### Numerical Example – 1.5 MW Baseline Turbine by NREL

```The Influence of Aerodynamic Damping in
the Seismic Response of HAWTs
Andrew T. Myers, PhD, PE, Assistant Professor
Department of Civil and Environmental Engineering
Northeastern University
Presentation Outline
• Motivation
• Dimensions of utility-scale HAWTs
• Vulnerability to earthquakes
• Derivation of aerodynamic damping
• Fore-aft direction
• Side-to-side direction
• Numerical example – 1.5 MW NREL baseline turbine
• Conclusions
Motivation: Exposure of HAWTs to Earthquakes
Installed wind capacity map as of Jan 2011
United States National Seismic Hazard Map
Dimensions and Period of HAWTs
Approximate dimensions of a utility-scale HAWT
First Period ~ 3 s
Vulnerability to Earthquakes
•
•
•
•
No redundancy in the support structure
Slender hollow sections (D/t as high as 280)
Farms consisting of many nearly identical structures
Large directional affect due to aerodynamic damping
Side-to-side
Fore-aft
Aerodynamic Damping of HAWTs in the Fore-Aft Direction
• Forces based on blade element
momentum theory (BEM)
• Flexibility of rotor is omitted
• Wind direction is along fore-aft
direction
• First mode of vibration is considered
mx + cst x + kx = Fx
1
= ρ
2
2
[
∅ +   ∅   ]
+ [ +   +  ] +  =  ( + ) (1 − )
A=
r
rhub
ρ ∙ Vw ∙ (1 − a) CL cos ∅ + CD sin ∅ c r dr

1
=
∙  ∙ (1 + ′) ( + )  ∅ + ( − )  ∅
ℎ 2
, =
( + )
2
Aerodynamic Damping of HAWTs in the Side-to-Side Direction
1
Fy = ρ
2
Nb
rtip
i=1 rhub
2
Vrel
CL sin ϕ − CD cos ϕ c r ∙ cos(γi t )dr
B ′ − A′
my + cST + Nb
y + ky = 0
2

1
=
1 −
ℎ 2
′
′ =

ℎ
+  sin ∅ +  −  cos ∅
Ω 1 + ′  sin ∅ −  cos ∅
, =
(′ − ′ )
4
Numerical Example – 1.5 MW Baseline Turbine by NREL
Nacelle
Power output
1.5 MW
Hub Height
84 m
Rotor Diameter
70 m
3
Max Rotational Speed
20 rpm
Cut in wind speed
5 m/s
Cut out wind speed
25 m/s
Nacelle Mass
51 Ton
Hub Mass
15 Ton
Tower Mass
123 Ton
Rotor Mass
11 Ton
Active Pitch Control
Yes
Rotor
Tower
Foundation
[Base image from Nuta, 2010]
Numerical Example – 1.5 MW Baseline Turbine by NREL
Aerodynamic damping in the fore-aft direction with W=20 rpm and b=7.5ᵒ
77
66
55
44
33
22
11
00
-1
-1
-2
-2
7
6
(%)
5
4
3
2
1
0
5
10
15
20
25
Vw(m/s)
, =
( + )
2
A=
r
rhub
55
10
10
15
15
Vw(m/s)
Vw(m/s)
2020
2525
ρ ∙ Vw ∙ (1 − a) CL cos ∅ + CD sin ∅ c r dr

1
=
∙  ∙ (1 + ′) ( + )  ∅ + ( − )  ∅
ℎ 2
Numerical Example – 1.5 MW Baseline Turbine by NREL
2
2
1.5
1.5
1
1
0.5
0.5
Aerodynamic damping in the side-to-side direction with W=20 rpm and b=7.5ᵒ
0
-0.5
0
-0.5
-1
-1
-1.5
-1.5
-2
-2
5
, =
10

′
(
15
Vw(m/s)
−
′
)
4
20
25

1
=
1 −
ℎ 2
′
′ =

ℎ
5
10
15
Vw(m/s)
20
25
+  sin ∅ +  −  cos ∅
Ω 1 + ′  sin ∅ −  cos ∅
Numerical Example – 1.5 MW Baseline Turbine by NREL
7
7
6
6
5
5
4
4
Aerodynamic damping in the fore-aft direction with b=7.5ᵒ (left) and W=20 rpm (right)
3
2
W=20
W=15
W=10
1
0
3
5
7
9
b=0˚
b=5˚
b=7.5˚
b=10˚
b=15˚
3
2
1
11 13 15 17 19
0
3
5
7
9
11 13 15 17 19
Numerical Example – 1.5 MW Baseline Turbine by NREL
Aerodynamic damping in the side-to-side direction with b=7.5ᵒ (left) and W=20 rpm (right)
1
W=20
W=15
W=10
0.8
0.6
0.4
0.2
0
b=0˚
b=5˚
b=7.5˚
b=10˚
b=15˚
0.8
0.6
1
0.4
0.2
0
-0.2
-0.2
-0.4
-0.4
3
5
7
9
11 13 15 17 19
3
5
7
9
11 13 15 17 19
Numerical Example – 1.5 MW Baseline Turbine by NREL
Validation with FAST in the fore-aft direction with b=7.5ᵒ and W=20 rpm
8
FAST
FAST
7
Derivation
Equation #15.
6
5
4
3
2
1
0
10
15
Vw(m/s)
20
25
Numerical Example – 1.5 MW Baseline Turbine by NREL
Effect of aerodynamic damping on the seismic response with W=20 rpm
0.9
0.8
0.7
0.6
0.5
Side to Side
Fore-Aft
b = 0
b = 0
b = 5
b = 5
b = 7.5
b = 7.5
b = 10
b = 10
b = 15
b = 15
0.4
0.3
0.2
0.1
0
3
5
7
9
11
13
15
17
19
Conclusions
• Aerodynamic damping of operational wind turbines strongly depends on wind speed. For the
considered example (1.5 MW turbine, W = 20 rpm, b = 7.5˚, wind speed between cut-in and
cut-out):
• The fore-aft aerodynamic damping varies between 2.6% and 6.4%
• The side-to-side aerodynamic damping varies between -0.1% and 0.9%
• For this same operational case, the derivative of the lift coefficient with respect to the angle
of attack is the most influential parameter in aerodynamic damping in the fore-aft direction
• The blade pitch angle and rotational speed also influence the aerodynamic damping in both
the fore-aft and side-to-side directions
• The directional effect strongly influences the seismic response, with median spectral drift
predicted to be as much as 70% larger in the side-to-side direction than in the fore-aft
direction
```