Investigation on Parametrically Excited Motions of Point Absorbers in Regular Waves

Abstract

Abstract.Free floating objects such as a self-reacting wave energy converter (WEC), may experience a condition known as parametric resonance. In this situation, at least two degrees of freedom become coupled when the incident wave has a frequency approximately twice the pitch or roll natural frequency. This can result in very large amplitude motion in pitch and/or roll. While classic linear theory has proven sufficient for describing small motions due to small amplitude waves, a point absorber WEC is often designed to operate in resonant conditions, and therefore, exhibits significant nonlinear responses. In this paper, a time-domain nonlinear numerical model is presented for describing the dynamic stability of point absorbers. The pressure of the incident wave is integrated over the instantaneous wetted surface to obtain the nonlinear Froude-Krylov excitation force and the nonlinear hydrostatic restoring forces, while first order diffraction-radiation forces are computed by a linear potential flow formulation. A numerical benchmark study for the simulation of parametric resonance of a specific WEC -the Wavebob -has been implemented and validated against experimental results. The implemented model has shown good accuracy in reproducing both the onset and steady state response of parametric resonance. Limits of stability were numerically computed showing the instability regions in the roll and pitch modes. AbstractFree floating objects such as a self reacting wave energy converter (WEC), may experience a condition known as parametric resonance. In this situation, at least two degrees of freedom become coupled when the incident wave has a frequency approximately twice the pitch or roll natural frequency. This can result in very large amplitude motion in pitch and/or roll. While classic linear theory has proven sufficient for describing small motions due to small amplitude waves, a point absorber WEC is often designed to operate in resonant conditions, and therefore, exhibits significant nonlinear responses. In this paper, a time-domain nonlinear numerical model is presented for describing the dynamic stability of point absorbers. The pressure of the incident wave is integrated over the instantaneous wetted surface to obtain the nonlinear Froude-Krylov excitation force and the nonlinear hydrostatic restoring forces, while first order diffraction-radiation forces are computed by a linear potential flow formulation. A numerical benchmark study for the simulation of parametric resonance of a specific WEC-the Wavebob-has been implemented and validated against experimental results. The implemented model has shown good accuracy in reproducing both the onset and steady state response of parametric resonance. Limits of stability were numerically computed showing the instability regions in the roll and pitch modes.

Mathematical modelling of wave energy converters: A review of nonlinear approaches

“…Self-reacting devices, where coupling between different modes is important, are highly sensitive to the nonlinear coupling of heave, roll or pitch. [60] clearly demonstrates that the nonlinear heave, roll and pitch coupling occurs at large motion amplitudes and that the partially linear potential model is able to predict the parametric resonance, validating the model against experimental tests in a wave tank.…”

“…Therefore, nonlinear potential flow approaches are a suitable solution. The fact that nonlinear radiation and diffraction appear to be negligible [31,32] and the main nonlinear effects arise from nonlinear Froude-Krylov forces [26,86,60], partially nonlinear approaches suit ideally, which is also convenient in terms of computational requirements. CFD approaches provide marginally higher fidelity [202,203] compared to potential flow models, but the excessive additional computation cost is hardly justified by the differences in the results.…”

“…The phenomenon of parametrically excited motions has also been identified in wave energy converters when testing devices in real wave tanks [27,59,60]. Since, it is related to a loss of hydrostatic stability in situations of large displacements, nonlinear potential models, such those presented in Section 3.2.2, should be able to predict the phenomenon.…”

“…HPA Wavestar [95] CETO [96] PowerBuoy [97] Parametric excitation High: crucial under large relative motions, for reproducing devices' behaviour [26,30], including parametrically excited motions [60].…”

Transverse motion instability of a submerged moored buoy

“…As the roll and yaw motions increase, the device pitch decreases, resulting in a drop in power extraction. Tarrant and Meskell [9] examine an axi-symmetric heaving device called Wavebob. Undesired amplification of roll and pitch modes is observed in experiments and numerical simulations.…”