Reduction of hydroelastic responses of a very-long floating structure by a floating oscillating-water-column breakwater system

The hydroelastic responses of a very-long floating structure (VLFS) placed behind a reverse T-shape freely floating breakwater with a built-in oscillating water column (OWC) chamber are analyzed in two dimensions. The Bernoulli–Euler beam equation is coupled with the equations of rigid and elastic motions of the breakwater and the VLFS. The interaction of waves between the floating rigid breakwater and the elastic VLFS is formulated in a consistent manner. It has been shown numerically that the structural deflections of the VLFS can be reduced significantly by a suitably designed reverse T-shape floating breakwater.     

Oblique Wave-Induced Responses of A VLFS Edged with A Pair of Inclined Perforated Plates

This paper is concerned with the hydroelastic responses of a mat-like, rectangular very large floating structure (VLFS) edged with a pair of horizontal/inclined perforated anti-motion plates in the context of the direct coupling method. The updated Lagrangian formulae are applied to establish the equilibrium equations of the VLFS and the total potential formula is employed for fluids in the numerical model including the viscous effect of the perforated plates through the Darcy''s law. The hybrid finite element-boundary element (FE-BE) method is implemented to determine the response reduction of VLFS with attached perforated plates under various oblique incident waves. Also, the numerical solutions are validated against a series of experimental tests. The effectiveness of the attached perforated plates in reducing the deflections of the VLFS can be significantly improved by selecting the proper design parameters such as the porous parameter, submergence depth, plate width and inclination angle for the given sea conditions.     

Application of smoothed particle hydrodynamics for modeling the wave-moored floating breakwater interaction

The application of a Smoothed Particle Hydrodynamics (SPH) model to simulate the nonlinear interaction between waves and a moored floating breakwater is presented. The main aim is to predict and validate the response of the moored floating structure under the action of periodic waves. The Euler equations together with an artificial viscosity are used as the governing equations to describe the flow field. The motion of the moored floating body is described using the Newton’s second law of motion. The interactions between the waves and structures are modeled by setting a series of SPH particles on the boundary of the structure. The hydrodynamic forces acting on the floating body are evaluated by summing up the interacting forces on the boundary particles from the neighboring fluid particles. The water surface elevations, the movements of the floating body and the moored forces are all calculated and compared with the available experimental data. Good agreements are obtained for the dynamic response and hydrodynamic performance of the floating body. The numerical results of different immersion depths of the floating body are compared with that of the corresponding fixed body. The effects of the relative length and the density of the structure on the performance of the floating body are analyzed.     

波浪作用下方箱-水平板浮式防波堤时域水动力分析

在线性化势流理论范围内求解方箱-水平板浮式防波堤的波浪绕射和辐射问题,从时域角度分析了浮式防波堤的水动力特性.采用格林函数法将速度势定解问题的控制微分方程变换成边界上的积分方程进行数值求解,浮式防波堤的运动方程采用四阶Runge-Kutta方法求解.对不同层数水平板的浮式防波堤的波浪透射系数、运动响应和锚链受力进行了计算分析,结果表明方箱相对宽度对方箱-水平板浮式防波堤的波浪透射作用有重要的影响,透射系数随着方箱相对宽度的增加而减小.对于方箱加二层水平板的浮式防波堤,在本研究的计算条件下,当方箱相对宽度从0.110增加至0.295时,透射系数从0.88减小至0.30.水平板有利于增加浮式防波堤对波浪的衰减作用,但随着水平板层数从0增加至2,这种波浪衰减作用增加的程度趋弱.方箱-水平板的浮式防波堤的运动量小于单一方箱防波堤的运动量.与此对应,方箱-水平板防波堤的锚链受力小于单一方箱防波堤的锚链受力.     

