Transverse motion instability of a submerged moored buoy

Abstract

Wave energy converters and other offshore structures may exhibit instability, in which one mode of motion is excited parametrically by motion in another. Here, theoretical results for the transverse motion instability (large sway oscillations perpendicular to the incident wave direction) of a submerged wave energy converter buoy are compared to an extensive experimental dataset. The device is axi-symmetric (resembling a truncated vertical cylinder) and is taut-moored via a single tether. The system is approximately a damped elastic pendulum. Assuming linear hydrodynamics, but retaining nonlinear tether geometry, governing equations are derived in six degrees of freedom. The natural frequencies in surge/sway (the pendulum frequency), heave (the springing motion frequency) and pitch/roll are derived from the linearized equations. When terms of second order in the buoy motions are retained, the sway equation can be written as a Mathieu equation. Careful analysis of 80 regular wave tests reveals a good agreement with the predictions of sub-harmonic (period-doubling) sway instability using the Mathieu equation stability diagram. As wave energy converters operate in real seas, a large number of irregular wave runs is also analysed. The measurements broadly agree with a criterion (derived elsewhere) for determining the presence of the instability in irregular waves, which depends on the level of damping and the amount of parametric excitation at twice the natural frequency.

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

“…These extrinsic rotations are referred to as roll, pitch and yaw respectively. Aspects of the derivation that follows are analogous to the work of [13], [16] and [15]. Figure 1 shows a diagram of the buoy under consideration.…”

Advances and Challenges in Wave Energy Park Optimization—A Review

“…Most of the experiments on arrays have been carried out using heaving buoys (Nader et al, 2017), despite the fact that the fullscale WECs may be designed for operation in more degrees of freedom. Several experimental works with waveactivated WECs free to move in multiple degrees of freedom have reported motion instabilities (Tarrant and Meskell, 2016;Gomes et al, 2017), which can often be attributed to the PTO settings and large amplitude motions and can be understood in terms of Mathieu equations (Orszaghova et al, 2019). Whereas experimental results in recent years have enabled validation of numerical models used to model and optimize wave energy parks, more work remains to be done in terms of quantifying the uncertainties in the numerical models, and with experiments using more realistic and advanced PTO and WEC dynamics.…”

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

“…Therefore, the first reported observations of parametric resonance in WECs stem from physical scale model wave tank testing, dating back to work on the frog in the late 1980s by Bracewell [13]. Numerous further observations of parametric resonance were subsequently reported from physical scale model wave tank testing of WECs [14][15][16][17][18][19][20][21][22][23][24][25][26], which in many cases was unanticipated when first observed, since the occurrence of parametric resonance was not predicted by the simple numerical modelling results that preceded the wave tank experiments.…”

“…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.…”