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

UPWIND WP4: Offshore Support Structures and Foundations
S [m 2 s]
Amplitude [m]
30
20
10
0
0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Incident wave frequency [Hz]
0.8
0.6
0.4
0.2
0
4 6 8 10 12 14 16 18
Incident wave period [s]
Figure 8.14: (Top) Pierson Moskowitz spectrum with Hs = 5.0 m (Tp = 11.18 s) described by sixteen components. (Bottom)
Wave amplitude and period associated with the top spectrum.
The absolute value of the sum- and difference- frequency force QTFs ( , ) computed for the OC3-Hywind
platform in surge, heave and pitch modes for the sixteen frequency components associated with these Pierson-
Moskowitz spectra is shown in Appendix A of [111]. As expected the sum-frequency components are symmetric
satisfying the relation: , whereas the difference-frequency components are
complex conjugate symmetric satisfying the relation: .
Pierson-Moskowitz spectrum with Hs=0.5 m
The first and second-order excitation forces in surge, heave and pitch for the OC3-Hywind associated with a
Pierson Moskowitz spectrum with Hs=0.5m (Tp=3.54s) are shown in Figure 8.15. For this spectrum the influence
of the second-order components is more important in surge and pitch modes than in heave. The time series
for surge and pitch show the presence of higher frequency components due to the predominance of the
sum-frequency force QTFs.
Excitation Force in surge [MN]
0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
0 5 10 15 20 25
Time [s]
Excitation Force in heave [MN]
0.01
0.005
0
-0.005
-0.01
0 5 10 15 20 25
Time [s]
106
Excitation Force (pitch) [MN.m]
15
10
5
0
-5
-10
-15
0 5 10 15 20 25
Time [s]
Figure 8.15: Comparisons between first and second-order excitation forces in surge, heave and pitch modes for a Pierson-
Moskowitz spectrum with Hs=0.5 m (Tp = 3.54 s).