Study of non-linear wave motions and wave forces on ship sections against vertical quay in a harbor

The resonance phenomenon of fluid motions in the gap between ship section, seabed and vertical quay wall is studied numerically and experimentally. The natural frequency of the fluid motions in the gap is derived. A two-dimensional time-domain coupled numerical model is developed to calculate the non-linear wave forces acting on a ship section against vertical quay in a harbor. The fluid domain is divided into an inner domain and an outer domain. The outer domain is the area between the left side of ship section and the incident boundary, where flow is expressed by Boussinesq equations. The rest area is the inner domain, which is the domain beneath the ship section plus the domain between the right side of ship section and vertical quay wall. The flow in the inner domain is expressed by Newton's Second Law. Matching conditions on the interface between the inner domain and the outer domain are the continuation of volume flux and the equality of pressures. The numerical results are validated by experimental data.     

A 3-D time-domain coupled model for nonlinear waves acting on a box-shaped ship fixed in a harbor

A 3-D time-domain numerical coupled model is developed to obtain an efficient method for nonlinear waves acting on a box-shaped ship fixed in a harbor. The domain is divided into the inner domain and the outer domain. The inner domain is the area beneath the ship and the flow is described by the simplified Euler equations. The remaining area is the outer domain and the flow is defined by the higher-order Boussinesq equations in order to consider the nonlinearity of the wave motions. Along the interface boundaries between the inner domain and the outer domain, the volume flux is assumed to be continuous and the wave pressures are equal. Relevant physical experiment is conducted to validate the present model and it is shown that the numerical results agree with the experimental data. Compared the coupled model with the flow in the inner domain governed by the Laplace equation, the present coupled model is more efficient and its solution procedure is simpler, which is particularly useful for the study on the effect of the nonlinear waves acting on a fixed box-shaped ship in a large harbor.     

A Time-Domain Coupled Model for Nonlinear Wave Forces on A Fixed Box-Shaped Ship in A Harbor

A 2-D time-domain numerical coupled model is developed to obtain an efficient method for nonlinear wave forces on a fixed box-shaped ship in a harbor.The domain is divided into an inner domain and an outer domain.The inner domain is the area beneath the ship and the flow is described by the simplified Euler equations.The other area is the outer domain and the flow is defined by the higher-order Boussinesq equations in order to consider the nonlinearity of the wave motions.Along the interface boundaries between the inner domain and the outer domain,the volume flux is assumed to be continuous and the wave pressures are equal.Relevant physical experiment is conducted to validate the present model.It is shown that the numerical results agree with the experimental data.Compared with the coupled model with the flow in the inner domain governed by the Laplace equation,the present coupled model is more efficient and its solution procedure is more simple,which is particularly useful for the study on the effect of the nonlinear wave forces on a fixed box-shaped ship in a large harbor.     

系泊船非线性波浪力时域计算:二维模型

为找到具有工程实用价值的港口系泊船波浪力的时域计算方法,建立了在港口中存在系泊船时非线性波浪力时域计算的垂直二维耦合模型:用Boussinesq方程计算船的两侧的外域,用欧拉方程计算船底面下的内域,两域在交界面处的连接条件是流量连续和压力相等.将复平面内的边界元方法应用于所研究问题,对耦合模型进行了验证.进行了相关模型实验,实验结果与数值计算结果比较表明这两种数值计算模型都具有满意的精度,但耦合模型的计算效率要远远高于边界元方法的计算效率.本耦合模型的数学处理简单,可适用于工程计算.     

Calculation Methods of Added Resistance and Ship Motion Response Based on Potential Flow and Viscous Flow Theory

To improve the energy efficiency of ships and to predict ship motion response under actual sea conditions, the far-field theory, strip theory, and Fujii and Takahashi’s modified semi-empirical method are based and studied to calculate the wave-induced added resistance. Firstly, a new modified formula based on the Maruo method is presented to calculate the radiation added resistance for the ship with a complex surface. Meanwhile, some calculation details such as the Green function, the shape of the sections (shape below the still water level or shape below the wave level) in the strip theory, and so on are discussed. Finally, the CFD method is used to simulate the motions of the hull and the added resistance, and the results of the CFD method and those of other numerical methods are analyzed and compared with the experiment results. The modified method in the paper can predict the added resistance in waves for the complex-hull-surface ships well and quickly.

     

Seakeeping of two ships in close proximity

Underway replenishment is an essential component of long-term naval operations. During underway replenishment, two ships travel in close proximity at moderate forward speed. This paper examines the hydrodynamic interactions that can influence seakeeping during such operations. Presented numerical predictions include the influence of interaction effects on hydrodynamic forces for two ships in waves. A scarcity of validation material for numerical predictions prompted new towing tank experiments for two ships in waves. The experiments used semi-captive models, and the numerical code was modified to include restraining forces for specified modes. The numerical predictions and experiments show that the presence of a larger ship can significantly influence the motions of a smaller ship in close proximity.     

