Study of Hydrodynamic Characteristics of A Sharp Eagle Wave Energy Converter

According to Newton''s Second Law and the microwave theory, mechanical analysis of multiple buoys which form Sharp Eagle wave energy converter (WEC) is carried out. The movements of every buoy in three modes couple each other when they are affected with incident waves. Based on the above, mechanical models of the WEC are established, which are concerned with fluid forces, damping forces, hinge forces, and so on. Hydrodynamic parameters of one buoy are obtained by taking the other moving buoy as boundary conditions. Then, by taking those hydrodynamic parameters into the mechanical models, the optimum external damping and optimal capture width ratio are calculated out. Under the condition of the optimum external damping, a plenty of data are obtained, such as the displacements amplitude of each buoy in three modes (sway, heave, pitch), damping forces, hinge forces, and speed of the hydraulic cylinder. Research results provide theoretical references and basis for Sharp Eagle WECs in the design and manufacture.     

An investigation into parametric roll resonance in regular waves using a partly non-linear numerical model

A partly non-linear time-domain numerical model is used for the prediction of parametric roll resonance in regular waves. The ship is assumed to be a system with four degrees of freedom, namely, sway, heave, roll and pitch. The non-linear incident wave and hydrostatic restoring forces/moments are evaluated considering the instantaneous wetted surface whereas the hydrodynamic forces and moments, including diffraction, are expressed in terms of convolution integrals based on the mean wetted surface. The model also accounts for non-potential roll damping expressed in an equivalent linearised form. Finally, the coupled equations of motion are solved in the time-domain referenced to a body fixed axis system.This method is applied to a range of hull forms, a post-Panamax C11 class containership, a transom stern Trawler and the ITTC-A1 containership, all travelling in regular waves. Obtained results are validated by comparison with numerical/experimental data available in the literature. A thorough investigation into the influence of the inclusion of sway motion is conducted. In addition, for the ITTC-A1 containership, an investigation is carried out into the influence of tuning the numerical model by modifying the numerical roll added inertia to match that obtained from roll decay curves.     

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.     

A general method for calculating hydrodynamic forces

This paper presents the derivation of a general method for calculating wave forces on the cylindrical members of offshore structures. By means of the proposed method one can calculate the wave loading on cylindrical members of fixed or floating offshore structures orientated randomly in waves. This method of calculating wave forces is based on the linear Airy wave theory. Calculation procedure of wave force components is presented in great detail on the basis of wave particle kinematic properties obtained from the linear Airy wave theory. In the procedure of calculating wave forces presented, definitions of the wave reference system for propagating wave, the structure reference system for the platform and the member reference system for the tubular members of the structure are first established, and then the calculation of wave forces is given in terms of its components, which are pressure, acceleration and velocity forces, including current forces. At the end of the paper, expressions of total heave, sway and surge forces and total roll, pitch and yaw moments acting on the platform are given as a sum of these forces acting on each member of the platform. The calculation procedure derived in this paper provides a very efficient means of calculating wave forces and moments during the time-domain simulations of a floating platform experiencing large amplitude motion in intact, progressive flooding and damaged conditions. Comparisons of the predictions with the measurements which will be presented elsewhere reveal that the calculation procedure developed can predict large amplitude oscillatory and steady motion characteristics of an intact and damaged platform in waves with an acceptable degree of accuracy.     

内孤立波下深水半潜式平台系统动力响应研究

我国南海海域海洋环境条件复杂且海水密度垂直层化现象显著,内孤立波活动频繁,因内孤立波而造成海洋开采平台破坏的案例屡见不鲜。依托水动力计算软件AQWA二次开发功能,采用Kdv方程,借助Fortran语言将深水半潜式平台立柱、浮箱、系泊系统3部分的内孤立波作用力叠加到外力项中,联合求解半潜式平台的6自由度动力响应特性。数值模拟结果表明,在内孤立波作用下,半潜式平台的运动及系泊线张力均受到了显著的影响。在不考虑系泊系统受内孤立波作用时,平台在纵荡和横荡方向上产生较大的漂移运动,最大偏移量较无内孤立波情况下增加了8倍;系泊线最大张力提高了17%,增加了系泊线断裂的风险。在考虑系泊系统受内孤立波作用时,平台的纵荡和横荡运动响应在原响应基础上继续提高15%,但是系泊线张力变化不大。内孤立波不同浪向下的平台纵荡和横荡响应相差也很明显;系泊系统合力在不同方向上的大小决定了平台不同方向上运动的大小。     

