Dynamic Analysis of a Turret-Moored Tanker

—In this paper,the second-order perturbation method in frequency domain is used to calculateRAO and spectra of motion and mooring line tension of a turret-moored tanker in ballast condition.Thecalculated results are compared with corresponding experiment results.In the experiment the wave head-ing is 180°,and the wave spectra is the P-M spectrum and white noise spectrum.In the theoretical calcu-lations,the damping coefficient of slow oscillation of the tanker is determined on the basis of the dampingobtained from a test of irregular waves where the mooring system is replaced by a nonlinear spring withnonlinear stiffness similar to that of the mooring system.From the comparison between theoretical calcula-tions and experimental results,it can be found that the theoretical results obtained by the second-orderperturbation method in frequency domain are in good agreement with the experimental results,indicatingthat the damping coefficient of slow oscillation of the tanker required in frequency domain calcu     

顺应式海洋平台慢漂运动物理模型试验研究

为研究顺应式海洋平台慢漂运动的影响因素,以截断圆柱和漂浮方箱为例进行了不规则波作用下的慢漂运动模型试验。测量了不同系泊刚度条件下的漂浮方箱以及相同系泊刚度条件下的截断圆柱和漂浮方箱在静水中自由衰减运动和在不规则波中的运动响应,并将运动响应分解成一阶波频运动响应和二阶低频运动响应,分析了系泊刚度和浮体形状对浮体运动的影响。通过物理模型试验发现了系泊刚度及浮体形状对顺应式系泊浮体一阶运动标准差和二阶低频运动平均漂移值和标准差的关系。结果表明由于顺应式浮体的固有周期远离波浪谱峰周期时,系泊刚度以及浮体形状对慢漂运动的一阶运动响应影响不大;二阶低频运动相对偏离平衡位置的平均值和标准差均随系泊刚度增大而减小,浮体形状同样对慢漂运动的二阶低频纵荡运动响应影响较大。试验结果为实际海洋工程的外形选择和系泊刚度选择提供数据支持。     

Mooring tension and motion characteristics of a submerged fish reef with net in waves and currents using numerical analysis

A numerical model was used to analyze the motion response and mooring tension of a submerged fish reef system. The system included a net attached to a rigid structure suspended up from the bottom with a single, high tension mooring by fixed flotation. The analysis was performed by using a Morison equation type finite element model configured with truss elements. Input forcing parameters into the model consisted of both regular and irregular waves, with and without a steady current. Heave, surge and pitch dynamic calculations of the reef structure were made. Tension response results of the attached mooring line were also computed. Results were analyzed in both the time and frequency domain in which appropriate, linear transfer functions were calculated. The influence of the current was more evident in the tension and heave motion response data. This is most likely the result of the large buoyancy characteristics of the reef structure and the length of the mooring cable. Maximum mooring component tension was found to be 13.9 kN and occurred when the reef was subjected to irregular waves with a co-linear current of 1.0 m/s velocity. The results also showed that the system had little damping (in heave) with damped natural periods of 2.8 s. This combination of system characteristics promotes a possible resonating situation in typical open sea conditions with similar wave periods.     

New Method for Predicting the Motion Responses of A Flexible Joint Multi-Body Floating System to Irregular Waves

A new hybrid method of frequency domain and time domain is developed in this paper to predict the motion responses of a flexibly joint multi-body floating system to irregular waves. The main idea of the method is that the three-dimensional frequency method is used to obtain the hydrodynamic coefficients and the response equations are solved in time domain step by step. All the forces can be obtained at the same time. The motions and nonlinear mooring forces of a box type six-body floating system are predicted. A comparison of the theoretical method-based solutions with experimental results has shown good agreement.     

