Qualitative aspects of nonlinear ship motions in following and quartering seas with high forward velocity

By utilizing a four-degrees-of-freedom numerical model with dense grids of control parameters and the sudden-change concept, the qualitative aspects of the nonlinear motions of a fishing vessel complying with the International Maritime Organization's intact stability criteria in following and quartering seas were intensively explored. As a result, capsizing due to broaching, capsizing without broaching, broaching without capsizing, stable surf-riding, and steady periodic motion were identified. The natures of the boundaries of these motions in the control parameter plane were investigated, and the effects of the initial conditions and the nonlinearity of calm-water maneuvering forces are also discussed. Furthermore, comparisons with a model experiment showed that the numerical model used here qualitatively explains capsizing phenomena, but quantitatively overestimates the danger of capsizing. Received: June 11, 2001 / Accepted: October 9, 2001     

Stability assessment for intact ships in the light of model experiments

A systematic method for assessing intact ship stability with a free-running model in a seakeeping and maneuvering basin is proposed in this paper. Model experiments were carried out in extremely steep regular waves for a model drifting, running in head seas, and quartering seas. This method was applied to two purse seiners, and efficiently identified thresholds in metacentric heights for capsizing of these ships. These capsizing thresholds are compared with requirements of the IMO Code on Intact Stability. This series of model experiments also confirms that capsizing at the threshold occurs only in quartering seas, and shows that capsizing is caused by broaching, loss of stability on a wave crest, or bow diving. Received for publication on Jan. 20, 1999; accepted on July 6, 1999     

骑浪/横甩薄弱性衡准和模型试验研究

目前国际海事组织(IMO)正在制定的第二代完整稳性衡准,其中就包括骑浪/横甩薄弱性衡准。文章首先介绍了最新骑浪/横甩薄弱性衡准方法,应用自编的衡准软件进行样船计算,分析了当前衡准的适用性。其次,开展了内倾船型在随浪和尾斜浪中的骑浪/横甩试验,试验中获得了四种与骑浪/横甩相关的运动特性:周期运动、稳定骑浪、横甩和横甩导致的倾覆,而且在某波浪条件下观察到船舶连续发生三次横甩的现象。最后,将内倾船型的骑浪/横甩薄弱性衡准计算结果与试验结果进行对比,验证了衡准方法对于内倾船型的适用性。     

基于二维半理论的船舶水动压力预报方法研究

二维半理论在单体和多体高速排水式船的耐波性预报中具有很好的数值预报精度。文中在二维半理论稳定求解高速船水动力和运动响应的基础之上,采用数值差分方法对高速船水动压力进行了计算,针对一条SL-7集装箱船进行了水动压力的数值预报,结果同模型试验结果进行了比较,表明文中提出的方法能够较好地预报高速船舶的线性脉动水动压力。     

Nonlinear analysis of parametric rolling in longitudinal and quartering seas with realistic modeling of roll-restoring moment

Parametric rolling of a containership in longitudinal and quartering seas is examined by applying nonlinear dynamics to a 1DOF mathematical model with realistic modeling of the wave effect on roll-restoring moment. In our previous work, we confirmed that a mathematical model with a roll-restoring moment in waves calculated with the Froude–Krylov assumption could considerably overestimate the danger of capsizing associated with parametric rolling. Therefore, in the present work, all numerical calculations based on nonlinear analysis were carried out with the direct aid of a measured roll-restoring moment in waves. For this purpose, captive model experiments were conducted for various sets of wavelengths in longitudinal seas. This experiment demonstrates that the Froude–Krylov prediction could not explain the wavelength effect on restoring moment as the wave-steepness effect. Using the numerical model with the aid of this measured roll-restoring moment, the Poincaré mapping technique was applied to identify bifurcation structures of roll motions not only in longitudinal seas, but also in quartering seas. As a result, it was confirmed that capsizing associated with parametric rolling is more likely to occur in following seas than in quartering seas. However, period-doubling and chaos appeared in quartering seas. Finally, an averaging method assuming a period-2 orbit was applied to the same model with the same conditions as the Poincaré map. Reasonably good agreement was obtained between the numerical results with a Poincaré map and those with the averaging method in longitudinal seas, but the averaging method has limited capability in quartering seas.     

