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Sub Structures

With the development of Floating Offshore Wind Turbines (FOWT), the design of a floater needs to be revisited. Indeed, the global system involves aerodynamic and hydrodynamic loadings together with a strongly coupled system. Therefore, in order to have the proper motions, the whole system has to be modelled at once. It is then interesting to directly obtain the internal loads in the floater to check its design. Most potential flow approaches considers the floaters as a rigid body and do not allow direct extraction of these loads. Due to the size of the floater, it can also be modelled with beam elements, the hydrodynamic loadings being provided by a Morison type formulation. Nonetheless, the validity of this formulation is restricted to larger wave periods, whereas at lower periods its limitations appear. In the present paper, an alternative solution is presented, the so called sub- structures approach, which aims at combining the advantages of both previous approaches. The floater is defined through beam elements but those elements are loaded with potential flow theory forces together with a drag correction..

For this type of floater, three modelling approaches are available (see JH2018 for comparisons with model tests):

  • Full Morison model
  • Potential flow model (hydrodynamic database)
  • Substructure model (SUB_HDB: each substructure has its own potential flow theory data, those data should be derived with the whole floater in the hydrodynamic calculations to obtain influence of one element on the other)

It should be kept in mind that the substructure model (SUB_HDB) is a combination of a Morison and a potential model, as detailed below: The flexible structure is composed of beam elements. It is then the equivalent of the full Morison model from a structural point of view, i.e. the beam elements directly provide the following:

  • Internal forces and moments due to beam strains and curvatures;
  • Mass and inertia loads excluding added masses;
  • Drag loads.

The substructure hydrodynamic database (Sub-HDB) computed by a potential-flow software like DIODORE, is used to calculate the hydrodynamic loads. From a global hydrodynamic point of view, this is equivalent to a full HDB model except that the floaters hull mesh has been divided into sub-meshes and pressures loads are integrated on every sub-structure. Finally:

  • The potential loads transfer reponse amplitudes are stored in a Sub-HDB file for each structural element that composes the floaters hull (Wave excitation forces, radiation damping and added mass);
  • the hydrostatic loads are directly computed during the time domain calculations from the panel mesh.

The three models are presented. The methodology used to define the three models is illustrated in Figure 1. It is based on the following steps:

  • Build the beam model and the associated panels mesh (e.g. ISYMOST software).
  • Define each substructure: a substructure is defined by a set of beam finite elments associated with the correponding panel mesh.
  • Run the potential flow analysis with Diodore. This generates the potential flow loads for each substructure (HDB).

Figure 1 : Definition of the three models

Once the beam model is built, it is imported in DeepLines Wind (.tdl file automatically created by ISYMOST), taking into account all mechanical mass and inertia, and the Hydrodynamic database properly defined with Diodore. The three models can easily be defined at once in DeepLines Wind, ensuring that they will be equivalent.

Figure 2 : Summary of input Morison, SUB_HDB and HDB model

The excitation loads, added mass and radiation damping terms of each substructure in the Sub-HDB file are expressed in the floaters global frame at the reduction point and not in the beam local frame. Therefore, a first step is to change the application point of the input in the Sub-HDB file, the application point being the center (or reference node) of the beam elements defining the substructure. Note that this process assumed that the floaters deformation remains small. The calculations of the hydrodynamic loads is then performed for each sub-structure as detailed in Figure 3.

Figure 3 : Sub-structure definition

Note that the drag force accounting for the viscous effects is directly added on the nodes through the beam element. Also the first order wave force can be further defined as an incident wave term and a diffracted term. In that case, the incident wave term can alternatively be computed at each step from pressure intergration on the sub-structure mesh