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.     

Hydroelastic responses and drift forces of a very-long floating structure equipped with a pin-connected oscillating-water-column breakwater system

The hydroelastic responses of a very-long floating structure (VLFS) in waves connected to a floating oscillating-water-column (OWC) breakwater system by a pin are analyzed by making use of the modal expansion method in two dimensions. The Bernoulli–Euler beam equation for the VLFS is coupled with the equations of motions of the breakwater taking account of the geometric and dynamic boundary conditions at the pin. The Legendre polynomials are employed as admissible functions representing the assumed modes of the VLFS with pinned-free-boundary conditions. It has been shown numerically that the deflections, bending moments and shear forces of the VLFS in waves can be reduced significantly by a pin-connected OWC breakwater. The time-mean horizontal drift forces of the VLFS equipped with the breakwater calculated by the near-field method are also presented.     

波浪作用下锚链系泊浮式防波堤动力响应的数值模型研究

浮式防波堤充分利用波能在水深方向的分布特性,在满足工程消浪要求的同时对海域水沙交换影响较小,且能够快速布置,在某些实际工程有一定应用前景。为了深入了解波浪作用下浮式防波堤的动力响应,基于OpenFOAM标准求解器olaFlow,在刚体运动求解计算中植入锚链求解模块MOODY(mooring cable dynamics),实现了基于重叠网格方法的浮体运动与锚链受力耦合求解,建立了锚链系泊浮式防波堤动力响应的二维数值模型。利用该数值模型对锚链系泊单方箱浮式防波堤在波浪作用下的透射系数、运动响应、锚链张力进行了模拟,并和相关试验结果进行了比较。结果表明,模型能够准确模拟二维波浪和浮式防波堤的相互作用,并用于三维模型的改进。     

Mooring forces in horizontal interlaced moored floating pipe breakwater with three layers

The paper presents the results from model scale experiments on the study of forces in the moorings of horizontally interlaced, multi-layered, moored floating pipe breakwaters. The studies are conducted with breakwater models having three layers subjected to waves of steepness H_i/L (H_i is the incident wave height and L the wavelength) varying from 0.0066 to 0.0464, relative width W/L (W is the width of breakwater) varying from 0.4 to 2.65, and relative spacing S/D (S is the spacing of pipes and D the diameter of pipe) of 2 and 4. The variation of measured normalized mooring forces on the seaward side and leeward side are analyzed by plotting non-dimensional graphs depicting f/γW² (f is the force in the mooring per unit length of the breakwater, γ the weight density of sea water) as a function W/L for various values of H_i/d (d is the depth of water). It is found that the force in the seaward side mooring increases with an increase in H_i/L for d/W values ranging between 0.081 and 0.276. The experimental results also reveal that the forces in the seaward side mooring decrease as W/L increases, up to a value of W/L=1.3, and then increases with an increase in W/L. It is also observed that the wave attenuation characteristics of breakwater model with relative spacing of 4 is better than that of the model with relative spacing of 2. The maximum force in the seaward side mooring for model with S/D=4 is lower compared to that for the breakwater model with S/D=2. A multivariate non-linear regression analysis has been carried out for the data on mooring forces for the seaside and leeside.     

Dynamic modeling of nylon mooring lines for a floating wind turbine

As current attention of the offshore industry is drawn by developing pilot farms of Floating Wind Turbines (FWTs) in shallow-water between 50m and 100m, the application of nylon as a mooring component can provide a more cost-effective design. Indeed, nylon is a preferred candidate over polyester for FWT mooring mainly because of its lower stiffness and a corresponding capacity of reducing maximum tensions in the mooring system. However, the nonlinear behaviors of nylon ropes (e.g. load-elongation properties, fatigue characteristics, etc.) complicate the design and modeling of such structures. Although previous studies on the mechanical properties and modeling of polyester may be very good references, those can not be applied directly for nylon both on testing and modeling methods. In this study, first, an empirical expression to determine the dynamic stiffness of a nylon rope is drawn from the testing data in the literature. Secondly, a practical modeling procedure is suggested by the authors in order to cope with the numerical mooring analysis for a semi-submersible type FWT taking into account the dynamic axial stiffness of nylon ropes. Both the experimental and numerical results show that the tension amplitude has an important impact on the dynamic stiffness of nylon ropes and, as a consequence, the tension responses of mooring lines. This effect can be captured by the present modeling procedure. Finally, time domain mooring analysis for both Ultimate Limit State (ULS) and Fatigue Limit State (FLS) is performed to illustrate the advantages and conservativeness of the present approach for nylon mooring modeling.     

