Negative Stiffness Mechanism on An Asymmetric Wave Energy Converter by Using A Weakly Nonlinear Potential Model

Salter's duck,an asymmetrical wave energy converter(WEC)device,showed high efficiency in extracting energy from 2D regular waves in the past;yet,challenges remain for fluctuating wave conditions.These can potentially be addressed by adopting a negative stiffness mechanism(NSM)in WEC devices to enhance system efficiency,even in highly nonlinear and steep 3D waves.A weakly nonlinear model was developed which incorporated a nonlinear restoring moment and NSM into the linear formulations and was applied to an asymmetric WEC using a time domain potential flow model.The model was initially validated by comparing it with published experimental and numerical computational fluid dynamics results.The current results were in good agreement with the published results.It was found that the energy extraction increased in the range of 6%to 17%during the evaluation of the effectiveness of the NSM in regular waves.Under irregular wave conditions,specifically at the design wave conditions for the selected test site,the energy extraction increased by 2.4%,with annual energy production increments of approximately 0.8MWh.The findings highlight the potential of NSM in enhancing the performance of asymmetric WEC devices,indicating more efficient energy extraction under various wave conditions.

Hydrodynamic Performance of An Integrated System of Breakwater and A Multi-Chamber OWC Wave Energy Converter

A multi-chamber oscillating water column wave energy converter(OWC-WEC)integrated to a breakwater is investigated.The hydrodynamic characteristics of the device are analyzed using an analytical model based on the linear potential flow theory.A pneumatic model is employed to investigate the relationship between the air mass flux in the chamber and the turbine characteristics.The effects of chamber width,wall draft and wall thickness on the hydrodynamic performance of a dual-chamber OWC-WEC are investigated.The results demonstrate that the device,with a smaller front wall draft and a wider rear chamber exhibits a broader effective frequency bandwidth.The device with a chamber-width-ratio of 1:3 performs better in terms of power absorption.Additionally,results from the analysis of a triplechamber OWC-WEC demonstrate that reducing the front chamber width and increasing the rearward chamber width can improve the total performance of the device.Increasing the number of chambers from 1 to 2 or 3 can widen the effective frequency bandwidth.

Extreme Responses of An Integrated System with A Semi-Submersible Wind Turbine and Four Torus-Shaped Wave Energy Converters in Different Survival Modes

Offshore wind power is a kind of important clean renewable energy and has attracted increasing attention due to the rapid consumption of non-renewable energy.To reduce the high cost of energy,a possible try is to utilize the combination of wind and wave energy considering their natural correlation.A combined concept consisting of a semi-submersible wind turbine and four torus-shaped wave energy converters was proposed and numerically studied under normal operating conditions.However,the dynamic behavior of the integrated system under extreme sea conditions has not been studied yet.In the present work,extreme responses of the integrated system under two different survival modes are evaluated.Fully coupled time-domain simulations with consideration of interactions between the semi-submersible wind turbine and the torus-shaped wave energy converters are performed to investigate dynamic responses of the integrated system,including mooring tensions,tower bending moments,end stop forces,and contact forces at the Column-Torus interface.It is found that the addition of four tori will reduce the mean motions of the yaw,pitch and surge.When the tori are locked at the still water line,the whole integrated system is more suitable for the survival modes.

Effect of Different Raft Shapes on Hydrodynamic Characteristics of the Attenuator-Type Wave Energy Converter

A numerical simulation method based on CFD has been established to simulate the fully coupled motion for an atten-uator-type wave energy converter(WEC).Based on this method,a detailed parametric analysis has been conducted to investigate the design of the rafts.The effects of different parameters(wave parameters,structural parameters and PTO parameters)on the hydrodynamic characteristics of the attenuator-type WEC were studied in detail.The results show that in terms of wave parameters,there is an optimal wave period,which makes the relative pitching angle amplitude of the WEC reach the maximum,and the increase of wave height is conducive to the relative pitching angle amplitude of wave energy.Under different wave conditions,the relative pitch angle of the parallelogram raft device is the maximum.In terms of structural parameters,the parallelogram attenuator-type device has the optimal values in different relative directions,different distances and different apex angle,which makes the relative motion amplitude of the device reach the maximum,and the spacing and the apex angle have influence on the motion frequency of the device,while the relative direction has almost no influence on it.In terms of PTO parameters,there is an optimal damping coefficient,which makes the power generation efficiency of the WEC reach the maximum.The research results provide a valuable reference for future research and design of the attenuator-type WEC.

