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.     

流体动力干扰对桩柱矩阵阵列波浪力的影响

随着超大型海洋结构物的设计和研究日益受到重视,研究多物体之间的流体动力干扰特性显得十分必要。用波动源在截面周线上分布的方法,就垂直桩柱间三维流体动力干扰对波浪力的影响进行了系统的研究,不仅可得到单行柱列的流体动力干扰力学机理的新特性,而且对多行桩柱阵列的研究也取得了若干新的发现：多行柱柱阵列的遮蔽作用强于单行的;无论是单行还是多行柱列,其流体动力干扰特性存在一个十分敏感的来波频域,在此区域内,力的幅值会大大超过其他频域的受力,而且桩柱阵列与交错阵列的力学特性也有所不同。这对超大型海洋结构物的设计有着重要的指导意义。     

混合模块大型浮式结构系统耦合动力响应分析

针对具有天然岛礁庇护或人工庇护的温和海洋环境,提出了一种混合模块大型浮式结构系统,即水动力性能更优的半潜式模块作为内侧主模块,消波效果更优的箱式模块作为外侧浮式防波模块和波浪能发电模块.波浪能装置利用外侧箱式模块与内侧半潜式模块的相对纵摇运动进行发电.考虑模块间多体水动力耦合效应和连接器机械耦合效应,基于ANSYS-AQWA程序重点研究了典型海况下混合5模块串联浮式结构系统的动力响应特征.结果表明,外侧箱式模块和波浪能发电装置能有效减弱内侧半潜式主模块运动响应、连接器动力响应和系泊缆绳张力,并且提供一定的能源供给.所得研究成果可为模块化超大型浮式结构系统的防波—发电集成系统设计提供参考.     

Interactions of cnoidal waves with cylinder arrays

The three-dimensional scattering of cnoidal waves by cylinder arrays are studied numerically by using the generalized Boussinesq equations. The boundary-fitted coordinate transformation and a dual-grid technique are used to simplify the finite-difference computation. Also, a set of open boundary conditions and an incident cnoidal wave are incorporated for time-domain simulation. The free-surface elevation and hydrodynamic forces on each cylinder are calculated to illustrate the evolution of nonlinear waves and their interactions with large cylinder arrays. Comparisons are made between the present nonlinear wave loads and those obtained from linear diffraction theory. The sheltering role played by the neighboring cylinders and the feature of wave interference are discussed.     

Water wave interaction with an array of bottom-mounted surface-piercing porous cylinders

The interaction of water waves with arrays of bottom-mounted, surface-piercing circular cylinders is investigated theoretically. The sidewall of each cylinder is porous and thin. Under the assumptions of potential flow and linear wave theory, a semi-analytical solution is obtained by an eigenfunction expansion approach first proposed for impermeable cylinders by Spring and Monkmeyer (1974), and later simplified by Linton and Evans (1990). Analytical expressions are developed for the wave motion in the exterior and all interior fluid regions. Numerical results are presented which illustrate the effects of various wave and structural parameters on the hydrodynamic loads and the diffracted wave field. It is found that the porosity of the structures may result in a significant reduction in both the hydrodynamic loads experienced by the cylinders and the associated wave runup.     

铰接柱式波能转换装置的水动力分析

铰接柱式波能转换装置是一种新型的波能转换装置,本文为该装置提出了一个合理而又便于计算的水动力学模型,并采用三维源分布法对该装置进行了水动力分析,通过与该装置的模型试验结果的比较,显示出所得的计算结果是令人满意的。     

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.     

弹性双柱在规则波作用下振动响应

通过速度势的特征展开方法,建立垂直圆柱对波浪绕射的解析解,得到作用在柱体上的波浪力计算表达式,通过谐波增量平衡法(IHB法),计算研究弹性双柱相对位置对双柱振动响应的影响。设计了弹性双柱体模型试验,数值结果与模型试验结果较吻合,为海洋工程结构振动设计提供一种解决方法。     

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.     

