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.     

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.     

Nonlinear dynamics of ship capsizing due to broaching in following and quartering seas

To provide a theoretical methodology to predict the critical condition for capsizing due to broaching, a nonlinear dynamical system approach was applied to the surge–sway–yaw–roll motion of a ship running with an autopilot in following and quartering seas. Fixed points of a mathematical model for the ship motion and unstable manifolds of the fixed point near the wave crest were systematically investigated. As a result, the existence of heteroclinic bifurcation was identified. With numerical experiments, it was confirmed that this heteroclinic bifurcation reasonably well represents the critical condition for capsizing due to broaching. Thus the nonlinear dynamical approach can be substituted for tedious numerical experiments. Received for publication on Nov. 20, 1998; accepted on March 16, 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     

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)     

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.     

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.     

Prediction methods for the surf-riding threshold and the wave-blocking threshold based on Melnikov’s method

A ship operating in following and/or quartering seas may be susceptible to broaching-to preceded by the surf-riding phenomenon. Therefore, for the safety assessment of fast vessels such as destroyers and patrol craft, the estimation of the surf-riding condition is important. As shown by previous research, there are two boundaries for ship motion in following and quartering seas. These are the surf-riding threshold and wave-blocking threshold. In this study, the theoretical methods to estimate both boundaries are obtained by making use of Melnikov’s method. In order to validate the formulae, free-running model experiments are conducted in the towing tank. Comparisons between the results obtained from calculations and experiments show good agreement. It is concluded that the formulae based on Melnikov’s method could be applicable to the safety assessment of surface ships.     

尾斜浪中船舶复原力计算

本文应用摄动法提出了一种尾斜浪中复原力计算的新方法．对四艘处于各种船一波相对位置的船舶进行了大量的计算，其中包括波高、波长对复原力的影响。最后，用一艘船模作了尾斜浪中半约束船模约稳性试验，证实了理论算法的正确性。     

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。     

随机横浪中船舶倾覆过程模拟与安全域计算

研讨了随机海浪中船舶非线性随机横摇运动倾覆过程和安全域问题.考虑非线性阻尼、非线性复原力矩和随机波浪,建立了随机横浪中船舶运动的随机非线性微分方程.考虑两参数海浪谱和不同的有义波高,计算随机波浪力矩,采用简谐加速度数值计算方法求解随机微分方程,进行了随机倾覆过程的数值模拟.考虑船舶运动的瞬时状态,发展了胞映射方法计算随机非线性横摇运动安全域的方法,并编制了计算机程序.模拟了一条渔船不同有义波高作用下横摇倾覆过程,考虑不同的初始条件及随机波浪参数,在初始值平面上采用胞映射法构造了渔船航行的安全域.波高较小时,安全域是一个连续的区域;随着有义波高增大,安全域面积减小并且不再连续,倾覆域和安全域相互包围.计算结果表明,船舶运动的瞬时状态对安全域具有重要影响,而且随机海浪中安全域具有随机特性.     

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.     

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.     

三体船横向结构波浪设计载荷试验与规范比较研究

三体船连接桥结构波浪设计载荷的确定对结构设计中关注的横向强度问题来说是非常重要的.为了研究一艘三体船连接桥横向波浪载荷,进行了该三体船的水池模型试验,包含不同浪向下规则波与不规则波试验.试验对连接桥遭受的分离弯矩Msp、分离剪力Qsp和横向扭矩Mtt进行了测量,分析了其传递函数和统计的特性.根据对这些连接桥横向波浪载荷在试验值、推断值与规范计算值之间的比较分析表明:劳氏规范关于这些横向波浪载荷的计算值可能对应于规则波双幅波高6.0m;对于不同的横向波浪载荷来说,保证率为99%的设计载荷推断值对横向扭矩Mtt来说要大于规范计算值,而分离弯矩Msp和分离剪力Qsp的推断值对应的规范计算值则相当,这意味着没计人员在用劳氏规范进行校核时,横向扭矩Mtt的规范计算值是偏向于冒险的,应给予特别关注.     

船舶参数激励非线性横摇运动方程

讨论了船舶在海浪上运动时参数激励产生的机理，建立了船舶参数激励和波浪激励非线性横摇运动方程。本文工作为研究倾覆机理奠定了基础。     

国外船舶破损稳性理论分析

船舶破损后的稳性问题是长期困扰造船界的难题,它涉及随机海况下破损船舶的摇摆、进水和倾覆等多方面的复杂技术问题。简要叙述了国外船舶破损进水后的稳性理论计算研究状况,介绍了国际上在破损船舶动力学模型、舱内进水与船体的相互作用、破损口处的进流与出流模拟等3方面的研究进展。研究表明,三自由度耦合的数学模型在处理舷侧破损问题方面很有效,而六自由度非线性数学模型是未来船舶破损稳性计算的发展趋势,而且必须将船体与进水当作相互高度耦合的动力系统,采用水动力学进水模型进行处理。今后,还需采用模型试验深入观测波浪中船舶破损后的物理现象,以了解破损稳性机理。     

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.     

穿浪双体船总体设计载荷研究

为了比较分析不同高速船规范的适用性,根据DNV、ABS、CCS和LR规范中关于高速双体船波浪载荷的评估方法,分别对一高速穿浪双体船进行了总体波浪设计载荷的评估。同时对该穿浪双体船进行了水池模型试验,包含规则波与不规则波的试验。试验对该双体船的纵垂向弯矩、横垂向弯矩、横向扭矩和纵摇有关扭矩进行了测量,分析了其传递函数和统计特性。根据对纵垂向弯矩、横垂向弯矩、横向扭矩和纵摇有关扭矩在规范与试验之间的比较分析表明,DNV规范中关于该穿浪双体船总体波浪设计载荷的评估与模型试验值最接近,CCS规范次之,ABS和LR规范中关于该穿浪双体船的总体波浪设计载荷的评估值较试验值大很多,尤其是横向波浪设计载荷的评估。通过对规范计算的总体波浪载荷与模型试验结果及其推断值的比较分析,进一步明确了现行规范对该双体船波浪设计载荷评估的适用性:采用DNV和CCS规范对该双体船进行结构设计是合理的;采用ABS和LR规范将偏于安全和保守。     

自卸砂船稳性分析及其倾覆后应急施救方案

自卸砂船船体结构具有一定特殊性,在稳性方面富余量较小.而运输过程中超载现象普遍且程度较严重,使该种船舶在航行过程中相对而言更容易发生倾覆沉没,对人命和财产造成极大损害.以一起事故为实例,对该类船舶的稳性进行分析;并结合船舶分舱和船舶静力学原理,提出了自卸砂船倾覆翻扣事故发生之后的应急救人措施建议方案.     

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.