Hydrodynamic Performance and Power Absorption of A Coaxial DoubleBuoy Wave Energy Converter

As an important wave energy converter(WEC),the double-buoy device has advantages of wider energy absorption band and deeper water adaptability,which attract an increasing number of attentions from researchers.This paper makes an in-depth study on double-buoy WEC,by means of the combination of model experiment and numerical simulation.The Response Amplitude Operator(RAO)and energy capture of the double-buoy under constant power take-off(PTO)damping are investigated in the model test,while the average power output and capture width ratio(CWR)are calculated by the numerical simulation to analyze the influence of the wave condition,PTO,and the geometry parameters of the device.The AQWA-Fortran united simulation sy stem,including the secondary developme nt of AQWA software coupled with the flowchart of the Fortran code,models a new dynamic system.Various viscous damping and hydraulic friction from WEC system are measured from the experimental results,and these values are added to the equation of motion.As a result,the energy loss is contained in the final numerical model the by united simulation system.Using the developed numerical model,the optimal period of energy capture is identified.The power capture reaches the maximum value under the outer buoy's natural period.The paper gives the peak value of the energy capture under the linear PTO damping force,and calculates the optimal mass ratio of the device.

CFD Simulation and Experimental Study of a New Elastic Blade Wave Energy Converter

Small moving vehicles represent an important category of marine engineering tools and devices(equipment)typically used for ocean resource detection and maintenance of marine rights and interests.The lack of efficient power supply modes is one of the technical bottlenecks restricting the effective utilisation of this type of equipment.In this work,the performance characteristics of a new type of elastic-blade/wave-energy converter(EBWEC)and its core energy conversion component(named wave energy absorber)are comprehensively studied.In particular,computational fluid dynamics(CFD)simulations and experiments have been used to analyze the hydrodynamics and performance characteristics of the EBWEC.The pressure cloud diagrams relating to the surface of the elastic blade were obtained through two-way fluid-solid coupling simulations.The influence of blade thickness and relative speed on the performance characteristics of EBWEC was analyzed accordingly.A prototype of the EBWEC and its bucket test platform were also developed.The power characteristics of the EBWEC were analyzed and studied by using the blade thickness and motion cycle as control variables.The present research shows that the EBWEC can effectively overcome the performance disadvantages related to the transmission shaft torque load and power curve fluctuations of rigid blade wave energy converters(RBWEC).

Dynamic Properties and Energy Conversion Efficiency of A Floating Multi-Body Wave Energy Converter

The present study proposed a floating multi-body wave energy converter composed of a floating central platform,multiple oscillating bodies and multiple actuating arms. The relative motions between the oscillating bodies and the floating central platform capture multi-point wave energy simultaneously. The converter was simplified as a forced vibration system with three degrees of freedom, namely two heave motions and one rotational motion. The expressions of the amplitude-frequency response and the wave energy capture width were deduced from the motion equations of the converter. Based on the built mathematical model, the effects of the PTO damping coefficient, the PTO elastic coefficient, the connection length between the oscillating body and central platform, and the total number of oscillating bodies on the performance of the wave energy converter were investigated. Numerical results indicate that the dynamical properties and the energy conversion efficiency are related not only to the incident wave circle frequency but also to the converter’s physical parameters and interior PTO coefficients. By adjusting the connection length, higher wave energy absorption efficiencies can be obtained. More oscillating bodies installed result in more stable floating central platform and higher wave energy conversion efficiency.

