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.     

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     

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     

Large-amplitude motion responses of a Ro–Ro ship to regular oblique waves in intact and damaged conditions

This article presents a nonlinear time-domain simulation method for the prediction of large-amplitude motions of a Ro–Ro ship in regular oblique waves in an intact and a damaged condition. Numerical computations and model tests have been carried out to investigate the dynamic motion responses of Ro–Ro ship Dextra to various wave amplitudes at three different wave headings. The results of numerical and experimental investigations for stern quartering waves are reviewed. Comparisons between predictions and measurements show good agreement except in the roll-resonant region. Nonlinear effects are significant in horizontal modes of motion, and resonant roll motion, and there is strong coupling between all modes of motion in the roll-resonant region for large-amplitude responses. On the other hand, the time-domain simulation technique suffers from numerical drift in horizontal modes of motion as wave amplitude increases. This is due to nonlinear equations of motion and the lack of a restoring force and moment in horizontal motion. Received: April 30, 2002 / Accepted: August 9, 2002 Acknowledgments. II Programme of the European Community Commission under contract No. BRPR-CT97-0513. Address correspondence to: H.S. Chan (hoi-sang.chan@ncl.ac.uk)     

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     

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     

A unified seakeeping and maneuvering analysis of ships in regular waves

The behavior of a ship in regular waves during maneuvering was studied by using a two-time scale model. The maneuvering analysis was based on Söding’s (Schiffstechnik 1982; 29:3–29) nonlinear slender-body theory generalized to account for heel. Forces and moments due to rudder, propeller, and viscous cross-flow follow from the state-of-the-art procedures. The developed unified theory of seakeeping and maneuvering was verified and validated for calm water by comparing it with experimental and calculated zigzag and circle maneuvers. Linear wave-induced motions and loads were determined by generalizing the Salvesen-Tuck-Faltinsen (Trans SNAME 1970; 78:250–287) strip theory. The mean second-order wave loads in incident regular deep water waves in oblique sea conditions were estimated by the potential flow theories of Faltinsen et al. (Proc 13th Symp Naval Hydrody 1980), Salvesen (Proc Intl Symp Dynam Mar Vehicl Struct Wave 1974), and Loukakis and Sclavounos (J Ship Res 1978; 22:1–19). The considered theories cover the whole range of important wavelengths. Comparisons between the different mean second-order wave load theories and available experimental data were carried out for different ship hull forms when the ship was advancing forward on a straight course. The mentioned methods have been incorporated into the maneuvering model. Their applicability from the perspective of the maneuvering ability of the selected types of ships was investigated in given wave environments. The wave conditions are valid for realistic maneuvering cases in open coastal areas. It was demonstrated that the incident waves may have an important influence on the maneuvering behavior of a ship. The added resistance, mean second-order transverse force, and yaw moment also play important roles.     

Prediction of ship steering capabilities with a fully nonlinear ship motion model. Part 1: Maneuvering in calm water

This paper introduces a new method for the prediction of ship maneuvering capabilities. The new method is added to a nonlinear six-degrees-of-freedom ship motion model named the digital, self-consistent ship experimental laboratory (DiSSEL). Based on the first principles of physics, when the ship is steered, the additional surge and sway forces and the yaw moment from the deflected rudder are computed. The rudder forces and moments are computed using rudder parameters such as the rudder area and the local flow velocity at the rudder, which includes contributions from the ship velocity and the propeller slipstream. The rudder forces and moments are added to the forces and moments on the hull, which are used to predict the motion of the ship in DiSSEL. The resulting motions of the ship influence the inflow into the rudder and thereby influence the force and moment on the rudder at each time step. The roll moment and resulting heel angle on the ship as it maneuvers are also predicted. Calm water turning circle predictions are presented and correlated with model test data for NSWCCD model 5514, a pre-contract DDG-51 hull form. Good correlations are shown for both the turning circle track and the heel angle of the model during the turn. The prediction for a ship maneuvering in incident waves will be presented in Part 2. DiSSEL can be applied for any arbitrary hull geometry. No empirical parameterization is used, except for the influence of the propeller slipstream on the rudder, which is included using a flow acceleration factor.     

