Stability of small fishing vessels in longitudinal waves

The dynamic stability of fishing vessels in longitudinal regular waves is investigated, both analytically and experimentally. In particular, the influence of stern shape on the parametric stability of fishing vessels is studied. Vessels TS and RS have very similar main characteristics, but their sterns are different. Although their linear responses are comparable, both analytical and experimental investigations indicate substantial differences in their dynamic stability in longitudinal regular waves. Strong resonances are found for the vessel with the deep transom. The analytical method takes into consideration the effects of the heave and pitch motions and wave passage and shows good agreement with experimental results. Stability limits are obtained for different conditions and are used as an aid in the discussion of the results obtained in the tests when relevant parameters are changed, such as wave amplitude and frequency, metacentric height and roll damping moment.     

Influence of non-linearities on the limits of stability of ships rolling in head seas

The present paper describes an investigation on parametric resonance in head seas in which a new third-order coupled mathematical model is considered. The restored modes of heave, roll and pitch are contemplated. The discussion is illustrated for the case of a transom stern fishing vessel at different speeds. It is pointed out that numerical simulations employing the new model are successfully compared to experimental results previously obtained for the vessel.Considering that analyticity is an important tool when handling complex stability issues, some theoretical dynamic characteristics of the equations are discussed. By means of the analysis of the coupled linear variational equation derived from an extended third-order model, the appearance of super-harmonics and increased rigidity proportional to wave amplitude squared due to third-order terms is demonstrated.In the present paper, an important tool is explored, that is the analysis of the limits of stability obtained from the new model. Limits of stability are a well-known and practical way of looking into the problem of parametric resonance. New limits of stability are derived and compared to the more conventional Strut diagram. Dynamic characteristics associated with the new limits of stability are discussed. The influence of different parameters is investigated, including vessel speed, damping and tuning. Consistent and revealing results are obtained through the analysis of the new limits of stability for different speeds and damping.     

Application of the extended Melnikov's method for single-degree-of-freedom vessel roll motion

Traditionally, when using Melnikov's method to analyze ship motions, the damping terms are treated as small. This is typically true for roll motion but not always true for other and/or multiple degrees of freedom. In order to apply Melnikov's method to other and/or multiple-degree-of-freedom motions, the small damping assumption must be addressed. In this paper, the extended Melnikov method is used to analyze ship motion without the constraint of small linear damping. Two roll motion models are analyzed here. One is a simple roll model with nonlinear damping and cubic restoring moment. The other is the model with biased restoring moment. Numerical simulations are investigated for both models. The effectiveness and accuracy of this method is demonstrated.     

A nonlinear model of parametric rolling stabilization by anti-roll tanks

The present paper describes a mathematical model in which the fluid motion inside a U-tank is nonlinearly coupled to the heave, roll and pitch motions of the ship. The main purpose of the investigation is centred on the control of roll motion in the case of parametric resonance in longitudinal waves. A transom stern small vessel, known to be quite prone to parametric amplification, is employed in the study. Four tank designs are employed in order to study the influence of tank mass, tank natural frequency and tank internal damping on the control of parametric rolling at different head seas conditions. Additionally, the influence of the vertical position of the tank is also investigated. The main results are presented in the form of limits of stability, with encounter frequency and wave amplitudes as parameters. Distinct dynamical characteristics are discussed and conclusions are drawn on the relevant parameters for the efficient control of the roll amplifications in head seas.     

Designing against parametric instability in following seas

We investigate the characteristics of parametric instability when very large variations of restoring between the wave trough and the wave crest are taking place, creating a restoring that is alternating between negative (or nearly negative) and strongly positive values. The possible ways to consider the nonlinearities in damping and in restoring are discussed in detail. The boundary separating parametric instability from pure-loss is identified. In depth studies are carried out to ascertain the practical relevance of the parametric mechanism. Instability regions are identified in terms of transient motions, rather than in terms of the customary asymptotic stability chart associated with Mathieu's equation. A basis for comparing parametric roll behavior for different representations of restoring is established. Asymmetric variation laws and bi-chromatic waves are considered.     

