Numerical study of a well boat operating at a fish farm in long-crested irregular waves and current

The dynamic response of a coupled well boat–fish farm system in irregular long-crested waves and current is analyzed numerically in the time domain. The main purpose is to investigate the influence of the well boat on the fish farm and then to determine the operational conditions of the well boat.The numerical study of slow-drift sway motion of the well boat is performed at first. Hydrodynamic and statistical theories are briefly introduced. The cross-flow principle is assumed valid for evaluating the transverse viscous loads and the needed cross-sectional drag coefficients are estimated empirically and validated against available experiments. The mean value and standard deviation of the slow-drift motion from time domain agree well with those from frequency domain when equivalent linearized drag damping is incorporated.The coupled system with the well boat placed at the weather side of the fish farm is then analyzed in detail. Special attention is paid to two critical response variables, i.e., maximum anchor-line loads and maximum floating collar stresses. Numerical results show that the examined two variables will increase more than 300% due to the well boat in moderate exposure sea states. A sensitivity analysis is also carried out to identify the important parameters influencing these two response variables. Cross-sectional drag coefficients for the well boat and fish-farm related parameters (pretension load in the anchor lines and anchor-line stiffness) have moderate influence on the two variables. Simplifying the modeling of the coupled system, for instance neglecting the net cage and the first-order motion, has more effect on the maximum anchor load than on the maximum floating-collar stress and reduced sensitivity is observed in current, especially for the latter variable.Lastly, the operational conditions of the well boat are determined through systematic simulations. Numerical results show that the maximum loads in the mooring lines are moderate compared with the corresponding breaking limits even in high exposure sea states, while for the maximum stress in the floating collar can be close to the yield stress when operating in moderate exposure regions.     

圆形重力式网箱锚碇系统的受力研究

依据Stokes二阶波浪理论和莫里森(Morison)方法,对圆形重力式网箱的浮架结构分别与工程上常用的两种锚碇系统(折线形与直线形)相结合情况下,锚碇系统的受力进行了数值计算及相应的物理模型试验。结果表明相同波况下折线形锚碇系统承受张力较小,在相同波浪周期条件下,波高越大锚碇点受力越大;相同波高下,锚碇点最大受力随周期变化不显著。将计算结果与模型试验对比,结果显示计算数值与试验数据较接近,表明了此计算方法的可行性,为进一步模拟浮架结构的运动变形打下基础。     

Experimental and numerical study of an aquaculture net cage with floater in waves and current

The mooring loads on an aquaculture net cage in current and waves are investigated by dedicated model tests and numerical simulations. The main purpose is to investigate which physical effects are dominant for mooring loads, and in this respect, to investigate the validity of different rational hydrodynamic load models. Also structural and numerical aspects are investigated. The model tests are performed to provide benchmark data, while the numerical model is used to study the effect and sensitivity of different load models and parameters.Compared to a realistic aquaculture plant, the total system is simplified to reduce the complexity. The system does, however, include all the four main components of an aquaculture plant: net cage, floater, sinker weights and moorings. The net cage is bottomless, flexible and circular. It is attached to a circular, elastic floater at the top and has 16 sinker weights at the bottom. The system is nearly linearly moored with four crow feet mooring lines.The loads are measured in the four mooring lines. A systematic variation of current only, wave only as well as combined current and wave conditions is carried out. The numerical simulation results are first benchmarked towards the experimental data. The mean loads in general dominate over the dynamic part of the loads in combined current and waves, and they significantly increase in long and steep waves, relative to current only. Next, a sensitivity study is carried out. A rigid floater significantly alters the loads in the mooring lines compared to a realistic, elastic floater. The theoretical model for the wave matters. The mooring loads are rather insensitive to a majority of the parameters and models, in particular: frequency dependent added mass of the floater and nonlinear restoring loads. It seems not to be necessary to represent the net cage with a very fine numerical mesh.     