Power Maximization of A Point Absorber Wave Energy Converter Using Improved Model Predictive Control

This paper considers controlling and maximizing the absorbed power of wave energy converters for irregular waves. With respect to physical constraints of the system, a model predictive control is applied. Irregular waves’ behavior is predicted by Kalman filter method. Owing to the great influence of controller parameters on the absorbed power, these parameters are optimized by imperialist competitive algorithm. The results illustrate the method’s efficiency in maximizing the extracted power in the presence of unknown excitation force which should be predicted by Kalman filter.

Study of Hydrodynamic Characteristics of A Sharp Eagle Wave Energy Converter

According to Newton＇s Second Law and the microwave theory, mechanical analysis of multiple buoys which form Sharp Eagle wave energy converter （WEC） is carried out. The movements of every buoy in three modes couple each other when they are affected with incident waves. Based on the above, mechanical models of the WEC are established, which are concerned with fluid forces, damping forces, hinge forces, and so on. Hydrodynamic parameters of one buoy are obtained by taking the other moving buoy as boundary conditions. Then, by taking those hydrodynamic parameters into the mechanical models, the optimum external damping and optimal capture width ratio are calculated out. Under the condition of the optimum external damping, a plenty of data are obtained, such as the displacements amplitude of each buoy in three modes （sway, heave, pitch）, damping forces, hinge forces, and speed of the hydraulic cylinder. Research results provide theoretical references and basis for Sharp Eagle WECs in the design and manufacture.

Experimental Study on A Pendulum Wave Energy Converter

Many of the existing wave energy converters （WEC） are of oscillating water column （OWC） and point absorber （PA） types. Fewer references have been published in public on the pendulum type WEC. A series of experimental tests on a bottom-hinged pendulum WEC model are carded out and some results are revealed in the present study. The purpose of this paper is to present a detailed description of the tests. It is found that wave energy conversion efficiency varies with the applied damping and wave conditions. In addition, special attention is given to the effect of the water ballast on the efficiency of the wave energy converter. It is demonstrated that the ballast plays an important role in energy extraction. Better understanding on how the performance of the device is influenced by damping, wave height, wave period and ballast is shown.

Wave Extraction and Attenuation Performance of An Edinburgh Duck Wave Energy Converter

Edinburgh Duck wave energy converter(ED WEC)has excellent energy extraction performance and shows a great potential to integrate with other marine structures.This paper aims to investigate its wave energy extraction performance as a WEC and wave attenuation performance as a protection method for shoreline or marine structures.The wave and ED WEC interactions in regular waves are modeled using the Star-CCM+software and verified by comparisons with published experimental results.The motion response,energy conversion efficiency,and transmission coefficient of the ED WEC with different attack angles,rotation center,and incident wave heights are investigated.Results indicate that the ED WEC with an attack angle of 42°and a rotation center of 0.55 m below the mean water line can achieve both good wave energy extraction and wave attenuation performances.The wave energy extraction and wave attenuation performance of the ED WEC decrease significantly with the increase of wave nonlinearity characterized by the wave steepness.This paper can guide the practical application of the ED WEC at the early stage of design.

Evaluation of the Double Snap-Through Mechanism on the Wave Energy Converter’s Performance

Lower efficiencies induce higher energy costs and pose a barrier to wave energy devices'commercial applications.Therefore,the efficiency enhancement of wave energy converters has received much attention in recent decades.The reported research presents the double snap-through mechanism applied to a hemispheric point absorber type wave energy converter(WEC)to improve the energy absorption perfomance.The double snap-through mechanism comprises four oblique springs mounted in an X-configuration.This provides the WEC with different dynamic stability behaviors depending on the particular geometric and physical parameters employed.The efficiency of these different WEC behaviors(linear,bistable,and tristable)was initially evaluated under the action of regular waves.The results for bistable or tristable responses indicated significant improvements in the WEC's energy capture efficiency.Furthermore,the WEC frequency bandwidth was shown to be significantly enlarged when the tristable mode was in operation.However,the corresponding tristable trajectory showed intra-well behavior in the middle potential well,which induced a more severe low-energy absorption when a small wave amplitude acted on the WEC compared to when the bistable WEC was employed.Nevertheless,positive effects were observed when appropriate initial conditions were imposed.The results also showed that for bistable or tristable responses,a suitable spring stiffness may cause the buoy to oscillate in high energy modes.

