With the increase in wind farms in hilly terrain, it is particularly important to explore the downstream wake expansion of wind turbines in hilly terrains. This study established two complex terrain-applicable super-Gaussian wake models based on the Coanda effect and the wind speed-up phenomenon. Then, by considering the wind shear effect and the law of mass conservation, two three-dimensional (3D) super-Gaussian wake models were obtained. The 3D super-Gaussian models were used to describe the shape of the wake deficit and could reflect the wake changes in the full wake region. The introduction of the Coanda effect could reflect the sinking of the wind turbine wake on the top of a hilly terrain. And considering that the wind speed-up phenomenon could better reflect the incoming velocity distribution of the actual hilly terrain. The validation results demonstrated that the prediction results of the 3D super-Gaussian wake models had negligible relative errors compared to the measured data and could better describe the vertical and horizontal expansion changes of the downstream wake. The models established in this study can assist with the development of complex terrain models and super-Gaussian models, as well as providing guidance for power prediction and wind turbine control strategies in complex terrain.

1.
S.
Dongran
,
L.
Ziqun
,
W.
Lei
,
J.
Fangjun
,
H.
Chaoneng
,
E.
Xia
et al, “
Energy capture efficiency enhancement of wind turbines via stochastic model predictive yaw control based on intelligent scenarios generation
,”
Appl. Energy
312
,
118773
(
2022
).
2.
S.
Dongran
,
T.
Yanping
,
W.
Lei
,
J.
Fangjun
,
L.
Ziqun
,
H.
Chaoneng
et al, “
Coordinated optimization on energy capture and torque fluctuation of wind turbines via variable weight NMPC with fuzzy regulator
,”
Appl. Energy
312
,
118821
(
2022
).
3.
J.
Feng
and
W. Z.
Shen
, “
Wind farm layout optimization in complex terrain: A preliminary study on a Gaussian hill
,”
J. Phys.
524
,
012146
(
2014
).
4.
P. H.
Alfredsson
and
A.
Segalini
, “
Introduction wind farms in complex terrains: An introduction
,”
Philos. Trans. R. Soc., A
375
,
20160096
(
2017
).
5.
E.
Mahmoud
,
A.
Maryam
,
A.
Ashraf
, and
Y. E. S.
Mohamed
, “
A review of wind turbines in complex terrain
,”
Int. J. Thermofluids
17
,
100289
(
2023
).
6.
S.
Cheng
,
M.
Elgendi
,
F.
Lu
, and
L. P.
Chamorro
, “
On the wind turbine wake and forest terrain interaction
,”
Energies
14
,
7204
(
2021
).
7.
F.
Porté-Agel
,
M.
Bastankhah
, and
S.
Shamsoddin
, “
Wind-turbine and wind-farm flows: A review
,”
Boundary-Layer Meteorol.
174
,
1
59
(
2020
).
8.
N. O.
Jensen
A note on wind generator interaction
,”
Risø National Laboratory
2411
, 1 (
1983
).
9.
S.
Frandsen
,
R.
Barthelmie
,
S.
Pryor
,
O.
Rathmann
,
S.
Larsen
,
J.
Højstrup
, et al. “
Analytical modelling of wind speed deficit large offshore wind farms
,”
Wind Energy.
9
,
39
53
(
2006
).
10.
G. C.
Larsen
and
A.
Crespo
, “
Wind turbine wakes for wind energy
,”
Wind Energy
14
,
797
798
(
2011
).
11.
M.
Bastankhah
and
F.
Porté-Agel
, “
A new analytical model for wind-turbine wakes
,”
Renewable Energy
70
,
116
123
(
2014
).
12.
F.
Blondel
and
M.
Cathelain
, “
An alternative form of the super-Gaussian wind turbine wake model
,”
Wind Energy Sci.
5
,
1225
1236
(
2020
).
13.
M.
Cathelain
,
F.
Blondel
,
P. A.
Joulin
, and
P.
Bozonnet
, “
Calibration of a super-Gaussian wake model with a focus on near-wake characteristics
,”
J. Phys.
1618
,
062008
(
2020
).
14.
X.
Gao
,
H.
Yang
, and
L.
Lu
, “
Optimization of wind turbine layout position in a wind farm using a newly-developed two-dimensional wake model
,”
Appl. Energy
174
,
192
200
(
2016
).
15.
X.
Gao
,
B.
Li
,
T.
Wang
,
H.
Sun
,
H.
Yang
,
Y.
Li
et al, “
Investigation and validation of 3D wake model for horizontal-axis wind turbines based on filed measurements
,”
Appl. Energy
260
,
114272
(
2020
).
16.
X.
Gao
,
S.
Zhang
,
L.
Li
,
S.
