Eventual stability of flooded ships

This paper deals with stability investigations of forced nonlinear rolling motion of a ship with a flooded compartment. The mathematical stability analysis has been realized in the sense of Eventual Stability. Two stability regions have been constructed through two Lyapunov functions generated by using Variable Gradient Method and the method of Puri. Having obtained stability conditions for the governing equations of the motion, dissipativeness of the motion, and maximum rolling angles have been obtained by using a theorem given by Bibikov and Sanovskii (1971).     

An Experimental Investigation on the Dynamic Response of a Damaged Ship with a realistic arrangement of the flooded compartment

The dynamics of a damaged ship in waves is a complex phenomenon regarding fluid and structure interactions. Flooded water motions in the damaged compartment could be influenced by decks, obstructions and obstacles in the compartment. This becomes particularly relevant in case of flooding in the engine room that is usually characterized by the presence of large objects such as engines and machineries. In such cases the possibility to better understand the behavior of a damaged ship, influenced by the fluid and structure interactions, could provide novel outcomes and thus enhance the damaged ship safety.In this paper an experimental campaign is conducted on a passenger ferry hull. The effects of obstacles in the engine room compartment, such as decks and engines, on ship roll responses, are studied. Roll decay in still water and steady roll responses in beam regular waves at zero speed are measured for the empty compartment and for the compartment with obstructions, as defined above.The main outcomes from the conducted experiments disclose a mitigation of the resonant behavior of the coupled system, ship with damaged compartment, by having engine shapes occupying the flooded engine room. Moreover it is possible to observe how the resonant frequency of the ship modifies having a more realistic arrangement of damaged compartment and how motion RAOs and roll decay characteristics modify accordingly.     

On the identification of ship coupled heave–pitch motions using neural networks

This paper outlines a procedure for the derivation of the differential equations describing the free response of a heaving and pitching ship from its stationary response to random waves. The coupled heave–pitch motion of a ship in random seas is modelled as a multi-dimensional Markov process. The partial differential equation describing the transition probability density function, known as the Fokker-Planck equation, for this process is derived. The Fokker-Planck equation is used to derive the random decrement equations for the coupled heave–pitch motion. The parameters in these equations are then identified using a neural network approach. The method is validated using numerical simulations and experimental results. The experimental data was obtained using an icebreaker ship model heaving and pitching in random waves. It is shown that the method produces good results when the system is lightly damped. An extension for using this method to identify couple heave–pitch motion in realistic seas is suggested.     

On the identification of ship coupled heave–pitch motions using neural networks

This paper outlines a procedure for the derivation of the differential equations describing the free response of a heaving and pitching ship from its stationary response to random waves. The coupled heave–pitch motion of a ship in random seas is modelled as a multi-dimensional Markov process. The partial differential equation describing the transition probability density function, known as the Fokker-Planck equation, for this process is derived. The Fokker-Planck equation is used to derive the random decrement equations for the coupled heave–pitch motion. The parameters in these equations are then identified using a neural network approach. The method is validated using numerical simulations and experimental results. The experimental data was obtained using an icebreaker ship model heaving and pitching in random waves. It is shown that the method produces good results when the system is lightly damped. An extension for using this method to identify couple heave–pitch motion in realistic seas is suggested.     

Motion Law of a Sphere in Bingham Fluid with Thixotropy

-The thixotropy properties and the motion law of a sphere in the Bingham fluid have been stu-died.Through observation of the settling motion of a single sphere in the Bingham fluid on the X-rayscreen,it has been discovered that the mud in estuaries and along sea bay,and the hyperconcentrated flowall behave as the Bingham fluid with thixotropy properties as the large sediment concentration.Throughderivation,the theoretical relationship between the yield stress and non-settling maximum sphere sup-ported by the stress for the Bingham fluid has been developed,the equations for calculating the increasingyield stress and the non-settling maximum sphere diameter with the duration at rest of the slurry have beenobtained.In consideration of the effect of thixotropy on fluid motion,the Navier-Stokes equation groupfor the Bingham thixotropy fluid has been developed.Through further study of the flow boundary condi-tion of settling motion of a single sphere in the Bingham thixotropy fluid,and the solving of theNavier     

Springing analysis of a seagoing vessel using fully coupled BEM-FEM in the time domain

