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. Investigation on parametrically excited motions of point absorbers in regular wavesKevin Tarrant a , Craig Meskell a, * 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.

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.

The unsteady flow around a stationary two-dimensional wind turbine blade section (NREL S809) has been simulated using unsteady RANS with the SST turbulence model at Re = 10 6 and high angles of attack. Vortex shedding frequency non-dimensionalised by the projected area of the blade is in the range 0.11 < St < 0.16. The fluctuating coefficients at the harmonics of the fundamental vortex shedding frequency for lift, drag and pitching moment are presented. The lift force and the pitching moment (calculated with respect to the midchord) are dominated by the fundamental vortex shedding frequency, but significant contributions at the higher harmonics are also present. For the drag the second harmonic is as significant as the fundamental frequency, with the third and fourth harmonics contributing to a lesser extent. From the results, it is inferred that the camber of the airfoil does not substantially affect the force coefficients, suggesting that the results presented may be generally applicable to turbine blades of different geometry.

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