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     

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     

Numerical prediction of the surf-riding threshold of a ship in stern quartering waves in the light of bifurcation theory

In order to develop design and operational criteria to be used at the International Maritime Organization (IMO), critical conditions for broaching are explored in the light of bifurcation analysis. Since surf-riding, which is a prerequisite to broaching, can be regarded as a heteroclinic bifurcation, one of global bifurcations, of a surge-sway-yaw-roll model in quartering waves, the relevant bifurcation condition is formulated with a rigorous mathematical background. Then an efficient numerical solution procedure suitable for tracing the surf-riding threshold hypersurface is presented with successful examples. This deals with all state and control variables in parallel, and excludes backward time integration and an orthogonal condition in the iteration process. The bifurcation conditions identified were compared with the results from a direct numerical simulation in the time domain. As a result, it was confirmed that the heteroclinic bifurcation provides a boundary between motions periodically overtaken by waves and nonperiodic motions such as surf-riding and broaching.     

随机风浪中舰船横摇倾覆概率分析

以路径积分法为基础,采用Gauss-Legendre公式探讨了随机风浪作用下舰船的运动及其倾覆概率计算。考虑阻尼力矩、复原力矩的非线性及风浪的随机性,建立了随机风浪中舰船运动的非线性微分方程,应用路径积分法给出白噪声随机扰动和定常风倾力矩作用时横摇角概率密度函数随时间的演变,按照现有的倾覆准则给出舰船倾覆概率的表达式。通过算例,验证了路径积分法的准确性,分析了各个参数对横摇角概率密度的影响,计算得出了不同风速、不同航速下的倾覆概率,以及倾覆概率随时间的变化。研究表明,此方法简便可行,并能在数量上预报舰船在随机风浪下的倾覆概率。     

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.     

Surf-riding and oscillations of a ship in quartering waves

The behavior of a ship encountering large regular waves from astern at low frequency is the object of investigation, with a parallel study of surf-riding and periodic motion paterns. First, the theoretical analysis of surf-riding is extended from purely following to quartering seas. Steady-state continuation is used to identify all possible surf-riding states for one wavelength. Examination of stability indicates the existence of stable and unstable states and predicts a new type of oscillatory surf-riding. Global analysis is also applied to determine the areas of state space which lead to surf-riding for a given ship and wave conditions. In the case of overtaking waves, the large rudder-yaw-surge oscillations of the vessel are examined, showing the mechanism and conditions responsible for loss of controllability at certain vessel headings.List of symbols c wave celerity (m/s) - C(p) roll damping moment (Ntm) - g acceleration of gravity (m/s²) - GM metacentric height (m) - H wave height (m) - I _x ,I _z roll and yaw ship moments of inertia (kg m²) - k wave number (m^–1) - K _H ,K _W ,K _R hull reaction, wave, rudder, and propeller - K _p forces in the roll direction (Ntm) - m ship mass (kg) - n propeller rate of rotation (rpm) - N _H ,N _W ,N _R hull reaction, wave, rudder, and propeller - N _P moments in the yaw direction (Ntm) - p roll angular velocity (rad/s) - r rate-of-turn (rad/s) - R(,x) restoring moment (Ntm) - Res(u) ship resistance (Nt) - t time (s) - u surge velocity (m/s) - U vessel speed (m/s) - v sway velocity (m/s) - W ship weight (Nt) - x longitudinal position of the ship measured from the wave system (m) - x _G ,z _G longitudinal and vertical center of gravity (m) - x _S longitudinal position of a ship section (S), in the ship-fixed system (m) - X _H ,X _W ,X _R hull reaction, wave, rudder, and propeller - X _P forces in the surge direction (Nt) - y transverse position of the ship, measured from the wave system (m) - Y _H ,Y _W ,Y _R hull reaction, wave, rudder, and propeller - Y _p forces in the sway direction (Nt) - z _Y vertical position of the point of action of the lateral reaction force during turn (m) - z _W vertical position of the point of action of the lateral wave force (m) Greek symbols angle of drift (rad) - rudder angle (rad) - wavelength (m) - position of the ship in the earth-fixed system (m) - water density (kg/m³) - angle of heel (rad) - heading angle (rad) - _e frequency of encounter (rad/s) Hydrodynamic coefficients K roll added mass - N _v ,N _r yaw acceleration coefficients - N _v N _r N _rr N _rrv ,N _vvr yaw velocity coefficients K. Spyrou: Ship behavior in quartering waves - X _u surge acceleration coefficient - X _u X _vr surge velocity coefficients - Y _v ,Y _r sway acceleration coefficients - Y _v ,Y _r ,Y _vv ,Y _rr ,Y _vr sway velocity coefficients European Union-nominated Fellow of the Science and Technology Agency of Japan, Visiting Researcher, National Research Institute of Fisheries Engineering of Japan     

