Wave driven free surface motion in the gap between a tanker and an FLNG barge

When two vessels are moored side-by-side with a narrow gap between them, intense free surface motions may be excited in the gap as a result of complex hydrodynamic interactions. These influence the motions of the two vessels, and the forces in any moorings. The present paper uses first and second order wave diffraction analysis to investigate this phenomenon. Key theoretical aspects of the numerical analysis are first summarised, including the vital need to suppress “irregular frequency” effects; and results are given to validate the code used. The case of a tanker alongside a large floating FLNG barge is then considered in detail.     

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.     

波浪对阻抗型圆柱群的绕射

应用柱面上阻抗型边界条件分析单柱和圆柱群上波面高度和总波浪力的分布规律。随着阻抗值减小波面高度明显减小,柱上总的波浪力也随之减小。由于柱间干扰和阻抗影响,波浪力在一定的波数尺寸范围内出现急降区,阻抗型柱的变化平缓,而刚性光滑壁面柱降低显著,说明阻抗越小柱间波浪散射强度越小。     

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。     

四柱结构波浪绕射模型试验研究

张力腿平台的支撑结构由四根直立圆柱构成,四根支撑圆柱周围波面高度的计算对张力腿平台结构安全以及气隙设计具有重要意义。采用模型试验的方法对四柱结构的波浪绕射问题进行研究。试验中对柱体附近多个位置处的波面高度进行测量,通过对测量数据的统计分析,得到一阶和二阶水面波高分量幅值。为了验证绕射理论在计算波面高度上的适用性,试验结果与数值模拟结果进行了对比。通过对比发现,即使波陡较大的情况下二阶绕射理论也可以很好地对波面高度进行模拟。同时,对发生在多柱结构内部的重要近场干涉现象也进行了观测。在特定的入射频率下,试验中观测到四柱结构内部流体发生明显的共振运动。     

波浪在三维圆形岛地形上的绕射研究

波浪在传播过程中遇到岛屿就会发生绕射。本文使用混合元方法对修正型缓坡方程进行了数值求解,并与KUO et al的解析解进行了比较验证。在此基础上研究了工程尺度背景下,波浪在三维圆形岛地形上的绕射,计算了不同入射波浪周期、浅滩形状参数和岛屿尺寸情况下,沿波浪传播方向断面上和岛屿岸线上的相对波高大小。计算结果表明：随着入射波周期的减小、浅滩形状参数的增大和岛屿尺寸的减小,圆形岛迎浪侧的相对波高振荡幅度、圆形岛背浪侧的相对波高大小以及岛屿岸线上的相对波高振幅和大小均随之增大。不同情况下,岛屿岸线上的相对波高最大值大多数发生在迎浪点,个别发生在迎浪点两侧20°~25°处;最小值发生在背浪点两侧30°附近。     

A method for second-order diffraction potential from an axisymmetric body

The paper provides a detailed analysis for the second-order diffraction of monochromatic waves. For the second-order potential on the free surface, the paper proposed a forward prediction method for computing the integration on the free surface. By this method we only need to run the infinity integration on the free surface directly for a few points; a one-step quadrature can then be applied successively outward from the body for potentials at other points. For wave diffraction from a body of revolution with a vertical axis, the paper derives a new integral equation, which can cancel the leading singularity in the derivative of ring Green's functions automatically. To obtain accurate results, different approaches are also used to deal with singularities in the ring Green's functions in the integration on both the body surface and free surface. The method has been implemented for bodies of revolution with vertical axes, but the theory is also available for arbitrary bodies.A numerical examination is made to validate the numerical code by comparing the second-order forces and moments on uniform and truncated cylinders and second-order diffraction potentials on the free surface with some published results. The comparison shows that the present results are in good agreement with those published. The method is also used to compute the second-order wave elevation around uniform and truncated cylinders.     

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。     

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。     

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.     

Radiation and diffraction of linear water waves by an infinitely long submerged rectangular structure parallel to a vertical wall

The radiation and the diffraction of linear water waves by an infinitely long floating rectangular structure submerged in water of finite depth with leeward boundary being a vertical wall are analyzed in this paper by using the method of separation of variables. Analytical expressions for the radiated and diffracted potentials are derived as infinite series with unknown coefficients determined by the eigenfunction expansion matching method. The expressions for wave forces and hydrodynamic coefficients are given. A comparison is made between the results obtained by the present analytical solution and those obtained by the boundary element method. By using the present analytical solution, the hydrodynamic influences of the submergence, the width, the thickness of the structure, and the distance between the structure and the wall on the wave forces and hydrodynamic coefficients are discussed in detail.     

