Theoretical study on the effect of parametric rolling on added resistance in regular head seas

A formula based on Maruo’s theory is presented for the added resistance in regular head seas when parametric rolling occurs. Firstly, the velocity potential of the radiation waves due to parametric rolling, sway and yaw motions should be superposed on the conventional velocity potential. Secondly, the added resistance is averaged within the time duration that is double the encounter period. Thirdly, the stationary-phase method which is used in Maruo’s method is also used to obtain the formula of added resistance in waves with parametric rolling taken into account as well as viscous roll damping. Fourthly, source distribution based on Maruo and Ishii's and Maruo and Iwase’s works is used to calculate the added resistance. Finally, the effect of parametric rolling on added resistance in regular head seas mainly results from viscous roll damping and it becomes larger as the amplitude of parametric rolling becomes larger.     

Predicting parametric rolling in irregular head seas with added resistance taken into account

Parametric rolling in irregular head seas is investigated using numerical simulation in the time domain in this paper. The effect of the change in speed due to added resistance on parametric rolling is taken into account. Three methods of calculating the added resistance in irregular head seas are applied to this problem, and then Pinkster’s method, which considers the time-varying added resistance in irregular head seas, is extended for further investigations in this paper. Furthermore, the Froude–Krylov component of restoring variation is estimated with coupling from heave and pitch motions, and the hydrodynamic effects are extrapolated nonlinearly with regards to roll angle. Finally, the “practical non-ergodicity” of parametric roll is investigated with a model experiment at zero forward speed and using the simulation, and the effect of added resistance is investigated with the simulation.     

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.     

考虑不确定性因素的路径优化(英文)

A route optimization methodology in the frame of an onboard decision support/guidance system for the ship’s master has been developed and is presented in this paper.The method aims at the minimization of the fuel voyage cost and the risks related to the ship’s seakeeping performance expected to be within acceptable limits of voyage duration.Parts of this methodology were implemented by interfacing alternative probability assessment methods,such as Monte Carlo,first order reliability method(FORM) and second order reliability method(SORM),and a 3-D seakeeping code,including a software tool for the calculation of the added resistance in waves of NTUA-SDL.The entire system was integrated within the probabilistic analysis software PROBAN.Two of the main modules for the calculation of added resistance and the probabilistic assessment for the considered seakeeping hazards with respect to exceedance levels of predefined threshold values are herein elaborated and validation studies proved their efficiency in view of their implementation into an on-board optimization system.     

Stochastic averaging for estimating a ship roll in random longitudinal or oblique waves

In this work, the C11 container ship is taken as an example to analyze its rolling performances in random longitudinal or oblique waves. Firstly, a dynamic model of C11 roll in random waves is improved, and it is verified by the model test and numerical simulation. Mathematically, this dynamic model is a one-dimensional stochastic differential equation with random parametric (and external) excitation. Secondly, an enhanced stochastic averaging method is proposed to solve this stochastic differential equation. The validity of the solutions was verified by Monte Carlo simulation. At last, the probabilistic characteristics of the extreme rolling response were investigated based on the calculated results using enhanced stochastic averaging method. According to the analysis, some advices for ship's manoeuvring can be put forward when ships are navigating in random waves.     

规则迎浪中船舶参数横摇的三维时域预报方法研究

参数横摇是船舶因复原特性改变而引起的典型非线性现象。文章采用三维时域方法预报规则迎浪中船舶的参数横摇运动。该方法引入匹配面将流域分为内域和外域,内域中采用Rankine源来满足物面条件和线性自由面条件,而外域中应用时域格林函数来满足线性自由面条件和远场辐射条件。数值方法中,Froude-Krylov力和恢复力是通过对船舶瞬时湿表面积积分获得,同时考虑了横摇、垂荡和纵摇三自由度之间的耦合作用,以及非线性横摇阻尼的影响。数值结果与试验结果吻合很好,说明该方法可以有效地预报参数横摇。     

A new weather-routing system that accounts for ship stability based on a real-coded genetic algorithm

The operation schedule of an oceangoing vessel can be influenced by wave or wind disturbances, and is therefore weather routed. The weather-routing problem is considered to be a multimodal function problem. Therefore, in the present research, the real-coded genetic algorithm technique (an evolutionary calculation technique) is applied to globally search for the optimum route. Additionally, to avoid maritime accidents due to parametric rolling, this route optimization method takes into account the risk of parametric rolling as one of its objective functions. Numerical verification is carried out for three kinds of objective functions with different weight ratios between fuel efficiency and ship safety in parametric rolling. As a result, it is numerically confirmed that the relation between economics and ship safety is a trade-off, and the safer route is not necessarily the most economical. Considering its robustness, the proposed method appears to be a powerful practical tool by choosing the most appropriate weights for economics and ship safety.     

