An experimental investigation of hydrodynamic coefficients for a vertical truncated rectangular cylinder due to regular and random waves

The research into hydrodynamic loading on ocean structures has concentrated mostly on circular cross-section members and relatively limited work has been carried out on wave loading on other cross-sections such as rectangular sections. These find applications in many offshore structures as columns and pontoons in semi-submersibles and tension-leg platforms. The present investigation demonstrates the behaviour of rectangular cylinders subject to wave loading and also supplies the hydrodynamic coefficients for the design of these sections.This paper presents the results of wave forces acting on a surface piercing truncated rectangular cylinder set vertically in a towing tank. The experiments are carried out in a water depth of 2.2 m with regular and random waves for low Keulegan–Carpenter number up to 6. The rectangular cylinder is of 2 m length, 0.2 m breadth and 0.4 m width with a submergence depth of 1.45 m from still water level. Based on Morison equation, the relationship between inertia and drag coefficients are evaluated and are presented as a function of KC number for various values of frequency parameter β, for two aspect ratios of cylinders, equals to 1/2 and 2/1. Drag and inertia coefficients obtained through regular wave tests are used for the random wave analysis to compute the in-line force spectrum.The results of the experiments show the drag and inertia coefficients are strongly affected by the variation in the aspect ratios of the cylinder. The drag coefficients decreases and inertia coefficients increases with increase in Keulegan–Carpenter number up to the range of KC number tested. The random wave results show a good correlation between measured and computed force spectrums. The transverse forces in both regular and random waves are found to be small compared to in-line forces.     

An analytical approach for the calculation of random wave forces on submerged tunnels

This paper deals with the random forces produced by high ocean waves on submerged horizontal circular cylinders. Arena [Arena F, Interaction between long-crested random waves and a submerged horizontal cylinder. Phys Fluids 2006;18(7):1–9 (paper 076602)] obtained the analytical solution of the random wave field for two dimensional waves by extending the classical Ogilvie solution [Ogilvie TF, First- and second-order forces on a cylinder submerged under a free surface. J Fluid Mech 1963;16:451–472; Arena F, Note on a paper by Ogilvie: The interaction between waves and a submerged horizontal cylinder. J Fluid Mech 1999;394:355–356] to the case of random waves. In this paper, the wave force acting on the cylinder is investigated and the Froude Krylov force [Sarpkaya T, Isaacson M, Mechanics of wave forces on offshore structures, Van Nostrand Reinhold Co.; 1981], on the ideal water cylinder, is calculated from the random incident wave field. Both forces represent a Gaussian random process of time. The diffraction coefficient of the wave force is obtained as quotient between the standard deviations of the force on the solid cylinder and of the Froude Krylov force. It is found that the diffraction coefficient of the horizontal force C_do is equal to the C_dv of the vertical force. Finally, it is shown that, since a very large wave force occurs on the cylinder, it may be calculated, in time domain, starting from the Froude Krylov force. It is then shown that this result is due to the fact that the frequency spectrum of the force acting on the cylinder is nearly identical to that of the Froude–Krylov force.     

三阶Stokes型随机波浪载荷谱研究

应用非线性谱分析理论，对三阶Stokes型随机波浪载荷谱进行了分析，将波面方程及海水质点的水平速度用一阶波面的非线性组表示，导出了随机波浪谱的表达式。为了便于求解随机波浪的载荷谱，将阻力项展开为幂级数式，并应用非线性谱分析理论，确定了幂级数的系数，进而将波浪载荷表示为一阶波面及其导数的非线性组合，最后得出波浪载荷谱密度的表达式，并应用数值分析方法，得出单位桩柱波浪力及总波浪力谱密度。     

Probabilistic model for wave forces acting on a cylinder in random waves

Generally, the sea-state (random waves) is best described by a wave spectrum. A number of statistical models for wave spectra has been well established and a sea-state can be specified. Once the specified sea-state is established, the corresponding model for wave forces acting on a single cylinder or a group of cylinders can be formulated. Since peak force is of more practical value, a multivariate or joint probability density function for wave forces has been developed for the peak force distribution of wave forces. This theoretical force model derives the tri-variate probability density function P(F, F′, F″), where F is the peak force defined by Morison equation. This model is of wide-band in nature and is tested by wave flume experiments.     

