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.     

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.     

Effect of under connected plates on the hydrodynamic efficiency of the floating breakwater

In this paper, the hydrodynamic efficiency of a floating breakwater system is experimentally studied by use of physical models. Regular waves with wide ranges of wave heights and periods are tested. The efficiency of the breakwater is presented as a function of the wave transmission, reflection, and energy dissipation coefficients. Different parameters affecting the breakwater efficiency are investigated, e.g. the number of the under connected vertical plates, the length of the mooring wire, and the wave length. It is found that, the transmission coefficient kt decreases with the increase of the relative breakwater width B/L, the number of plates n and the relative wire length l/h, while the reflection coefficient kr takes the opposite trend. Therefore, it is possible to achieve kt values smaller than 0.25 and kr values larger than 0.80 when B/L is larger than 0.25 for the case of l/h-1.5 and n=4. In addition, empirical equations used for estimating the transmission and reflection coefficients are developed by using the dimensionless analysis, regression analysis and measured data and verified by different theoretical and experimental results.     

Scattering of gravity waves by multiple surface-piercing floating membrane

Interaction of surface gravity waves with multiple vertically moored surface-piercing membrane breakwaters in finite water depth is analyzed based on the linearized theory of water waves. The study is carried out using least square approximation method to understand the effect of the vertical membrane as effective breakwater. Initially the problem is studied for a single membrane wave barrier but for the case of multiple membrane breakwaters the study is carried out using the method of wide-spacing approximation. In the present study, it is observed that the deflection of the membrane is reduced with the increase in the stiffness parameter of the mooring lines attached to the membrane. In the case of single surface-piercing membrane with moored and fixed edge conditions, the reflection and transmission coefficients are compared and analyzed in detail. The resonating pattern in the reflection coefficients are also observed for multiple floating membrane which can also be referred as Bragg's resonance. In the presence of the porosity constant the wave reflection is also observed to be decreasing and the change in the distance between the vertical floating breakwaters also helps in the attenuation of wave height. It is observed that the presence of multiple floating breakwater helps in the reduction of wave height in the transmitted region.     

A model for obliquely incident wave interacting with a multi-layered object

This paper presents an analytical solution for scattering of oblique incident, small amplitude, monochromatic wave trains by a stationary rigid multi-layered objects with rectangular cross-section. The object is infinite long and consists of multilayers, which can be either solid or permeable. This paper extends the previous work by Hu and Liu [1] from normal incident wave condition with a special object configuration to oblique incident waves with multi-layered object. The present model is validated with several existing solutions for normal/oblique waves interacting with a single object; excellent agreement is observed. New numerical results are presented to investigate the effects of incidence angle on reflection, transmission and energy loss coefficients for a combined floating and bottom-mounted permeable breakwater. A new floating board-cage breakwater is developed from the present model and its solutions are discussed in detail. A computer program, AWAS-P, has been updated so that it is applicable for both oblique and normal incident waves, while the object is multi-layered.     

Experimental Study of Wave Attenuation in Trapezoidal Floating Breakwaters

A comprehensive experimental study was carried out on the regular wave attenuation with a trapezoidal pontoontype floating breakwater(FB) in deep water. The functionalities of two simple FB geometries consist of a rectangle and a trapezoid with the slope of 60° were investigated under the wave attack. A two-dimensional wave flume was used in the experiment; the incident, transmitted waves, mooring line forces and motion responses of the floating breakwaters were measured. Also the influence of the sea state conditions(incident wave height and wave period)and structural parameters(draught of the structure) were investigated using the trapezoidal FB. Our experimental results indicated that the trapezoidal FB significantly reduced the wave transmission and mooring line force when compared with rectangular FBs. A new formula was developed in order to predict the value of the transmission coefficient in trapezoidal FBs with the slope of 60°. Experimental data showed to be consistent with the results of the formula.     

Wave interaction with a wave absorbing double curtain-wall breakwater

This study examines the hydrodynamic performance of a wave absorbing double curtain-wall breakwater. The breakwater consists of a seaward perforated wall and a shoreward impermeable wall. Both walls extend from above the seawater to some distance above the seabed. Then the below gap allows the seawater exchange, the sediment transport and the fish passage. By means of the eigenfunction expansion method and a least square approach, a linear analytical solution is developed for the interaction of water waves with the breakwater. Then the reflection coefficient, the transmission coefficient and the wave forces acting on the walls are calculated. The numerical results obtained for limiting cases agree very well with previous predictions for a single partially immersed impermeable wall, the double partially immersed impermeable walls and the bottom-standing Jarlan-type breakwater. The predicted reflection coefficients for the present breakwater also agree reasonable with previous experimental results. Numerical results show that with appropriate structure parameters, the reflection and transmission coefficients of the breakwater may be both below 0.5 at a wide range of the relative water depth. At the same time, the magnitude of wave force acting on each wall is small. This is significant for practical engineering.     