On the parametric rolling of ships using a numerical simulation method

This paper has shown a numerical motion simulation method which can be employed to study on parametric rolling of ships in a seaway. The method takes account of the main nonlinear terms in the rolling equation which stabilize parametric rolling, including the nonlinear shape of the righting arm curve, nonlinear damping and cross coupling among all 6 degrees of freedom. For the heave, pitch, sway and yaw motions, the method uses response amplitude operators determined by means of the strip method, whereas the roll and surge motions of the ship are simulated, using nonlinear motion equations coupled with the other 4 degrees of freedom. For computing righting arms in seaways, Grim's effective wave concept is used. Using these transfer functions of effective wave together with the heave and pitch transfer functions, the mean ship immersion, its trim and the effective regular wave height are computed for every time step during the simulation. The righting arm is interpolated from tables, computed before starting the simulation, depending on these three quantities and the heel angle. The nonlinear damping moment and the effect of bilge keels are also taken into account. The numerical simulation tool has shown to be able to model the basic mechanism of parametric rolling motions. Some main characteristics of parametric rolling of ships in a seaway can be good reproduced by means of the method. Comprehensive parametric analyses on parametric rolling amplitude in regular waves have been carried out, with that the complicated parametric rolling phenomena can be understood better.     

Dynamics of ships and fenders during berthing in a time domain

When designing fixed or semi-fixed structures used for berthing ships, it is generally assumed that the entire kinetic energy of the ship is absorbed by the fender or the system of fenders. The fenders have the functions of ensuring a safe berthing both for the ships and the piers by absorbing shock loads and preventing direct contact between the berthed ship and the pier. In this study, the problem is analyzed in the stages of berthing, collision and leaving. Each of the stages is analyzed and solved in the time domain. The system is assumed to consist of three components: pier, fender and the ship. Environmental effects that simultaneously affect berthing are wave, current and wind effects. Cummins equation was assumed to be a good representation of the problem and was solved in time domain taking various factors into account. Nonlinear effects related to the instantaneous values of forces, moments and ship motions, which are time dependent, were studied by the Cummins equation and its later developments by Ogilvie. Fender forces were added to the calculation scheme by the authors. A case study for a passenger ferry operating in Izmir bay is presented.     

港口内靠码头系泊船运动的计算

本文以英国南海岸处Ｓｈｏｒｅｈａｍ港内系泊船为例，研究了港口内靠码头系泊船运动的数值计算问题。该船的实船实验和模型实验已经完成，为验证本文计算结果提供了依据。运动方程在时域内求解。在计算船体脉冲响应函数时，引入了船体阻尼系数在频率很低时的渐近表达式和一迭代算法。分析了港内共振波浪和其对船体的作用力。讨论了靠码头系泊船运动的非线性特征。计算结果与实验结果符合很好。     

Robust adaptive control of underactuated ships on a linear course with comfort

This paper addresses an important problem in ship control application—the robust stabilization of underactuated ships on a linear course with comfort. Specifically, we develop a multivariable controller to stabilize ocean surface ships without a sway actuator on a linear course and to reduce roll and pitch simultaneously. The controller adapts to unknown parameters of the ship and constant environmental disturbances induced by wave, ocean current and wind. It is also robust to time-varying environmental disturbances, time-varying change in ship parameters and other motions of the ship such as surge and heave. The roll and pitch can be made arbitrarily small while the heading angle and sway are kept to be in reasonably small bounds. The controller development is based on Lyapunov’s direct method and backstepping technique. A Lipschitz continuous projection algorithm is used to update the estimate of the unknown parameters to avoid the parameters’ drift due to time-varying environmental disturbances. Simulations on a full-scale catamaran illustrate the effectiveness of our proposed controller.     