Comparison of linear spring and nonlinear FEM methods in dynamic coupled analysis of floating structure and mooring system

This paper compares the dynamic coupled behavior of floating structure and mooring system in time domain using two numerical methods for the mooring lines such as the linear spring method and the nonlinear FEM (Finite Element Method). In the linear spring method, hydrodynamic coefficients and forces on the floating body are calculated using BEM (Boundary Element Method) and the time domain equation is derived using convolution. The coupled solution is obtained by simply adding the pre-determined spring constants of the mooring lines into the floating body equation. In FEM, the minimum energy principle is applied to formulate the nonlinear dynamic equation of the mooring system with a discrete numerical model. The ground contact model and Morison formula for drag forces are also included in the formulation. The coupled solution is obtained by iteratively solving the floating body equation and the FEM equation of the mooring system. Two example structures such as weathervane ship and semi-submersible structure are analyzed using linear spring and nonlinear FEM methods and the difference of those two methods are presented. By analyzing the cases with or without surge-pitch or sway-roll coupling stiffness of mooring lines in the linear spring method, the effect of coupling stiffness of the mooring system is also discussed.     

浮式垂直轴风机的动力学建模、仿真与实验研究

考虑气动力和水动力的耦合研究浮式垂直轴风机系统的运动响应,将固定式垂直轴风机的气动载荷计算方法进一步推广到海上浮式垂直轴风机的气动载荷计算.考虑阻尼力、波浪力、风载荷、系泊力等,建立了浮式垂直轴风机系统的纵荡-垂荡-纵摇运动方程.考虑动态失速和浮式基础运动,基于双致动盘多流管理论,推导了风机叶片气动载荷计算公式,编制了数值计算程序.以Sandia 17 m风机为例,验证了气动载荷计算程序的正确性.最后进行了模型实验,其中模型的风机为Φ型达里厄垂直轴风机,支撑基础为桁架式Spar型浮式基础,将模型实验结果与数值计算结果进行了对比,验证了耦合计算程序.结果表明,数值计算得到的风机系统的垂荡、纵摇运动的RAO(幅值响应算子)曲线与模型实验结果吻合较好,验证了耦合程序的正确性.然而,由于数值计算与模型实验在运动自由度、阻尼、风载荷等方面存在差别,数值计算结果与模型实验结果仍有一定的差异.     

Analysis of hydrodynamic behaviors of multiple net cages in combined wave–current flow

Numerical simulation is performed to analyze the hydrodynamic response of a net cage and submerged mooring grid system exposed to waves and current. A series of experiments are conducted to validate the numerical model of net cage and grid mooring system. The numerical results of this model correspond with those obtained from experimental observations. Then, the numerical simulation of a multi-cage and mooring system under the action of waves combined with current is conducted. The influence of waves and current directions and the length of grid lines on the cage responses are discussed. The twin mooring system and the orthogonal mooring system are compared. Results show that for the orthogonal mooring system, the maximum tension force on the anchor line of the four-cage system is less than four times of that of the single-cage system, when both waves and current travel along the x-axis. The minimum net cage volume holding coefficient of the single-cage system is smaller than that of the four-cage system. The amplitude of the mooring line tension force for the twin mooring system is larger than the orthogonal mooring system.     

Offshore floating wind turbine and its dynamic problems

Green energy sources and ocean wind power are plentiful in deep sea. More and more offshore wind power plants are constructed in the deep water over hundred meters below the surface. While offshore floating wind turbine system is working, wind turbine, floating foundation, and mooring system affect each other with wind, waves, and currents acting on them. Various offshore floating wind turbine systems and the encountered environmental loads are briefly reviewed and discussed. It is difficult and crucial to comprehensively analyze the aerodynamic-hydrodynamic-service system-structure under the coupling effect of offshore floating wind turbine system. The environmental flow field, structure scale, and rational applications of theories and approaches should be well considered in advance.     

