Wave enhancement due to blockage in semi-submersible and TLP structures

An exact analytical method is described to solve the diffraction problem of a group of truncated vertical cylinders. In order to account for the interaction between the cylinders, Kagemoto and Yue's exact algebraic method is utilised (Kagemoto, H., Yue, D.K.P., 1986. Interactions among multiple three-dimensional bodies in water waves: an exact algebraic method. J Fluid Mech, 46, 129–139). The isolated cylinder diffraction potential is obtained using Garret's solution and evanescent mode solutions are derived in a similar manner (Garret, C.J.R., 1971. Wave forces on a circular dock. J Fluid Mech, 46, 129–139).Free surface elevations are calculated for an array of four cylinders and compared with experiments. Comparisons show good agreement.     

Approximation of wave forces on cylinder arrays

An approximate method for the estimation of wave forces on groups of fixed vertical cylinders is presented. The method is based upon a large spacing approximation and involves replacing scattered diverging waves by plane waves. The method is shown to give good results when compared with an exact method, even when the spacing is small. Some new results for a group of five cylinders are presented.     

柱对称双浮子波能装置散射问题的解析方法

通过构造绕射势特解的一种新表达式,基于特征函数展开法提出了线性入射波作用下柱对称双振荡浮子波能装置散射问题的一种新的表达式,并在此基础上计算了垂向波浪激励力.从速度势的求解过程可知,绕射势和辐射势的计算量相当,但垂向波浪激励力的计算比采用Haskind关系方法简单得多,两种方法的结果一样.另外对不同工况下垂向波浪激励力的变化趋势进行了分析.     

Wave loads on large vertical cylinders: A design method

The finite element method based on linear diffraction theory proposed by Zienkiewicz and Bettess (1977) has been used to compute wave loads and moments about the bed of surface piercing cylinders of circular, square, rectangular and elliptical sections for different angles of wave incidence. On the basis of the results obtained, a design method is presented in the form of simple design charts for estimating wave forces and moments on large cylinders of arbitrary sections. The numerical solutions obtained have been checked for their validity by comparing with other theoretical solutions and experimental data. Further the application of the design method to a case study shows good correlation with experimental and other theoretical solutions.     

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。     

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.     

Wave Action on Structures of Combined Cylinders

1.Introduction Owingtoitssignificanteffectofreductionofwaveloadsandwaverun up,theperforatedwallon anarrayofcylindricalstructureshasreceivedconsiderableattentioninrecentyears.Manyresearches havebeencarriedoutinthisfield.Anexactsolutionforthediffractionoflinearwaterwaveswithan arrayofimpermeablecylinderswasfirstgivenbySpringandMonkmeyer(1974)usinganeigenfunction expansionapproach.Subsequently,LintonandEvans(1990)madeamajorsimplificationtothetheo ry,whichallowedthenear fieldquantitiessuchasload…     

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.     

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。     

Solitary wave interaction with a concentric porous cylinder system

Theoretical investigations on solitary waves interacting with a surface-piercing concentric porous cylinder system are presented in this paper. The outer cylinder is porous and considered thin in thickness, while the inner cylinder is solid. Both cylinders are rigidly fixed on the bottom. Following Isaacson's [Isaacson, Micheal de St. Q., 1983. Solitary wave diffraction around large cylinder. Journal of the Waterway, Port, Coastal and Ocean Engineering 109(1), 121–127.] approach, we obtained the solutions for free-surface elevation and the corresponding velocity potential in terms of Fourier integrals. Numerical results are presented to show the effects of incident wave condition, porosity of the outer cylinder and radius ratio on wave forces and wave elevations around the inner and outer cylinders.     

Hydrodynamic interference between floating cylinders in oblique seas

The hydrodynamic interference phenomena arising from multiple two-dimensional horizontal cylinders interacting with obliquely incident linear monochromatic waves are treated. A finite element method incorporating radiation boundary dampers is employed to solve the corresponding diffraction/radiation boundary value problems, where flexural mode responses are assumed. Both extreme cases of a rigidly connected catamaran and freely floating cylinders are studied in detail. Numerical results of both cases compare closely with those obtained by the method of multipoles. Important interference phenomena are identified which would assist in the design of facilities and operations involving multiple structures.     

