Wave loads on a stationary floating bottomless cylindrical body with finite wall thickness

This paper aims at presenting a method for solving the linearised diffraction problem of the interaction between regular sinusoidal, small amplitude incident waves and a bottomless cylindrical floating body with a vertical symmetry axis and finite wall thickness, through the idealisation of the flow field around the structure using ring elements. The horizontal and vertical excitation forces, the rolling moment, the resulting wave motion inside the cylinder, as well as the pressure distribution on the wetted surface of the structure are obtained by solving the diffraction boundary-value problem through the implementation of the Galerkin method. The analytical predictions are compared with other analytical results and pertinent experimental data. Finally, the influence of the wall thickness on the wave loads and the fluid motion inside the pond is examined.     

Time-domain floating body dynamics by rational approximation of the radiation impedance and diffraction mapping

The problem of approximating the dynamics of a floating structure in a transient wave environment with a set of constant-coefficient differential equations is explored. It is assumed that the solutions of the corresponding steady-state time-harmonic radiation and diffraction problems are available. It is proposed to fit the frequency responses associated with the ‘radiation impedance' and wave-exciting forces with appropriate analytic functions. In the case of the radiation problem, these possess certain properties corresponding to the passivity of the radiation mapping. By choosing rational approximations, the transformation from the frequency to the time domain is facilitated. The method is illustrated for both two-dimensional and three-dimensional problems using a floating cylinder, sphere, and a model of Salter's Duck which exhibits hydrodynamic coupling between sway, heave, and pitch motions.     

波浪对上部开孔带内柱的圆筒结构的绕射

应用透空壁内流体速度与两壁间压力差成正比的线性模型和特征函数展开方法,建立了外壁上部开孔并带有内柱的圆筒结构对波浪绕射的解析解.通过数值计算研究了外壁开孔率的大小、圆筒与内柱半径之比、筒内水深等因素对圆筒上总的波浪作用力和圆筒周围波浪高度的影响.经数值研究发现随着外壁开孔率的增大圆筒迎浪端的波浪高度和圆筒结构上总的波浪力明显减小,外壁孔隙特性G虚部的增加对波高和波浪力的衰减也有一定的影响;增加圆筒内部的水深可减小圆筒周围的波浪高度,降低圆筒结构上的总波浪力.     

Wave radiation by a floating rectangular structure in oblique seas

The linear wave radiation by a long floating rectangular structure in oblique seas of finite depth is investigated by use of the method of separation of variables and the eigenfunction expansion matching method. Analytical expressions for the radiated potentials, wave forces and hydrodynamic coefficients are given. The correctness of these expressions is verified through two specific examples investigated previously by other numerical methods. Using the present analytical solution, the hydrodynamic effects of the angle of incidence, the draft and the width of the structure on the wave forces and hydrodynamic coefficients are discussed in detail which may provide some useful information for the design of rectangular structures in oblique seas.     

Oblique wave interaction with a floating structure near a wall with stepped bottom

Diffraction of obliquely incident waves by a floating structure near a wall with step-type bottom topography is investigated under the three-dimensional small amplitude wave theory. Full solution of the problem under the potential flow approach is obtained by the matched eigenfunction expansion method. The wave-induced forces on the structure and on the wall, the reflection and transmission characteristics and the wave elevations in the free surface regions are studied for different incident wave angles, water depth ratios and dimension of the structure and the distance of the wall from the center of the structure. The problem is reformulated under shallow water approximations and results are compared with the finite depth results.     

波浪对透空外双壁筒柱的绕射

应用透空壁内流体速度与两壁间压力差成正比的线性模型，建立了外壁透空的双筒圆柱对波浪绕射的解析解。通过数值计算研究了外壁透空率的大小、内外柱半径之比等因素对桩柱上总波浪作用力和波面高度的影响。数值结果表明圆柱外壁透空系数的增加，将明显地降低圆柱周围的波浪高度和圆柱上的波浪力；内外柱径之比的大小对波浪力和波高的最大值无太大影响，而对波浪力剧烈衰减区的位置和波高的振荡周期有决定作用。     

Water entry of a finite width wedge near a floating body

The problem of a two-dimensional finite-width wedge entering water near a freely floating body is considered through the velocity potential theory for the incompressible liquid with the fully nonlinear boundary conditions on the free surface. The problem is solved by using the boundary element method in the time domain. The numerical process is divided into two phases based on whether the interaction between the wedge and floating body is significant. In the first phase, when the single wedge enters water at initial stage, only a small part near its tip is in the fluid, the problem is studied in a stretched coordinate system and the presence of the floating body has no major effect. In the second phase, the disturbance by water entry of the wedge has reached the floating body, and both are considered together in the physical system. The auxiliary function method is adopted to decouple the nonlinear mutual dependence between the motions of the wedge and floating body, both in three degrees of freedom, and the fluid flow, as well as the interaction effects between them. Case studies are undertaken for a wedge entering water in forced or free fall motion, vertically or obliquely. Results are provided for the accelerations, velocities, pressure distribution and free surface deformation, and the interaction effects are discussed.     