Large capacity multi-float configurations for the wave energy converter M4 using a time-domain linear diffraction model

The moored three-float line absorber WEC M4 has been developed to optimise power capture through experiments and linear diffraction modelling. With the progression down wave from small to medium to large floats, the device heads naturally into the wave direction. The bow and mid floats are rigidly connected by a beam and a beam from the stern float is connected to the hinge point above the mid float for power take off (PTO). Increasing the bow to mid float spacing to be more than 50% greater than the mid to stern float spacing has been found to improve power capture. To increase power capture further and potentially reduce electricity generation cost the number of mid floats and stern floats is increased while maintaining a single bow float for mooring connection. The bow and mid floats still form a rigid body while the stern floats may respond independently. A time domain linear diffraction model based on Cummins method has been applied to configurations of 121, 123, 132, 133, and 134 floats where the numbers indicate the number of floats: bow, mid, stern. This shows how power capture is increased while response remains similar. We only consider uni-directional (long-crested) waves with narrow band width typical of swell. By considering scatter diagrams for various offshore sites capacities may range from 3.7 MW to 17.3 MW for the eight float system with a capacity factor of 1/3 while the cost of electricity assuming capital cost to be a fixed multiple of steel cost is reduced from that for the three-float system.     

Long Waves Induced by Wave Groups over a Trench

The second order long waves of the mean water free surface displacement induced by the wave groups over a trench are discussed in this paper. The incident wave groups are supposed to be superposed by 2 linear waves with different amplitudes, phases and slightly different frequencies. Some of the theoretical formulas and numerical results are presented.     

Wave radiation and diffraction by a two-dimensional floating body with an opening near a side wall

The radiation and diffraction problem of a two-dimensional rectangular body with an opening floating on a semi-infinite fluid domain of finite water depth is analysed based on the linearized velocity potential theory through an analytical solution procedure. The expressions for potentials are obtained by the method of variation separation, in which the unknown coefficients are determined by the boundary condition and matching requirement on the interface. The effects of the position of the hole and the gap between the body and side wall on hydrodynamic characteristics are investigated. Some resonance is observed like piston motion in a moon pool and sloshing in a closed tank because of the existence of restricted fluid domains.     

A comparison of several wave spectra for the random wave diffraction by a semi-infinite breakwater

A comparison of the diffraction of multidirectional random waves using several selected wave spectrum models is presented in this paper. Six wave spectrum models, Bretschneider, Pierson–Moskowitz, ISSC, ITTC, Mitsuyasu, and JONSWAP spectrum, are considered. A discrete form for each of the given spectrum models is used to specify the incident wave conditions. Analytical solutions based on both the Fresnel integrals and polynomial approximations of the Fresnel integrals and numerical solutions of a boundary integral approach have been used to obtain the two-dimensional wave diffraction by a semi-infinite breakwater at uniform water depth. The diffraction of random waves is based on the cumulative superposition of linear diffraction solution. The results of predicted random wave diffraction for each of the given spectrum models are compared with those of the published physical model presented by Briggs et al. [1995. Wave diffraction around breakwater. Journal of Waterway, Port, Coastal and Ocean Engineering—ASCE 121(1), 23–35]. Reasonable agreement is obtained in all cases. The effect of the directional spreading function is also examined from the results of the random wave diffraction. Based on these comparisons, the present model for the analysis of various wave spectra is found to be an accurate and efficient tool for predicting the random wave field around a semi-infinite breakwater or inside a harbor of arbitrary geometry in practical applications.     

三维二阶水波绕射问题的有限元时域计算

本文用有限元法配合时步处理来求解三维非线性水波的绕射问题,自由表面条件和物面条件都满足到二阶,采用人工阻尼区来吸收反射波,流场内的速度势通过求解有限元方程得到。对垂直圆柱体的绕射问题进行了计算,得到了自由表面波高时间历程和圆柱所受到的波浪力,计算结果和有关文献的理论计算结果进行了比较。     

On the radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas

The radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas of finite depth is investigated. The analytical expressions for the radiated and diffracted potentials are derived as infinite series by use of the method of separation of variables. The unknown coefficients in the series are determined by the eigenfunction expansion matching method. The expressions for wave forces, hydrodynamic coefficients and reflection and transmission coefficients are given and verified by the boundary element method. Using the present analytical solution, the hydrodynamic influences of the angle of incidence, the submergence, the width and the thickness of the structure on the wave forces, hydrodynamic coefficients, and reflection and transmission coefficients are discussed in detail.     

The diffraction of linear waves by a uniform vertical cylinder with cosine-type radial perturbations

The interaction of linear waves with a uniform, bottom-mounted, surface-piercing cylinder whose diameter exhibits a cosine-type variation is investigated. Two solution methods are presented. One method is based on a perturbation theory, using a perturbation parameter defined in terms of the surface geometry of the cylinder. The analysis includes terms up to the first-order in this parameter, where the zeroth-order solution corresponds to a circular cylinder. The velocity potentials at the zeroth and first orders are expressed as eigenfunction expansions involving unknown coefficients that are subsequently determined through the cylinder boundary conditions. The second method is based on Green's theorem and gives rise to an integral equation for the fluid velocity potential on the cylinder surface. A comparison between the results of these two methods has proved that they are in good agreement for small values of the perturbation parameter. Numerical results are presented that illustrate the influence of the magnitude and frequency of these perturbations on the resulting hydrodynamic force and the wave runup on the cylinder.     

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.