Experimental Study and System Identification of Hydrodynamic Force Acting on Heave Damping Plate

Although Morison equation is often applied for simulating hydrodynamic force of marine structure, it may give poor results when non-linear behavior is severe or random wave is encountered. This leads to some modifications of Morison equation or other methods for predicting hydrodynamic force. One of them is the system identification technique. In this paper, NARMAX model theory is firstly used to identify the hydrodynamic system of heave damping plates, which are commonly installed on spar platform. Both linear and non-linear models are obtained. The comparisons between the predieted results and measured data indicate that NARMAX model can predict hydrodynamic force of a heave damping plate very well. The measured data for identification originate from forced oscillation tests, which are random records with given spectrum. The forced oscillation forms in experiment also contain simple harmonic, multi-frequency ones.     

Wave Radiation by A Submerged Ring Plate in Water of Finite Depth

A plate submerged at a certain depth underneath the sea surface has been proposed as a structure type for different purposes, including motion response reduction, wave control, and wave energy harvesting. In the present study, the three-dimensional wave radiation problem is investigated in the context of the linear potential theory for a submerged ring plate in isolation or attached to a floating column as an appendage. In the latter case, the ring plate is attached at a certain distance above the column bottom. The structure is assumed to undergo a heave motion. An analytical model is developed to solve the wave radiation problem via the eigenfunction expansion method in association with the region-matching technique. With the velocity potential being available, the hydrodynamic coefficients, such as added mass and radiation damping, are obtained through the direct pressure integration. An alternative solution of radiation damping has also been developed in this study, in which the radiation damping is related to the Kochin function in the wave radiation problem. After validating the present model, numerical analysis is performed in detail to assess the influence of various plate parameters, such as the plate size and submergence depth. It is noted that the additional added mass due to the attached ring plate is larger than that when the plate is in isolation. Meanwhile, the radiation damping of the column for the heave motion can vanish at a specific wave frequency by attaching a ring plate, corresponding to a condition that there exist no progressive waves in the exterior region.     

The hydrodynamic coefficients for an oscillating rectangular structure on a free surface with sidewall

Based on a two dimensional linear water wave theory, the boundary element method (BEM) is developed and applied to study the heave and the sway problem of a floating rectangular structure in water to finite depth with one side of the boundary is a vertical sidewall and the other boundary is an open boundary. Numerical results for the added mass and radiation damping coefficients are presented. These coefficients are not only depend on the submergence and the width of the structure, but also depend on the clearance between structure and sidewall. Negative added mass and sharp peaks in the damping and added mass coefficients have been found when the clearance with a value close to integral times of half wave length of wave generated by oscillation structure. The important effect of the clearance on the added mass and radiation damping coefficients are discussed in detail. An analytical solution method is also presented. The BEM solution is compared with the analytical solution, and the comparison shows good agreement.     

Added mass and damping of a vertical cylinder in finite-depth waters

A comprehensive set of theoretical added masses and wave damping data for a floating circular cylinder in finite-depth water is presented. The hydrodynamic problem is solved by matching eigen functions of the interior and exterior problems. The resulting infinite system is solved directly and found to have excellent truncation characteristics. Added mass and damping are given for heave, sway, and roll motion, as well as coupling coefficients for sway and roll. It is shown that the heave added mass is logarithmic singular and the damping approaches a constant in the low-frequency limit. Transition of the behaviour in finite-depth water to deep water is also discussed.     

On the radiation and diffraction of water waves by a rectangular structure with a sidewall

A radiation and diffraction boundary value problem is investigated. It arises from the interaction of linear water waves with a freely floating rectangular structure in a semi-infinite fluid domain of finite water depth with the leeward boundary being a vertical wall. Analytical expressions for the radiated potentials and the diffracted potential are obtained by use of the method of separation of variables and the eigenfunction expansion method. The added masses and damping coefficients for the structure heaving, swaying and rolling in calm water are obtained by use of the corresponding radiated potentials and the wave excitation forces are calculated by use of the diffracted potential. To verify the correctness of the method, a boundary element method is used. A comparison of the analytical results with those obtained by the boundary element method is made and good agreement is achieved, which shows that the analytical expressions for the radiated and diffracted potentials are correct. By use of the present analytical solution, the added mass, damping coefficients, wave excitation force, together with the hydrodynamic effects of the draft, width of the structure and the clearance between the structure and the sidewall are also investigated.     

