Research on the Hydrodynamic Characteristics of Heave Plate Structure with Different Form Edges of A Spar Platform

The hydrodynamic characteristics of heave plates with different form edges of Truss Spar Platform are studied in this paper. Numerical simulations are carried out for the plate forced oscillation by the dynamic mesh method and user defined fimctions of FLUENT. The added mass coefficient Cm and the damping coefficient Cd of heave plate with tapering condition and the chamfer condition are calculated. The results show that, in a certain range, the hydrodynamic performance of heave plate after being tapered is better.

Experimental Investigation on Hydrodynamic Behavior of the Geometric Spar Platform

In recent years, attention has been focused on the spar platform for gas and oil exploitation in deep water. With the development of offshore technology, many new spar concepts have been put forward and fully studied. This paper presents the results of an experimental investigation on the hydrodynamic behavior of a new spar concept from Novellent Offshore LLC, USA, which is called Ceometrie Spar （G-spar）. A new type of buoyancy can concept from the same company, viz. Integratod Buoyancy Can （IBC）, is researched in the meantime. The G-spar and IBC models with a 1：70 scale are tested in the State Key Laboratory of Ocean Engineering at Shanghai Jiao Tong University for the global performance of the spar hull, in which the second-order wave drift force is involved, as well as the effect of heave plates on the motion characteristics and mooring force of the G-spar platform.

Numerical and Experimental Research on the Global Performances of Cell-Truss Spar Platform

Spar technology has been applied to the deep-sea oil and gas exploitation for several years. From the first generation of classic spar, the spar platform has developed into the second generation of truss spar and the latest cell spar. Owing to its favorable adaptability to wide range of water depth and benign motion performances, spar has aroused quite a lot of interests from oil companies, universities and research institutes. In the present paper, a new cell-truss spar concept, put forward by the State Key Laboratory of Ocean Engineering （SKLOE） at Shanghai Jiao Tong University, is studied both numerically and experimentally. The numerical simulation was conducted by means of nonlinear time-domain fully coupled analysis, and its results were compared to the experimental data. Whereafter, detailed analysis was carried out to obtain the global performances of＇ the new spar concept. Proposals for the improvement of numerical calculation and experimental technique were tabled meanwhile.

Nonlinear Random Motion Analysis of Coupled Heave-Pitch Motions of a Spar Platform Considering lst-Order and 2nd-Order Wave Loads

In this study, the coupled heave-pitch motion equations of a spar platform were established by considering lst-order and 2nd-order random wave loads and the effects of time-varying displacement volume and transient wave elevation. We generated random wave loads based on frequency-domain wave load transfer functions and the Joint North Sea Wave Project （JONSWAP） wave spectrum, designed program codes to solve the motion equations, and then simulated the coupled heave-pitch motion responses of the platform in the time domain. We then calculated and compared the motion responses in different sea conditions and separately investigated the effects of 2nd-order random wave loads and transient wave elevation. The results show that the coupled heave-pitch motion responses of the platform are primarily dominated by wave height and the characteristic wave period, the latter of which has a greater impact. 2nd-order mean wave loads mainly affect the average heave value. The platform＇s pitch increases after the 2nd-order low frequency wave loads are taken into account. The platform＇s heave is underestimated if the transient wave elevation term in the motion equations is neglected.

Numerical Modeling of a Spar Platform Tethered by a Mooring Cable

Virtual simulation is an economical and efficient method in mechanical system design. Numerical modeling of a spar platform, tethered by a mooring cable with a spherical joint is developed for the dynamic simulation of the floating structure in ocean. The geometry modeling of the spar is created using finite element methods. The submerged part of the spar bears the buoyancy, hydrodynamic drag force, and effect of the added mass and Froude-Krylov force. Strip theory is used to sum up the forces acting on the elements. The geometry modeling of the cable is established based on the lumped-mass-and-spring modeling through which the cable is divided into 10 elements. A new element-fixed local frame is used, which is created by the element orientation vector and relative velocity of the fluid, to express the loads acting on the cable. The bottom of the cable is fixed on the seabed by spring forces, while the top of the cable is connected to the bottom of the spar platform by a modified spherical joint. This system suffers the propagating wave and current in the X-direction and the linear wave theory is applied for setting of the propagating wave. Based on the numerical modeling, the displacement-load relationships are analyzed, and the simulation results of the numerical modeling are compared with those by the commercial simulation code, Proteus DS. The comparison indicates that the numerical modeling of the spar platform tethered by a mooring cable is well developed, which provides an instruction for the optimization of a floating structure tethered by a mooring cable system.