Optimized support vector regression algorithm-based modeling of ship dynamics

This study contributes to solving the problem of how to derive a simplistic model feasible for describing dynamics of different types of ships for maneuvering simulation employed to study maritime traffic and furthermore to provide ship models for simulation-based engineering test-beds. The problem is first addressed with the modification and simplification of a complicated and nonlinearly coupling vectorial representation in 6 degrees of freedom (DOF) to a 3 DOF model in a simple form for simultaneously capturing surge motions and steering motions based on several pieces of reasonable assumptions. The created simple dynamic model is aiming to be useful for different types of ships only with minor modifications on the experiment setup. Another issue concerning the proposed problem is the estimation of parameters in the model through a suitable technique, which is investigated by using the system identification in combination with full-scale ship trail tests, e.g., standard zigzag maneuvers. To improve the global optimization ability of support vector regression algorithm (SVR) based identification method, the artificial bee colony algorithm (ABC) presenting superior optimization performance with the advantage of few control parameters is used to optimize and assign the particular settings for structural parameters of SVR. Afterward, the simulation study on identifying a simplified dynamic model for a large container ship verifies the effectiveness of the optimized identification method at the same time inspires special considerations on further simplification of the initially simplified dynamic model. Finally, the further simplified dynamic model is validated through not only the simulation study on a container ship but also the experimental study on an unmanned surface vessel so-called I-Nav-II vessel. Either simulation study results or experimental study results demonstrate a valid model in a simple form for describing the dynamics of different types’ ships and also validate the performance of the proposed parameter estimation method.     

Numerical and experimental study on seakeeping performance of ship in finite water depth

Vessels operating in shallow waters require careful observation of the finite-depth effect. In present study, a Rankine source method that includes the shallow water effect and double body steady flow effect is developed in frequency domain. In order to verify present numerical methods, two experiments were carried out respectively to measure the wave loads and free motions for ship advancing with forward speed in head regular waves. Numerical results are systematically compared with experiments and other solutions using the double body basis flow approach, the Neumann-Kelvin approach with simplified m-terms, and linearized free surface boundary conditions with double-body m-terms. Furthermore, the influence of water depths on added mass and damping coefficients, wave excitation forces, motions and unsteady wave patterns are deeply investigated. It is found that finite-depth effect is important and unsteady wave pattern in shallow water is dependent on both of the Brard number τ and depth Froude number F_h.     

Experimental and Numerical Investigations of Ship Parametric Rolling in Regular Head Waves

Parametric rolling is one of five types of the ship stability failure modes as proposed by IMO. The periodic change of the metacentric height is often considered as the internal cause of this phenomenon. Parametric rolling is a complex nonlinear hydrodynamic problem, often accompanied by large amplitude vertical motions of ships. In recent years,the Reynolds-averaged Navier–Stokes(RANS) equation simulations for viscous flows have made great progress in the field of ship seakeeping. In this paper, the parametric rolling for the C11 containership in regular waves is studied both experimentally and numerically. In the experiments, parametric rolling amplitudes at different drafts, forward speeds and wave steepnesses are analyzed. The differences in the steady amplitudes of parametric rolling are observed for two drafts. The effect of the incident wave steepness(or wave amplitude) is also studied, and this supports previous results obtained on limits of the stability for parametric rolling. In numerical simulations, the ship motions of parametric rolling are analyzed by use of the potential-flow and viscous-flow methods. In the viscousflow method, the Reynolds-averaged Navier–Stokes equations are solved using the overset grid method. The numerical accuracies of the two methods at different wave steepnesses are also discussed.     

Numerical analysis and validation of weakly nonlinear ship motions and structural loads on a modern containership

This paper aims to validate a numerical seakeeping code based on a 3D Rankine panel method by comparing its results with experimental data. Particularly, the motion response and hull-girder loads on a real modern ship, a 6500 TEU containership, are considered in this validation study. The method of solution is a 3D Rankine panel method which adopts B-spline basis function in the time domain. The numerical code is based on the weakly nonlinear scheme which considers nonlinear Froude-Krylov and restoring forces. The main focus of this study is given to investigate the nonlinear characteristics of wave-induced loads, and to validate this present scheme for industrial use in the range of low Froude number. The comparisons show that the nonlinear motions and hull-girder loads, computed by the present numerical code, have good overall agreements with experimental results. It is found that, for the better accuracy of computational results, particularly at extreme waves in oblique seas, the careful treatment of soft-spring (or compatible) system is recommended to the control of non-restoring motions such as surge, sway, and yaw.     

Fast computation of the transient motions of moving vessels in irregular ocean waves

A fast time-domain method is developed in this paper for the real-time prediction of the six degree of freedom motions of a vessel traveling in an irregular seaway in infinitely deep water. The fully coupled unsteady ship motion problem is solved by time-stepping the linearized boundary conditions on both the free surface and body surface. A velocity-based boundary integral method is then used to solve the Laplace equation at every time step for the fluid kinematics, while a scalar integral equation is solved for the total fluid pressure. The boundary integral equations are applied to both the physical fluid domain outside the body and a fictitious fluid region inside the body, enabling use of the fast Fourier transform method to evaluate the free surface integrals. The computational efficiency of the scheme is further improved through use of the method of images to eliminate source singularities on the free surface while retaining vortex/dipole singularities that decay more rapidly in space. The resulting numerical algorithm runs 2–3 times faster than real time on a standard desktop computer. Numerical predictions are compared to prior published results for the transient motions of a hemisphere and laboratory measurements of the motions of a free running vessel in oblique waves with good agreement.     

