Combined effects of current and waves on fluid force

Combined effects of current and waves on the force exerted on an element of a cylinder in a random gravity wave field in deep water are studied. Wave-current interactions are taken into account. Statistical quantities of the fluid force such as force spectrum and root mean square value of the force are obtained numerically and presented in graphical forms. Comparisons are made of the cases in which wave-current interactions are considered and ignored. It is shown that wave-current interactions contribute to changes in fluid force to an appreciable extent and therefore should be considered in the evaluation of fluid forces on objects.     

Wave-current force on horizontal cylinder

For the calculation of wave-current force on horizontal cylinder a modified Morison's equation is used. A redefined Keulegan- Carpenter number KC2 is determined for the horizontal cylinder in wave-current co-existing field. The force coefficients are well related to the redefined KC2 number. As to the comparison with the force on vertical cylinder, the characteristics of force on horizontal cylinder are quite similar to those on vertical cylinder, but the force coefficients for horizontal cylinder are larger than those for vertical cylinder. It is proved by the authors' calculation that the results of monochromatic wave can be used directly for the determination of irregular wave-current force on horizontal cylinder in time domain.     

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。     

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.     

不同运动自由度组合串列双圆柱涡激振动数值模拟

基于自主研发的紧致插值曲线CIP (Constrained Interpolation Profile)方法数学模型,对均匀来流条件时不同运动自由度组合下的串列双圆柱涡激振动问题开展二维数值模拟。模型针对雷诺数Re=100,质量比m*=2的串列双圆柱涡激振动问题,选取上、下游圆柱不同运动自由度组合工况进行模拟。重点分析圆柱的升阻力系数、运动位移随折合速度Ur变化的响应。研究表明:当上游圆柱双自由度运动时,随着下游圆柱运动自由度的增加,下游圆柱对上游圆柱涡激振动响应的影响减弱;当下游圆柱双自由度运动时,随着上游圆柱运动自由度的增加,上游圆柱对下游圆柱涡激振动响应的影响变强。研究结果表明圆柱运动自由度组合形式对串列双圆柱涡激振动的影响不可忽略。     

Wave drift enhancement effects in multi column structures

A theoretical assessment is made of mean wave drift forces on groups of vertical circular cylinders, such as the columns of a floating offshore platform. A complete analytical solution is obtained for two cylinders extending from seabed to free surface, and a long wave approximation is found to provide reliable predictions of the drift force in line with the waves at low frequencies. For moderate separation between the two cylinders, this force is found to tend at low frequencies to a value four times the force on an isolated cylinder.A numerical method is employed to study two surface piercing cylinders truncated below the free surface, and an arrangement of four vertical cylinders characteristic of a floating offshore platform. The mean vertical drift force is found to be reasonably well approximated, over the frequency range of practical interest, by the force on an individual cylinder considered in isolation multiplied by the number of cylinders in the group. Interaction effects, however, have a profound influence on the total horizontal drift force. At low frequencies this force is found to tend to the force on an isolated cylinder multiplied by the squate of the number of cylinders in the group.     

固壁附近水平圆柱在波浪水流共存场中的流动显示及水动力特征

固壁附近的水平的圆柱体在波浪、波流作用下的受力情况与其周围的流场状态密切相关。为探讨圆柱形成的机理，应当对流场的涡结构有充分的认识，受力过程与记演化过程的同步分析万为重要。本文通过实验研究并对比数值分析的结果，对波浪、波流场中圆柱体受力与流场状态的关系做一初步讨论。     

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.     

Experimental investigation of the forces and motion responses of two interfering VIV circular cylinders at various tandem and staggered positions

Experimental results are presented in the paper of two elastically supported rigid circular cylinders subjected to steady flows in a flume. The two cylinders were initially placed at various tandem and staggered positions with one in the wake of the other when subject to the steady flows. The in-line centre-to-centre distance varied from 2 to 5 diameters whilst the cross-flow distance from 0 to 2 diameters. The nominal Reynolds numbers were in the sub-critical regime and ranged from 1.12 × 10⁴ to 5.52 × 10⁴, and the nominal reduced velocities from 1.78 to 8.77. The damping ratio of the test set-up is low at 0.003 which gives a combined mass-damping parameter of 0.0046. Both the cylinders were free to respond in both the in-line and the cross-flow directions. The cylinder motion was measured simultaneously with the hydrodynamic loading in the two directions. It was found that the motion trajectories of the downstream cylinder show qualitative difference depending upon whether it is in tandem with the upstream cylinder or in the wake with a transverse offset. The VIV response of the downstream cylinder is dependent upon the reduced velocity of the upstream cylinder and its own reduced velocity based upon the actual mean wake velocity. The drag amplification of the downstream cylinder in the wake appears to be fundamentally different from that of a single VIV cylinder in isolation. Furthermore, unlike the two fixed cylinders in cross flow, the downstream cylinder undergoing VIV no longer experiences a marked non-zero mean lift. The upstream cylinder is largely unaffected by the downstream cylinder when the initial spacing is greater than 3 diameters. On the other hand, the motion response of and the fluid loading on the downstream cylinder are strongly influenced by the upstream cylinder in the spacing range tested.     