Effect of wave nonlinearity on fatigue damage and extreme responses of a semi-submersible floating wind turbine

Floating wind turbine has been the highlight in offshore wind industry lately. There has been great effort on developing highly sophisticated numerical model to better understand its hydrodynamic behaviour. A engineering-practical method to study the nonlinear wave effects on floating wind turbine has been recently developed. Based on the method established, the focus of this paper is to quantify the wave nonlinearity effect due to nonlinear wave kinematics by comparing the structural responses of floating wind turbine when exposed to irregular linear Airy wave and fully nonlinear wave. Critical responses and fatigue damage are studied in operational conditions and short-term extreme values are predicted in extreme conditions respectively. In the operational condition, wind effects are dominating the mean value and standard deviation of most responses except floater heave motion. The fatigue damage at the tower base is dominated by wind effects. The fatigue damage for the mooring line is more influenced by wind effects for conditions with small wave and wave effects for conditions with large wave. The wave nonlinearity effect becomes significant for surge and mooring line tension for large waves while floater heave, pitch motion, tower base bending moment and pontoon axial force are less sensitive to the nonlinear wave effect. In the extreme condition, linear wave theory underestimates wave elevation, floater surge motion and mooring line tension compared with fully nonlinear wave theory while quite close results are predicted for other responses.     

A case study of a modified gravity type cage and mooring system using numerical and physical models

A modified gravity-type cage, developed by SADCO Shelf Ltd., was examined using numerical and physical models to determine if the cage and mooring system is suitable for an exposed site south of the Isles of Shoals, NH. The 3000-m/sup 3/ SADCO Shelf Submersible Fish Cage has angled stays between the upper framework and the ballasted bottom rim (in addition to net) to resist the horizontal shear deformation. The mooring system consists of three legs-each made up of a taut vertical chain and an angled rope, both leading to deadweight anchors. Normalized response amplitudes (response amplitude operators) were found for motion response in heave, surge and pitch, and load response in the anchor and bridle lines, in regular (single frequency) waves. In addition, a stochastic approach was taken to determine the motion and load transfer functions in random waves using a spectrum representative of seas at the selected site. In general, the system motion had a highly damped response, with no resonant peaks within the wave excitation range of 0.05 to 0.45 Hz. The anchor line force response was at all frequencies below 5 kN per meter of wave amplitude. The physical model tests showed consistently more conservative (larger) results compared to those for the numerical model.     

Analysis of hydrodynamic behaviors of gravity net cage in irregular waves

Based on the lumped-mass method and rigid-body kinematics theory, a mathematical model of a gravity cage system attacked by irregular waves is developed to simulate the hydrodynamic response of cage system, including the maximum tension of mooring lines and the motion of float collar. The normalized response amplitudes (response amplitude operators) are calculated for the cage motion response in heave and surge, and the mooring line tension response, in regular waves. In addition, a statistical approach is taken to determine the motion and tension transfer functions in irregular waves. In order to validate the numerical model of a gravity cage attacked by irregular waves, numerical predictions have been compared with the experimental observations in the time and frequency domain. The effect of wave incident angle on the float collar motion, mooring line tension and net volume reduction of the gravity cage system in irregular waves is also investigated. The results show that at high frequencies, the cage system has no significant heave motion. It tends to contour itself to longer waves. The variation amplitude of mooring line forces decreases as the wave frequency increases. With the increasing of wave incident angle, the horizontal displacement of the float collar increases.     

Dynamics of large-truncated mooring systems coupled with a catenary moored semi-submersible

With the floating structures pushing their activities to the ultra-deep water,model tests have presented a challenge due to the limitation of the existing wave basins.Therefore,the concept of truncated mooring system is implemented to replace the full depth mooring system in the model tests,which aims to have the same dynamic responses as the full depth system.The truncated mooring system plays such a significant role that extra attention should be paid to the mooring systems with large truncation factor.Three different types of large truncation factor mooring system are being employed in the simulations,including the homogenously truncated mooring system,non-homogenously truncated mooring system and simplified truncated mooring system.A catenary moored semi-submersible operating at 1000 m water depth is presented.In addition,truncated mooring systems are proposed at the truncated water depth of 200 m.In order to explore the applicability of these truncated mooring systems,numerical simulations of the platform’s surge free decay interacting with three different styles of truncated mooring systems are studied in calm water.Furthermore,the mooring-induced damping of the truncated mooring systems is simulated in the regular wave.Finally,the platform motion responses and mooring line dynamics are simulated in irregular wave.All these simulations are implemented by employing full time domain coupled dynamic analysis,and the results are compared with those of the full depth simulations in the same cases.The results show that the mooring-induced damping plays a significant role in platform motion responses,and all truncated mooring systems are suitable for model tests with appropriate truncated mooring line diameters.However,a large diameter is needed for simplified truncated mooring lines.The suggestions are given to the selection of truncated mooring system for different situations as well as to the truncated mooring design criteria.     