The quasi-steady resonant vibration of a flexible seagoing vessel under resonant wave excitation force, called springing, is studied in this paper. A higher-order B-spline Rankine panel method is used to represent the effects of the fluid motion surrounding this flexible seagoing vessel, and a finite element formulation based on Vlasov beam is employed for structural response. The boundary integral equation and finite element equation, both for fluid and structural domains, are fully coupled with each other using an iterative implicit method in the time domain. Coupling between the two field equations is achieved by relying on fixed-point iteration with relaxation aided by Aitken's δ² process to maximize convergence speed. The steady-unsteady coupling term or m-term in the linearized body boundary condition derived by Timman and Newman is taken into account for accurate prediction of flexible body motion when forward speed is present. The 2nd derivative of basis potential in the m-term is obtained by modifying Nakos approach, which was originally developed using the Stokes theorem for rigid body ship motion problem. For the solution of the FE equation, instead of conventionally used modal superposition method, a direct integration scheme based on Newmark method is employed. It is believed that this technique is more attractive in the sense that it allows us free from the selection of optimum number of mode-shapes in the computation.     

The effect of nonlinear damping and restoring in ship rolling

Many researchers have studied a wide range of nonlinear equations of motion describing a ship rolling in waves. In this study, a form of nonlinear equation governing the motion of a rolling ship subjected to synchronous beam waves is suggested and solved by the generalized Duffing's method in the frequency domain. Various representations of damping and restoring terms found in the literature are investigated and their solutions are analyzed by the above-mentioned method. Comparative results of nonlinear roll responses are obtained for four distinct vessel types at resonance conditions which constitute the worst situation. The results indicate the importance of roll damping and restoring, when constructing a nonlinear roll model. An inappropriate selection of damping and restoring terms may lead to serious discrepancies with reality, especially in peak roll amplitudes.     

Design of passive anti-roll tanks for roll stabilization in the nonlinear range

The best way of reducing roll motion is by increasing roll damping. Bilge keels are the most common devices for increasing roll damping. If more control is required, anti-roll tanks and fins are used. Tanks have the advantage of being able to function when the ship is not underway. Our objective is to develop design procedures for passive tanks for roll reduction in rough seas. This paper focuses on the design of passive U-tube tanks. The tank-liquid equation of motion is integrated simultaneously with the six-degree-of-freedom (6DOF) equations of the ship motion. The coupled set of equations is solved by using the Large Amplitude Motion Program ‘LAMP’, which is a three-dimensional time-domain simulation of the motion of ships in waves. The unstabilized and stabilized roll motions of a S60-70 ship with forward speed and beam waves have been analyzed. For high-amplitude waves, the unstabilized roll angle exhibits typical nonlinear phenomena: a shift in the resonance frequency, multi-valued responses, and jumps. The performance of a S60-70 ship with a passive tank is investigated in various sea states with different encounter wave directions. It is found that passive anti-roll tanks tuned in the linear or nonlinear ranges are very effective in reducing the roll motion in the nonlinear range. The effect of the tank damping, frequency, and mass on the tank performance is studied. Also, it is found that passive anti-roll tanks are very effective in reducing the roll motion for ships having a pitch frequency that is nearly twice the roll frequency in sea states 5 and 6.     

Studies on Stochastic Parametric Roll of Ship with Stochastic Averaging Method

The paper studies the parametric stochastic roll motion in the random waves. The differential equation of the ship parametric roll under random wave is established with considering the nonlinear damping and ship speed. Random sea surface is treated as a narrow-band stochastic process, and the stochastic parametric excitation is studied based on the effective wave theory. The nonlinear restored arm function obtained from the numerical simulation is expressed as the approximate analytic function. By using the stochastic averaging method, the differential equation of motion is transformed into Ito's stochastic differential equation. The steady-state probability density function of roll motion is obtained, and the results are validated with the numerical simulation and model test.     

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.     