Internal Resonances for Heave, Roll and Pitch Modes of A Spar Platform Considering Wave and Vortex-Induced Loads in the Main Roll Resonance

We present a study of the nonlinear coupling internal resonance for the heave roll and pitch performance of a spar platform under the wave and vortex-induced loads when the ratio of the frequencies of heave, roll and pitch are approximately 2：1：1. In consideration of varying wet surface, the three DOFs nonlinear coupled equations are established for the spar platform under the effect of the first-order wave loads in the heave and pitch, and vortex-induced loads in the roll. By utilizing the method of multi-scales when the vortex-induced frequency is close to the natural roll frequency, the first-order perturbation solution is obtained analytically and further validated by the numerical integration. Sensitivity analysis is performed to understand the influence of the damping and the internal detuning parameter. Two cases with internal resonance are shown. The first case is that no saturation phenomenon exists under small vortex-induced loads. The first order perturbation solution illustrates that only the vortex-induced frequency motion in roll and the super-harmonic frequency motion in heave are excited. The second case is that the vortex-induced loads are large enough to excite the pitch and a saturation phenomenon in the heave mode follows. The results show that there is no steady response occurrence for some cases. For these cases chaos occurs and large amplitudes response can be induced by the vortex-induced excitation.

Parametric Resonance Analyses for Spar Platform in Irregular Waves

The parametric instability of a spar platform in irregular waves is analyzed. Parametric resonance is a phenomenon that may occur when a mechanical system parameter varies over time. When it occurs, a spar platform will have excessive pitch motion and may capsize. Therefore, avoiding parametric resonance is an important design requirement. The traditional methodology includes only a prediction of the Mathieu stability with harmonic excitation in regular waves. However, real sea conditions are irregular, and it has been observed that parametric resonance also occurs in non-harmonic excitations. Thus, it is imperative to predict the parametric resonance of a spar platform in irregular waves. A Hill equation is derived in this work, which can be used to analyze the parametric resonance under multi-frequency excitations. The derived Hill equation for predicting the instability of a spar can include non-harmonic excitation and random phases. The stability charts for multi-frequency excitation in irregular waves are given and compared with that for single frequency excitation in regular waves. Simulations of the pitch dynamic responses are carried out to check the stability. Three-dimensional stability charts with various damping coefficients for irregular waves are also investigated. The results show that the stability property in irregular waves has notable differences compared with that in case of regular waves. In addition, using the Hill equation to obtain the stability chart is an effective method to predict the parametric instability of spar platforms. Moreover, some suggestions for designing spar platforms to avoid parametric resonance are presented, such as increasing the damping coefficient, using an appropriate RAO and increasing the metacentric height.

The Nonlinear Bifurcation and Chaos of Coupled Heave and Pitch Motions of a Truss Spar Platform

This paper presents the results from a numerical study on the nonlinear dynamic behaviors including bifurcation and chaos of a truss spar platform. In view of the mutual influences between the heave and the pitch modes, the coupled heave and pitch motion equations of the spar platform hull were established in the regular waves. In order to analyze the nonlinear motions of the platform, three-dimensional maximum Lyapunov exponent graphs and the bifurcation graphs were constructed, the Poincare maps and the power spectrums of the platform response were calculated. It was found that the platform motions are sensitive to wave fre- quency. With changing wave frequency, the platform undergoes complicated nonlinear motions, including 1/2 sub-harmonic motion, quasi-periodic motion and chaotic motion. When the wave frequency approaches the natural frequency of the heave mode of the platform, the platform moves with quasi-periodic motion and chaotic motional temately. For a certain range of wave frequencies, the platform moves with totally chaotic motion. The range of wave frequencies which leads to chaotic motion of the platform increases with increasing wave height. The three-dimensional maximum Lyapunov exponent graphs and the bifurcation graphs reveal the nonlinear motions of the spar platform under different wave conditions.

