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Potential (HDB) or Morison approach
The potential theory is currently the most advanced engineering solution to compute the hydrodynamic loads on a floater represented by a rigid body. Of course, more advanced approaches resorting to CFD can be envisaged but they are not mature yet to be used during a design loop. The potential approach allows accounting for incident, diffracted and radiated flows; viscous damping on the hull shall be derived by CFD or basin tests and are often added through damping matrices.
The conventional full Morison approach is fit for detailed floater design (as opposed to a floater represented by a whole rigid body) since it directly provides distributed loads along the structural flexible elements, but is expected to become less accurate since the Morison formulation ignores the diffracted flow and may over estimate hydrodynamic loads at lower wave periods.
Therefore, a new potential-flow approach (so-called sub-structure model) was developed in order to combine the advantages of both approaches by the generation of local hydrodynamic loads from a diffraction/radiation data base that are loaded on a flexible model. Defoy et al. [47] showed that substructure modelisation for a floating wind turbine produced results close to those observed in model tests.
Wave loads classification according to Chakrabarti [54]
The ratio of Morison drag term over inertia term gives the following expression:
Considering \(C_D\simeq 1\) and \(C_M\simeq 2\), the last relation can be expressed as:
The following figure represents the regions where diffraction/inertia/drag effects are predominant; the y-axis \(H/D\) is equivalent to the Keulegan-Carpenter number whereas the x-axis is the diffraction parameter \(\pi D/L\).
Determination of wave loads according to H,D, and \(\lambda\) by Chakrabarti
If the diameter of the cylinder has the same order of magnitude than the wavelength, the potential flow theory has to be applied in order to consider diffraction effects (zone II, IV). This corresponds to the right part on the x-axis. On the contrary, for small diameters compared to the wavelength, Morison empirical formula can be used to predict wave loads on the cylinder (zone I, III, V and VI):
- For \(KC<3\) (zone I), the inertia term is dominant and drag loads are negligible. Thus both the potential flow theory and Morison formulation are applicable.
- For \(3<KC<15\) (zone III), drag load becomes significant, the drag term can be linearised.
- For \(15<KC<45\) (zone V), Morison expression is applied to describe loads on the structure.
- For \(KC>45\) (zone VI), the drag force is dominant.