A second order random wave model for predicting the power performances of a wave energy converter

The power performances of a point absorber wave energy converter(WEC)operating in a nonlinear multidirectional random sea are rigorously investigated.The absorbed power of the WEC Power-Take-Off system has been predicted by incorporating a second order random wave model into a nonlinear dynamic filter.This is a new approach,and,as the second order random wave model can be utilized to accurately simulate the nonlinear waves in an irregular sea,avoids the inaccuracies resulting from using a first order linear wave model in the simulation process.The predicted results have been systematically analyzed and compared,and the advantages of using this new approach have been convincingly substantiated.

Theoretical and Experimental Study of A Coaxial Double-Buoy Wave Energy Converter

The double-body heave wave energy converter(WEC)is one of the most conducive devices to absorb the wave energy from relative motion while the law of which is not well understood.This paper makes an in-depth study on this wave energy converter,by means of the combination of theoretical analysis and physical model experiment.The hydrodynamic characteristics and energy capture of the double-buoy under constant and linear Power Take-Off(PTO)damping are investigated.Influences of absolute mass and mass ratio are discussed in the theoretical model.Relative displacement amplitude and average power output are tested in the experiment to analyze the effect of the wave period and outer buoy’s mass,while the capture width ratio(CWR)is also calculated.Results show that the wave period and mass of the buoys have a significant effect on the converter.Different forms of PTO damping have no influence on the optimal wave period and mass ratio of this device.It is recommended to select the double-buoy converter with a mass ratio of 0.80 and to place it in an area with the frequent wave period close to the natural period of the outer buoy to achieve the optimal energy capture.

Developments, Expectations of Wave Energy Converters and Mooring Anchors in the UK

The paper introduces the important developments of Wave Energy Converters (WECs) in the UK, and the generic an- chor types for WECs and similar structures. Several WECs and their characteristics are introduced to explain the development direction. The anchors are discussed in relation to the behaviour and performance of WECs, and comparisons are made with simi- lar aspects of the offshore industry. Typical and desirable features of anchors for WECs are summarized. Additionally, expectations and research suggestions for WECs and their anchor design are presented.

Width effects on hydrodynamics of pendulum wave energy converter

Based on two- and three-dimensional potential flow theories, the width effects on the hydrodynamics of a bottom-hinged trapezoidal pendulum wave energy converter are discussed. The two-dimensional eigenfunction expansion method is used to obtain the diffraction and radiation solutions when the converter width tends to be infinity. The trapezoidal section of the converter is approximated by a rectangular section for simplification. The nonlinear viscous damping effects are accounted for by including a drag term in the two- and three-dimensional methods. It is found that the three- dimensional results are in good agreement with the two-dimensional results when the converter width becomes larger, especially when the converter width is infinity, which shows that both of the methods are reasonable. Meantime, it is also found that the peak value of the conversion efficiency decreases as the converter width increases in short wave periods while increases when the converter width increases in long wave periods.

A novel method for predicting the power outputs of wave energy converters

This paper focuses on realistically predicting the power outputs of wave energy converters operating in shallow water nonlinear waves. A heaving two-body point absorber is utilized as a specific calculation example, and the generated power of the point absorber has been predicted by using a novel method（a nonlinear simulation method） that incorporates a second order random wave model into a nonlinear dynamic filter. It is demonstrated that the second order random wave model in this article can be utilized to generate irregular waves with realistic crest–trough asymmetries, and consequently, more accurate generated power can be predicted by subsequently solving the nonlinear dynamic filter equation with the nonlinearly simulated second order waves as inputs. The research findings demonstrate that the novel nonlinear simulation method in this article can be utilized as a robust tool for ocean engineers in their design, analysis and optimization of wave energy converters.