On unstable ship motions resulting from strong non-linear coupling

In this paper, the modelling of strong parametric resonance in head seas is investigated. Non-linear equations of ship motions in waves describing the couplings between heave, roll and pitch are contemplated. A third-order mathematical model is introduced, aimed at describing strong parametric excitation associated with cyclic changes of the ship restoring characteristics. A derivative model is employed to describe the coupled restoring actions up to third order. Non-linear coupling coefficients are analytically derived in terms of hull form characteristics.The main theoretical aspects of the new model are discussed. Numerical simulations obtained from the derived third-order non-linear mathematical model are compared to experimental results, corresponding to excessive motions of the model of a transom stern fishing vessel in head seas. It is shown that this enhanced model gives very realistic results and a much better comparison with the experiments than a second-order model.     

Roll performance of a small fishing vessel with live fish tank

The concept of live fish tanks in trawlers is to use the catch in a better condition and to reduce marine pollution. It also reduces the infrastructure meant to freeze the catch to preserve it for longer period. But the presence of additional free surface in the vessel challenges the stability of the vessel. This is besides the sloshing effect due to the moving liquid mass in the tank. Roll motions are initiated due to various factors related to the hull characteristics of the vessel, loading and operating conditions and its interaction with the environment. Location of fish tank, its orientation, arrangement of baffles inside the tank to reduce the free surface affects and careful design of tank opening are to be given priority during the design, manufacturing and tank testing. The results obtained from tank test of model are compared with that of analytical method. The non-linear roll performance become further complicated due to the free surface and sloshing effects of the mass in the live fish tank. Wave makers are used for generating waves under laboratory conditions compatible with the scaled down model of the trawler model. The tests are conducted in the towing tank of Pusan National University.     

Theoretical, numerical and experimental study on the problem of ergodicity and ‘practical ergodicity’ with an application to parametric roll in longitudinal long crested irregular sea

This paper addresses the problem of ergodicity of stochastic processes starting from a theoretical point of view, with the aim of obtaining a deeper understanding for practical applications. The problem is tackled bearing in mind the concept of ‘practical ergodicity’, that is, the possibility of obtaining reliable information about ensemble averages by using temporal averages. Some general analytical tools are given to address the problem of accuracy of temporal averages and an example of their use in a possible design of experiments is given. A series of Monte Carlo numerical simulations are performed by means of an analytical non-linear 1.5-DOF model of parametrically excited roll motion. The outcomes of such simulations are analysed to show the effect of ship speed and sea spectrum shape. The effect of wave grouping phenomenon is discussed with particular attention to the Doppler effect. Qualitative indications given by the numerical simulations are then compared with experimental tests showing a good agreement. Practical ergodicity of generated sea in towing tank is also briefly addressed.     

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.     

Roll damping characteristics of a small fishing vessel with a central wing

The roll damping characteristics of three models of a 3-ton class fishing vessel representing the bare hull, hull with bilge keels, and hull with bilge keels and a central wing are investigated by the free roll decay tests in calm water and also in uniform head waves in a towing tank. Speed and roll initial angle and OG (distance between the centers of gravity and roll) are varied to check their dependence on roll damping. The experimental results are compared with the numerical results of mathematical modeling by the energy method and the energy dissipation patterns are also compared for these three models. The bilge keel contributes significantly to the increment of the roll damping for zero speed but as speed increases, the lift generated by the central wing contributes significantly to the roll damping increase. In addition, it is shown that the roll damping is more or less influenced by the regular head waves.     

Theoretical and experimental study on dynamic behavior of a damaged ship in waves

Most of the large scaled casualties are caused by loss of structural strength and stability due to the progressive flooding and the effect of waves and wind. To prevent foundering and structural failure, it is necessary to predict the motion of the damaged ship in waves.This paper describes the motion of damaged ship in waves resulting from a theoretical and experimental study. A time domain theoretical model, which can be applied to any type of ship or arrangement, for the prediction of damaged ship motion and accidental flooding has been developed considering the effects of flooding of compartments. To evaluate the accuracy of the model, model tests are carried out in ship motion basin for three different damaged conditions: engine room bottom damage, side shell damage and bow visor damage of Ro–Ro ship in regular and irregular waves with different wave heights and directions.     

