Investigation of motions of catamarans in regular waves—I

In this paper an analytical technique based on the two-dimensional Green function method associated with a cross-flow approach for taking viscous effects into account to estimate the motion response of catamarans in the frequency domain is presented. In order to validate this method, the numerical results are compared with experimental values obtained for two different catamarans (ASR5061 [Wahab, R., Pritchett, C. and Ruth, L.C. 1971. On the behaviour of the ASR catamaran in waves. Marine Technology, 8, 334–360] and Marintek [Faltinsen, O., Hoff, J.R., Kvalsvold, J. and Zhao, R. 1992. Global loads on high speed catamarans. 5th Int. Symp. on Practical Design of Ships and Mobile Units, University of Newcastle-upon-Tyne, 1.360–1.373]).In the second part of the paper the tests carried out with a third catamaran configuration at the Hydrodynamics Laboratory of the University of Glasgow are presented to evaluate the non-linear effects. These test results cover different speeds and wave heights at a wide range of wave frequencies. The paper concludes that the two-dimensional method correlates very well with measurements of small amplitude motions. For large amplitude motion tests, the non-linear effects become significant when the model speed and wave amplitudes increase. The peak values of heave and pitch motions measured around the resonance frequency are smaller than those obtained from the linear theory.     

The motions and internal forces of a moored semi-submersible in regular waves

The motion of a moored semi-submersible in regular waves and the wave-induced internal forces in the semi-submersible have been studied both numerically and experimentally. In the numerical formulation, the semi-submersible is modelled as an externally constrained floating body, which is regarded as being composed of several rigidly connected parts. The linearized equations of motion of each part were obtained in a common reference system fixed on the body. A consistent formulation of the wave-induced internal forces between two parts as well as the external constraining forces is presented.Model tests were carried out using a 1:36 scale model of the semi-submersible, Glomar Arctic III. Very good agreement was achieved between the numerical and model-test results in the practical wave-frequency range.     

Modelling of multi-bodies in close proximity under water waves—Fluid forces on floating bodies

This work presents two-dimensional numerical results of the dependence of wave forces of multiple floating bodies in close proximity on the incident wave frequency, gap width, body draft, body breadth and body number based on both viscous fluid and potential flow models. The numerical models were validated by the available experimental data of fluid oscillation in narrow gaps. Numerical investigations show that the large amplitude responses of horizontal and vertical wave forces appear around the fluid resonant frequencies. The convectional potential flow model is observed to un-physically overestimate the magnitudes of wave forces as the fluid resonance takes place. By introducing artificial damping term with appropriate damping coefficients μ∈[0.4, 0.5], the potential flow model may work as well as the viscous fluid model, which agree with the damping coefficients used in our previous work for the predication of wave height under gap resonance. In addition, the numerical results of viscous fluid model suggest that the horizontal wave force is highly dependent on the water level difference between the opposite sides of an individual body and the overall horizontal wave force on the floating system is generally smaller than the summation of wave force on each body.     

The nonlinear rolling response of a vessel including chaotic motions leading to capsize in regular seas

The rolling motion of a ship has been successfully modelled using a semi-empirical nonlinear differential equation by a number of researchers. Experimental data has been used to model nonlinear damping and righting lever characteristics and comparison with observed behaviour has been reasonably good. The present article describes a numerical, phenomenological approach to analyse this type of behaviour. The stability of the periodic motion, and in particular the possibility of capsize, is explored with reference to qualitative prediction techniques. The appearance of chaotic motions in regular beam seas is a new feature which should be of interest to designers. The inability of traditional quantitative methods, such as the perturbation technique, to detect chaos is a further justification for using numerical simulation guided by dynamical systems theory.     

Investigation of Π-type breakwaters performance under regular and irregular waves

In this paper, performance of solid and perforated Π-type breakwaters was investigated experimentally. Both regular and irregular waves were used during testing. Four depths of immersions were selected for each breakwater and wave type. Different wave groups were generated over these breakwaters, and the transmission, reflection and energy-dissipation characteristics were determined. The results of the experimental study were evaluated and some empirical expressions based on the results were suggested to define the transmission, reflection and energy-dissipation coefficients for different immersion depths of solid and perforated breakwaters under regular and irregular waves. Moreover, performance of solid and perforated Π-type breakwaters were compared with that of solid and perforated U-type breakwaters investigated by Günaydın and Kabdaşlı [2006. Performance of solid and perforated U-type breakwaters under regular and irregular waves. Ocean Engineering 31, 1377–1405]. These comparisons showed that the most reasonable model and wave type are selected to determine requiring performance parameters.     

浅水不规则波浪中油轮运动研究

本文对一般油轮在浅水不规则波浪中六自由度运动进行了试验分析,并对其碰底情况做了研究。试验时对有流情况下不同波高、不同装载的条件进行了分析比较。模型的六自由度运动是用非接触式六自由度运动测量与分析方法求得。该方法应用位置测量仪（ＰＳＤ）对安置在模型上的红外线发光源（ＬＥＤ）进行测量,然后所编制的软件计算出模型的六个自由度运动情况。     

The water motions in a moonpool

Moonpools are vertical wells in a floating body, frequently found in drilling ships—to give passage to the drill pipe—and in diving support vessels—to launch diving bells and equipment through it. Observations showed that inside a moonpool considerable relative motions may occur, depending on the shape and depth of the moonpool and on the frequency range of the waves to which the ship is exposed.Recently, a research program has been carried out at the Netherlands Ship Model Basin in which the hydrodynamics with respect to a moonpool were investigated. A mathematical model describing the relative water motions inside a moonpool was developed, while also model tests were carried out to obtain empiric results with respect to the damping mechanisms and motion behaviour.     