Optimal configurations of wave energy device arrays

In this paper, the influence of the spatial configuration of a wave energy device array upon total power output is investigated. Hydrodynamic interactions are computed using a method capable of producing the linear wave theory solution to arbitrary accuracy. The overall performance of devices with two different power take-off arrangements is maximised at one incident wave frequency and direction by altering the formation of the array. Minimisation of the power is also carried out in a third case in order to demonstrate potential array-related losses. The optimisation is applied using two different approaches in each case: the Parabolic Intersection (PI) method and a Genetic Algorithm (GA). The former is a heuristic technique that has been devised for this study to enable rapid array construction using only simple calculations. The latter is an existing method, applied here with a novel crossover operator. Although considerably more computational effort is required, superior results may be obtained using the GA compared to the PI method. All of the arrays are subsequently analysed under incident waves of different frequency and direction, the resulting behaviour explained in terms of certain geometrical features of the arrangements.     

Approximate hydrodynamic analysis of multi-column ocean structures

An approximate, semi-analytical technique is developed to calculate the wave-induced loads and added-mass and radiation damping coefficients for idealized ocean structures consisting of arrays of large-diameter, truncated, vertical circular cylinders. The approach involves replacing the complete wave field scattered/radiated by one cylinder in the vicinity of another cylinder by a plane wave together with a non-planar correction term and so is essentially a large-spacing approximation. Numerical results are presented which illustrate the accuracy of the approximate approach and provide estimates of the hydrodynamic characteristics of several practical array configurations.     

Solitary wave interactions with an array of two vertical cylinders

This paper addresses a numerical investigation of nonlinear waves interactions with an array of two surface-piercing vertical cylinders and the corresponding nonlinear hydrodynamic loads on each individual cylinder. The primary interest of this study is concentrated on the problem of three-dimensional scattering of solitary waves by cylinder arrays and the nonlinear interactions between scattered waves. The theoretical model adopted for simulation is the generalized Boussinesq two-equation model. The boundary-fitted coordinate transformation and multiple-grid technique are utilized here to simplify the computation domain and to facilitate the applications of the boundary conditions on the cylinder surfaces. The velocity potential, free-surface elevation and subsequent evolution of the scattered wave field are numerically evaluated. The hydrodynamic forces on each cylinder during wave impact are also determined. A study of the sheltering effect by the neighboring structures on wave loads is conducted. It is found that the presence of the neighboring cylinder has shown significant influence on the wave loads and the scattering of the primary incident waves. For two transversely arranged cylinders, the transverse force coefficient increases as the separation distance decreases.     

Interaction of cnoidal waves with an array of vertical concentric porous cylinders

An array of large concentric porous cylinder arrays is mounted in shallow water exposed to cnoidal waves. The interactions between waves and cylinders are studied theoretically using an eigenfunction expansion approach. Semi-analytical solutions of hydrodynamic loads and wave run-up on each cylinder are obtained using first approximation to cnoidal waves. The square array configuration of four-legged identical concentric porous cylinder is investigated in present study. Numerical results reveal the variation of dimensionless wave force and wave run-up on individual cylinder with angle of incidence, porosity parameter, spacing between outer and inner cylinders, spacing between concentric porous cylinders and wave parameter. Different mechanism of wave force is found under different range of scattering parameter.     

大万山波浪能试验场泊位间水动力影响分析

当前我国近海海域属稀缺资源,波浪能试验场建设须通过合理布局各测试泊位,在保证试验场各泊位可同时正常开展测试工作的前提下,尽量减小用海面积。拉近试验泊位距离,是减小用海面积的直接手段,但在此过程中,必须保证在试验场场址海域水动力环境下,泊位接入测试波浪能装置后,其之间的水动力影响在可接受的范围内。以大万山波浪能试验场泊位设计为例,介绍一种有效的泊位间水动力影响分析方法。方法采用自主开发的二维Boussinesq波浪模型,开展水动力影响分析工作,同时引入相对波高比概念,对泊位接入装置后影响距离和影响面积进行了定量的分析。文中研究得出的分析方法,可用于判定泊位布局设计的合理性。     

阵列筏式波浪能发电装置建模与仿真分析

为了提高阵列筏式波浪能发电装置采能效率,对不同排列方式的振荡浮子与不同楔形角的试验平台模型进行组合,优化水动力结构模型装置。建立了振荡浮子和采能装置试验平台三维模型,并进行了仿真分析。分别分析了由3种排列方式的振荡浮子和3种楔形角情况下的9种模型在水深15 m、平台吃水1.2 m、振荡浮子吃水0.5 m海况下垂直方向的时域响应和频域响应,结果发现当模型的振荡浮子以错开方式排列且试验平台楔形角为60°时,振荡浮子在垂直方向的振荡速度最快,其RAO值也最大,说明该组合模型更有利于提高筏式波浪能发电装置的采能效率。     

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.     