Hybrid Verification of A Deepwater Cell-Truss Spar

Hybrid model testing technique is widely used in verification of a deepwater floating structure and its mooring system,but the design of the truncated mooring systems which can reproduce both static and dynamic response same as the full-depth mooring system is still a big challenge,especially for the mooting systems with large truncation.A Cell-Tress Spar operated in 1500 m water depth is verified in a wave basin with 4 m water depth.A large truncation factor arises even though a small model scale 1:100 is adopted.Computer program modules for analyzing the static and frequency domain dynamic response of mooting line are combined with multi-objective genetic algorithm NSGA-II to optimize the truncared mooting system.Considering the asymmetry of layout of mooring hnes,two different truncated mooring systems are respectively designed for both directions in which the restoring forces of the.mooting system are quite,different.Not only the static characteristics of the mooting systems are calibrated,but also the dynamic responses of the single truncated mooting line are evaluated through time domain numerical simulation and model tests.The model test results of 100-year storm in the GOM are reconstructed and extrapolated to a full depth.It is found that the experimental and numerical resuits of Spar wave frequency motion agree well,and the dynamic responses of the full-depth mooring lines are better reproduced,but the low frequency surge motion is overestimated due to the smaller mooring-induced damping.It is a feasible method adopting different truncated mooring systems for different directions in which the restoring force characteristics are quite different and cannot be simulated by one truncated mooring system.Hybrid verification of a deepwater platform in wave basin with shallow water depth is still feasible if the truncated mooring systems are properly designed,and numerical extrapolation is necessary.     

Measuring directional wave spectra using the 3D-ACM WAVE on fixedand taut-wire moorings

Field data were analyzed from a simultaneous deployment of two 3D-ACM WAVE instruments; one on a fixed seabed frame in the nearshore zone, and the other further offshore on a taut-wire mooring. An intercomparison of measurements of vertical and horizontal wave-orbital currents with pressures was used to evaluate the velocity sensor response under field conditions. Results using the fixed frame have validated the measured horizontal wave-orbital velocities, but found the vertical velocities to be less coherent with the pressure time-series. The influence of the instrument mooring system on the velocity measurements was investigated. The oscillation of the taut-wire mooring was found to influence the magnitude of the measured horizontal wave-orbital velocities and induce a phase lag between velocity and sea-surface elevation. Examination of other data from similar taut-wire moorings indicates a systematic relationship between the length of the mooring cable and the measured phase lag, consistent with the behavior of the mooring system considered as a forced, linearly damped oscillator. A comparison was made between the spectra of wave direction derived from both velocity and pressure data with that derived solely from velocity data. The results show a high coherence for the fixed mooring, but significant directional variability in the higher frequencies (>0.13 Hz) on the taut-wire mooring we employed, which we attribute to the mooring oscillation. The analysis further indicates that on taut-wire moorings, the spectra of wave direction should be resolved solely from velocity data. Using these findings, directional wave spectra were produced for the nearshore and offshore sites from 233 coincident events over a two-month period, and these data are presented in a time-averaged spectral format     

Experimental and numerical investigations on the intact and damage survivability of a floating–moored oscillating water column device