Hydrodynamic coefficients for vertical composite cylinders

An efficient method of calculation for vertical, composite cylinders at finite depth is presented. Hydrodynamic coefficients calculated by this method are compared with numerical results obtained by a surface element method.     

Diffraction of oblique waves by thick rectangular barriers

A complete analytical solution is presented for the linear diffraction of oblique waves by horizontal rectangular cylinders either fixed at the free surface or mounted on the sea bed in a finite-depth of water. Helmholtz equation is employed as the governing differential equation obtained by reducing the 3-D oblique wave scattering problem to a 2-D case. According to the method proposed, the fluid region is divided into three sub-regions in which the governing differential equation is solved by the separation of variables. The solutions for each region are then matched on the common boundaries of sub-regions to determine the unknowns of the eigen series expansions and Fourier series. Thus transmitted and reflected waves are obtained in the far-field, and forces and moments acting on the rectangular cylinder fixed at the free surface are also given. Comparisons are made in order to check the accuracy of the method.     

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.     

Hydrodynamic interactions between two vertical circular cylinders in linear oscillatory flow

Linear potential theory is used to investigate the hydrodynamic interactions between two vertical cylinders in harmonic flow. The behaviour of the added mass and damping is studied for various cylinder diameters, lengths of immersion and spacing between the cylinders. In practice, the results have relevance to the fluid loading on offshore structural members, such as risers and platform legs, and pipeline bundles. On a more theoretical level, comparisons are possible between the results of a three-dimensional diffraction program and various asymptotic expressions to establish the range of validity of the latter and the need, where appropriate, of the former.     

Multipole expansions for wave diffraction and radiation in deep water

A multipole expansion of the velocity potential is described for two- and three-dimensional wave diffraction and radiation problems. The velocity potential is expressed in terms of a series of multipole potentials. The wave terms and the local disturbance terms are represented by separated multipole potentials. Floating bodies and submerged bodies are treated in the same way. This approach differs from that of some other authors, who considered floating bodies and submerged bodies separately and derived entirely different multipoles. Semi-analytical solutions for a circular cylinder in two-dimensional motions are given. It is found that the local disturbance decays rapidly and steadily. The general application of the multipole expansion to arbitrary geometries is also presented, based on a method coupling multipoles to a boundary integral expression. Numerical results for several floating and submerged cylinders are presented.     

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.     

两层流体中多个圆柱浮体波浪力的解析方法

采用解析方法研究了线性入射波作用下两层流体中多个圆柱形淹没浮体的渡浪力特性.首先基于多极子展开方法,建立了散射势函数的解析表达式,并进一步得到浮体散射渡浪力的计算公式,然后利用边界元方法验证了本文的解析解,最后分析了不同参数的变化对双圆柱形浮体结构波浪力的特有影响.     

Benchmark computations of wave run-up on single cylinder and four cylinders by naoe-FOAM-SJTU solver

The benchmark simulations of wave run-up on a fixed single truncated circular cylinder and four circular cylinders are presented in this paper. Our in-house CFD solver naoe-FOAM-SJTU is adopted which is an unsteady two-phase CFD code based on the open source package OpenFOAM. The Navier-Stokes equations are employed as the governing equations, and the volume of fluid (VOF) method is applied for capturing the free surface. Monochromatic incident waves with the specified wave period and wave height are simulated and wave run-up heights around the cylinder are computed and recorded with numerical virtual wave probes. The relationship between the wave run-up heights and the incident wave parameters are analyzed. The numerical results indicate that the presented naoe-FOAM-SJTU solver can provide accurate predictions for the wave run-up on one fixed cylinder and four cylinders, which has been proved by the comparison of simulated results with experimental data.     

Computations of forces on, and particle orbits around, horizontal cylinders under steep waves

A numerical method, based on a boundary integral equation combined with a non-linear time stepping procedure for the free water surface, is developed for simulations of the interaction between highly non-linear water waves and submerged horizontal cylinders. The method is based on potential theory, and the omission of viscous effects restricts the wave-structure interaction computations to low Keulegan-Carpenter numbers where inertia forces are dominant. The numerical scheme is verified by computations with a steep wave of exact form during several wave periods, and by computations of a breaking wave. A new method for tracing the orbits of water particles in the fluid domain is developed, and the influence from submerged structures on the orbits is visualized through several computational examples. The wave forces on submerged structures are computed and are found to correspond well with other computed results for low Keulegan-Carpenter numbers.