Investigation on the Dynamic Responses of a Truss Spar Platform for Different Mooring Line Groups

The dynamic responses of any floating platform arc dependent on the mass, stiffness and damping characteristics of the body as well as mooring system. Therefore, it is very essential to study the effect of individual contributions to the system that can finally help to economise their cost. This paper focuses on the effect of mooring stiffness on the responses of a truss spar platform, obtained by different grouping of lines. The study is part of our present researches on mooring systems which include the effect of line pretension, diameter and azimuth angles. The platform is modelled as a rigid body with three degrees-of-freedom and its motions are analyzed in time-domain using the implicit Newmark Beta technique. The mooring lines restoring force-excursion relationship is evaluated using a quasi-static approach. It is observed that the mooring system with lines arranged in less number of groups exhibits better performance in terms of the restoring forces as well as mean position of platform. However, the dynamic motions of platform remain unaffected for different line groups.

Study on Collision Characters for SPAR Platform

This paper presents the research on the external mechanism of collision characters for a SPAR platform. The collision characters of SPAR platform have not attracted so much attention as that of ships in the past, because short of this kind of collision accidents reported. But with the increasing number of SPAR platforms in the world, the possibility of such kind of accident also increases. Therefore, it is necessary to master the character of SPAR collision. Model test technique is employed to study the external mechanism. The collision scenario is a ship colliding with a SPAR platform moored in the site with 1500 meters water depth. The striking ship hits the SPAR platform on the hard tank near water surface in its longitudinal direction. The specifics of the SPAR＇s motions and the tension forces of the mooring lines are collected to summarize the hydrodynamic characters in the collision scenario. It is found that the maximal displacements and the maximal pitch angles of the SPAR platform, and the maximal tension forces of mooring lines are all linearly proportional to the initial velocity of the striking ship basically. Mooring lines play elastic roles in the collision course.

Coupling Response of Heave and Moonpool Water Motion of A Truss Spar Platform in Random Waves

This paper presents the heave responses and the moonpool water motions of a truss Spar platform with semi-closed moonpool in random waves. A 2-DOF（degree of freedom） coupling dynamical equations of the platform heave and vertical motions of the moonpool water are derived. The linear wave theory is used to simulate the random waves. The response statistical values and the power spectrums are calculated to analyze the mutual influences between the platform heave and the moonpool water motions for different opening ratios of the moonpool. The effect of coupling parameters on the platform heave and the moonpool water motions are analyzed. The results show that motions of the moonpool water significantly affected the platform heave when the characteristic wave period is far away from the natural period of the platform heave, and different moonpool opening ratios lead to different heave amplitudes of the platform. In the actual design, an optimized moonpool opening ratio can be designed to reduce heave motions of the platform.

Stochastic Analysis of Nonlinear Coupled Heave-Pitch Motion for the Truss Spar Platform

Considering the static stability and the change of the displacement volume, including the influences of higher order nonlinear terms and the instantaneous wave surface, the nonlinear coupled heave-pitch motion was established in stochastic waves. The responses of heave-pitch coupling motion for the Truss Spar platform were investigated. It was found that, when the characteristic frequency of a stochastic wave is close to the natural heave frequency, the large amplitude pitch motion is induced under the parametric-forced excitation, which is called the Mathieu instability. It was observed that the heave mode energy is transferred to pitch mode when the heave motion amplitude exceeds a certain extent. In addition, the probability of internal resonant heave-pitch motion is greatly reduced while the characteristic wave frequency is away from the natural heave frequency.

