Experimental investigation of a fast monohull in forced harmonic motions

The paper presents the results of an experimental investigation of added masses and damping coefficients of a model of a fast monohull. A model of 4.5 m length between perpendiculars was constructed of fiber glass reinforced plastic (FRP) with four segments connected by a backbone. The backbone was instrumented with load cells at the positions of the cuts. This configuration, combined with load cells measuring the force exerted by the forced motion actuators, made it possible to obtain the hydrodynamic coefficients for each of the four hull segments.

The investigation focused on the vertical motions. Thus, the experimental program included forced harmonic heave and pitch motions in calm water (no incident waves). Subtracting inertial and restoring forces from total measured forces, one obtained the hydrodynamic component, which then resulted in the hydrodynamic coefficients. The effects of steady forward speed on the radiation forces were investigated by conducting model tests at four forward speeds. Finally, nonlinear effects were assessed by conducting model tests for three amplitudes of forced heave and forced pitch motions.     

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.     

Wave radiation due to oscillation of two parallel spaced cylinders

The radiation problem for two parallel-spaced cylinders is studied. The solution is expressed explicitly in terms of well-behaved convergent series with elementary functions, which are convenient for numerical computation and readily applicable for two-dimensional two-body potential problems. The added mass and damping coefficients together with the phase angles of radiated wave potentials for the forced heave and sway motions of two identical submerged cylinders are presented. The results are useful for determination of the hydrodynamic properties of multi-hull semi-submersibles. In view of the close relationship between a radiation and a scattering problem, the application of the results to the problem of energy extraction from water waves is also noted.     

Nonlinear hydroelastic analysis of a moored floating body

By integration of the second-order fluid pressure over the instantaneous wetted surface, the generalized first- and second-order fluid forces used in nonlinear hydroelastic analysis are obtained. The expressions for coefficients of the generalized first- and second-order hydrodynamic forces in irregular waves are also given. The coefficients of the restoring forces of a mooring system acting on a flexible floating body are presented. The linear and nonlinear three-dimensional hydroelastic equations of motion of a moored floating body in frequency domain are established. These equations include the second-order forces, induced by the rigid body rotations of large amplitudes in high waves, the variation of the instantaneous wetted surface and the coupling of the first order wave potentials. The first-order and second-order principal coordinates of the hydrelastic vibration of a moored floating body are calculated. The frequency characteristics of the principal coordinates are discussed. The numerical results indicate that the rigid resonance and the coupling resonance of a moored floating body can occur in low frequency domain while the flexible resonance can occur in high frequency domain. The hydroelastic responses of a moored box-type barge are also given in this paper. The effects of the second-order forces on the modes are investigated in detail.     

Experimental and Numerical Investigations of Ship Parametric Rolling in Regular Head Waves

Parametric rolling is one of five types of the ship stability failure modes as proposed by IMO. The periodic change of the metacentric height is often considered as the internal cause of this phenomenon. Parametric rolling is a complex nonlinear hydrodynamic problem, often accompanied by large amplitude vertical motions of ships. In recent years,the Reynolds-averaged Navier–Stokes(RANS) equation simulations for viscous flows have made great progress in the field of ship seakeeping. In this paper, the parametric rolling for the C11 containership in regular waves is studied both experimentally and numerically. In the experiments, parametric rolling amplitudes at different drafts, forward speeds and wave steepnesses are analyzed. The differences in the steady amplitudes of parametric rolling are observed for two drafts. The effect of the incident wave steepness(or wave amplitude) is also studied, and this supports previous results obtained on limits of the stability for parametric rolling. In numerical simulations, the ship motions of parametric rolling are analyzed by use of the potential-flow and viscous-flow methods. In the viscousflow method, the Reynolds-averaged Navier–Stokes equations are solved using the overset grid method. The numerical accuracies of the two methods at different wave steepnesses are also discussed.     

