Manoeuvring characteristics of twin-rudder systems: rudder-hull interaction effect on the manoeuvrability of twin-rudder ships

With a recent increase in ship capacity and propulsion performance, a wide-beam ship fitted with a twin-rudder system has been adopted in many cases. However, to improve ship manoeuvring, it is still necessary to have a better understanding of rudder-hull interactions in twin-rudder ships. Captive model tests (oblique towing and circular motion test) as well as free-running tests with a single-propeller twin-rudder ship and a twin-propeller twin-rudder ship are carried out. The effect of drift angle on the rudder forces and some peculiar phenomena concerning rudder normal force for twin-rudder ships are evaluated. A method for estimating the hull-rudder interaction coefficients based on free-running experimental results is proposed.     

Prediction of the maneuverability of a large container ship with twin propellers and twin rudders

The maneuvering characteristics of a large container ship with twin propellers and twin rudders were investigated using the horizontal planar motion mechanism (HPMM) test and computer simulation. A mathematical model for maneuvering motion with four degrees of freedom (DOF) for twin-propeller and twin-rudder systems was developed and included the effects of roll motion. To obtain the roll-coupling hydrodynamic coefficients of a container ship, a four-DOF HPMM system having a roll motion mechanism and a roll moment measurement system was used. At the full load condition, HPMM tests were carried out for two different 12 000-TEU container ship models, one with twin propellers and the other with a single propeller. Using the hydrodynamic coefficients obtained from the tests, computer simulations were carried out. Simulation results for the container ship with twin propellers and twin rudders were compared with the results for the container ship with a single propeller and single rudder.     

船舶在波浪中操纵运动仿真

本文研究了双浆双舵船在规则波中的回转运动，首先进行了约束模型试验，得到了操纵运动数学模型中的水动力系数，然后，进行了静水操纵运动数值仿真，并与自航模型试验结果进行了比较。最后，预报船舶在规则波中的回转运动，对一些影响回转运动的因素进行了讨论。     

Study on the maneuverability of a large vessel installed with a mariner type Super VecTwin rudder

The suitability of the Mariner type Super VecTwin rudder (hereinafter, the MSV rudder) for a large vessel is assessed in this article. Several experiments in a maneuvering pond were carried out and their results analyzed and summarized. Free-running tests such as turning, zigzag, and stopping tests were carried out with a 4-m free-running model of a very large crude carrier (VLCC) ship with the MSV rudder and the Mariner rudder. The results were compared to validate the maneuverability of a VLCC-sized a ship installed with the MSV rudder. A mathematical model of an MSV rudder is proposed for maneuvering simulation of a large vessel. To develop a maneuvering simulation for the model ship that was used in the free-running tests, hydrodynamic coefficients were estimated based on Kijima's regression formula. The coefficients of interaction between the hull and rudder (t_R, a_H, x_H) were obtained from a self-propulsion test in a towing tank. The complicated flow around the rudders is simplified to model the flow speed around the rudders. This simplified flow speed is utilized to compare the time histories of the free-running tests with the simulations. The mathematical model of the MSV rudder was further improved using the results of this comparison.     

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.     

Roll-induced bifurcation in ship maneuvering under model uncertainty

In this paper, a mathematical model is developed for the maneuvering motion of a naval ship and bifurcations of its equilibrium are identified in roll-coupled motion. The subject ship is a high-speed surface combatant with twin-propeller twin-rudder system. Captive model tests are conducted for the ship using planar motion mechanism. Maneuvering coefficients are calculated by polynomial curve fitting of the test data. Uncertainty distribution in the coefficients is assumed same as that of the curve fitting errors. Uncertainty in the model coefficients is propagated to full-scale simulation results by the stochastic response surface method (SRSM). This method is computationally efficient as compared to standard Monte Carlo simulation technique. The SRSM uses polynomial chaos expansion of orthogonal to fit any probability distribution. Bifurcation analysis of the mathematical model is performed by varying the vertical center of gravity as the bifurcation parameter. Hopf bifurcation is identified. It is found that the bifurcations occur due to the coupling of roll motion with sway, yaw motion and rudder angle. In the presence of wind, roll angle response in bifurcation diagram is discussed.     

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.     

