Frequency (rad/s)Feathered-Narcelle Sway, Hs=12, Tp=14.2, V=38.7M/S

(1)

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, wavedir0 and wave dir90 Wave dir=0

0 0.1 0.2 0.3 0.4 0.5 0.6

0 10 20 30 40 50 60

Frequency (rad/s) S()[m2 /s/rad]

Feathered-Narcelle Sway, Hs=12, Tp=14.2, V=38.7M/S

postition1 position2 position3

wp1: sway wp2: roll wave dir=90

0 0.2 0.4 0.6 0.8 1 1.2

0 10 20 30 40 50 60 70 80 90 100

Feathered-Narcelle Sway, Hs=12, Tp=14.2, V=38.7M/S Wavedir90

(2)

The feathered blades excited wave-induced response Wave dir=0

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

Frequency (rad/s) S (  )[ m

2

/s /r ad ]

Feathered-Narcelle Sway Accer., Hs=12, Tp=14.2, V=38.7M/S

Wave dir=90

0 0.5 1 1.5

0 0.5 1 1.5 2 2.5 3 3.5 4

Frequency (rad/s) S (  )[ m

2

/s /r ad ]

Feathered-Narcel. Sway Acc., Hs=12, Tp=14.2, V=38.7M/S Wavedir90

(3)

0 0.2 0.4 0.6 0.8 1 1.2 0

20 40 60 80 100

Frequency (rad/s) S (  )[ m

2

/s /r ad ]

Feathered-Narcelle Surge, Hs=12, Tp=14.2, V=38.7M/S

Wave dir=90

0 0.1 0.2 0.3 0.4 0.5

0 10 20 30 40 50 60 70 80 90 100

Frequency (rad/s) S (  )[ m

2

/s /r ad ]

Feathered-Narcelle Surge, Hs=12, Tp=14.2, V=38.7M/S Wavedir90

(4)

Wave dir=0

0 1 2 3 4 5

0 1 2 3 4 5 6

x 10⁶

Frequency (rad/s) S (  )[ m

2

/s /r ad ]

Feathered-Flapwise Mx Blade1, Hs=12, Tp=14.2, V=38.7

Wave dir=90

0 1 2 3 4 5

0 1 2 3 4 5 6 7 8 9 10

x 10⁶

Frequency (rad/s) S (  )[ m

2

/s /r ad ]

Feathered-Flapwise Mx Blade1, Hs=12, Tp=14.2, V=38.7 Wavedir90

(5)

0 2 4 6 8 10 0

1 2 3 4 5 6 7 8

x 10⁵

Feathered-edgewise My Blade1, Hs=12, Tp=14.2, V=38.7

Wp1: wave induced wp2: first nat. blade Wave dir 90

0 2 4 6 8 10

0 1 2 3 4 5 6 7 8

x 10⁵

Feathered-edgewise My Blade1, Hs=12, Tp=14.2, V=38.7 Wavedir90

(6)

0 1 2 3 4 5 0

1 2 3 4 5 6 7 8 9

x 10⁶

Frequency (rad/s) S (



)[ m

2

/s /r ad ]

Feathered-Flapwise Mx Blade2, Hs=12, Tp=14.2, V=38.7

Wave dir0

0 2 4 6 8 10

0 0.5 1 1.5 2 2.5 3 3.5 4

x 10⁶

Feathered-edgewise My Blade2, Hs=12, Tp=14.2, V=38.7

Wave dir90

(7)

0 2 4 6 8 10 0

2 4 6 8 10

x 10⁵

Feathered-edgewise My Blade2, Hs=12, Tp=14.2, V=38.7 Wavedir90

0 0.5 1 1.5 2 2.5 3

0 0.5 1 1.5 2

x 10¹⁰

Frequency (rad/s) S (



)[ m

2

/s /r ad ]

Feathered-Tower bottom Mx, Hs=12, Tp=14.2, V=38.7

Wave dir90

(8)

0 0.5 1 1.5 2 2.5 3 0

0.5 1 1.5 2 2.5 3

x 10⁹

Feathered-Tower bottom Mx, Hs=12, Tp=14.2, V=38.7 Wavedir90

Wp1=0.2, pitch Wave dir0

0 0.5 1 1.5 2 2.5 3

0 2 4 6 8 10 12

x 10⁸

Feathered-Tower bottom My, Hs=12, Tp=14.2, V=38.7

(9)

0 0.5 1 1.5 2 2.5 3 0

2 4 6 8 10

x 10⁹

Feathered-Tower bottom My, Hs=12, Tp=14.2, V=38.7 Wavedir90

Wave dir0

0 0.5 1 1.5 2 2.5 3

0 0.5 1 1.5 2 2.5

x 10⁶

Feathered-Tower bottom Fy, Hs=12, Tp=14.2, V=38.7

Wave dir90

(10)

