Time-domain analyses of elastic response and second-order mooring force on a very large floating structure in irregular waves

Real sea areas where very large floating structures are installed are random wave fields. Then, it is necessary to analyze the responses in the time domain due to directional waves. There exist hydroelastic deflections and slow drift motions in the responses of VLFSs in ocean waves. However, it is very time consuming to solve the equations of motion in the time domain and obtain these responses due to directional waves. It is unnecessary to solve such equations in the time domain, if mooring forces can be turned into on equivalent linear system. In this paper, we analyze the time-series responses without solving the equations of motion in the time domain. And, the corresponding model tests in uni- and two-directional irregular waves are carried out. The present method is validated by comparisons between the analytical and measured results of time histories, and moreover, the analytical method of a slowly varying wave drift force is also validated.     

A B-spline Galerkin scheme for calculating the hydroelastic response of a very large floating structure in waves

This paper presents an effective scheme for computing the wave-induced hydroelastic response of a very large floating structure, and a validation of its usefulness. The calculation scheme developed is based on the pressure-distribution method of expressing the disturbance caused by a structure, and on the mode-expansion method for hydroelastic deflection with the superposition of orthogonal mode functions. The scheme uses bi-cubic B-spline functions to represent unknown pressures, and the Galerkin method to satisfy the body boundary conditions. Various numerical checks confirm that the computed results are extremely accurate, require relatively little computational time, and contain few unknowns, even in the region of very short wavelengths. Measurements of the vertical deflections in both head and oblique waves of relatively long wavelength are in good agreement with the computed results. Numerical examples using shorter wavelengths reveal that the hydroelastic deflection does not necessarily become negligible as the wavelength of incident waves decreases. The effects of finite water depth and incident wave angle are also discussed.     

Simplified estimation for the dynamic behavior and reliability analysis of very large floating structures under wave-induced loads

This paper deals with the dynamic response and strength of very large floating structures (VLFS) in regular and irregular waves, considering the propagation of the hydroelastic deflection wave of the structure. First, a simplified estimation method is presented for the dynamic response and strength of the structure in regular waves. Then, the validity of the method is demonstrated by comparing its results with analytical results and experimental results for a mat-type floating structure model. Next, a simplified estimation method for dynamic responses under long crested irregular wave conditions is presented by using the above results and by combining them with irregular sea wave spectra. Finally, the applicability of the method is investigated through numerical examples carried out for a 4,800-m class VLFS under trial design. Characteristics of the hydroelastic waves, short-term responses, and reliability levels are numerically identified. Received for publication on April 14, 1999; accepted on Sept. 10, 1999     

Minimizing differential deflection in a pontoon-type,very large floating structure via gill cells

When a pontoon-type, very large floating structure is heavily loaded in the central portion, it will deform with its central deflection much larger than its corner deflections. The resulting differential deflection, if large enough, may cause machines and equipment sensitive to differential deflection to cease operation or the floating structure to be subjected to additional large stresses. In this paper, we introduce the so-called gill cells which are compartments within the floating structure with holes or slits at the bottom floor to allow water to flow in and out freely. It will be shown herein that these gill cells reduce the differential deflection and the bending stresses significantly while maintaining the structural stiffness integrity by using the example problem of a super-large floating container terminal.     

On the dispersion relation of hydroelastic waves in a plate

This paper deals with the dispersion relation of hydroelastic waves in pontoon-type very large floating structures (VLFS) using a simple beam modeling, where the term hydroelastic waves means propagation of deflection vibrations in VLFS. The purpose of this paper is to show the properties of the hydroelastic waves. The dispersion relation of hydroelastic waves propagating in an infinite plate floating on the water is derived based on the linear water wave theory. The effects of the water depth and of the bending rigidity of the floating plate on the wavelength, phase velocity, and group velocity of the hydroelastic waves are shown theoretically or numerically. Then, the dispersion relation of hydroelastic waves in a finite plate floating on shallow water is investigated. It is shown that the wavelength or the phase velocity of the hydroelastic waves varies with the location in the plate. Received for publication on April 7, 1999; accepted on Aug. 20, 1999     

Load effects on vessel-shaped fish cage steel structures,nets and connectors considering the effects of diffraction and radiation waves under irregular waves

