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WP 2

Hydrodynamic studies and coupled hydro-aero-elastic analysis of the moored multi-purpose floating platform

Objective: To analyze the coupled behavior of the system and conclude the design of its components in full scale

Task 2.1: Hydrodynamic analysis of the floating structure with the OWC device.

Objectives: To evaluate the frequency-dependent first- and second-order hydrodynamic characteristics of the floating structure with the OWC; to calculate the hydrodynamic parameters and the second-order wave drift damping1; to evaluate the dynamic pressure fluctuation and the associated air flow rate for the dimensioning of the OWC’s air turbine.

Description: The analysis will be carried out in the frequency domain using analytical and panel methodologies that take properly into account the hydrodynamic interactions in case of multiple interacting floaters ^{[12], [13]}. The coupled effects of the OWC and the floater are analyzed within the framework of the linear theory. For the Power Take off (PTO) system, a generic wells turbine will be assumed that is modeled in a similar way as in ^[14]. The effect of the OWC on the platform motions, which in turn may affect the performance of the W/T.. is evaluated and incorporated in the coupled analysis of the multi-purpose floating energy conversion system (see T2.3 below).

Task 2.2: Mooring system analysis and design

Objectives: To define the geometrical and inertial characteristics of the mooring system (mooring line length, diameter, weight, etc.), its stiffness and the pretention level; to evaluate the quasi-static and time-dependent restoring forces; to evaluate the mooring-line induced damping. The task will provide the necessary input for the coupled analysis foreseen in T2.3 below.

Task 2.3: Coupled hydro-aero-elastic behaviour of the moored floating energy conversion system

Objectives: To analyse the coupled dynamics of the wind turbine and the moored platform with the OWC’s devices mounted on it, by solving the equations of motions in the frequency- and the time-domain; to predict motions of the floating structure, those of the W/T first in terms of its basic modes and then in its full form, the air flow rate in OWC device, the loads in the mooring lines and at the mounting locations of the wind turbine on the floater under specified environmental conditions.

Description: The fully-coupled problem will be formulated in the context of the multi-body non-linear dynamics. Each of the basic components: the blades, the drive train, the tower; the floater components and the mooring lines will be considered as interconnected bodies. At the connection points (i.e. the hub, the top of the tower, the bottom of the tower and the mooring connections to the floater) full kinematic and dynamic compliance will be imposed. External excitations to this multi-body structure will be provided by the wind inflow (basically on the blades) and the wave hydrodynamic loading (basically on the floater). All components of the system will be considered flexible. In its full form the resulting equations are non-linear and therefore time-domain simulations must be performed. However especially for stability analysis, less demanding simulations are needed. To this end the equations will be linearized with respect to a reference state by means of Taylor expansions, which allows defining (linearized) coupled modes. Such linearizations can be also defined separately for any of the sub-systems. In the present Task, this option will be applied to the W/T. Considering the basic modes of the W/T system, it is possible to formulate reduced modal equations that will only depend on the floater motions and therefore allow both frequency and time-domain simulations of significantly reduced cost. The tools and the required input data concerning the wind turbine system for its coupling with the floater will be obtained in WP4 which will run partially in parallel with the present WP. By the way of example the linearized equation of motion of the moored floating energy conversion system in the frequency domain for harmonic excitations is given below:

       

The frequency dependent mass, damping and stiffness characteristics of the W/T will be obtained in T4.2, while the corresponding hydrodynamic parameters (added mass and the damping) of the floater together with the damping and restoring characteristics offered to the floating energy conversion system by the OWC will be evaluated in T2.1. The restoring coefficients due to the mooring system will be calculated in T2.2. The six-by-one vector F(ω) contains the linearized hydrodynamic exciting forces.

 

[12] Mavrakos, S.A., Koumoutsakos, P. 1987. “Hydrodynamic interaction among vertical axisymmetric bodies restrained in waves”, Applied Ocean Research, 9(3), 128-140.

[13]Mavrakos, S.A., Konispoliatis, D. 2011. “Hydrodynamics of a floating oscillating water column device”, Proceedings, 14th IMAM2011 Congress, September 13-16, Genoa, Italy (accepted).

[14]Gato, L.M.C., Falcao, A.F. 1988. “Aerodynamics of the wells turbine”, Int. J. Mech. Sci., 30(6), 383-395