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.     

基于非线性数学模型的半潜式平台共振运动特性研究

共振运动是深海浮式平台设计的关键考虑因素之一,对海洋平台的作业具有重要影响。采用半潜式平台运动的非线性耦合数学模型,考虑浮筒和横撑出入水以及垂荡、横摇和纵摇运动耦合对平台浮力和恢复力的影响,研究半潜式平台非线性共振运动特性,以及不规则波浪参数对运动的影响。研究表明:在非线性耦合运动和浮力变化的影响下,半潜式平台纵摇和垂荡运动的固有周期会随运动幅值的增大而逐渐减小,且最终趋于稳定,对纵摇运动周期的影响更为显著;非线性效应会使半潜式平台产生显著的低频纵摇共振响应,以及共振频率漂移的现象,且受随机种子和波浪周期的影响较小。     

波流组合作用下SPAR平台垂荡-纵摇耦合运动研究

探讨SPAR平台在波流组合作用下的运动响应机理。运用Matlab程序分析了SPAR平台产生内共振的运动过程,运用刚体动力学理论建立了平台垂荡-纵摇耦合方程,对波流共同作用下Spar平台的垂荡、纵摇运动进行数值模拟,结果表明:流的加入对于内共振的影响并不明显;同时采用AQWA软件研究了流的加入对于纵荡二阶慢漂力的影响,研究发现,当波流同向时能大大增加Spar平台的纵荡运动,而波流反向时却能明显削弱纵荡运动。本文研究成果对于指导深海浮式结构设计开发具有一定的理论借鉴作用。     

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。     

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.     

A nonlinear model of parametric rolling stabilization by anti-roll tanks

The present paper describes a mathematical model in which the fluid motion inside a U-tank is nonlinearly coupled to the heave, roll and pitch motions of the ship. The main purpose of the investigation is centred on the control of roll motion in the case of parametric resonance in longitudinal waves. A transom stern small vessel, known to be quite prone to parametric amplification, is employed in the study. Four tank designs are employed in order to study the influence of tank mass, tank natural frequency and tank internal damping on the control of parametric rolling at different head seas conditions. Additionally, the influence of the vertical position of the tank is also investigated. The main results are presented in the form of limits of stability, with encounter frequency and wave amplitudes as parameters. Distinct dynamical characteristics are discussed and conclusions are drawn on the relevant parameters for the efficient control of the roll amplifications in head seas.     

Parametric model identification of high-speed craft dynamics

Parametric models of heave, pitch and roll dynamics of a high-speed craft have been estimated for different wave incidence angles in the frequency domain. Several issues that make the identification problem interesting are the following: type of parameterization, starting values, non-quadratic functions, excitation signals and short data record. The method employed guarantees a fine linear approximation of the nonlinear dynamics of a fast ship for the ultimate goal of stabilization control to reduce motion sickness associated with heave, pitch and roll accelerations. In addition, the approach achieves high-quality starting values and avoids non-quadratic terms in the cost function, which results in less computational load and significantly more accurate models when compared with a previous method employed for the same problem.     

Triangular Configuration Tension Leg Platform behaviour under random sea wave loads

This study investigates the dynamic response of a Triangular Configuration Tension Leg Platform (TLP) under random sea wave loads. The random wave has been generated synthetically using the Monte-Carlo simulation with the Peirson–Moskowitz (P–M) spectrum. Diffraction effects and second-order wave forces have not been considered. The evaluation of hydrodynamic forces is carried out using the modified Morison equation with water particle kinematics evaluated using Airy's linear wave theory. Wave forces are taken to be acting in the surge degree-of-freedom. The effect of coupling of various structural degrees-of-freedom (surge, sway, heave, roll, pitch and yaw) on the dynamic response of the TLP under random wave loads is studied. Parametric studies for random waves with different H_s and T_z under the presence of current have also been carried out. For the orientation of the TLP, surge, heave and pitch degrees-of-freedom responses are influenced significantly. The surge power spectral density function (PSDF) indicates that the mean square response is affected by the amplification at the natural frequency of the surge degree-of-freedom and also at the peak frequency of the wave loading. The PSDF of the heave response shows higher peak values near the surge frequency and near the peak frequency of the wave loading. Surge response, therefore, influences heave response to the maximum. Variable submergence seems to be a major source of nonlinearity and significantly enhances the responses in surge, heave and pitch degrees-of-freedom. In the presence of current, the response behaviour of the TLP is altered significantly introducing a non-zero mean response in all degrees-of-freedom.     

