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.     

Hydrodynamic coefficients for a thick-walled bottomless cylindrical body floating in water of finite depth

The paper deals with the linearized hydrodynamic forces acting on a thick-walled, bottomless cylindrical body having vertical symmetry axis and oscillating in water of finite depth. For the solution of the radiation problem, the flow field around the structure is subdivided into ring-shaped fluid regions, in each of which an axisymmetric eigenfunction expansion for the velocity potential is made. By implementing Galerkin's method the various potential solutions are then matched and numerical results concerning the hydrodynamic coefficients for heave, surge and pitch motions, as well as the coupling terms between the last two modes are obtained.     

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.     

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.     

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.     

半潜式超大型浮式结构水动力系数研究

以半潜式超大型浮式结构在动力响应分析中的各水动力系数为研究对象,经理论推导得到D’Alembert动力学方程中的移动式海上基地(MOB)单模块运动的结构质量、结构附加质量、静恢复力系数的简易计算公式。以MOB的"三模块模型"为例,研究其在6级海况浪向角为0°~90°条件下,各模块的附加质量系数及静恢复力系数的历时规律,以实例MOB中的第1个模块为代表展示了计算结果,并统计其最大值与文献资料中的结果进行对比。结果表明:运用本理论公式计算的结果与文献中所得结果相似,可验证本理论公式的正确性、可行性与合理性,为求解半潜式超大型浮式结构模块动力响应位移及转角提供简便的方法。     

Hydrodynamic coefficients in heave of two concentric surface-piercing truncated circular cylinders

The paper aims at presenting a solution of the linearized hydrodynamic radiation problem for two concentric, free surface-piercing truncated vertical cylinders that are forced to independently oscillate in heave in finite depth waters. For the solution of the problem, the flow field around the two bodies is subdivided into ring-shaped fluid regions, in each of which axisymmetric eigenfunction expansions for the velocity potential are made. By implementing Galerkin's method, the various potential solutions are matched and extensive numerical results concerning the hydrodynamic and interaction coefficients in heave for various geometrical configurations presented and discussed.     

Measurements of higher harmonic wave forces on a vertical truncated circular cylinder

Wave forces on a vertical truncated circular cylinder in Stokes waves with the wave slopes ranging from 0.06 to 0.24, are measured in a wave tank. The higher harmonic wave forces are compared with the available values from theories of the FNV (Faltisen–Newman–Vinje) model and Varyani solution. The first harmonic horizontal forces measured are much larger than the theoretical values from the FNV model, while the first harmonic vertical forces are well predicted by the Varyani theory. It was also found that the FNV model significantly overpredicts the second harmonic horizontal forces in high frequency waves, but under predicts the third harmonic forces. The differences between the actual measurement and the theory, in the second and third harmonic horizontal forces, become smaller at low wave frequencies as the wave slope increases. In addition, the transverse instabilities in the incoming waves with high wave slope were observed, which is due to the nonlinear modulation. Measurements were, thus, carried out before the instability occurred.     

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.     

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 performance of a T-shaped floating breakwater

The comprehensive utilization of floating breakwaters, specially acting as a supporting structure for offshore marine renewable energy explorations, has received more and more attention recently. Based on linear water-wave theory, the hydrodynamic performance of a T-shaped floating breakwater is semi-analytically investigated through the matched eigenfunction expansion method (MEEM). Auxiliary functions, to speed up the convergence and improve the accuracy in the numerical computations, are introduced to represent the singular behavior of fluid field near the lower salient corners of the structure. The effects of the height and installation position of the vertical screen on the reflection and transmission coefficients, dynamic response and wave forces are examined. It is found that the presence of the screen shifts the resonance frequency of RAO for both surge and pitch modes to the low-frequency area, while has no effect on heave mode. The identical added masses, damping and transmission coefficients can be obtained in the cases where the screen holds the same distance away from the longitudinal central axis of the upper box-type structure. Moreover, a relatively small pitch response can be achieved in a wide wave–frequency range, when the breakwater is Γ-shaped.     

Hydrodynamic response of a pneumatic floating platform

This paper describes a numerical approach to model the dynamic response of a pneumatic floating platform, and the laboratory experiments and parametric study to verify the numerical results. The pneumatic platform is composed of an array of open-bottom vertical cylinders trapping pressurized air that displaces the water. The cylinder diameter is assumed to be small compared to the wavelength and the water inside each cylinder oscillates as a piston. These assumptions simplify the mathematical formulation in that the bottom of the platform can be treated as a continuous surface on which the source distribution method can be applied. In the laboratory experiments, the compressibility and displacement of the trapped air are modeled by a spring and float assembly. The comparison between the numerical and experimental results indicates favorable agreement. The oscillation of the water columns and the overall dynamic characteristics of the platform are illustrated and discussed in the parametric study.     

