1- yr Contour surface
0
5
10
15
0 5
10 15 200
5 10 15 20 25 30
Hs (m/s) Tp
U w
0 2 4 6 8 10 12
0 5 10 15 20 25 30
Hs
U w
Projection of 1-yr contour surface to 2-D
Since the responses of floating spar is less sensitive to the Tp, three cases are selected on the Uw-Hs contour line
Uw Hs Tp
CASE1 25.87 10.97 14.18
CASE2 28.43 9.53 12.90
CASE3 27.80 10.60 13.71
The significant wave height fora 1-hour simulation Hs=k2*Hs1, k2=1.09
Uw is extrapolated to the hub height with power factor 0.14, plus a 10% increase in wind speed for scaling the 1-hour average wind speed to 10-min average wind speed.
The real cases run
Uw Hs Tp Sigma
Sea state1 38.7 12.0 14.2 0.12
Sea state2 42.5 10.4 12.90 0.12
Sea state3 41.6 11.6 13.71 0.12
1- hour long simulation is run, the seed num for each 15 min wind and wave sim. Is different.
Turbulence intensity is a function of wind speed. The U
Sensitivity of the response to the blade azimuth angle position1,2,3 Case1 Standstill-feathered_wind41.7_Hs13.33Tp14.4_no direction
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 freq. =0.436 rad/s
0 500 1000 1500 2000 2500 3000 3500 4000 -5
0 5 10 15
20 spar bottom displacement -y
position1 position2 position3
0 500 1000 1500 2000 2500 3000 3500 4000
-3000 -2000 -1000 0 1000 2000 3000
4000 Tower Bottom Shear Force -y
position1 position2 position3
0 500 1000 1500 2000 2500 3000 3500 4000 -2
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
3x 105 tower bottom moment Mx
position1 position2 position3
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 ]
Tower bottom BM, Hs=12.2, Tp=14.4, V=41.9
postition1 position2 position3
Mx
Wp1=0.20 (pitch resonance), wp2=0.42(wave freq.), wp3=2.14?
0 500 1000 1500 2000 2500 3000 3500 4000 -6
-4 -2 0 2 4
6x 104 tower bottom moment My position1
position2 position3
0 0.5 1 1.5 2 2.5 3
0 2 4 6 8 10 12
x 108
Frequency (rad/s) S (
)[ m
2/s /r ad ]
Tower bottom My, Hs=12.2, Tp=14.4, V=41.9
postition1 position2 position3
wp1=0.2 rad/s, wp2=0.94 rad/s, wp3=2.16 rad/s
0 500 1000 1500 2000 2500 3000 3500 4000 -8000
-6000 -4000 -2000 0 2000 4000 6000 8000
10000 Flapwise blade1 bending moment Mx
position1 position2 position3
0 0.5 1 1.5 2
0 1 2 3 4 5 6 7 8 9
x 106
Frequency (rad/s) S (
)[ m
2/s /r ad ]
Feathered-Flapwise BM Blade1, Hs=12.2, Tp=14.4, V=41.9
postition1 position2 position3
Blade resonance
The variance of the total root bending moment fluctuations is equal to the sum of the resonant and background response variances.
2 2 2
1
M M MB
It would be interesting to look at the root bending moment.
Since the lowest natural frequency of the blades in the flapwise and edgewise modes are below 1 Hz, the resonant response might be significant.
0 500 1000 1500 2000 2500 3000 3500 4000
-4000 -3000 -2000 -1000 0 1000 2000
3000 edgewise blade1 bending moment My position1
position2 position3
0 200 400 600 800 1000 1200 1400 1600
-1 -0.5 0 0.5 1
1.5 Tower top accer. in x dir.
position1 position2 position3
0 500 1000 1500 2000 2500 3000 3500 4000 -6
-4 -2 0 2 4
6 Tower top accer. in y dir.
position1 position2 position3
0 500 1000 1500 2000 2500 3000 3500 4000
-10 -5 0 5 10
15 Tower Displ. in X dir.
position1 position2 position3
0 0.1 0.2 0.3 0.4 0.5 0.6 0
10 20 30 40 50
Frequency (rad/s) S (
)[ m
2/s /r ad ]
Feathered-Narcelle Sway, Hs=12.2, Tp=14.4, V=41.9M/S
postition1 position2 position3
Wp1=0.03 rad/s, close to the sway nat. freq.=0.05 rad/s Wp2=0.19 rad/s, close to the roll nat. freq.=0.192 The responses in –x directions are more sensitive to the azimuth angle of the blade.
