Motion Tp(s) f(rad/s)
Surge 115 0.055
Sway 125 0.05
Heave 31.4 0.2
Roll/pitch 32.7 0.19
Yaw 7.5 0.838
Wave: 0.44
Cased 1 All blades are feathered V=38.7, Hs=12, Tp=14.2 position1
Cased 2 Blade1&3 feathered, blade2 seized and flat to the wind, V=38.7, Hs=12, Tp=14.2 position1 I Dynamic response
0 0.1 0.2 0.3 0.4 0.5 0.6
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Frequency (rad/s) S (
)[ m
2/s /r ad ]
Comparison Narcelle Accer., Hs=12, Tp=14.2, V=38.7M/S
feathered bd2 seized
The nacelle accer. Is dominated by pitch resonant response
0 0.2 0.4 0.6 0.8 1 1.2
0 0.5 1 1.5 2
Frequency (rad/s) S()[m2 /s/rad]
Compar. wavedir45 Narcelle Accer., Hs=12, Tp=14.2, V=38.7M/S
feathered bd2 seized
0 0.2 0.4 0.6 0.8 1 1.2 0
0.5 1 1.5 2 2.5 3 3.5 4 4.5
Frequency (rad/s) S()[m2 /s/rad]
Compar. Wavedir90 Narcelle Accer., Hs=12, Tp=14.2, V=38.7M/S
feathered bd2 seized
0 0.2 0.4 0.6 0.8 1 1.2
0 50 100 150 200
Frequency (rad/s) S()[m2 /s/rad]
Comparison Narcelle Surge, Hs=12, Tp=14.2, V=38.7M/S
feathered bd2 seized
0 0.2 0.4 0.6 0.8 1 0
50 100 150 200 250
Frequency (rad/s) S()[m2 /s/rad]
Compar. wavedir45 Narcelle Surge, Hs=12, Tp=14.2, V=38.7M/S
feathered bd2 seized
When blade2 is seized, the wave frequency is the same as that of the feathered case, but the pitch resonant response and the surge resonant response is much larger
0 0.1 0.2 0.3 0.4 0.5
0 50 100 150 200 250
Frequency (rad/s) S()[m2 /s/rad]
Compar. Wavedir90 Narcelle Surge, Hs=12, Tp=14.2, V=38.7M/S
feathered bd2 seized
Wp1: surge resonance. Wp2: pitch resonance
When blade2 is flat to the wind while the wave comes from another direction, the aerodynamic damping provided by the blades are not enough to
0 0.2 0.4 0.6 0.8 1 0
5 10 15
Frequency (rad/s) S ( )[ m
2/s /r ad ]
Comparison Spar pitch, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
The pitch resonance response for the seized case is more pronounced. The wave freq. response is not affected.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0 5 10 15 20
Frequency (rad/s) S (
)[ m
2/s /r ad ]
Compar. wavedir45 Spar pitch, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
0 0.1 0.2 0.3 0.4 0.5 0.6 0
5 10 15 20
Frequency (rad/s) S (
)[ m
2/s /r ad ]
Compar. Wavedir90 Spar pitch, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
The reason for larger resonance pitch response for blade2seized case is that more aerodynamic force are concentrated on blade2.
0 500 1000 1500 2000 2500 3000 3500 4000 -12
-10 -8 -6 -4 -2 0 2 4 6
Time (s)
Y a w ( d eg )
Comparison of yaw motion
feathered bd2 seized
0 500 1000 1500 2000 2500 3000 3500
-10 -8 -6 -4 -2 0 2 4 6 8
Time (s)
Y a w ( d eg )
Compar. Wavdir0 of yaw motion
Fault type 0, blades feathered Fault type 1, blade 2 seized Fault type 3, all blades seized
0 500 1000 1500 2000 2500 3000 3500 4000 -10
-8 -6 -4 -2 0 2 4 6 8
Time (s)
Yaw (deg)
Compar. Wavedir90 yaw motion
feathered bd2 seized
0 0.5 1 1.5
0 2 4 6 8 10 12 14 16
Frequency (rad/s) S (
)[ m
2/s /r ad ]
Comparison Spar Yaw, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
When 1 blade is seized, more resonant response besides the yaw resonance is excited.
Both the roll and wave freq. resonance are present in the seized case. When one blade is flat to the wind, more resonant responses are excited.
But the amplitude of the spectrum of the yaw resonance is damped.
0 0.5 1 1.5 0
5 10 15 20 25 30
Frequency (rad/s) S ( )[ m
2/s /r ad ]
Compar. wavedir45 Spar Yaw, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
0 0.5 1 1.5
0 2 4 6 8 10 12 14 16
Frequency (rad/s) S ( )[ m
2/s /r ad ]
Compar. Wavdir90 Spar Yaw, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
It seems that the wave direction has virtually no impact on the response of the spar. But the seized blade has a direct influence: wave frequency resonance pops up, and there is a slight peak for roll motion.