随机波浪下Truss Spar平台垂荡运动时域分析

研究Truss Spar平台在随机波浪下的垂荡运动特性。采用ITTC双参数谱,考虑绕射作用,数值计算了平台所受的随机波浪力。利用已有的水动力试验和数值模拟结果及Morison方程,估计了Truss Spar平台垂荡方向的附加质量和粘滞阻尼大小。考虑非线性阻尼和瞬时波面的影响,运用Runge-Kutta数值迭代算法,比较了不同随机波浪参数对平台运动响应的影响,特别是波浪特征周期接近垂荡固有周期时。结果表明,当波浪特征周期接近平台垂荡固有周期时,平台产生大幅垂荡运动,频域的运动分析结果比时域结果偏小。     

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.     

Mooring tension and motion characteristics of a submerged fish reef with net in waves and currents using numerical analysis

A numerical model was used to analyze the motion response and mooring tension of a submerged fish reef system. The system included a net attached to a rigid structure suspended up from the bottom with a single, high tension mooring by fixed flotation. The analysis was performed by using a Morison equation type finite element model configured with truss elements. Input forcing parameters into the model consisted of both regular and irregular waves, with and without a steady current. Heave, surge and pitch dynamic calculations of the reef structure were made. Tension response results of the attached mooring line were also computed. Results were analyzed in both the time and frequency domain in which appropriate, linear transfer functions were calculated. The influence of the current was more evident in the tension and heave motion response data. This is most likely the result of the large buoyancy characteristics of the reef structure and the length of the mooring cable. Maximum mooring component tension was found to be 13.9 kN and occurred when the reef was subjected to irregular waves with a co-linear current of 1.0 m/s velocity. The results also showed that the system had little damping (in heave) with damped natural periods of 2.8 s. This combination of system characteristics promotes a possible resonating situation in typical open sea conditions with similar wave periods.     

Experiment Study of Dynamics Response for Wind Turbine System of Floating Foundation

The floating foundation is designed to support a 1.5 MW wind turbine in 30 m water depth. With consideration of the viscous damping of foundation and heave plates, the amplitude-frequency response characteristics of the foundation are studied. By taking into account the elastic effect of blades and tower, the classic quasi-steady blade-element/momentum (BEM) theory is used to calculate the aerodynamic elastic loads. A coupled dynamic model of the turbine-foundation- mooring lines is established to calculate the motion response of floating foundation under Kaimal wind spectrum and regular wave by using the FAST codes. The model experiment is carried out to test damping characteristics and natural motion behaviors of the wind turbine system. The dynamics response is tested by considering only waves and the joint action of wind and waves. It is shown that the wind turbine system can avoid resonances under the action of wind and waves. In addition, the heave motion of the floating foundation is induced by waves and the surge motion is induced by wind. The action of wind and waves is of significance for pitch.     

筏式海水养殖设施在波浪作用下的水弹性分析

由于台风等恶劣海洋条件的影响,海上浮筏式养殖结构极易遭受破坏。浮筏式海水养殖结构系统由多个浮子、连接走板和系泊缆组成。文中研究了不同走板材料对浮筏结构在波浪中动力响应的影响。通过基于势流理论的软件WAMIT计算获得了浮子的附加质量系数。利用海洋工程软件OrcaFlex计算模拟了浮筏结构在波浪中的时历响应,并分析比较了采用不同走板材料的浮筏结构在海浪中的水弹性差异。研究结果表明,木制浮筏相对新型高密度聚乙烯（high density polyethylene,简称HDPE）材料在波浪中受到的弯矩更大,可能更容易受到破坏。另外,对比分析了直接计算的结构最大响应和基于瑞利分布预测的最大响应值（MPM）,结果表明结构最大垂向运动基本符合瑞利分布,而水平运动最大值由于受系泊系统非线性影响,与瑞利分布有一定差异。     

两层流体中矩形箱浮体的附加质量和阻尼系数

研究了两层流体中矩形箱浮体的辐射问题。基于特征函数匹配理论,针对矩形箱浮体的三种振荡运动模式(横荡、垂荡和横摇),建立两层流体中矩形箱浮体辐射势的求解方法,导出矩形箱浮体附加质量和阻尼系数的计算公式。对所建立的求解模型进行了数值计算分析,结果表明在矩形箱浮体的某个振荡频率范围内,流体的分层效应对其附加质量和阻尼系数有显著影响的。     