Head-wave parametric rolling of a surface combatant

Complementary CFD, towing tank EFD, and nonlinear dynamics approach study of parametric roll for the ONR Tumblehome surface combatant both with and without bilge keels is presented. The investigations without bilge keels include a wide range of conditions. CFD closely agrees with EFD for resistance, sinkage, and trim except for Fr>0.5 which may be due to free surface and/or turbulence modeling. CFD shows fairly close agreement with EFD for forward-speed roll decay in calm water, although damping is over/under predicted for largest/smaller GM. Most importantly CFD shows remarkably close agreement with EFD for forward-speed parametric roll in head waves for GM=0.038 and 0.033 m, although CFD predicts larger instability zones at high and low Fr, respectively. The CFD and EFD results are analyzed with consideration ship motion theory and compared with Mathieu equation and nonlinear dynamics approaches. Nonlinear dynamics approaches are in qualitative agreement with CFD and EFD. The CFD and nonlinear dynamics approach results were blind in that the actual EFD radius of gyration k_xx was not known a priori.     

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.     

Improved prediction of the threshold of surf-riding of a ship in steep following seas

An extended version of Melnikov's method is implemented in order to predict more accurately the threshold of global surf-riding for a ship operating in steep following seas. The key advantage of the proposed method is that it overcomes the limitation of small damping and/or small forcing that are intrinsic to the implementation of the standard Melnikov's method. A reference ITTC ship is used here by way of example and the result is compared to that obtained from standard analysis as well as numerical simulations. Because of the primary drawback of the extended Melnikov's method is the inability to arrive at a closed form equation, in this work the authors arrive at a “best fit” approximation to the extended Melnikov numerically predicted result.     

CFD, system-based and EFD study of ship dynamic instability events: Surf-riding, periodic motion, and broaching

CFD and system-based simulation are used to predict broaching, surf-riding, and periodic motion for the ONR Tumblehome model, including captive and free model test validation studies. CFD shows close agreement with EFD for calm water resistance, static heel (except for sway force and yaw moment), and static drift (except for roll moment). CFD predictions of static heel in following waves also compare well with EFD except for surge force, sway force, and pitch angle. Froude-Krylov calculations of wave-induced surge force in following waves provides good agreement for high Froude number, but significantly overestimates for Froude number less than 0.2. On the other hand, CFD successfully reproduces the reduction of the wave-induced surge force near Froude number 0.2, probably because CFD can capture the 3D wave pattern. CFD free model simulations are performed for several speeds and headings and validated for the first time for surf-riding, broaching, and periodic motions. System-based simulations are carried out based on inputs from EFD, CFD, and Froude-Krylov for a dense grid of speeds and headings to predict the instability map, which were found to produce fairly similar results.     

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.     

Design of the roll stabilization controller, using fin stabilizers and pod propellers

Ships experience roll motion due to waves in a seaway. Therefore, fin stabilizers are installed to stabilize such roll motion. A fin stabilizer is effective at reducing the roll motion at moderate speeds but not at low speeds. Recently, pod propellers have been used with fin stabilizers for roll stabilization. In the paper, a MIMO (multi-input multi-output) optimal control system that has two control inputs such as fin stabilizers and pod propellers is designed. The LQR (linear quadratic regulator) control algorithm is applied to reduce the roll motion of cruise ships in regular waves. Also, the nominal plant and the frequency-weighted LQR are applied to reduce the roll motion in irregular waves. The roll motion of cruise ships is effectively reduced when the fin and pod propeller are used as the control actuators at low speeds. The optimal control gain is easily found when the frequency-weighted LQR is applied.     

随机波浪下Truss Spar平台垂荡运动时域分析

研究Truss Spar平台在随机波浪下的垂荡运动特性。采用ITTC双参数谱,考虑绕射作用,数值计算了平台所受的随机波浪力。利用已有的水动力试验和数值模拟结果及Morison方程,估计了Truss Spar平台垂荡方向的附加质量和粘滞阻尼大小。考虑非线性阻尼和瞬时波面的影响,运用Runge-Kutta数值迭代算法,比较了不同随机波浪参数对平台运动响应的影响,特别是波浪特征周期接近垂荡固有周期时。结果表明,当波浪特征周期接近平台垂荡固有周期时,平台产生大幅垂荡运动,频域的运动分析结果比时域结果偏小。     

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.