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。     

随机参数激励下船舶的横摇运动

本文用能量包线统计平均法研究船舶在随浪和斜浪作用下的横摇运动,适用于阻尼较小因而激励谱的带宽较之响应谐的带宽大得多的情况。通过解 FPK方程可得出能量包线的概率密度,进而计算出各种响应统计量。这一方法允许把激励谱的具体形式考虑进去,特别适用于有强非线性恢复力矩情况。     

On the Parametric Resonance of Tumblehome Hullforms in a Longitudinal Seaway

This work presents a numerical study of the influence of topside shape on parametric roll in longitudinal seas. The ONR 3 Topsides hulls are used to compare the single degree-of-freedom rolling response of a destroyer-sized vessel with flared (model 5613), tumblehome (model 5613-1), and wallsided (model 5613-2) shapes above the waterline. Through this relative comparison, the key aspects of parametric resonance of a tumblehome hullform are highlighted, namely the reduction in head seas forward speed required to encounter parametric roll. A variant on the Mathieu equation is used to simulate roll motions.     

An investigation of different methods for the prevention of parametric rolling

The parametric rolling of modern containerships is emerging as a serious problem, to the extent that its effects warrant a study into its prevention. In light of this, two methods for reduction of parametric rolling are proposed and examined by physical model experiments. The first is a sponson attached to the side of a ship, the purpose being to decrease the rate of change of the rollrestoring moment. The second is an antirolling tank to increase roll damping. By conducting free-running model experiments for a 6600-TEU post-Panamax container ship with sponsons under typical parametric rolling conditions, it was found that the sponsons could decrease the magnitude of parametric rolling. The antirolling tank could prevent parametric rolling completely in certain conditions, even in severe head seas. Using the damping coefficients from experimentally derived data of a model ship with an antiroll tank, a numerical simulation was established. The numerical model was then compared with the free-running model experiments. The results indicated that the numerical model could qualitatively verify the experimental results. Finally, an attempt to optimise the size of an antirolling tank for preventing parametric rolling for the subject post-Panamax container ship in the North Pacific Ocean is presented.     

纵向规则波中参数横摇的数值模拟

基于ITTC推荐的参数横摇运动方程,采用估算方法确定方程中的阻尼系数和复原力矩系数,数值模拟出船舶在规则波中的参数横摇情况,将上述方法具体应用于一艘滚装船船模的参数横摇预报,并与试验数据进行对比,验证了所采用方法的有效性。     

Analytical formulae for predicting the surf-riding threshold for a ship in following seas

Making use of Melnikov’s method, a generalized formula for predicting the surf-riding threshold is developed as an extension to the applications of Kan and Spyrou. A new analytical formula for calculating the surf-riding threshold of a ship in following seas is also proposed in light of nonlinear dynamical system theory. By applying a continuous piecewise linear approximation to the wave-induced surge force, a heteroclinic bifurcation point is obtained analytically with an uncoupled surge equation. Results calculated using these formulae are presented, and they show good agreement with those obtained utilizing numerical bifurcation analysis. Further, it was confirmed that the surf-riding threshold obtained using the proposed formulae agrees reasonably well with that obtained experimentally for an unconventional vessel.     

