Final report for WP4.3: Enhancement of design methods ... - Upwind
Final report for WP4.3: Enhancement of design methods ... - Upwind
Final report for WP4.3: Enhancement of design methods ... - Upwind
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UPWIND WP4: Offshore Support Structures and Foundations<br />
cordant damping by using the linear beam theory. Although this is a significant simplification <strong>of</strong> the structural<br />
arrangement <strong>of</strong> the line’s fibers, it is necessary to reduce the model’s complexity and thereby simulation time.<br />
Using chain mooring lines, this stiffness and damping could be neglected.<br />
Spar Buoy<br />
Fairlead<br />
Joint<br />
129<br />
ϕ x<br />
ϕ z<br />
u y<br />
rigid body<br />
3 DOF<br />
c r, d r<br />
Seabed<br />
c t, d t<br />
c s d s<br />
Figure 8.40: MBS mooring line configuration<br />
Anchor<br />
The degrees <strong>of</strong> freedom (DOF) are reduced to a minimum <strong>of</strong> one translational and two rotational directions. To<br />
enable the simulation <strong>of</strong> the line’s elongation the DOF in cylinder’s longitudinal direction has to be maintained.<br />
Also the transverse rotational movements have to be enabled. The line’s twist DOF could be eliminated because<br />
there is no significant effect on the hydrodynamic behaviour due to the use <strong>of</strong> symmetric cylinders <strong>for</strong><br />
discretization.<br />
The very complex behaviour <strong>of</strong> the seabed is reduced to a unilateral spring-damper-model with high stiffness<br />
and damping to represent a rigid floor. The lateral friction is modelled by a simple coulombic element with an<br />
empiric friction coefficient.<br />
The hydrodynamic effects to the mooring line are represented by a variation <strong>of</strong> the Morison-Equation. Östergaard<br />
and Schellin describe this variation <strong>for</strong> slender hydrodynamic transparent cylindrical structures with arbitrary<br />
orientation to the current <strong>of</strong> the surrounding fluid.<br />
Where is the fluid’s velocity, the relative velocity between structure and fluid and index the normal direction<br />
to the segment. The drag and inertia coefficients and are chosen empirically which could lead to further<br />
uncertainties. By using the potential theory the Morison-Equation considers hydrodynamic drag and inertia<br />
but neglects effects based on dissipative flow, like vortex induced vibrations.<br />
Investigations <strong>of</strong> the discretization show only small effects on the results when increasing the number <strong>of</strong> elements<br />
beyond a certain number <strong>of</strong> discretized elements. This number has to be identified by a sensitivity analysis.<br />
Following this procedure enables to come up with a moderate discretization and limit simulation time while<br />
keeping accuracy <strong>of</strong> the results.<br />
Comparisons in Figure 8.41 <strong>of</strong> the plat<strong>for</strong>m’s surge motion to quasi-static models show significant differences<br />
caused by the non-linear additional hydrodynamic damping <strong>of</strong> the MBS model. Accordingly, similar differences<br />
in the <strong>for</strong>e-aft bending moment at the tower base can be identified in Figure 8.42.