Research of Power Take-off System for “Sharp Eagle Ⅱ” Wave Energy Converter

The "Sharp Eagle" device is a wave energy converter of a hinged double floating body. The wave-absorbing floating body hinges on the semi-submerged floating body structure. Under the action of wave, the wave-absorbing floating body rotates around the hinge point, and the wave energy can be converted into kinetic energy. In this paper, the power take-off system of "Sharp Eagle II" wave energy converter(the second generation of "Sharp Eagle") was studied, which adopts the hydraulic type power take-off system. The 0-1 power generation mode was applied in this system to make the "Sharp Eagle II" operate under various wave conditions. The principle of power generation was introduced in detail, and the power take-off system was simulated. Three groups of different movement period inputs were used to simulate three kinds of wave conditions, and the simulation results were obtained under three different working conditions. In addition, the prototype of "Sharp Eagle II" wave energy converter was tested on land and in real sea conditions. The experimental data have been collected, and the experimental data and simulation results were compared and validated. This work has laid a foundation for the design and application of the following "Sharp Eagle" series of devices.     

鹰式一号波浪能装置频域运动分析与优化设计

波浪能发电装置的波能转换通常分为两级能量转换:第一级能量转换是波浪作用下波浪能装置部件发生相对运动驱动PTO做功捕获波浪能;第二级能量转换为将捕获的波浪能转换为电能。其中一级波浪能转换系统的优化设计是提高波浪能装置能量转换效率的重要手段和关键技术。波浪作用下波浪能装置的运动与PTO做功运动相互耦合和影响,本文通过对不同波浪要素环境下、不同PTO阻尼下波浪能装置的频域运动模拟,以迎波宽度比为尺度对波浪能装置的一级能量转换系统进行优化设计,获得波浪能装置的最优做功阻尼,为实型装置负载加载设计提供设计依据,提高波浪能装置能量转化效率。鹰式一号波浪能装置的实海况运动证明,通过对一级能量转换系统的优化设计,能够有效提高装置的发电效率和提高装置对波浪响应频带宽度。     

Numerical modeling on hydrodynamic performance of a bottom-hinged flap wave energy converter

The hydrodynamic performance of a bottom-hinged flap wave energy converter(WEC) is investigated through a frequency domain numerical model.The numerical model is verified through a two-dimensional analytic solution,as well as the qualitative analysis on the dynamic response of avibrating system.The concept of "optimum density" of the bottom-hinged flap is proposed,and its analytic expression is derived as well.The frequency interval in which the optimum density exists is also obtained.The analytic expression of the optimum linear damping coefficient is obtained by a bottom-hinged WEC.Some basic dynamic properties involving natural period,excitation moment,pitch amplitude,and optimum damping coefficient are analyzed and discussed in detail.In addition,this paper highlights the analysis of effects on the conversion performance of the device exerted by some important parameters.The results indicate that "the optimum linear damping period of 5.0 s" is the most ideal option in the short wave sea states with the wave period below 6.0 s.Shallow water depth,large flap thickness and low flap density are advised in the practical design of the device in short wave sea states in order to maximize power capture.In the sea state with water depth of 5.0 m and wave period of 5.0 s,the results of parametric optimization suggest a flap with the width of 8.0 m,thickness of 1.6 m,and with the density as little as possible when the optimum power take-off(PTO) damping coefficient is adopted.     

应用于海洋物性监测仪的小型浮标水动力分析

为验证研制的国产气象水文传感器的性能,设计了直径3 m的圆盘式小型浮标,拟搭载所有传感器在2000 m以深海域开展应用试验。统计了试验海域的有义波高、波浪周期、最大风速和表层流速等环境参数,计算了浮标的质量、重心、吃水、受力投影面积和惯性矩等设计参数。以三维势流理论和波浪辐射-绕射理论为基础,使用AQWA软件在频域内对浮标进行水动力计算,仿真了浮标工作时所受的一阶波浪力、附加质量、附加阻尼和运动幅值响应因子,通过仿真结果对浮标设计方案进行优化,优化后的浮标计算结果随波浪频率变化平缓,幅值合理且无激增点,表明该浮标与工作海域内的波浪没有发生明显谐振,对环境载荷有足够的承受能力,方案可用于浮标研制。     

On the radiation and diffraction of water waves by a rectangular buoy

An analytical method is presented to analyze the radiation and diffraction of water waves by a rectangular buoy in an infinite fluid domain of finite water depth. Analytical expressions for the radiated potentials and the diffracted potentials are obtained by use of the method of separation of variables. The unknown coefficients in the expressions are determined by use of the eigenfunction expansion matching method. The added masses and damping coefficients for the buoy heaving, swaying and rolling in calm water are obtained by use of the corresponding radiated potentials. Wave excitation forces are calculated by two different approaches, one is by use of the radiated potentials through Haskind’s theorem and the other is by the diffracted potential. It can be seen that the latter approach for wave forces on a rectangular buoy is much simpler than the former. To verify the correctness of the method, two specific examples in the past references are recomputed and the obtained results are in good agreement with those by use of other methods, which shows that the present method is correct.     