0 0.5 1 1.5 2 2.5 3 0

1 2 3 4 5 6 7 8 9

x 10⁴

Feathered-Tower bottom Fy, Hs=12, Tp=14.2, V=38.7 Wavedir90

Wave dir0

0 500 1000 1500 2000 2500 3000 3500 4000

-6 -4 -2 0 2 4

6 Spar Yaw Angle

position1 position2 position3

(11)

0 0.5 1 1.5 0

2 4 6 8 10 12 14 16

Feathered-Spar Yaw, Hs=12, Tp=14.2, V=38.7

Wave dir90

0 500 1000 1500 2000 2500 3000 3500 4000

-6 -4 -2 0 2 4 6

8 Spar Yaw Angle Wavedir90

(12)

0 0.5 1 1.5 0

5 10 15 20 25 30

Feathered-Spar Yaw, Hs=12, Tp=14.2, V=38.7 Wavedir90

Wave freq. is present in the yaw motion Wavedir 0

Yaw resonance freq. =0.93, higher than the calculated nat. freq.

No other frequency is present.

-2 0 2 4 6 8

(13)

0 0.2 0.4 0.6 0.8 1 0

2 4 6 8 10

Feathered-Spar pitch, Hs=12, Tp=14.2, V=38.7

wp1: pitch wp2: wave wave dir90

0 0.2 0.4 0.6 0.8 1

0 1 2 3 4 5 6 7 8 9

Frequency (rad/s) S (



)[ m

2

/s /r ad ]

Feathered-Spar pitch, Hs=12, Tp=14.2, V=38.7 Wavedir90

No wave freq. is present in the response Vx blade1 r=60m

(14)

0 500 1000 1500 2000 2500 3000 3500 4000 -6

-4 -2 0 2 4 6

8 Blade1 Vx R=60m

Wave dir0

0 0.2 0.4 0.6 0.8 1 1.2

0 0.5 1 1.5 2 2.5 3

X: 0.2033 Y: 1.804

Feathered-Vx bd1, R=60m, Hs=12, Tp=14.2, V=38.7

(15)

0 0.2 0.4 0.6 0.8 1 1.2 0

2 4 6 8 10 12 14 16 18

Feathered-Vx bd1, R=60m, Hs=12, Tp=14.2, V=38.7 Wavedir90

Vy blade1 r=60m

0 500 1000 1500 2000 2500 3000 3500 4000

-6 -4 -2 0 2 4

6 Blade1 Vy R=60me

Wave dir0

(16)

0 0.2 0.4 0.6 0.8 1 1.2 0

0.5 1 1.5 2 2.5 3 3.5

Frequency (rad/s) S (



)[ m

2

/s /r ad ]

Feathered-Vy bd1, R=60m, Hs=12, Tp=14.2, V=38.7

Wp1 pitch wp2 yaw?

Wave dir90

0 0.2 0.4 0.6 0.8 1 1.2

0 5 10 15 20 25 30 35

Frequency (rad/s) S (



)[ m

2

/s /r ad ]

Feathered-Vy bd1, R=60m, Hs=12, Tp=14.2, V=38.7 Wavedir90

Wp1: pitch wp2: wave freq.

(17)

0 0.2 0.4 0.6 0.8 1 0

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Feathered-Spar Roll, Hs=12, Tp=14.2, V=38.7

Wave dir90

0 0.2 0.4 0.6 0.8 1

0 1 2 3 4 5 6

Frequency (rad/s) S (  )[ m

2

/s /r ad ]

Feathered-Spar Roll, Hs=12, Tp=14.2, V=38.7 Wavedir90

Dynamic response of the feathered case, wave dir0 and wave dir90

The response spectrums are sensitive to the wave direction. The wave resonance response will be unaffected by the change of azimuth angle. Yaw angle is most susceptible to the blade azimuth position, position 1 gives the largest response. No wave-induced peak is present in the yaw response is the direction is 0 but slight wave resonance is observed at 90 deg wave angle. The symmetrical position3 leads to the lowest yaw response. No wave-induced peak is present in the roll motion if wave dir=0, but in wave dir=90 there is a large peak. Take the sway response spectrum. The wave

(18)

induced part will be unaffected by the azimuth angle. The roll-induced and one will be slightly affected. The responses of the blades are sensitive to the azimuth angle. The pitch response is least sensitive to the azimuth angle. The roll motion spectrum as well as the surge spectrum is largely unaffected by the change of azimuth angle.