Vessel-shaped fish cages are mainly composed of a large floating body, aquaculture nets and a number of steel frames. Due to the large scale of vessel-shaped fish cages, the velocity field induced by the diffraction waves and radiation waves cannot be ignored in the calculation of the loads on the net and steel frames. In turn, the loads can affect the wave-induced response of the floating body and hence the radiation waves as well as the sectional forces. In this paper, a novel method is proposed to consider the coupling effect. First, considering the irregular waves in short-term periods, the global response of the floating body is calculated in the time domain by the state-space method based on potential flow theory. Meanwhile, the velocity field considering the influence of the floating body is built according to the velocity transfer function. Then, the Morison formula is used to calculate the loads on the nets and the steel frames. Finally, the coupling achieved through numerical iterations is considered in the calculation of the twine tension, load effect of connector and the global cross-section under irregular waves. It is found that the diffraction and radiation waves make a significant difference in the twine tension and connector load effect.     

考虑浮体弹性变形的锚泊系统分析方法

传统的锚泊系统分析方法一般是假设结构物为刚性不可变形的,这种假设对于常规海洋结构物的锚泊系统分析,其精度是可以接受的,然而对于弹性体(比如超大型浮体)来说,这种浮体刚性的假设显然是不合理的.本文基于摄动理论,分别给出了锚泊浮体(同时包括弹性体和刚性体)和锚泊系统的一阶运动方程.分别用三维水弹性理论和Goodman-Iance法求解浮体的动力响应和锚泊线的运动,并给出了两者之间的协调关系.通过数值算例分析表明,对于超大型浮体,其弹性特性对锚泊系统特性的影响是不可忽略的.     

Numerical calculation method for the hydroelastic response of a pontoon-type very large floating structure close to a breakwater

This paper presents an effective scheme for calculating the wave-induced hydroelastic response of a pontoon-type very large floating structure (VLFS) when it is near a breakwater. The basic numerical calculation method is the one previously developed by the same author for a VLFS in the open sea (no breakwater), which is expanded to include the effect of the hydrodynamic mutual interaction between the breakwater and the floating structure. The efficiency and accuracy of the proposed method are validated through comparisons with other numerical results and with existing experimental results. After that confirmation, various numerical calculations were conducted, paying special attention to the resonance phenomena which will occur depending on the relation between the wavelength and the clearance between the breakwater and the floating structure. The irregular frequency phenomenon which appears in the calculation of the fluid dynamic problem is discussed in the appendices, including a method for its elimination. Received: October 31, 2000 / Accepted: December 19, 2000     

Hydroelastic analysis of oblique irregular waves with a pontoon-type VLFS edged with dual inclined perforated plates

The fluid-structure interaction of oblique irregular waves with a pontoon-type very large floating structure (VLFS) edged with dual horizontal/inclined perforated plates has been investigated in the context of the direct time domain modal expansion theory. For the hydroelastic analysis, the boundary element method (BEM) based on time domain Kelvin sources is implemented to establish water wave model including the viscous effect of the perforated plates through the Darcy’s law, and the finite element method (FEM) is adopted for solving the deflections of the VLFS modeled as an equivalent Mindlin thick plate. In order to enhance the computing efficiency, the interpolation-tabulation scheme is applied to assess rapidly and accurately the free-surface Green function and its partial derivatives in finite water depth, and the boundary integral equation of a half or quarter VLFS model is further established taking advantage of symmetry of flow field and structure. Also, the numerical solutions are validated against a series of experimental tests. In the comparison, the empirical relationship between the actual porosity and porous parameter is successfully applied. Numerical solutions and model tests are executed to determine the hydroelastic response characteristics of VLFS with an attached anti-motion device. This study examines the effects of porosity, submerged depth, inclined angle and gap distance of such dual perforated anti-motion plates on the hydroelastic response to provide information regarding the optimal design. The effects of oblique wave angle on the performance of anti-motion and hydroelastic behavior of VLFS are also emphatically examined.     

支撑条件对浮动式厚弹性板水弹性行为的影响分析（英文）

The hydroelastic response of very large floating structures(VLFS) under the action of ocean waves is analysed considering the small amplitude wave theory. The very large floating structure is modelled as a floating thick elastic plate based on TimoshenkoMindlin plate theory, and the analysis for the hydroelastic response is performed considering different edge boundary conditions.The numerical study is performed to analyse the wave reflection and transmission characteristics of the floating plate under the influence of different support conditions using eigenfunction expansion method along with the orthogonal mode-coupling relation in the case of finite water depth. Further, the analysis is extended for shallow water depth, and the continuity of energy and mass flux is applied along the edges of the plate to obtain the solution for the problem. The hydroelastic behaviour in terms of reflection and transmission coefficients, plate deflection, strain, bending moment and shear force of the floating thick elastic plate with support conditions is analysed and compared for finite and shallow water depth. The study reveals an interesting aspect in the analysis of thick floating elastic plate with support condition due to the presence of the rotary inertia and transverse shear deformation. The present study will be helpful for the design and analysis of the VLFS in the case of finite and shallow water depth.     

