Hydrodynamic coefficients for vertical circular cylinders at finite depth

Hydrodynamics coefficients for vertical circular cylinders at finite water depth are obtained and presented for different depth to radius and draft to radius ratios. A summary of equations for computer application is presented. Limiting values for heave added mass for zero frequency are discussed. A matching technique is used to satisfy the continuity of pressure and normal velocities.     

Hydrodynamic coefficients for inclined cylinders

The wave induced dynamic pressures around a circular cylinder of diameter 0.2 m due to regular waves were measured in a wave flume in a water depth of 1 m and in a wave basin in a water depth of 3 m. The experimental investigations were carried out with the cylinder inclined along and against the direction of wave propagation. The least-squares technique was employed to evaluate the coefficients of drag (C_D) and inertia (C_M) from the sectional force time histories obtained by integrating the measured circumferential pressure distribution. The variation of drag and inertia coefficients are presented as a function of Keulegan-Carpenter number (KC) for different inclinations of the cylinder. The comparison between the measured and the theoretical force derived from the evaluated hydrodynamic coefficients is found to be good.     

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.     

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.     

前板可旋转的双垂板结构水动力特性的理论研究

振荡水柱波能转换装置的最大转换效率往往受到腔内水柱共振机制的直接影响。通过对装置的基本结构进行简化,提出了一种前墙可绕固定轴旋转的双垂板式结构系统,旨在通过前墙的旋转运动进一步加剧水柱的振荡,从而对腔内水柱的共振机制进行调节和控制。基于线性波理论,采用匹配特征函数展开法对波浪与双垂板结构的相互作用进行理论研究,针对流场在结构物尖角附近的奇异性特征,将公共界面上的速度分布基于切比雪夫多项式近似展开,并应用区域间的速度与压力连续条件进行求解。通过分析结构的几何参数对反射透射系数、平均波面高程、前墙旋转振幅以及前墙与水面间相位差的影响,深究其共振机理,为振荡水柱波能转换装置的效率优化机制提供理论依据。结果表明,在所研究的波浪频率范围内,前墙的自由旋转运动会加剧板间的平均波面高程,应用于波浪能转换装置中能进一步拓宽高效频率带宽。     

Hydrodynamic coefficients of a floating,truncated vertical cylinder in shallow water

The paper seeks to apply the methodology of matched asymptotic expansions to obtain analytical solutions for hydrodynamic properties of a circular cylindrical platform (truncated circular cylinder) in extremely shallow water. By matching potentials of the fluid flows outside and under the cylinder bottom with the inner flow near its edge the radiation problems are solved for heave, surge and pitch motions. Closed asymptotic formulae are derived for all hydrodynamic coefficients of the floating cylinder, which include the first-order terms in the gap height. The formulae are discussed and shown to compare well with numerical results published in literature.     

Hydrodynamic coefficients of a two-dimensional,truncated rectangular floating structure in shallow water

The paper seeks to examine hydrodynamic coefficients of a rectangular structure in shallow water and to establish analytical formulae for fast computations. A two-dimensional rectangular profile is considered with the under-bottom clearance assumed to be small compared with structure dimensions and the water depth. Following the method of matched asymptotic expansions, the radiation problem is solved under assumptions of the linear wave theory, by matching two ‘outer’ flows with the ‘inner’ flow near the structure edge. Closed asymptotic formulae are obtained for all hydrodynamic coefficients for heave, sway and roll motions. The zero and infinite frequency values of the added mass are examined and formulae are derived intended for quick engineering estimations. Numerical results compare well with those published in literature, and the approach is shown to be consistent with known fundamental relations in the body–wave interaction theory.     

两层流体中多个振荡水平圆柱潜体水动力特性

采用解析方法研究了无限水深两层流体中多个振荡水平圆柱潜体的水动力特性。在线性势流理论框架内,基于多极子方法建立了辐射势的解析表达式,在此基础上导出了附加质量和阻尼系数的计算公式,采用边界元方法对这种解析方法进行验证,同时研究了两种不同工况下多个振荡水平圆柱潜体水动力的特性,结果表明,两层流体的密度比、圆柱的淹没深度以及圆柱的排列方式和间距等参数的变化对水平圆柱群附加质量和阻尼系数有很大的影响。     

Water wave interaction with an array of bottom-mounted surface-piercing porous cylinders

The interaction of water waves with arrays of bottom-mounted, surface-piercing circular cylinders is investigated theoretically. The sidewall of each cylinder is porous and thin. Under the assumptions of potential flow and linear wave theory, a semi-analytical solution is obtained by an eigenfunction expansion approach first proposed for impermeable cylinders by Spring and Monkmeyer (1974), and later simplified by Linton and Evans (1990). Analytical expressions are developed for the wave motion in the exterior and all interior fluid regions. Numerical results are presented which illustrate the effects of various wave and structural parameters on the hydrodynamic loads and the diffracted wave field. It is found that the porosity of the structures may result in a significant reduction in both the hydrodynamic loads experienced by the cylinders and the associated wave runup.     