Effects of the shape and size of a mooring line surface buoy on the mooring load of wave energy converters

This paper describes the physical model testing of a wave energy converter (WEC) undertaken in the Heriot-Watt wave basin during October 2010 as part of the SUPERGEN2 project funded by the British government,and provides a preliminary analysis of the extreme mooring loads.Tests were completed at 1/20 scale on a single oscillating water column device deployed with a 3-line taut mooring configuration.The model was fully instrumented with mooring line load cells and an optical motion tracker.The tests were preceded by calibration of instrumentation and the wave test environment,and carried out in long crested waves regimes with 12 combinations of peak period T p and significant wave height H s.The main objective for these experiments was to examine the effect of shape and size of the tethered buoy on the leading mooring line on the maximum mooring loads and the excursion of the device.Comparison of the loads at different configurations of the tethered buoy suggests that the results are consistent with the hypothesis that the mooring forces should depend on the change in stiffness of the mooring system.In particular,the results indicate that with the spectral peak period close to the natural period of the moored device of 8 s,peak loads in a configuration with a smaller buoy may be considerably higher than those with a larger buoy.However,when T p was dissimilar,a harder mooring with a smaller spherical buoy appears to result in lower peak loads.The exact configuration should,therefore,be chosen according to the prevalent conditions of any particular location,and will also depend on the design and expected maintenance schedule,as well as matters related to the risk to navigation,environmental effects and the conservation status of the area.

Performance Evaluation of Advanced Wave Energy Converters in the Nearshore Areas of the North Indian Ocean

The 21st Century Maritime Silk Road is a profound measure for mankind,whilst its development is severely restricted by the energy shortage of surrounding countries.As the core construction area of Maritime Silk Road,the North Indian Ocean is rich in wave energy.The development and utilization of wave energy not only can overcome energy shortage,but also promote communication between peripheral countries.However,previous researchers often focused on wave energy itself,without combining devices to analyze wave energy resources.Therefore,we conducted an overall assessment of wave energy resources using 20-year ERA5 data and determined the sites considered as superior for the construction of Wave Energy Farm(WEF)in the coastal areas.In order to point out which type of Wave Energy Converter(WEC)is best suited for the sites,we carried out the performance evaluation of eight advanced WECs using three parameters:the mean power output,the capacity factor and the capture width ratio.The results show that the performance of Wave Star is superior to other devices,which is supposed to be the primary consideration of the Wave Energy Farms(WEFs)in the future.

Application of the Latching Control System on the Power Performance of a Wave Energy Converter Characterized by Gearbox,Flywheel,and Electrical GeneratorGustavor

The latching control represents an attractive alternative to increase the power absorption of wave energy converters(WECs)by tuning the phase of oscillator velocity to the wave excitation phase.However,increasing the amplitude of motion of the floating body is not the only challenge to obtain a good performance of the WEC.It also depends on the efficiency of the power take-off system(PTO).This study aims to address the actual power performance and operation of a heaving point absorber with a direct mechanical drive PTO system controlled by latching.The PTO characteristics,such as the gear ratio,the flywheel inertia,and the electric generator,are analyzed in the WEC performance.Three cylindrical point absorbers are also considered in the present study.A wave-to-wire model is developed to simulate the coupled hydro-electro-mechanical system in regular waves.The wave energy converter(WEC)performance is analyzed using the potential linear theory but considering the viscous damping effect according to the Morison equation to avoid the overestimated responses of the linear theory near resonance when the latching control system is applied.The latching control system increases the mean power.However,the increase is not significant if the parameters that characterize the WEC provide a considerable mean power.The performance of the proposed mechanical power take-off depends on the gear ratio and flywheel.However,the gear ratio shows a more significant influence than the flywheel inertia.The operating range of the generator and the diameter/draft ratio of the buoy also influence the PTO performance.