Nonlinear identification of mooring lines in dynamic operation of floating structures

An adaptive algorithm for on-line estimation of physical coefficients of cables in viscous environment is presented. The procedure is useful for obtaining cable characteristics, which are needed in stability analysis and control system design for moored floating structures. It uses measurements of position and forces from on-board instrumentation. It is also able to track changes in the depth and to test for parameter consistency in order to confer the estimation robustness with respect to dynamic perturbations. It is based on nonlinear solvers, which can cope with transcendental functions of the model structure. The proof of asymptotic convergence is presented. Finally, three basic case studies are analyzed.     

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.     

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.     

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。     

新型浮式防波堤水动力性能数值研究

针对设计的新型双浮筒+Savinious型(S型)桨叶浮式防波堤的结构形式,基于势波理论和结构耦合水动力分析理论,利用面元积分和Newmark-β时间步进格式进行计算,研究其在线性规则波作用下的消波性能、运动响应和系泊张力响应,验证该结构的合理性。数值计算结果表明,阻尼修正后的防波堤纵摇运动响应合理,在波高H=1.5 m、波浪周期T=3 s下其消浪性能较为理想,透射系数达到0.65,同时系泊线张力呈周期响应并满足最大破断力的条件。此外,还研究了浮筒相对间距S1/L,浮筒—桨叶相对间距S2/L以及Savinious型桨叶高径比d/h三个无量纲关键几何参数对防波堤透射系数Ct和系泊线时域张力响应的影响。计算结果表明,浮筒间距S1越接近波长,防波堤消波性能越好,但迎浪侧张力响应幅值越大;随着浮筒—桨叶相对间距S2/L由0趋近于1,其透射系数随之减小,但迎浪侧张力响应幅值基本保持不变;减小桨叶的高径比d/h可以提高防波堤消波性能的稳定性,但张力响应幅值随之增大。     

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.     

Numerical modeling of nonlinear elastic components of mooring systems

This paper deals with the finite-element analysis of compliant structures containing nonlinear elastic components and subjected to loading by waves and currents. An efficient procedure to model such components is developed and implemented in a computer program. It can be applied to analyze nonlinear elastic ropes, rubber tethers, risers, and hoses. The elastic modulus is assumed to depend on the amount of strain in a component. The Newton-Raphson iteration scheme is modified to account for the change of elastic properties on each step of time integration procedure. The approach is applied to develop feed buoy mooring systems for the University of New Hampshire Open Ocean Aquaculture site. The complex nonlinear and viscoelastic load-elongation behavior of suitable high stretch mooring elements for this application is modeled to obtain realistic numerical predictions at sea conditions. Various designs and environmental loading scenarios are considered. Numerical simulations provide predictions of the overall dynamics of the system and maximum values of tensions in critical components.     

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.     

聚焦波作用下透水潜堤消波特性数值模拟研究

基于非静压数值计算模型,本文系统研究了聚焦波作用下透水潜堤的消波特性,通过设置合理的计算工况,详细分析了波高、堤顶水深、谱峰周期、孔隙率以及堤顶宽度5种因素对透水潜堤消波特性的影响。与此同时,本文将透水潜堤的计算结果同不透水潜堤的计算结果进行了对比分析。计算结果表明：透水潜堤对聚焦波的消减作用要强于不透水潜堤,从而说明,透水潜堤能更有效地降低畸形波对海岸基础设施的影响;波高和堤顶水深是影响潜堤消波特性的重要因素,随入射波高增加、堤顶水深减小,透水潜堤对波浪的消减作用逐渐增强。透水潜堤对长周期波浪的消波效果较差。在本文考虑的孔隙率范围内,孔隙率越大,透水潜堤消波效果越好;当孔隙率为0.4,堤顶宽度为0.612 5 m时,透水潜堤可消减54%的入射波能,比不透水潜堤对入射波能的消减增加36.1%。本文研究结果可为进一步认识透水潜堤的消波特性和海岸防护工程设计提供相应的参考。     

潜堤上破碎波浪传播变形的数值模型及其验证

为模拟潜堤上破碎波浪传播时产生能量的耗散这一特性,在改进的具有四阶色散的Boussinesq水波方程中中入二阶紊动粘性项,建立了考虑波浪破碎的水波数学模型.在非交错网格下建立了有限差分数值模型,并利用三阶Adams-Bash forth格式预报、四阶Adams-Mouton格式校正对数值模型进行求解.通过数值试验,模拟...     

