New insight into the wave-induced nonlinear vertical load effects of ultra-large container ships based on experiments

Accurate estimation of the wave-induced extreme hogging vertical bending moment (VBM) is of vital importance for the design of container ships because container ships are normally under hogging conditions in still water. According to the empirical formulas proposed by the classification society rules, the design hogging VBM can be approximately 20 % smaller than the design sagging VBM for vessels with small block coefficients. High-order harmonic components in the vertical load effects, which are induced by the nonlinearities in the hydrodynamic forces and ship hull geometry, contribute to the asymmetry. Previous studies have shown that the nonlinear hydrostatic and Froude–Krylov forces increase the sagging VBM significantly. Current numerical tools are able to reveal this asymmetry to a certain extent. There is, however, little focus on the nonlinear pressure under the bow bottom, which is a more likely contributor to the hogging VBM. Several unexpected phenomena have been observed for large container ships. The wave-frequency sagging and hogging VBMs followed each other closely, and hence did not reflect the significant nonlinear factors as expected. In this paper, the test data of two (8600-TEU and 13000-TEU) ultra-large containership models in both regular and irregular head waves are systematically studied. In regular waves, the influence of the second and third harmonics on the fundamental hogging peaks and sagging troughs is estimated by comparing both the amplitude and phase difference relative to the first harmonic peaks. In irregular waves, the focus is on the statistical characteristics of the wave-induced nonlinear vertical load effects. To achieve a balance between results in regular and irregular waves, the influence of the second harmonics is evaluated through bispectral analysis.     

Comparison of numerical and experimental results of nonlinear wave-induced vertical ship motions and loads

 A nonlinear time-domain procedure is presented which is used to calculate the vertical responses of a container ship advancing in head waves. The method assumes linear radiation forces represented by time convolution of memory functions, infinite frequency added masses, and radiation restoring coefficients. The nonlinear hydrostatic restoring and Froude–Krilov forces are computed exactly over the instantaneous wetted surface of the ship's hull. Forces due to green water on deck are calculated using the momentum method. Nonlinear effects are identified on different vertical ship responses, namely on the heave and pitch motions, the vertical accelerations, and the vertical bending moment. These non-linear effects are expressed by the variation of the transfer function with the wave amplitude, the higher-order harmonics of the time signals, the offset of the time series, and the asymmetry of the peaks. The numerical results and the quantified nonlinear effects are compared with experimental results showing an ability to reproduce the main nonlinear effects. Received: December 17, 2001 / Accepted: January 31, 2002     

Nonlinear effects from wave-induced maximum vertical bending moment on a flexible ultra-large containership model in severe head and oblique seas

Vertical bending moment (VBM) is of crucial importance in ensuring the survival of vessels in rough seas. With regard to conventional vessels, wave-induced maximum VBM is normally considered to be experienced in head seas. It is conservative to determine the extreme VBM based on either numerical simulations or model tests in long-crested head seas. Extensive model tests have been conducted in head seas with focus on the nonlinear vertical responses in severe seas, and the measured results were compared with numerical calculations for validation. Unexpected phenomena, however, were observed during the model tests of an ultra-large containership. The maximum sagging and hogging VBMs were encountered in oblique seas. Furthermore, the significant wave height used in oblique seas was even smaller than that used in head seas. The nonlinear vertical load effects in oblique seas require further investigations for this particular vessel. Limited experimental results in oblique seas have been reported, in which the lateral responses were always more concerned than the vertical responses. Up to now, rare systematic comparisons of the nonlinear vertical responses between head and oblique seas have been published, especially when the hydroelastic effects are also accounted for. A 13000-TEU ultra-large containership model, which was designed by Hyundai Heavy Industries (HHI), has been tested in the towing tank and the ocean basin at the Marintek center in Trondheim. The experimental results in regular waves are first compared between head and oblique seas. The statistical characteristics of the VBM amidships under nineteen irregular wave conditions are then investigated. Next, the extreme hogging and sagging VBMs are compared under different wave conditions with focus on the extreme hogging VBMs. At the end of the paper, the uncertainties in the experiments are discussed.     

