活動現場為 國立成功大學工程科學系 吳毓庭助理教授於 10/1(二) 在國立高雄科技大學 建工校區

1. 大型風力發電廠之發電效率分析與預測
吳毓庭 Wu Yu-Ting
國立成功大學工程科學系
Dept. of Engineering Science
National Cheng Kung University
Taken in the EPFL WIRE wind tunnel

2. Horns Rev I offshore wind farm

5. Horns Rev I offshore wind farm
Horns Rev II offshore wind farm
1 km
2 km

6. 1 km
1 km
Nysted offshore wind farm
Lillgrund offshore wind farm

7. One big issue- power deficits
1 km

8. Introduction
 In a large wind farm, the power losses due to turbine wakes are influenced by
[1] Inflow condition: wind direction, wind speed, turbulence intensity, turbulent stress
[2] Wind turbine design: blade geometry, generator efficiency
[3] Wind farm layout: turbine spacing, turbine siting density
 Accurate numerical prediction can provide insight into the characteristics of turbine
wakes and power losses in a large wind farm.
 Challenges include turbulence modeling and turbine parameterization
 LES + actuator-disk models: Jimenez et al (2007, 2008, 2010), Ivanell et al (2009), Calaf et al (2010,
2011), Meyers and Meneveau (2011, 2013)
[1] Turbulence modeling: large-eddy simulation (LES) technique
[2] Turbine parameterizations: actuator-disk/-line/-surface models
Porté-Agel et al (2000), Bou-Zeid et al (2005), Stoll and Porté-Agel (2006), Lu and Porté-Agel (2010, 2013)
Sørensen and Kock (1995), Sørensen and Shen (2002), Shen et al (2009)
8
 Rigorous validation studies for turbine wakes in turbulent boundary layer are needed

9. Rough terrain
(forest)
Less rough
(prairie)
Smooth surface
(sea surface)
Wu and Porté-Agel (2012)

10. Rough terrain
(forest)
Less rough
(prairie)
Smooth surface
(sea surface)
Wu and Porté-Agel (2012)
How far the downstream turbines should be installed

11. Solution
Numerical modelling
Laboratory experiment Field campaign

12. Wind tunnel facility
►28 m × 2.57m × 2 m test section
►25 m/s (90 km/h) maximum velocity
► < 0.1 % free stream turbulence intensity
► 5:1 contraction ratio
► 130 kW fan power
► 16 levels of air temperature control
► 20 m floor temperature control (test section)
►[−10°C ; 120°C] air/floor temperature range
► 450 kW heating and cooling units

13. Wind tunnel facility

17. Wind measurements
Meteorological Masts
Remote-sensing Measurements (e.g., LIDAR, SODAR)
17

18. Meteorological Masts
18

19. 台電離岸式測風塔
19

21. 海氣象觀測塔設備
氣象儀器
儀器
項目
風速計 風向計 大氣壓力計 溫溼度計 雨量計 日輻射儀
廠牌-型號
Thies
4.3351.10.000
Thies
4.3150.10.400
Thies
3.1157.10.000
Driesen+Kern Gmbh
DKRF400
Campbell
TE525MM
Kipp&Zonen
CNR4
規格
範圍 0.3~70 m/s 0~360° 300~1100 mb
-40~+80°C
0~100% RH
4.73 ml/tip
300 to 2800 nm
4.5 to 42 μm
解析度
0.05 m wind
run
0.1° 0.01hPa
0.01°C
0.05%
0.1 mm/tip 0.01 w/m2
精度 < 0.2 m/s 1° ± 0.25 hPa
±0.3°C
±1.8%RH
±1% <1%
安裝於塔架
位置(數量)
EL+95m(2)
EL+50m(1)
EL+30m(1)
EL+10m(1)
EL+95m(1)
EL+50m(1)
EL+30m(1)
EL+10m(1)
EL+95m(1)
EL+10m(1)
EL+95m(1)
EL+10m(1)
EL+10m(1) EL+19m(1)