应用两次展开法求解系泊柱体慢漂运动方程

在深海中系泊的海洋平台,如Spar平台,水下部分为带有系泊的圆柱结构,其水平方向运动响应往往具有较低的自振频率,容易在低频波浪力(源于非线性的差频效应)作用下发生共振响应,使结构发生大幅水平慢漂。当浮体的瞬时位置大幅偏离初始位置时,基于初始平衡位置的摄动展开法会存在较大误差。针对这一问题,采用两次展开方法,对大幅慢漂运动开展时域模拟研究。对双色波作用下自由漂浮圆柱的大幅运动响应问题进行数值分析,并与采用基于初始平衡位置的摄动展开法的计算结果进行了对比。结果表明,采用新的两次展开法可以计算出波浪遭遇频率的变化和波浪漂移阻尼,而这无法从基于初始平衡位置的常规摄动展开法中得到,体现了两次展开法在分析大幅慢漂问题上的优势。     

PREDICTION OF MOTION OF SEMI-SUBMERSIBLE DRILLING PLATFORM IN MAVES

Starting from potential theory, this paper presents a new procedure for computing the hydrodynamic forces and six-degrees-of-freedom motion for a semi-submersible platform at an arbitrary heading in waves by using strip theory and linearized viscous damping hypothesis, taking the effects of the free surface and the interaction between main hulls into account. The differential equations of motion for the floating platform are formulated in a new way and the associated computer programs are developed. Comparisons between the theoretical computing results and the full-scale and model-scale experiments show that the present method gives more accurate results than those by previous methods.     

Coupled heave and pitch motions of planing hulls at non-zero heel angle

Current paper presents a mathematical model based on 2D-asymmetric wedge water entry to model heave and pitch motions of planing hulls at non-zero heel angles. Vertical and horizontal forces as well as heeling moment due to asymmetric water entry are computed using momentum theory in conjunction with added mass of impact velocity in vertical and horizontal directions. The proposed model is able to compute sway and yaw forces, roll moment, as well as heave and pitch motions in calm water and regular waves. Validity of the proposed model is verified by comparing the results against existing experimental data in both symmetric and asymmetric conditions. Ultimately, different parametric studies are conducted to examine the effects of non-zero heel angle on dynamic vertical motions. The resulting sway and yaw forces due to asymmetric motion are also derived and effects of heel angle on these side forces are investigated.     

Dynamic interaction of breaking waves and inverted sailing yachts: Explaining the efficacy of mast height retention relative to vertical centre of gravity

The ability of a sailing yacht to re-right due to the effect of a breaking wave is investigated experimentally. Free and constrained physical models with varying mast height and centre of gravity were tested. To investigate the influence of retained mast height on sway force and roll moment, models were constrained by attachment to a force balance for sway motion tests in calm water and stationary tests in regular and breaking waves. Free model testing, with varying mast height and centre of gravity position, were carried out in breaking waves. For these tests, model motions in six degrees of freedom were measured using photogrammetry. The constrained tests showed that while the mast height had little effect on forces when stationary in waves it had a large effect when in sway motion. As models experience large sway motions when subject to a breaking wave the mast remnant plays a critical role in re-righting dynamics. This work demonstrates that re-righting probability is more dependent on mast height retention and wave characteristics than vertical centre of gravity. This conclusion has direct implications on re-righting safety assessment as the dominant design feature in most safety standards is the vertical centre of gravity.     