URANS analysis of a broaching event in irregular quartering seas

Ship motions in a high sea state can have adverse effects on controllability, cause loss of stability, and ultimately compromise the survivability of the ship. In a broaching event, the ship losses control, naturally turning broadside to the waves, causing a dangerous situation and possibly capsizing. Classical approaches to study broaching rely on costly experimental programs and/or time-domain potential or system-based simulation codes. In this paper the ability of Reynolds averaged Navier–Stokes (RANS) to simulate a broaching event in irregular waves is demonstrated, and the extensive information available is used to analyze the broaching process. The demonstration nature of this paper is stressed, as opposed to a validated study. Unsteady RANS (URANS) provides a model based on first principles to capture phenomena such as coupling between sway, yaw, and roll, roll damping, effects of complex waves on righting arm, rudders partially out of the water, etc. The computational fluid dynamics (CFD) method uses a single-phase level-set approach to model the free surface, and dynamic overset grids to resolve large-amplitude motions. Before evaluating irregular seas two regular wave cases are demonstrated, one causing broaching and one causing stable surf riding. A sea state 8 is imposed following an irregular Bretschneider spectrum, and an autopilot was implemented to control heading and speed with two different gains for the heading controller. It is concluded that the autopilot causes the ship to be in an adverse dynamic condition at the beginning of the broaching process, and thus is partially responsible for the occurrence of the broaching event.     

随浪中纯稳性丧失直接评估方法研究

  目的  由纯稳性丧失引发的船舶倾覆是国际海事组织（IMO）针对船舶第二代完整稳性的重点研究问题之一。  方法  基于黏性流理论建立CFD数值模拟方法,结合动态重叠网格技术与操纵运动反馈控制模块,对带螺旋桨、带舵的自航船舶在艉斜浪下保持航向操纵运动进行数值模拟,预报纯稳性丧失下船舶的六自由度运动,并对船舶的失稳运动及倾覆特性进行直接评估。  结果  结果显示,船舶在持续的稳性丧失情况下会产生大幅度的横摇运动,最终会因横摇角过大而导致倾覆现象的发生;在稳性丧失的状态下,船舶艏摇角显著增大,说明船舶在该状态下依靠操舵已无法有效控制船舶航向,会导致较为明显的横甩现象。  结论  所做研究表明,采用CFD方法模拟船舶失稳运动与倾覆现象准确性较高,研究成果对于研究船舶第二代完整稳性衡准具有一定的参考意义,可为纯稳性丧失的直接稳性评估方法研究提供支撑。     

Dynamic stability in following seas: predictive and experimental approaches

This article presents work based on the development of a performance-based stability assessment method. It describes a numerical method used to determine the survival limit for a dynamic intact stability assessment procedure. The numerical method utilises a time-domain vessel motion program to assess the limit for a range of vertical centres of gravity (KG). The appropriateness of the numerical predictions was examined through comparison with model experiment results. Free-running model tests were conducted in regular following waves at discrete KGs. A comparison between the survival limits determined through the numerical and experimental methods is presented. The current International Maritime Organisation (IMO) stability criteria are also evaluated against the numerical and experimental dynamic performance-based stability assessment methods.     