Experimental studies on a perforated horizontal floating plate breakwater

In recent years floating breakwaters are considered for creating calm basin under open sea conditions for short period of time. In this paper, experimental studies on the performance characteristics of a horizontal floating plate breakwater are presented. The results of this two-dimensional model study are for regular waves of shallow and intermediate water depths. Analysis of the results shows that the transmission coefficient is strongly influenced by wave steepness and relative length of breakwater. It is also found to be dependent, to a lesser extent, on the relative depth of draft. Mooring forces are found to increase with increasing wave steepness and relative depth of draft. The performance of this breakwater is compared with other types of breakwater reported by earlier workers.     

Stiffness of mooring lines and performance of floating breakwater in three dimensions

In the present paper, the performance of a moored floating breakwater under the action of normal incident waves is investigated in the frequency domain. A three-dimensional hydrodynamic model of the floating body is coupled with a static and dynamic model of the mooring lines, using an iterative procedure. The stiffness coefficients of the mooring lines in six degrees of freedom of the floating breakwater are derived based on the differential changes of mooring lines' tensions caused by the static motions of the floating body. The model of the moored floating system is compared with experimental and numerical results of other investigators. An extensive parametric study is performed to investigate the effect of different configurations (length of mooring lines and draft) on the performance of the moored floating breakwater. The draft of the floating breakwater is changed through the appropriate modification of mooring lines' length. Numerical results demonstrate the effects of the wave characteristics and mooring lines' conditions (slack-taut). The existence of ‘optimum’ configuration of the moored floating breakwater in terms of wave elevation coefficients and mooring lines' forces is clearly demonstrated, through a decision framework.     

Theoretical Calculation of Floating Breakwater Performance

- In this paper, the theoretical calculation of floating breakwater performance in regular waves with arbitrary wave direction is discussed. Under the hypothesis of linearized system and applying the strip theory, we can solve the boundary condition problems of diffraction potential and radiation potential. Introducing the asymptotic expression of the wave velocity potential at infinity and using wave energy conservation, we can separately calculate the transmitted waves generated by the sway, heave and roll motion of the floating breakwater and by the fixed breakwater. Finally, we define the amplitude ratio of the transmitted wave to the incident wave as the transmitted wave coefficient CT which describes the floating breakwater effectiveness. Two examples are given and the theoretical results obtained by the present method agree well with experimental results.     

Hydroelastic analysis of pontoon-type circular VLFS with an attached submerged plate

This paper is concerned with the hydroelastic analysis of a pontoon-type, circular, very large floating structure (VLFS) with a horizontal submerged annular plate attached around its perimeter. The coupled fluid–structure interaction problem may be solved by using the modal expansion method in the frequency domain. It involves, firstly, the decomposition of the deflection of a circular Mindlin plate with free edges into vibration modes that are obtained analytically. Then the hydrodynamic diffraction and radiation forces are evaluated by using the eigenfunction expansion matching method which can also be done in an exact manner. The hydroelastic equation of motion is solved by the Rayleigh–Ritz method for the modal amplitudes, and then the modal responses are summed up to obtain the total response. The effectiveness of the attached submerged annular plate in reducing the motion of VLFS has been confirmed by the analysis.     

Asymptotic analysis of the interaction between linear long waves and a submerged floating breakwater of wavy surfaces

In this work, we carried out an asymptotic analysis, up to the second order in a regular expansion, of the interaction of linear long waves with an impermeable, fixed, submerged breakwater composed of wavy surfaces. Below the floating breakwater, there is also a step with a wavy surface. The undulating surfaces are described by sinusoidal profiles. The effects of three different geometric parameters — the amplitude of the wavy surfaces and the submerged length and width of the structure — on the reflection and transmission coefficients are analyzed. The hydrodynamic forces are also determined. The governing equations are expressed in dimensionless form. Using the domain perturbation method, the small wavy surfaces of the breakwater are linearized. The wavy surfaces of the breakwater generate larger values of the reflection coefficient than those obtained for breakwaters with flat surfaces, and the largest values of this coefficient are obtained when the length of the breakwater is of the same order of magnitude as the wavelength. The asymptotic solution is compared with the theoretical solutions that have been reported in the specialized literature and with a numerical solution. The present mathematical model can be used as a practical reference for the selection of the geometric configuration of a submerged floating breakwater under shallow flow conditions.     