Third order wave force on axisymmetric bodies

The third order triple-frequency wave load on fixed axisymmetric bodies by monochromatic waves is considered within the frame of potential theory. Waves are assumed to be weak non-linearity and a perturbation method is used to expand velocity potentials and wave loadings into series according to a wave steepness of kA. Integral equation method is used to compute velocity potentials up to second order in wave steepness. The third order triple-frequency wave loads are computed by an indirect method and an efficient method is applied to form the third order forcing term on the free surface quickly. The method can be used to compute third order triple-frequency surge force, heave force and pitch moment on any revolution bodies with vertical axes. The comparison with Malenica and Molin's results is made on surge force on a uniform cylinder, and comparison with experimental results is made on third order surge force, heave force and pitch moment on a truncated cylinder. More numerical computations are carried out for third order forces and moments on a uniform cylinder, truncated cylinders and a hemisphere.     

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.     

内孤立波作用下竖直圆柱体的横向力研究

本文对内孤立波作用下圆柱体的水动力特性进行了数值研究。对不同直径、不同水深比、不同浸没深度的圆柱进行了水平方向受力分析,从多个因素出发,研究了内孤立波对水下竖直圆柱的水平作用情况。通过分析水平作用力和力矩的时程曲线,得到内孤立波行进过程中对于圆柱体的横向作用力和力矩与时间的关系。通过对比不同工况下内孤立波橫向作用力幅值,得到内孤立波作用力幅值与圆柱直径、水深比以及浸没深度的关系。结果表明,内孤立波横向作用力(力矩)幅值与圆柱直径呈线性相关关系,但与水深比相关关系不明显,随着圆柱浸没深度的增加,内孤立波横向作用力幅值呈现出先增大后减小的趋势。     

A quasi-cloaking phenomenon to reduce the wave drift force on an array of adjacent floating bodies

The mooring of offshore floating structures, such as offshore platforms, in large waves against drift forces and rotational moments is a challenging problem in offshore engineering. To accurately investigate such problems, called positioning problems, the time-averaged steady forces of the second order known as the wave drift forces must be taken into account. Fortunately, a cloaking phenomenon occurs under certain conditions and dramatically reduces the wave drift force acting on such a floating body, as previously reported by several researchers. In the diffraction problem of water waves, cloaking refers to the condition where there is no scattering in the form of radial outgoing waves. The reduction of wave drift force on a truncated cylinder with the occurrence of cloaking phenomenon has been numerically and experimentally confirmed. In this paper, the arrangement of several small circular cylinders at regular intervals in a circle concentric with a fixed floating body is considered as an effective means of reducing the wave drift force. Using a combination of a higher-order boundary element method (HOBEM) and wave interaction theory, the influences of the geometric parameters of the outer surrounding cylinders on the wave drift force and the total scattered-wave energy are systematically investigated and discussed. A quasi-cloaking phenomenon is first found and reported in the present study, which is beneficial and flexible for application in practical engineering. More than one quasi-cloaking trigger (where a trigger is an occurrence condition) can be found simply by varying the distance between the inner and outer floating bodies.     

Experimental Study on Ocean Internal Wave Force on Vertical Cylinders in Different Depths