Wave forces on a single and on a group of cylinders in response to two wave spectra of same significant wave height

Spectral analysis is used to determine the wave force characteristics on structures exposed to random waves. Considerable work has been carried out to determine the magnitude of random wave forces acting on a single cylinder, but little information is available in the case of a group of cylinders in random waves. Such situations arise when structures comprise multiple tubular members which are in close proximity, and wave forces cannot be calculated precisely by analytical methods due to complicated flow conditions past the group. Experimental studies are also required for proper understanding and analysis. An experimental scheme was carried out to study the wave force characteristics on a single cylinder and on a group of cylinders in response to two different wave spectra with the same significant wave height, and the results are compared.     

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.     

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.     

Vibration of two elastically mounted cylinders of different diameters in oscillatory flow

Vibration of two elastically mounted cylinders in an oscillatory flow at a Keulegan-Carpenter number of 10 is simulated numerically. The two cylinders are rigidly connected with each other and are allowed to vibrate in the cross-flow direction only. The aim of this paper is to identify the effects of the orientation of the cylinders and the gap between the cylinders on the vibration. The two-dimensional Reynolds-Averaged Navier-Stokes equations are solved to predict the flow and the cylinder vibration is predicted using the equation of motion. When the two cylinders are in a tandem arrangement, a combined single pair flow regime and attached pair flow regime are observed as reduced velocity exceeds 10 and this combined regime and the single pair regime occurs intermittently. Periodic vibration is found when the two cylinders are in a staggered arrangement with a 45° flow attack angle. When the two cylinders are in a side-by-side arrangement, a new single vortex regime is observed. This single vortex remains attached to the cylinder surface and rotates around the cylinder. The intermittent switch between this single vortex regime and the single pair regime are observed.     

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.     

Wave-Induced Seepage Force Acting on Cylinder Groups

Wave-induced seepage force acting on cylinder groups is studied by using Biot consolidation theory in this paper. Both tandem arrangement and side by side arrangement are considered simultaneously. The variations of the coefficient of grouping effect with the distance between cylinders for different KD are discussed. In order to verify the numerical solution, several sets of experiments are conducted. The agreement between numerical and experimental solutions is satisfactory.     

五圆柱体结构群绕流特性及互扰效应研究

基于Fluent流体计算平台,运用大涡模拟方法对亚临界雷诺数Re=3900下“X”形排列五圆柱体结构群三维绕流特性进行研究,主要分析来流攻角α与间距比L/D两个关键参数对五圆柱体结构群的尾流区三维涡结构演化与流体力系数的影响,并揭示其内在流动互扰机理。研究表明:来流攻角和间距比的变化对五圆柱体结构群流动控制及互扰效应的影响显著。在小间距比工况下,观察到柱体群间隙区域内流体高速流动的现象,导致五圆柱体之间的互扰作用十分强烈。间隙流对中间圆柱体和下游圆柱体有较强的冲击作用,对其表面的流体力分布特性有显著的影响。另外,大间距比工况下,当α=0°与L/D≥5.0工况时,柱体群尾流效应强于其间隙流效应。当α=22.5°与L/D=7.0时,位于下游与中间处的圆柱体流体绕流特性存在较大差异。而当α=45°与L/D≥6.0时,位于上游与中间处的圆柱体尾流区均会产生正负交替的漩涡结构。     

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.     

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.     

Analysis of single and tandem cylinder data using an orthogonal Volterra model approach

The development of a definitive predictive model that accurately accounts for the nonlinear hydrodynamics and structural response behavior observed in arrays of closely spaced risers on deep water structures will require a more detailed understanding of this fluid–structure interaction. Through the analysis and interpretation of data from model basin tests on single and paired tandem cylinder configurations this study is directed at uncovering the nature of some aspects of this nonlinear response behavior using an orthogonal third-order Volterra technique that can delineate between linear, quadratic and cubic nonlinear frequency dependent behavior. As part of the analysis procedure the data was organized in input–output pairs that would provide logical groupings of the measured quantities. The data pairs presented in this study include wave excitation and inline cylinder displacement, wave excitation and transverse cylinder displacement, wave excitation and inline reaction force, and, upstream cylinder and downstream cylinder response. This information is presented in terms of spectral and coherence plots. The single cylinder data is presented as a means to contrast the behavior of the tandem cylinders. Both configurations were analyzed at two different pretensions adding another dimension to this investigation. It is shown that although a primary variable such as displacement may be more easily measured, pretension and force measurements provide an important key to our understanding of this difficult problem.     

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.