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.     

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.     

带空气透平的后弯管浮式防波堤实验研究

针对海工作业平台、海洋养殖网箱等海洋装备的安全防护问题,提出了一种带空气透平的后弯管浮式防波堤,该空气透平既可将作用在防波堤上的波浪能转化成机械能并用于发电,还可显著减小防波堤的锚链力。在介绍了防波堤原理和结构特点的基础上,设计了物理实验模型,并在实验室造波池内进行了模型试验,研究了波浪周期、波高、吃水深度与弯管数量等因素对后弯管浮式防波堤透射系数和锚链力的影响规律。研究结果表明,波浪周期越短,波高越低,防波堤的透射系数越小,锚 链力越小,其消波性能优于传统的浮式防波堤.     

Study on Performance of Savonius Rotor Type Wave Energy Converter Used in Conjunction with Floating Breakwater

In the present study, the performance characteristics of a Savonius rotor type wave energy converter used in conjunction with a conventional double-buoy floating breakwater is investigated using physical model studies. The Savonius rotor type converter is suspended under the double-buoy floating breakwater to achieve wave attenuation while generating electricity, thereby enhancing the overall wave-elimination effect of the combination. The Savonius rotor is tested with different water submergence depths, and a reasonable relative submergence depth is determined within the scope of the research parameters. The hydrodynamics and energy capture performance of the combined breakwater with four different sizes of Savonius rotor under different wave conditions are studied, and the transmission coefficient of the experimental device is analyzed. The results show that when the optimal relative submergence depth is 0.65 D, where D is the impeller diameter, there is a correspondence between the optimal performance of Savonius rotor with different rotor sizes and the wave period and wave height. The optimal energy capture efficiency of the wave energy converter reaches 17%-20.5%, and the transmission coefficient is reduced by35%-45% compared with the conventional double-buoy breakwater.     

强非线性规则波在防波堤上爬高公式研究

为了研究波浪非线性对爬高的影响,解决防波堤等工程设计的实际问题,通过对数学模型试验、物理模型试验、规范公式得到的防波堤波浪爬高对比分析,分析了非线性主要影响参数厄塞尔数、相对水深和波陡对波浪爬高的影响规律,指出规范公式计算时存在的缺陷,并对其计算公式、适用范围进行修正、拟合,得到了强非线性规则波浪爬高的计算方法,可适用于斜坡堤断面的波浪爬高计算,与物理模型试验和数学模型试验结果对比表明,新的波浪爬高计算公式具有较好的计算精度,研究结果可为防波堤等实际工程设计提供重要参考。     

Physical model studies on wave transmission of a submerged inclined plate breakwater

This paper examines the results of physical model studies conducted in a monochromatic wave flume, to evaluate the wave transmission characteristics of a submerged plate breakwater consisting of a fixed plate of 0.50 m length and 0.003 m thickness. The model was oriented at varying inclinations and submergence. The influence of wave steepness, relative depth, relative submergence and angle of inclination on wave transmission was analysed. It was found that the horizontal plate is effective for short waves with steepness parameter higher than 5×10^?3 in relative depth grater than 0.21. The plate oriented at an angle of inclination of 60° is found to be effective for the entire ranges of wave parameters considered for the study and it reduces the wave height by about 40%.     

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.     

带胸墙斜坡堤越波量的试验研究

带胸墙斜坡式防波堤堤顶标高的合理确定，有赖于越波量的正确计算。本文基于水力学中流量系数的概念，建立越波量的计算公式。对影响流量系数的几个主要因素：波高、波陡、胸墙高、平台宽度、相对水深和护面结构等，进行了较系统的试验和讨论，提出了确定流量系数的经验公式。另外，还根据越波量的大小及越波波态，将堤分为：不越水堤、少量越水堤、越水堤及半潜堤四类，可作为合理确定堤顶标高时参考。     

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 performance of the multiple-layer breakwater

Based on the idea of disturbing the water motion in the upright direction, a new kind of multiple-layer breakwater is proposed in this article, which mainly consists of several horizontal plates. The breakwater's performance of dissipating waves has been investigated in detail in the regular wave tests. The factors identified with the characteristics of the breakwater are discussed, such as the relative width, the wave steepness and the models geometrical parameters (the width and the gap). The comparison and analysis of the transmission and reflection coefficients with respect to different factors are presented. The model test results indicate that the multiple-layer breakwater has the good characteristic of dissipating waves. Further more, only in a little extent can it reflect the waves. The multiple-layer breakwater proposed in the paper is very significative to promote the open type breakwater to be the permanent wave attenuator in the application.     

扭王字块体护面斜坡堤越浪量试验研究

针对现行规范中缺少扭王字块体护面斜坡堤越浪量的计算方法,考虑波陡、相对水深、相对堤顶超高、相对坡肩宽度、相对胸墙高度和相对块体尺寸等影响因素,通过波浪水槽物模试验,运用多元回归方法,给出了扭王字块体斜坡堤越浪量中护面结构影响系数和平均越浪量的计算公式。与试验值和其它计算公式进行了验证对比,结果基本吻合,具有一致性的规律。研究成果丰富了规范内容,对斜坡堤工程设计具有重要参考意义。     

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.     