Wave forces acting on a vertical circular cylinder with a constant forward velocity

Wave forces acting on submerged circular cylinders moving forward with a constant velocity in regular waves are investigated experimentally. Hydrodynamic forces acting on the cylinder forced to surge in a steady are also measured and hydrodynamic coefficients were obtained. Wave force coefficients obtained from wave force measurements are compared with the hydrodynamic coefficients from surging tests, and the similarity and difference between them are discussed. Experiments show that these coefficients are quite different from those of the cylinder without a forward velocity.     

Solitary wave interactions with an array of two vertical cylinders

This paper addresses a numerical investigation of nonlinear waves interactions with an array of two surface-piercing vertical cylinders and the corresponding nonlinear hydrodynamic loads on each individual cylinder. The primary interest of this study is concentrated on the problem of three-dimensional scattering of solitary waves by cylinder arrays and the nonlinear interactions between scattered waves. The theoretical model adopted for simulation is the generalized Boussinesq two-equation model. The boundary-fitted coordinate transformation and multiple-grid technique are utilized here to simplify the computation domain and to facilitate the applications of the boundary conditions on the cylinder surfaces. The velocity potential, free-surface elevation and subsequent evolution of the scattered wave field are numerically evaluated. The hydrodynamic forces on each cylinder during wave impact are also determined. A study of the sheltering effect by the neighboring structures on wave loads is conducted. It is found that the presence of the neighboring cylinder has shown significant influence on the wave loads and the scattering of the primary incident waves. For two transversely arranged cylinders, the transverse force coefficient increases as the separation distance decreases.     

Wave effects on ascending and descending motions of the autonomous underwater vehicle

In the paper, a hydrodynamic model including the characteristics of maneuvering and seakeeping is developed to simulate the six-degree of freedom motions of the underwater vehicle steering near the sea surface. The corresponding wave exciting forces on the underwater vehicle moving in waves are calculated by the strip theory, which is based on the source distribution method. With the hydrodynamic coefficients relevant to the maneuvering and seakeeping, the fourth-order Runge–Kutta numerical method is adopted to solve the equations of motions and six-degrees of freedom of the motions for the underwater vehicle steering near the free surface can be obtained. The wave effect on the corresponding motions of the underwater vehicle is investigated and some interesting phenomena with respect to different wave frequencies and headings are observed. The hydrodynamic numerical model developed here can be served as a valuable tool for analyzing the ascending and descending behaviors of the underwater vehicle near the sea surface.     

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.     

Investigation of motions of catamarans in regular waves—II

By extending the linear frequency domain theory, a quasi-non-linear time-domain technique has been developed to investigate the large amplitude motions of catamarans in regular waves. The non-linearity of hydrodynamic forces included in this practical method comes from variations of a ship's submerged portion. These forces are obtained from a database generated by the linear frequency domain method at each time step. The coupled equations, heave and pitch, are solved in the time domain by using the Runge-Kutta method with proper initial values. In order to investigate the non-linear effects of large amplitude motions of the V-1 catamaran in the head-sea condition, numerical results obtained from the linear and non-linear strip methods have been compared with those obtained from a series of experiments carried out in the towing tank of the Hydrodynamics Laboratory at the University of Glasgow. Based on the comparative studies, the numerical results obtained from the time-domain program can provide better predictions for the large amplitude motions of catamarans than the linear frequency domain method. It is concluded that the non-linear effects are significant when the model speeds and wave amplitudes increase. The peak values of large amplitude motions around the resonance frequencies, as obtained from the non-linear time-domain predictions as well as from measurements, are smaller than those obtained from the linear theory.     

