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.     

Hydrodynamic performance of a T-shaped floating breakwater

The comprehensive utilization of floating breakwaters, specially acting as a supporting structure for offshore marine renewable energy explorations, has received more and more attention recently. Based on linear water-wave theory, the hydrodynamic performance of a T-shaped floating breakwater is semi-analytically investigated through the matched eigenfunction expansion method (MEEM). Auxiliary functions, to speed up the convergence and improve the accuracy in the numerical computations, are introduced to represent the singular behavior of fluid field near the lower salient corners of the structure. The effects of the height and installation position of the vertical screen on the reflection and transmission coefficients, dynamic response and wave forces are examined. It is found that the presence of the screen shifts the resonance frequency of RAO for both surge and pitch modes to the low-frequency area, while has no effect on heave mode. The identical added masses, damping and transmission coefficients can be obtained in the cases where the screen holds the same distance away from the longitudinal central axis of the upper box-type structure. Moreover, a relatively small pitch response can be achieved in a wide wave–frequency range, when the breakwater is Γ-shaped.     

Coupled-dynamic analysis of floating structures with polyester mooring lines

A theory and numerical tool are developed for the coupled-dynamic analysis of a deepwater floating platform with polyester mooring lines. The formulas allow relatively large elongation and nonlinear stress–strain relationships, as typically observed in polyester fibers. The mooring-line dynamics are based on a rod theory and the finite element method (FEM), with the governing equations described in a generalized coordinate system. The original rod theory [Nordgren, R.P., 1974. On Computation of the Motion of Elastic Rods. Journal of Applied Mechanics, 41, 777–780] is generalized to allow larger elongation and nonlinear stress–strain relationship. The dynamic modulus of polyester is modeled following an empirical regression formula suggested by [Bosman, R.L.M., Hooker, J., 1999. The Elastic Modulus Characteristic of Polyester Mooring Ropes. In: Proceedings of the Offshore Technology Conference, OTC 10779. Houston, Texas], in which the axial stiffness is not constant, but depends on loading conditions. Two case studies, the static and dynamic behavior of a tensioned buoy and a classic spar with polyester mooring lines, are conducted. The time-domain simulation results are systematically compared with those from the original rod theory. The effects of large elongation and nonlinear stress–strain relations are separately assessed. It is seen that the mean offset, motions, and tension with polyester lines can be different from those by original rod theory with linear elastic lines.     

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.     

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。     

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.     

Reliability assessment of mooring lines for floating structures considering statistical parameter uncertainties

This work focuses on the effect of parameter uncertainty on the reliability index and on the predictive reliability of mooring lines for floating structures under loading from extreme sea-states. A first-order analytic formulation is developed which takes into consideration uncertain parameters in the statistical models of the maximum dynamic tension and the breaking resistance of the mooring lines. Expressions are derived for the mean and the variance of the reliability index in terms of the mean values and the covariance matrix of the uncertain parameters, and of the sensitivity of the reliability index to the uncertain parameters. The predictive reliability index is expressed in terms of the mean and the variance of the reliability index. The formulation is applied to case studies of catenary and taut-leg mooring lines of an offshore structure and the relative effects of the sources of statistical uncertainty are assessed. The case studies demonstrated the applicability and capability of the formulation to capture and represent the relative contributions of the different sources of uncertainty on the predictive reliability and predictive failure probability, as well as on the statistics of the uncertain reliability index.     

海上浮体系泊缆自动化设计方法研究

随着智能化研究成为当今科技发展的热点,结合智能优化算法的浮体系泊系统自动化设计成为一个将现代方法应用于传统工程领域并提高设计效率的研究对象。针对浮体的系泊系统,以悬链线式系泊方式为研究对象,分析得出了系泊缆与不同选材参数之间的规律,建立系泊系统自动化设计方法,选用遗传算法作为算法基础,实现方案的智能优选,进行了有效的探索研究;开发了系泊系统自动化设计的自主程序,完成了典型的单根系泊缆的单点系泊系统以及多段组成风分布式系泊系统的研究,验证了方法的可行性,为系泊系统的自动化设计这一技术问题提供了解决方法与工程的应用手段。     

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.     

双筒双板式浮式防波堤消浪性能研究

浮式防波堤具有对海洋环境友好、施工方便、造价受水深影响小等优点,在海岸工程领域有广阔的应用前景。但受消波效果不稳定、结构易破坏且对锚泊系统要求高等因素的影响,浮式防波堤在实际工程应用中面临较大的挑战。本文采用物理模型试验以及基于OpenFoam的数值模拟方法,对一种由双浮筒、双竖板与水平连接板组成的新型浮式防波堤结构进行消浪性能研究。讨论波浪要素、相对竖板高度、相对水平连接板宽度等因素对双筒双板式浮式防波堤（DCDPFB）消浪性能的影响,分析其周围形成的局部涡量与速度场变化,确定相对最优的结构尺寸。结果表明,相对水平连接板宽度、相对竖板高度和半圆柱体尺寸是影响DCDPFB消浪性能的关键因素;波高与入水深度对透射系数的影响较小;DCDPFB周围形成的局部涡量与速度场变化是耗散波浪能量的重要因素;按照相对最优结构尺寸建造的DCDPFB试验段,在海上原型试验中表现出良好的消波性能。     

