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

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.

Download Full-text

Optimisation of the geometry of axisymmetric point-absorber wave energy converters

Journal of Fluid Mechanics ◽

10.1017/jfm.2021.993 ◽

2021 ◽

Vol 933 ◽

Author(s):

Emma C. Edwards ◽

Dick K.-P. Yue

Keyword(s):

Surface Area ◽

Wave Energy ◽

Basis Functions ◽

Motion Constraints ◽

Point Absorber ◽

Wave Energy Converters ◽

Rigorous Framework ◽

Point Absorbers ◽

Well Posed ◽

Energy Converters

We propose a scientifically rigorous framework to find realistic optimal geometries of wave energy converters (WECs). For specificity, we assume WECs to be axisymmetric point absorbers in a monochromatic unidirectional incident wave, all within the context of linearised potential theory. We consider separately the problem of a WEC moving and extracting wave energy in heave only and then the more general case of motion and extraction in combined heave, surge and pitch. We describe the axisymmetric geometries using polynomial basis functions, allowing for discontinuities in slope. Our framework involves ensuring maximum power, specifying practical motion constraints and then minimising surface area (as a proxy for cost). The framework is robust and well-posed, and the optimisation produces feasible WEC geometries. Using the proposed framework, we develop a systematic computational and theoretical approach, and we obtain results and insights for the optimal WEC geometries. The optimisation process is sped up significantly by a new theoretical result to obtain roots of the heave resonance equation. For both the heave-only, and the heave-surge-pitch combined problems, we find that geometries which protrude outward below the waterline are generally optimal. These optimal geometries have up to 73 % less surface area and 90 % less volume than the optimal cylinders which extract the same power.

Download Full-text

Modeling of the Efficiency of a Semisubmerged Ocean Wave Energy Converter

Marine Technology Society Journal ◽

10.4031/mtsj.47.4.19 ◽

2013 ◽

Vol 47 (4) ◽

pp. 177-186 ◽

Cited By ~ 1

Author(s):

Michael T. MacNicoll ◽

Krish P. Thiagarajan ◽

John Rohrer

Keyword(s):

Mathematical Model ◽

Wave Energy ◽

Analytical Investigation ◽

Wave Energy Converter ◽

Wave Forces ◽

Energy Converter ◽

Ocean Wave Energy ◽

Air Chamber ◽

Compression And Expansion ◽

Oriented Parallel

AbstractThe RTI G2 is a terminator-type wave energy converter (WEC) that converts energy through a power take-off (PTO) system located within an elongated, wave-front facing compressible air chamber. The compression and expansion of the chamber is driven by both kinetic and potential energy due to the surge and heave wave forces acting on an actuator plate oriented parallel to oncoming waves. The RTI G2 converter is mounted on a stabilizing frame, which may float or be fixed to the seabed and allows the air chamber to be totally submerged below wave troughs during severe seas. The present work examines the performance of the RTI G2 on a fixed frame. Model tests conducted on a 1:8 scale are reviewed, and a mathematical model to describe the performance of the RTI G2 is developed. The experimental results are used for calibration and validation of the mathematical model. Several orientation angles of the compression chamber are modeled, with higher orientation angles yielding better efficiencies at higher wave frequencies. The RTI G2 is a novel WEC concept, and the present work provides the first analytical investigation into its behavior.

Download Full-text

The inclusion of non-linearities in a mathematical model for U-Oscillating Water Column wave energy converters

Energy ◽

10.1016/j.energy.2020.119320 ◽

2021 ◽

Vol 218 ◽

pp. 119320

Author(s):

Pietro Scandura ◽

Giovanni Malara ◽

Felice Arena

Keyword(s):

Mathematical Model ◽

Water Column ◽

Wave Energy ◽

Oscillating Water Column ◽

Wave Energy Converters ◽

Energy Converters

Download Full-text

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

Journal of Marine Science and Engineering ◽

10.3390/jmse8100819 ◽

2020 ◽

Vol 8 (10) ◽

pp. 819

Author(s):

Josh Davidson ◽

Tamás Kalmár-Nagy

Keyword(s):

Control System ◽

Real Time ◽

Parametric Resonance ◽

Wave Energy ◽

Detection System ◽

Maximum Amplitude ◽

Recursive Least Squares ◽

Wave Energy Converters ◽

Real Time Detection ◽

Energy Converters

Parametric resonance is a dynamic instability due to the internal transfer of energy between degrees of freedom. Parametric resonance is known to cause large unstable pitch and/or roll motions in floating bodies, and has been observed in wave energy converters (WECs). The occurrence of parametric resonance can be highly detrimental to the performance of a WEC, since the energy in the primary mode of motion is parasitically transferred into other modes, reducing the available energy for conversion. In addition, the large unstable oscillations produce increased loading on the WEC structure and mooring system, accelerating fatigue and damage to the system. To remedy the negative effects of parametric resonance on WECs, control systems can be designed to mitigate the onset of parametric resonance. A key element of such a control system is a real-time detection system, which can provide an early warning of the likely occurrence of parametric resonance, enabling the control system sufficient time to respond and take action to avert the impending exponential increase in oscillation amplitude. This paper presents the first application of a real-time detection system for the onset of parametric resonance in WECs. The method is based on periodically assessing the stability of a mathematical model for the WEC dynamics, whose parameters are adapted online, via a recursive least squares algorithm, based on online measurements of the WEC motion. The performance of the detection system is demonstrated through a case study, considering a generic cylinder type spar-buoy, a representative of a heaving point absorber WEC, in both monochromatic and polychromatic sea states. The detection system achieved 95% accuracy across nearly 7000 sea states, producing 0.4% false negatives and 4.6% false positives. For the monochromatic waves more than 99% of the detections occurred while the pitch amplitude was less than 1/6 of its maximum amplitude, whereas for the polychromatic waves 63% of the detections occurred while the pitch amplitude was less than 1/6 of its maximum amplitude and 91% while it was less than 1/3 of its maximum amplitude.

Download Full-text

Wave Energy Extraction by Flexible Floaters

Energies ◽

10.3390/en13236167 ◽

2020 ◽

Vol 13 (23) ◽

pp. 6167

Author(s):

Simone Michele ◽

Federica Buriani ◽

Emiliano Renzi ◽

Marijn van Rooij ◽

Bayu Jayawardhana ◽

...

Keyword(s):

Mathematical Model ◽

Wave Energy ◽

Scale Up ◽

Irregular Waves ◽

Experimental Investigations ◽

Wave Power ◽

Resonant Frequencies ◽

Wave Energy Converters ◽

The University ◽

Incident Waves

We present a novel mathematical model to investigate the extraction of wave power by flexible floaters. The model is based on the method of dry modes, coupled with a matched eigenfunction expansion. Our model results compare satisfactorily with preliminary data obtained from a demonstrator device, developed at the University of Groningen. We show that the role of elasticity is to increase the number of resonant frequencies with respect to a rigid body, which has a positive effect on wave power output. The mathematical model is then extended to irregular incident waves, described by a JONSWAP spectrum. Our results show that the peak capture factors decrease in irregular waves, as compared to the monochromatic case. However, the system becomes more efficient at non-resonant frequencies. This work highlights the need to scale-up experimental investigations on flexible wave energy converters, which are still a small minority, compared to those on rigid converters.

Download Full-text