波浪作用下缆船拖带系统非线性运动数值模拟

基于船舶操纵性运动方程和拖缆的三维动力学运动方程,提出了被拖点位置匹配的方法,建立了拖船—拖缆—被拖船系统整体非线性拖带动力学模型。为了考察被拖船航向稳定性与横向稳性的关系以及波浪载荷作用的影响,被拖船采用水平面四自由度运动方程,并引入了波浪的作用力和力矩。拖船采用PD控制方法较真实地模拟了拖船航向改变的运动过程。对一个拖船—拖缆—被拖船系统(5 000 t的拖船和3 000 t的被拖船)在时域内进行了规则波浪作用下拖带运动的模拟,计算结果表明被拖带船舶在波浪中运动呈现运动稳定、不稳定和临界状态3种可能的特性。根据模拟计算结果,认为波浪中拖带航向稳定是被拖带船舶保持稳性的必要条件。     

Hadley and Rossby regimes in a simple model of convection of a rotating fluid

This paper analyzes the properties of solutions to the equations describing the motion of a stratified fluid in the class of velocity and temperature fields linear in coordinates. For an ideal fluid, these equations, on the one hand, are exact for the corresponding hydrodynamic problem and, on the other hand, are identical to the equations of motion for a heavy top. In a conservative case, the equations of motion of a top share common solutions with the equations of geophysical fluid dynamics and reproduce motions similar to those existing in the theory of the large-scale atmospheric circulation. This study considers the effects of viscosity and heat conduction in the fluid, which are, in a sense, similar to the effect of friction in the case of a top. The influence of deflections of the vectors of gravity and external rotation from their standard directions for a plane-parallel atmosphere is also considered. The regimes of motions that are described by the starting equations and approximations commonly used to model the atmospheric general circulation (the quasi-geostrophic approximation) are analyzed. It is shown that these equations correctly describe the Hadley and Rossby circulation regimes and transitions between them that are observed in numerical and laboratory experiments. Particular attention is given to the consistency between different regimes of the exact equations and their quasi-geostrophic approximations, which is manifested for small Rossby numbers and is generally absent for large Rossby numbers. The asymptotic behaviors of the curves of transition between the Hadley and Rossby regimes under the conditions of breaking the external symmetry of flows are obtained. These asymptotics explain the corresponding transition boundaries for the regimes observed in the known experiments in annuluses.     

System-based investigation on 4-DOF ship maneuvering with hydrodynamic derivatives determined by RANS simulation of captive model tests

For the non-negligible roll-coupling effect on ship maneuvering motion, a system-based method is used to investigate 4-DOF ship maneuvering motion in calm water for the ONR tumblehome model. A 4-DOF MMG model is employed to describe ship maneuvering motion including surge, sway, roll, and yaw. Simulations of circular motion test, static drift and heel tests are performed by solving the Reynolds-averaged Navier-Stokes (RANS) equations, after a convergence study quantifying the necessary grid spacing and time step to resolve the flow field adequately. The local flow field is analyzed for the selected cases, and the global hydrodynamic forces acting on the ship model are compared with the available experiment data. Hydrodynamic derivatives relating to sway velocity, yaw rate, and heel angle are computed from the computed force/moment data using least square method, showing good agreement with those obtained from EFD data overall. In order to investigate further the validity of these derivatives, turning circle and zigzag tests are simulated by using the 4-DOF MMG model with these derivatives. The trajectories and the time histories of the kinematic variables show satisfactory agreement with the data of free-running model tests, indicating that the system-based method coupled with CFD simulation has promising capability to predict the 4-DOF ship maneuvering motion for the unconventional vessel.     

船舶随浪运动稳性仿真计算

本文利用Ｌｉａｐｕｎｏｖ理论，研究了船舶在规则波浪运动的稳性；利用摄动理论，求解出船舶运动响应；并讨论了船舶横摇与垂荡运动频率、最大横摇角和波浪要素对稳性曲线ＧＺ的影响，以及流体动压力对稳性曲线的修正，从而给计算船舶在随浪中的稳性提供了一种方法。     

Unsteady ship waves in shallow water of varying depth based on Green–Naghdi equation

Based on Green–Naghdi equation this work studies unsteady ship waves in shallow water of varying depth. A moving ship is regarded as a moving pressure disturbance on free surface. The moving pressure is incorporated into the Green–Naghdi equation to formulate forcing of ship waves in shallow water. The frequency dispersion term of the Green–Naghdi equation accounts for the effects of finite water depth on ship waves. A wave equation model and the finite element method (WE/FEM) are adopted to solve the Green–Naghdi equation. The numerical examples of a Series 60 (C_B=0.6) ship moving in shallow water are presented. Three-dimensional ship wave profiles and wave resistance are given when the ship moves in shallow water with a bed bump (or a trench). The numerical results indicate that the wave resistance increases first, then decreases, and finally returns to normal value as the ship passes a bed bump. A comparison between the numerical results predicted by the Green–Naghdi equation and the shallow water equations is made. It is found that the wave resistance predicted by the Green–Naghdi equation is larger than that predicted by the shallow water equations in subcritical flow , and the Green–Naghdi equation and the shallow water equations predict almost the same wave resistance when , the frequency dispersion can be neglected in supercritical flows.     

