This paper describes an experimental study of the asymmetries and self-similarity/self-preservation of yawed rotor wakes and the similarity between different yaw angle scenarios. The wake asymmetry is found to increase with increasing yaw angle and also increases in the streamwise direction before the wake reaches a state of self-similarity. Furthermore, if we divide the profiles into left and right parts, the normalized profiles are the same for different streamwise locations even in the region where the profiles have not reached a state of self-similarity. The relation between the asymmetry of the velocity deficit profiles and the yaw angle is derived theoretically and validated by the present experimental measurements. A critical yaw angle is determined for the similarity in the streamwise evolution of the wake between different yaw angle scenarios. Specifically, there is a similarity between different yaw angle scenarios when the yaw angle is below the critical value. The results of this study will be helpful in understanding yawed rotor wakes and establishing a yawed rotor wake model.

1.
P.
Veers
,
K.
Dykes
,
E.
Lantz
 et al, “
Grand challenges in the science of wind energy
,”
Science
366
(
6464
),
eaau2027
(
2019
).
2.
M. S.
Adaramola
and
P.-Å.
Krogstad
, “
Experimental investigation of wake effects on wind turbine performance
,”
Renewable Energy
36
(
8
),
2078
2086
(
2011
).
3.
R. J.
Barthelmie
,
S. C.
Pryor
,
S. T.
Frandsen
 et al, “
Quantifying the impact of wind turbine wakes on power output at offshore wind farms
,”
J. Atmos. Oceanic Technol.
27
(
8
),
1302
1317
(
2010
).
4.
C. L.
Archer
,
A.
Vasel-Be-Hagh
,
C.
Yan
 et al, “
Review and evaluation of wake loss models for wind energy applications
,”
Appl. Energy
226
(
4
),
1187
1207
(
2018
).
5.
E.
Simley
,
P.
Fleming
, and
J.
King
, “
Field validation of wake steering control with wind direction variability
,”
J. Phys.: Conf. Ser.
1452
,
12012
(
2020
).
6.
F.
Porté-Agel
,
M.
Bastankhah
, and
S.
Shamsoddin
, “
Wind-turbine and wind-farm flows: A review
,”
Boundary-Layer Meteorol.
174
(
1
),
1
59
(
2020
).
7.
P. M.
Gebraad
,
F. C.
van Dam
, and
J.-W.
van Wingerden
, “
A model-free distributed approach for wind plant control
,” in
2013 American Control Conference
(
IEEE
,
2013
), pp.
628
633
.
8.
K. E.
Johnson
and
G.
Fritsch
, “
Assessment of extremum seeking control for wind farm energy production
,”
Wind Eng.
36
(
6
),
701
715
(
2012
).
9.
P. A.
Fleming
,
P. M.
Gebraad
,
S.
Lee
 et al, “
Evaluating techniques for redirecting turbine wakes using SOWFA
,”
Renewable Energy
70
(
6
),
211
218
(
2014
).
10.
D.
Dilip
and
F.
Porté-Agel
, “
Wind turbine wake mitigation through blade pitch offset
,”
Energies
10
(
6
),
757
(
2017
).
11.
J.
Lee
,
E.
Son
,
B.
Hwang
 et al, “
Blade pitch angle control for aerodynamic performance optimization of a wind farm
,”
Renewable Energy
54
,
124
130
(
2013
).
12.
A.
Vasel-Be-Hagh
and
C. L.
Archer
, “
Wind farms with counter-rotating wind turbines
,”
Sustainable Energy Technol. Assess.
24
(
1
),
19
30
(
2017
).
13.
Á.
Jiménez
,
A.
Crespo
, and
E.
Migoya
, “
Application of a LES technique to characterize the wake deflection of a wind turbine in yaw
,”
Wind Energy
13
(
6
),
559
572
(
2010
).
14.
J.
Bartl
,
F.
Mühle
, and
L.
Sætran
, “
Wind tunnel study on power output and yaw moments\break for two yaw-controlled model wind turbines
,”
Wind Energy Sci.
3
(
2
),
489
502
(
2018
).
15.
J.
Bartl
,
F.
Mühle
,
J.