Case2 Standstill-blade2seized_wind41.7_Hs13.33 Tp14.4 wave dir=0 and wave dir=90 deg Wave dir. 0

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 ]

Bd2seized-Narcelle Sway Accer., Hs=12, Tp=14.2, V=38.7M/S

Wp1: roll Wave dir. 90

0 0.2 0.4 0.6 0.8 1 1.2

0 0.5 1 1.5 2 2.5 3 3.5

Bd2seized-Sway Accer., Hs=12,Tp=14.2,V=38.7,Wavdir90

(19)

0 0.1 0.2 0.3 0.4 0.5 0.6 0

20 40 60 80 100 120 140 160 180

200 _{X: 0.1917}

Y: 205.8

Bd2seized-Narcelle Sway, Hs=12, Tp=14.2, V=38.7M/S

wp1: sway wp2: roll nat. freq.

Wave dir. 90

0 0.2 0.4 0.6 0.8 1 1.2

0 20 40 60 80 100 120 140 160 180

Frequency (rad/s)

S (



)[ m

2

/s /r ad ]

Bd2seized-Nar. Sway,Hs=12,Tp=14.2,V=38.7,Wavdir90

roll and sway are coupled

The symmetrical position3 result in least responses Wave dir. 0

(20)

0 0.2 0.4 0.6 0.8 1 1.2 0

50 100 150 200 250

Frequency (rad/s) S (



)[ m

2

/s /r ad ]

Bd2seized-Narcelle Surge, Hs=12, Tp=14.2, V=38.7M/S

Wave dir. 90

0 0.1 0.2 0.3 0.4 0.5

0 50 100 150 200 250 300

Bd2seized-Narcelle Surge, Hs=12,Tp=14.2,V=38.7,Wavdir90

(21)

0 0.1 0.2 0.3 0.4 0.5 0

5 10 15 20

Bd2seized-Spar Roll, Hs=12, Tp=14.2, V=38.7

The sway resonance is present in the response of roll motion due to the symmetry position of the blades.

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 ]

Bd2seized-Spar Roll,Hs=12,Tp=14.2,V=38.7,Wavdir90

The sway resonant frequency is present in position3. The roll resonant peak of position3 is significantly smaller than that of position1 and 2. The wave frequency part keeps unchanged.

Wave dir0

(22)

0 1 2 3 4 5 0

1 2 3 4 5 6x 10⁶

Frequency (rad/s) S (



)[ m

2

/s /r ad ]

Bd2seized-Flapwise Mx Blade1, Hs=12, Tp=14.2, V=38.7

Wave dir90

0 1 2 3 4 5

0 1 2 3 4 5 6 7

x 10⁶

Frequency (rad/s) S (



)[ m

2

/s /r ad ]

Bd2seized-Flapwise Mx Blade1, Hs=12,Tp=14.2,V=38.7,Wavdir90

(23)

0 2 4 6 8 10 0

0.5 1 1.5 2 2.5 3 3.5

x 10⁵

Bd2seized-edgewise My Blade2, Hs=12, Tp=14.2, V=38.7

0 2 4 6 8 10

0 1 2 3 4 5 6 7 8 9

x 10⁵

Bd2seized-edgewise My, Hs=12,Tp=14.2,V=38.7,Wavdir90

The edgewise response of blade2 has significantly large resonance for position3. Because there is larger aerodynamic loading on it. 1Hz

(24)

0 0.5 1 1.5 2 2.5 3 0

2 4 6 8 10 12 14

x 10⁹

Bd2seized Tower bottom Mx, Hs=12, Tp=14.2, V=38.7

wp1: pitch, wp2: wave freq.

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 5

x 10⁹

Bd2seized Tower bottom Mx, Hs=12,Tp=14.2,V=38.7,Wavdir90

(25)

0 0.5 1 1.5 2 2.5 3 0

0.5 1 1.5 2 2.5 3 3.5

x 10⁹

Frequency (rad/s) S (



)[ m

2

/s /r ad ]

Bd2seized Tower bottom My, Hs=12, Tp=14.2, V=38.7

0 0.5 1 1.5 2 2.5 3

0 2 4 6 8 10

x 10⁹

Bd2seized Tower bottom My, Hs=12,Tp=14.2,V=38.7,Wavdir90

Wp1=0.2 roll

(26)

0 0.5 1 1.5 2 2.5 3 0

2 4 6 8 10 12 14 16

x 10⁵

X: 0.4449 Y: 1.474e+006

Frequency (rad/s) S (



)[ m

2

/s /r ad ]

Bd2seized Tower bottom Fy, Hs=12, Tp=14.2, V=38.7

wp1=0.2 pitch, wp2=0.44, wave, wp3=2.15, first tower fore-aft

0 0.5 1 1.5 2 2.5 3

0 2 4 6 8 10 12 14x 10⁴

Bd2seized Tower bottom Fy, Hs=12,Tp=14.2,V=38.7,Wavdir90

(27)

0 500 1000 1500 2000 2500 3000 3500 4000 -10

-8 -6 -4 -2 0

2 Bd2seized Spar Yaw Angle

Wave dir0

0 0.5 1 1.5

0 2 4 6 8 10 12

Frequency (rad/s) S (



)[ m

2

/s /r ad ]

Bd2seized Spar Yaw, Hs=12, Tp=14.2, V=38.7

For position1, Wp1=0.15 (roll), wp2=0.44, wp2=0.95(yaw) Wave dir90

(28)

0 0.5 1 1.5 0

5 10 15 20 25 30

Bd2seized Spar Yaw, Hs=12,Tp=14.2,V=38.7,Wavdir90

Yaw resonance response is highly sensitive to the azimuth angle of the blade as well as the wave direction. The wave resonant response is largely damped out by the feathered blades 1 and 2.