双浮箱式浮式防波堤消浪性能试验研究

浮式防波堤在港口海岸工程、近海工程、海洋工程和水产养殖等诸多领域有广阔的应用前景。与单浮箱式浮式防波堤相比,多浮箱式浮式防波堤可提高其消浪性能。对双浮箱式浮式防波堤进行了二维波浪物理模型试验,分析了浮箱宽度、前后浮箱连接方式、前后浮箱间距以及浮箱入水深度等因素对浮式防波堤消浪性能的影响。研究结果表明:对于单浮箱式浮式防波堤,试验范围内浮箱宽度增大一倍后消浪效果改善并不相对明显;前后浮箱刚性连接的双浮箱式浮堤的波浪透射系数均小于前后浮箱自由的双浮箱式浮堤和相同浮箱宽度的单浮箱式浮堤,浮堤消浪性能提高;由于前后浮箱相对间距太大时前后浮箱的相互作用减弱,浮堤的波浪反射系数变小,而不同前后浮箱相对间距的波能损耗系数整体上差别较小,双浮箱式浮堤的波浪透射系数整体上随着前后浮箱相对间距D/2B的增大先减小然后变大,在相对间距D/2B为1.0~1.5时双浮箱式浮堤的波浪透射系数相比最小;不同波高和波浪周期下,浮堤的波浪透射系数均随着浮箱相对入水深度的增大而减小。     

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。     

Hydrodynamic interactions and relative motions of two floating platforms with mooring lines in side-by-side offloading operation

The hydrodynamic interaction and mechanical coupling effects of two floating platforms connected by elastic lines are investigated by using a time-domain multi-hull/mooring/riser coupled dynamics analysis program. Particular attention is paid to the contribution of off-diagonal hydrodynamic interaction terms on the relative motions during side-by-side offloading operation. In this regard, the exact method (CMM: combined matrix method) including all the vessel and line dynamics, and the 12×12 hydrodynamic coefficients in a combined matrix is developed. The performance of two typical approximation methods (NHI/No Hydrodynamic Interaction: iteration method between two vessels without considering hydrodynamic interaction effects; SMM/Separated Matrix Method: iteration method between two vessels with partially considering hydrodynamic interaction effects, i.e. ignoring off-diagonal cross-coupling terms in the 12×12 hydrodynamic coefficient matrix) is also tested for the same side-by-side offloading operation in two different environmental conditions. The numerical examples show that there exists significant discrepancy at sway and roll modes between the exact and the approximation methods, which means that the cross-coupling (off-diagonal block) terms of the full hydrodynamic coefficient matrix play an important role in the case of side-by-side offloading operation. Therefore, such approximation methods should be used with care. The fender reaction forces, which exhibit large force with contact but no force without contact, are also numerically modeled in the present time-domain simulation study.     

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.     

A study of spar buoy floating breakwater

A floating breakwater produces less environmental impact, but is easily destroyed by large waves. In this paper, the spar buoy floating breakwater is introduced with a study on the wave reflection and transmission characteristics and mooring line tension induced by the waves. Mei (The Applied Dynamics of Ocean Surface Waves, Wiley, New York (1983) 740 p) proposed a theoretical solution for the reflection and transmission coefficients as the wave propagates through a one-layer slotted barrier. For a multiple-layer fence system, the analytical solution is proposed linearly. The results show that the theoretical computations agree well with the experimental trends. For a multiple-layer fence system, the transmission coefficients become maximal as the layer spacing to wavelength ratio moves to 1/2. Conversely, the coefficients become minimal, as the ratio moves to 0.3. To estimate the maximum tension of the mooring line, both numerical calculations and laboratory experiments were executed. The numerical calculation results were similar to the experimental results.     

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.     

A simple mathematical model of a floating breakwater

A simple mathematical model, based on the solution of the two-dimensional problem of a vertical floating plate and on rigid body dynamics, is used to investigate the influence of different characteristics (such as mass, draft and anchoring) on the breakwater performance. The results include information about the transmission coefficient as well as about the plate displacement and anchoring forces, as functions of the plate and incident wave parameters.     

Moored floating breakwater response to regular and irregular waves

The simple, yet versatile numerical technique particularly suitable for investigating the problem of the wave attenuation by moored floating breakwater was recently developed by the author. In order to verift the theory, nearly full scale model tests were conducted in a large wave tank ($\text{3.6}\text{m wide}\text{× 4.5}\text{m high}\text{× 106}\text{m long}$). Both random waves and monochromatic waves were used to compare the results. A breakwater with a rectangular cross-section and a hydrodynamically shaped «three-cycle cylinderå breakwater were tested. Incident wave spectra were successfully decomposed from the multi-reflected sea spectra. Frequency response functions of transmitted wave, sway, heave and roll motions of the breakwater as well as mooring forces were all experimentally determined and compared with the theory. Generally, excellent agreements between the theory, the random wave tests and the monochromatic wave tests were obtained for the hydrodynamically shaped breakwater. Except near the modal frequencies of body motion generally good agreement between theory and experiment was obtained for the rectangular breakwater. Near the modal frequencies, the body motion was damped by the flow separation at the sharp corners of the rectangular breakwater. Generation of higher harmonics in wave, body motion and mooring forces was observed and measured, but was generally small. The slow drift oscillation and its effects on the performance of the spring moored breakwaters were also small. From the comaprisons of the small scale test and the large scale tests, it was found that the scale effects were negligibly small on the performance of the spring-moored breakwaters.     

Experimental study on wave transmission coefficient, mooring lines and module connector forces with different designs of floating breakwaters

This paper presents the results and conclusions obtained from the physical model tests carried out with four different designs of floating breakwaters. Changes from a basic design have been introduced in order to evaluate the improvement in the efficiency as a coastal protection structure. Incident and transmitted waves have been measured, as well as the efforts in the mooring lines and module connectors. It has been found that the width of the pontoons is one of the key design parameters, while small modifications in the floating breakwater's cross section shape are less determinant in its hydrodynamic behaviour and in mechanical loads in the discussed ranges. 2D and 3D tests were conducted, observing the great influence that the wave obliquity has in the module connector forces.