Nonlinear dynamics of a coupled surge-heave small-body ocean mooring system

An investigation of coupled surge-heave motion of a symmetric small-body ocean mooring system is carried out in this paper. The dynamical system, formulated using a Lagrangian approach in the vertical plane of motion, is characterized by a strong geometric mooring nonlinearity and includes a quadratic relative motion Morison form for the hydrodynamic damping. Numerical simulations reveal complex periodic and aperiodic solutions which include torus multiplying and chaotic motion. The onset of instabilities is discussed and a comparison with a limiting decoupled surge model is performed.     

内孤立波作用下Spar平台动力响应特性

以三类内孤立波理论(Kd V、e Kd V和MCC)的适用性条件为依据,采用Morison和傅汝德-克雷洛夫公式分别计算Spar平台内孤立波水平力和垂向力,结合时域有限位移运动方程,建立了有限深两层流体中内孤立波与带分段式系泊索Spar平台相互作用的理论模型。以东沙群岛某海域实测内孤立波为对象,数值分析了在内孤立波作用下某经典式Spar平台的内孤立波动态载荷、运动响应及其系泊张力的变化特性。研究表明,内孤立波不仅会对Spar平台产生突发性冲击载荷,使其产生大幅度水平漂移运动,而且还会使其系泊张力显著增大。因此,在Spar平台等深海平台的设计应用中,内孤立波的影响不可忽视。     

Coupled dynamic analysis for wave interaction with a truss spar and its mooring line/riser system in time domain

A full time-domain analysis program is developed for the coupled dynamic analysis of offshore structures. For the hydrodynamic loads, a time domain second order method is developed. In this approach, Taylor series expansions are applied to the body surface and free-surface boundary conditions, and the Stokes perturbation procedure is then used to establish the corresponding boundary value problems with time-independent boundaries. A higher-order boundary element method (HOBEM) is developed to calculate the velocity potential of the resulting flow field at each time step. The free-surface boundary condition is satisfied to the second order by fourth order Adams–Bashforth–Moultn method. An artificial damping layer is adopted on the free surface to avoid the wave reflection. The mooring-line/tendon/riser dynamics are based on the rod theory and the finite element method (FEM), with the governing equations described in a global coordinate system. In the coupled dynamic analysis, the motion equation for the hull and dynamic equations for mooring-lines/tendons/risers are solved simultaneously using the Newmark method. The coupled analysis program is applied for a truss Spar motion response simulation. Numerical results including motions and tensions at the top of mooring-lines/risers are presented, and some significant conclusions are derived.     

Effect of slowly varying drift forces on the motion characteristics of truss spar platforms

Spar platform has been regarded as a competitive floating structure for deep and ultra deep water oil and gas production. In this paper, an efficient methodology has been developed to determine the slow motion responses of slender floating offshore structures due to wave forces. Based on this methodology, a MATLAB program named ‘TRSPAR’ was developed to predict the dynamic responses in time domain and it was used in this study to obtain the numerical results of a typical truss spar platform connected to sea bed using nine taut mooring lines. The difference frequency forces were calculated using the principles of the extension of Morison equation for an inclined cylinder and the wave kinematics were predicted using hyperbolic extrapolation. Mooring lines were modelled as nonlinear springs and their stiffness was obtained by conducting the static offset simulation. Because of the lack of detailed calculations in literature, most of the equations used were derived and presented in this paper. The effects of the different sources of the second order difference frequency forces were compared for inertia and drag forces in terms of response spectra. To validate the TRSPAR code, its results were compared to results of a typical truss spar model test.     

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 functions of FLUENT.The added mass coefficient and the damping coefficient 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.     

极限海况下Spar平台系泊系统耦合动力分析

在复杂的风浪流海洋环境中,Spar及其系泊系统的耦合作用受多方面的影响。对极限海况下的某Classic-Spar平台及其系泊缆索的动力响应做了时域非线性耦合研究。重点分析了极限海况下一根或者多根系泊缆索断裂时平台运动及其缆索张力动力响应的统计特性。分析结果表明,在风浪流同向且共线的极限海况下,不同位置处的系泊缆索发生断裂,对整个平台系泊系统安全的影响程度不尽相同,尤其以迎浪方向系泊缆索的断裂影响显著。     

Analytical and numerical analysis of the dynamics of a marine riser connected to a floating platform

Forced dynamics of the system comprised of a riser, connected to a floating platform and conveying fluid, is studied in the presence of ocean waves and ocean currents. Shear effects based on nonlinear elastic theory are included in the formulation. The effects of the structural and hydrodynamic parameters on motion amplitude are evaluated and analytically studied based on an approach developed by Butenin. It is demonstrated that when the nonlinearities are small, the solutions obtained using Butenin's method match the numerical results.     