Numerical modeling of dynamic responses and mooring forces of submerged floating breakwater

Using the volume of fluid (VOF) method, a numerical model is developed to estimate the nonlinear dynamics of a pontoon type moored submerged breakwater under wave action and the forces acting on the mooring lines, for both the vertical and inclined mooring alignments. The model is developed for a two-dimensional wave field in a vertical plane. The finite displacements of the breakwater such as sway, heave and roll in a very small time step are considered and the numerical grid cells intersected by the breakwater surfaces for changing its position due to wave action are treated using the concept of porous body model. Also, two-dimensional experimental studies are carried out to investigate the performance of the proposed model. The comparison of the computed and measured results reveals that the developed numerical model can reproduce well the dynamics of the floating body and the mooring line forces.     

Numerical and Experimental Investigation of Interactions Between Free-Surface Waves and A Floating Breakwater with Cylindrical-Dual/Rectangular-Single Pontoon

This paper investigates the hydrodynamic performance of a cylindrical-dual or rectangular-single pontoon floating breakwater using the numerical method and experimental study. The numerical simulation work is based on the multi-physics computational fluid dynamics (CFD) code and an innovative full-structured dynamic grid method applied to update the three-degree-of-freedom (3-DOF) rigid structure motions. As a time-marching scheme, the trapezoid analogue integral method is used to update the time integration combined with remeshing at each time step. The application of full-structured mesh elements can prevent grids distortion or deformation caused by large-scale movement and improve the stability of calculation. In movable regions, each moving zone is specified with particular motion modes (sway, heave and roll). A series of experimental studies are carried out to validate the performance of the floating body and verify the accuracy of the proposed numerical model. The results are systematically assessed in terms of wave coefficients, mooring line forces, velocity streamlines and the 3-DOF motions of the floating breakwater. When compared with the wave coefficient solutions, excellent agreements are achieved between the computed and experimental data, except in the vicinity of resonant frequency. The velocity streamlines and wave profile movement in the fluid field can also be reproduced using this numerical model.     

Wave Attenuation Performance and the Influencing Factors of A Lower Arc-Plate Breakwater

Comprehensive experimental and numerical studies have been undertaken to investigate wave energy dissipation performance and main influencing factors of a lower arc-plate breakwater. The numerical model, which considers nonlinear interactions between waves and the arc-plate breakwater, has been constructed by using the velocity wave- generating method, the volume of fluid (VOF) method and the finite volume method. The results show that the relative width, relative height and relative submergence of the breakwater are three main influencing factors and have significant influence on wave energy dissipation of the lower arc-plate open breakwater. The transmission coefficient is found to decrease with the increasing relative width, and the minimum transmission coefficient is 0.15 when the relative width is 0.45. The reflection coefficient is found to vary slightly with the relative width, and the maximum reflection coefficient is 0.53 when the relative width is 0.45. The transmission and reflection coefficients are shown to increase with the relative wave height for approximately 85% of the experimental tests when the relative width is 0.19 0.45. The transmission coefficients at relative submergences of 0.04, 0.02 and 0 are clearly shown to be greater than those at relative submergences of 0.02 and 0.04, while the reflection coefficient exhibits the opposite relationship. After the wave interacts with the lower arc-plate breakwater, the wave energy is mainly converted into transmission, reflection and dissipation energies. The wave attenuation performance is clearly weakened for waves with greater heights and longer periods.     

Experiments on wave transmission coefficients of floating breakwaters

To find a simple, inexpensive, and effective type of floating breakwater for deep-sea aquaculture, we studied three types of structures: the single box, the double box, and the board net. We conducted two-dimensional physical model tests in a wave-current flume in the laboratory to measure the wave transmission coefficients of the three types of breakwaters under regular waves with or without currents. Based on the initial comparison of the wave transmission coefficients, we proposed the use of the board-net floating breakwater for use with fish cages; we then conducted detailed experiments to examine how wave transmission coefficients are affected by several factors, including the width of the board, the row number of the net, the rigidity of the board, and the current velocity. The experimental results show that the board-net floating breakwater, which is a simple and inexpensive type of structure, can effectively protect fish and fish cages and may be adopted for aquaculture engineering in deep-water regions.     

Wave reflection from partially perforated-wall caisson breakwater

In 1995, Suh and Park developed a numerical model that computes the reflection of regular waves from a fully perforated-wall caisson breakwater. This paper describes how to apply this model to a partially perforated-wall caisson and irregular waves. To examine the performance of the model, existing experimental data are used for regular waves, while a laboratory experiment is conducted in this study for irregular waves. The numerical model based on a linear wave theory tends to over-predict the reflection coefficient of regular waves as the wave nonlinearity increases, but such an over-prediction is not observed in the case of irregular waves. For both regular and irregular waves, the numerical model slightly over- and under-predicts the reflection coefficients at larger and smaller values, respectively, because the model neglects the evanescent waves near the breakwater.     

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.     

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.     