Numerical analysis of finite amplitude motion of waves and a moored floating body under severe storm conditions

The motion of a moored floating body under the action of wave forces, which is influenced by fluid forces, shape of the floating body and mooring forces, should be analysed as a complex coupled motion system. Especially under severe storm conditions or resonant motion of the floating body it is necessary to consider finite amplitude motions of the waves, the floating body and the mooring lines as well as non-linear interactions of these finite amplitude motions. The problem of a floating body has been studied on the basis of linear wave theory by many researchers. However, the finite amplitude motion under a correlated motion system has rarely been taken into account. This paper presents a numerical method for calculating the finite amplitude motion when a floating body is moored by non-linear mooring lines such as chains and cables under severe storm conditions.     

Structural response of high solidity net cage models in uniform flow

Hydrodynamic loads acting on a fish farm may be affected by the growth of different biofouling organisms, mainly due to increased solidity of the nets. In this paper, the hydrodynamic loads acting on high solidity net cage models subjected to high uniform flow velocities and the corresponding deformation of the net cages are studied. Model tests of net cylinders with various solidities were performed in a flume tank with a simulated current. Standard Morison-type numerical analyses were performed based on the model tests, and their capability of simulating the occurring loads and the observed net cage deformations for different flow velocities was evaluated.Large deformations of the net cage models were observed, and at high velocities the deformations were close to what is physically possible. Net cage deformation appeared to be less dependent on solidity than on flow velocity and weights. Drag forces increased with increasing flow velocity and were dependent on both bottom weights and netting solidity. For the lowest solidity net, drag forces were close to proportional to flow velocity. For the three high solidity nets, the measured drag forces were of similar magnitude, and drag increased less with increasing flow velocity above approximately 0.5 m/s than at lower velocities.This study shows that a basic reduced velocity model is not sufficient to model the interaction between the fluid flow and net (hydroelasticity) for high solidity net cages subjected to high flow velocities.The standard numerical analysis was in general able to make good predictions of the net shape, and was capable of making an acceptable estimate of hydrodynamic loads acting on the lowest solidity net model (Sn=0.19). For high solidities and large deformations, numerical tools should account for changes in water flow and the global drag coefficient of the net.     

Vortex induced vibrations measured in service in the Foinaven dynamic umbilical, and lessons from prediction

The Foinaven Umbilical Monitoring System (FUMS) has been provided to measure the stresses in a subsea umbilical of the Foinaven floating production facility. The FUMS provides high-quality data for vortex induced vibrations. A novel approach has been adopted to clearly demonstrate the variation with time of the contributions of umbilical excitation at mooring system, wave, and vortex shedding frequencies. The Foinaven case is of particular interest owing to the existence of strong currents which may be substantially sheared, and the large number of modes of vibration which may be induced by vortex shedding. This paper presents some of the responses measured, and makes comparison with vortex induced vibration predictions. The predictions include drag coefficient amplification resulting from VIV, which is important for the design of future umbilicals owing to its influence on the total hydrodynamic load, and on station keeping of the vessel. Comments on design assumptions for estimation of vortex induced vibration are included.     

Nonlinear network modeling of multi-module floating structures with arbitrary flexible connections

Multiple floating modules connected by flexible connectors can be viewed as a network structure. A standard modeling process for multi-module floating structures in arbitrary topology is presented by using network theory. A three-dimensional model is developed using the linear wave theory, dynamic model of single floating module, constitutive model of flexible connectors and model of a mooring system. As a typical application, a floating airport model is established and further its nonlinear dynamic responses and connector loads are analyzed. Numerical results show that the traditional linear analysis may underestimate the actual results. The methodology applied in this paper is extensible to many engineering problems with network structures alike.     

Dynamics of dual pontoon floating structure for cage aquaculture in a two-dimensional numerical wave tank

The trend of using floating structures with cage aquaculture is becoming more popular in the open sea. The purpose of this paper is to investigate the dynamic properties of a dual pontoon floating structure (DPFS) when attached to a fish net by using physical and numerical models. A two-dimensional (2-D) fully nonlinear numerical wave tank (NWT), based on the boundary element method (BEM), is developed to calculate the wave forces on the DPFS. The wave forces on a fish net system are then evaluated using a modified Morison equation. The comparisons of dynamic behaviors between numerical simulations and experimental measurements on the DPFS show good agreement. Results also display that a fish net system causes the resonant response of body motions and mooring forces to be slightly lower due to the net's damping effect. Finally, for designing the rearing space of cage aquaculture, the influences which net depth and net width have on the DPFS dynamic responses are also presented in this paper.     