Wave radiation by a uniform cylinder in front of a vertical wall

In this paper, an exact analytical method is developed for the problem of wave radiation by a uniform cylinder in front of a vertical wall. Based on the image principle, the hydrodynamic problem of a cylinder in front of a vertical wall is transformed into the equivalent problem of double cylinders in unbounded fluid domain. Consequently, an analytical method of eigenfunction expansion is adopted to calculate the radiation of the cylinder due to the motion in surge, sway, roll and pitch, respectively. Moreover, numerical analysis has been carried out in detail in order to discuss the influences of the distance between the cylinder and the vertical wall and water depth on the added mass and radiation damping of the cylinder. It is shown that added mass and damping of the cylinder in front of a vertical wall are evidently different from those in case of the cylinder in unbounded fluid domain from the numerical results. It is also found that the added mass and radiation damping oscillate with wave number, and the oscillating frequency increases with the increasing of the distance between the cylinder and the wall.     

波浪对直墙前垂直圆柱的绕射

应用映像原理，将直墙前单个圆柱对波浪的绕射问题，变换为双柱对双向波浪的绕射问题，应用速度势的特征展开方法，建立了直墙前垂直圆柱对波浪绕射的解析解。通过数值计算研究了圆柱与直墙间距离大小、波浪入射角等因素对圆柱上总波浪作用力的影响。计算结果表明，直墙前圆柱上的波浪力将成倍地增加，且随着波数的变化而发生振荡。     

Wave diffraction and near-trapping by a multi-column gravity-based structure

This paper is concerned with the diffraction of water waves by offshore structures, with the ultimate aim of proposing tools for guiding airgap design. The diffraction of monochromatic waves by an array of four bottom mounted cylinders and a gravity-based structure is studied in detail using linear and second order theory. The phenomenon of near-trapping is investigated, allowing guidelines for airgap design to be established. When contemplating airgap design, however, it is crucially important that consideration is given to the largest waves in a sea state. Therefore, in this study a design wave, called NewWave, is proposed as a realistic model for large ocean waves and is used as the incident wave field in the wave-structure diffraction analysis.     

大深度分层流体中二维淹没浮体的波浪力分析

研究了大深度分层流体中二维任意形状淹没浮体的波浪力特性。首先基于一种合适的格林函数,采用边界积分方程法研究了流体中浮体对水波散射问题,然后通过单个淹没圆柱体的透射能和反射能与解析方法结果的比较,对所提出的方法进行了验证,最后分析了在不同的几何和物理条件下几种形状的浮体对波浪力的特有影响,得到了一些有意义的结果,这对分层海洋中淹没浮体的设计具有重要的参考价值。     

透水cosine-type同心圆柱波浪绕射研究

在势能流及微小振幅波理论假设下,采用复合边界元素法(CBEM)数值解析规则波通过单根外壁透水cosine-type型同心圆柱结构物绕射。将cosine-type外壁不透水条件改为透水外,并在内部设有一半径为b的不透水内圆柱共同组成同心圆柱,为了验证CBEM数值模式正确性与可行性,将其退化成圆柱,均得到合理结果。数值计算条件包含波浪正向入射凸端、透水参数及绕射参数,探讨波浪通过单根cosine-type同心圆柱体四周水面波动变化情况,并与双重圆筒同心圆柱作比较。计算结果显示结构物外壁采用透水型式,可以大幅降低cosine-type同心圆柱体四周整个波浪绕射场的水面波动。     

Wave diffraction by large offshore structures: an exact second-order theory

An exact second order theory has been formulated in this paper to calculate the wave forces on offshore structures. Lighthill's method for deep water waves has been extended to shallow water waves. Exact expression for linear velocity potential applicable to the circular cylindrical strcutures for shallow water waves have been used in these calculations. These results have been verified with those obtained by direct perturbation technique reported recently by Rahman and Heaps. It is interesting to note that both the methods yield identical results.     

Wave reflection by a vertical wall with a horizontal submerged porous plate

By applying the linear water wave theory and the eigenfunction expansion method, the wave reflection by a vertical wall with a horizontal submerged porous plate is investigated in this paper. The numerical results, concerning the effects of the dimensionless plate length, the relative water depth, and the porous effect parameter of the plate on the wave loads on the plate and the wave height near the wall as well as the reflection coefficient, are discussed. It is found that the submerged plate increases the complexity of the phenomenon related to the wave reflection and refraction in the close region of the wall, and leads to the occurrence of the phenomenon of wave trapping. The results indicate that there may exist a process of focusing wave energy near the wall for small dimensionless porous effect parameters, whereas the increase of the dimensionless porous effect parameter decreases gradually the wave height until setdown occurs. The behavior of a larger plate with proper porosity is similar to that of a wave absorber which can significantly suppress not only the wave height above the plate but also the reflection waves. The ability of the porous plate to reduce the wave height on the wall surface is, in general, directly proportional to the dimensionless plate length and may be strongest for a proper value of the dimensionless porous effect parameter. It is also demonstrated that the wave loads on a porous plate are smaller than those on an impermeable plate.     