6750箱集装箱船非线性波激振动和颤振响应分析

本文采用三维时域非线性水弹性方法分析了一艘6750箱集装箱船的水弹性响应以及运动和垂向弯矩特征。通过考虑入射波力、静水恢复力、砰击效应的非线性,研究了在恶劣海况下船体的非线性运动和垂向弯矩响应,同时分析了波激振动及颤振对垂向弯矩的影响。数值计算结果表明:(1)非线性入射波力对运动的影响较小,但是对垂向弯矩的影响较大,使得其有明显的倍频成分,同时中垂弯矩显著大于中拱弯矩。另外,非线性入射波力也引起了明显的非线性波激振动;(2)非线性静水恢复力对运动和载荷的影响均较大,但是没有引起明显的非线性响应。非线性计算的垂荡响应小于线性结果,而纵摇和垂向弯矩响应大于线性结果;(3)砰击效应对运动的影响较小,但对垂向弯矩的影响较大,砰击效应引起了显著的船体弹性高频振动,增大了载荷幅值,但是其引起的合成中垂和中拱幅值相差不大;(4)非线性水动力的作用主要引起垂向弯矩的倍频响应,包括倍频可能引起的二节点垂向弯矩弹性共振,而砰击效应主要引起船体二节点垂向弯矩共振;(5)本文的非线性水弹性响应计算结果与Kim给出的数值计算结果吻合很好。     

Vertical and horizontal bending moments on the hydroelastic response of a large-scale segmented model in a seaway

Wave-induced vertical bending moment (VBM) and horizontal bending moment (HBM) on a large-scale segmented model with a box-type backbone beam in short-crested irregular seas are systematically analyzed using sea trial measurement data. New insights into the relationship between nonlinear VBM and HBM of the ship sailing in short-crested sea waves are explored and presented. The results indicate that the HBM significantly contributes to the total sectional loads when the ship is sailing in a seaway and the HBM has a strong correlation with VBM in both magnitude and tendency. Therefore, design loads of HBM and the corresponding lateral structural strength issues should also be concerned in addition to VBM at the ship design phase.     

系泊船舶动力学特性的计算机仿真研究

以三阶操纵运动方程为基础，引入定常的风力、潮流作用力和二阶波浪力，建立了系泊系统三自由度的运动微分方程。在此数学模型的基础上．建立了系泊系统的多自由度的计算机仿真模型。在潮流作用、潮流和风作用以及风浪流联合作用等三种情形下，对系泊船舶的动力学响应分别进行了仿真研究。研究表明，系泊系统的动力学行为具有强烈的非线性特征。对于单点系泊船舶而言，在定常的风浪流作用下．顶风顶浪顶流状态并不一定是最为危险的工况。     

迎浪规则波中小水线面双体船纵向运动及波浪载荷非线性特性数值分析

基于RANS方程和VOF模型求解船体粘性兴波流场,开展了小水线面双体船(Small Waterplane Area Twin Hulls,SWATH)迎浪规则波中纵向运动及波浪载荷的非线性特性研究.通过数值计算结果与模型试验结果的对比分析,验证了文中方法的有效性;在此基础上,较为系统地分析了SWATH船的垂荡及纵摇运动响应、垂向加速度和波浪载荷的一阶及二阶量随入射波高的变化规律,指出SWATH船的运动响应及载荷与波高存在非线性的关系,尤其体现在响应共振区附近;相比于船体垂荡和纵摇运动,垂向加速度及波浪载荷的非线性特性更为显著.     