Shapes of the fastest fish and optimal underwater and floating hulls

A streamlined shape of the best swimmers removes the boundary-layer separation and ensures a laminar flow pattern. The fastest fish have a very sharp convex nose (rostrum), the purpose of which remains unclear. The bodies of revolution similar to their shapes are analyzed in steady underwater and floating motion. The sources and sinks were located on the axis of symmetry and above the water surface to estimate the pressure on the body and the vertical velocities on the water surface. It was shown that the flow patterns on a special shaped body with concave nose has no stagnation points and ensure small values of the water surface elevation. These fact allow diminishing the maximum pressure on the surface and wave drag. Special shapes with the sharp concave nose and negative pressure gradients on their surface could be parts of the low drag underwater and floating hulls.     

潮流发电装置运动衰减特性与不规则波响应

为了研究基于竖轴水轮机的漂浮式潮流能发电装置的运动衰减特性与不规则波响应,提出了基于船模拖曳水池的系泊试验方法,设计了试验模型和装置,构建了系泊试验平台,进行了组合模型的自由衰减试验、系泊衰减试验和系泊状态下的不规则波响应试验. 衰减试验中测量了模型的摇动衰减特性,不规则波响应试验中测量了系缆的拉力响应和组合模型的摇动响应. 试验研究得到了关于漂浮式潮流能发电装置的衰减运动特性和4级海况、0.6m/s流速时1号系缆的拉力响应以及组合模型的摇动响应. 研究可为基于竖轴水轮机的漂浮式潮流能发电装置的理论研究和工程应用提供参考和借鉴.     

UNSTEADY HYDROELASTICITY OF FLOATING PLATES

Asymptotic and numerical analyses of unsteady hydroelastic behaviour of a floating plate due to given external loads are presented. The main parameters are the plate length and duration of the external loads. For very long plates (VLFS) the problem is decoupled and its approximate solution is given by the method of matched asymptotic expansions. For a short duration of the external loads and small length of the plate (impact onto a floating plate) the problem is coupled, but gravity effects can be neglected in determining the maximum of both the plate deflection and bending stresses in the plate. In this case, the problem is solved numerically by the method of normal modes. If the plate is short but the load duration is moderate, the rigid-body motion of the plate and its elastic vibrations can be approximately separated. In the general case, it is suggested that the coupled problem can be treated numerically by the method of normal modes. In order to construct an appropriate numerical algorithm, ideas inspired by the asymptotic analysis are used.     

水流中锚链阻力系数测量的实验设计

为了在水池内测出船模拖曳时锚链在水流中的阻力系数,设计了一套简单而有效的实验方案。考虑到锚链的柔软与笨重,故采取了三项措施:(1)将锚链相邻链环连接处点焊住,使其成一根直杆;(2)将该锚链水平悬挂于拖车之下,用拖车运行速度模拟流速,通过锚链悬挂绳与铅垂线的夹角来计算水流对锚链的作用力;(3)为了消除锚链两个端部对阻力测试的影响,用长、短锚链的阻力差值除以锚链长度差,既得到了单位长度锚链的阻力,又有效地解决了端部影响,进而计算出锚链阻力系数。     