Performance characteristics of a conceptual ring-shaped spar-type VLFS with double-layered perforated-wall breakwater

A ring-shaped spar-type Very Large Floating Structure (VLFS) is proposed as an intermediate base for supporting deepwater resource exploitation far away from the coast line. The proposed VLFS is composed of eight rigidly connected deep-draft spar-type modules and an inside harbor. A double-layered perforated-wall breakwater is vertically attached to the VLFS and pierces through the water surface to attenuate the wave energy in the inside harbor. The hydrodynamic performance characteristics of the ring-shaped VLFS was experimentally evaluated in the present study, focusing on the motion responses, wave elevations, and wave run-ups. The natural periods of the motions in vertical plane were determined to be larger than 40 s, which is much larger than common wave periods. This enhanced the motion performance in vertical plane and afforded favorable habitation and operation condition on the VLFS. A large surge damping was induced by the vertical breakwater, which tended to significantly affect the surge and pitch motions, but had a negligible effect on the heave motion. The component frequencies of the wave elevations in the inside harbor and the wave run-ups were identical with those of the incident waves. The wave attenuation was frequency-dependent and effective for the common wave frequencies, with a smaller loss coefficient observed in higher sea state. The wave attenuation and wave run-ups tended to improve in the absence of the leeward walls.     

Numerical Solution of Membrane Forces for A Free-Free Floating Plate with Large Deflection

1 .IntroductionVerylargefloatingstructures (VLFS)haveattractedconsiderableattentionrecentlyduetoitspo tentialuseintheexploitationofoceanresourcesandintheutilizationofoceanspaces (Cui,2 0 0 2 ) .Owingtoitslargesizeandrelativelysmallthickness ,theinfluenceofelasticdeformationonthehydro dynamicresponseisimportant.Thisisknownashydroelasticity .Threedimensionallinear (Wu ,1 984;PriceandWu ,1 985)andnonlinear (Chenetal.,2 0 0 3)hydroelasticityiswellappliedtotheanalysisofthreedimensionalshipsando…     

Evaluation of bending moments and shear forces at unit connections of very large floating structures using hydroelastic and rigid body analyses

This paper investigates the characteristics of bending moments, shear forces and stresses at unit connections of very large floating structures (VLFS) under wave loads. The responses of VLFS are calculated by solving multi-body motion equation considering hydroelasticity and connection stiffness. Hydroelastic responses are calculated by the direct method. Higher-order boundary element method (HOBEM) is used for fluid analysis and finite element method (FEM) is introduced for structural analysis. The equation of motion is modified to describe the unit connections by employing spring elements. Bending moments and shear forces at the connections are obtained from the dynamic equilibrium condition for pressures and inertia forces. Two types of VLFS units such as tandem arranged units and side-by-side arranged units are considered in the numerical examples. The influences of connection stiffness, wave frequency and heading angle on responses of VLFS are investigated through the numerical examples. Rigid body analysis along with hydroelastic analysis is also carried out in the numerical analysis and comparison of those two approaches is discussed.     

波浪与起伏水平板防波堤相互作用数值模拟

利用自主研发的基于紧致插值曲线CIP(constrained interpolation profile)方法的数学模型,开展规则波与起伏水平板防波堤相互作用的数值模拟研究。模型在笛卡尔直角坐标下建立,以CIP方法为流场基本求解器,分步求解Navier-Stokes方程,利用高精度的流体体积类型的THINC/SW (tangent of hyperbola for interface capturing with slope weighting)方法重构自由液面,采用浸入边界IBM(immersed boundary method)方法处理波浪与起伏板防波堤的耦合作用问题,通过动量源项造波方法模拟波浪的产生。重点关注波浪的浅水变形和板两端涡旋脱落的非线性现象,分析不同潜深、波要素下的板周围流场分布、板的运动响应和波浪的反透射系数。结果表明:起伏水平板主要通过能量反射、板上浅水变形和板两端的涡脱落消能,能有效减小板后波高,具有作为防波堤的可行性。     

