直立浮式柱群波浪荷载计算

为了研究类似张力腿平台（ＴＬＰ）等海洋工程结构物的运动,浮式直立柱群的波浪荷载计算是十分重要的。应用匹配渐进和特征函数展开法得到单柱流场速度势的半解析解,再引入大间距假设,将柱群中某一柱体对其它柱体的扰动作用用平面入射波来代替。同时对该问题进行了非平面波修正,计入柱间水动力相互作用,解决了柱群的绕射问题。应用该方法计算了不同条件下的双柱波浪荷载的幅频特征。     

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.     

Hydrodynamic interactions in floating cylinder arrays—I. Wave scattering

The hydrodynamic interactions due to wave scattering between the numbers of an array of stationary, truncated circular cylinders simulating the columns of an idealized tension-leg platform (TLP) are investigated. The method of solution for the fluid velocity potential involves replacing scattered waves by equivalent plane waves together with non-planar correction terms. This technique is, therefore, essentially a large spacing approximation. Use of this approach makes it possible to determine the hydrodynamic interactions between the array members utilizing only the diffraction characteristics of an isolated cylinder.Numerical results are presented for six array configurations consisting of 2–6 cylinders representing the legs of idealized TLPs. Calculations of the wave loads on these cylinders have been performed for a range of wave and structural parameters. It is found that, for certain parameter combinations, the influence of neighbouring bodies on the total wave field leads to hydrodynamic loading on individual columns which is significantly greater than the loading they would experience in isolation. The presented results demonstrate the significance of hydrodynamic interactions between TLP columns and clearly indicate that these effects should be considered by the designers and researchers associated with TLPs.     

Interaction of cnoidal waves with an array of vertical concentric porous cylinders

An array of large concentric porous cylinder arrays is mounted in shallow water exposed to cnoidal waves. The interactions between waves and cylinders are studied theoretically using an eigenfunction expansion approach. Semi-analytical solutions of hydrodynamic loads and wave run-up on each cylinder are obtained using first approximation to cnoidal waves. The square array configuration of four-legged identical concentric porous cylinder is investigated in present study. Numerical results reveal the variation of dimensionless wave force and wave run-up on individual cylinder with angle of incidence, porosity parameter, spacing between outer and inner cylinders, spacing between concentric porous cylinders and wave parameter. Different mechanism of wave force is found under different range of scattering parameter.     

Interaction of linear waves with an array of infinitely long horizontal circular cylinders in a two-layer fluid of infinite depth

The linear water wave scattering and radiation by an array of infinitely long horizontal circular cylinders in a two-layer fluid of infinite depth is investigated by use of the multipole expansion method. The diffracted and radiated potentials are expressed as a linear combination of infinite multipoles placed at the centre of each cylinder with unknown coefficients to be determined by the cylinder boundary conditions. Analytical expressions for wave forces, hydrodynamic coefficients, reflection and transmission coefficients and energies are derived. Comparisons are made between the present analytical results and those obtained by the boundary element method, and some examples are presented to illustrate the hydrodynamic behavior of multiple horizontal circular cylinders in a two-layer fluid. It is found that for two submerged circular cylinders the influence of the fluid density ratio on internal-mode wave forces is more appreciable than surface-mode wave forces, and the periodic oscillations of hydrodynamic results occur with the increase of the distance between two cylinders; for four submerged circular cylinders the influence of adding two cylinders on the wave forces of the former cylinders is small in low and high wave frequencies, but the influence is appreciable in intermediate wave frequencies.     

Approximate hydrodynamic analysis of multi-column ocean structures

An approximate, semi-analytical technique is developed to calculate the wave-induced loads and added-mass and radiation damping coefficients for idealized ocean structures consisting of arrays of large-diameter, truncated, vertical circular cylinders. The approach involves replacing the complete wave field scattered/radiated by one cylinder in the vicinity of another cylinder by a plane wave together with a non-planar correction term and so is essentially a large-spacing approximation. Numerical results are presented which illustrate the accuracy of the approximate approach and provide estimates of the hydrodynamic characteristics of several practical array configurations.     

