Abstract
In this paper the dynamics of a submerged axi-symmetric wave energy converter are studied, through mathematical models and wave basin experiments. The device is disk-shaped and taut-moored via three inclined tethers which also act as a power take-off. We focus on parasitic yaw motion, which is excited parametrically due to coupling with heave. Assuming linear hydrodynamics throughout, but considering both linear and nonlinear tether geometry, governing equations are derived in 6 degrees of freedom (DOF). From the linearized equations, all motions, apart from yaw, are shown to be contributing to the overall power absorption. At higher orders, the yaw governing equation can be recast into a classical Mathieu equation (linear in yaw), or a nonlinear Mathieu equation with cubic damping and stiffness terms. The well-known stability diagram for the classical Mathieu equation allows prediction of onset/occurrence of yaw instability. From the nonlinear Mathieu equation, we develop an approximate analytical solution for the amplitude of the unstable motions. Comparison with regular wave experiments confirms the utility of both models for making relevant predictions. Additionally, irregular wave tests are analysed whereby yaw instability is successfully correlated to the amount of parametric excitation and linear damping. This study demonstrates the importance of considering all modes of motion in design, not just the power-producing ones. Our simplified 1 DOF yaw model provides fundamental understanding of the presence and severity of the instability. The methodology could be applied to other wave-activated devices.
Highlights
Dynamic instabilities in floating wave energy converters (WECs) have recently received much attention in the literature
Wave-activated WECs which are free to move in multiple degrees of freedom (DOF) are prone to such dynamic instabilities
This is analogous to the behaviour under regular waves predicted by our models derived in §2b,c, whereby linear damping determines the presence of the instability, and the nonlinear terms in the governing equations govern the severity of the unstable response (i.e. the limiting amplitude solution in equation (2.14))
Summary
Dynamic instabilities in floating wave energy converters (WECs) have recently received much attention in the literature. Tarrant and Meskell [1,2] examine an axi-symmetric two-body heaving device called Wavebob which exhibits undesired roll and pitch oscillations in experiments Numerical simulations of their model with the appropriate nonlinearities included satisfactorily predict the onset of the instabilities and to some degree the magnitude of the unstable motions. In another study [5], the same authors investigate roll instability in an oscillating water column spar buoy, inspired by the experimental work of [6] They are able to consider irregular wave conditions, unlike most other studies which focus on regular waves, thanks to the efficiency of their model for axi-symmetric devices. Three-tethered point-absorber WECs have been studied by [14,15]
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