Transient design waves for green-water loading on bulk carriers

The wave surface profiles associated with extreme relative motion between a slender stationary vessel and the adjacent wave surface are investigated for long-crested head seas. The methodology is based upon an established statistical relationship for a Gaussian random process which indi-cates that in the vicinity of an extreme event the most probable shape of the time history approaches that of the autocorrelation function. Attention is given to the relative motion at a longitudinal position which is representative of the No. 1 hatch cover location on a bulk carrier. Second-order corrections to the wave surface profiles are used to provide estimates of nonlinear relative motions. It is shown that extreme relative motion at the hatch cover location is associated with the vessel encountering a steep-fronted wave with pronounced asymmetry in the horizontal and vertical directions. In order to evaluate the exceedence probabilities, it is hypothesized that the peaks of the nonlinear relative motions are closely correlated with the peaks of an underlying linear process. The overall methodology is applied to an investigation of relative motion exceedence probabilities for vessel lengths of 250 m and 300 m over a range of survival seastates. Received: July, 1999 / Accepted: November, 1999     

Experimental study on the nonlinear pressure acting on a high-speed vessel in regular waves

It is well known that the hydrodynamic responses of a high-speed vessel traveling in regular head waves of even moderate wave height can show significant nonlinear behavior, and so linear statistical techniques become insufficient for predicting the statistics of responses in irregular waves. On the other hand, it has been shown that an approximate third-order Volterra model is applicable to handling the statistics of some nonlinear seakeeping problems, such as motions and vertical hull girder loads. In the present study, the focus is on the nonlinear behavior of the pressure responses of the hull surface, especially on the pressures acting on alternately wet and dry areas near the waterline and on the bow zone with high deadrise angles that may be subject to slight impact and water pile-up effects. To clarify the validity of applying Volterra modeling to this problem, a series of experiments in regular and irregular head waves were carried out, and approximate third-order and fifth-order Volterra models with the proposed algorithm for finding frequency response functions (FRFs) were applied as a means of validation. In the present article, the first part of the validation was performed using experimental data in regular waves. It was confirmed that the third-order Volterra model has adequate accuracy to simulate deterministically the variation of pressure responses in regular waves of different wave steepness up to a wave amplitude to wavelength ratio of 0.01 even for the highly nonlinear pressures acting on the above-mentioned areas of the hull surface.     

顺应式垂直通路立管的动力响应优化研究

海洋立管的动力响应优化要考虑复杂的环境载荷,如波浪、流以及浮体运动,有时还需考虑立管与海床的耦合作用,这个过程需要执行大量耗时较大的有限元分析,从而使动力优化的工作进展困难。针对此问题,本文将近似模型技术运用到FPSO的顺应式垂直通路立管（CVAR）的动力响应优化问题。优化以壁厚、管径等几何参数作为变量,优化目标是使总重量最小及等效应力在许用应力水平之下。研究给出了3种近似模型方法的比较分析,使得优化结果更具有可靠性。结果表明,3种近似模型方法的优化效果和效率彼此都非常接近,并且都能在CVAR的优化效果和减小耗时方面有出色表现。     

振荡来流下柔性立管涡激振动响应特性试验研究

在顶部浮体的带动下,悬链线立管的动力响应会诱发其周围产生相对来流,而这种振荡来流将激励立管悬垂段产生“间歇性”的涡激振动。文章在海洋工程水池中对不同最大约化速度URmax、KC数组合下的振荡来流作用下的柔性立管开展模型试验研究,利用光纤应变片测量模型的涡激振动响应。结合模态分析与小波变换对试验数据进行分析,讨论并总结了最大约化速度URmax以及KC数对涡激振动位移幅值响应特性的影响规律。文中进一步分析发现振荡来流下的涡激振动响应还存在“迟滞”及“高阶谐频”现象。     

系泊系统的时域仿真及其非线性动力学特性分析

应用时域仿真的方法研究了系泊系统的非线性动力学特性。以三阶操纵运动方程为基础,引入定常的风力、潮流作用力和二阶波浪力,建立了系泊系统三自由度的运动微分方程。在此数学模型的基础上,建立了系泊系统的多自由度的计算机仿真模型。在风浪流联合作用的情形下,对一艘单点系泊油轮的动力学行为进行了仿真研究。以潮流速度和系缆程度为分岔控制参数,在参数平面上给出了局部分岔集。研究表明,系泊系统的动力学行为具有强烈的非线性特征。在仿真过程中观察到了吸引子的共存和Hopf分岔。局部分岔集将参数平面分为3个系统动力学行为本质不同的区域。极值系泊力水平与系泊系统的动力学行为有着密切的关系。对于单点系泊船舶而言,顶风顶浪顶流的状态并不一定是最为危险的工况。局部分岔集的确定为系泊系统参数的选择提供了决策依据。     

