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.     

随机波中船舶参数横摇研究

针对随机波中船舶参数横摇,提出一种数值预报方法。采用新的随机波成形方法,求解出船舶无横倾时在随机波中时间序列垂荡和纵摇运动,确定出船-波相对位置。利用3个坐标系之间的转换关系确定船体各横剖面左右舷与波面瞬时交点,然后对波浪压力沿船长湿表面积分,得出船舶复原力的Froude-Krylov部分。提出复原力之辐射力和绕射力部分和横摇角的非线性假定。确定一个参数横摇数学模型,实现随机波中参数横摇计算;通过试验和数值模拟对一艘巴拿马型集装箱船进行了参数横摇预报,研究了随机波中参数横摇的实际非各态历经的特点。     

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.     

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.     

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)     

Efficient calculation of slamming pressures on ships in irregular seas

An efficient method for calculation of the slamming pressures on ship hulls in irregular waves is presented and validated for a 290-m cruise ship. Nonlinear strip theory was used to calculate the ship–wave relative motions. The relative vertical and roll velocities for a slamming event were input to the slamming calculation program, which used a two-dimensional boundary element method (BEM) based on the generalized 2D Wagner formulation presented by Zhao et al. To improve the calculation efficiency, the method was divided into two separate steps. In the first step, the velocity potentials were calculated for unit relative velocities between the section and the water. In the next step, these precalculated velocity potentials were used together with the real relative velocities experienced in a seaway to calculate the slamming pressure and total slamming force on the section. This saved considerable computer time for slamming calculations in irregular waves, without significant loss of accuracy. The calculated slamming pressures on the bow flare of the cruise ship agreed quite well with the measured values, at least for time windows in which the calculated and experimental ship motions agreed well. A simplified method for calculation of the instantaneous peak pressure on each ship section in irregular waves is also presented. The method was used to identify slamming events to be analyzed with the more refined 2D BEM method, but comparisons with measured values indicate that the method may also be used for a quick quantitative assessment of the maximum slamming pressures.     

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.     

迎浪规则波中波浪增阻和船体垂向运动的数值预报(英文)

The numerical prediction of added resistance and vertical ship motions of one ITTC (International Towing Tank Conference) S-175 containership in regular head waves by our own in-house unsteady RANS solver naoe-FOAM-SL JTU is presented in this paper. The development of the solver naoe-FOAM-SJTU is based on the open source CFD tool, OpenFOAM. Numerical analysis is focused on the added resistance and vertical ship motions (heave and pitch motions) with four very different wavelengths (0.8Lpp≤λ≤1.5Lpp) in regular head waves. Once the wavelength is near the length of the ship model, the responses of the resistance and ship motions become strongly influenced by nonlinear factors, as a result difficulties within simulations occur. In the paper, a comparison of the experimental results and the nonlinear strip theory was reviewed and based on the findings, the RANS simulations by the solver naoe-FOAM-SJTU were considered competent with the prediction of added resistance and vertical ship motions in a wide range of wave lengths.     

基于三维时域混合源法的顶浪 不规则波参数横摇研究

国际海事组织(IMO)船舶设计建造分委会(SDC)第4次会议把参数横摇稳性直接评估提上议程,如何准确预报和评估不规则波中的参数横摇是亟待解决的问题。文章提出采用一种三维时域面元法进行不规则波中参数横摇的预报和评估,该方法首先采用混合源法,即在内域采用Rankine源,在外域采用瞬态的时域Green函数,该混合源法充分考虑了船体的定常和非定常运动,以及定常运动对非定常运动的影响;其次考虑了船体与不规则波浪的瞬时相对位置,沿船体瞬时湿表面进行压力积分求解Froude-Krylov力和静水力;然后通过时域求解垂荡—纵摇—横摇三自由度耦合方程计算参数横摇。文中以国际标模C11集装箱船为研究对象,研究了不同随机波浪谱下参数横摇的发生规律,进行了统计分析,并通过已有的试验结果验证了文中采用方法的有效性。结果表明,该文采用的三维时域面元法可有效用于顶浪不规则波中参数横摇的直接数值预报。     

Dynamic motions of planing vessels in head seas

The dynamic response of planing vessels in regular head seas is investigated numerically. Nonlinear time domain simulations were performed using a 2D + t theory (two-dimensional plus time dependent theory). A prismatic hull form was assumed. We employed a two-dimensional (2D) boundary element method to solve the initial boundary value problems in 2D cross planes, in which nonlinear free-surface conditions and exact body boundary conditions were satisfied. At each time step, the total force and moment on the hull could be obtained by using the sectional forces calculated in those 2D planes. Heave and pitch motions were then acquired by solving the equations for those motions. The calculated heave and pitch responses were compared with the experiments by Fridsma (A systematic study of the rough-water performance of planing boats. Davidson Laboratory Report R-1275, 1969) for two different Froude numbers. Three-dimensional (3D) corrections at the transom stern were applied to show the influence of the 3D effect at the stern on the numerical results. Ship motions were affected by the 3D corrections, especially near the resonance frequency, while the phase angles were slightly affected and the acceleration peaks at the bow near the resonance frequency were sensitive to the 3D corrections. Other error sources in the theoretical results are also mentioned.     