Numerical modeling of perforated plates in oscillating flow

Perforated plates, relevant for several marine applications, are experimentally and numerically investigated. The numerical investigations are performed using a presently developed Navier–Stokes solver. Several comparison and sensitivity studies are presented, in order to validate and verify the solver. Forced heave experiments are performed on two perforated plates with perforation ratios 19% and 28%. Amplitude-dependent added mass and damping coefficients are presented. Good agreement is obtained between the solver and the present experiments. Consistent with existing data, the results show that the hydrodynamic coefficients of perforated plates are highly amplitude dependent. The damping force is found to dominate over added mass force. The damping force dominance increases with increasing perforation ratio. It is highlighted that plate-end flow separation has an important effect on the damping coefficient. The developed numerical solver is two-dimensional, but is found to yield reasonable estimates of hydrodynamic force coefficients when compared with a previous three-dimensional experimental investigation. This could indicate that three-dimensional effects are not dominant for the hydrodynamic forces of perforated plates, and that a two-dimensional viscous flow solver could have relevance as a tool for estimating hydrodynamic forces on three-dimensional perforated structures.     

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.     

The effects of yawing motion with different frequencies on the hydrodynamic performance of floating vertical-axis tidal current turbines

Under real sea conditions, the hydrodynamic performance of floating vertical-axis tidal current turbines is affected by waves and currents. The wave circular frequency is a significant factor in determining the frequencies of the wave-induced motion responses of turbines. In this study, the ANSYS-CFX software (manufacturer: ANSYS Inc., Pittsburgh, Pennsylvania, United States) is used to analyse the hydrodynamic performance of a vertical-axis turbine for different yawing frequencies and to study how the yawing frequencies affect the main hydrodynamic coefficients of the turbine, including the power coefficient, thrust coefficient, lateral force coefficient, and yawing moment coefficient. The time-varying curves obtained from the CFX software are fitted using the least-squares method; the damping and added mass coefficients are then calculated to analyse the influence of different yawing frequencies. The simulation results demonstrate that when analysing non-yawing turbines rotating under constant inflow, the main hydrodynamic coefficient time-varying curves of yawing turbines exhibit an additional fluctuation. Furthermore, the amplitude is positively correlated with the yawing frequency, and the oscillation amplitudes also increase with increasing yawing frequency; however, the average values of the hydrodynamic coefficients (except the power coefficient) are only weakly influenced by yawing motion. The power coefficient under yawing motion is lower than that under non-yawing motion, which means that yawing motion will cause the annual energy production of a turbine to decrease. The fitting results show that the damping term and the added mass term exert effects of the same level on the loads and moments of vertical-axis turbines under yawing motion. The results of this study can facilitate the study of the motion response of floating vertical-axis tidal current turbine systems in waves.     

Dynamic Performance Analysis of the Tuned Heave Plate System for Semi-Submersible Platform

Logistical supply is costly for the deepwater oil and gas exploitation, thereby it is necessary to develop a novel power supply solution to improve the offshore structure’s self-holding capacity. The two-body point absorbers, as a renewable energy device, have achieved a rapid development. Heave plate is used to constrain the truss’s motion in the two-body point absorber, and the floater moves along the truss up and down. This two-body point absorber can be considered to be an essentially mass-spring-damper system. And it is well known that the heave plates have been widely used in the Spar platform to suppress the heave motions. So if the two-body point absorber can be modified to combine with offshore floating structures, this system can not only offer electric power to support operations or daily lives for the platform, but also control the large motions in the vertical plane. Following this concept, a novel tuned heave plate (THP) system is proposed for the conventional semi-submersible platform. In order to investigate the dynamic performances of the single THP, two experiments are conducted in this paper. First, the hydrodynamic coefficients of the heave plates are studied, and then the THP experiments are carried out to analyze its dynamic performance. It can be concluded that this THP is feasible and achieves the design objective.     

Dynamic behaviour of square and triangular offshore tension leg platforms under regular wave loads

Among compliant platforms, the tension leg platform (TLP) is a hybrid structure. With respect to the horizontal degrees of freedom, it is compliant and behaves like to a floating structure, whereas with respect to the vertical degrees of freedom, it is stiff and resembles a fixed structure and is not allowed to float freely. The greatest potential for reducing costs of a TLP in the short term is to go through previously applied design approaches, to simplify the design and reduce the conservatism that so far has been incorporated in the TLP design to accommodate for the unproven nature of this type of platform. Dynamic analysis of a triangular model TLP to regular waves is presented, considering the coupling between surge, sway, heave, roll, pitch and yaw degrees of freedom. The analysis considers various nonlinearities produced due to change in the tether tension and nonlinear hydrodynamic drag force. The wave forces on the elements of the pontoon structure are calculated using Airy's wave theory and Morison's equation, ignoring the diffraction effects. The nonlinear equation of motion is solved in the time domain using Newmark's beta integration scheme. Numerical studies are conducted to compare the coupled response of a triangular TLP with that of a square TLP and the effects of different parameters that influence the response are then investigated.     