Large angular motions of tethered surface buoys

A three-dimensional coupled analysis of the interaction of a floating buoy and its mooring is studied. External loads include hydrodynamic forces, tether tensions, wind loads and system weight and buoyancy. Nonlinearities include large rotational and translational motions and non-conservative fluid loads. The mooring problem is formulated as a nonlinear two-point-boundary-value-problem. At each instant in time, the mooring problem is solved by direct integration using a successive iterative algorithm to satisfy boundary conditions. Buoy kinetic and kinematic equations are derived assuming large angles represented by Euler parameters. Coupling between the buoy and the mooring is enforced by matching the velocities of the tether and buoy at the attachment point. A predictor-corrector coupling algorithm is used with multiple sizes of time steps used to provide stability for the separate mooring and buoy models. Numerical results are compared to experimental responses of three types of buoys (sphere, spar and disc) subject to both regular and irregular waves.     

Hydrodynamic Analysis and Power Conversion for Point Absorber WEC with Two Degrees of Freedom Using CFD

Point absorber wave energy device with multiple degrees of freedom (DOF) is assumed to have a better absorption ability of mechanical energy from ocean waves. In this paper, a coaxial symmetric articulated point absorber wave energy converter with two degrees of freedom is presented. The mechanical equations of the oscillation buoy with power take-off mechanism (PTO) in regular waves are established. The three-dimensional numerical wave tank is built in consideration of the buoy motion based upon the CFD method. The appropriate simulation elements are selected for the buoy and wave parameters. The feasibility of the CFD method is verified through the contrast between the numerical simulation results of typical wave conditions and test results. In such case, the buoy with single DOF of heave, pitch and their coupling motion considering free (no PTO damping) and damped oscillations in regular waves are simulated by using the verified CFD method respectively. The hydrodynamic and wave energy conversion characteristics with typical wave conditions are analyzed. The numerical results show that the heave and pitch can affect each other in the buoy coupling motion, hydrodynamic loads, wave energy absorption and flow field. The total capture width ratio with two coupled DOF motion is higher than that with a single DOF motion. The wave energy conversion of a certain DOF motion may be higher than that of the single certain DOF motion even though the wave is at the resonance period. When the wave periods are high enough, the interaction between the coupled DOF motions can be neglected.     

海洋观测浮标体水中平衡性分析

海洋观测浮标系统应用广泛,浮标体的平衡性能是影响海洋观测浮标使用的重要因素之一(着重观测波浪等水文参数除外)。以一种主体直径为2.3 m的浮标体为例,运用动力学平衡理论,通过数学分析法进行推演计算,分析后得到了此浮标体的重心和浮心的位置。其中,重心位于主浮体的中轴线偏下位置;按照浮标体倾斜一定角度的情况下,推算出浮标体浮心位置,并由此得出其稳心的位置。依据计算,得出浮标体倾斜20°的情况下,此浮标体依然处于稳态平衡,理论结果表明此浮标体设计具有一定的可行性。通过海上实际测试,验证了理论计算分析的正确性。文中对浮标体平衡性的研究采用了理论分析与实验印证相结合的方法,其分析计算方法具有普适性,适用于其他型号的海洋观测浮标体,乃至所有水面浮体的平衡性分析,可为水面浮体设计提供借鉴。     

A low-scattering approximation for the hydrodynamic interactions of small wave-power devices

This paper concerns mathematical modelling of the hydrodynamic interaction forces between small vertically axisymmetric wave-power devices. The model takes into account small-body approximations for the first order scattered waves but neglects multiple scattering. Further, the local wave fields are neglected, making the model inapplicable for very closely spaced bodies.The model, which is called the low-scattering approximation, comprises analytical formulae for the forces in any of the translation modes surge, sway and heave. It requires, however, that the following isolated-body parameters are known or externally supplied: the added mass and the force coefficients for both heave and surge motion.Comparison with accurate numerical results of a two-buoy system indicates that the present approach is fairly good even when the buoy diameter is as large as 1/6 of the wavelength and the buoy spacing is as small as 5 buoy radii.     