Performance of pile-restrained flexible floating breakwaters

The overall performance of pile-restrained flexible floating breakwaters is investigated under the action of linear monochromatic incident waves in the frequency domain. The aforementioned floating breakwaters undergo only vertical structural deflections along their length and are held in place by means of vertical piles. The total number of degrees of freedom equals the six conventional body modes, when the breakwater moves as a rigid body, plus the extra bending modes. These bending modes are introduced to represent the structural deflections of the floating breakwater and are described by the Bernoulli–Euler flexible beam equation. The number of bending modes introduced is determined through an appropriate iterative procedure. The hydrostatic coefficients corresponding to the bending modes are also derived. The numerical analysis of the flexible floating breakwaters is based on a three-dimensional hydrodynamic formulation of the floating body. A parametric study is carried out for a wide range of structural stiffness parameters and wave headings, to investigate their effect on the performance of flexible floating breakwaters. Moreover, this performance is compared with that of the corresponding pile-restrained rigid floating breakwater. Results indicated that the degree of structural stiffness and the wave heading strongly affect the performance of flexible floating breakwaters. The existence of an “optimum” value of structural stiffness is demonstrated for the entire wave frequency range.     

Wave diffraction on arc-shaped floating perforated breakwaters

An analytical method is developed to study the sheltering effects on arc-shaped floating perforated breakwaters. In the process of analysis, the floating breakwater is assumed to be rigid, thin, vertical, and immovable and located in water with constant depth. The fluid domain is divided into two regions by imaginary interface. The velocity potential in each region is expanded by eigenfunction in the context of linear theory. By satisfying continuity of pressure and normal velocity across the imaginary fluid interface, a set of linear algebraic equations can be obtained to determine the unknown coefficients for eigenfunction expansions. The accuracy of the present model was verified by a comparison with existing results for the case of arc-shaped floating breakwater. Numerical results, in the form of contour maps of the non-dimensional wave amplitude around the breakwater and diffracted wave amplitude at typical sections, are presented for a range of wave and breakwater parameters. Results show that the sheltering effects on the arc-shaped floating perforated breakwater are closely related to the incident wavelength, the draft and the porosity of the breakwater.     

An experimental investigation into the wave power extraction of a floating box-type breakwater with dual pneumatic chambers

The oscillating water column (OWC) device is in a leading position for wave power extraction but has not achieved fully commercial at the current stage. In addition to enhancing the OWC performance, installing OWCs on floating breakwaters, which owns the merits of both cost-sharing and offshore power supply, is a practicality with high economic viability. In this study, a series of wave-flume experiments were conducted in regular waves to examine the wave power extraction of a floating box-type breakwater with dual pneumatic chambers. The flow characteristics of the orifices used to simulate the PTOs was pre-calibrated through another series of experiments, so the power extraction in this study can be obtained with only the pressure measurement. The effects of wave period, chamber draft, water depth and arrangement of chambers on the power extraction were examined. Our experimental results showed that the power extraction was mainly due to the water column oscillation inside the chamber, and differentiation in the designed natural periods of dual chambers could widen the efficiency bandwidth of power extraction. The front chamber always played the main role in power extraction and its natural period should be designed against the dominating period of the wave spectrum; in contrast, the power extraction of the rear chamber was only a supplement and its natural period should be designed against longer waves which were more easily transmitted, thus a PTO of small power capacity maybe more realistic. It was also worth noting that the water column oscillation was more dependent on the wave period rather than controlled by the wave scattering under different water depths.     