水下爆炸及随机外力下破损舰船的倾覆概率分析

探讨了水下爆炸载荷和随机风浪联合作用下破损舰船的运动及其倾覆概率的计算.将爆炸载荷作用及平均风扰动力矩处理为定常横倾力矩,建立了爆炸载荷和随机风浪中舰船运动的非线性微分方程.结合扩维技巧,将横摇方程转化为五维Ito随机微分方程,应用Gauss-Legendre路径积分法给出随机扰动为白噪声时横摇角度的概率密度函数随时间的演变,按照现有的倾覆准则给出预报一定装药量下舰船倾覆概率的表达式.通过算例,计算了破损舰船不同装药量下不同时刻的倾覆概率,分析不同装药量对倾覆概率的影响.研究表明,此方法简便可行,并能在数量上预报破损舰船在水下爆炸及随机风浪下的倾覆概率,为进一步研究舰船倾覆及稳性横准提供有益的参考.     

船舶在随浪中的运动与横甩预报

本文在水平的随船坐标系下,建立了船舶在波浪中的六自由度操纵运动方程。进行船舶在波浪中的回转运动和Z形操纵运动模型试验,验证数学模型的正确性。通过不同波浪和航速条件下船舶Z形操纵运动的模拟计算,预报船舶在随浪中的横甩,预报结果与试验结果比较一致。     

Parametrical studies of a new numerical model for controlled ship motions in extreme astern seas

Parametrical studies based on numerical simulations were carried out for very steep regular waves to assess possible improvements in the state-of-the art numerical modelling of the control and capsizing behaviour of ships in following and quartering seas. A nonlinear 6-DOF numerical model has been developed with the inclusion of frequency-dependent terms, the so called memory effects, and a flexible axis system that allows straightforward combination of seakeeping and manoeuvring models while accounting for extreme motions. The previously undertaken validation analyses using extensive model test data provided qualitatively good agreement, whereas the comparison with numerical models without coupling of the vertical motions and frequency-dependent hydrodynamic terms embodied in radiation forces identified improvements in the accuracy. However, to broaden the assessment of the numerical model, further parametrical numerical analyses were carried out using two ships, which had previously been tested in the validation analyses, for various operational and environmental conditions. These parameters were changed in accordance with the recommendations from international organisations and experience from model tests to realise and avoid dangerous conditions that often result in capsizing, such as broaching associated with surf riding and low-cycle resonance. As a result of the parametric analysis, we discuss the sensitivity of the improvements in the numerical model for various critical operational and design parameters and its possible use to provide a link between the ship's behavior and these parameters.     

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.     

A risk-based first-principles approach to assessing green seas loading on the hatch covers of bulk carriers in extreme weather conditions

This paper aims to present and explain the work undertaken at the SSRC on the Safety of Bulk Carriers in extreme weather conditions over the past 3 years, to draw conclusions deriving there from, concerning key influencing design, operational and environmental parameters and to offer recommendations regarding the rule development process and on the way forward considering research, development and implementation to ship design and operation with the view to improving the safety of these ships cost-effectively. In severe storms, hatch covers of low freeboard vessels such as bulk carriers are the first-line of protection against flooding. Present methods of hatch covers design are still empirical because impact loads due to green seas and structural behaviour due to this type of loads have not been examined, hence not known accurately. The loading due to green seas is implicitly non-linear and, as model test results demonstrated, bulk carriers in extreme conditions are exposed to significant loads, which in some cases exceed current design standards. Since the consequences of hatch cover failure are potentially catastrophic, the risk of this happening should be quantified in probabilistic terms as required by modern safety standards. To this end, the paper aims to propose and implement a methodology for estimating probabilities of deck wetness and impact loads due to green seas as a function of key design and operational parameters.     

Parametric rolling prediction in irregular seas using combination of deterministic ship dynamics and probabilistic wave theory

In recent years there have been reports of serious accidents of parametric rolling for modern container ships and car carriers. For avoiding such accidents, a prediction method of parametric rolling in irregular seas is required. Since parametric rolling is practically non-ergodic, repetitions of numerical simulations or experiments could be not feasible to ascertain the behaviour. Therefore, in this paper, a method combining a stochastic approach with a deterministic approach in order to estimate the probabilistic index without such simple repetitions is developed. The ship's response in regular seas is estimated by solving an averaged system of the original 1-DoF roll model, and random waves necessary for occurrence of parametric rolling is achieved by using Longuet-Higgins’s or Kimura’s wave group theory. As a result, a fast and robust computation method of the probabilistic index is established. Finally, it is concluded that the proposed method is considered to be one of the useful tools for discussing the new IMO Intact Stability Code.     