The heave response of a spar buoy

The vertical response of spar buoys to waves is examined. The response is the product of a rather complex wave forcing function and the resonant response of the buoy. With compound spar buoys (that is, consisting of more than one section of different diameters) the forcing function has a zero at a frequency which is usually close to the resonant frequency, but which can be arranged to be somewhat higher with beneficial effects on the response. Only the effects of pressure and inertia are considered, since this paper is mainly concerned to clarify some specific general principles and it is difficult to include the effects of drag, which are complex.     

Design analysis of a truss pontoon semi-submersible concept in deep water

Truss pontoon semi-submersible (TPS) is a new offshore structure concept in industry, where a truss spar is used to create the added mass by the heave plates. In the present paper, the effect of the heave plates on the vertical motion of the floating structure is demonstrated. A TPS is analyzed by utilizing the linear diffraction theory as well as the linear part of the Morison equation. The close agreement of the analysis results with the experimental results suggests that the simplified Morison equation can be used for the present analysis without sacrificing the quality of the results. However, good engineering judgment is required for estimating the values of the hydrodynamic coefficients as well as the amount of damping introduced in the structure. It is also found that the heave plates indeed introduce large added mass and considerable damping in the system motion in the vertical direction such that the resonant oscillation becomes less of a problem. This suggests that the TSP concept may have merits as a heave-controlled floating production structure in the deepwater development.     

Spar平台与刚性立管及浮力罐耦合动力研究综述

Spar平台是深水和超深水海域中极具竞争力的平台类型。Spar平台中刚性立管顶端所需的张力由月池内部的浮力罐提供,浮力罐在水平方向由导向架支撑。平台运动过程中,浮力罐及立管与平台主体发生相对运动和相互动力作用,在水平方向上发生带有空隙效应的碰撞现象,在垂向产生库仑摩擦效应。这是一种复杂的非线性多点接触耦合动力现象,对平台主体和浮力罐的运动及性能都有着重要影响。因此,无论从平台主体设计及水动力性能方面,还是从浮力罐疲劳分析及安全性方面考虑,都有必要对Spar平台与浮力罐之间的耦合动力作用进行深入的研究。在介绍目前国际上Spar平台与浮力罐相关研究情况及进展的基础上,提出了今后研究的有关建议。     

Wave response of a spar buoy with and without a damping plate

Report on a computer analysis of wave response of a spar buoy that has been operated successfully in the Mediterranean over the past ten years, to find out how the presence of a large horizontal plate at the bottom affects its wave response. The calculations show that the addition of a damping plate decreases have response for short waves but increases the response for very long waves.     

Marine tether dynamics: retrieval and deployment from a heaving platform

A tether management system of a winch module in a marine environment is proposed. For the purpose of this study the subsea body is considered as a mass attached at the free end of a long tether which is wrapped around a circular drum controlled by an external torque. The winch is considered mounted on a heaving platform. The effect of the heaving platform on the motions of the drum, tether and attached mass are studied with respect to the longitudinal vibrations of the tether in one dimension. The hydrodynamic effects are considered on the deployed portion of the tether and the tethered mass, both of which are assumed submerged in otherwise still water. The resulting nonlinear system of equations of motion is developed and solved numerically for an example of a marine tether system. The effect of the tether extensibility on the operation threshold of the system is identified. Comparison with an inextensible tether case is provided. The numerical results and their analysis for the retrieval/deployment of the system are presented.     

基于谱分析法的深水半潜式平台疲劳强度分析

以某新型深水半潜式钻井平台为分析对象,依据三维绕射理论计算单位波幅下波浪诱导载荷,通过建立三维有限元模型计算完成了热点应力响应。运用热点应力的谱分析法计算得到危险节点的疲劳寿命,并进一步分析了各个短期海况和不同浪向对节点总的疲劳损伤度的贡献。研究结果表明,危险节点的疲劳寿命都满足设计寿命要求;在各种中低海况下,疲劳损伤主要来自于平均跨零周期在6 s附近,有义波高转大的短期海况;平台关键连接部位的疲劳损伤主要是在横浪和斜浪状态下产生的,并且对某单一方向的波浪非常敏感。此研究对该类型平台的连接处结构设计和疲劳分析方法有参考意义。     

Experimental survey of the hydrodynamic performance of a small spar buoy

The objective in this experimental work is to evaluate the capability of several cylindrical buoys to follow and measure waves. Eleven configurations have been studied, eight among which were furnished with disks of different diameters at the waterline. The experiments took place in the test basin at ISITV. On the one hand, we have obtained a set of transfer coefficients for each frequency and each configuration in regular waves. On the other hand, we have determined the corresponding transfer functions, then we have used the latter to measure irregular waves. The time signals as measured by the buoys with and without corrections have been compared with wave gage measurements and subjected to a wave-by-wave analysis. The results allow the conclusion that the buoy with a medium size disk constitutes the best compromise. In fact, it permits the buoy to follow the free surface while minimizing parasitic motions.     