The dynamics of wave induced ship motions in shallow water

The analytical method developed by Svendsen (1968) for a forced heave motion is extended to the general problem of wave induced heave, roll and sway motions of a long ship at a depth of water which is only slightly larger than the draught of the ship. This corresponds, for example, to the situation of a fully loaded ship in a harbour area.After linearization of the problem, the water motion is considered for each of the three individual motions and for the wave reflection-transmission problem for a fixed ship. The ensuing results for the forces on the ship are then synthesized to form the equations of motion, which are presented with all coefficients given, including mooring forces.Analytical and numerical results are given for the three components of motion, for the associated resonance frequencies, and for the hydrodynamic masses and moments of inertia. Finally, the assumptions used are analyzed and evaluated by comparison with measurements and with other results for a special case.     

Wave forces acting on a submerged horizontal circular cylinder in oblique waves and on a vertical cylinder in deep waves

This paper presents a method of estimating wave forces acting on a submerged horizontal circular cylinder fixed in oblique waves.The experiments show that drag and inertia coefficients in beam sea are available for calculating the wave forces in oblique waves.Wave forces exerted on a vertical circular cylinder in deep waves are also investigated.The experimental results show that wave forces acting on the vertical cylinder coincide approximately with hydrodynamic forces acting on a submerged circular cylinder in an oscillating fluid.     

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.     

Hull/mooring/riser coupled dynamic analysis and sensitivity study of a tanker-based FPSO

A computer program is developed for hull/mooring/riser coupled dynamic analysis of a tanker-based turret-moored FPSO (Floating Production Storage and Offloading) in waves, winds, and currents. In this computer program, the floating body is modeled as a rigid body with six degrees of freedom. The first- and second-order wave forces, added mass, and radiation damping at various yaw angles are calculated from the second-order diffraction/radiation panel program WAMIT. The wind and current forces for various yaw angles of FPSO are modeled following the empirical method suggested by OCIMF (Oil Company International Marine Forum).

The mooring/riser dynamics are modeled using a rod theory and finite element method (FEM), with the governing equations described in a generalized coordinate system. The dynamics of hull, mooring lines, and risers are solved simultaneously at each time step in a combined matrix for the specified connection condition. For illustration, semi-taut chain-steel wire-chain mooring lines and steel catenary risers are employed and their effects on global FPSO hull motions are investigated. To better understand the physics related to the motion characteristics of a turret-moored FPSO, the role of various hydrodynamic contributions is analyzed and assessed including the effects of hull and mooring/riser viscous damping, second-order difference-frequency wave-force quadratic transfer functions, and yaw-angle dependent wave forces and hydrodynamic coefficients. To see the effects of hull and mooring/riser coupling and mooring/riser damping more clearly, the case with no drag forces on those slender members is also investigated. The numerical results are compared with MARIN's wave basin experiments.     

On the nonlinear hydrodynamic forces for a ship advancing in waves

In this paper, using a second-order steady-state approach and a three-dimensional (3D) pulsating source distribution method derives the nonlinear hydrodynamic forces on a ship advancing in waves. The nonlinear hydrodynamic forces considered here consist of the mean lateral drifting force and the added resistance, which can be expressed as products of the ship-motion responses, the radiation potential, diffraction potential and the incident-wave potential. All related velocity potentials applied in the calculations are in 3D form. The Series 60 and Marine ship hulls are used for numerical calculations and the results are compared with existing experimental data and two-dimensional (2D) solutions. The comparisons show that the results obtained in the paper generally agree with experimental data well. It is also found that the nonlinear hydrodynamic forces obtained based on the present 3D source distribution methods are indeed improved in some calculations compared with the 2D method, especially for the mean lateral drifting force.     