不同间距大直径圆筒防波堤波压力试验研究

通过开展物理模型试验,进行不规则波作用下不同间距大直径圆筒防波堤的波峰压力分布规律研究,分析了圆筒相对间距、相对水深、波陡等主要影响因素对圆筒波压力的影响规律,并通过波压力试验值与各家理论公式计算值的比较,进行不同间距圆筒波压力的计算方法研究。基于直立墙结构和大尺度孤立墩柱结构波压力公式给出修正系数以及横向衰减函数的拟合公式,用以计算圆筒周身不同位置处的波压力,从而为工程设计和理论研究提供参考。     

双平板式透空堤消能效果评价方法

双平板式透空堤具有较为优越的消浪性能备受专家学者关注。目前关于其消浪性能的评价多采用透射波高法开展,仅考虑波高一个参数。本文采用透射波高法、波浪能量法和波能流法分别对平板式透空堤的消能效果进行评价,结果表明,综合考虑波高、水深和周期三个参数的波能流法更加全面与深入。探讨了双平板式透空堤迎浪向与背浪向处波能流的主要影响因素,结果表明,相对板宽、位置参数和波高大小对波能流的影响较板间距和潜深更加显著。     

Hydrodynamic behavior of curtainwall-pile breakwaters

A numerical model is developed that can predict the interaction of regular waves normally incident upon a curtainwall-pile breakwater; the upper part of which is a vertical wall and the lower part consists of an array of vertical piles. The numerical model is based on an eigenfunction expansion method, and utilizes a boundary condition nearby the vertical piles that accounts for wave energy dissipation. Numerical solution comprises a finite number of terms, which is a superposition of propagating waves and a series of evanescent waves. The modeling is validated by comparison with previous experimental studies and overall agreement between measurement and calculation is fairly good. The numerical results are related to reflection, transmission, and dissipation coefficient; wave run-up, wave force, and wave overturning moment are also presented. Effect of porosity, relative draft, and relative water depth are discussed; the choice of suitable range of them is described. The relative draft is more effective for shallow water waves. Model shows decrease in relative draft and leads to reduction of relative wave force, overturning moment, and runup. It is shown that curtainwall-pile breakwaters can operate both effectively and efficiently in the range of relative draft between 0.15 and 0.75. The range 0.5 to 0.2 is also recommended for porosity.     

Wave interaction with ‘’-type breakwaters

The wave transmission, reflection and energy dissipation characteristics of ‘’-type breakwaters were studied using physical models. Regular and random waves in a wide range of wave heights and periods and a constant water depth were used. Five different depths of immersion (two emerged, one surface flushing and two submerged conditions) of this breakwater were selected. The coefficient of transmission, K_t, and coefficient of reflection, K_r, were obtained from the measurements, and the coefficient of energy loss, K_l was calculated using the law of balance of energy. It was found that the wave transmission is significantly reduced with increased relative water depth, d/L, whether the vertical barrier of the breakwater is surface piercing or submerged, where ‘d’ is the water depth and ‘L’ is the wave length. The wave reflection decreases and energy loss increases with increased wave steepness, especially when the top tip of the vertical barrier of this breakwater is kept at still water level (SWL). For any incident wave climate (moderate or storm waves), the wave transmission consistently decreases and the reflection increases with increased relative depth of immersion, Δ/d from −0.142 to 0.142. K_t values less than 0.3 can be easily obtained for the case of Δ/d=+0.071 and 0.142, where Δ is the height of exposure (+ve) or depth of immersion (−ve) of the top tip of the vertical barrier. This breakwater is capable of dissipating wave energy to an extent of 50–80%. The overall performance of this breakwater was found to be better in the random wave fields than in the regular waves. A comparison of the hydrodynamic performance of ‘’-type and ‘T’-type shows that ‘T’-type breakwater is better than ‘’-type by about 20–30% under identical conditions.     

Dynamic pressures and run-up on semicircular breakwaters due to random waves

The dynamic pressures due to random waves of predefined spectral characteristics exerted on a semicircular breakwater model at five different elevations along the depth are measured. In addition, the wave run-up on the model and its reflection characteristics are measured. The results on the variation of the frequency pressure spectra along the depth and the run-up spectra are reported in this paper. The average spectral characteristics as well as statistical properties of the above two parameters are presented. The average reflection coefficient is reported as a function of the wave steepness, described as the ratio of the significant wave height to the square of the peak period.     

Computation of wave transmission over a shore protecting submerged breakwater

Among the offshore breakwaters which are increasingly used in shore protection projects, a bevelled block submerged breakwater with 1 on 1.67 seaward slope and a vertical shoreward face is most advantageous, especially from the point of view of optimum wave damping, minimum wave reflection and maximum sand trapping effects. Different computational methods of wave transmission coefficient of this breakwater are examined with laboratory tests. The Goda's method is found to be the simplest and most suitable in the case of the shore protecting submerged breakwater. However, the consideration of wave steepness also, in selecting the constants may yield better results with this method.     

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.