迎浪规则波中波浪增阻和船体垂向运动的数值预报(英文)

The numerical prediction of added resistance and vertical ship motions of one ITTC (International Towing Tank Conference) S-175 containership in regular head waves by our own in-house unsteady RANS solver naoe-FOAM-SL JTU is presented in this paper. The development of the solver naoe-FOAM-SJTU is based on the open source CFD tool, OpenFOAM. Numerical analysis is focused on the added resistance and vertical ship motions (heave and pitch motions) with four very different wavelengths (0.8Lpp≤λ≤1.5Lpp) in regular head waves. Once the wavelength is near the length of the ship model, the responses of the resistance and ship motions become strongly influenced by nonlinear factors, as a result difficulties within simulations occur. In the paper, a comparison of the experimental results and the nonlinear strip theory was reviewed and based on the findings, the RANS simulations by the solver naoe-FOAM-SJTU were considered competent with the prediction of added resistance and vertical ship motions in a wide range of wave lengths.     

平台运动对深水钻井隔水管非线性动力响应的影响

文章建立了波浪、海流和船体运动等载荷综合作用下的深水钻井隔水管非线性时域动力响应模型,模型考虑了顶部张力和隔水管内部泥浆对隔水管动力响应的影响,计人了张力沿隔水管长度的变化,并采用有限差分法求解了四阶偏微分运动方程.计算了随机波浪和规则波浪下船体运动对深水钻井隔水管非线性动力响应的影响,研究分析了船体平均偏移以及波频响应和低频响应的周期和幅值对深水钻井隔水管动力响应的影响.结果表明,船体运动对深水钻井隔水管动力响应有较大的影响,在随机波浪和海流作用下,考虑船体运动时,隔水管上部最大弯矩增大了59%.船体的平均偏移主要影响底部最大弯矩.船体波频运动对上部最大弯矩有较大影响,随着波频响应的周期和幅值的变化,上部最大弯矩变化较快,而低频响应的则主要影响隔水管上部弯矩.     

基于细长体公式的Truss SPAR在波流中的运动响应预报方法

利用细长体公式和刚体非线性运动方程建立Truss SPAR在波浪与流中运动响应预报方法。通过波浪自由表面和SPAR中心线方程构造辅助函数,迭代计算Truss SPAR瞬时湿长度。根据SPAR主体形状特点和流场中水质点运动规律,分段高效积分Truss SPAR上的水动力载荷。通过Runge-Kutta-Fehlberg方法求解运动方程,得Truss SPAR在波浪与流中的运动响应。对一座Truss SPAR在不同波流工况中的运动响应进行了预报,结果显示波浪和流使Truss SPAR产生了明显漂移运动和振荡运动,漂移运动的大小与流的方向有关,而振荡运动的幅值与波浪的方向有关。     

海上供应船旁靠大型浮式平台耦合 响应的模型试验研究

对大型浮式平台与供应船之间的旁靠带缆系统进行选型设计,同时开展两船旁靠作业时耦合响应特性的水池试验研究。重点分析两船体六自由度的相对运动特点、旁靠系泊缆的受力以及护舷的挤压应力随风浪流角度的变化规律。试验表明:两船在纵荡、横荡及首摇这三个低频方向的相对运动幅度较小,一般不会成为制约旁靠卸载作业的控制因素,但另外三个波频方向运动具有一定的独立性,且不受旁靠缆绳的约束,是影响旁靠作业窗口期的重要因素;缆绳张力和护舷挤压力对来流角度较为敏感,且供应船处于上风位时,缆绳的张力、护舷的挤压力比其位于下风位有明显增大,建议供应船尽可能位于浮式平台的下风位旁靠作业。     

Formulation of consistent nonlinear restoring stiffness for dynamic analysis of tension leg platform and its influence on response

