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

UPWIND WP4: Offshore Support Structures and Foundations
L (|F |)
∞ X1
L (|F |)
∞ X3
L (|F |)
∞ X5
10 0
10 -5
10 -2
10 -3
10 -4
10 0
10 -2
10 -4
10 2
Number of unknowns
10 2
Number of unknowns
10 2
Number of unknowns
98
10 4
10 4
10 4
L (|F |)
∞ X2
L (|F |)
∞ X4
L (|F |)
∞ X6
10 -2
10 -3
10 -4
10 -5
10 -10
10 -15
10 -12
10 -14
10 -16
10 2
Number of unknowns
10 2
Number of unknowns
10 2
Number of unknowns
Figure 8.5: Evolution of the convergence in terms of the error norm for the linear excitation force associated with the
OC3-Hywind.
Convergence studies for the semi-submersible platform
To simplify the model used to compute the hydrodynamic loads of the semi-submersible platform it was assumed
that the major contributions of the hydrodynamic interaction are due only to the three cylindrical columns
and horizontal damping plates. The influence of the submerged braces which interconnect the three columns
was considered negligible with regard to the hydrodynamic loads (see Figure 8.3 b).
The geometry of this structure was discretised for three grid sizes with the panel size parameter equal to 10.0
m, 5.0 m and 2.5 m. The hydrodynamic quantities were computed for five wave periods selected randomly between
5 s to 16 s. The three discretisations considered for the convergence analysis are shown in Figure 8.6.
Figure 8.6: Three discretisations of the geometry of the semi-submersible platform used in the convergence tests. The
panel size parameter equal to (a) 10.0 m (b) 5.0 m and (c) 2.5m.
The convergence ratio (R) associated with the excitation forces obtained for the discretisation triplet used in this
study is shown in Table 8.8. As with the previous geometry, most of the values are between -1 and 1 and the
solution for these quantities can be classified as convergent. The estimation of the exact solution for the linear
excitation force at the incident wave periods considered in this study is presented in Table 8.9 and the
uncertainty associated with the finer mesh is presented in Table 8.10. The evolution of the convergence for four
different discretisations presented in terms of the error norm for the linear excitation forces is presented in
Figure 8.7. Once again the uncertainty estimates are several orders of magnitude smaller than the excitation
force values, which is reassuring of the quality of the numerical solutions. The relation between the panel size
parameter and the number of equations (N) in the linear system to be solved by WAMIT which is used as a
measure of the total number of panels is shown in Table 8.11.
10 4
10 4
10 4