Optimal causal control of a wave energy converter in a random sea

This paper concerns the design of feedback control systems to maximize power generation of a wave energy converter (WEC) in a random sea. In the literature on WEC control, most of the proposed feedback controllers fall into three categories. Many are static; i.e., they extract power by imposing an equivalent damping or resistive load on the power take-off (PTO) devices. Others are dynamic and are designed to maximize power generation at all frequencies, which results in an anticausal feedback law. Other dynamic control design methods are causal, and are tuned to achieve the anticausal performance at only a single frequency. By contrast, this paper illustrates that the determination of the true optimal causal dynamic controller for a WEC can be found as the solution to a nonstandard linear quadratic Gaussian (LQG) optimal control problem. The theory assumes that the control system must make power generation decisions based only on present and past measurements of the generator voltages and/or velocities. It is shown that unlike optimal anticausal control, optimal causal control requires knowledge of the stationary spectral characteristics of the random sea state. Additionally, it is shown that the efficiency of the generator factors into the feedback synthesis. The theory is illustrated on a linear dynamical model for a buoy-type WEC with significant resonant modes in surge and pitch, and equipped with three spatially-distributed generators.     

Hydrodynamic analysis and shape optimization for vertical axisymmetric wave energy converters

The absorber is known to be vertical axisymmetric for a single-point wave energy converter (WEC). The shape of the wetted surface usually has a great influence on the absorber’s hydrodynamic characteristics which are closely linked with the wave power conversion ability. For complex wetted surface, the hydrodynamic coefficients have been predicted traditionally by hydrodynamic software based on the BEM. However, for a systematic study of various parameters and geometries, they are too multifarious to generate so many models and data grids. This paper examines a semi-analytical method of decomposing the complex axisymmetric boundary into several ring-shaped and stepped surfaces based on the boundary discretization method (BDM) which overcomes the previous difficulties. In such case, by using the linear wave theory based on eigenfunction expansion matching method, the expressions of velocity potential in each domain, the added mass, radiation damping and wave excitation forces of the oscillating absorbers are obtained. The good astringency of the hydrodynamic coefficients and wave forces are obtained for various geometries when the discrete number reaches a certain value. The captured wave power for a same given draught and displacement for various geometries are calculated and compared. Numerical results show that the geometrical shape has great effect on the wave conversion performance of the absorber. For absorbers with the same outer radius and draught or displacement, the cylindrical type shows fantastic wave energy conversion ability at some given frequencies, while in the random sea wave, the parabolic and conical ones have better stabilization and applicability in wave power conversion.     

New Determinations of the Ages of Tide in the North Atlantic Ocean

Ages of tide provide relevant information about the spatial distribution of existing anomalies in the normal modes of the oceans, because a delay may be associated with bottom friction energy dissipation, closely located resonances, bathymetric gradients, or radiational effects. The determination of other parameters, such as the age of diurnal tide or age of parallax, also provide further knowledge about the ocean's hydrodynamical response to acting forces. Following the development of new ocean models and the availability of a greater amount of data, these parameters can be redetermined. We present the spatial distribution of these parameters in the Northeast Atlantic Ocean and the Mediterranean Sea, obtained from 507 stations. The results are discussed in terms of bathymetric models, coastal features, sea surface temperature, wind and other environmental factors.     

The effect of sub-optimal control and the spectral wave climate on the performance of wave energy converter arrays

A linear hydrodynamic model is used to assess the sensitivity of the performance of a wave energy converter (WEC) array to control parameters. It is found that WEC arrays have a much smaller tolerance to imprecision of the control parameters than isolated WECs and that the increase in power capture of WEC arrays is only achieved with larger amplitudes of motion of the individual WECs. The WEC array radiation pattern is found to provide useful insight into the array hydrodynamics. The linear hydrodynamic model is used, together with the wave climate at the European Marine Energy Centre (EMEC), to assess the maximum annual average power capture of a WEC array. It is found that the maximum annual average power capture is significantly reduced compared to the maximum power capture for regular waves and that the optimum array configuration is also significantly modified. It is concluded that the optimum configuration of a WEC array will be as much influenced by factors such as mooring layout, device access and power smoothing as it is by the theoretical optimum hydrodynamic configuration.     

