Abstract
Parametric resonance is a non-linear phenomenon in which a system can oscillate at a frequency different from its exciting frequency. Some wave energy converters are prone to this phenomenon, which is usually detrimental to their performance. Here, a computationally efficient way of simulating parametric resonance in point absorbers is presented. The model is based on linear potential theory, so the wave forces are evaluated at the mean position of the body. However, the first-order variation of the body's centres of gravity and buoyancy is taken into account. This gives essentially the same result as a more rigorous approach of keeping terms in the equation of motion up to second order in the body motions. The only difference from a linear model is the presence of non-zero off-diagonal elements in the mass matrix. The model is benchmarked against state-of-the-art non-linear Froude–Krylov and computational fluid dynamics models for free decay, regular wave, and focused wave group cases. It is shown that the simplified model is able to simulate parametric resonance in pitch to a reasonable accuracy even though no non-linear wave forces are included. The simulation speed on a standard computer is up to two orders of magnitude faster than real time.
Highlights
Parametric resonance in an oscillating system is a resonance which is excited parametrically, that is, by a time variation of some parameter of the system, as opposed to some external excitation
In Figure 6c), the pitch response predicted by WECSim appears to oscillate at a shorter period than those predicted by the simplified model and OpenFOAM, which seem to agree in phase, despite having different decay rate
A simplified model to capture parametric resonance in pitch has been presented and applied to model a hypothetical wave energy converters (WECs) in the form of a floating axisymmetric body, where power is taken from heave only
Summary
Parametric resonance in an oscillating system is a resonance which is excited parametrically, that is, by a time variation of some parameter of the system, as opposed to some external excitation. For freely floating WECs, the mechanism that triggers parametric resonance is usually thought to be a time-varying metacentric height due to the heaving motion of the body relative to the free surface. This would modulate the roll or pitch restoring stiffness and excite the roll or pitch resonance. Similar simplified approaches (i.e. without the use of non-linear wave forces) exist in the literature and have been used to model parametric resonances of ships [1], spars [22], and WECs [12, 23, 24], we note that there are differences in these models. The three simulation cases are described and discussed in turn, including remarks on typical computation times
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