Design of mooring system of vessels inside breakwater

A method of simulation calculation for a mooring system of vessels inside a breakwater is illustrated. Using a simulation program based on the above method, a test design for a mooring system for oil-storage vessels of total 5.6 million kiloliters was conducted.In order to obtain data for the simulation program, various experiments, such as wind tunnel tests to test wind resistance, and wave tank tests to test the waves transmitted through or over the breakwater, and the motions of vessels inside the breakwater due to waves, were conducted.Some proposals concerning design criteria and safety factors are presented.Finally, the results of the test design under estimated sea and weather conditions are shown, and the design is concluded to be both technically and economically feasible.     

Measurements of static and dynamic mooring line damping and their importance for floating WEC devices

The dynamic response of the mooring line will be a dominant factor to consider in their use for the station keeping of a wave energy converter (WEC). Due to the relatively small size of WECs and their being moored in relatively shallow waters the effect of waves, tide and current can be of greater significance than for other floating offshore systems. Axial line stretching and high-frequency ‘top-end’ dynamics can importantly modify damping and top-end loading.If a ‘farm’ of devices is to be considered then limitations in sea space may necessitate that the devices be relatively densely packed. This will mean that the ‘footprint’ of the mooring should be constrained, to ensure that the moorings from each device do not interfere and this will have great significance for the loading experienced by the line. One must also consider how the mooring system might change the response of the WEC and so alter its ability to extract power from the waves. Unlike a typical offshore system, the design of moorings for a WEC device must consider reliability and survivability, and the need to ensure efficient energy conversion.The design and operation of a chain mooring for a WEC is considered here. Generic experimental measurements of mooring line damping were conducted in the Heriot-Watt University wave basin at a scale of 1:10. The measurements were conducted on a single mooring line for surge motions and include the study of axial stretching and high top-end dynamics. The laboratory procedures were designed to resemble tests undertaken earlier at ‘full’ scale in 24 m water depth. The measurements were also compared with numerical studies. The experimental findings for WEC devices, supports the conclusion that dynamic mooring line motion will be an important variable, needing to be considered carefully within the design.     

岛礁附近浮式平台运动响应特性数值分析

利用基于开源平台Open FOAM自主开发的船舶与海洋工程水动力性能求解器naoe-FOAM-SJTU,数值模拟了近岛礁环境下规则波的演化特性以及带有系泊系统的浮式平台在相应波浪作用下的水动力性能。对于平台的水动力性能的研究发现,仿真结果与试验结果在平台自由衰减运动固有周期及RAO(response amplitude operator)方面吻合良好。对于波浪在近岛礁地形下的演化现象的研究,分析了波浪演化不对称性特性的成因,并分别给出了不同参数下波浪在地形上爬升时演化的具体特性,对于波高变化及波浪演化的频率成分进行量化的探究。研究发现,波浪周期越大,波高变化越明显,演化的非线性现象越明显,且波浪随着传播距离的增大演化出的阶数也在增大。     

Simulation of the nonlinear dynamic interactions between waves, a submerged breakwater and the seabed

This study employed direct numerical simulation to simulate the fully nonlinear interaction between the water waves, the submerged breakwater, and the seabed under differing wave conditions. In the numerical simulation, the laminar flow condition in the seabed was applied to evaluate the more exact fluid resistance acting on the porous media. Varying incident wave conditions were applied to the flow field resulting from the wave–structure–seabed interaction, and the variation in the pore water pressure beneath the submerged breakwater was investigated along the cross-section of the submerged breakwater. Structural safety and scouring were also considered on the basis of the numerical results for the flow field around the structure and the variation of the pore water pressure.