Mooring System Optimisation and Effect of Different Line Design Variables on Motions of Truss Spar Platforms in Intact and Damaged Conditions

This paper presents the effect of mooring diameters, fairlead slopes and pretensions on the dynamic responses of a truss spar platform in intact and damaged line conditions. The platform is modelled as a rigid body with three degrees-of-freedom and its motions are analysed in time-domain using the implicit Newmark Beta technique. The mooring restoring force-excursion relationship is evaluated using quasi-static approach. MATLAB codes DATSpar and QSAML, are developed to compute the dynamic responses of truss spar platform and to determine the mooring system stiffness. To eliminate the conventional trial and error approach in the mooring system design, a numerical tool is also developed and described in this paper for optimising the mooring configuration. It has a graphical user interface and includes regrouping particle swarm optimisation technique combined with DATSpar and QSAML. A case study of truss spar platform with ten mooring lines is analysed using this numerical tool. The results show that optimum mooring system design benefits the oil and gas industry to economise the project cost in terms of material, weight, structural load onto the platform as well as manpower requirements. This tool is useful especially for the preliminary design of truss spar platforms and its mooring system.

Heave-Roll-Pitch Coupled Nonlinear Internal Resonance Response of a Spar Platform Considering Wave and Vortex Exciting Loads

Many studies have been done on the heave-pitch unstable coupling response for a spar platform by a 2-DOF model.In fact,in addition to the heave and pitch which are in one plane,the nonlinear unstable motion will also occur in roll.From the results of the experiments,the unstable roll motion plays a dominant role in the motion of a spar platform which is much stronger than that of pitch.The objective of this paper is to study 3-DOF coupling response performance of spar platform under wave and vortex-induced force.The nonlinear coupled equations in heave,roll and pitch are established by considering time-varying wet surface and coupling.The first order steady-state response is solved by multi-scales method when the incident wave frequency approaches the heave natural frequency.Numerical integration of the motion equations has been performed to verify the first-order perturbation solution.The results are confirmed by model test.There is a saturation phenomenon associated with heave mode in 3-DOF systems and all extra energy is transferred to roll and pitch.It is observed that sub-harmonic response occurs in roll and pitch when the wave force exceeds a certain value.The energy distribution in roll and pitch is determined by the initial value and damping characteristics of roll and pitch.The energy transfers from heave to pitch and then transfers from pitch to roll.Due to the influence of the low-frequency vortex-excited force,the response of roll is more complicated than that of pitch.

Internal Resonances for the Heave Roll and Pitch Modes of a Spar Platform Considering Wave and Vortex Exciting Loads in Heave Main Resonance

The objective of this paper is to study the nonlinear coupling internal resonance of the heave,roll,and pitch response performance of a spar platform when their frequencies are in the ratio of 2:1:1 under wave and vortex exciting loads.The three degree-of-freedom(DOF)nonlinear coupled equations are established by considering a time-varying wet surface with a first-order wave force in heave and pitch and a vortex-induced force in roll.The first-order steady-state response is solved using the multi-scale method in heave main resonance.The multiple solutions of the motion equations are discussed using the analytic method and a numerical simulation.A sensitivity analysis is conducted to test the influence of the damping and internal detuning parameter.The regions of multiple solutions are found,and the jump phenomenon exists with the changes of the wave excitation.The regions of multiple solutions depend on the values of damping and detuning parameter.

15 MW级Spar漂浮式风电平台的设计方案及水动力性能研究

[目的]针对15 MW级浮式风机,提出一种新型的Spar漂浮式风电平台设计方案,并对平台性能进行分析。[方法]基于势流理论对平台进行频域水动力计算,对不同浪向下的平台波浪力和运动响应特性进行研究;应用叶素动量法计算叶轮气动载荷并将其等效为风力系数,从而计算不同工况风浪流联合作用下的平台时域响应,同时对系泊缆的受力情况进行分析。[结果]结果显示,平台垂荡和纵摇在平台运动固有频率处出现了峰值点,且发生的位置均远离波浪的主要能量区域;在风浪流作用下,相较于工作工况,极限工况下的平台最大纵摇角略小,而最大纵荡和垂荡响应幅值以及最大系泊张力更大。[结论]研究证明新型Spar漂浮式风电平台具有良好的稳性和水动力性能,在设计环境载荷下,平台响应和系泊力均能满足要求,能够保障风力发电机组的安全性和稳定性。