Postion1:
Wave dir0
0 0.1 0.2 0.3 0.4 0.5 0
20 40 60 80 100 120 140 160 180 200
Frequency (rad/s) S()[m2 /s/rad]
Comparison Narcelle Sway, Hs=12, Tp=14.2, V=38.7M/S
feathered bd2 seized
The roll resonant response is much larger for the seized case，but the sway resonance peak is lower.
0 0.2 0.4 0.6 0.8 1
0 10 20 30 40 50 60 70 80 90 100
Frequency (rad/s) S()[m2 /s/rad]
Compar. wavedir45 Narcelle Sway, Hs=12, Tp=14.2, V=38.7M/S
feathered bd2 seized
Wave dir90
0 0.2 0.4 0.6 0.8 1 0
10 20 30 40 50 60 70 80 90 100
Frequency (rad/s) S()[m2 /s/rad]
Compar. Wavedir90 Narcelle Sway, Hs=12, Tp=14.2, V=38.7M/S
feathered bd2 seized
Wp1=0.05 sway, wp2=0.2 roll, wp3=0.43 wave Position 3:
0 0.1 0.2 0.3 0.4 0.5 0.6
0 10 20 30 40 50 60 70 80 90 100
Frequency (rad/s) S()[m2 /s/rad]
Narcelle Sway Wavdir0, Azimuth 60deg , Hs=12, Tp=14.2, V=38.7M/S
feathered bd2 seized
The roll motion and sway motion are coupled for a spar-type wind turbine with lateral symmetry.[1] In the feathered and parked case, all of the blades are flat to the wave direction and parallel to the wind direction, providing enough aerodynamic damping to counteract the roll resonant effect in the sway motion. Compared with the feathered case, the seized case leads to large unwanted roll resonance.
0 0.1 0.2 0.3 0.4 0.5 0
5 10 15 20
Frequency (rad/s) S()[m2 /s/rad]
Comparison Spar Roll, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
When one blade is seized,
0 0.2 0.4 0.6 0.8 1
0 5 10 15 20
X: 0.1956 Y: 23.33
Frequency (rad/s) S()[m2 /s/rad]
Compar. Wavedir90 Spar Roll, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
0 0.2 0.4 0.6 0.8 1 0
5 10 15 20 25
Frequency (rad/s) S()[m2 /s/rad]
Compar. wavedir45 Spar Roll, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
When blade2 is seized, it results in more roll resonance due to the aerodynamic excitation on blade2.
0 500 1000 1500 2000 2500 3000 3500 4000
-3 -2 -1 0 1 2 3 4 5
Time (s)
Roll (deg)
Comparison of roll motion
feathered bd2 seized
0 500 1000 1500 2000 2500 3000 3500 4000 -6
-4 -2 0 2 4 6
Time (s)
Roll (deg)
Compar. Wavedir90 of roll motion
feathered bd2 seized
0 1 2 3 4 5
0 1 2 3 4 5 6
x 106
Frequency (rad/s) S()[m2 /s/rad]
Comparison-Flapwise Mx Blade1, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
0 1 2 3 4 5 0
1 2 3 4 5 6
x 106
Frequency (rad/s) S()[m2 /s/rad]
Compar. wavedir45-Flapwise Mx Blade1, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
0 1 2 3 4 5
0 1 2 3 4 5 6 7 8 9 10
x 106
Frequency (rad/s) S()[m2 /s/rad]
Compar. Wavedir90-Flapwise Mx Blade1, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
When blade2 is seized and flat to the wind direction, the impact on flapwise motion of blade1 seems to be positive.
0 0.5 1 1.5 2 2.5 3 0
2 4 6 8 10 12 14
x 109
Frequency (rad/s) S (
)[ m
2/s /r ad ]
Comparison Tower bottom Mx, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
0 0.5 1 1.5 2 2.5 3
0 1 2 3 4 5 6 7 8 9 10
x 109
Frequency (rad/s) S()[m2 /s/rad]
Compar. wavedir45 Tower bottom Mx, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
0 0.5 1 1.5 2 2.5 3 0
0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 109
Frequency (rad/s) S()[m2 /s/rad]
Compar. Wavedir90 Tower bottom Mx, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
The seized blade added more aerodynamic damping to the motion in fore-aft of the spar, which leads to decreased resonant of the Mx. This benefit is sensitive to the wave direction.
0 0.5 1 1.5 2 2.5 3
0 0.5 1 1.5 2 2.5 3 3.5 4
x 109
Frequency (rad/s) S()[m2 /s/rad]
Comparison Tower bottom My, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
0 0.5 1 1.5 2 2.5 3 0
1 2 3 4 5
x 109
Frequency (rad/s) S()[m2 /s/rad]
Compar. wavedir45 Tower bottom My, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
I
0 0.5 1 1.5 2 2.5 3
0 2 4 6 8 10
x 109
Frequency (rad/s) S()[m2 /s/rad]
Compar. Wavedir90 Tower bottom My, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
Wp2-2.15rad/s=0.34Hz
n a similar way, the wp1 of My is most affected by the roll resonant response. When only two blades are flat in –y direction, the corresponding damping decreased, leading to a higher response for case2.
The seized blade, hence the reduced aerodynamic damping in –x direction will always leads to larger roll resonance in the tower root bending moment My.