基于局部线性化方法的瘫船稳性敏感性分析及衡准完善

  目的  瘫船稳性是当船舶失去动力后,在横风横浪状态下发生共振横摇甚至倾覆的运动模式,是公认的较危险的稳性失效模式。国际海事组织（IMO）船舶设计与建造分委会（SDC）预计将于2019年完成第2代完整稳性衡准规则定稿,目前亟需大量的样船计算以完善规则。  方法  基于局部线性化方法,对3艘集装箱船进行了瘫船稳性第2层衡准校核计算,并分析了瘫船稳性敏感性与船舶各设计参数的关系。  结果  分析结果表明,随着船舶吃水深度的增大,船舶倾覆概率将先增大后减小,并对第2层衡准的标准值选取及衡准完善提出了建议。  结论  可为瘫船稳性衡准研究提供技术支持。     

海上长球首球尾双体风电维护船波浪增阻研究

为研究不同球首球尾长度双体风电维护船在波浪中的阻力性能,基于CFD技术,探究适用于双体船运动响应和波浪增阻的数值计算方法.通过与试验结果的对比分析,在计算域设定和网格尺寸方面提出适用于双体船的计算方案.利用此方法计算不同球首球尾长度双体风电维护船的升沉与纵摇以及波浪增阻,为球首球尾双体船以及风电维护船的船型设计与优化提供参考.     

海上长球首球尾双体风电维护船波浪增阻研究

为研究不同球首球尾长度双体风电维护船在波浪中的阻力性能,基于CFD技术,探究适用于双体船运动响应和波浪增阻的数值计算方法。通过与试验结果的对比分析,在计算域设定和网格尺寸方面提出适用于双体船的计算方案。利用此方法计算不同球首球尾长度双体风电维护船的升沉与纵摇以及波浪增阻,为球首球尾双体船以及风电维护船的船型设计与优化提供参考。     

规则纵浪中船舶参数激励横摇运动研究

考虑船舶横摇运动中恢复力矩及阻尼力矩的非线性,建立船舶在规则波浪中参数激励下的非线性横摇运动方程,并对规则纵浪中船舶参数激励横摇运动进行研究,探讨船舶发生参数激励横摇运动的条件及大幅横摇的动力学特征,分析船速、波高及波长等因素对参数激励横摇运动的影响。     

Experimental and numerical study of containership responses in severe head seas

An accurate determination of the global load effects in a ship is vital for the design of the vessel. This paper addresses an experimental and numerical study of containership responses in severe head seas. Experimental results were obtained using a flexible model of a containership of newer design. The experiments showed that, taking hull flexibility into account, the fourth and sixth harmonic of the vertical bending moments had a maximum value of between 25% and 50% of the first harmonic. We also demonstrated that hull flexibility can increase the vertical bending moment by up to 35% in sea states relevant for design. Comparisons of moments found experimentally with results from a nonlinear hydroelastic strip theory method showed that the effect of nonlinearities on the rigid body moments was slightly over-predicted in the aft body. The method also tends to over-predict the increase of the bending moments due to hull flexibility. In general however, the numerical results compared reasonably well with the experimental ones.     

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.     

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.     

A B-spline method used to calculate added resistance in waves

Making an exact computation of added resistance in sea waves is of high interest due to the economic effects relating to ship design and operation. In this paper, a B-spline based method is developed for computation of added resistance. Based on the potential flow assumption, the velocity potential is computed using Green's formula. The Kochin function is applied to compute added resistance using Maruo's far-field method, the body surface is described by a B-spline curve and potentials and normal derivation of potentials are also described by B-spline basis functions and B-spline derivations. A collocation approach is applied for numerical computation, and integral equations are then evaluated by applying Gauss–Legendre quadrature. Computations are performed for a spheroid and different hull forms; results are validated by a comparison with experimental results. All results obtained with the present method show good agreement with experimental results.     

航行于波浪中的肥大型船波浪增阻计算研究(英文)

Under the background of the energy saving and emission reduction, more and more attention has been placed on investigating the energy efficiency of ships. The added resistance has been noted for being crucial in predicting the decrease of speed on a ship operating at sea. Furthermore, it is also significant to investigate the added resistance for a ship functioning in short waves of large modern ships. The researcher presents an estimation formula for the calculation of an added resistance study in short waves derived from the reflection law. An improved method has been proposed to calculate the added resistance due to ship motions, which applies the radiated energy theory along with the strip method. This procedure is based on an extended integral equation (EIE) method, which was used for solving the hydrodynamic coefficients without effects of the irregular frequency. Next, a combined method was recommended for the estimation of added resistance for a ship in the whole wave length range. The comparison data with other experiments indicate the method presented in the paper provides satisfactory results for large blunt ship.