Shortcomings of the traditionally used nonlinear restoring stiffness of TLPs, i.e. unrealistically high stiffness of horizontal motions, their uncoupling and secant formulation are pointed out. Therefore, new consistent restoring stiffness is derived. The platform is considered as a rigid body moored by flexible pretensioned tendons. Global horizontal low frequency motions (surge, sway and yaw) with large amplitudes as a result of dominant second order wave excitation and small stiffness, and vertical local motions (heave, roll and pitch) of higher frequency and small amplitudes excited by the first order wave forces, are distinguished. Hence, horizontal displacements represent position parameters in analysis of vertical motions. First, the linear restoring stiffness, which consists of the tendon conventional axial stiffness, the tendon geometric stiffness and the platform hydrostatic stiffness, is established. Then it is extended to large displacements resulting in new secant restoring stiffness. It depends on surge, sway and yaw displacements and is the same in any horizontal direction. Also, the tangent stiffness, which gives more accurate results, is derived. Heave is defined as vertical projection of axial tendon vibrations and platform tangential oscillations, which are analyzed in their natural moving coordinate system. Inertia force due to setdown, as a slave d.o.f. of the master horizontal motions, is taken into account in the dynamic equilibrium equations. As a result the complete tangential stiffness matrix of horizontal and vertical motions includes 7 d.o.f. The known secant restoring stiffness matrices are compared with the new one and noticed differences are discussed. All theoretical contributions are illustrated by relatively simple numerical example.     

Numerical study on the dynamic response of a truncated ship-hull structure under asymmetrical slamming

Dynamic response of ship-hull structure under slamming has tracked widespread attention in the marine structural design. However, our understanding on the dynamic characteristics largely relies on the symmetrical slamming cases. This paper presented a preliminary numerical investigation on the dynamic response of a truncated ship-hull structure under asymmetrical slamming based on the uncoupled CFD-FE method. Asymmetrical slamming loads were predicted through combining the seakeeping analysis and CFD method. In there, three kinds of motions (vertical, horizontal and roll motions) of 2D ship sections were obtained through the seakeeping analysis and then the slamming pressure was predicted through simulating the water entry with various motions based on CFD method. The dynamic response was analyzed through finite element method. Numerical predictions including ship motions, slamming loads and dynamic analysis were validated against published experimental data and numerical calculations. The characteristics of asymmetrical slamming loads were analyzed showing obvious asymmetry in space, and the dynamic characteristic of the ship bow structure was further clarified through discussing the deformation and stress distribution. These results are useful for readers for better understanding the dynamic characteristics of the bow structure under slamming.     

Experimental study on the nonlinear pressure acting on a high-speed vessel in irregular waves

The present study focuses on the nonlinear behavior of pressure on the hull surface of a high-speed vessel in irregular waves, particularly the pressure responses of alternately wet and dry areas near the waterline and on the bow zone. The vessel has high deadrise angles that may be subject to slight impact and water pile-up effects. A series of experiments in regular and irregular head waves were conducted, and the validity of applying Volterra modeling was investigated. In a previous article using experimental data in regular waves, it was confirmed that the approximate third-order Volterra model adequately simulated the variation of pressure responses in regular waves of different steepness up to a wave amplitude with a wavelength ratio of 0.01, even for the highly nonlinear pressures acting on the abovementioned areas of the hull surface. In this article, further validation for the second part of the study was obtained using experimental data in irregular waves. The frequency response functions obtained from the previous study’s experimental data in regular waves were applied to the third-order Volterra model by combining the input of irregular waves to simulate the responses in irregular waves of sea state five. Then, the spectra and statistics were analyzed. For the motions, accelerations, and pressure responses in irregular waves (as well as for the simulated time histories) variance spectra and statistics such as cumulative distributions of peak values and probability density functions were compared with the experimental results. It was confirmed that even for highly nonlinear and non-Gaussian pressures on the abovementioned areas of the hull surface, the approximate third-order Volterra model simulates the pressure responses in irregular head waves up to a sea state of five with adequate accuracy on deterministic and statistical bases.