Final report for WP4.3: Enhancement of design methods ... - Upwind

UPWIND WP4: Offshore Support Structures and Foundations
A 11
A 44
10000
A 15
5000
0
0 10 20
Wave Period [s]
x 106
7.6
7.4
7.2
0 10 20
Wave Period [s]
x 104
2
0
-2
0 10 20
Wave Period [s]
A 33
A 66
A 24
x 104
1.35
1.3
1.25
0 10 20
Wave Period [s]
x 106
10
5
0
0 10 20
Wave Period [s]
x 104
2
0
-2
0 10 20
Wave Period [s]
110
B 11
B 44
B 15
4000
2000
0
0 5 10 15 20 25
Wave Period [s]
x 105
2
1
0
0 5 10 15 20 25
Wave Period [s]
x 104
2
0
-2
0 5 10 15 20 25
Wave Period [s]
B 33
B 66
B 24
100
50
0
0 5 10 15 20 25
Wave Period [s]
x 106
5
0
0 5 10 15 20 25
Wave Period [s]
x 104
2
0
-2
0 5 10 15 20 25
Wave Period [s]
Figure 8.22: Added-mass and hydrodynamic damping coefficients for the semi-submersible platform for incident wave
periods up to 25 s
Table 8.17: Non-dimensional hydrostatic coefficients for the semi-submersible platform.
Coefficient Value Coefficient Value
C33 269.76 C45 0.13018E-01
C34 -0.16089E-02 C46 0.13611
C35 -0.14339E-02 C55 0.14636E+06
C44 0.14636E+06 C56 -0.70826E-01
The frequency dependence of the response amplitude operator (RAO) for the unrestrained motions of the
semi-submersible platform is shown in Figure 8.23. For this structure, resonance occurs in heave for the unrestrained
submerged motions at about 17 s. At this wave period the motions in surge, roll and pitch have also
maximum amplitude.
|X 1 |
|X 2 |
|X 3 |
1
0.5
0.04
0.02
0
0 5 10 15 20 25
Wave Period [s]
0
0 5 10 15 20 25
Wave Period [s]
100
50
0
0 5 10 15 20 25
Wave Period [s]
Phase X 1 [deg]
Phase X 2 [deg]
Phase X 3 [deg]
200
0
-200
0 5 10 15 20 25
Wave Period [s]
200
0
-200
0 5 10 15 20 25
Wave Period [s]
200
0
-200
0 5 10 15 20 25
Wave Period [s]
|X 4 |
|X 6 |
|X 5 |
0.04
0.02
0
0 5 10 15 20 25
Wave Period [s]
0.4
0.2
0
0 5 10 15 20 25
Wave Period [s]
0.01
0.005
0
0 5 10 15 20 25
Wave Period [s]
Phase X 4 [deg]
Phase X 5 [deg]
Phase X 6 [deg]
200
0
-200
0 5 10 15 20 25
Wave Period [s]
200
0
-200
0 5 10 15 20 25
Wave Period [s]
200
0
-200
0 5 10 15 20 25
Wave Period [s]
Figure 8.23: Frequency dependence of the response amplitude operator (RAO) for the linear unrestrained motions in
surge (x1), sway (x2), heave (x3), roll (x4), pitch (x5) and yaw (x6) associated with the semi-submersible platform.
Second-order hydrodynamic loads and unrestrained motions for monochromatic waves
Given the input wave spectrum represented by N components, the time-series of the total excitation force is
computed as for the OC3-Hywind platform. The second-order solution requires the additional discretisation of
the free-surface. This mesh is shown in Figure 8.24 for the semi-submersible platform.