Study of damaged ship motions taking into account floodwater dynamics

This paper presents an application of shallow water theory to describe the motion of floodwater inside a rolling ship in damage condition. The time domain theoretical approach to the coupled problems of ship and water inside compartment motions is briefly described, including the method used to solve for the water motion characteristics and forces exerted on the ship. This approach is applied to the study of the behaviour of a passenger Ro–Ro ship in regular beam seas and numerical results are given for the intact and damaged conditions. Comparison is made with experimental results. For the damaged condition, the characteristics of the floodwater motion are studied in the time domain for a number of different wave frequencies. The shape of the free-surface and phase of water motion in relation to the ship roll motion are shown for several wave frequencies. The dynamic floodwater roll moment is also shown and compared with the static roll moment (flat horizontal free surface), allowing the conclusion that the dynamic roll moment is much larger than the static roll moment, for high wave frequencies, and is in phase opposition in relation to the roll motion.     

IMO第二代完整稳性衡准对现有万箱船设计的影响

国际海事组织（IMO）正在制定基于水动力学的第二代完整稳性衡准,新衡准的实施必然对现有船舶的设计带来巨大影响。集装箱船大型化是航运界的发展趋势,万箱船船型订单近年也大幅上升。已有的事故发现大型集装箱船对参数横摇、过度加速度等衡准相对敏感,但现有船舶的设计对此类事故模式考虑较少,因此有必要开展相关研究。本文选取了某万箱集装箱船,对其大量装载工况进行四种稳性失效模式的计算分析,研究了第二代完整稳性的实施对大型集装箱船的稳性影响,并对其装载、设计等提出一定的建议。     

参数横摇下大型集装箱船外飘砰击的近似计算方法（英文）

Since the research of flare slamming prediction is seldom when parametric rolling happens, we present an efficient approximation method for flare slamming analysis of large container ships in parametric rolling conditions. We adopt a 6-DOF weakly nonlinear time domain model to predict the ship motions of parametric rolling conditions. Unlike previous flare slamming analysis, our proposed method takes roll motion into account to calculate the impact angle and relative vertical velocity between ship sections on the bow flare and wave surface. We use the Wagner model to analyze the slamming impact forces and the slamming occurrence probability. Through numerical simulations, we investigate the maximum flare slamming pressures of a container ship for different speeds and wave conditions. To further clarify the mechanism of flare slamming phenomena in parametric rolling conditions, we also conduct real-time simulations to determine the relationship between slamming pressure and 3-DOF motions, namely roll, pitch, and heave.     

Probabilistic assessment of parametric instability of a top tensioned riser in irregular waves

A reliability analysis was used to investigate the parametric instability of a top tensioned riser (TTR) operating under irregular sea conditions. In practical applications, the parametric instability evaluation of a riser is a very difficult task, owing to uncertainty of various parameters such as the environmental conditions of the load, the structural geometric parameters, and material properties. Considering the uncertainties of these parameters, it is vital to adopt a probabilistic approach in evaluating the instability. In this work, the Hill equation of a TTR operating under real sea conditions is first derived, and the corresponding stochastic external excitation is obtained using the Pierson–Moskowitz wave spectrum. The effects of various random variables on the parametric instability are studied by a sensitivity analysis. A surrogate model is used to construct the response surface for assessing the reliability of the parametric instability of the riser. The distribution regularity of parametrically unstable cases is examined using the contour of the parametrically excited responses. The effect of three significant uncertain factors on the probability of the parametric stability is investigated using the surrogate model. The proposed approach is demonstrated to be efficient for evaluating the reliability of the parametric instability of a TTR.     

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.     

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.     

New method for ship finite element method preprocessing based on a 3D parametric technique

A new method for ship finite element method (FEM) preprocessing is presented as well as its program development. The method is applicable for all kinds of ships at different levels, such as a whole ship, cargo hold parts or detailed structures. The 3D parametric technique is used when creating ship structures, which improves the modeling efficiency greatly and makes the model easy to modify. A 3D geometric constraint solver is developed to solve the constraint system of the parametric model. A meshing procedure is presented to automatically convert the parametric structure model into a finite element model, by which high quality mesh is generated in the stress concentrated area. It also becomes possible to create finite element models for different levels from the same structure model. Using this method, the engineers avoid much of the complex and laborious work of FEM preprocessing, which consumes a very significant amount of time in finite element analysis, and can pay more attention to post-processing. This method has proved to be practical and highly efficient by several engineering trials. This work is sponsored by “Liaoning BaiQianWan Talents Program”.