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.     

Identification of hydrodynamic coefficients in ship maneuvering equations of motion by Estimation-Before-Modeling technique

Estimation-Before-Modeling (EBM) technique (or the two-step method) is a system identification method that estimates parameters in a dynamic model. Given sea trial data, the extended Kalman filter and modified Bryson–Frazier smoother can be used to estimate motion variables, hydrodynamic force, and the speed and the direction of current. And using these estimated data, we can use the ridge regression method to estimate the hydrodynamic coefficients in a model. An identifiable state space model is constructed in case that current effect is included and the maneuvering characteristics of a ship are analyzed by correlation analysis. To better identify hydrodynamic coefficients, we suggest the sub-optimal input scenario that considers the D-optimal criterion. Finally, the algorithm is confirmed against real sea trial data of 113K tanker.     

On damping models in free and forced rolling motion

In this paper two different models for the damping moment to introduce in the rolling equation of the ship are proposed. They contain two terms, respectively linear-quadratic and linear-cubic in the angular velocity, and furthermore they foresee a non-linear term representing the dependence of the damping from the heeling angle. These models constitute a generalization of all the models up to now used in the naval literature.With the Bogoliubov-Krilov asymptotic method approximate relations, describing the decay curve of the free oscillations and the maximum roll amplitude in synchronism condition, are obtained. The analysis shows that the choice of the more realistic damping model cannot be based on the simple verification of a good fitting of the free oscillation decay curves. It is necessary to examine also the behaviour of the forced oscillations in synchronism.Finally, a plan of experiments which allows the determination of separate values for the different non-linear damping coefficients is proposed.     

Numerical analysis on ship maneuvering coupled with ship motion in waves

This paper considers a numerical analysis of ship maneuvering performance in the presence of incident waves and resultant ship motion responses. To this end, a time-domain ship motion program is developed to solve the wave–body interaction problem with the ship slip speed and rotation, and it is coupled with a modular-type 4-DOF maneuvering problem. In this coupled problem, the second-order mean drift force, which can play an important role in the ship maneuvering trajectory, is estimated by using a direct pressure integration method. The developed method is validated by observing the second-order mean drift force, and planar trajectories in maneuvering tests with and without the presence of incident waves. The comparisons are made for two ship models, Series 60 with block coefficient 0.7 and the S-175 containership, with existing experimental data. The maneuvering tests observed in this study include a zig-zag test in calm water, and turning tests in calm water and in regular waves. The present results show a fair agreement of overall tendency in maneuvering trajectories.     

Effects of ship motion on a neutrally-stable towed fish

Digital computer simulation in two dimensions of a neutrally-stable fish towed on a faired cable has been used to investigate the response of the fish to disturbances in the ship motion. The numerical methods used are described broadly, excluding mathematical detail, and selected results are presented which indicate typical behaviour of the system.The free oscillations of the fish-cable system and its response to deterministic and random ship disturbances are investigated. This reveals the dynamic principles governing the motion and allows the formulation of simple rules to give a first approximation to the magnitude of the fish response. It is shown that, provided resonances of the ship and fish-cable system do not coincide, the overall amplitude of motion of the fish is proportional to the sine of the angle made by the top of the cable with the horizontal. Formulae are given for calculating approximately the resonant frequencies of the towed system.     

A study of the ship induced roll-yaw motion of a heavy towed fish

The lateral motions of roll, yaw and sway of a heavy towed fish are investigated. Perturbation lateral ship motion propagates down the cable as a damped wave and non-dimensional tables are provided that allow the attenuation of the motion to be estimated. The tables are supplemented by a short BASIC computer program for calculations outside the tabular range.Three-dimensional dynamic simulation of the Bath Mk 3 Sonar Fish is used to establish the effects of fish weight, towstaff length and vertical fin size on the amplitude of rolling and yawing motion. It is shown that very careful adjustment of fin size can reduce the amplitude of yawing motion by a factor of about 3. It is also shown that attaching the cable to the fish with a towstaff free to pivot only in pitch improves the towing properties of the fish and reduces the amplitude of rolling motion.     

Application of extended state space to nonlinear ship rolling

It is well known in the field of marine hydrodynamics that the added mass, damping and wave exciting forces are functions of frequency (Newman, 1977. Marine Hydrodynamics. MIT Press, Cambridge). Although most previous studies of nonlinear ship rolling motion have assumed that these forces do not vary with frequency, in this study the frequency dependent added mass and damping coefficients are approximated in the time domain with extended state space variables. Using numerical time simulation (integration), the extended state space model is compared to the constant coefficient model with a constant frequency forcing and the results for two constant value approximations of the added mass and damping are compared to the extended state space model with a multiple component pseudo random forcing.     