CT-Spar平台及其系泊与立管系统优化

以CT-Spar平台及其系泊与立管系统为对象,识别出平台垂荡板数目、张紧式系泊缆预张力、钢悬链线立管上浮子位置及浮力大小为CT-Spar平台-系泊-立管系统设计时的关键参数。基于SESAM运用频域分析、时域耦合分析等手段,以系统运动响应及受力为指标,对这些关键参数进行分析与优化,结果表明,垂荡板数目由4调整为3、张紧式系泊缆预张力为1800 kN、3600 kN的浮子安装在距钢悬链线立管距顶端悬垂长度段的60%处的参数设计是适应1500 m深海风-浪-流复杂动力环境的优选方案。对该方案在极端动力条件及平台系统部分破损状态下进行时域耦合分析,发现该方案也能满足石油平台安全相关规范要求,并显著改善系泊缆、立管受力状态。

Spar平台多自由度耦合的涡激运动数值模拟研究

为研究Spar平台在均匀流作用下多自由度耦合的涡激运动特性,本文基于STAR-CCM+求解器建立了考虑流固耦合的Spar平台涡激运动数值模型,探讨了纵荡、横荡、垂荡、纵摇和横摇五个自由度的耦合效应。结果表明:Spar平台在横荡、垂荡与横摇三个自由度发生明显“涡激共振”现象,并且垂荡与横摇自由度“涡激共振”现象发生的速度区间基本一致;横荡与横摇自由度保持着较高的耦合性,横荡共振时横荡与横摇的运动主频保持1:1的关系,横摇共振时横荡运动频谱的次峰频率等于横摇运动主频;纵荡、垂荡与纵摇三个自由度存在复杂的非线性耦合运动关系,不仅纵荡、垂荡的运动主频始终存在于纵摇频谱中,而且纵摇与纵荡、纵摇与垂荡的耦合程度在不同的折合速度范围内存在差异。

新型漂浮式风力机Spar平台动态响应及系泊研究

提出漂浮式风力机Spar平台安装螺旋布置扰流片的设计方法,通过对水动力学软件AQWA的二次开发,实现风波作用下浮式风力机动态响应的求解,对比研究扰流片螺旋布置高度对漂浮式风力机Spar平台动态响应的影响以及对扰流片平台安装系泊配重后对平台动态响应与系泊张力的影响。结果表明:扰流片平台的辐射阻尼较原平台在纵荡、垂荡、纵摇方向上均有所提升;扰流片平台的纵荡、垂荡、纵摇幅值响应算子较原平台均有所降低;随扰流片布置高度提升对平台纵摇方向运动响应抑制效果最好、垂荡方向次之。在风波耦合作用下,扰流片能够降低平台纵荡、纵摇响应,一定程度上抑制垂荡运动响应;安装扰流片可降低风力机转子推力、平台系泊张力有所上升;对系泊安装配重浮筒,在有效降低系泊张力的同时能够抑制平台纵荡、垂荡运动响应,对纵摇运动影响较小。

内孤立波与Spar型浮式风机平台耦合作用研究

针对内孤立波与系泊浮式平台的耦合作用问题,本文以单立柱Spar型浮式风机平台为研究对象,研究了平台在内孤立波作用下的耦合运动特性。利用重叠网格技术及自编耦合动力程序,以计算流体动力学求解Navier-Stokes流体控制方程,建立了Spar型浮式风机平台与内孤立波(Internal solitary waves,ISWs)流固耦合作用数值模型。通过系列数值模拟,研究了Spar型浮式风机平台在内孤立波作用下的水平动态载荷和纵荡、横荡规律。研究表明,内孤立波对Spar平台会产生较显著的水平作用力,并产生大幅的水平位移;在水深一定时,同一流体分层比下,随着内孤立波振幅提高,纵荡运动幅值增大;当振幅一定时,随着流体分层比的增大,纵荡幅值减小;通过调整系泊系统,发现非线性系泊系统下平台纵荡幅值要大于线性系泊系统下的情况,即线性系泊系统会低估纵荡运动幅值。