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.     

The motions of a ship in swallow water

A general formulation is given of the hydrodynamic forces on a ship, oscillating about a state of rest in 6df in response to excitation by a harmonic wave in shallow water. A method is described to obtain a numerical approximation of the velocity potential, describing the flow around the moving ship by means of a distribution of discrete three-dimensional sources.With this method it is possible to take the influence of a quay into account.Calculated values of wave excited forces, hydrodynamic coefficients and motions of a 200,000 tdw tanker in shallow water are presented and compared with experimental results.     

Second-order wave maker theory using force-feedback control. Part II: An experimental verification of regular wave generation

This paper provides an experimental verification of the new wave maker theory outlined by Spinneken and Swan [2009. Second-order wave maker theory using forcefeedback control. Part I. A new theory for regular wave generation. Ocean Engineering, in press, doi:10.1016/j.oceaneng.2009.01.019]. This theory concerns the generation of regular waves by a flap-type wave maker using force-feedback control, providing the first quantitative evidence of the inherent advantages of this latter approach. When the wave maker is controlled by a first-order force command signal, comparisons between the theory and experimental observations confirm two key points: (i) The first-order behaviour is crucial for the absorption characteristics of the machine. (ii) The second-order behaviour leads to a spurious, or unwanted, freely propagating second harmonic that is substantially smaller in amplitude when compared to an identical wave paddle operating with first-order position control. Both aspects of this work, effective absorption and reduced second-order spurious wave generation, are investigated over a broad range of wave frequencies and shown to be widely applicable. Furthermore, the theory also provides a force command signal correct to second order. This is introduced in a separate set of experiments and shown to provide further improvement in the quality of the wave generation.     

Calculation of dynamic motions and tensions in towed underwatercables

A matrix method for mooring system analysis is extended to address the dynamic response of towed underwater systems. Key tools are equivalent linearization and small perturbation theory, and a pitching towfish model. Two examples of application of the technique are provided. The first studies a fundamental limitation to constrained passive heave compensation, while the second concerns the use of floated tethers as a means for dynamic decoupling     

Intense near-bed sediment motions in waves and currents

In the past few years, two-phase models have been developed to describe the detail behaviour of fluid/sediment interactions and transport under the sheet flow conditions. Due to the complexity of the governing equations and uncertainties in the formulations of various stress terms, few complete solutions of these equations are known and the validations are thus far limited to only a few experimental data. In this paper, the numerical predictions of the behaviour of sheet flows using an improved version of an earlier two-phase flow model [Coastal Eng. 36(2) (1999) 87] are described. Although the general structure of the model was retained, a number of improvements had been made to give better account the underlying physics of the flow in areas very close to the stationary bed. All key flow parameters have been predicted and analysed in order to gain insight into the processes. Calculated time-dependent as well as time-averaged concentrations are compared with experimental data from purely oscillatory flows and oscillatory flow plus a current. Good qualitative agreements between predictions and measurements were achieved for the time-dependent concentrations while the time-averaged concentrations are quantitatively accurate as well.     

规则波作用下水下拖缆数值分析研究

研究了水面波浪对水下拖缆的干扰。首先基于集中质量法给出了三维非均匀拖缆在规则波作用下的数学模型,然后通过四阶龙格库塔方法进行数值求解,并根据仿真计算讨论了拖缆在不同波浪作用下的稳态响应特性。仿真结果表明,水下拖缆在规则波的作用下,不仅作近似的简谐振动,还会在横向、垂向产生一个偏移量,且随浪向角的变化呈现不同的响应特征。     

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.     

Large angular motions of tethered surface buoys

A three-dimensional coupled analysis of the interaction of a floating buoy and its mooring is studied. External loads include hydrodynamic forces, tether tensions, wind loads and system weight and buoyancy. Nonlinearities include large rotational and translational motions and non-conservative fluid loads. The mooring problem is formulated as a nonlinear two-point-boundary-value-problem. At each instant in time, the mooring problem is solved by direct integration using a successive iterative algorithm to satisfy boundary conditions. Buoy kinetic and kinematic equations are derived assuming large angles represented by Euler parameters. Coupling between the buoy and the mooring is enforced by matching the velocities of the tether and buoy at the attachment point. A predictor-corrector coupling algorithm is used with multiple sizes of time steps used to provide stability for the separate mooring and buoy models. Numerical results are compared to experimental responses of three types of buoys (sphere, spar and disc) subject to both regular and irregular waves.     

Artificial upwelling in regular and random waves

Mathematical modeling conducted in this study evaluated the hydrodynamic performance of a wave-driven artificial upwelling device in ocean waves off the Hawaiian islands. The device consisted of a buoy (4.0 m in diameter) and a tail pipe (1.2 m in diameter, 300 m in length) with a flow controlling valve. Random ocean waves off the Hawaiian islands used in the device's modeling analysis were synthesized from a wave spectrum obtained from available data. For comparison, the device's performance was also evaluated in regular waves whose height and period are the same as the significant wave height and wave period of random Hawaiian waves. Modeling results indicated that an upwelling flow of 0.95 m³/sec can be generated by this device in random Hawaiian waves and an upwelling flow rate of 0.45 m³/sec can be generated in regular waves. A simple mathematical model which assumed that the device exactly follows the incident waves was used in previous studies. Analysis results also indicated that the simple model cannot satisfactorily simulate the relative velocity and acceleration of the water column in the device. Since the relative velocity and acceleration are important factors in determining the rate of upwelling flow, the simple model must be applied with caution.     

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.