Experimental studies of a damaged ship section in forced heave motion

This work documents a detailed series of experiments performed in a wave flume on a thin walled prismatic hull form. The model consists of a rectangular opening located on the side. The length of the model is slightly smaller than the flume breadth to achieve two-dimensional (2D) behavior in the experiments. Forced oscillatory heave tests in calm water have been carried out by varying the model-motion parameters and examining both intact and damaged conditions. Video recordings, measurements of the wave elevation inside the damaged compartment and of the force on the model were performed in all the experiments. The effect of damage opening in the model on hydrodynamic loads is examined by comparing with an intact section. A theoretical analysis is used to explain the behavior of added mass and damping coefficients in heave for a 2D damaged section. The presented results demonstrate occurrence of sloshing and piston mode resonances in the tests and their influence on the hydrodynamics loads of a damaged ship. Detailed physical investigations are presented at these resonance frequencies for the damaged section. Effect of filling level in the damage compartment, damage-opening length and air compressibility in the airtight compartment is examined. Nonlinear effects are documented and appear dominant, especially, for lowest filling level where we have shallow-water depth conditions in the damaged compartment. Resonance phenomena that can lead to significant local loads are identified for the shallow water condition. Air compressibility in the airtight compartment and floodwater act as a coupled system and influence inflow/outflow of floodwater in the compartment. It has a significant effect on local floodwater behavior in the damaged compartment.     

Application of extended state space to nonlinear ship rolling

It is well known in the field of marine hydrodynamics that the added mass, damping and wave exciting forces are functions of frequency (Newman, 1977. Marine Hydrodynamics. MIT Press, Cambridge). Although most previous studies of nonlinear ship rolling motion have assumed that these forces do not vary with frequency, in this study the frequency dependent added mass and damping coefficients are approximated in the time domain with extended state space variables. Using numerical time simulation (integration), the extended state space model is compared to the constant coefficient model with a constant frequency forcing and the results for two constant value approximations of the added mass and damping are compared to the extended state space model with a multiple component pseudo random forcing.     

Assessment of direct determination uncertainties of incoming radiation fluxes associated with the ship motion

The paper considers the impact of ship oscillations on the accuracy of radiation flux measurements in the absence of a gyroplatform and a gimbal suspension. As an example, we discuss the simultaneous determinations of the radiation fluxes and careen during the 20th mission of the R/V Akademik Joffe. A sampling rate of 10 s was found to be sufficient to neglect the careen when estimating the hourly sums of the short-wave solar radiation at sun heights exceeding 10°. At smaller sun heights, the careen is able to effect the estimates of the solar radiation within 20%. Due to the harmonic nature of such oscillations, these errors tend to become low against the instrumental accuracy if one deals with the hourly and daily means of the short-wave solar radiation fluxes during sufficiently long observations. In addition, a significant effect occurs at rather low sun and a sea roughness of Beaufort number 4 or higher. A rough sea is usually associated with the diminishing of the clear sky area and the higher repeatability of the cloudiness conditions, which reduces the effect of rolling upon the measurement accuracy.     

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.     

Stochastic rolling motion of ships in following seas

The aim of this study is to examine both the stochastic rolling motion of ships in following seas by using analytical and numerical safe basin concept and to show how the concept of safe basin can be utilized for the assessment of the stability of ships. First, the boundary of the analytic safe basins of stochastic rolling motion is obtained by using the Lyapunov function used by Schurz (2009). Second, the safe basins of stochastic rolling motion are obtained numerically by using stochastic Euler (Euler–Maruyama) method. It is concluded that the analytically and numerically obtained safe basins are coherent. Lastly, the practical intact stability criterion for ships in following seaway is developed by proposing a formula given for the maximum width of analytic safe basin.     

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.     

Parametric estimation of ship maneuvering motion with integral sample structure for identification

This documentation presents the parametric identification modeling of ship maneuvering motion with integral sample structure for identification (ISSI) and Euler sample structure for identification (ESSI) based on least square support vector machines (LS-SVM), where ISSI is used for the construction of in–out sample pairs. By using Mariner Class Vessel, the sample dataset are obtained from 15°/15° zigzag maneuvering simulation based on Abkowitz model. By analyzing the simulation data including rudder angle, surge velocity, sway velocity, yaw rate and so forth, the hydrodynamic derivatives in Abkowitz model are all identified. The validation of the proposed identification algorithm is verified by the high precisions of the identified hydrodynamic derivatives and maneuvering prediction results. The comparison is also conducted between the proposed ISSI and the conventional Euler sample structure for identification (ESSI), and the experimental results shows that ISSI is much more appropriate for parametric identification modeling of ship maneuvering motion.     