Schottler
 et al, “
Wind tunnel experiments on wind turbine wakes in yaw: Effects of inflow turbulence and shear
,”
Wind Energy Sci.
3
(
1
),
329
343
(
2018
).
16.
S.
Guntur
,
N.
Troldborg
, and
M.
Gaunaa
, ed., “
Application of engineering models to predict wake deflection due to a tilted wind turbine
,” in
Proceedings of EWEA 2012—European Wind Energy Conference & Exhibition European Wind Energy Association (EWEA)
,
2012
.
17.
J.
Bossuyt
,
R.
Scott
,
N.
Ali
 et al, “
Quantification of wake shape modulation and deflection for tilt and yaw misaligned wind turbines
,”
J. Fluid Mech.
917
,
908
(
2021
).
18.
D.
Medici
and
P. H.
Alfredsson
, “
Measurements on a wind turbine wake: 3D effects and bluff body vortex shedding
,”
Wind Energy
9
(
3
),
219
236
(
2006
).
19.
K. A.
Kragh
and
M. H.
Hansen
, “
Load alleviation of wind turbines by yaw misalignment
,”
Wind Energy
17
(
7
),
971
982
(
2014
).
20.
W.
Miao
,
C.
Li
,
G.
Pavesi
 et al, “
Investigation of wake characteristics of a yawed HAWT and its impacts on the inline downstream wind turbine using unsteady CFD
,”
J. Wind Eng. Ind. Aerodyn.
168
(
1
),
60
71
(
2017
).
21.
P.
Gebraad
,
J. J.
Thomas
,
A.
Ning
 et al, “
Maximization of the annual energy production of wind power plants by optimization of layout and yaw-based wake control
,”
Wind Energy
20
(
1
),
97
107
(
2017
).
22.
M.
Bromm
,
A.
Rott
,
H.
Beck
 et al, “
Field investigation on the influence of yaw misalignment on the propagation of wind turbine wakes
,”
Wind Energy
21
(
11
),
1011
1028
(
2018
).
23.
M. F.
Howland
,
S. K.
Lele
, and
J. O.
Dabiri
, “
Wind farm power optimization through wake steering
,”
Proc. Natl. Acad. Sci.
116
(
29
),
14495
14500
(
2019
).
24.
Z.
Ye
,
X.
Wang
,
Z.
Chen
 et al, “
Unsteady aerodynamic characteristics of a horizontal wind turbine under yaw and dynamic yawing
,”
Acta Mech. Sin.
36
(
2
),
320
338
(
2020
).
25.
S.
Macrí
,
S.
Aubrun
,
A.
Leroy
 et al, “
Experimental investigation of wind turbine wake and load dynamics during yaw maneuvers
,”
Wind Energy Sci.
6
(
2
),
585
599
(
2021
).
26.
P. A.
Fleming
,
A. K.
Scholbrock
,
A.
Jehu
 et al, “
Field-test results using a nacelle-mounted lidar for improving wind turbine power capture by reducing yaw misalignment
,”
J. Phys.: Conf. Ser.
524
,
12002
(
2014
).
27.
P.
Fleming
,
P. M.
Gebraad
,
S.
Lee
 et al, “
Simulation comparison of wake mitigation control strategies for a two-turbine case
,”
Wind Energy
18
(
12
),
2135
2143
(
2015
).
28.
P.
Fleming
,
J.
Annoni
,
M.
Churchfield
 et al, “
A simulation study demonstrating the importance of large-scale trailing vortices in wake steering
,”
Wind Energy Sci.
3
(
1
),
243
255
(
2018
).
29.
L. A.
Martínez-Tossas
,
J.
Annoni
,
P. A.
Fleming
 et al, “
The aerodynamics of the curled wake: A simplified model in view of flow control
,”
Wind Energy Sci.
4
(
1
),
127
138
(
2019
).
30.
C. J.
Bay
,
J.
King
,
P.
Fleming
 et al, “
Unlocking the full potential of wake steering: Implementation and assessment of a controls-oriented model
,”
Wind Energ. Sci. Discuss.
2019
,
1
20
.
31.
J.
Meyers
and
C.
Meneveau
, “
Flow visualization using momentum and energy transport tubes and applications to turbulent flow in wind farms
,”
J. Fluid Mech.
715
,
335
358
(
2013
).