A series of experimental studies about the force of internal solitary wave and internal periodic wave on vertical cylinders have been carried out in a two-dimensional layered internal wave flume. The internal solitary waves are produced by means of gravitational collapse at the layer thickness ratio of 0.2, and the internal periodic waves are produced with rocker-flap wave maker at the layer thickness ratio of 0.93. The wave parameters are obtained through dyeing photography. The vertical cylinders of the same size are arranged in different depths. The horizontal force on each cylinder is measured and the vertical distribution rules are researched. The internal wave heights are changed to study the impact of wave heights on the force. The results show that the horizontal force of concave type internal solitary wave on vertical cylinder in the upper-layer fluid has the same direction as the wave propagating, while it has an opposite direction in the lower-layer. The horizontal force is not evenly distributed in the lower fluid. And the force at different depths increases along with wave height. Internal solitary wave can produce an impact load on the entire pile. The horizontal force of internal periodic waves on the vertical cylinders is periodically changed at the frequency of waves. The direction of the force is opposite in the upper and lower layers, and the value is close. In the upper layer except the depth close to the interface, the force is evenly distributed; but it tends to decrease with the deeper depth in the lower layer. A periodic shear load can be produced on the entire pile by internal periodic waves, and it may cause fatigue damage to structures.     

基于粘性流模型的筒型基础防波堤波浪力数值分析

筒型基础防波堤是一种新型港口海岸工程结构,其基础上部是由连续排列的圆筒构成的直立防浪墙.采用粘性流数值模型,研究连续圆筒防波堤上波浪力竖向分布、水平(沿圆筒环向)分布和波浪力合力特性,并对粘性流数值模型计算的平面直墙波浪力与海港水文规范方法计算结果;粘性流数值模型计算的连续圆筒墙面波浪力与平面直墙波浪力;无限长连续圆筒墙面波浪力与有限长连续圆筒墙面波浪力进行比较分析.针对所选工程算例,建议按<海港水文规范>中平面直墙波浪力计算方法确定连续圆筒防波堤上的波浪力时,波峰时考虑0.90左右的折减系数,波谷时考虑0.95左右的折减系数.     

Interaction of regular waves with a group of dual porous circular cylinders

Diffraction of linear waves around a group of dual porous cylinders consisting of a thin and porous outer cylinder with an impermeable inner cylinder is investigated analytically based on the eigenfunction expansion method proposed by Spring and Monkmeyer [Spring BH, Monkmeyer PL. Interaction of plane waves with vertical cylinders. In: Proceedings 14th international coastal engineering conference. 1974. p. 1828–47] and further modified by Linton and Evans [Linton CM, Evans DV. The interaction of waves with arrays of vertical circular cylinders. Journal of Fluid Mechanics 1990;215:549–69]. The present formulation is an extension of the work of Wang and Ren [Wang KH, Ren X. Wave interaction with a concentric porous cylinder system. Ocean Engineering 1994;21(4):343–60], wherein; the interaction of linear waves with a single concentric porous cylinder system was studied. This paper aims at investigating the influence of multiple interactions between the cylinders in the group on the hydrodynamic wave forces, wave run-up and free-surface elevation in their vicinity. Further, the study focuses on the variation of the forces and run-up on the individual cylinders within the group compared to that on isolated cylinders.     

Wave forces acting on a vertical circular cylinder with a constant forward velocity

Wave forces acting on submerged circular cylinders moving forward with a constant velocity in regular waves are investigated experimentally. Hydrodynamic forces acting on the cylinder forced to surge in a steady are also measured and hydrodynamic coefficients were obtained. Wave force coefficients obtained from wave force measurements are compared with the hydrodynamic coefficients from surging tests, and the similarity and difference between them are discussed. Experiments show that these coefficients are quite different from those of the cylinder without a forward velocity.     

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.     

Short-crested wave interaction with a concentric porous cylindrical structure

In this paper, theoretical study is carried out to investigate the general 3D short-crested wave interaction with a concentric two-cylinder system. The interior cylinder is impermeable and the exterior cylinder is thin in thickness and porous to protect the interior cylinder. Both cylinders are surface-piercing and bottom mounted. Analytical solution is derived based on the linear potential theory. The effects of the wide range wave parameters and structure configuration including porosity of the exterior cylinder and the annular spacing on the wave forces, surface elevations and the diffracted wave contours are examined.     