This paper investigates the intact and damage survivability of a floating–moored Oscillating Water Column (OWC) device using physical model experiments and Computational Fluid Dynamics (CFD) simulations. Different extreme wave conditions have been tested using irregular and regular wave conditions. The device was moored to the tank floor via four vertical taut lines and the effect of the mooring line pre–tension on the device response was studied. It was found that the instantaneous position of the floating device was a key factor in the survivability analysis such that a certain irregular wave train that might not include the largest wave could induce the maximum response. Reducing the pre–tension minimized the maximum surge, but significantly increased the maximum tension due to mooring slack events causing snatch loads. A design regular wave with a period equal to the peak period and a height of 1.9–2.0 times the significant wave height could reasonably predict the same maximum line tension as the irregular sea state, but a smaller wave height was required to achieve the maximum surge. A single failure in the mooring system increased the maximum tension by 1.55 times the intact tension. For a damaged mooring system, using the same design regular wave condition derived from the survivability analysis with an intact mooring system could result in overestimating the maximum tension by more than 20% in comparison to the tension from the irregular sea state, but a smaller regular wave height or a different regular wave condition representing another sea state could lead to the same maximum tension. This highlighted the importance of investigating survival conditions with a damaged mooring system instead of simply using the same conditions derived for the intact mooring system.     

Large angular motions of tethered surface buoys

A three-dimensional coupled analysis of the interaction of a floating buoy and its mooring is studied. External loads include hydrodynamic forces, tether tensions, wind loads and system weight and buoyancy. Nonlinearities include large rotational and translational motions and non-conservative fluid loads. The mooring problem is formulated as a nonlinear two-point-boundary-value-problem. At each instant in time, the mooring problem is solved by direct integration using a successive iterative algorithm to satisfy boundary conditions. Buoy kinetic and kinematic equations are derived assuming large angles represented by Euler parameters. Coupling between the buoy and the mooring is enforced by matching the velocities of the tether and buoy at the attachment point. A predictor-corrector coupling algorithm is used with multiple sizes of time steps used to provide stability for the separate mooring and buoy models. Numerical results are compared to experimental responses of three types of buoys (sphere, spar and disc) subject to both regular and irregular waves.     

畸形波作用下半潜浮式风机系泊失效停机响应分析

半潜浮式风机逐渐在深海风电开发中受到关注,建立风机、平台与系泊结构耦合数值计算模型,通过FAST与AQWA链接进行风机塔基荷载及平台运动响应相互耦合传递,基于随机波与极限波组合模型生成畸形波时程序列,进行半潜浮式风机系泊失效全过程时域模拟计算分析,得出系泊锚链张力、风机、塔筒和平台运动时程响应,探究系泊失效、风机停机和叶片变桨速率对浮式风机平台系泊结构动力响应的影响。结果表明：畸形波作用下浮式平台和系泊结构动力响应显著,系泊失效导致塔基剪力增加,平台纵荡和纵摇运动响应显著增大;风机停机会引起系泊锚链张力显著减小,转子推力、塔基剪力和叶尖挥舞位移响应逐渐衰减,平台纵荡、纵摇和横摇运动响应显著减小;随着叶片变桨速率增加,风机转子推力和塔基剪力波动幅值增大。     

新型网箱浮架系统水动力分析及系泊方式研究

设计了一种新型网箱浮架系统,利用SESAM对其进行了频域水动力分析以及考虑不规则波浪、风、流载荷和系泊共同作用的时域耦合分析,并与传统双浮管网箱浮架系统进行了分析对比,得到方形网箱与圆形网箱的水动力特性的差异以及各自的优缺点,对实际中网箱的开发设计有一定的借鉴意义;通过计算,证明新型网箱浮架系统在工作海况能正常工作,在极端海况下也能满足安全性的要求;最后对4种常见系泊方式进行了时域耦合分析,得到了四种系泊方式的系泊特性,对实际工程中系泊方式的选择有一定的参考意义。     

Difference-frequency wave loads on a large body in multi-directional waves

The second-order difference-frequency wave forces on a large three-dimensional body in multi-directional waves are computed by the boundary integral equation method and the so-called FML formulation (assisting radiation potential method). Semi-analytic solutions for a bottom-mounted vertical circular cylinder are also developed to validate the numerical method. Difference-frequency wave loads on a bottom-mounted vertical cylinder and stationary four legs of the ISSC tension-leg platform (TLP) are presented for various combinations of incident wave frequencies and headings. These force quadratic transfer functions (QTF) can directly be used in studying slowly varying wave loads in irregular short-crested seas described by a particular directional spectrum. From our numerical results, it is seen that the slowly varying wave loads are in general very sensitive to the directional spreading function of the sea, and therefore wave directionality needs to be taken into account in relevant ocean engineering applications. It is also pointed out that the uni-directionality of the sea is not necessarily a conservative assumption when the second-order effects are concerned.     