32.
I.
Grant
,
P.
Parkin
, and
X.
Wang
, “
Optical vortex tracking studies of a horizontal axis wind turbine in yaw using laser-sheet, flow visualization
,”
Exp. Fluids
23
(
6
),
513
519
(
1997
).
33.
W.
Haans
,
T.
Sant
,
G.
van Kuik
 et al, “
Measurement of tip vortex paths in the wake of a HAWT under yawed flow conditions
,”
J. Sol. Energy Eng.
127
(
4
),
456
463
(
2005
).
34.
M.
Bastankhah
and
F.
Porté-Agel
, “
Experimental and theoretical study of wind turbine wakes in yawed conditions
,”
J. Fluid Mech.
806
,
506
541
(
2016
).
35.
N. O.
Jensen
,
A Note on Wind Generator Interaction
(
Risø National Laboratory
,
Roskilde
,
1983
).
36.
J. F.
Ainslie
, “
Calculating the flow field in the wake of wind turbines
,”
J. Wind Eng. Ind. Aerodyn.
27
(
1–3
),
213
224
(
1988
).
37.
M.
Bastankhah
and
F.
Porté-Agel
, “
A new analytical model for wind-turbine wakes
,”
Renewable Energy
70
,
116
123
(
2014
).
38.
T.
Ishihara
and
G.-W.
Qian
, “
A new Gaussian-based analytical wake model for wind turbines considering ambient turbulence intensities and thrust coefficient effects
,”
J. Wind Eng. Ind. Aerodyn.
177
,
275
292
(
2018
).
39.
M.
Abkar
,
J.
Sørensen
, and
F.
Porté-Agel
, “
An analytical model for the effect of vertical wind veer on wind turbine wakes
,”
Energies
11
(
7
),
1838
(
2018
).
40.
S.
Shamsoddin
and
F.
Porté-Agel
, “
A model for the effect of pressure gradient on turbulent axisymmetric wakes
,”
J. Fluid Mech.
837
,
R3
(
2018
).
41.
Y.
Cheng
,
M.
Zhang
,
Z.
Zhang
 et al, “
A new analytical model for wind turbine wakes based on Monin-Obukhov similarity theory
,”
Appl. Energy
239
,
96
106
(
2019
).
42.
P. M. O.
Gebraad
,
F. W.
Teeuwisse
,
J. W.
van Wingerden
 et al, “
Wind plant power optimization through yaw control using a parametric model for wake effects-a CFD simulation study
,”
Wind Energy
19
(
1
),
95
114
(
2016
).
43.
C. R.
Shapiro
,
D. F.
Gayme
, and
C.
Meneveau
, “
Modelling yawed wind turbine wakes: A lifting line approach
,”
J. Fluid Mech.
841
,
1261
(
2018
).
44.
G.-W.
Qian
and
T.
Ishihara
, “
A new analytical wake model for yawed wind turbines
,”
Energies
11
(
3
),
665
(
2018
).
45.
D.-Z.
Wei
,
N.-N.
Wang
, and
D.-C.
Wan
, “
Modelling yawed wind turbine wakes: Extension of a Gaussian-based wake model
,”
Energies
14
(
15
),
4494
(
2021
).
46.
C. R.
Shapiro
,
G. M.
Starke
,
C.
Meneveau
 et al, “
A wake modeling paradigm for wind farm design and control
,”
Energies
12
(
15
),
2956
(
2019
).
47.
I.
Grant
and
P.
Parkin
, “
A DPIV study of the trailing vortex elements from the blades of a horizontal axis wind turbine in yaw
,”
Exp. Fluids
28
(
4
),
368
376
(
2000
).
48.
M.
Gaumond
,
P. ‐E.
Réthoré
,
S.
Ott
 et al, “
Evaluation of the wind direction uncertainty and its impact on wake modeling at the Horns Rev offshore wind farm
,”
Wind Energy
17
(
8
),
1169
1178
(
2014
).
49.
B.
Dou
,
M.
Guala
,
L.
Lei
 et al, “
Wake model for horizontal-axis wind and hydrokinetic turbines in yawed conditions
,”
Appl. Energy
242
,
1383
1395
(
2019
).