波浪作用下沙质海床上大直径圆筒结构动态响应的实验研究

通过物理模型实验,对沙质海床上沉入式大直径圆筒结构对波浪的动态响应进行了较系统的实验研究。实验中考虑了大直径圆筒、波浪和海床三者之间的耦合作用,并实时记录了大直径圆筒结构的动态响应。实验数据分析表明,大直径圆筒在波浪作用下的动态响应以大圆筒随波浪的前后摆动为主,其摆动轴心并不是固定不变的。最后通过回归分析给出了估算大直径圆筒摆动转角幅值的经验公式。     

Numerical simulation of solitary wave scattering by a circular cylinder array

The interaction of a solitary wave with an array of surface-piercing vertical circular cylinders is investigated numerically. The wave motion is modeled by a set of generalized Boussinesq equations. The governing equations are discretized using a finite element method. The numerical model is validated against the experimental data of solitary wave reflection from a vertical wall and solitary wave scattering by a vertical circular cylinder respectively. The predicted wave surface elevation and the wave forces on the cylinder agree well with the experimental data. The numerical model is then employed to study solitary wave scattering by arrays of two circular cylinders and four circular cylinders respectively. The effect of wave direction on the wave forces and the wave runup on the cylinders is quantified.     

聚焦波作用下平面网衣结构的水动力特性研究

由于沿海区域的限制以及愈加严重的环境污染,渔业养殖正从近海走向深远海。深远海海域的海况更加恶劣,给养殖装备的设计与性能评估带来新的挑战。为解决该问题,对极端波浪与养殖装备网衣结构的相互作用开展研究。基于waves2Foam建立数值波浪水池,极端波浪模拟采用基于NewWave理论的聚焦波模型,网衣结构模拟采用多孔介质模型,并通过与Morison模型计算的网衣受力等效分析,获得多孔介质模拟网衣结构阻力系数的直接估计方法。然后将多孔介质模型嵌入waves2Foam中,开展聚焦波与网衣结构相互作用的数值模拟,同时开展水槽试验,验证数值模拟的准确性。基于数值模拟结果,系统地分析了不同网衣密实度及不同波浪参数下网衣结构的升阻力特性以及网衣结构对波浪场的扰动规律。研究表明：聚焦波波峰幅值和网衣密实度对网衣结构的升阻力影响较大,且升力峰值出现在阻力为0的时刻;网衣结构对聚焦波的时空演化特性有影响,改变了聚焦波波形。     

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.     

马蹄波波形特征和对圆柱作用实验研究

为了研究真实海洋表面马蹄波特性以及对建筑物的作用,通过物理模型实验研究了马蹄波的波形特征参数以及马蹄波对圆柱体的作用。实验中通过对浪高仪采集的波面升高时间历程曲线进行分析得出了不同水深情况下马蹄波的垂向几何特征,并通过快速傅里叶变换得出了马蹄波波幅谱的特征,研究了马蹄波各组成波波幅沿空间的变化从而得出了圆柱存在对马蹄波演化的影响,同时给出马蹄波绕射形成的波面分布和不同频率谐波在圆柱周围的分布,讨论了马蹄波不同于Stokes波对圆柱作用的特征。结果表明,马蹄波波形受水深影响较大,水深越浅,马蹄波的波面形状越接近椭圆余弦波。圆柱体的存在干扰了马蹄波不稳定的增长,使其在接近圆柱时呈下降趋势,导致不稳定幅值最大值的位置提前并且出现在偏离圆柱迎浪点的侧表面,从而使圆柱受到侧向力的作用。     

多向不规则波浪作用下群墩结构上爬高的计算研究

波浪的方向分布对波浪的传播及其与工程结构物的作用都具有明显影响,目前现有的研究大多是基于单向波浪进行的。为了研究方向分布对群墩结构上的爬高影响,基于规则波浪与群墩作用的理论解,结合多向不规则波浪的造波方法,建立了多向不规则波浪与群墩作用的计算模型,同时进行了物理模型试验对模型的有效性进行了验证。系统地对群墩周围及表面上的波浪爬高进行了计算分析,结果表明,方向分布对波浪爬高具有较大的影响,且不同位置处的影响并不相同,在实际的工程设计中如果按照单向波浪计算,可能低估或者高估群墩周围的爬高。