Numerical analysis of a propeller during heave motion in cavitating flow

In practical maritime conditions, ship hulls experience heave motion due to the action of waves, which can further drive the ship’s propellers to oscillate relative to the surrounding water. In order to investigate the motion of a propeller working behind a surface vessel sailing in waves, a numerical simulation is conducted on a propeller impacted by heave motion in cavitating flow using the Reynolds-averaged Navier-Stokes (RANS) method. The coupling of the propeller’s rotation and translation is fulfilled using equations of motion defined for this purpose. The heave motion is simplified as a periodic motion based on a sinusoidal function. The numerical transmission of information from the unsteady flow field is achieved using the overset grid approach. In this manner, the unsteady thrust coefficient and torque coefficient of propellers in different periods of heave motion are analyzed. A comparative study is implemented on the unsteady cavitation performance and wake characteristics of propeller. With the propeller’s heave motion, the flow field non-uniformity constantly changes the load on the propeller during each revolution period and each heaving period, the propeller load and the wake field are closely related to the variation of heave motion period. The results obtained from the numerical simulation are expected to serve as a useful theoretical reference for the numerical analysis of a propeller in a heave motion.     

Estimation of survival probability for a ship in beam seas using the safe basin

The purpose of this paper is to analyze the nonlinear ship roll motion equation and the main parameters that induce ship capsizing in beam seas, estimate the survival probability of a ferry in random seas and to find out a risk assessment method for the ship’s intact stability. A single degree of freedom (1-DOF) dynamic system of ship rolling in beam seas is investigated and the nonlinear differential equation is solved in the time domain by the fourth order Runge-Kutta algorithm. The survival probability of a ferry in beam seas is investigated using the theory of “safe basin”. The survival probability is calculated by estimating erosion of “safe basin” during ship rolling motion by Monte Carlo simulations. From the results it can be concluded that the survival probability of a ship in beam sea condition can be predicted by combining Monte Carlo simulations and the theory of “safe basin”.     

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 time-domain method to evaluate the use of moving weights to reduce the roll motion of a ship

A method to evaluate the use of actively controlled moving weights on board ships to reduce roll motion is developed. The weights can simulate in principle anti-roll-tank systems, or they can be considered a possible anti-roll device in their own right. The ship, the moving weight, and the control device are considered components of a single dynamic system. The full eight-degree-of-freedom set of coupled governing equations for the complete dynamic system is derived. And a three-degree-of-freedom non-linear approximation for the roll motion only (MOTSIM) is derived from these eight equations. The reduced set of equations is used to determine the influence of various parameters and to evaluate control strategies. A PID controller is developed to command the position of the weight and a servomechanism model is used to predict its actual position. Then, the moving-weight system is incorporated into LAMP (Large–Amplitude–Motion Program), a computer code that integrates the governing equations of the sea and the motion of the ship interactively and simultaneously and predicts the motion of the ship in the time domain. A comparison of the results from the two simulations shows that there is fairly good correlation between the simple and complex models, but the simple model is a little optimistic in predicting the effectiveness of the moving-weight system. The results predict that the moving-weight system can be an excellent roll-suppressing device when the moving weight is as small as 1% of the displacement of the ship and the maximum distance the weight moves is as small as 15% of the half-beam.     

Numerical study of propagation of ship waves on a sloping coast

The aim of this paper is to investigate the propagation of ship waves on a sloping coast on the basis of results simulated by a 2D model. The governing equations used for the present model are the improved Boussinesq-type equations. The wave breaking process is parameterized by adding a dissipation term to the depth-integrated momentum equation. To give the boundary conditions at the ship location, the slender-ship approximation is used. It was verified that, although ship waves are essentially transient, the Snell's law can be applied to predict crest orientation of the wake system on a sloping coast. Based on simulated results, an applicable empirical formula to predict the maximum wave height on the slope is introduced. The maximum wave height estimated by the proposed method agrees well with numerical simulation results.