On the radiation and diffraction of water waves by a rectangular structure with a sidewall

A radiation and diffraction boundary value problem is investigated. It arises from the interaction of linear water waves with a freely floating rectangular structure in a semi-infinite fluid domain of finite water depth with the leeward boundary being a vertical wall. Analytical expressions for the radiated potentials and the diffracted potential are obtained by use of the method of separation of variables and the eigenfunction expansion method. The added masses and damping coefficients for the structure heaving, swaying and rolling in calm water are obtained by use of the corresponding radiated potentials and the wave excitation forces are calculated by use of the diffracted potential. To verify the correctness of the method, a boundary element method is used. A comparison of the analytical results with those obtained by the boundary element method is made and good agreement is achieved, which shows that the analytical expressions for the radiated and diffracted potentials are correct. By use of the present analytical solution, the added mass, damping coefficients, wave excitation force, together with the hydrodynamic effects of the draft, width of the structure and the clearance between the structure and the sidewall are also investigated.     

Analytical method of radiation by a wave energy device with dual rectangular floating bodies

The system with one floating rectangular body on the free surface and one submerged rectangular body has been applied to a wave energy conversion device in water of finite depth. The radiation problem by this device on a plane incident wave is solved by the use of an eigenfunction expansion method, and a new analytical expression for the radiation velocity potential is obtained. The wave excitation force is calculated via the known incident wave potential and the radiation potential with a theorem of Haskind employed. To verify the correctness of this method, an example is computed respectively through the bound element method and analytical method. Results show that two numerical methods. are in good agreement, which shows that the present method is applicable. In addition, the trends of hydrodynamic coefficients and wave force are analyzed under different conditions by use of the present analytical method.     

Wave radiation by a deep submerged cylinder with application to ocean structure

The radiation problem for a deep submerged cylinder is analysed and an asymptotic expression, uniformly valid in the whole range of frequencies, is derived for the radiation damping and exciting force. The obtained expression is a natural extension of the inertia term in the well known Morison's formula and may be useful in the analysis of certain ocean structures such as a tension leg platform, for example. In particular it makes it possible to define a geometry tuned to have null excitation at some desired frequency.     

Dynamics of an elastically moored floating body by the three-dimensional infinite element method

The three-dimensional problem of the dynamics of a moored floating object under the action of regular waves is solved numerically as a boundary value problem by use of the finite-infinite element method. The cross-sectional shape of the floating body and the mooring arrangements may all be arbitrary. The mathematical formulations of the problem and procedures of the numerical method are presented in this paper. A corresponding computer program WALOAD has been developed, which is capable of computing wave forces on fixed and floating structures. Numerical computations using this program could give very accurate results, even though rather coarse meshes were used. The program is easy to use and is readily applicable in many practical situations.     

远海浮式结构物与供应船旁靠系泊特性研究

针对远海浮式结构物与供应船进行旁靠作业时,水动力干扰、两船的相对运动、旁靠系缆系统和护舷系统的受力特征等问题开展研究。建立各船的有限元模型,设计出两船旁靠连接缆系统,选取合适的系泊缆和护舷参数。研究表明:浮式结构物和供应船的横荡、纵荡方向存在一定的同步性或跟随性,幅值相差不大,其它方向的运动并不存在明显的同步特征;供应船的各自由度运动幅值均比浮式结构物偏大;旁靠护舷的受力时历出现了明显的低频效应,说明护舷的受力较大程度上受船体低频慢漂运动的影响;浮式结构物对供应船的水动力干扰较大,当浮式结构物在供应船的上风位置时,表现为屏蔽效应,供应船的运动较小;在其背风位置时,运动加剧,出现多次共振、峰值放大现象,供应船对浮式结构物的水动力性能几乎无影响,因此,供应船从浮式结构物的下风口一侧靠泊作业将更有利于船舶的安全性能。这些研究结论可为实际工程操作提供参考。     

Wave shoaling and diffraction in current over a mild-slope

The wave relative frequency in the coordinate system moving with current and the angle between the direction of wave propagation and that of current are computed based on the wave dispersion relation. The current field is computed by solving the depth averaged shallow water equations. The wave field is computed by solving the mildslope equation which has taken the current‘s effect into account. A numerical model is established using a finite element method for simulating the wave shoaling and diffraction in current over a mild-slope, and the numerical results are reasonable to compare with the experimental data.