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.     

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.     

Prediction potential of the parametric rolling behaviour of a post-panamax containership

A systematic investigation on the prediction of parametric rolling exhibited by a post-panamax containership is described, on the basis of several techniques. Analytical formulae that appear in current industrial guidelines are evaluated in a step-by-step process against various numerical predictions. The method of continuation of nonlinear dynamics is introduced in order to expedite the identification of the instability boundary and the prediction of steady amplitudes of roll oscillation. A well-known panel code is shown to be capable of reproducing parametric roll growth.     

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.     

On the parametric resonance of container ships

This work deals with parametric resonance which poses a great danger especially for container ships sailing in following or head seas. Important parameters that are effective in roll resonance are pointed out. For this purpose, a containership is taken as an example to analyze its stability in longitudinal waves based on the method worked out by American Bureau of Shipping (ABS). Unfavorable sailing conditions such as heading and speed, which directly depend on the environmental conditions, have been determined for this particular ship. These conditions may be reported to the master to guide him to keep his ship out of parametric resonance zones. Numerical details of the procedure have been worked out and provided as well.     

Simplified model for predicting the onset of parametric rolling

The world container fleet shows the fastest growth of any ship type. The infrastructure for loading and unloading container ships are also growing in many ports around the world. Such a trend is due to the fact that the containerized transportation is becoming more and more attractive due to many factors. The increasing demand in container transportation is met by use of more number of container ships including Post-Panamax and Malacca-max containers. Loss of containers in seas and accidents of container vessels are reported from many parts of seas. New generation containers are severely hit by parametric rolling. Pure loss of stability, due to exponential increase of roll in either broaching—to or head sea conditions, is called parametric rolling, is subjected to rigorous investigation by many researchers. Algebraic expression based on well known Duffing's method is proposed for solutions in parametric rolling. The variation in GM and damping values from trough to crest conditions associated with bow flare immersion and emergence in head sea conditions with pitch resonance with the heading waves are said to be the prime reason for parametric rolling. A simple model to predict the beginning of parametric rolling is described in this paper.     

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.     

Analysis of roll motion and stability of a fishing vessel in head seas

The present paper describes an investigation on the relevance of parametric resonance for a typical fishing vessel in head seas. Results for different Froude numbers are discussed based on experimental, numerical and analytical studies.The first region of resonance is investigated. Distinct wave amplitudes are considered. Some intense resonances are found to occur. The paper compares the experimental results with non-linear time simulations of the roll motion. Very good agreement is found, even when large motions take place.Finally, in order to analyze the experimental/numerical results, analytic consideration is given to distinct parameters affecting the dynamic process of roll amplification. The influence of heave, pitch, wave passage effect, speed and roll restoring characteristics are discussed.     

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.     

Estimation of ship motions using closed-form expressions

A semi-analytical approach is used to derive frequency response functions for the wave-induced motions for monohull ships. The results are given as closed-form expressions and the required input information for the procedure is restricted to the main dimensions: length, breadth, draught, block coefficient and water plane area together with speed and heading. The formulas make it simple to obtain quick estimates of the wave-induced motions and accelerations in the conceptual design phase and to perform a sensitivity study of the variation with main dimensions and operational profile.     

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.     

Numerical simulation of sloshing waves in a 3D tank based on a finite element method

The sloshing waves in a three dimensional (3D) tank are analysed using a finite element method based on the fully non-linear wave potential theory. When the tank is undergoing two dimensional (2D) motion, the calculated results are found to be in very good agreement with other published data. Extensive calculation has been made for the tank in 3D motion. As in 2D motion, in addition to normal standing waves, travelling waves and bores are also observed. It is found that high pressures occur in various circumstances, which could have important implications for many engineering designs.     

A parametric study of wave loads on trimaran ships traveling in waves

In this paper, we present a spectral analysis based on wave loads to select suitable side-hull arrangements for a trimaran ship traveling in waves. Neglecting the steady flow effect, the three-dimensional source-distribution method, using a pulsating source potential incorporating the panel method, is adopted to solve the corresponding hydrodynamic coefficients. The significant values for wave loads, including shear forces, bending moments, and torsion moments at different locations on the main hull and connected deck with respect to different staggers and clearances, are derived by the spectral analysis. Several ship speeds and wave headings are also considered for comparison. This study offers more information for selecting the side-hull arrangement from the viewpoint of wave loads on trimaran ships, which may be regarded as helpful references for seakeeping design of these types of ships.     

南海冬、夏季环流的三维数值模拟

本文利用一个斜压三维陆架海模式——HAMSOM模式对12月份和8月份的南海环流进行数值模拟,结果为:对上层流场,在12月份,在西沙群岛－中沙群岛海区间呈现一个气旋式环流,在越南中部东岸存在一支南向西边界流,在金兰湾的远海为一局地反气旋涡,在南海南部,主要表现为万安滩的气旋式大弯曲(气旋涡)及在北康暗沙北侧的反气旋涡;在8月份,在东沙群岛－中沙群岛－吕宋岛西侧海域间存在一大尺度的气旋涡,在南海西部主要表现为以西沙群岛南部的气旋涡与金兰湾－礼乐滩间的反气旋式大环流相对峙的局面,同时在万安滩东侧有－气旋涡.由于斜压效应、底形效应的作用,使冬、夏季的南海南部中层流场几乎与上层流场相反.     

