteorol.
,
146
(
2
), pp.
181
205
.
21.
Smagorinsky
,
J.
,
1963
, “
General Circulation Experiments With the Primitive Equations: I. The Basic Experiment
,”
Mon. Weather Rev.
,
91
(
3
), pp.
99
164
.
22.
Moeng
,
C. H.
,
1984
, “
A Large-Eddy-Simulation Model for the Study of Planetary Boundary-Layer Turbulence
,”
J. Atmos. Sci.
,
41
(
13
), pp.
2052
2062
.
23.
Stull
,
R. B.
,
2009
,
An Introduction to Boundary Layer Meteorology
,
Springer
,
Dordrecht, Netherlands
.
24.
Churchfield
,
M. J.
,
Lee
,
S.
,
Michalakes
,
J.
, and
Moriarty
,
P. J.
,
2012
, “
A Numerical Study of the Effects of Atmospheric and Wake Turbulence on Wind Turbine Dynamics
,”
J. Turbul.
,
13
(
14
), pp.
1
32
.
25.
Calaf
,
M.
,
Meneveau
,
C.
, and
Meyers
,
J.
,
2010
, “
Large Eddy Simulation Study of Fully Developed Wind-Turbine Array Boundary Layers
,”
Phys. Fluids
,
22
(
1
), p.
015110
.
26.
Wu
,
Y. T.
, and
Porté-Agel
,
F.
,
2011
, “
Large-Eddy Simulation of Wind-Turbine Wakes: Evaluation of Turbine Parametrisations
,”
Boundary Layer Meteorol.
,
138
(
3
), pp.
345
366
.
27.
Sorensen
,
J. N.
, and
Shen
,
W. Z.
,
2002
, “
Numerical Modeling of Wind Turbine Wakes
,”
ASME J. Fluids Eng.
,
124
(
2
), pp.
393
399
.
28.
Martínez-Tossas
,
L. A.
,
Churchfield
,
M. J.
, and
Leonardi
,
S.
,
2015
, “
Large Eddy Simulations of the Flow Past Wind Turbines: Actuator Line and Disk Modeling
,”
Wind Energy
,
18
(
6
), pp.
1047
1060
.
29.
Stevens
,
R. J. A. M.
,
Martínez-Tossas
,
L. A.
, and
Meneveau
,
C.
,
2018
, “
Comparison of Wind Farm Large Eddy Simulations Using Actuator Disk and Actuator Line Models With Wind Tunnel Experiments
,”
Renew. Energy
,
116
, pp.
470
478
.
30.
Porté-Agel
,
F.
,
Wu
,
Y. T.
,
Lu
,
H.
, and
Conzemius
,
R. J.
,
2011
, “
Large-Eddy Simulation of Atmospheric Boundary Layer Flow Through Wind Turbines and Wind Farms
,”
J. Wind Eng. Ind. Aerodyn.
,
99
(
4
), pp.
154
168
.
31.
Jonkman
,
J. M.
,
2007
, “
Dynamics Modeling and Loads Analysis of an Offshore Floating Wind Turbine
,” Technical Report No. NREL/TP-500-41958, National Renewable Energy Laboratory, Golden, Colorado, USA.
32.
Jonkman
,
J.
,
Butterfield
,
S.
,
Musial
,
W.
, and
Scott
,
G.
,
2009
, “
Definition of a 5-MW Reference Wind Turbine for Offshore System Development
,” Technical Report No. NREL/TP-500-38060, National Renewable Energy Laboratory, Golden, CO, USA.
33.
Fleming
,
P. A.
,
Gebraad
,
P. M. O.
,
Lee
,
S.
,
van Wingerden
,
J. W.
,
Johnson
,
K.
,
Churchfield
,
M.
,
Michalakes
,
J.
,
Spalart
,
P.
, and
Moriarty
,
P.
,
2014
, “
Evaluating Techniques for Redirecting Turbine Wakes Using SOWFA
,”
Renew. Energy
,
70
, pp.
211
218
.
34.
Gebraad
,
P. M. O.
,
Teeuwisse
,
F. W.
,
van Wingerden
,
J. W.
,
Fleming
,
P. A.
,
Ruben
,
S. D.
,
Marden
,
J. R.
, and
Pao
,
L. Y.
,
2016
, “
Wind Plant Power Optimization Through Yaw Control Using a Parametric Model for Wake Effects—A CFD Simulation Study
,”
Wind Energy
,
19
(
1
), pp.
95
114
.
35.
Issa
,
R. I.
,
1986
, “
Solution of the Implicitly Discretised Fluid Flow Equations by Operator-Splitting
,”
J. Comput. Phys.
,
62
(
1
), pp.
40
65
.
36.
Archer
,
C. L.
,
Mirzaeisefat
,
S.
, and
Lee
,
S.
,
2013
, “
Quantifying the Sensitivity of Wind Farm Performance to Array Layout Options Using Large-Eddy Simulation
,”
Geophys. Res. Lett.
,
40
(
18
), pp.
4963
4970
.
37.
Desmond
,
C.
,
Murphy
,
J.
,
Blonk
,
L.
, and
Haans
,
W.
,
2016
, “
Description of an 8 MW Reference Wind Turbine
,”
J. Phys.: Conf. Ser.
,
753
(
9
), p.
092013
.
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