Mooring forces and motion responses of pontoon-type floating breakwaters

The experimental and theoretical investigations on the behaviour of pontoon-type floating breakwaters are presented. A two-dimensional finite element model is adopted to study the behaviour of pontoon-type floating breakwaters in beam waves. The stiffness coefficients of the slack mooring lines are idealized as the linear stiffness coefficients, which can be derived from the basic catenary equations of the cable. The theoretical model is supported by an experimental programme conducted in a wave flume. The motion responses and mooring forces are measured for three different mooring configurations, and the results are reported and discussed in detail in this paper. The wave attenuation characteristics are presented for the configurations studied.     

畸形波作用下锚泊方柱系泊张力特性研究

基于物理模型试验,探究畸形波和不规则波作用下浮体系泊张力差异问题。讨论相对波高、相对周期和畸形波参数α₁对系泊张力的影响。结果显示:畸形波参数α₁和浮体系泊张力显著相关。在α₁=2.0～2.83范围内,畸形波作用下迎浪侧系泊张力最大值可达不规则波作用的1.9倍。在相对波高H_s/d=0.032～0.097范围内,畸形波作用下迎浪侧系泊张力最大值显著大于不规则波的作用结果,但畸形波和不规则波对应的1/3值及平均值几乎一致。就相对周期影响而言,迎浪侧系泊张力最大差别出现在谱峰周期T_p0p范围内。频域方面采用小波分析方法讨论畸形波和不规则波作用下浮体系泊张力时频谱特征,两种波浪作用下系泊张力时频特征有显著差别。     

Dynamics of elastically moored floating objects

The two-dimensional problem of wave transformation by, and motions of, moored floating objects is solved numerically as a boundary value problem by direct use of Green's identity formula for a potential function. The cross-sectional shape of the floating object, the bottom configuration and the mooring arrangements may be all arbitrary. For a given incident wave, the three modes of body motion, the wave system and mooring forces are all solved at the same time. A laboratory experiment is conducted to verify the theory. Generally good agreements between the theory and experiments are obtained as long as the viscous damping due to flow separation is small. A numerical experiment indicates that a conventional sluck mooring is to worsen the wave attenuation by a floating breakwater and that a properly arranged elastic mooring can considerably improve the wave attenuation by a floating breakwater.     

Hydrodynamic efficiency of partially immersed caissons supported on piles

The efficiency of the breakwater, which consists of caissons supported on two or three rows of piles, was studied using physical models. The efficiency of the breakwater is presented as a function of the transmission, reflection and the wave energy dissipation coefficients. Regular waves with wide ranges of wave heights and periods and constant water depth were used. Different characteristics of the caisson structure and the supporting pile system were also tested. It was found that, the transmission coefficient (k_t) decreases with increasing the relative breakwater draft D/L, increasing the relative breakwater width B/h, and decreasing the piles gap-diameter ratio G/d. It is possible to achieve k_t values less than 0.25 when D/L≥0.1. The reflection coefficient takes the opposite trend especially when D/L≤0.15. The proposed breakwater dissipates about 10-25% of the incident wave energy. Also, simple empirical equations are developed for estimating the wave transmission and reflection. In addition, the proposed breakwater model is efficient compared with other floating breakwaters.     

Dual pontoon floating breakwater

The hydrodynamic properties of a dual pontoon floating breakwater consisting of a pair of floating cylinders of rectangular section, connected by a rigid deck, is investigated theoretically. The structure is partially restrained by linear symmetric moorings fore and aft. The fluid motion is idealized as linearized, two-dimensional potential flow and the equation of motion of the breakwater is taken to be that of a two-dimensional rigid body undergoing surge, heave and pitch motions. The solution for the fluid motion is obtained by the boundary integral equation method using an appropriate Green's function. Numerical results are presented which illustrate the effects of the various wave and structural parameters on the efficiency of the breakwater as a barrier to wave action. It is found that the wave reflection properties of the structure depend strongly on the width, draft and spacing of the pontoons and the mooring line stiffness, while the excess buoyancy of the system is of lesser importance.     

Experimental study on the hydrodynamic performance of rectangular floating breakwater influenced by reef areas

Abstract

In this paper, series of experimental studies under regular wave actions to investigate the hydrodynamic performance of the rectangular floating breakwater (FB) affected by reefs with different slopes were carried out in a wave flume. The wave transmission coefficients, motion responses and mooring forces can be calculated on the basis of the data obtained from the experiments. A comparative experiment of the only rectangular FB is also conducted. The experimental results reveal that the rectangular FB with different reefs can make more positive effects on wave energy dissipation than that of the only rectangular FB, especially for short-period waves. The characteristics of three degrees of freedom of the rectangular FB affected by reefs are also observed, which can be used to further explain the variation tendency appeared in transmission coefficients. The roll motion of the FB influenced by reefs is intenser than that of the only FB and the changes of slopes have limited effects on the sway motion of the FB. Furthermore, the heave motion of the only rectangular FB is intenser than that of the FB affected by reefs for short-period waves and vice versa for long-period waves.