Wave interaction with multiple horizontal cylinders

The interaction of waves with submerged two-dimensional circular cylinder groups is investigated. Linear wave theory is used in the analysis and the viscous effects are neglected. The boundary value problem for the wave potential is based on Green's theorem, and the resulting integral equation is solved numerically. The added mass and damping coefficients in sway, heave and roll of oscillating twin-cylinders and the total wave forces on a fixed cylinder in a group are examined. The effects of the free surface, and particularly, the spacing of the cylinders are shown. The numerical results are tested against known solutions. Results for a two-cylinder configuration at different orientations are presented. It is found that the interaction between closely spaced cylinders is large. The spacings at which the interaction effect is important are shown graphically.     

Robust path-following of underactuated ships: Theory and experiments on a model ship

A method is proposed to design a new global controller that forces an underactuated ship to follow a reference path under disturbances induced by wave, wind and ocean-current. The controller is designed such that the ship moves on the path with an adjustable forward speed and its total velocity is tangential to the path. The ship under consideration is not actuated in the sway axis, and the mass and damping matrices are not assumed to be diagonal. Nonlinear damping terms are also included to cover both low- and high-speed applications. The new result is facilitated by choosing an appropriate origin of the body-fixed frame, designing a suitable filter of sway velocity, several nonlinear coordinate changes, the backstepping technique, and utilizing the ship dynamic structure. Experimental results on a model ship illustrate the effectiveness of the proposed method.     

分隔板对Spar平台涡激运动响应影响的分析研究

当流体流经单柱式结构物时,由于流体黏性和逆压梯度的存在,会产生非定常的升力、阻力和涡旋脱落,即涡激运动现象,对一座Truss Spar平台的硬舱部分附加长度为1.0D(D为硬舱直径)的刚性来流侧分隔板,基于开源平台OpenFOAM,采用基于剪切应力运输的延迟分离涡模拟(SST-DDES)方法,在不可压缩黏性流场中,对其进行三维数值模拟,以研究在不同流速下,来流侧分隔板对Spar平台涡激运动特性和运动响应的影响。结果表明：在较高流速下,横荡周期减小22.21%,横荡最大幅值减小81.3%。说明在较高流速下,附加分隔板有助于减少Spar平台的运动响应幅值。     

A field experiment on the small-scale model of a gravity offshore platform

The 1:50 scale model of a big offshore gravity platform was placed off the beach at Reggio-Calabria, where the wind waves typically have significant height ranging from 0.20 to 0.40 m and peak period from 1.8 to 2.6 sec. A first set of pressure transducers was assembled at the boundary of the platform and a second set, with the same configuration as the first one, was assembled in the undisturbed wave field, in order to compare the force amplitude on the platform to the force amplitude on an ideal equivalent mass of water (Froude-Krylov force amplitude). Along with the pressure transducers, a few wave gauges were functioning in the undisturbed wave field. It was found that the time histories of the pressure induced by the highest waves, at the columns and at the platform base, were very similar to the measured covariances of the pressure fluctuations. The statistical distribution of the forces on the platform proved to be coincident with the statistical distribution of the Froude-Krylov forces. The spectrum of the force process proved always to be narrow even in the case of the broad wave spectrum. The diffraction coefficient (ratio of the actual force amplitude to the Froude-Krylov force amplitude) was found to depend essentially on a marked reduction of the propagation speed of the pressure head waves, both at the columns and at the platform base.     

两层流体中内波作用下Spar平台运动响应

研究两层流体中Spar平台在内波作用下的运动响应问题。在线性势流理论框架,提出在内波作用下Spar平台运动响应及分段式悬链线系泊张力特性的计算方法。数值分析两层流体内界面位置、入射内波的波长以及系泊索初始预张力对Spar平台运动响应及其系泊索张力特性的影响规律,结果表明内波对Spar平台纵摇运动响应的影响是小的,但对Spar平台纵荡与垂荡运动响应及其系泊索张力的影响是不可忽视的。因此,在Spar平台的设计中,考虑内波的影响是重要的。     