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.     

Nonlinear coupled response of offshore tension leg platforms to regular wave forces

Among the compliant platforms, the tension leg platform (TLP) is a vertically moored structure with excess buoyancy. The TLP is designed to behave in the same way as any other moored structure in horizontal plane, at the same time inheriting the stiffness of a fixed platform in the vertical plane. Dynamic response analysis of a TLP to deterministic first order wave forces is presented, considering coupling between the degrees-of-freedom surge, sway, heave, roll, pitch and yaw. The analysis considers nonlinearities produced due to changes in cable tension and due to nonlinear hydrodynamic drag forces. The wave forces on the elements of the pontoon structure are calculated using Airy's wave theory and Morison's equation ignoring diffraction effects. The nonlinear equation of motion is solved in the time domain by Newmark's beta integration scheme. The effects of different parameters that influence the response of the TLP are then investigated.     

Analysis of roll motion and stability of a fishing vessel in head seas

The present paper describes an investigation on the relevance of parametric resonance for a typical fishing vessel in head seas. Results for different Froude numbers are discussed based on experimental, numerical and analytical studies.The first region of resonance is investigated. Distinct wave amplitudes are considered. Some intense resonances are found to occur. The paper compares the experimental results with non-linear time simulations of the roll motion. Very good agreement is found, even when large motions take place.Finally, in order to analyze the experimental/numerical results, analytic consideration is given to distinct parameters affecting the dynamic process of roll amplification. The influence of heave, pitch, wave passage effect, speed and roll restoring characteristics are discussed.     

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。     

On the nonlinear uncoupled roll and pitch of submerged vehicles

This paper presents an exact solution of the problem of free nonlinear rolling or pitching motion of a submerged vehicle. The nondimensional frequency-amplitude relationship of free uncoupled roll or pitch is universal, i.e. the single curve describes the behavior of any vehicle. This relationship is softening, i.e. the decreasing frequencies correspond to larger amplitudes of roll or pitch. The amplitudes of vibrations in the region of frequencies corresponding to the resonance are very sensitive to small variations of the frequency. These conclusions, i.e. the softening nonlinearity and the high sensitivity of the amplitudes to small variations of the vibration frequency are valid also for the problem of forced nonlinear roll or pitch motion of submerged vehicles.     

台风海况下半潜式钻井平台动力性能监测与分析

半潜式钻井平台在海洋油气资源开发中发挥着重要作用,目前主要采用模型试验和数值模拟方法对其动力性能进行研究,非常缺乏台风等极端海况下半潜式平台动力响应的实海域监测数据。以某半潜式钻井平台为研究对象,构建了一套比较完善的平台动力性能监测系统,并对台风“杜苏芮”过境阶段的监测数据进行了分析。根据平台艏部气隙及运动监测数据推算了平台吃水及环境波高;采用随机波浪的统计分析方法,计算得到短期海况的有效波高、谱峰周期、能量谱等信息,通过与多种典型海浪谱对比发现Jonswap谱与所测波谱吻合较好;对平台的横摇、纵摇及垂荡运动进行了时域统计分析和频域谱分析,得到了台风海况下被测平台波频运动的实际响应特征,对于指导平台抗台作业具有重要意义。     

一种新型Semi-Spar式海上风机平台系泊系统优化分析

参考英国的Kincardine风机采用的新式的Semi-Spar概念,结合spar式基础和半潜式基础的特点,提出了一种新式海上浮式风机平台模型,并基于三维势流理论,利用AQWA软件进行水动力计算,验证新式平台可靠性。分析了在风、浪、流荷载联合作用下,锚链竖向夹角、系缆数量对风机浮式平台运动性能和系泊张力的影响,对系泊系统进行优化,并验证极端工况下的可靠性。结果证明风机平台水平运动和纵摇运动幅值较小,但垂荡幅值略大,而通过减小锚链竖向夹角可以控制平台运动响应幅值,增加系缆数量可以同时减小系泊张力大小。计算结果证明了新型Semi-Spar式海上风机平台可行性,为浮式风机平台及系泊系统的设计提供参考。     

