Onset and limiting amplitude of yaw instability of a submerged three-tethered buoy

Abstract

<jats:p>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.</jats:p>

Numerical simulation of parametric resonance in point absorbers using a simplified model

“…It is clear how this would be detrimental to power absorption for devices whose absorbing mode is heave. An additional observation is that parametric resonance is relatively narrow banded, with increasing bandwidth as the wave amplitude is increased, in agreement with the Mathieu equation's stability diagrams (see [15] or [16]). We also observe that the normalised amplitudes, including those of the subharmonic surge and pitch motions, are reduced as the incident wave height is increased, which is expected due to the greater drag forces, which increase quadratically with motion amplitudes.…”

“…Floating wave energy converters (WECs) are in some respects similar to a ship without a forward speed, and we might expect that WECs are also prone to parametric resonance. Indeed, parametric resonance has been observed in model experiments of a variety of WECs, including floating oscillating water columns [2][3][4][5], self-reacting floating WECs of various configurations [6][7][8][9][10][11][12], and WECs tethered to the sea bed, either surface piercing [13] or completely submerged [14][15][16]. A reduction in power capture usually accompanies the occurrence of parametric resonance, and thus the importance of avoiding it has been recognised for some time [17].…”

A Real-Time Detection System for the Onset of Parametric Resonance in Wave Energy Converters

“…Therefore, several modelling approaches have been employed to capture this mooring induced effect. For the case of a taut moored WEC, Nicoll et al [42] utilised the pendulum equation to model the parametric excitation, whereas Orszagova et al [21,25,43] utilised a 2nd order Taylor series for the mooring system dynamics to successfully capture the parametric resonance phenomenon.…”

Nonlinear Dynamic and Kinematic Model of a Spar-Buoy: Parametric Resonance and Yaw Numerical Instability

“…Moreover, the rotational displacement and velocity are normally assumed to be small. Few nonlinear studies are performed in six DoFs, especially considering roll/pitch parametric resonance or yaw instability [29,30].…”