22. 22

23. LIDAR(光達)
• LIDAR: Light Detection And Ranging
23
3D scanning LIDAR
Galion HALO Photonics WindCube

24. LIDAR(光達)
• HALO Photonics 3D scanning LIDAR
24

25. LIDAR(光達)
• LIDAR: Light Detection And Ranging
25
Profiling LIDAR

26. Light Doppler shift
𝜆 − 𝜆0
𝜆0
=
𝑣
𝑐
𝜆 = Observed wavelength
𝑣 = Emitted velocity of light source
𝑐 = Speed of light
𝜆0= Rest emitted wavelength
Eq:
Observer
Source

27. WindSentinel
 Floating LiDAR device by AXYS
 Buoy System (Vindicator,
Anemometers, Solar Panels,
Turbines, Batteries, etc)
 Vindicator by OADS (Optical Air
Data Systems )

28. WindSentinel
RM YOUNG
Wind Wind Sensor 3.72mZephyr Airdolphin Turbine
SANYO Solar Panels
VectorAnemometer 3.45m
Vector Wind Vane 3.36m
Temperature RH
Vindicator
55m
71m
90m
110m
150m
200m
= deg
R 53.6m
R40.2m
R 29.5m
R 24.1m
R 19.0m
R 14.7m
R
LiDAR
Vindicator has three laser beams shooting simultaneously

29. WindSentinel
𝑈 𝑅1(𝛼1)
𝑈 𝑅2(𝛼2)𝑈 𝑅3(𝛼3)
Buoy
LIDAR
𝑢
𝑣
𝑈 𝑅1
𝑈 𝑅2
𝑈 𝑅3
=
sin 𝛼1 cos 𝛼1 1
sin 𝛼2 cos 𝛼2 1
sin 𝛼3 cos 𝛼3 1
sin 𝛽 0 0
0 sin 𝛽 0
0 0 cos 𝛽
𝑢
𝑣
𝑤
⟹
𝑈 𝑅1
𝑈 𝑅2
𝑈 𝑅3
= 𝐵
𝑢
𝑣
𝑤
⟹ 𝒖 𝒐𝒃𝒔 =
𝑢
𝑣
𝑤
= 𝐵−1
𝑈 𝑅1
𝑈 𝑅2
𝑈 𝑅3

30. WindSentinel
Gyroscope
 Angles: Pitch(𝜃), Roll(𝜙), Yaw(𝜓)
 Angular speeds: Pitch( ሶ𝜃), Roll( ሶ𝜙), Yaw( ሶ𝜓)
𝑼 = 𝑻 𝒖 𝒐𝒃𝒔 + 𝛀 𝒐𝒃𝒔 × 𝑹 + 𝒖 𝒔𝒉𝒊𝒑
Motion correction(compensation) scheme (Edson et al, 1998)
𝑼 = 𝑈, 𝑉, 𝑊 : wind speed vector in the earth’s coordinate
𝑻: transformation matrix for a rotation of the ship coordinate to the earth’s coordinate
𝛀 𝒐𝒃𝒔: angular velocity vector of the ship coordinate system
𝑹: position vector of the wind measurement location with respect to the motion package
𝒖 𝒔𝒉𝒊𝒑: translational velocity vector of the ship with respect to the earth’s coordinate
𝒖 𝒐𝒃𝒔 = 𝒖, 𝒗, 𝒘 : observed wind speed with respect to the ship coordinate

31. Motion correction scheme
𝑼 = 𝑻 𝒖 𝒐𝒃𝒔 + 𝛀 𝒐𝒃𝒔 × 𝑹 + 𝒖 𝒔𝒉𝒊𝒑
𝑻 =
cos 𝝍 sin 𝝍 𝟎
−sin 𝝍 cos 𝝍 𝟎
𝟎 𝟎
𝒀𝒂𝒘
cos 𝜽 𝟎 sin 𝜽
𝟎 𝟎
− sin 𝜽 𝟎 cos 𝜽
𝑷𝒊𝒕𝒄𝒉
𝟎 𝟎
𝟎 cos 𝝓 − sin 𝝓
𝟎 sin 𝝓 cos 𝝓
𝑹𝒐𝒍𝒍
𝒖 𝒐𝒃𝒔 =
𝒖
𝒗
𝒘
𝛀 𝒐𝒃𝒔 =
ሶ𝝓
ሶ𝜽
ሶ𝝍
𝑹 =
𝟎
𝟎
𝒛𝒍𝒊𝒅𝒂𝒓