垂荡板对浮式风机水动—气动耦合性能影响研究

随着风电产业向深远海发展,浮式风机已经成为海上风机未来的发展趋势.由于复杂的风浪联合环境载荷作用,浮式风机作业时通常会产生大幅度的运动响应,这一方面会使得浮式风机系统受到的水动力载荷更加复杂,另一方面会影响浮式风机的输出功率.因此,如何有效地抑制浮式风机系统的运动响应就成为了设计的关键.基于非稳态致动线模型和两相流求解器naoeFOAM-SJTU,进行了带垂荡板的浮式风机耦合性能研究.首先在OC3-Hywind Spar平台上附加垂荡板,并结合NREL-5 MW风力机建立带垂荡板的浮式风机模型.其次对比不同形状的垂荡板对Spar-5 MW型浮式风机气动—水动耦合结果,分析相同风浪联合作用条件下垂荡板形状对浮式风机耦合响应的影响.研究结果表明:垂荡板能够减小纵荡和垂荡等运动响应幅值,但是对纵摇运动响应影响较小;当垂荡板直径和吃水位置相同时,相同风浪条件下圆形垂荡板能使浮式风机的气动平均功率增大约0.844％,而正方形垂荡板却使平均功率减小1.492％,这说明圆形垂荡板对浮式风机系统的作用效果整体而言优于正方形.     

深吃水半潜式平台参数共振研究

深吃水半潜式平台(deep draft semi-submersible,DDS)作为一种新型海洋结构物,既继承了传统半潜式平台的优点,又改善了传统半潜式平台垂荡运动性能差的不足。但随着吃水的增加,DDS纵摇运动参数共振也成为一个不容忽视的问题。当DDS纵摇运动固有周期和垂荡运动周期满足一定关系时,纵摇运动将发生参数共振,纵摇角度将会显著增大。研究推导了DDS纵摇运动方程,并简化为标准的马修方程,运用希尔无穷行列式法求解马修方程,得到了含阻尼的马修稳定性图谱,并结合具体算例讨论了不同参数对DDS纵摇运动参数共振问题的影响。研究表明:深吃水半潜式平台的参数共振,是设计人员在设计之初必须考虑的问题;通过合理选取平台的系统参数,可以有效避免纵摇运动参数共振现象的发生。     

Influence of wave approach angle on TLP's response

The current study focuses on the response analysis of triangular tension leg platform (TLP) for different wave approach angles varying from 0° through 90° and its influence on the coupled dynamic response of triangular TLPs. Hydrodynamic loading is modeled using Stokes fifth-order nonlinear wave theory along with various other nonlinearities arising caused by change in tether tension and change in buoyancy caused by set down effect. Low frequency surge oscillations and high frequency tension oscillations of tethers are ignored in the analysis. Results show that wave approach angle influences the coupled dynamic response of triangular TLP in all degrees of freedom except heave. Response in roll and sway degrees of freedom are activated which otherwise are not present in TLP's response to unidirectional waves. Pitch and roll responses are highly stochastic in nature indicating high degree of randomness. Variation in surge, sway and heave responses are nonlinear and are not proportional to change in wave height for the same period.     

Design of passive anti-roll tanks for roll stabilization in the nonlinear range

The best way of reducing roll motion is by increasing roll damping. Bilge keels are the most common devices for increasing roll damping. If more control is required, anti-roll tanks and fins are used. Tanks have the advantage of being able to function when the ship is not underway. Our objective is to develop design procedures for passive tanks for roll reduction in rough seas. This paper focuses on the design of passive U-tube tanks. The tank-liquid equation of motion is integrated simultaneously with the six-degree-of-freedom (6DOF) equations of the ship motion. The coupled set of equations is solved by using the Large Amplitude Motion Program ‘LAMP’, which is a three-dimensional time-domain simulation of the motion of ships in waves. The unstabilized and stabilized roll motions of a S60-70 ship with forward speed and beam waves have been analyzed. For high-amplitude waves, the unstabilized roll angle exhibits typical nonlinear phenomena: a shift in the resonance frequency, multi-valued responses, and jumps. The performance of a S60-70 ship with a passive tank is investigated in various sea states with different encounter wave directions. It is found that passive anti-roll tanks tuned in the linear or nonlinear ranges are very effective in reducing the roll motion in the nonlinear range. The effect of the tank damping, frequency, and mass on the tank performance is studied. Also, it is found that passive anti-roll tanks are very effective in reducing the roll motion for ships having a pitch frequency that is nearly twice the roll frequency in sea states 5 and 6.