Parallel finite element simulation of mooring forces on floating objects

The coupling between the equations governing the free‐surface flows, the six degrees of freedom non‐linear rigid body dynamics, the linear elasticity equations for mesh‐moving and the cables has resulted in a fluid‐structure interaction technology capable of simulating mooring forces on floating objects. The finite element solution strategy is based on a combination approach derived from fixed‐mesh and moving‐mesh techniques. Here, the free‐surface flow simulations are based on the Navier–Stokes equations written for two incompressible fluids where the impact of one fluid on the other one is extremely small. An interface function with two distinct values is used to locate the position of the free‐surface. The stabilized finite element formulations are written and integrated in an arbitrary Lagrangian–Eulerian domain. This allows us to handle the motion of the time dependent geometries. Forces and momentums exerted on the floating object by both water and hawsers are calculated and used to update the position of the floating object in time. In the mesh moving scheme, we assume that the computational domain is made of elastic materials. The linear elasticity equations are solved to obtain the displacements for each computational node. The non‐linear rigid body dynamics equations are coupled with the governing equations of fluid flow and are solved simultaneously to update the position of the floating object. The numerical examples includes a 3D simulation of water waves impacting on a moored floating box and a model boat and simulation of floating object under water constrained with a cable. Copyright © 2003 John Wiley & Sons, Ltd.     

Experimental investigation of hydrodynamic loads and pressure distribution during a pyramid water entry

In the maritime environment slamming is a phenomenon known as short duration impact of water on a floating or sailing structure. Slamming loads are local and could induce very high local stresses. This paper reports a series of impact test results and investigate the slamming loads and pressures acting on a square based pyramid. In this study the slamming tests have been conducted at constant velocity impact with a hydraulic high speed shock machine. This specific experimental equipment avoids the deceleration of the structure observed usually during water entry with drop tests. Three velocities of the rigid pyramid have been used (10, 13 and 15 m s⁻¹). Time-histories of local pressures, accelerations and slamming loads were successfully measured. The relationship between the pressure magnitude and the impact velocity is obtained and the spatial distribution of pressures on pyramid sides is characterized. The impact velocity was found to have a negligible influence in predicting the maximum pressure coefficient.     

A moderate deflection composite helicopter rotor blade model with an improved cross-sectional analysis

The compatibility between a composite beam cross-sectional analysis based on the variational asymptotic approach, and a helicopter rotor blade model which is part of a comprehensive rotorcraft analysis code is examined. It was found that the finite element cross-sectional analysis code VABS can be combined with a moderate deflection rotor blade model in spite of the differences between the formulations. The new YF/VABS rotor blade model accounts for arbitrary cross-sectional warping, in-plane stresses, and moderate deflections. The YF/VABS composite rotor blade model was validated against experimental data and various rotor blade analyses by examining displacements and stresses under static loads, as well as aeroelastic stability of a composite rotor blade in hover, and forward flight vibratory hubloads of a four bladed composite rotor.     

Multi-modes approach to modelling of vortex-induced vibration

In this work the fluid–structure interactions are considered by investigating a straight but slender pipe interacting with uniform water flow. Two configurations are studied, namely vertically and horizontally positioned pipes, which are modelled as an Euler–Bernoulli beam with flexural stiffness. Both pretension and length-wise mass distribution are considered. The structure is assumed to be moving only in the direction normal to flow (cross-flow motion) hence its in-line motion is neglected. The external fluid force acting on the structure is the result of the action of sectional vortex-induced drag and lift forces. Only mean drag force is considered, with time varying lift force modelled using a non-linear oscillator equation of the Van der Pol type. The obtained coupled system of non-linear partial differential equations is simplified employing Galerkin-type discretisation. The resulting ordinary differential equations are solved numerically providing multi-mode approximations of cross-flow displacement and non-dimensional lift coefficient. The comparison between the responses of vertical and horizontal structures shows that, as expected, due to a balancing between pretension and weight, in general a higher amplitude of vibration is observed for the vertical configuration than in the same location along the pipe for the horizontal configuration in the lower part of the structure. However, lower amplitudes are obtained in the upper part of the pipe. The horizontal configuration solutions are identical in symmetrical locations along the pipe due to constant pretension. The influence of the wake equation coefficients and the fluid force coefficients on the response amplitudes has been also considered together with the length of the pipe and pretension level, and the appropriate response curves are included. Finally, for the higher mode approximations it has been shown that the vibrations level at lower frequencies is predicted reasonably well by retaining only a small subset of modes.