Melnikov integral formula for beam sea roll motion utilizing a non-Hamiltonian exact heteroclinic orbit: analytic extension and numerical validation

In the research field of nonlinear dynamical system theory, it is well known that a homoclinic/heteroclinic point leads to unpredictable motions, such as chaos. Melnikov’s method enables us to judge whether the system has a homoclinic/heteroclinic orbit. Therefore, in order to assess a vessel's safety with respect to capsizing, Melnikov’s method has been applied for investigations of the chaos that appears in beam sea rolling. This is because chaos is closely related to capsizing incidents. In a previous paper (Maki et al. in J Mar Sci Technol 15:102–106, 2010), a formula to predict the capsizing boundary by applying Melnikov’s method to analytically obtain the non-Hamiltonian heteroclinic orbit was proposed. However, in that paper, only limited numerical investigation was carried out. Therefore, further comparative research between the analytical and numerical results is conducted, with the result being that the formula is validated.     

Validation of earthquake analysis methodology of a suction-caisson foundation-structure through model testing

Suction caissons are one of the most widely used foundation solutions for subsea structures and wind farms. Seismic response of subsea structures is however seldom documented properly, often just treated as a foundation capacity issue applying a quasi-static acceleration and not considering the inertial interaction between the structure and the soil. The more relevant tasks to document are the motions of the unit and the response of the externally connected flowlines and equipment/systems on the unit.Based on a case study located in the Shah Deniz field in the Caspian Sea, model centrifuge tests and numerical modelling were carried out to validate the global response of a 4-caisson supported manifold structure subject to seismic motions in soft clay. The centrifuge tests were carried out at 58 g at the centre for geotechnical modelling at UC Davis. To simulate the soil-structure interaction, a series of non-linear springs defined by kinematic hardening models were used in analyses with the ABAQUS software. This development includes the algorithms for determining the required model parameters. A very good agreement between recorded response from the centrifuge test and calculated response from the FE-analyses was achieved.The development and validation of the soil model presented in this paper is an improvement in design methodology for caisson foundations subjected to earthquake loading. The non-linear soil springs are well suited to incorporate in more detailed structural analyses where an accurate representation of the foundation response is required. The paper also briefly describes how the subsequent earthquake design analyses were performed for the Shah Deniz manifold structures making use of the validated soil spring model and the added value it gave to the project.     

Broaching prediction of a wave-piercing tumblehome vessel with twin screws and twin rudders

The new intact stability criteria which are under development at the International Maritime Organization (IMO) are required to cover a broaching phenomenon, well known as a great threat to high-speed vessels which can lead to capsizing. Some reports exist which demonstrate that their numerical models can predict a highly nonlinear phenomenon of broaching. However, additional validation studies are needed for unconventional vessels, in addition to conventional ones, to develop direct stability assessment methods for the new intact stability criteria. In this research, we selected as the subject ship a wave-piercing tumblehome vessel with twin screws and twin rudders, a design expected to be one of a new generation of high-speed monohull ships. Firstly, a series of captive model tests were conducted to measure the resistance, the manoeuvring forces, the wave-exciting forces, the heel-induced hydrodynamic forces, and the roll restoring variation for the unconventional tumblehome vessel. Secondly, the existing mathematical model which had been developed for broaching prediction of conventional vessels with a single propeller and a single rudder was extended to unconventional vessels with twin propellers and twin rudders. Finally, comparisons between numerical simulations and the existing free running model experiments were conducted. As a result, it was demonstrated that fair quantitative prediction of broaching is realised when the rudder force variation, the roll restoring variation and the heel-induced hydrodynamic force for large heel angles are taken into account.     

On the time dependence of survivability of ROPAX ships

The time dependence of survivability of ROPAX vessels, when sustaining side collision damage in waves, is investigated herein by use of numerical simulations of ship motion and flooding. Conducted research confirms that ROPAX ships characteristically capsize fast, when sustaining damage leading to capsizing. A probabilistic analysis of the survive time after collision damage reveals that even for the most generic damage conditions assumed, the survival time in the case of capsizing remains short, which is characteristic of this type of ship design, disposing the typically large undivided deck to be subject to flooding in higher waves. In a case study, the unconditional survivability in waves, corresponding to survival s-factor of SOLAS regulations, is alternatively assessed with numerical simulations. The estimated survivability proves to be time independent in terms of practical implications. Observed deviations between current SOLAS formulation and simulations, suggest the employment of comprehensive simulation methods when more reliable estimations and assessments of survivability are required.     