浅水半潜型浮式风机基础概念设计与模型试验研究

目前我国海上风电开发主要集中在近海海域。我国近海海域水深相对较浅,在浅水非线性波浪载荷作用下,浮式基础动力响应呈现显著非线性特性,导致浮式风机基础及其系泊系统设计极具挑战。针对我国近海浅水海域环境条件,基于半潜型浮式风机基础概念SPIC,采用参数化建模与优化方法,开展了42 m水深条件下半潜型浮式风机基础概念设计,并在海洋工程水池开展1∶50缩尺模型试验。模型试验的结果表明：半潜式浮式风机基础概念设计具有稳定性好、动力性能优良等优点,浮式基础纵摇运动、机舱加速度等指标满足规范要求。模型试验结果验证了该概念的可行性。     

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.     

Hydrodynamic characteristics of ship sections in shallow water with complex bottom geometry

The method of boundary integral equation developed by the authors was applied for computing inertial and damping characteristics of ship sections for the cases of multi-stepped and inclined bottoms. Comparative calculations for three typical ship hull sections were performed and analyzed. The frequency-dependent data computed for these ship sections can be used to assess the bottom geometry's influence onto the ship motions in waves by means of the strip theory. Limiting values of the same characteristics corresponding to the close-to-zero frequency can also be used for estimation of hydrodynamic forces in manoeuvring over shallow and confined waterways.     

Reverberation vertical coherence and sea-bottom geoacoustic inversion in shallow water

Optimal array-processing techniques in the ocean often require knowledge of the spatial coherence of the reverberation. A mathematical model is derived for the reverberation vertical coherence (RVC) in shallow water (SW). A method for analysis of RVC data is introduced. Measured reverberation cross-correlation coefficients as a function of time and frequency, obtained during the Asian Seas International Acoustic Experiment (ASIAEX) in the East China Sea, are reported. SW reverberation from a single shot provides a continuous spatial sampling of the surrounding sound field up to several tens of kilometers and holds valuable information on the geoacoustic properties of the sea floor over this distance. SW reverberation data can, therefore, be used as the basis for a quick and inexpensive method for geoacoustic inversion and has the obvious advantage that acquiring the data in situ requires only a single platform. This paper considers the use of the vertical coherence of the reverberation as the starting point for such an inversion. Sound speed and attenuation in the sea bottom at the ASIAEX site are obtained over a frequency range of 100-1500 Hz by finding values that provide the best match between the measured and predicted RVC.     

Hydrodynamic characteristics of floating toroidal bodies

The paper deals with the linearized exciting wave forces and hydrodynamic coefficients of a toroidal body floating in water of finite depth. For the solution of the diffraction and the radiation problems the flow field around the body is subdivided into ring-shaped fluid regions, in each of which axisymmetric eigenfunction expansions for the velocity potential is made. By implementing Galerkin's method the various potential solutions are matched and numerical results concerning the exciting wave forces and the hydrodynamic coefficients in all modes of motion are obtained.     

Water wave interaction with a floating porous cylinder

The interaction of water waves with a freely floating circular cylinder possessing a side-wall that is porous over a portion of its draft is investigated theoretically. The porous side-wall region is bounded top and bottom by impermeable end caps thereby resulting in an enclosed fluid region within the structure. The problem is formulated based on potential flow and linear wave theory and assuming small-amplitude structural oscillations. An eigenfunction expansion approach is then used to obtain semi-analytical expressions for the hydrodynamic excitation and reaction loads on the structure. Numerical results are presented which illustrate the effects of the various wave and structural parameters on these quantities. It is found that the permeability, size and location of the porous region may have a significant influence on the horizontal components of the hydrodynamic excitation and reaction loads, while its influence on the vertical components in most cases is relatively minor.     

Hydrodynamic coefficients of a submerged pulsating sphere in finite depth

By extending the work of Linton (Linton, C.M., 1991. Radiation and diffraction of waver waves by a submerged sphere in finite depth. Ocean Engineering 18 (1/2), 61–74), the problem of radiation of water waves by a submerged pulsating sphere in finite depth is formulated using the multipole method. As in Linton (1991), this leads to an infinite system of linear equations, which are easily solved numerically. Simple expressions are derived for the hydrodynamic characteristics of such a body. Results showing the effect of varying both the immersion depth and the water depth on the hydrodynamic coefficients of the pulsating sphere are given. The paper resumes the work presented in Lopes (Lopes, D.B.S., 1999. On the study of the Archimedes wave swing device for wave energy utilization (in Portuguese). MSc on the Management and Modelling of the Marine Environment, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa.).     

Hydrodynamic behavior of a straight floating pipe under wave conditions

This paper examines the hydrodynamic behavior of a floating straight pipe under wave conditions. The main problem in calculating the forces acting on a small-sized floating structure is obtaining the correct force coefficients C_n and C_t, which differ from a submerged structure. For a floating straight pipe of small size, we simplify it into a 2D problem, where the pipe is set symmetrically under wave conditions. The force equations were deduced under wave conditions and a specific method proposed to resolve the wave forces acting on a straight floating pipe. Results of the numerical method were compared to those from model tests and the effects of C_n and C_t on numerical results studied. Suggestions for the selection of correct C_n and C_t values in calculating wave forces on a straight floating pipe are given. The results are valuable for research into the hydrodynamic behavior of the gravity cage system.