0 500 1000 1500 2000 2500 3000 3500 4000
-10 0 10 20 30 40
50 Tower Displ. in y dir.
position1 position2 position3
0 0.2 0.4 0.6 0.8 1 1.2 0
20 40 60 80 100 120 140
Frequency (rad/s) S (
)[ m
2/s /r ad ]
Feathered-Narcelle Surge, Hs=12.2, Tp=14.4, V=41.9M/S
postition1 position2 position3
Wp1:surge, wp2:pitch, wp3: wave freq. 0.44rad/s
Conclusion: When the blades are feathered, the responses are not sensitive to the azimuth angle.
Case2 Standstill-blade2seized_wind41.7_Hs13.33Tp14.4_no direction
Case2 Standstill-blade2seized_wind41.7_Hs13.33Tp14.4_no direction
0 500 1000 1500 2000 0
5 10 15 20 25
30 spar bottom displacement -y
position1 position2 position3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
0 50 100 150 200 250 300 350 400 450 500
Frequency (rad/s) S ( )[ m
2/s /r ad ]
Feathered-seized sparbottom -y, Hs=12.2, Tp=14.4, V=41.9M/S
postition1 position2 position3
Wp1: surge wp2:pitch
0 500 1000 1500 2000 -1.5
-1 -0.5 0 0.5 1 1.5 2 2.5
3x 105 tower bottom moment Mx position1
position2 position3
0 0.5 1 1.5 2 2.5 3
0 5 10 15
x 109
Frequency (rad/s) S (
)[ m
2/s /r ad ]
Tower bottom BM, Hs=12.2, Tp=14.4, V=41.9
postition1 position2 position3
0 0.1 0.2 0.3 0.4 0.5 0.6 0
20 40 60 80 100 120 140 160 180 200
Frequency (rad/s) S (
)[ m
2/s /r ad ]
Bd2Seized Sway, Hs=12.2, Tp=14.4, V=41.9M/S
postition1 position2 position3
0 0.2 0.4 0.6 0.8 1 1.2
0 50 100 150 200 250
Frequency (rad/s) S()[m2 /s/rad]
Bd2Seized Narcelle Surge, Hs=12.2, Tp=14.4, V=41.9M/S
postition1 position2 position3
0 0.5 1 1.5 2 0
1 2 3 4 5 6 7x 106
Frequency (rad/s) S()[m2 /s/rad]
Bd2Seized Flapwise BM Blade1, Hs=12.2, Tp=14.4, V=41.9
postition1 position2 position3
0 2 4 6 8 10
0 1 2 3 4 5 6
x 105
Frequency (rad/s) S()[m2 /s/rad]
Bd2Seized edgeewise BM, Hs=12.2, Tp=14.4, V=41.9
postition1 position2 position3
Comparison between feathered and seized case, p1 Spar bottom –y
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0
50 100 150 200 250 300 350 400
Frequency (rad/s) S (
)[ m
2/s /r ad ]
Comparison sparbottom -y, Hs=12.2, Tp=14.4, V=41.9M/S
seized feathered
Nacelle Surge –y
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 ]
Comparison Narcelle Surge, Hs=12.2, Tp=14.4, V=41.9M/S
seized feathered
Nacelle Sway –x
0 0.1 0.2 0.3 0.4 0.5 0.6 0
50 100 150 200
Frequency (rad/s) S()[m2 /s/rad]
Comparison Sway, Hs=12.2, Tp=14.4, V=41.9M/S
seized feathered
Nacelle accer. –y
Tower bottom Mx
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 ]
Comparion Tower bottom Mx, Hs=12.2, Tp=14.4, V=41.9
seized feathered
Tower bottom My
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 (
)[ m
2/s /r ad ]
Comparion Tower bottom My, Hs=12.2, Tp=14.4, V=41.9
seized feathered
Blade1 Mx
0 0.5 1 1.5 2
0 1 2 3 4 5 6 7 8 9
x 106
Frequency (rad/s) S (
)[ m
2/s /r ad ]
Comparion Flapwise BM Blade1, Hs=12.2, Tp=14.4, V=41.9
seized feathered
Blade1 My
0 2 4 6 8 10 0
1 2 3 4 5 6 7 8x 105
Frequency (rad/s) S()[m2 /s/rad]
Comparion edgeewise BM, Hs=12.2, Tp=14.4, V=41.9
seized feathered
Blade2 Mx
Blade2 My