Interactions of cnoidal waves with cylinder arrays

The three-dimensional scattering of cnoidal waves by cylinder arrays are studied numerically by using the generalized Boussinesq equations. The boundary-fitted coordinate transformation and a dual-grid technique are used to simplify the finite-difference computation. Also, a set of open boundary conditions and an incident cnoidal wave are incorporated for time-domain simulation. The free-surface elevation and hydrodynamic forces on each cylinder are calculated to illustrate the evolution of nonlinear waves and their interactions with large cylinder arrays. Comparisons are made between the present nonlinear wave loads and those obtained from linear diffraction theory. The sheltering role played by the neighboring cylinders and the feature of wave interference are discussed.     

A comparison of complete and approximate solutions for second-order diffraction loads on arrays of vertical ci cular cylinders

This paper presents a comparison between two theoretical methods for computing the second-order diffraction loads on arrays of bottom-mounted, surface-piercing vertical circular cylinders in regular waves. One method presents a complete solution for the second-order hydrodynamic loads on the cylinder array via a numerical integration over the mean fluid free-surface. The other method is based on a large spacing approximation between the array members and involves the solution of a set of equivalent isolated body problems to obtain estimates for the second-order hydrodynamic loads. Numerical results for a pair of cylinders indicate very good agreement between the two methods at center-to-center spacing of both three and five radii, indicating that the approximate method may be sufficient to compute hydrodynamic interference effects to the second-order in many practical engineering situations.     

Interference effects between flexible cylinders in waves

An approximate method is presented to estimate the hydrodynamic loading and associated structural response of each of a pair of free-standing, bottom-nounted, flexible circular cylinders subjected to a regular train of linear surface waves. The cylinders are aligned parallel to the incident wave direction and the response of each is assumed to be one-dimensional and governed by a beam equation. The solution technique for the fluid velocity potential involves replacing scattered waves by equivalent plane waves together with non-planar, first-correction terms, and can be shown to be a large-spacing approximation. Numerical results are presented which show the influence of the various wave and structural parameters on the hydrodynamic loading and dynamic response of the individual cylinders.     

弹性双柱在规则波作用下振动响应

通过速度势的特征展开方法,建立垂直圆柱对波浪绕射的解析解,得到作用在柱体上的波浪力计算表达式,通过谐波增量平衡法(IHB法),计算研究弹性双柱相对位置对双柱振动响应的影响。设计了弹性双柱体模型试验,数值结果与模型试验结果较吻合,为海洋工程结构振动设计提供一种解决方法。     

Wave interaction with a concentric porous cylinder system

This is a theoretical investigation of wave interaction with a concentric surface-piercing two-cylinder system. The exterior cylinder is porous and considered to be thin in thickness and the interior cylinder is impermeable. Both cylinders are rigidly fixed at the sea bed. The fluid motion is idealized as a linearized potential flow. The free-surface elevation and the total net hydrodynamic forces acting on both cylinders are determined analytically. The wave-induced overturning moments are also evaluated. It is found that, with the existence of the exterior porous cylinder, the hydrodynamic force acting on the interior cylinder is reduced if compared to the force exerted on the interior cylinder by a direct wave impact. The reduction of the wave amplitude around the leeward side of the outer porous cylinder is shown from the free-surface computations. In this paper, results are also presented to illustrate the effects of wave parameter and structural porosity on this wave and cylinder interaction problem. The role played by the ratio of radii of the inner and outer cylinders is duscussed.     

Diffraction of Water Waves by A Vertically Floating Cylinder in A Two-Layer Fluid

In this paper, the diffraction of water waves by a vertically floating cylinder in a two-layer fluid of a finite depth is studied. Analytical expressions for the hydrodynamic loads on the vertically floating cylinder are obtained by use of the method of eigenfunction expansions. The hydrodynamic loads on the vertically floating cylinder in a two-layer fluid inelude not only the surge, heave and pitch exciting forces due to the incident wave of the surface-wave mode, but also those due to the incident wave of the internal-wave mode. This is different from the case of a homogenous fluid. Some given examples show that, for a two-layer fluid system with a small density difference, the hydrodynamic loads for the surface-wave mode do not differ significantly from those due to surface waves in a single-layer fluid, but the hydrodynamic loads for the internal-wave mode are important over a wide range of frequencies. Moreover, also considered are the free surface and interface elevations generated by the diffraction wave due to the incident wave of the surface-wave and interhal-wave modes, and transfer of energy between modes.     