Hydrodynamic performance of solid and porous heave plates

Heave plates have been widely utilized in floating offshore structures as they can provide additional damping and added mass to improve the hydrodynamic response of the system. This study investigates the hydrodynamic characteristics (added mass and damping) of oscillatory solid or porous disks using model scale experiments. All experiments were conducted via forced oscillation model tests using a planar motion mechanism (PMM). The hydrodynamic coefficients of the solid or porous disk obtained from the force measurements are analysed and presented. The sensitivities of the damping and added mass coefficients to both motion amplitude and the disk porosity are examined.     

Second-order resonance among an array of two rows of vertical circular cylinders

Experimental and theoretical works are conducted on the first-order and second-order wave interactions among an array of two rows of vertical circular cylinders.We show that both the first-order and the second-order resonance of dynamic free-surface displacement could in some cases be quite relevant among an array of two rows of vertical cylinders not only in theory but also in real phenomena. In some cases, on the other hand, we show that large free-surface displacement predicted theoretically is quite attenuated in reality probably due to viscous dissipation.     

Semi-analytical solution for the water wave diffraction by arrays of truncated circular cylinders in front of a vertical wall

The present study investigates the combined wave field that is induced by the continuous interaction of plane waves with an array of truncated circular cylinders in front of a rigid wall. The long-term goal of the study is the investigation of possible increase in the efficiency of cylindrical Wave Energy Converters (WECs) by putting in the vicinity of the array a barrier to propagation, a wall, that could assist the reflection of the incoming waves. The main task is to develop a generic solution method that is free of conceptual simplifications employed, e.g. by the method of images and the assumption of “pure” wave reflection. To cope with the set task, the proposed method relies on the semi-analytical formulation of the velocity potentials, while the solution is sought by combined expressions that involve polar and elliptical harmonics. The wall is represented as an elliptical cylinder with zero semi-minor axis. This assumption has eventually a beneficial effect to the underlying formulation given that it simplifies significantly the expansions of the involved diffraction potentials.     

On the estimation of Morison force coefficients and their predictive accuracy for very rough circular cylinders

This paper makes an assessment of the various method that may be used to analyse experiment data on the force experienced by a circular cylinder in waves and combined wave and current flows to estimate drag and inertia coefficients for use in Morison's equation. Most of the widely used techniques are considered together with a weighted least squares approach for time domain analysis. A set of data obtained from experiments on heavily roughened circular cylinders of diameters 0.513 and 0.216 m in the Delta wave flume at De Voorst in Holland in waves and simulated current has been analysed in turn by all these techniques. The experiment data was split into two halves. The first was used for the analyses and the second was used to assess the predictive accuracy of Morison's equation. Using the force coefficients obtained from the different analysis techniques corresponding predicted force time series were constructed using the particle kinematics measured in the second parts of the data sets. These predicted time series were then compared with the corresponding measured force time histories. The root mean square error and the bias in the estimation of maximum force in each wave cycle are used as measures of predictive accuracy and as a basis for comparing the efficiency of the different analysis techniques. It was found that the weighted least square method generally gave the best predictive accuracy, but only by a small margin.     

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 of a harmonically oscillated tower

A tower hinged at the bottom was oscillated mechanically in a sinusoidal fashion in a plane in still water. An instrumented section in the tower measured the inline and transverse forces locally on the tower due to the hydrodynamic effects. These forces are analyzed for the added mass, drag and lift coefficients which are presented as functions of Keulegan-Carpenter and Reynolds number. The lift force frequencies are also investigated. The measured overall reactions on the tower are used to verify the values of the local coefficients. The results presented here are not only applicable to articulated towers but to other moving elements of an offshore structure, e.g. risers, tension-legs, etc.     

不同排列方式和间隙比下双圆柱流致振动特性研究

采用基于ALE的流固耦合分析方法,将圆柱体振动模型简化为平面双自由度质量-弹簧-阻尼系统,进行了计算参数无关性分析。对不同θ角和间隙比T下的双圆柱流致振动进行数值模拟,并与单圆柱振动计算结果进行比较,得到了不同θ角和间隙比T下中心圆柱的升阻力系数、流场分布和运动轨迹变化情况。通过分析发现小间隙比下由于两圆柱间的相互干扰,改变了中心圆柱的尾涡结构,导致了升力和阻力系数随不同θ角而发生变化;小间隙比下由于两圆柱间的相互干扰影响,均使中心圆柱的轨迹在不同θ角下发生了较大的变化,顺流向的振动频率与单圆柱振动时相比出现了多倍频,导致其运动轨迹发生了变化。     

On the assessment of hydrodynamic coefficients of cylinders in heaving

A detailed comparison is made of the common two-dimensional methods for the evaluation of the hydrodynamic coefficients. Special attention was given to the conformal transformation method and the parameters which influence the accuracy of this method are studied. The results were compared with the Frank close-fit method with respect to accuracy and time taken. Finally the correlation between the geometric and hydrodynamic errors is examined and some relations are proposed.     

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.     

Hydrodynamic coefficients for a vertical tube in an array

In a wave tank test with vertical tube array arranged transverse to the wave direction, forces on two 1 ft instrumented sections as well as on the tubes are measured. The effect of the spacing of the tubes upon the forces on the tubes are investigated. The mass and drag coefficients are determined from the forces on the instrumented sections of the tubes. They are presented as functions of the Keulegan-Carpenter number (or the period parameter) and the tube spacing. The total forces on the tubes are computed based on the mean values of the hydrodynamic coefficients. The correlation between these calculated values and the measured forces is found to be good.