动力定位船舶二阶低频慢漂力模型试验研究

对一艘动力定位船舶二阶低频慢漂力进行了模型试验,并将试验得到的纵向慢漂力谱、横向慢漂力谱与势流理论方法得到的理论值进行比较,结果表明,该模型试验方法与理论计算较为吻合。可为动力定位系统的设计和应用提供参考。     

Nonlinear coupled response of offshore tension leg platforms to regular wave forces

Among the compliant platforms, the tension leg platform (TLP) is a vertically moored structure with excess buoyancy. The TLP is designed to behave in the same way as any other moored structure in horizontal plane, at the same time inheriting the stiffness of a fixed platform in the vertical plane. Dynamic response analysis of a TLP to deterministic first order wave forces is presented, considering coupling between the degrees-of-freedom surge, sway, heave, roll, pitch and yaw. The analysis considers nonlinearities produced due to changes in cable tension and due to nonlinear hydrodynamic drag forces. The wave forces on the elements of the pontoon structure are calculated using Airy's wave theory and Morison's equation ignoring diffraction effects. The nonlinear equation of motion is solved in the time domain by Newmark's beta integration scheme. The effects of different parameters that influence the response of the TLP are then investigated.     

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.     

Viscous drift forces in regular and irregular waves

A method to compute wave- and current-induced viscous drift forces and moments on floating platforms in regular and random waves is presented. The relative velocity drag term of Morison's equation is used in conjunction with frequency domain first-order motion transfer functions to compute the drift forces and moments. Mean viscous drift forces and moments in regular waves in all six degrees-of-freedom of a tension leg platform are computed. The relative importance of the free-surface force integration, steady current, wave-current interaction and platform motions on the computed drift forces and moments are discussed. The results from this method, in the frequency domain, are used to compute the drift forces and responses in irregular waves using existing methods developed for potential drift computations. Comparisons with results from time-domain computations are also presented and good agreement between the frequency-domain and time-domain results is found. Some comparisons with experimental data are also made. The frequency-domain method is found to be an efficient and useful tool for the analysis of semi-submersible and tension leg platforms during the preliminary design stage in which extensive parametric studies need to be undertaken.     

Added mass and damping of a vertical cylinder in finite-depth waters

A comprehensive set of theoretical added masses and wave damping data for a floating circular cylinder in finite-depth water is presented. The hydrodynamic problem is solved by matching eigen functions of the interior and exterior problems. The resulting infinite system is solved directly and found to have excellent truncation characteristics. Added mass and damping are given for heave, sway, and roll motion, as well as coupling coefficients for sway and roll. It is shown that the heave added mass is logarithmic singular and the damping approaches a constant in the low-frequency limit. Transition of the behaviour in finite-depth water to deep water is also discussed.     

Parametric Resonance Analyses for Spar Platform in Irregular Waves

The parametric instability of a spar platform in irregular waves is analyzed. Parametric resonance is a phenomenon that may occur when a mechanical system parameter varies over time. When it occurs, a spar platform will have excessive pitch motion and may capsize. Therefore, avoiding parametric resonance is an important design requirement. The traditional methodology includes only a prediction of the Mathieu stability with harmonic excitation in regular waves. However, real sea conditions are irregular, and it has been observed that parametric resonance also occurs in non-harmonic excitations. Thus, it is imperative to predict the parametric resonance of a spar platform in irregular waves. A Hill equation is derived in this work, which can be used to analyze the parametric resonance under multi-frequency excitations. The derived Hill equation for predicting the instability of a spar can include non-harmonic excitation and random phases. The stability charts for multi-frequency excitation in irregular waves are given and compared with that for single frequency excitation in regular waves. Simulations of the pitch dynamic responses are carried out to check the stability. Three-dimensional stability charts with various damping coefficients for irregular waves are also investigated. The results show that the stability property in irregular waves has notable differences compared with that in case of regular waves. In addition, using the Hill equation to obtain the stability chart is an effective method to predict the parametric instability of spar platforms. Moreover, some suggestions for designing spar platforms to avoid parametric resonance are presented, such as increasing the damping coefficient, using an appropriate RAO and increasing the metacentric height.