基于减摇鳍辅助回转的船舶操纵性能研究

基于MMG分离式建模思想，考虑作用在船体、螺旋桨、舵、鳍的水动力作用，建立双桨双舵船舶四自由度非线性数学运动模型，对某船模在静水中的回转性能进行仿真分析，将单独舵控制的仿真结果与船模试验结果进行了验证和分析，并对比了单独舵控制和舵、鳍联合控制下的回转性能，结果表明鳍参与控制回转时能明显缓解回转过程中的横倾。     

船舶舵鳍联合减摇模糊变结构控制研究

分析了船舶运动的非线性模型,根据实际情况进行假设,得到了船舶舵鳍联合减摇控制系统的状态方程,把非线性船舶舵鳍联合控制模型转化为可控正则型;将船舶运动模型看作是由横摇、艏摇、横荡3个子系统构成的大系统,进行了舵鳍联合控制,设计了舵鳍联合控制器和分散非线性变结构控制器,为了改善控制的品质,又进一步提出了模糊趋近律变结构控制的方法,最后针对减摇控制器进行了MATLAB仿真研究。仿真结果表明:舵鳍联合控制器能够很好的抑制船舶的横摇和艏摇,并能尽可能的减小横荡。     

船舶大舵角转向时艏摇与横摇的耦合仿真研究

摘要：为进一步研究船舶在大幅度转向时艏摇和横摇的耦合机制,在非线性船舶运动数学模型的基础上,进行了不同情形下的操纵仿真试验。试验结果显示在大舵角转向时,船舶的艏摇和横摇运动存在较强的耦合作用,横摇幅度和艏摇幅度存在正相关性。指出大幅度的横摇使艏摇出现相位滞后和偏离基准航向的现象;在横摇过大的情况下,大幅度动舵和加速操纵将导致稳性迅速消失和航向打横。     

Fatigue damage prediction of ship rudders under vortex-induced vibration using orthonormal modal FSI analysis

Recently, the fatigue failure of ship rudders owing to vortex-induced vibration has increased as commercial ships become faster and larger. However, previous methods are inappropriate for fatigue failure prevention owing to the lack of fluid–structure interaction considerations. This study aims to develop a fatigue damage prediction method that can be applied at the design stage to prevent fatigue failure of ship rudders under vortex-induced vibration. The developed prediction method employed the fluid–structure interaction (FSI) method to properly consider the fluid–structure interaction and implemented orthonormal mode shapes to reflect the complex geometry and boundary conditions of the ship rudders. For validation, vortex-induced vibration of the hydrofoil model was obtained using the developed method, and the prediction results matched well with the experimental results. Then, the fatigue damage of the ship rudder model under vortex-induced vibration was predicted using the developed method, and their characteristics are discussed. The stress distribution obtained using the developed method matched well with the geometrical characteristics of the ship rudders. The potential for fatigue failure due to the resonance of vortex-induced vibration was expected by comparing the stress distributions for various flow velocities to the S–N curves provided by the DNV classification.     

对舵系设计中几个主要参数的对比分析

通过对不同船级社规范中公式的分析,给出双桨双舵船舵面积的建议,并对展弦比、舵杆直径的确定提出自己独到的见解,有助于加深读者对舵系优化设计的理解。     

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)     

35000吨肥大船浅水操纵性能改进

本文叙述浅吃水肥大船的操纵性改进试验研究，采取安装不同的稳定鳍，采用西林舵和鱼尾组合舵，增大舵面积等改进措施，通过自由自航模的常规试验和淌航试验，比较了每一单项改进措施对船舶浣操纵性指标及淌航操纵性指标的定量影响。     

Turn and zigzag maneuvers of a surface combatant using a URANS approach with dynamic overset grids

Unsteady Reynolds averaged Navier–Stokes (URANS) computations of standard maneuvers are performed for a surface combatant at model and full scale. The computations are performed using CFDShip-Iowa v4, a free surface solver designed for 6DOF motions in free and semi-captive problems. Overset grids and a hierarchy of bodies allow the deflection of the rudders while the ship undergoes 6DOF motions. Two types of maneuvers are simulated: steady turn and zigzag. Simulations of steady turn at 35° rudder deflection and zigzag 20/20 maneuvers for Fr = 0.25 and 0.41 using constant RPM propulsion are benchmarked against experimental time histories of yaw, yaw rate and roll, and trajectories, and also compared against available integral variables. Differences between CFD and experiments are mostly within 10 % for both maneuvers, highly satisfactory given the degree of complexity of these computations. Simulations are performed also with waves, and with propulsion at either constant RPM or torque. 20/20 zigzag maneuvers are simulated at model and full scale for Fr = 0.41. The full scale case produces a thinner boundary layer profile compared to the model scale with different reaction times and handling needed for maneuvering. Results indicate that URANS computations of maneuvers are feasible, though issues regarding adequate modeling of propellers remain to be solved.     