50.
B.
Dou
,
T.
Qu
,
L.
Lei
 et al, “
Optimization of wind turbine yaw angles in a wind farm using a three-dimensional yawed wake model
,”
Energy
209
(
5
),
118415
(
2020
).
51.
H.
Zong
and
F.
Porté-Agel
, “
A point vortex transportation model for yawed wind turbine wakes
,”
J. Fluid Mech.
890
,
A8
(
2020
).
52.
M.
Bastankhah
,
C. R.
Shapiro
,
S.
Shamsoddin
,
D. F.
Gayme
, and
C.
Meneveau
, “
A vortex sheet based analytical model of the curled wake behind yawed wind turbines
,”
J. Fluid Mech.
933
,
A2
(
2022
).
53.
Z.
Li
and
X.
Yang
, “
Large-eddy simulation on the similarity between wakes of wind turbines with different yaw angles
,”
J. Fluid Mech.
921
,
31012
(
2021
).
54.
T. Y.
Chen
and
L. R.
Liou
, “
Blockage corrections in wind tunnel tests of small horizontal-axis wind turbines
,”
Exp. Therm. Fluid Sci.
35
(
3
),
565
569
(
2011
).
55.
L. P.
Chamorro
,
R. E. A.
Arndt
, and
F.
Sotiropoulos
, “
Reynolds number dependence of turbulence statistics in the wake of wind turbines
,”
Wind Energy
15
(
5
),
733
(
2012
).
56.
L. P.
Chamorro
and
F.
Porté-Agel
, “
A wind-tunnel investigation of wind-turbine wakes: Boundary-layer turbulence effects
,”
Boundary-Layer Meteorol.
132
(
1
),
129
149
(
2009
).
57.
L. J.
Vermeer
,
J. N.
Sørensen
, and
A.
Crespo
, “
Wind turbine wake aerodynamics
,”
Prog. Aerosp. Sci.
39
(
6–7
),
467
(
2003
).
58.
X.
Wang
and
G. A.
Kikkert
, “
Behaviour of oblique jets released in a moving ambient
,”
J. Hydraul. Res.
52
(
4
),
490
501
(
2014
).
59.
P.
Lyu
,
W.-L.
Chen
,
H.
Li
 et al, “
A numerical study on the development of self-similarity in a wind turbine wake using an improved pseudo-spectral large-eddy simulation solver
,”
Energies
12
(
4
),
643
(
2019
).
60.
X.-L.
Xiong
,
P.
Lyu
,
W.-L.
Chen
 et al, “
Self-similarity in the wake of a semi-submersible offshore wind turbine considering the interaction with the wake of supporting platform
,”
Renewable Energy
156
(
6
),
328
341
(
2020
).
61.
I.
Neunaber
,
J.
Peinke
, and
M.
Obligado
, “
Application of the Townsend-George theory for free shear flows to single and double wind turbine wakes–A wind tunnel study
,”
Wind Energ. Sci.
7
(
1
),
201
(
2022
).
62.
S.
Xie
and
C.
Archer
, “
Self‐similarity and turbulence characteristics of wind turbine wakes via large‐eddy simulation
,”
Wind Energy
18
(
10
),
1815
(
2015
).
63.
M.
Abkar
and
F.
Porté-Agel
, “
Influence of atmospheric stability on wind-turbine wakes: A large-eddy simulation study
,”
Phys. Fluids
27
(
3
),
035104
(
2015
).
64.
C.-R.
Chu
and
P.-H.
Chiang
, “
Turbulence effects on the wake flow and power production of a horizontal-axis wind turbine
,”
J. Wind Eng. Ind. Aerodyn.
124
,
82
(
2014
).
65.
W.
Tian
,
A.
Ozbay
, and
H.
Hu
, “
Effects of incoming surface wind conditions on the wake characteristics and dynamic wind loads acting on a wind turbine model
,”
Phys. Fluids
26
(
12
),
125108
(
2014
).
66.
T.
Burton
,
N.
Jenkins
,
D.
Sharpe
 et al,
Wind Energy Handbook
(
John Wiley & Sons, Ltd
,
Chichester
,
2011
).
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