集成波能转换功能的方箱—挡浪板式浮式防波堤水动力特性研究

浮式防波堤与振荡浮子式波浪能转换装置集成是一种较为合理的波浪能开发利用方式,基于方箱式浮式防波堤—波浪能转换集成系统和幕帘式防波堤的研究成果,提出了一种新型方箱—垂直挡浪板式浮式防波堤—波浪能转换集成系统,建立数学模型对该集成系统的水动力特性和能量输出特性进行研究。模型基于N-S方程,采用紧致插值曲线(CIP)方法结合浸没边界法(IBM)求解。运用数值模型探究在一定波浪条件下,动力输出系统(PTO)阻尼力的大小以及挡浪板对集成系统的水动力特性和能量转换特性的影响,得到如下结论:集成系统的俘获宽度比随PTO阻尼力的增大呈现先增大后减小的趋势,在阻尼力F_(PTO)=150 N时达到最大;相对于方箱型集成系统,增设0.1 m挡浪板后可使其最大俘获宽度比η_e提高33%左右;此外,集成系统的俘获宽度比随挡浪板长度增加而增大,增长趋势逐渐变缓,在挡浪板长度S_p=0.5 m时达到最大,此时俘获宽度比η_e=0.563 1。     

Limiting heave response of a wave energy device by draft adjustment with upper surface immersion

Many studies have been published concerning the influence of the immersed shape (in still water) of a floating body on its response and power capture from ocean waves. With a few notable exceptions, much of this analysis has assumed small amplitude motion and linear models have been employed to predict response. The form of the upper surface of such a body has received little attention. Here, we show how the shape of the upper (top) surface of a floating body can be designed to ensure that the response amplitude of the body is within a specified value. This is of considerable importance to the survivability of wave energy devices. The approach used is to achieve a large increase of both natural period and hydrodynamic damping for only a small change of float mass. These two factors impose a hydrodynamic limit on the displacement which may be exploited to avoid the ‘end-stop’ problem often encountered in wave device design. To demonstrate the change of response, experimental measurements are presented of the response of an axisymmetric float with rounded base and conical upper surface with rounded perimeter due to a range of regular, irregular and focused wave conditions. Power extraction is not considered since the mechanically undamped response represents the worst case. In contrast to a simple, straight-sided axisymmetric float, a smaller change of mass is required to satisfy a particular response amplitude limit. Although a significant reduction is not expected, hydrodynamic damping may reduce with increasing physical scale, and this remains to be quantified.     

Three dimensional wave scattering by arrays of elliptical and circular cylinders

Recently, Chatjigeorgiou and Mavrakos (2009, 2010a) provided an analytic solution for the three dimensional wave scattering by arrays of elliptical cylinders. The present paper extends the contents of the existing study to tackle the problem of the hydrodynamic interactions between elliptical and circular cylinders. The main task is to derive an analytic solution for the total velocity potential for an arbitrary body of the array and accordingly, to express the hydrodynamic pressure, the exciting forces and the wave elevation in compact analytic closed-forms.The solution method is rather complicated as it considers the circular cylinders as different geometries and not special cases of elliptical cylinders with zero elliptic eccentricity. Nevertheless, the adopted procedure enhances the mathematical reconstruction of the physical subject as it requires the derivation and the employment of addition theorems that transform expressions from elliptic to polar coordinate systems in all four possible combinations.     

Wave power statistics for individual waves

The paper provides a bivariate distribution of wave power and wave height, as well as a bivariate distribution of wave power and wave period; both bivariate distributions are for individual waves within a sea state. This is relevant for e.g. making assessments of wave power devices and their potential for converting energy from waves. The results can be applied to compare systematically the wave power potential for individual waves in a given sea state at different locations.