Time-domain numerical and experimental analysis of hydroelastic response of a very large floating structure edged with a pair of submerged horizontal plates

This paper is concerned with the hydroelastic problem of a pontoon-type, very large floating structure (VLFS) edged with the perforated plates, non-perforated plates or their combination anti-motion device both numerically and experimentally. A direct time domain modal expansion method, taking amount of the time domain Kelvin sources in hydrodynamic forces, in which the fluid flows across the perforated anti-motion plate by applying the Darcy's law, is applied to the fluid–structure interaction problem. A quarter of numerical model is built based on the symmetry of flow field and structure in hydrodynamic forces, and special care is paid to the rapid and accurate evaluation of time domain free-surface Green functions and its spatial derivatives in finite water depth by using interpolation–tabulation method. Using the developed numerical tools and the model tests conducted in a wave basin, the response-reduction efficiency of the perforated plates is systematically assessed for various wave and anti-motion plate parameters, such as plate width, porosity and submergence depth. As a result of the parametric study, the porosity 0.11 is selected as the optimal porosity, and the relationship between the porosity and the porous parameter is developed by using the least-squares fitting scheme. After simulation and verification, the dual anti-motion plates which are the perforated-impermeable-plate combination attached to the fore-end and back-end of the VLFS, are designed for more wave energy dissipation and added damping. Considering variation of the water depths in offshore, discussion on the effectiveness of these anti-motion devices at different water depths is highlighted.     

Design,modelling, and analysis of a large floating dock for spar floating wind turbine installation

Installation of floating wind turbines at the offshore site is a challenging task. A significant part of the time efficiency and costs are related to the installation methods which are sensitive to weather conditions. This study investigates a large floating dock concept, which can be used to shield a floating wind turbine during installation of tower, nacelle, and rotor onto a spar foundation. In this paper, the concept is described in detail, and a design optimisation is carried out using simple design constraints. Hydrodynamic analysis and dynamic response analysis of the coupled system of the optimum dock and spar are conducted. Two spars of different sizes are considered, and the motion responses of the spars with and without the dock in irregular waves are compared. Through analysis of the motion spectra and response statistics, dynamic characteristics of the coupled system is revealed. The present design of the dock reduces the platform-pitch responses of the spars and potentially facilitates blade mating, but may deteriorate the heave velocity of the spars in swell conditions. Finally, future design aspects of the floating dock are discussed.     

Slamming load on a very large floating structure with shallow draft

The objective of this paper is to estimate the slamming load acting on a pontoon-type very large floating structure with a shallow draft. Experiments were carried out using elastic models with different rigidities in regular waves. The results revealed that the slamming load was strongly influenced by the rigidity of the model. The conditions under which slamming occurs depended on the extent of the bottom emergence and the velocity of the relative wave height at the bow of the model. These results were related to a simple procedure for estimating slamming load.     

Hydrodynamic experiment of submerged floating tunnel under regular wave and current actions during construction period

Submerged floating tunnel (SFT) is an innovative cable-supported structural system for crossing deep and long-distance ocean environments. In the complex ocean environment, the construction of SFT needs to consider wave and current forces. Specific construction measures and control also require in-depth study and understanding of the dynamic response of SFT under such environmental loads. In this study, the dynamic response of SFT and cable forces under the action of waves alone and wave-current interactions are investigated by using a large wave-current basin. A total of 138 regular wave and wave-current cases were conducted during the experiments, and the influence of waves and wave-current interactions on the dynamic response of SFT and cable forces are discussed in detail by combining experimental data with corresponding analysis. Results show that the wave height, current velocity, and ratio of wavelength to structure size are important factors affecting the dynamic response of SFT and cable forces. The multi-anchor cable arrangement used in the present experimental tests distribute cable force more effectively and reduce the potential safety hazard caused by cable breakage. This study can provide a useful reference for the construction and control of the single SFT segment under construction in a complex ocean environment, especially under the interaction of waves and currents.     