Manoeuvring behaviour of ships in extreme astern seas

In an attempt to contribute to efforts for a robust and effective numerical tool addressing ship motion in astern seas, this paper presents the development of a coupled non-linear 6-DOF model with frequency dependent coefficients, incorporating memory effects and random waves. A new axes system that allows straightforward combination between seakeeping and manoeuvring, whilst accounting for extreme motions, is proposed. Validation of the numerical model with the results of benchmark tests commissioned by ITTC's Specialist Group on Stability demonstrated qualitative, yet not fully satisfactory agreement between numerical and experimental results in line with other predictive tools. The numerical results indicate that the inclusion of frequency coefficients definitely affects the accuracy of the predictions. In order to enhance further the numerical model and obtain useful information on motion coupling, extensive captive and free running model tests were carried out. Good agreement with the experimental results was achieved. These studies provide convincing evidence of the capability of the developed numerical model to predict the dangerous conditions that a ship could encounter in extreme astern seas. As a result, it could offer new insights towards establishing relationships linking ship behaviour to design, environmental and operational parameters.     

Time domain modelling of the transient asymmetric flooding of Ro-Ro ships

This work aims at contributing to improve knowledge on transient asymmetric flooding through theoretical and experimental research. First, a time domain theoretical model of ship motions and flooding is described. Results from experimental work are presented evidencing that transient asymmetric flooding may cause the capsizing of a Ro-Ro shaped barge. The theoretical model is used to predict the capsize of the Ro-Ro shaped barge. Reasonable agreement between experimental and theoretical results was found. Finally, a review of the European Gateway accident is given and the theoretical model is applied to the study of this type of accident. The conclusion is that this theoretical model, together with an accurate modelling of the flooding of machinery compartments, reproduces successfully the capsizing of the European Gateway due to transient asymmetric flooding. Therefore, the internal arrangement of Ro-Ro ships should be carefully studied at the design stage in order to avoid this phenomenon.     

Three-dimensional numerical simulation of solitary wave run-up using the IB method

Although the finite difference method is computationally efficient, it is acknowledged to be inferior when dealing with flow-over on structures with a complex geometry because of its rectilinear grid system. Therefore, we developed a numerical procedure that can cope with flow over structures with complex shapes while, at the same time, retaining the simplicity and efficiency of a rectilinear grid system. We used the immersed boundary method, which involves application of immersed boundary forces at solid boundaries rather than conventional boundary conditions, to investigate wave interactions with coastal structures in a three-dimensional numerical wave tank by solving the Navier–Stokes equations for two-phase flows. We simulated the run-up of a solitary wave around a circular island. Maximum run-up heights were computed around the island and compared with available laboratory measurements and previous numerical results. The three-dimensional features of the run-up process were analyzed in detail and compared with those of depth-integrated equations models.     

Determination of wave energy dissipation factor and numerical simulation of wave height in the surf zone

Based on the time-dependent mild slope equation including the effect of wave energy dissipation, an expression for the energy dissipation factor is derived in conjunction with the wave energy balance equation. The wave height of regular and irregular waves is numerically simulated by use of the parabolic mild slope equation considering the energy dissipation due to wave breaking. Comparison of numerical results with experimental data shows that the expression for the energy dissipation factor is reasonable. The effects of the wave breaking coefficient on the breaking point and the distribution of wave height after breaking are discussed through the study of a specific experimental topography.     

Analysis of formation pressure test results in the Mount Elbert methane hydrate reservoir through numerical simulation

Targeting the methane hydrate (MH) bearing units C and D at the Mount Elbert prospect on the Alaska North Slope, four MDT (Modular Dynamic Formation Tester) tests were conducted in February 2007. The C2 MDT test was selected for history matching simulation in the MH Simulator Code Comparison Study. Through history matching simulation, the physical and chemical properties of the unit C were adjusted, which suggested the most likely reservoir properties of this unit. Based on these properties thus tuned, the numerical models replicating “Mount Elbert C2 zone like reservoir”, “PBU L-Pad like reservoir” and “PBU L-Pad down dip like reservoir” were constructed. The long term production performances of wells in these reservoirs were then forecasted assuming the MH dissociation and production by the methods of depressurization, combination of depressurization and wellbore heating, and hot water huff and puff. The predicted cumulative gas production ranges from 2.16 × 10⁶ m³/well to 8.22 × 10⁸ m³/well depending mainly on the initial temperature of the reservoir and on the production method.This paper describes the details of modeling and history matching simulation. This paper also presents the results of the examinations on the effects of reservoir properties on MH dissociation and production performances under the application of the depressurization and thermal methods.     

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.