Analysis of dynamic effects relevant for the wear damage in hydraulic machines for wave energy conversion

The present paper deals with a mathematical model of a heaving-buoy Wave Energy Converter (WEC) equipped with high-pressure hydraulic power take-off machinery for energy conversion. This model is based on linear hydrodynamic theory, and a hybrid frequency-time domain model is used to study the dynamics of the heaving-body exposed to an irregular incident wave. For the power take-off system, end-stop devices are provided to protect the hydraulic machinery when the buoy is exposed to severe sea states. The model also takes into account the lubricated friction force and pressure drops of orifice flow through the valves in the hydraulic system. All the forces mentioned in the hydraulic power take-off machinery have non-linear features. A complete non-linear state space model for the WEC system is presented in this study.The WEC system was numerically simulated for different cylinder lengths under a fixed volume. The effect of fluid compressibility in the cylinder has been investigated in the mathematical model. High frequency oscillations (HFOs) caused by the compressibility of the fluid are displayed in the time series and in corresponding power spectra, and variation is shown for different cylinder sizes. Piston ring and cylinder bore wear damage is estimated by using Archard’s equation on the basis of the simulation results. A comparison of these results with a performance of an identical WEC system which neglects fluid compressibility has been done in this work. It shows that although the spectral power is small, HFO can make a large contribution to both the ring and cylinder bore wear. For the purpose of wear prediction, oscillations at or below the wave frequency and HFO may be equally important.     

Modelling of a wave energy converter array with a nonlinear power take-off system in the frequency domain

This paper presents a nonlinear frequency domain model and uses this to assess the performance of a wave energy converter (WEC) array with a nonlinear power take-off (PTO). In this model, the nonlinear PTO forces are approximated by a truncated Fourier series, while the dynamics of the WEC array are described by a set of linear motion equations in the frequency domain, and the hydrodynamic coefficients are obtained with the boundary element method. A single heave absorber is firstly investigated to establish the accuracy of the new model in capturing the nonlinear behaviour of the pumping system. Subsequently, simulations of a 2D array with 18 WECs and a pillar in the centre (representing the tower of a wind turbine) are carried out to understand wave interference effects. Several optimisation strategies are proposed to improve the overall performance of the WEC array. These results demonstrate a computationally effective method for accounting for nonlinear effects in large WEC arrays. The proposed approach may potentially be applied for developing control algorithms for the adaptability of a 2D array to incoming wave excitation.     

Design and testing of a non-linear power take-off simulator for a bottom-hinged plate wave energy converter

Eddy current brakes provide a versatile way of simulating the power take-off system (PTO) in model testing of small scale wave energy converters (WECs). This type of PTO simulator is based on the principle that a conductive material moving in a magnetic field generates a braking force proportional to its velocity. A bottom-hinged pitching plate WEC model has been designed using an eddy current brake as a PTO simulator. A dedicated electric current source unit was developed to provide a controllable and reliable level of DC current intensity to feed the magnetic field generating coils. Using a real-time data acquisition and control, this unit can be used to impose non-linear damping PTO characteristic curves in several types of WEC models based on eddy current brakes. In the present case, this current source has been used to simulate a constant damping PTO on a small scale pitching WEC model that has been tested in the IST wave flume. Two different cases were considered: one corresponding to a surface piercing plate and another to a fully submerged plate. Experimental results are presented for plate motion and for non-dimensional capture width.     

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.     

Constrained near-optimal control of a wave energy converter in three oscillation modes

This paper investigates the performance of a small axisymmetric buoy under wave-by-wave near optimal control in surge, heave, and pitch modes in long-crested irregular waves. Wave prediction is obtained using a deterministic propagation model. The paper describes the overall formulation leading up to the derivation of the feedforward control forces in surge and heave, and the control moment in pitch. The radiation coupling between surge and pitch modes is accounted for in the model. Actuation is relative to deeply submerged reaction masses. Heave oscillations are constrained by the swept-volume limit. Oscillation constraints are also applied on the surge and pitch oscillations. The paper discusses time-domain simulations for an irregular wave input with and without the present control. Also discussed are results obtained over a range of irregular wave conditions derived for energy periods from 7 s to 17 s, and a significant wave height of 1 m. It is found that, while the gains in power capture enabled by the present control are significant, the actuation forces are also very large, given the small size of the buoy. Further, due to the small size, heave is found to be the dominant contributor to power capture, with relatively modest contributions from surge and pitch.     

Evaluation of the wave transformation in an open bay with two spectral models

An evaluation of two state of the art phase averaged wave models for the transformation scale, SWAN and STWAVE, is carried out in the present work. The target area is the Obidos Bay located in the central part of the Portuguese continental nearshore. The wave input for the two models is provided by an offshore buoy. In order to compare the nearshore outputs of the wave models against in-situ measurements, a directional buoy and an ADCP, operating in intermediate water depth, are used. The wave parameters considered for comparisons are significant wave height, peak period and wave direction. Sensitivity analyses studies and evaluations in the spectral and geographical spaces concerning the results of the two models are also carried out in both intermediate and shallow water. The present study provides some information on the performances of the two wave models in different forcing conditions as well as on their sensitivity in relationship with various input parameters and some physical processes. STWAVE appears to be faster and more robust than SWAN, which on the other hand has more options and flexibility. In statistical terms the results are comparable.