Effect of mooring-line stiffness on the performance of a dual coaxial-cylinder Wave-Energy Converter

A point-absorber-type Wave-Energy Converter (WEC) consisting of a floating vertical inner cylinder and an annular outer cylinder that slides along the inner one is considered. The two cylinders heave differently under wave excitation, and wave energy can be harnessed from the relative heave motion between the two cylinders using a Permanent Magnet Linear Generator (PMLG) as the Power Take-Off unit. A mooring cable is attached to the bottom of the inner cylinder. This paper aims to examine the effect of the stiffness of the mooring cable on the performance of the coaxial-cylinder WEC system. The two limiting cases of no mooring cable (freely floating inner and outer cylinders) and an infinitely stiff mooring cable (fixed inner cylinder) were also considered. To perform the analysis, hydrodynamic and interference coefficients of the two heaving cylinders were computed semi-analytically using the method of matched eigenfunction expansions. Experimentally determined viscous corrections on damping were also included in the model in order to have more realistic predictions. The performance of the system in terms of motion responses and capture width were predicted and discussed for both regular and irregular waves. The results of the analysis indicate that both the freely floating design and the design with rigidly moored inner cylinder are viable. The two limiting cases show similar optimal performances, albeit with very different optimal generator damping. However, an ill-chosen mooring-cable stiffness may cause the inner and the outer cylinders to have the same resonance frequency, eliminating the relative heave motion and leading to almost no energy extraction. This situation needs to be avoided when designing the mooring system for a coaxial-cylinder WEC.     

Laboratory study of deep-water breaking waves

In an attempt to elucidate the mechanics of deep-water wave breaking, a variety of breaking waves, including spilling and plunging waves, of different length scales and geometries was studied. The waves were generated through wave-wave interactions using wave packets with constant-steepness components, constant-amplitude components, and also components following the Pierson-Moskowitz distribution. Wave steepening prior to breaking were found to cause an increase in the high frequency spectral slope of the wave spectrum. The slopes were correlated to the type of breaking and the intensity of the breaking. The energy loss through breaking varied with the spectral characteristics of the wave packet. On the other hand, it was also noted that, irrespective of the wave packet, the losses were from the higher frequency end of the first harmonics.     

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。     

浮式塔的动力计算

采用频域二阶摄动法研究了浮式塔在给定环境条件下的动力响应.计算了浮式塔在不规则波上的一阶运动响应函数和运动谱以及张力谱,同时进行了相应的模型试验.由结果的比较可以看出,试验结果与理论方法计算得到的结果吻合较好.计算结果表明,波浪的二阶作用对浮式塔的低频纵荡有影响.计算结果与试验结果的比较说明频域二阶摄动法可以用于浮式塔的动力分析.     

Modelling of the passive turning of a turret moored vessel in conditions of compact ice

The concept of the offshore oil and gas field development using floating ship-shaped platforms, frequently named floating production units (FPU further), with turret mooring is widely used in the world, including regions with harsh environment. The direct transfer of this concept to the Arctic seas is not possible, mostly due to the difficulties of maintaining a weathervaning, or passive turning regime in heavy ice conditions. The main danger relates to the fact that the expected FPU rotation under the action of high ice loads can be accompanied by a translational displacement of the FPU away from the mooring point. As a result, the mooring system may reach an overloaded state until the FPU turns to a favourable position relative to the ice drift direction. In the paper, we are focused on the investigation of a mathematical model of the passive FPU turning on a spot under the assumption that the ice cover is described by a rigid-plastic continuum. The study is performed both analytically and by numerical simulations. A number of specific FPU motion patterns are analytically derived from the model in quasi-static approximation in the form of successive limit states of the system FPU – ice continuum. Some results of the corresponding numerical simulation are presented that confirm the existence of similar solutions in the full dynamic setting of the problem. A partial parametric analysis of the problem is also performed.