Xu
,
Y.
Chen
,
X.
Zhu
et al, “
Quantification of 3D spatiotemporal inhomogeneity for wake characteristics with validations from field measurement and wind tunnel test
,”
Energy
254
,
124277
(
2022
).
17.
H.
Sun
and
H.
Yang
, “
Study on an innovative three-dimensional wind turbine wake model
,”
Appl. Energy
226
,
483
493
(
2018
).
18.
R.
He
,
H.
Yang
,
H.
Sun
, and
X.
Gao
, “
A novel three-dimensional wake model based on anisotropic Gaussian distribution for wind turbine wakes
,”
Appl. Energy
296
,
117059
(
2021
).
19.
X.
Gao
,
L.
Li
,
S.
Zhang
,
X.
Zhu
,
H.
Sun
,
H.
Yang
et al, “
LiDAR-based observation and derivation of large-scale wind turbine's wake expansion model downstream of a hill
,”
Energy
259
,
125051
(
2022
).
20.
H.
Sun
,
H.
Yang
, and
X.
Gao
, “
Investigation into wind turbine wake effect on complex terrain
,”
Energy
269
,
126767
(
2023
).
21.
R.
Brogna
,
J.
Feng
,
J. N.
Sørensen
,
W. Z.
Shen
, and
F.
Porté-Agel
, “
A new wake model and comparison of eight algorithms for layout optimization of wind farms in complex terrain
,”
Appl. Energy
259
,
114189
(
2020
).
22.
W.
Tian
,
K.
Zheng
, and
H.
Hu
, “
Investigation of the wake propagation behind wind turbines over hilly terrain with different slope gradients
,”
J. Wind Eng. Ind. Aerodyn.
215
,
104683
(
2021
).
23.
A.
Hyvärinen
,
G.
Lacagnina
, and
A.
Segalini
, “
A wind-tunnel study of the wake development behind wind turbines over sinusoidal hills
,”
Wind Energy
21
,
605
617
(
2018
).
24.
S.
Shamsoddin
and
F.
Porté-Agel
, “
Wind turbine wakes over hills
,”
J. Fluid Mech.
855
,
671
702
(
2018
).
25.
X.
Yang
,
M.
Pakula
, and
F.
Sotiropoulos
, “
Large-eddy simulation of a utility-scale wind farm in complex terrain
,”
Appl. Energy
229
,
767
777
(
2018
).
26.
J. Y. J.
Kuo
,
D. A.
Romero
,
J. C.
Beck
, and
C. H.
Amon
, “
Wind farm layout optimization on complex terrains—Integrating a CFD wake model with mixed-integer programming
,”
Appl. Energy
178
,
404
414
(
2016
).
27.
W. Z.
Shen
,
W. J.
Zhu
,
E.
Barlas
, and
Y.
Li
, “
Advanced flow and noise simulation method for wind farm assessment in complex terrain
,”
Renewable Energy
143
,
1812
1825
(
2019
).
28.
O. M. A. M.
Ibrahim
,
S.
Yoshida
,
M.
Hamasaki
, and
A.
Takada
, “
Wind turbine wake modeling in accelerating wind field: A preliminary study on a two-dimensional hill
,”
Fluids
4
,
153
(
2019
).
29.
A.
Abdelkhalig
,
M.
Elgendi
, and
M. Y. E.
Selim
, “
Review on validation techniques of blade element momentum method implemented in wind turbines
,”
IOP Conf. Ser.
1074
,
012008
(
2022
).
30.
S.
Zhang
,
X.
Gao
,
W.
Ma
,
H.
Lu
,
T.
Lv
,
S.
Xu
et al, “
Derivation and verification of three-dimensional wake model of multiple wind turbines based on super-Gaussian function
,”
Renewable Energy
215
,
118968
(
2023
).
31.
J.
Feng
,
W. Z.
Shen
, and
Y.
Li
, “
An optimization framework for wind farm design in complex terrain
,”
Appl. Sci.
8
,
2053
(
2018
).
32.
J. C.
Kaimal
and
J. J.
Finnigan
,
Atmospheric Boundary Layer Flows: Their Structure and Measurement
(
Oxford University Press
,
1994
).
33.
D. R.
Lemelin
,
D.
Surry
, and
A. G.
Davenport
, “
Simple approximations for wind speed-up over hills
,”
J. Wind Eng. Ind. Aerodyn.
28
,
117
127
(
1988
).
34.
H. G.
Kim
,
C. M.
Lee
,
H. C.
Lim
, and
N. H.
Kyong
, “
An experimental and numerical study on the flow over two-dimensional hills
,”
J. Wind Eng. Ind. Aerodyn.
66
,
17
33
(
1997
).
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