Motion response simulation of a twin-hulled semi-submersible

The purpose of the study was to develop a prediction technique to simulate the motion response of a damaged platform under wave, wind and current forces. The equations of motion were obtained using Newton's second law and the numerical solution technique of non-linear equations of motion is explained for intact and damaged cases. The analysis technique employs large displacement non-linear equations of motion. Solutions were obtained in the time-domain to predict the motion characteristics. In this study, analysis procedures were developed to calculate: (a) wave loading on asymmetrical structural configurations; (b) hydrodynamic reaction forces (inertia or moment of inertia, damping and restoring forces) on asymmetrical shapes. During the damage simulation, change in the mass of the structure as well as wave and hydrodynamic reaction forces, were taken into account. The computer program developed for the time-domain simulation is introduced. In order to avoid slowly decaying transient motions of the structure due to wave excitation forces, an exponential ramp function is used. The application of a ramp function enables a quick convergence in the time-domain solution of equations of motion. Results of a numerical motion simulation program and the experimental studies are also presented in order to make comparisons. Comparison of the test results with the numerical simulations shows good agreement for heave, roll and pitch motions. The formulations and the computational procedures given in this paper provide useful tools for the investigation of the non-linear dynamic stability characteristics of floating structures in waves for intact, damaged and post-flooding conditions in six-degrees of freedom.     

张力腿平台内孤立波作用特性数值模拟

依据三类内孤立波理论KdV、eK dV和MCC的适用性条件,采用Navier-Stokes方程为流场控制方程,以内孤立波诱导上下层深度平均水平速度作为入口边界条件,建立了两层流体中内孤立波对张力腿平台强非线性作用的数值模拟方法。结果表明,数值模拟所得内孤立波波形及其振幅与相应理论和实验结果一致,并且在内孤立波作用下张力腿平台水平力、垂向力及力矩数值模拟结果与实验结果吻合。研究同时表明,张力腿平台内孤立波载荷由波浪压差力、粘性压差力和摩擦力构成,其中摩擦力很小,可以忽略;水平力的主要成分为波浪压差力和粘性压差力,粘性压差力与波浪压差力相比较小却不可忽略,流体粘性的影响较小;垂向力中粘性压差力很小,流体粘性影响可以忽略。     

Numerical and experimental study on seakeeping performance of a SWATH vehicle in head waves

The seakeeping characteristics of a Small Waterplane Area Twin Hull (SWATH) vehicle equipped with fixed stabilizing fins was investigated by experimental and numerical methods The calculation methods range from viscous CFD simulation based on an unsteady RANS approach to Boundary Element Method (BEM) based on Three Dimensional Translating-pulsating Source Green Function (3DTP). Responses of ship motions in head regular waves and nonlinear effects on motion responses with increasing wave amplitude were analyzed. Numerical simulations have been validated by comparisons with experimental tests. The results indicate that the heave and pitch transfer functions depict two peaks with the increase of wave length. Comparisons amongst experimental data and different numerical calculations illustrate that the RANS method predicts ship motions with higher accuracy and allows the detection of nonlinear effects. The heave and pitch transfer functions see a downward trend with the increasing wave amplitude in the resonant zone at low speed.     

Time-domain computation of large amplitude 3D ship motions with forward speed

Time-domain computations of 3D ship motions with forward speed are presented in this paper. The method of computation is based upon transient Green function. Both linear and nonlinear (large-amplitude) computations are performed where the included nonlinearities are those arising from the incident wave, but the diffraction and radiation forces are otherwise retained as linear. The incident wave can be described by any explicit nonlinear model. Computations over a variety of wave and speed parameters establish the robustness of the algorithm, which include high speed and following waves. Comparison of linear and nonlinear computations show that nonlinearities have a considerable influence on the results, particularly in predicting the instantaneous location of the hull in relation to the wave, which is crucial in determining forefoot emergence and deck wetness.     

潜堤后高阶自由谐波的研究

基于高阶边界元方法的完全非线性数值水槽模型模拟潜堤地形上波浪的传播变形,通过与实验值进行比较,考察数学模型的正确性.采用两点法分离得到堤后高倍频自由波来研究入射波参数、水深对堤后高倍频自由波的影响.研究发现:基频波、二阶和三阶自由波幅值分别与入射波波幅成线性、二次和三次函数关系,基频波幅值基本不随波浪周期变化,而二阶和...