Three dimensional wave scattering by arrays of elliptical and circular cylinders

Recently, Chatjigeorgiou and Mavrakos (2009, 2010a) provided an analytic solution for the three dimensional wave scattering by arrays of elliptical cylinders. The present paper extends the contents of the existing study to tackle the problem of the hydrodynamic interactions between elliptical and circular cylinders. The main task is to derive an analytic solution for the total velocity potential for an arbitrary body of the array and accordingly, to express the hydrodynamic pressure, the exciting forces and the wave elevation in compact analytic closed-forms.The solution method is rather complicated as it considers the circular cylinders as different geometries and not special cases of elliptical cylinders with zero elliptic eccentricity. Nevertheless, the adopted procedure enhances the mathematical reconstruction of the physical subject as it requires the derivation and the employment of addition theorems that transform expressions from elliptic to polar coordinate systems in all four possible combinations.     

Fully nonlinear analysis of near-trapping phenomenon around an array of cylinders

The wave diffraction around an array of fixed vertical circular cylinders is simulated in a numerical wave tank by using a fully nonlinear model in the time domain. The emphasis of the paper lies in the insightful investigation of the nonlinear properties of the near-trapping phenomenon associated with the multiple cylinders. The numerical model is validated by analytical solutions as well as experimental data for waves propagating past two and four vertical cylinders in certain arrangements. An array of four identical circular cylinders at the corners of a square with an incident wave along the diagonal of the square is the main focus here for investigating the near-trapping phenomenon. When near-trapping occurs, the present study shows that an extremely high wave elevation near the cylinders can be observed. At the same time, the hydrodynamic forces on different cylinders are found to be either in phase or out of phase, leading to some characteristic force patterns acting on the whole structure. Due to the nature of the numerical model adopted, nonlinearity at different orders can be captured using a harmonic analysis. In addition to first- and second-order near-trapping, the third-order (triple-frequency) nonlinear component is presented for the first time. For the configuration selected, it is found that at one specific incident wave frequency and direction one trapped mode is excited by second-order effects, while a different trapped mode (having similar symmetries) is excited by the third harmonic of the incident wave frequency.     

Numerical calculation of forces induced by short-crested waves on a vertical cylinder of arbitrary cross-section

Most off-shore oil platforms are supported by vertical cylinders extending to the ocean floor. An important problem in off-shore engineering is the calculation of the wave loading exerted on these vertical cylinders. Analytical solutions have been found for the case of plane incident waves incident on a circular cylinder by MacCamy and Fuchs [(1954), Wave forces on piles: a diffraction theory. U.S. Army Corps of Engineering, Beach Erosion Board, Technical Memorandum No. 69] and also for short-crested waves incident on a circular cylinder by Zhu [(1993), Diffraction of short-crested waves around a circular cylinder. Ocean Engng 20, 389–407]. However, for a cylinder of arbitrary cross-section, no analytic solutions currently exist. Au and Brebbia [(1983), Diffraction of water waves for vertical cylinders using boundary elements. Appl. Math. Modelling 7, 106–114] proposed an efficient numerical approach to calculate the wave loads induced by plane waves on vertical cylinders by using the boundary element method. However, wind-generated waves are better modelled by short-crested waves. Whether or not these short-crested waves can induce larger wave forces on a structure is of great concern to ocean engineers. In this paper wave loads, induced by short-crested incident waves, on a vertical cylinder of arbitrary cross-section are discussed. For a cylinder of certain cross-section, the wave loads induced by short-crested waves can be larger than those induced by plane waves with the same total wave number.     