Cause and countermeasure of long-period oscillations of moored ships and the quantification of surge and heave amplitudes

Long-period oscillations of moored ships whose periods are about 1 or 2 min cause many troubles in many ports and harbours. It is necessary to investigate these phenomena and verify their causes and countermeasures in each case because they are strongly dependent on the environment of each port and harbour. From this point of view, long-period oscillations of moored ships in the Port of Shibushi in Japan were investigated by means of wave observations, the image processing of moored ship motions using the video camera and motion-capture software and numerical simulations. From observation results, the relationship between offshore long-period waves and long-period oscillations of moored ships was recognized and surge and heave amplitudes were quantified by using wave data in order to forecast moored ship motions. Furthermore, from observation and numerical results, it was revealed that long-period waves with the peak period of 120 s from the offshore typhoon kept or exaggerated the local harbour oscillation of 60–70 s and it caused long-period oscillations of moored ships. Numerical results in case of reducing the reflection coefficient of the target berth implied that it ceased the local harbour oscillation and it would give an effective countermeasure to reduce long-period oscillations of moored ships in the Port of Shibushi.     

A time-domain prediction method of ship motions

A time-domain analysis is used to predict wave loading and motion responses for a ship traveling at a constant speed in regular oblique waves. Considered as a distribution of normal velocities on the wetted hull surface, the combined diffraction and radiation perturbations caused by the forward moving ship and her motions are determined simultaneously. This way, the ship-hull boundary condition is exactly fulfilled. The 3-D time domain Green's function is used to express the combined diffraction/radiation potential in terms of impulsive and memory potentials. Application of the Bernoulli equation yields the pressure distribution and accordingly, the necessary hydrodynamic forces. The equations of motion of the ship are then developed and solved in the time domain.Forces and motions at forward speed are predicted for a Wigley ship-hull in head waves and for a catamaran-ferry in oblique waves. Comparison is made with published theoretical and experimental results for the Wigley ship-hull, and the agreement is good. For the catamaran, a self-propelled model is built and tested both in a large towing tank and in a seakeeping basin in order to measure the six-degrees-of-freedom forces, moments and motions at forward speed in regular waves of different directions. For the longitudinal motions, the agreement between measurements and predictions is generally good. For the transverse motions, however, acceptable discrepancy exists. The discrepancy is thought to be mainly due to the exclusion from the analysis of the rudder forces and viscous damping. The inclusion of such nonlinear effects in the time domain simulation involves complex analysis and this problem is left to a future research.     

Experimental studies on the slowly varying drift motion of a berthed container ship model

The effects of free-surface waves on the floating structures are of great importance in the offshore industry. Among the six degrees of motions of a surface ship the absence of restoring forces in surge, sway and yaw led to critical situations for moored ships in the recent times. The order of forces in horizontal plane and their exciting frequencies are matters of interest. The resonance with the presence of moored chains led to many accidents in the recent past. The lines in dry conditions may not give good damping and in wet condition they may trigger the system to chaotic motions and jumps. Two different loading conditions of a container ship model are tested with waves in laboratory conditions in two different drafts. The mooring lines are chosen as per scale law and the energy under the response spectrum is determined from the plots. The results give new insights into the movement of a berthed ships subjected to waves. Response of the moored ship to different loading conditions in different water depths are discussed in this paper. The paper gives the order of energy due to first-order and slowly varying movement of a berthed container model in a towing tank.     

Modelling of the internal mechanics in ship collisions

A method for analysis of the structural damage due to ship collisions is developed. The method is based on the idealized structural unit method (ISUM). Longitudinal/transverse webs which connect the outer and the inner hulls are modelled by rectangular plate units. The responses are determined by taking into account yielding, crushing, and rupture. Some plates of the outer and the inner shell subjected to large membrane tensions are modelled by membrane tension triangular/rectangular plate units, while the remaining shell panels are modelled by the usual plate units. The effect of stiffeners on the stiffness and the strength is considered as well. In order to include the coupling effects between local and global failure of the structure, the usual non-linear finite-element technique is applied. In order to deal with the gap and contact conditions between the striking and the struck ships, gap/contact elements are employed. Dynamic effects are considered by inclusion of the influence of strain-rate sensitivity in the material model. On the basis of the theory a computer program has been written. The procedure is verified by a comparison of experimental results obtained from test models of double-skin plated structures in collision/grounding situations with the present solutions. As an illustrative example the procedure has been used for analyses of a side collision of a double-hull tanker. Several factors affecting ship collision response, namely the collision speed and the scantlings/ arrangements of strength members, are discussed.