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.     

新型多柱桁架式Spar平台疲劳寿命分析

利用谱分析方法对新型多柱桁架式Spar平台的关键点进行了疲劳寿命分析计算.首先建立平台的有限元计算模型,并在频域内进行动力分析;然后利用热点应力法求出关键点应力传递函数,根据应力传递函数得到每个短期海况的应力谱和应力谱参数;最后采用Miner线性累积损伤准则计算出关键点的疲劳寿命,计算结果表明关键点疲劳寿命符合规范要求.     

Nonlinear hydroelastic analysis of a moored floating body

By integration of the second-order fluid pressure over the instantaneous wetted surface, the generalized first- and second-order fluid forces used in nonlinear hydroelastic analysis are obtained. The expressions for coefficients of the generalized first- and second-order hydrodynamic forces in irregular waves are also given. The coefficients of the restoring forces of a mooring system acting on a flexible floating body are presented. The linear and nonlinear three-dimensional hydroelastic equations of motion of a moored floating body in frequency domain are established. These equations include the second-order forces, induced by the rigid body rotations of large amplitudes in high waves, the variation of the instantaneous wetted surface and the coupling of the first order wave potentials. The first-order and second-order principal coordinates of the hydrelastic vibration of a moored floating body are calculated. The frequency characteristics of the principal coordinates are discussed. The numerical results indicate that the rigid resonance and the coupling resonance of a moored floating body can occur in low frequency domain while the flexible resonance can occur in high frequency domain. The hydroelastic responses of a moored box-type barge are also given in this paper. The effects of the second-order forces on the modes are investigated in detail.     

On dynamic coupling effects between a spar and its mooring lines

The responses of a spar constrained by slack mooring lines to steep ocean waves and tensions in the mooring lines are simulated using two different numerical schemes: a quasi-static approach (SMACOS) and a coupled dynamic approach (COUPLE). The two approaches are the same in computing wave loads on the structure. Their difference is in modeling dynamic forces of mooring lines; that is the dynamic forces are included in the computation of COUPLE but neglected in SMACOS. The numerical simulation is examined against the laboratory measurements of the JIP Spar in a water depth of 318 m. The dynamic coupling effects between the JIP Spar and its mooring lines in different water depths (318, 618 and 1018 m) are investigated by the comparison of numerical simulations obtained using the quasi-static and coupled dynamic approaches. It is found that the damping of mooring lines reduces the slow-drift surge and pitch of the Spar, especially in deep water. The reduction in the amplitude of slow-drift surge can reach about 10% in a water depth of 1018 m. The tension in mooring lines may greatly increase in the wave frequency range when dynamic forces in mooring lines are considered. The mooring-line tension in the wave frequency range predicted by the coupled dynamic approach can be eight times as great as the corresponding prediction by the quasi-static approach in a water depth of 1018 m. This finding may have important implications for the estimation of the fatigue strength and life span of the mooring lines deployed in deep water oceans.     

Spar平台垂荡-纵摇耦合运动失稳机理

研究参数激励和强迫激励共同作用下Spar平台垂荡-纵摇耦合运动的失稳机理.考虑静稳性和排水体积的变化,推导平台的垂荡回复力和纵摇回复力矩表达式,建立规则波浪中平台垂荡-纵摇耦合的运动方程.以经典Spar平台为例,分析平台垂荡-纵摇耦合运动发生马休类型不稳定运动的条件以及平台运动失稳的形式,给出波高和波浪周期平面上平台因大幅运动失稳的参数域.结果表明,当波高相对较小时,波浪的临界周期接近于垂荡固有周期,平台失稳的形式为马休失稳;当波高相对较大时,波浪的临界周期远离垂荡固有周期,平台由于大幅摇摆运动而失稳.     

Non-linear analysis of a dynamically positioned platform in stochastic seaway

Safety is the topmost priority considered by the designers of floating systems or any other structural systems. Reliability, economy and environmental pollutions and the liability of the structure in the case of accidents are also considered by the designers. The paper concentrates on the non-linear behavior of a moored floating platform in stochastic seaway generated using the Pierson–Moskowitz spectrum. Second-order wave forces (slow drift force) acting on the structure is considered as they contribute to a major percentage of the excursion of a large platform. Wave drift damping and skin friction damping have also been considered.It has been shown that the principal frequency of the second-order motion of the platform due to drift forces closely matches the natural frequency of the system in surge motion. This has been subsequently used in tuning a PID (proportionate integral and differential)-based control system for the surge mode, where reduction in the order of 90% has been observed.