Fully nonlinear simulations of wave resonance by an array of cylinders in vertical motions

The finite element method(FEM) is employed to analyze the resonant oscillations of the liquid confined within multiple or an array of floating bodies with fully nonlinear boundary conditions on the free surface and the body surface in two dimensions.The velocity potentials at each time step are obtained through the FEM with 8-node quadratic shape functions.The finite element linear system is solved by the conjugate gradient(CG) method with a symmetric successive overelaxlation(SSOR) preconditioner.The waves at the open boundary are absorbed by the combination of the damping zone method and the Sommerfeld-Orlanski equation.Numerical examples are given by an array of floating wedgeshaped cylinders and rectangular cylinders.Results are provided for heave motions including wave elevations,profiles and hydrodynamic forces.Comparisons are made in several cases with the results obtained from the second order solution in the time domain.It is found that the wave amplitude in the middle region of the array is larger than those in other places,and the hydrodynamic force on a cylinder increases with the cylinder closing to the middle of the array.     

Interaction between waves and an array of floating porous circular cylinders

The present study theoretically as well as experimentally investigates the interaction between waves and an array of porous circular cylinders with or without an inner porous plate based on the linear wave theory.To design more effective floating breakwaters,the transmission rate of waves propagating through the array is evaluated.Each cylinder in the array is partly made of porous materials.Specifically,it possesses a porous sidewall and an impermeable bottom.In addition,an inner porous plate is horizontally fixed inside the cylinders.It dissipates the wave more effectively and eliminates the sloshing phenomenon.The approach suggested by Kagemoto and Yue(1986) is adopted to solve the multiple-scatter problem,while a hierarchical interaction theory is adopted to deal with hydrodynamic interactions among a great number of bodies,which efficiently saves computation time.Meanwhile,a series of model tests with an array of porous cylinders is performed in a wave basin to validate the theoretical work and the calculated results.The draft of the cylinders,the location of the inner porous plate,and the spacing between adjacent cylinders are also adjusted to investigate their effects on wave dissipation.     

Fully Nonlinear Simulations of Wave Resonance by An Array of Cylinders in Vertical Motions

The finite element method (FEM) is employed to analyze the resonant oscillations of the liquid confined within multiple or an array of floating bodies with fully nonlinear boundary conditions on the free surface and the body surface in two dimensions. The velocity potentials at each time step are obtained through the FEM with 8-node quadratic shape functions. The finite element linear system is solved by the conjugate gradient (CG) method with a symmetric successive overelaxlation (SSOR) preconditioner. The waves at the open boundary are absorbed by the combination of the damping zone method and the Sommerfeld-Orlanski equation. Numerical examples are given by an array of floating wedge- shaped cylinders and rectangular cylinders. Results are provided for heave motions including wave elevations, profiles and hydrodynamic forces. Comparisons are made in several cases with the results obtained from the second order solution in the time domain. It is found that the wave amplitude in the middle region of the array is larger than those in other places, and the hydrodynamic force on a cylinder increases with the cylinder closing to the middle of the array.     

海洋结构物小尺度桩柱的水动力系数研究与进展

本文主要归纳了基于Morison方程求解小尺度桩柱的水动力系数方面的研究成果。分别从单桩柱和群桩两个方面对水动力系数的研究成果,包括纯波、波流混合、横向力、直立桩柱、倾斜桩柱、复杂结构桩柱、粗糙度等进行了阐述,给出了在波流条件下水动力系数的变化规律;归纳了当前水动力系数的求解方法;介绍了在水动力系数的物模实验、数值仿真以及实验数据处理方法上的研究进展,并提出了相关研究的建议。     

Interaction of Linear Waves with Infinitely Long Horizontal Cylinders Studied by Boundary Element Method

The two-dimensional problems concerning the interaction of linear water waves with cylinders of arbitrary shape in two-layer deep water are investigated by use of the Boundary Integral Equation Method (BIEM). Simpler new expressions for the Green functions are derived, and verified by comparison of results obtained by BIEM with those by an analytical method. Examined are the radiation and scattering of linear waves by two typical configurations of cylinders in two-layer deep water. Hydrodynamic behaviors including hydrodynamic coefficients, wave forces, reflection and transmission coefficients and energies are analyzed in detail, and some interesting physical phenomena are observed.