Numerical and experimental investigation of a hinged 5-body wave energy converter
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- Institutt for marin teknikk 
This thesis deals with modeling and simulation of a hinged 5 body wave energy converter (WEC), including verification by comparison with experimental results. The WEC consists of a shallow draft cylindrical center floater hinged to 4 semisubmerged spherical buoys. One important design feature is that the hinges are submerged such that the buoys will move in a diagonal-like mode of motion. In the first part of the thesis, the linear theory of power absorption by oscillating bodies is reviewed, having particular emphasis on multi-degree-offreedom systems and optimization of power take-off parameters bounded by motion amplitude constraints (and a few other constraints). The major part of the thesis deals with time domain analysis and address some modeling challenges associated with the hinged 5-body WEC and similar WECs. These modeling challenges are associated with: • Strongly frequency dependent added mass and damping and a long hydrodynamic “memory”, representing a challenge when a time domain representation of the radiation forces are sought in the form of a state space model. • Complex equations of motion accounting for rigid hinge constraints. • Large angular motion, particularly in the hinges, giving rise to inertia force nonlinearities. • Large amplitude motion giving rise to greatly varying wetted body surface, making the validity of linear hydrodynamic theory questionable. The first challenge is addressed by introducing a new frequency domain identification technique, originally developed for complex electrical networks, which (to the author’s knowledge) have not been used on hydrodynamic radiation forces before. Assessment and enforcement of the physical property of passivity of the obtained state space models (related to the stability of the equations of motion) will also be addressed. We show that the method is capable of obtaining passive and accurate state space radiation models for the hinged 5- body WEC and an even more challenging system consisting of 17 equidistant circular cylinders. Equations of motion (EOM) for the hinged 5-body WEC are developed assuming rigid hinge constraints and by using a minimal number of generalized coordinates. Large angular motions are accounted for. We show that by describing the velocities of all bodies in the body fixed frame of the center floater, the EOM simplify significantly. The large angular motion yields inertia force nonlinearities manifested as a hinge angle dependent mass matrix and a Coriolis-Centrifugal force term. However, a numerical study of the hinged 5-body WEC in a typical operating condition shows that a linearized EOM, assuming small angles, will suffice when the aim is to predict the mean power absorption. Still, the inertia force nonlinearities yields nonlinear behavior and affects the largest maxima and minima significantly, especially in the pitch mode of the center floater. The most important type of nonlinearity is associated with the greatly varying submergence of the bodies, especially for the buoys. In the numerical model, this nonlinearity is accounted for in a simplified manner by including nonlinear Froude-Krylov and restoring forces, while still relying on linear radiation and diffraction forces. The aim of the experiments conducted as part of the thesis work was to verify the numerical model. In addition, different numerical models based on different physical assumptions have been compared. The experiments included five sea states corresponding to typical operating conditions. The overprediction of mean absorbed power by the simulation model in these sea states is between - 15% (underprediction) and 18%. When the Froude-Krylov and restoring forces are linearized in the traditional manner, the overprediction range from 60%, in a sea state producing large amplitude motion, down to 15%, occurring for a milder sea state. The experiments revealed that mean and low frequency motions of the same order of magnitude as the wave frequency motions are present in all modes of motion except for the collective heave mode. The nonlinear simulation model captures this effect with reasonable accuracy. One interesting finding is that the mean and low frequency surge motion is well captured without inclusion of the explicit second order wave forces traditionally used to analyze slow drift motions.