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

UPWIND WP4: Offshore Support Structures and Foundations
Table 8.12. These coefficients do not depend on the frequency of the incident wave and are computed relatively
to the centre of mass of the structure. The axi-symmetry of the structure implies that the hydrostatic coefficient
in roll (C44) is the same as in pitch (C55). The dimensional values of these coefficients can be obtained by multiplying
the non-dimensional values by the density of water (ρ) and the gravitational constant (g):
Table 8.12: Non-dimensional hydrostatic coefficients associated with the OC3-Hywind.
Coefficient Value
102
C33
C44, C55
33.183
0.22370E+06
[8-10]
The frequency dependence of the response amplitude operator (RAO) for the unrestrained motions of the OC3-
Hywind platform is shown in Figure 8.10 for incident waves with periods up to 25 s. The freely floating OC3-
Hywind platform has a resonance period in surge and pitch close to 17 s. For this wave period, the unrestrained
motion amplitude in surge is of about 7 times the wave amplitude and in pitch of about 0.5rad (~30deg.) per
meter of wave amplitude. The unrestrained motions in heave have a maximum of about one third of the amplitude
of the incident wave occurring at a wave period close to 20s.
|X 1 |
|X 3 |
|X 2 |
10
5
0
0 5 10 15 20 25
Wave Period [s]
x 10-7
2
1
0
0 5 10 15 20 25
Wave Period [s]
0.4
0.2
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]
100
0
-100
0 5 10 15 20 25
Wave Period [s]
100
50
0
0 5 10 15 20 25
Wave Period [s]
|X 5 |
|X 6 |
|X 4 |
x 10-8
2
1
0
0 5 10 15 20 25
Wave Period [s]
0.5
0
0 5 10 15 20 25
Wave Period [s]
0.5
x 10-17
1
0
0 5 10 15 20 25
Wave Period [s]
Phase X 4 [deg]
Phase X 5 [deg]
Phase X 6 [deg]
100
0
-100
0 5 10 15 20 25
Wave Period [s]
200
0
-200
0 5 10 15 20 25
Wave Period [s]
91
90
89
0 5 10 15 20 25
Wave Period [s]
Figure 8.10: 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 OC3-Hywind.
Second-order hydrodynamic loads and unrestrained motions for monochromatic waves
The second-order solution requires the free-surface to be discretised. An example of the mesh associated with
the OC3-Hywind structure used in the present study is shown in Figure 8.11.