0 0.5 1 1.5 2 2.5 3 0
0.5 1 1.5 2 2.5
x 106
Frequency (rad/s) S()[m2 /s/rad]
Comparison Tower bottom Fy, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
0 0.5 1 1.5 2 2.5 3
0 2 4 6 8 10
x 105
Frequency (rad/s) S()[m2 /s/rad]
Compar. wavedir45 Tower bottom Fy, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
0 0.5 1 1.5 2 2.5 3
0 2 4 6 8 10 12
x 104
Frequency (rad/s) S()[m2 /s/rad]
Compar. Wavedir90 Tower bottom Fy, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
Wp1=0.19 rad/s, pitch resonance wp2=2.15 rad/s, 0.34 Hz, first tower fore-aft
Wave direction has a significant influence on the response. When wave direction=0, the Fy has a prominent peak at wp2 for the feathered case. While wave direction=0, Fy is peaked at the pitch resonance.
0 0.2 0.4 0.6 0.8 1 1.2
0 1 2 3 4 5
Frequency (rad/s) S (
)[ m
2/s /r ad ]
Compar. Wavdir0 Vy bd1, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
0 0.2 0.4 0.6 0.8 1 1.2
0 2 4 6 8 10 12
Frequency (rad/s) S (
)[ m
2/s /r ad ]
Compar. wavedir45 Vy bd1, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
0 0.2 0.4 0.6 0.8 1 1.2 0
5 10 15 20 25
Frequency (rad/s) S()[m2 /s/rad]
Compar. Wavedir90 Vy bd1, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
0 500 1000 1500 2000 2500 3000 3500 4000
-10 -5 0 5 10 15
Time (s)
V e lo ci ty ( m /s )
Compar. Wavedir90 Blade1 Vy R=60m
feathered bd2 seized
The seized blade leads to larger pitch resonance of the tip speed velocity of blade1 due to the pitch rigid body motion of the platform. The degree of this influence depends very much on the wave direction. Wave direction0 causes more severe pitch resonance compared with wave direction 90.
0 0.5 1 1.5 2 0
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Frequency (rad/s) S()[m2 /s/rad]
Comparison Vx bd1, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
0 0.5 1 1.5 2
0 1 2 3 4 5 6 7 8 9
X: 0.1841 Y: 1.435
Frequency (rad/s) S (
)[ m
2/s /r ad ]
Compar. Wavedir90 Vx bd1, Hs=12, Tp=14.2, V=38.7
feathered bd2 seized
Similar to pitch and yaw behavior.
II. Extreme value and normalized peak responses The extreme values can be estimated as µx+kσx
0 0.5 1 1.5 2 2.5 3 0
2 4 6 8 10 12 14 16
x 109
Frequency (rad/s) S()[m2 /s/rad]
Compar. wavdir90 Tower bottom My, Hs=10.4, Tp=12.9, V=42.5
Fault type 0, blades feathered Fault type 1, blade 2 seized Fault type 3, all blades seized
Tower bottom bending moment My spectrum, blade azimuth γ1=30 deg, wave misalignment γ2=90 deg, Sea State B,
0 0.5 1 1.5
0 5 10 15 20 25
Frequency (rad/s) S()[m2 /s/rad]
Compar. wavdir90 Spar Roll, Hs=10.4, Tp=12.9, V=42.5
Fault type 0, blades feathered Fault type 1, blade 2 seized Fault type 3, all blades seized
0 0.5 1 1.5 2 2.5 3 0
2 4 6 8 10
x 109
Frequency (rad/s) S() [kNm2 /s/rad]
Fault type 0, blades feathered Fault type 1, blade 2 seized Fault type 3, all blades seized
Tower bottom bending moment Mx spectrum, blade azimuth γ1=30 deg, wave misalignment γ2=0 deg, Sea State B
0 0.5 1 1.5 2 2.5 3
0 1 2 3 4 5
x 109
Frequency (rad/s) S() [kNm2 /s/rad]
Fault type 0, blades feathered Fault type 1, blade 2 seized Fault type 3, all blades seized
Tower bottom bending moment Mx spectrum, blade azimuth γ1=90 deg, wave misalignment γ2=90 deg, Sea State B
0 0.5 1 1.5 2 2.5 3 0
0.5 1 1.5 2
x 105
Frequency (rad/s) S (
) [k N
2/s /r ad ]
Compar. wavdir90 Tower bottom Fy, Hs=10.4, Tp=12.9, V=42.5
Fault type 0, blades feathered Fault type 1, blade 2 seized Fault type 3, all blades seized
Tower bottom shear force Fy spectrum, blade azimuth γ1=90 deg, wave misalignment γ2=90 deg, Sea State B
1 2 3
0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4
Case No.
Normalized response maximum
Blade2 seized
Mx tower, 1-year with fault type1 My tower, 1-yr with fault type1 Fy tower, 1-yr with fault type1 Mx blade1, 1-yr with fault type1 1-yr with fault type 0
[1] Faltinsen OM. Sea loads on ships and offshore structures: Cambridge Univ Pr; 1993.