Effect of freeboard and metacentric height on capsizing probability of purse seiners in irregular beam seas

The probability of capsize of purse seiners in irregular beam seas and the effect of freeboard height and metacentric height on trapped water on the deck was investigated. The aim was to quantify a safety level that can be achieved by direct stability assessment for this type of fishing vessel. The amount of trapped water on deck was numerically estimated using a hydraulic flow assumption. The long-term capsizing probabilities were estimated using a piecewise linear approach together with wave statistics from major Japanese fishing areas. The estimated safety level of capsizing probability was compared with that obtained by the IMO weather criterion and by the water-on-deck criterion of the IMO Torremolinos Convention. Numerical results for four typical Japanese purse seiners indicated that the effect of freeboard, on the amount of trapped water on deck, is more important than that of the metacentric height. Besides the metacentric height and the freeboard, it was shown that the danger of capsizing is a function of the rise of floor. The safety level obtained by the capsizing probability approach is generally higher than that based on the IMO weather criterion. However, the water-on-deck criterion provides a higher safety level than the capsizing probability approach for ships with a low rise of floor.     

半约束模型试验--一种验证随浪和斜浪中波浪力计算的手段

本文采用半约束模型试验技术，对一条高速船在规则波中随浪和斜浪工况进行了流体动力系列试验，以探讨航运的安全性，验证作用于船体上波浪力的估算方法。对每次试验，以波动方程的形式采用数值估算方法确定环绕船模的波浪运动的时间历程。并用同样的方法从测量数据中提取垂荡和纵摇与模型测量运动，一阶波导纵荡、横荡作用力和首摇力矩。因此合理比较理论计算的波浪力与力矩的时间历程成为可能。这表明SSPA海事动力学的研究所(MDL)模型试验设施可以提供高质量的测量，与所述计算方法结合起来可用来验证理论计算和建立半经验方法。     

高速双体船斜浪中运动响应及连接桥波浪载荷预报

应用二维时域格林函数法对二维半定解问题进行了求解,应用发展的二维半理论和程序对WP60高速穿浪双体船在斜浪中的垂荡、纵摇、横摇和垂向加速度等运动响应及连接桥结构的波浪载荷进行预报,并把理论计算结果与模型试验结果及其它程序计算结果比较分析,初步验证了文中方法和程序在预报高速双体船运动及载荷性能中的适用性.     

基于船模水池试验的船舶顺浪纯稳性损失计算扩展模式

船舶顺浪航行的纯稳性损失研究,已成为国际航海界和国际海事组织(IMO)关注的课题之一.在Ю.И.涅查耶夫根据28艘渔船和运输船船模水池试验的船舶顺浪纯稳性损失计算方法的基础上,提出了扩展模式,扩大了其适用范围,并给出了大长宽比(船长/船宽)舰艇纯稳性损失的算例,同时实现了该扩展模式的程序化,生成了实用化的软件.最后通过与CFD试验方法和一般理论计算法所得结果的对比,验证了该扩展模式计算结果的可信度.     

Experimental and numerical investigation of fatigue damage due to wave-induced vibrations in a containership in head seas

Fatigue cracks have been known to occur in welded ships for several decades. For large ocean-going ships wave-induced vibrations can, depending on trade and design, cause up to 50% of the fatigue damage. The vibrations may be due to springing and whipping effects. In this paper, we address the fatigue damage caused by wave-induced vibrations in a containership of newer design trading in the North Atlantic. The fatigue damage was obtained both experimentally and numerically. The experimental results were found from tests performed with a flexible model of the ship, while the numerical predictions were done using nonlinear hydroelastic strip theory. The measurements showed that the wave-induced vibrations contributed approximately 40% of the total fatigue damage. The numerical method predicted the wave frequency damage well, but was found to overestimate the total fatigue damage by 50%. This was mainly due to an overprediction of the wave-induced vibrations. The discrepancy is partly related to three-dimensional (3D) effects which are not included in the two-dimensional (2D) slamming calculation, and partly to an overprediction of the springing contribution. Moreover, the numerical method does not account for the steady wave due to forward speed. By using a simplified approach we show that high-frequency damage can be significantly reduced by including the steady wave for the relevant vessel, implying better agreement with the experimental results.