Wave dir0

0 500 1000 1500 2000 2500 3000 3500 4000

-12 -10 -8 -6 -4 -2 0 2

Time (s)

Y a w A ng le ( de g)

Bd2seized Spar Yaw Angle

When blade2 is seized, wave-induced response is present in the yaw spectrum of postion3, not in position1 and 2. Since aerodynamic damping of position 2 is largest due to the relative out-of-plane motion of the blade2.

(29)

0 500 1000 1500 2000 2500 3000 3500 4000 -10

-5 0 5

Time (s)

Y a w A ng le ( de g)

Bd2seized Spar Yaw Angle

0 500 1000 1500 2000 2500 3000 3500 4000

-4 -2 0 2 4 6 8 10 12

Time (s)

Pitch Angle (deg)

Bd2seized Spar Pitch Angle

(30)

0 0.2 0.4 0.6 0.8 1 0

2 4 6 8 10 12 14 16

Frequency (rad/s) S (



)[ m

2

/s /r ad ]

Bd2seized Spar pitch, Hs=12, Tp=14.2, V=38.7

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

0 5 10 15 20 25

Bd2seized Spar pitch, Hs=12,Tp=14.2,V=38.7,Wavdir90

The pitch spectrum is least sensitive to the azimuth position.

(31)

0 500 1000 1500 2000 2500 3000 3500 4000 -8

-6 -4 -2 0 2 4 6 8

Time (s)

V e lo ci ty ( m /s )

Blade1 Vx R=60m

0 0.2 0.4 0.6 0.8 1 1.2

0 0.5 1 1.5 2 2.5 3

Blade2seized-Vx bd1, R=60m, Hs=12, Tp=14.2, V=38.7

(32)

0 0.2 0.4 0.6 0.8 1 1.2 0

2 4 6 8 10 12 14 16 18

Blade2seized-Vx bd1, R=60m,Hs=12,Tp=14.2,V=38.7,Wavdir90

0 500 1000 1500 2000 2500 3000 3500 4000

-6 -4 -2 0 2 4 6

Time (s)

V e lo ci ty ( m /s )

Blade1 Vy R=60m

(33)

0 0.2 0.4 0.6 0.8 1 1.2 0

2 4 6 8 10 12

Blade2seized--Vy bd1, R=60m, Hs=12, Tp=14.2, V=38.7

0 0.2 0.4 0.6 0.8 1 1.2

0 5 10 15 20 25 30 35

Blade2seized--Vy bd1,R=60m,Hs=12 Tp=14.2,V=38.7,Wavdir90

Observations of case 2

For the seized case, nacelle sway acceleration and displacement is very sensitive to the azimuth angle.

Since when blade2 is seized, the aerodynamic loads in –x direction come from the lift force of blade1 and blade3 only. Position 1 induces the largest sway motion due to ? The out of plane and in-plane tip speed of blade1 is also sensitive to the azimuth angle. T.

Nacelle sway is sensitive to the azimuth angle is the wave direction is 0 because sway is coupled with roll motion. The sway motion is less sensitive to change of blade position if wave direction is 90.

Surge motion is largely unaffected by the azimuth angle. The sway resonant frequency is present in position3, but not in position1 and 2. The roll resonant peak of position3 is significantly smaller than that of position1 and 2. The wave frequency part keeps unchanged.

The blade2 edgewise moment My is connected with the roll and sway motion and hence is sensitive to the azimuth angle. Yaw resonance response is highly sensitive to the azimuth angle of the blade as

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well as the wave direction. P3 gives the lowest response of yaw motion due to the symmetric aerodynamic drag loading about the tower axis. P1 could be the most critical one which results in the largest responses among three. The mean yaw angle is -4.2 deg. The turbine is moving in this tilted position. Due to the large yaw stiffness provided by the delta line, no instability is found.

When the wave direction is 0, position 3 offers largest aerodynamic damping and reduces the wave resonance most. When the wave direction is 90 deg, The wave resonant response is largely damped out by the feathered blades 1 and 2. Pitch response spectrum, like the feathered case, is least to the azimuth angle of the blades.