32. Large-eddy simulation framework
𝜕෤𝑢𝑖
𝜕𝑥𝑖
= 0
𝜕෤𝑢𝑖
𝜕𝑡
+ ෤𝑢𝑗
𝜕෤𝑢𝑖
𝜕𝑥𝑗
−
𝜕෤𝑢𝑗
𝜕𝑥𝑖
= −
𝜕 ෤𝑝∗
𝜕𝑥𝑖
−
𝜕𝜏𝑖𝑗
𝜕𝑥𝑖
+ 𝜈
𝜕2 ෤𝑢𝑖
𝜕𝑥𝑗
2 −
𝑓𝑖
𝜌
+ 𝛿𝑖1 𝐹𝑝
: air kinematic viscosity
: modified pressure
: resolved (filtered) velocity
: a filter scale (Δ)~
෤𝑢𝑖
෤𝑝∗
𝜈
: subgrid-scale (SGS) stress
: turbine-induced body forces
: constant pressure gradient𝐹𝑝
𝜏𝑖𝑗
𝑓i

33. Lagrangian scale-dependent dynamic model
𝜏𝑖𝑗 − 1
3
𝛿 𝑖𝑗 𝜏 𝑘𝑘
= −2 Δ2 𝐶𝑆
2
Δ ሚ𝑆 ሚ𝑆ij
𝐶𝑆
2
Δ =
𝐿𝑖𝑗 𝑀𝑖𝑗 𝐿
𝑀𝑖𝑗 𝑀𝑖𝑗 𝐿
=
𝑄𝑖𝑗 𝑁𝑖𝑗 𝐿
𝑁𝑖𝑗 𝑁𝑖𝑗 𝐿
■ Traditional Smagorinsky model
̶ Smagorinsky coefficient
→ dynamically compute based on the flow information
Refs: Porté-Agel et al (2000); Stoll and Porté-Agel (2006)
z/dz/d
x/d
x/d
𝐶𝑆
𝐶𝑆
Wu and Porté-Agel (2011)
Wu and Porté-Agel (2013)
33

34. Ω
• Blade element theory
Δr
c : chord length
Blade Element
Vrel : relative velocity
Vx
: velocity at the rotor
Ω : angular velocity
α : angle of attack
γ : twist angle
projection
Total (shaft) Torque: 𝑄 = σ 𝐹𝜃 ∙ 𝑟
Rotor Power: 𝑃𝑅 = 𝑄 ∙ Ω
Power Output: 𝑃𝑂 = 𝑃𝑅 ∙ 𝜂
Ω r-V θ =Ω r(1+a’)
L
D
Fx
Fθ θ
α
φ
γ
F
Vx = u(1-a)~
x
r
θ
x
c
Δr
Actuator-disk model with rotation (ADM-R)
34

35. ADM-NR ADM-R
Uniform distribution of thrust
No considering rotation effect
Integrating thrust force over time
Non-uniform distribution of thrust
Considering rotation effect
Integrating the forces over time
Actuator-disk model without rotation Actuator-disk model with rotation
Jimenez et al (2007; 2008)
Calaf et al (2010; 2011)
Wu & Porté-Agel (2011, 2013)
Sørensen & Kock (1995)
Kasmi & Masson (2008)
Wu & Porté-Agel (2011, 2013)
Blade element theory1D momentum theory
Actuator-disk models (ADM)
ADM-R cannot predict Ω and P
Dynamic procedure:
[1] Calculate 𝑉𝑥 and 𝑉𝜃;
[2] Guess an initial value for Ω 𝑜
;
[3] Calculate the shaft torque Q
using the ADM-R;
[4] Calculate the new Ω 𝑛
based on
the torque-speed relationship;
[5] Calculate 𝜖 𝑡𝑜𝑙 = 1 − ΤΩ 𝑜
Ω 𝑛
;
[6] Replace Ω 𝑜
with Ω 𝑛
[7] Return to [3] until 𝜖 𝑡𝑜𝑙 < 0.01;
[8] Compute the forces and power
Ω r-V θ =Ω r(1+a’)
L
D
Fx
Fθ θ
α
φ
γ
F
Vx = u(1-a)~
x
r
θ
x
c
Δr
ADM-NR requires 𝑪 𝑻 and 𝑪 𝒑 35