不规则波对方箱浮式防波堤作用的数值模拟

采用线性波浪叠加法对不规则波进行数值模拟,采用时域边界元法对不规则波作用下的方箱浮式防波堤进行数值模拟。首先验证了不规则波的数值模拟的准确性,进而对不规则波作用下固定方箱浮式防波堤的受力进行数值模拟,并与规则波结果进行比较。结果表明不规则波作用下,单位宽度方箱垂向受力最大值要大于水平受力的最大值;与规则波情况相比,方箱的水平向受力变化幅度减小,垂向受力和横摇力矩则幅值增加。     

蛇形造波机计算机程序的设计

用C语言和汇编语言编制了蛇形造波机的控制和数据处理程序,用于生成规则波、斜向规则波、不规则波、斜向不规则波和多方向不规则波。介绍了驱动信号的生成、采样间隔的确定、方向函数的估计和方向谱的修正方法。     

基于浮体Morison方程的半潜式超大型浮式结构波浪力简化计算方法

研究了半潜式超大型浮式结构中移动式海上基地（MOB）在高海况随机波作用下波浪力的简化计算方法。文中基于修正后的浮体Morison方程,经理论推导得出了MOB结构波浪力的计算公式。以MOB结构“三模块模型”为例,研究其在6级海况条件下基于Bretschneider谱模拟的随机不规则波中浪向角变化在0°~90°范围内,各模块的波浪力-历时规律,将本文简化算法的计算结果统计值与势流理论的结果相互对比,并对二者进行误差分析。结果表明：运用本文简化算法得到的MOB波浪力统计结果与势流理论的结果吻合程度高,且二者之间的相对误差在工程允许的范围之内,可充分验证本文方法的正确性、合理性与可行性。本文算法相比于势流理论而言更加简单,建议在结构初步设计阶段运用该方法可高效地评估大量不同工况下MOB结构的波浪荷载,研究成果可为半潜式超大型浮式结构动力响应研究奠定基础。     

不同间距下大直径圆筒防波堤波吸力试验研究

防波堤的波浪力计算对防波堤的设计和稳定具有重要意义。针对目前圆筒防波堤波吸力的设计计算方法尚未成熟,通过开展物理模型试验,进行不规则波作用下不同间距下大直径圆筒结构波吸力的分布规律、影响因素和计算方法研究。结果表明:波谷作用下,大直径圆筒结构波吸力的横向分布规律与圆筒的间距有关,纵向分布规律表现为随着水深增加先线性增大然后线性减小,且最大波吸力的位置出现在静水位一倍波高以下。圆筒的相对间距、相对水深以及波陡对不同间距大直径圆筒防波堤的波吸力影响较大。基于直立墙结构波吸力公式给出折减系数的拟合公式,用以计算圆筒周身迎浪面的波吸力。     

基于离散模块梁单元水弹性理论的复杂连接处建模方法

[目的]在离散模块?梁单元(DMB)水弹性理论框架下,提出针对连接形式复杂的超大型浮体结构(VLFS)的新的建模方法,并与已有方法进行对比分析.[方法]首先,概述基于DMB的水弹性分析方法,给出求解连续VLFS结构在波浪作用下的动力响应步骤;然后,针对VLFS复杂连接处进行建模,通过定义连接处的刚度矩阵,对与连接处相邻...     

Validation of a dynamic mooring model coupled with a RANS solver

Standard design procedures and simulation tools for marine structures are aimed primarily for use by the offshore oil and gas. Mooring system restoring forces acting on floating offshore structures are obtained from a quasi-static mooring model alone or from a coupled analysis based on potential flow solvers that do not always consider nonlinear mooring-induced restoring forces, fluid structure interactions, and associated hydrodynamic damping effects. This paper presents the validation of a dynamic mooring system analysis technique that couples the dynamic mooring model with a Reynolds-averaged Navier-Stokes (RANS) equations solver. We coupled a dynamic mooring model with a RANS equations solver, and analyzed a moored floating buoy in calm water, regular and irregular waves and validated our motion and mooring force predictions against experimental measurements. The mooring system consisted of three catenary chains. The analyzed response comprised decaying oscillating buoy motions, linear and quadratic damping characteristics, and tensile forces in mooring lines. The generally favorable comparison of predicted buoy motions and mooring forces to experimental data confirmed the reliability of our implemented coupling technique to predict system response. Additional comparative results from a potential flow solver demonstrated the benefits of the coupled dynamic mooring model with RANS equations. The successful validated tool of coupling the dynamic mooring model with the RANS solver is available as open source, and it shows the potential of the coupled methodology to be used for analyzing the moored offshore structures.