Monocolumn behavior in waves: Experimental analysis

A series of tests with a model of a monocolumn platform with a moonpool were performed at the LabOceano/COPPE, at the Universidade Federal do Rio de Janeiro, with the objective of determining the entrance area at the bottom of the moonpool that minimizes vertical motion in waves. The tests include measurements of monocolumn surge, pitch and heave motion, vertical motion of the water column inside the moonpool, with different mooring systems, in regular, irregular and transient waves.This paper presents experimental results of the monocolumn vertical motion and the internal water column motion in the moonpool in transient waves and results of vertical motion of the water column inside the moonpool with the model held still in transient waves. These measurements allow an analysis of the impact of the moonpool's bottom opening on the monocolumn vertical motion in waves.The theoretical analysis of a mass–spring–damper system with two degrees of freedom, similar to the studied system, has shown some analogy with den Hartog's damped vibration absorber; however, there are significant differences in terms of added mass and coupled terms of added mass and damping coefficients dependent on oscillation frequencies.     

Dual pontoon floating breakwater

The hydrodynamic properties of a dual pontoon floating breakwater consisting of a pair of floating cylinders of rectangular section, connected by a rigid deck, is investigated theoretically. The structure is partially restrained by linear symmetric moorings fore and aft. The fluid motion is idealized as linearized, two-dimensional potential flow and the equation of motion of the breakwater is taken to be that of a two-dimensional rigid body undergoing surge, heave and pitch motions. The solution for the fluid motion is obtained by the boundary integral equation method using an appropriate Green's function. Numerical results are presented which illustrate the effects of the various wave and structural parameters on the efficiency of the breakwater as a barrier to wave action. It is found that the wave reflection properties of the structure depend strongly on the width, draft and spacing of the pontoons and the mooring line stiffness, while the excess buoyancy of the system is of lesser importance.     

Effect of mooring-line stiffness on the performance of a dual coaxial-cylinder Wave-Energy Converter

A point-absorber-type Wave-Energy Converter (WEC) consisting of a floating vertical inner cylinder and an annular outer cylinder that slides along the inner one is considered. The two cylinders heave differently under wave excitation, and wave energy can be harnessed from the relative heave motion between the two cylinders using a Permanent Magnet Linear Generator (PMLG) as the Power Take-Off unit. A mooring cable is attached to the bottom of the inner cylinder. This paper aims to examine the effect of the stiffness of the mooring cable on the performance of the coaxial-cylinder WEC system. The two limiting cases of no mooring cable (freely floating inner and outer cylinders) and an infinitely stiff mooring cable (fixed inner cylinder) were also considered. To perform the analysis, hydrodynamic and interference coefficients of the two heaving cylinders were computed semi-analytically using the method of matched eigenfunction expansions. Experimentally determined viscous corrections on damping were also included in the model in order to have more realistic predictions. The performance of the system in terms of motion responses and capture width were predicted and discussed for both regular and irregular waves. The results of the analysis indicate that both the freely floating design and the design with rigidly moored inner cylinder are viable. The two limiting cases show similar optimal performances, albeit with very different optimal generator damping. However, an ill-chosen mooring-cable stiffness may cause the inner and the outer cylinders to have the same resonance frequency, eliminating the relative heave motion and leading to almost no energy extraction. This situation needs to be avoided when designing the mooring system for a coaxial-cylinder WEC.     

Natural frequencies of vertical cylindrical oscillating water column devices

This paper deals with the evaluation of the natural frequencies in heave motion of a single floating Oscillating Water Column device along with the natural frequencies of the water column inside the oscillating chamber. Two types of OWCs are examined, a simple-type device, consisting of a partially immersed toroidal body and a novel-type device, consisting also of a partially immersed toroidal body supplemented however by a coaxial interior truncated cylinder moving in phase with the outer chamber, thus forming a floating unit. Numerical results are given concerning the three boundary value problems, namely, the diffraction, the motion- and the pressure- dependent radiation problems, obtained through an analytical solution method using matched axisymmetric eigenfunction expansion formulations. The effect of the air pressure distribution inside the oscillating chamber on the natural frequencies in heave motion of the two examined types of OWCs and on the natural frequency of the water column motion inside the chamber, is presented and discussed thoroughly. It is demonstrated that the heave natural frequencies are strongly dependent on the type of the examined OWC and the device’s inner air pressure and should be taken into consideration when designing a floating OWC device.