船舶在随机波浪中操纵运动预报

将船舶操纵运动模型和船舶耐波性理论结合起来,建立了适用于求解船舶在随机波浪中运动的六自由度数学模型.该模型采用水平随船坐标系,与操纵运动有关的水动力采用经验公式估算;与耐波性相关的水动力除二阶力外采用从频域到时域的方法,其中一阶波浪力通过脉冲响应函数的卷积求取,记忆效应力由时延函数的卷积表示;对于二阶波浪力则只考虑其定常部分.最后,应用该模型对一艘集装箱船在静水、规则波、随机波下的回转运动进行了预报,并就波浪对回转运动的影响做了讨论.认为一阶力对船舶操纵运动影响不明显;在考察波浪对船舶操纵运动的影响,必须考虑二阶力的作用.     

Hydrodynamic derivatives and motion response of a submersible surface ship in unbounded water

A submersible surface ship (SSS) is based on a novel concept that the SSS goes on surface like conventional ships in moderate seas but goes underwater in rough seas to the depth sufficient to avoid wave effects. The SSS has a wing system that produces downward lift to go underwater with preserving the residual buoyancy for its safety. The SSS is expected to be able to keep both safety and punctuality even if it encounters unexpected bad weather.The motion of the SSS is studied. The equations of motion are formulated and the procedures for estimating hydrodynamic derivatives are presented. The hydrodynamic derivatives are estimated for a SSS having a configuration, a hull with a pair of main wings and a pair of horizontal tail wings. Using these estimated hydrodynamic derivatives, calculation of the SSS motion is carried out.The calculation results show some specific aspects of the SSS especially for effects of the elevator of main wings and horizontal tail wings, aileron of main wings, rudder and propeller revolution. It is confirmed that the existence of static roll restoring moment and having large hull comparing with wing area play important roles in the motion of the SSS.     

Study on coupling effects of ship motion and sloshing

This study considers the coupling effects of ship motion and sloshing. The linear ship motion is solved using an impulse-response-function (IRF) method, while the nonlinear sloshing flow is simulated using a finite-difference method. The IRF method requires the frequency-domain solution prior to conversion to time domain, but the computational effort is much less than that of direct time-domain approaches. The developed scheme is verified by comparing the motion RAOs between the frequency-domain solution and the solution obtained by the IRF method. Furthermore, a soft-spring concept and linear roll damping are implemented to predict more realistic motions of surge, sway, yaw, and roll. For the simulation of sloshing flow in liquid tanks, a physics-based numerical approach adopted by Kim [2001. Numerical simulation of sloshing flows with impact load. Applied Ocean Research 23, 53–62] and Kim et al. [2004. Numerical study on slosh-induced impact pressures on three-dimensional prismatic tanks. Applied Ocean Research 26, 213–226] is applied. In particular, the present method focuses on the simulation of the global motion of sloshing flow, ignoring some local phenomena. The sloshing-induced forces and moments are added to wave-excitation forces and moments, and then the corresponding body motion is obtained. The developed schemes are applied for two problems: the sway motion of a box-type barge with rectangular tanks and the roll motion of a modified S175 hull with rectangular anti-rolling tank. Motion RAOs are compared with existing results, showing fair agreement. It is found that the nonlinearity of sloshing flow is very important in coupling analysis. Due to the nonlinearity of sloshing flow, ship motion shows a strong sensitivity to wave slope.     

The adjustment of fin size to minimise the ship induced pitching motion of a towed fish

The hydrodynamic forces and moments that act on a towed fish are described and related to fundamental static and dynamic towing characteristics. It is shown that, when the fin height is reduced almost to the point giving neutral stability in pitch, the fish maintains almost constant pitch attitude while it is forced to heave or surge by ship motion transmitted down the cable.Wind tunnel tests provide the necessary hydrodynamic data for a computer simulation in two dimensions of the Bath Mk 3 sonar fish towed on faired cable. The results show that the magnitude of the pitch attitude variations of the fish can be greatly reduced by decreasing the fin size, with further reduction being possible by correctly locating the pointwhere the cable is attached to the fish. It is also shown that decreasing the fin size reduces the magnitude of the tension variations in the cable, thereby lowering the probability that the cable will go slack.These results generalise to a large class of towed systems using either or bare cable, and a formula is included by which the magnitude of the ship-inducing pitching motion of a fish can be estimated, given the necessary hydrodynamic data.Possible difficulties associated with towing a low stability fish are considered and a method is included for assessing the minimum stability likely to be necessary to achieved satisfactory towing behaviour.     

Transformed equations of motion for underwater vehicles

A method for dynamics investigation and coupling detection between velocities of autonomous underwater vehicles (AUVs) is presented in this paper. The method is based on transformation of equations of motion, which are usually used for an underwater vehicle, into equations with a diagonal mass matrix. The obtained equations contain quasi-velocities and allow one to give a further insight into the AUV dynamics especially for an underactuated system. Some advantages of the proposed approach are discussed, too. An analytical example for a 3-DOF AUV shows possible application of the transformed equations. Moreover, the given approach is validated via simulation on a 6-DOF vehicle.     

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.