A study on improving the course-keeping ability of a pure car carrier in windy conditions

The course-keeping ability of a pure car carrier (PCC) in windy conditions is discussed in this article. Numerical simulations of two PCCs were carried out to compare their course-keeping abilities in wind. The two PCCs had the same hull form but different types of rudder. One PCC was fitted with a semispade rudder (hereinafter, the normal rudder), whereas the other was fitted with a spade-type Schilling rudder (hereinafter, the Schilling rudder). Both PCCs were designed to a new concept for the accommodation structure and hull form above the load water line. In this new design concept, there are no sharp corners in the superstructure so as to reduce wind resistance and improve steering performance. The limits of course keeping for the two PCCs were investigated through simulations. The course-keeping abilities of the two PCCs, each with two different types of autopilot system, were also investigated in wind. To develop the numerical simulation, the hydrodynamic coefficients of the two PCCs were predicted based on the data published for a third PCC having similar principal particulars. The numerical model of the two PCCs was validated by comparing its behavior with the respective full-scale trial results. Wind resistance coefficients were predicted by combining the results of wind tunnel experiments of the object PCCs and a regression model. Numerical simulations under steady wind conditions were also carried out and the results compared with some full-scale experiments to validate the mathematical model of the PCC.     

Self-propulsion computations using a speed controller and a discretized propeller with dynamic overset grids

A method that can be used to perform self-propulsion computations of surface ships is presented. The propeller is gridded as an overset object with a rotational velocity that is imposed by a speed controller, which finds the self-propulsion point when the ship reaches the target Froude number in a single transient computation. Dynamic overset grids are used to allow different dynamic groups to move independently, including the hull and appendages, the propeller, and the background (where the far-field boundary conditions are imposed). Predicted integral quantities include propeller rotational speed, propeller forces, and ship’s attitude, along with the complete flow field. The fluid flow is solved by employing a single-phase level set approach to model the free surface, along with a blended k−ω/k−ɛ based DES model for turbulence. Three ship hulls are evaluated: the single-propeller KVLCC1 tanker appended with a rudder, the twin propeller fully appended surface combatant model DTMB 5613, and the KCS container ship without a rudder, and the results are compared with experimental data obtained at the model scale. In the case of KCS, a more complete comparison with propulsion data is performed. It is shown that direct computation of self-propelled ships is feasible, and though very resource intensive, it provides a tool for obtaining vast flow detail.     

船—缆拖曳系统操纵性能分析

为获取拖船在拖曳时的操纵性的变化规律。文章采用MMG船舶运动数学模型的建模思想,建立了六自由度拖船运动数学模型,采用有限差分法,建立了拖缆模型。然后,在此基础上建立将船-缆耦合起来以形成整个系统的运动数学模型,并分别采用龙格库塔方法对船舶运动积分求解,采用后向差分法对拖缆运动进行求解。通过对比仿真计算分析了水面拖船在拖带过程中的加速性能、旋回性能及偏转抑制性能。仿真结果表明在拖船与拖缆的相互影响下,拖船的加速性能和旋回性能有所下降而偏转抑制性能有所增强。     

基于细长体理论的小水线面双体船操纵性预报

小水线面双体船(SWATH)由于具有良好的船舶快速性、耐波性、稳性和效率高等特点,已经成为新船型的代表。根据小水线面双体船的船型结构特点,在操纵运动数学模型的基础上,充分考虑小水线面船的结构特点和双体、双桨、双舵之间水动力的相互影响,采用细长体理论计算了附加质量、附加惯性矩和线性水动力导数,编制了双体船操纵运动预报程序,并结合实例对SWATH的操纵性能进行了预报。     

降低船体振动的桨舵偏置设计方案

采用比水面船舶常规桨舵配置多一只舵或少一二只舵，通过合理布置桨舵相对位置，以降低船舶的振动和噪声、提高船舶推进效率、提高船舵控制航向的性能。此方法特别对水面船舶设计有实用价值。