Modelling of Parametric Resonance for Heaving Buoys with Position-Varying Waterplane Area

János Lelkes,Josh Davidson,Tamás Kalmár-Nagy

doi:10.3390/jmse9111162

János Lelkes, Josh Davidson + Show 1 more

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https://doi.org/10.3390/jmse9111162

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Abstract

Exploiting parametric resonance may enable increased performance for wave energy converters (WECs). By designing the geometry of a heaving WEC, it is possible to introduce a heave-to-heave Mathieu instability that can trigger parametric resonance. To evaluate the potential of such a WEC, a mathematical model is introduced in this paper for a heaving buoy with a non-constant waterplane area in monochromatic waves. The efficacy of the model in capturing parametric resonance is verified by a comparison against the results from a nonlinear Froude–Krylov force model, which numerically calculates the forces on the buoy based on the evolving wetted surface area. The introduced model is more than 1000 times faster than the nonlinear Froude–Krylov force model and also provides the significant benefit of enabling analytical investigation techniques to be utilised.

Highlights

The present paper proposes a new method for exploiting parametric resonance in heaving wave energy converters (WECs) utilising a heave-to-heave Mathieu instability
To examine the ability of the analytical model to capture parametric resonance, numerous simulations were performed at frequencies close to twice the buoy’s natural frequency for a range of wave heights
The target application of the mathematical model is to evaluate the ability of heaving wave energy converters to leverage large amplitude oscillations triggered by the occurrence of parametric resonance due to a position-varying waterplane area

Summary

Introduction

Modelling of Renewable energy sources are an attractive form of energy supply for the growing human population, since these resources are inexhaustible and clean. Ocean wave energy presents an enormous renewable energy resource, spurring significant research towards the development of wave energy converters (WECs) in recent decades [1,2]. WECs are typically designed to resonate with the dominant frequency of the input waves. The concept of resonance is very well known and applied within the field of wave energy conversion. The phenomenon of parametric resonance has received far less attention, and its potential to increase WEC performance is mostly unexplored

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