箱式超大型浮体在非均匀海洋环境下的水弹性试验

超大型浮体(Very Large foating Structure,VLFS)作为人类开发海洋的前沿基地,正在成为世界各国海洋工程界研究的一个热点。由于超大型浮体覆盖的面积比普通的船舶和海洋结构物要大很多,其首尾两端所处的海洋环境可能有显著的差异,因此必须考虑非均匀海洋环境对其水弹性性能的影响。介绍了国内首次进行的箱式超大型浮体在非均匀海洋环境中的水弹性试验,对非均匀海洋环境、超大型浮体的水弹性性能以及两者相互之间的关系进行了研究。     

Extracting energy while reducing hydroelastic responses of VLFS using a modular raft wec-type attachment

This paper presents the use of a modular raft Wave Energy Converter (WEC)-type attachment at the fore edge of a rectangular Very Large Floating Structure (VLFS) for extracting wave energy while reducing hydroelastic responses of the VLFS under wave action. The proposed modular attachment comprises multiple independent auxiliary pontoons (i.e. modules) that are connected to the fore edge of the VLFS with hinges and linear Power Take-Off (PTO) systems. For the hydroelastic analysis, the auxiliary pontoons and the VLFS are modelled by using the Mindlin plate theory while the linear wave theory is used for modelling the fluid motion. The analysis is performed in the frequency domain using the hybrid Finite Element-Boundary Element (FE-BE) method. Parametric studies are carried out to investigate the effects of pontoon length, PTO damping coefficient, gap between auxiliary pontoons, and incident wave angle on the power capture factor as well as reductions in the hydroelastic responses of the VLFS with the modular attachment. It is found that in oblique waves, the modular attachment comprising multiple narrow pontoons outperforms the corresponding rigid attachment that consists of a single wide pontoon with respect to the power capture factor and the reduction in the deflection of the VLFS. In addition, it is possible to have a considerable gap between pontoons without significantly compromising the effectiveness of the modular attachment.     

Nonlinear hydroelastic analysis of a moored floating body

By integration of the second-order fluid pressure over the instantaneous wetted surface, the generalized first- and second-order fluid forces used in nonlinear hydroelastic analysis are obtained. The expressions for coefficients of the generalized first- and second-order hydrodynamic forces in irregular waves are also given. The coefficients of the restoring forces of a mooring system acting on a flexible floating body are presented. The linear and nonlinear three-dimensional hydroelastic equations of motion of a moored floating body in frequency domain are established. These equations include the second-order forces, induced by the rigid body rotations of large amplitudes in high waves, the variation of the instantaneous wetted surface and the coupling of the first order wave potentials. The first-order and second-order principal coordinates of the hydrelastic vibration of a moored floating body are calculated. The frequency characteristics of the principal coordinates are discussed. The numerical results indicate that the rigid resonance and the coupling resonance of a moored floating body can occur in low frequency domain while the flexible resonance can occur in high frequency domain. The hydroelastic responses of a moored box-type barge are also given in this paper. The effects of the second-order forces on the modes are investigated in detail.     

多模块超大型浮体中连接器刚度对其运动响应的影响

多模块超大型浮体一般由连接器连接,实现海上浮动机场等功能。实际操作中,为约束超大型浮体模块之间的相对运动,连接器通常将承受非常巨大的载荷,给连接器的制造带来巨大的困难。通过对不同环境力情况下不同刚度连接器的研究,分析了连接器刚度对超大型浮体模块之间相对运动与连接器自身承受载荷的影响。研究发现,随着柔性连接器刚度的增加,连接器对超大浮体模块之间相对运动的约束逐渐增强,同时连接器也将承受更大的载荷;此外,较大的连接器刚度,并不利于抵抗模块之间的冲击载荷;最后,连接器刚度的改变会影响其固有振动频率,因此需要尽可能避开共振区域,否则系统容易出现较大的振动,导致模块间相对运动过大,连接器过载。研究结果确定了连接器刚度最佳匹配原则,以指导连接器的工程设计。