36. Model validation
Horns Rev offshore wind farm
(Wu and Porte-Agel, 2015)
A model wind farm in ABL wind tunnel (Wu and Porte-Agel, 2013)

37. U [m s-1]
LES+ADM-R
37
Grid number: 𝟔𝟒𝟎 × 𝟔𝟒𝟎 × 𝟐𝟖
CPU cores: 256 cores
Computational time: 24 hours
Simulation time: 80 mins
LES of turbine wakes in the Horns Rev offshore wind farm

38. Model validation: farm power prediction
Horns Rev offshore wind farm
 Wind farm area : 20 [km2]
 80 Vestas V80 2MW wind turbines
 Total wind farm output: 160 MW
 Cut-in wind speed: 4 [m s-1]
 Cut-out wind speed: 25 [m s-1]
 Constant CT for wind speed < 10 [m s-1]
 Rotor diameter (d) = 80 [m]
 Turbine hub height (HHUB) = 70 [m]
 Three masts around the farm
5 8 11 14 17 20
0
0.5
1
1.5
2
Power[MW]
Wind Speed [ms-1
]
5 8 11 14 17 20
0
0.25
0.5
0.75
1
ThrustCoefficient
Measured Power
Manufacturers CT
(Hansen et al, 2012)
From: Fredy Rodriguez @ http://vimeo.com/28745771
38

39. U [m s-1]
Yaw misalignment is ignored in the sorting of the observed power data, which can cause an overestimation on the
power output of downstream turbines in a narrow full wake condition (e.g. 270o±1o).
Lines: simulated power
Symbols: measured power
Power prediction for different wind sectors

40. Time-averaged streamwise velocity

41. Streamwise turbulence intensity

43. Case Circles 1st circle 2nd circle 3rd circle 4th circle
Turbines Radius Turbines Radius Turbines Radius Turbines Radius
Case 1 1 80 31.23 d
Case 2 2 60 31.23 d 20 10.41 d
Case 3 3 44 31.23 d 28 18.74 d 8 6.25 d
Case 4 4 36 31.23 d 24 21.86 d 16 13.43d 4 4.37 d
Wind farm Horns Rev I Case 1 Case 2 Case 3 Case 4
Efficiency (%) 82.4 78.6 79.6 81.5 81.3

44. Simulations of large wind farms
44
𝐿 𝑥 = 24,000 𝑚 = 300 𝑑
𝐿 𝑦 = 1,200 𝑚 = 15 𝑑
𝐿 𝑧 = 996.8 𝑚 = 12.5 𝑑
120 wind turbines are sited in the simulations
𝑁𝑥 = 1,200
𝑁 𝑦 = 192
𝑁𝑧 = 160

45. Inflow condition
45
A constant pressure gradient is specified up to 800 m to drive the boundary-layer flow
Surface characteristics: 𝑢∗ = 0.488 𝑚/𝑠 and 𝑧0 = 0.05 𝑚
Wind speed at hub: 9.3 𝑚/𝑠

46. Turbine model
46
 Vestas V80 2MW
 Rotor diameter:80 m
 Constant CT for wind speed < 10 [m s-1]
Ref: Wu & Porté-Agel (2015),
Renewable energy

47. Simulated power output
47
0.50
0.55
0.60
0.65
0.70
0.75
0.80
WF1 WF2 WF3 WF4 WF5 WF6 WF7 WF8
Average Power (1-10) Average Power (11-20) Average Power (21-30) Average Power (1-30)

49. Averaged streamwise velocity
49

51. Published: Wu et al, Renewable Energy, 2019

52. Lu & Porté-Agel (2011)
Thanks for your attention
Q&A