A proposal for propulsion performance prediction of a single-propeller twin-rudder ship

The influence of a rudder’s axial force on the prediction of full-scale powering performance of a ship is investigated in this paper. Axial force characteristics of different rudder types were investigated by open water experiments. Viscous scale effects on the rudder’s axial force were investigated by carrying out open water experiments with different sizes of rudder. Experiments were carried out in the towing tank for a model ship fitted with different rudder systems to investigate the influence of rudder’s axial force on full-scale propulsion performance prediction. Based on the experiment results, a new prediction method is proposed for estimating full-scale power that considers scale effect on rudder’s axial force. Good performance of the proposed prediction method is demonstrated by estimating the engine power of a ship installed with a special high lift twin-rudder system from model experiments and comparing it with the values measured on the ship during full-scale experiments.     

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。     

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.     

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。     

船舶在波浪中航行时的安全操纵

船舶在波浪中航行,纯稳性丧失、参数激振和横甩是造成船舶倾覆的主要原因。针对波长与船长、波高与波长、波与船的波舷角三者对船舶稳性的影响进行讨论,揭示了船舶在波浪中航行时的稳性变化规律,提出了应合理地选择船舶的航行姿态、谨慎用舵等操船建议,保证船舶的航行安全。     

Model experiment reproducing an incident of fast ferry

A model scale experiment at a new basin reproduced a phenomenon occurring for a fast ferry; large roll motion and subsequent cargo shift in a quartering sea. Wave generators surrounding the whole periphery of the basin realized a designated directional sea. A carriage system tracked a free-running model ship and a movable weight simulated the cargo shift. Measuring the directional wave field in the basin confirmed the all-around wave generator successfully reproduced the intended wave field that was estimated for the location and the time of the incident. The encounter wave spectrum analyzed using measured data agree well with the theoretically predicted one. The reproduced ship motion, triggered by a small concentrating wave, tells how the ship responded in the successive large quartering waves and the validity of the procedure to reproduce the incident. Repeated measurements of the model ship’s extreme motion confirm a high repeatability of the experiment.     

大开口船波浪载荷长期预报和弯扭强度整船有限元分析

大开口船全船弯扭联合变形与应力的精确计算，必须在整船结构模型上完成。本文以一艘5万吨级大开口船为例，用三维流体动力计算程序进行了波浪随机载荷的长期预报，并在此基础上导出设计波参数组，进而在全船整体结构有限元模型上计算了船体结构在各设计波上的应力分布，并采用嵌入精细舱口角区有限元网络的方法，在整船分析的同时计算出舱口角的应力集中值，获得了船体结构强度的详尽信息。文中阐述了波浪载荷的特点，设计波的确定，浮体完整结构计算的惯性平衡及大开口船的全船计算方法。     

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.     

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.     

Circular motion tests and uncertainty analysis for ship maneuverability

Circular motion test data and uncertainty analysis results of investigations of the hydrodynamic characteristics of ship maneuvering are presented. The model ships used were a container ship and two tankers, and the measured items were the surge and sway forces, yaw moment, propeller thrust, rudder normal and tangential forces, pitch and roll angles, and heave. The test parameters were the oblique angle and yaw rate for the conditions of a hull with a rudder and propeller in which the rudder angle was set to zero and the propeller speed was set to the model self-propulsion conditions. Carriage data showing the accuracy of the towing conditions in the circular motion test are also presented. It was confirmed that the uncertainties in the hydrodynamic forces such as the surge and sway forces, yaw moment, rudder tangential and normal forces, and propeller thrust were fairly small. The reported uncertainty analysis results of the circular motion test data may be beneficial in validating data quality and in discussing reliability for simulation of ship maneuvering performance.     

水动反冲击力及其应用

船艇迎浪前进时,在风浪冲击下,艏部会高高翘起、而后又在波谷中跌落,形成纵摇、拍击、颠簸、失速、航速下降、稳定安全性降低等缺点。为了克服这样的不良航态,必须在水动力流场中,造成克服这些弱点的水动力和相应的水动力矩沿船体合理分布。为此,提出设置不同于常规船艇的船底浸湿面外形,使之产生足够强大的水动反冲击力、水动升力及相应的水动航向稳定扶正力矩,确保船艇不偏离目标;凭借足够强大的的水动升力和相应的船艇纵向稳定扶正力矩,消除船艇的纵摇拍击;以相应的船体横向稳定扶正力矩来克服船艇的横摇摆动。最终确保船艇平稳高速地破浪前进。而在风浪中转弯时所激起的强大水动离心力、水动反冲击力、水动升力和相应的水动助回转力矩、水动抗船体向心倾覆扶正力矩又能使船艇以很小的回转半径高速、稳定、安全地在风浪中转弯。