Importance of several nonlinear factors on broaching prediction

In order to realize a more quantitative prediction of broaching and capsizing in following and quartering seas, existing mathematical modelling techniques should be upgraded. Therefore, it is necessary to systematically examine all factors relevant to capsizing in following and quartering seas. To this end, we first attempted to examine the prediction accuracy of wave-induced forces by comparing calculations with captive model experiments. As a result, we found that a wave-induced surge force has a certain nonlinearitiy with respect to wave steepness. The nonlinearity of sway–roll coupling with respect to sway velocity was also found, and our numerical result with these nonlinearities improves the prediction accuracy of the critical ship speed of capsizing in following and quartering seas. The importance of the wave effect on propeller thrust was also examined. We found that this effect is not negligibly small and could improve capsizing predictions in heavy following and quartering seas. Finally, we attempted to investigate the importance of nonlinear heel-induced hydrodynamic forces on numerical predictions of capsizing due to broaching. Here, we propose a new procedure for captive model experiments to obtain hydrodynamic forces with various heel angles up to 90°, and data on heel-induced hydrodynamic forces with respect to heel angle in calm water are provided. We then compare the numerical simulations with the nonlinear heel-induced hydrodynamic forces and without them. These time series comparisons show that the effect of nonlinear heel-induced hydrodynamic forces in calm water is not negligibly small for the case of ship capsizing due to broaching.     

随机横浪中甲板上浪船舶的倾覆研究

应用相空间转移率,定量研究了随机海浪中甲板上浪船舶的倾覆,给出了甲板上浪对船舶抗倾覆能力的影响.综合考虑非线性阻尼、非线性恢复力矩和随机横浪激励,建立了无甲板上浪和有甲板上浪时船舶随机非线性横摇运动的一般方程.以一艘倾覆的拖网船为例,分别求解了无甲板上浪和有甲板上浪时,不同海况激励下船舶横摇的相对相空间转移率.以相空间转移率作为船舶稳性损失的度量,定量比较了两种情况下船舶的抗倾覆能力.研究表明,甲板上浪后,船舶在较低的海况下会产生较大的相对相空间转移率,甲板上浪严重降低船舶的抗倾覆能力,从理论上进一步揭示了甲板上浪船舶的倾覆机理.     

Time domain simulations of the wave-induced motions of ships in maneuvering condition

The wave-induced motions of ships in maneuvering condition are numerically studied based on potential theory. The total disturbance potential is decomposed into a basic part and a perturbation part. The basic flow is evaluated based on the double-body model with a trailing vortex sheet. The perturbation flow is solved by using a time domain Rankine panel method to determine the hydrodynamic forces, and the wave-induced ship motions are then evaluated by an Adam–Moulton scheme. The solving process of the wave-induced motion is integrated with the maneuvering prediction by using a two–time scale model. Numerical tests are firstly carried out for a Series 60 ship, and the numerical results are compared with the experimental data to validate the numerical method for the basic flow. Then the wave-induced motions of the S-175 container ship in straight course and in turning condition are simulated; the numerical results are compared with the ITTC data and the experimental data, which show fairly good agreements.     

Prediction of capsizing probability for a ship with trapped water on deck

The authors have already examined a method for evaluating the capsizing probability of a ship in the dead ship condition based on a piecewise linear approximation of the restoring arm. Here, this method is extended to ships with trapped water on deck. This is because the stability of ships having a relatively high bulwark, such as fishing vessels, could substantially deteriorate due to trapped water on deck. First, the mean amount of water trapped on deck was estimated as a function of the significant wave height and the mean wave period using a model experiment in irregular beam seas. Second, the restoring arm curve with trapped water on deck was calculated hydrostatically and then approximated with a piecewise linear curve. Third, the roll angle was estimated using a nonlinear and uncoupled equation of absolute roll angle under stochastic wave and wind exciting moments. The short-term and long-term capsizing probabilities were calculated for a fishing vessel operating off Kyushu. Numerical results quantitatively demonstrated that the effect on capsizing probability of trapped water on deck cannot be ignored when accurately evaluating the stability of fishing vessels.     

Broaching prediction in the light of an enhanced mathematical model,with higher-order terms taken into account

 We have attempted to develop a more consistent mathematical model for capsizing associated with surf-riding in following and quartering waves by taking most of the second-order terms of the waves into account. The wave effects on the hull maneuvring coefficients were estimated, together with the hydrodynamic lift due to wave fluid velocity, and the change in added mass due to relative wave elevations. The wave effects on the hydrodynamic derivatives with respect to rudder angles were estimated by using the Mathematical Modelling Group (MMG) model. Then captive ship model experiments were conducted, and these showed reasonably good agreements between the experiments and the calculations for the wave effects on the hull and the rudder maneuvring forces. It was also found that the wave effects on restoring moments are much smaller than the Froude–Krylov prediction, and the minimum restoring arm appears on a wave downslope but not on a wave crest amidship. Thus, an experimental formula of the lift force due to the heel angle of the ship is provided for numerical modelling. Numerical simulations were then carried out with these second-order terms of waves, and the results were compared with the results of free-running model experiments. An improved prediction accuracy for ship motions in following and quartering seas was demonstrated. Although the boundaries of the ship motion modes were also obtained with both the original model and the present one, the second-order terms for waves are not so crucial for predicting the capsizing boundaries themselves. Received: June 20, 2002 / Accepted: October 10, 2002 Acknowledgments. This research was supported by a Grant-in-Aid for Scientific Research of the Ministry of Education, Culture, Sports, Science and Technology of Japan (No. 13555270). The authors thank Prof. N. Rakhmanin of the Krylov Ship Research Institute for providing the Russian literature, as well as Mr. H. Murata of NHK (Japan Broadcasting Corporation) for translating it into Japanese. Address correspondence to: N. Umeda (e-mail: umeda@naoe.eng.osaka-u.ac.jp)     

Experimental study of freak wave impacts on a tension-leg platform

This study investigates the freak wave impinging on a tension-leg platform through wave flume experiments. The freak waves are generated using the focused wave theory. By adjusting the wave focusing location, different incident wave scenarios at the structure location are produced. Simultaneous measurements of wave shape evolutions upon impingement, wave impact pressures on the platform deck, platform motions and tether forces are carried out for synchronized analyses of the wave kinematics/dynamics and structural responses. The variation of these parameters with the incident wave profile is studied. It is found that although applying less intensive local impact pressures as compared to the highly-breaking freak wave, the slightly-breaking or non-breaking freak wave imposes the same level of adverse effect on the platform's global stability in terms of motions and tether forces. In addition, the high-crest freak wave causes violent motions of the floating platform, which are likely to induce snap loads of large amplitude and high occurrence frequency in tethers. The published results would provide useful benchmarks for validating numerical and analytical models.     

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。     

Characteristics of low-frequency motions of ships moored inside ports and harbors on the basis of field observations

In order to understand characteristics of low-frequency motions of ships moored inside ports and harbors, analysis on actual cargo handling logbook of stevedoring services company, including events of interruption of cargo handling, and countermeasure for ship mooring problems are investigated by field observations at two ports and numerical simulation on moored ship motions. First model port concerns with interruption of cargo handling due to the low-frequency motions. Second model port relates to a resonant effect of long-period waves or harbor oscillations, and its countermeasure by mooring system. From the investigation, it is confirmed that the low-frequency motions of ships are induced by a resonance between surge motions and long-period waves or harbor oscillations and an asymmetry in the mooring system, and affect safe ship mooring and operation efficiency of cargo handling in ports and harbors significantly.     

风帆助航船非线性横摇倾覆概率研究

风帆助航技术为船舶利用可再生能源提供了途径,但随着横摇的幅度加大,导致船舶倾覆的概率也增大。文章采用数值分析的方法对风帆助航船舶的非线性横摇方程进行分析求解,对有风帆助航与无风帆助航船在风浪作用下产生倾覆的概率作了比较,为采用风帆助航技术的远洋船舶在符合初稳性和气象衡准稳性条件下的横摇倾覆防范提供研究思路。     

基于CFD的内河船深浅水中操纵性预报

由于岸壁效应和浅水效应,内河船舶在限制水域作操纵运动时通常受到比在开阔水域中更大的水动力.这些水动力对船舶操纵性具有不利影响,有可能导致船舶碰撞或触底等海上事故.因此,为了在船舶设计阶段预报其操纵性能,考虑浅水效应和岸壁效应以准确计算内河船舶操纵运动水动力非常重要.本文基于CFD方法,通过对粘性绕流进行数值模拟,对长江中营运的三艘内河船舶的操纵运动水动力进行计算.首先,为了验证数值方法的可靠性,对标模KVLCC2纯横荡和纯首摇试验的水动力进行计算,并将计算结果与现有的试验数据进行对比.然后,对三艘内河船舶在不同水深下的静舵试验、纯横荡和纯首摇试验进行数值模拟,计算得到水动力及相应的线性水动力导数.最后,基于计算得到的水动力导数,获得Nomoto模型中的操纵性参数,对比分析三艘内河船舶在深浅水中的操纵性能.结果表明,本文方法可以揭示不同水深下三艘内河船舶的操纵性变化趋势.该方法可为船舶设计阶段内河船舶深浅水中的操纵性预报提供一种实用的工具.     

船用大功率柴油机新型燃油系统的数值仿真

本文数值仿真了一种适合劣质燃油（重油）的循环式燃油系统（一泵二嘴四针阀），提出了处理喷油器和燃油分配器边界条件的准维模型以及用于喷油泵边界条件的新模型。该燃油系统已应用于MANB&WL60MC／MCE等大功率柴油机。与常规的数值仿真相比，求解管内流动的二队双曲型偏微分方程的边界条件发生了很大变化，这是燃油系统研究的难点和关键。预测结果与试验结果较为一致。本研究还进行了不同功率点变型方案的模拟研究和结构参数的优化设计分析，以满足不同船舶的需要。