波浪作用下网帘的水动力载荷和变形计算

 离岸水产养殖中的网箱养殖逐渐成为全球水产养殖业的主导．海洋环境中网箱的水动力荷载对网箱结构的整体设计提出了更高的要求．本文建立了一种计算波浪荷载下网帘结构水动力和变形的数值计算方法,利用质点杆单元模型模拟网帘结构,通过Morison 公式求解网帘结构在波浪荷载下的受力,得到网帘结构的空间分布,同时运用迭代法对网帘结构结点受力及运动变形时的位移进行数值迭代计算,通过双目测距系统对网帘结构变形测量的结果,获得等效弹性系数,并对数值结果进行了验证．     

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.     

Structural analysis of aquaculture net cages in current

A method for structural analysis of aquaculture net cages has been developed and verified for a netting solidity of 0.23, water current velocities from 0.1 to 0.5 m/s and relatively large deformations (volume reduction up to 70%) by comparing the numerical results to tests in a flume tank. Strength analysis was performed using commercial explicit finite element software to calculate distribution of loads in the net cage due to current, weights and gravity. The net cage was modelled using truss elements that represented several parallel twines. Sub-elements allowed the trusses to buckle in compression, and only negligible compressive forces were seen in the numerical results. Resulting drag loads and cage volume were shown to be dependent on the net cage size and weight system. Drag loads increased almost proportional to the current velocity for velocities in the range of 0.2–0.5 m/s, while the cage volume was reduced proportional to the current velocity. The calculated forces in ropes and netting of full-size net cages were well below the design capacity for current velocities up to 0.5 m/s. However, netting seams in the bottom panel of the net cage were identified as a potential problem area as the forces could reach the design capacity.     

Linear wave-induced dynamic structural stress analysis of a 2D semi-flexible closed fish cage

Closed fish cages in the sea are proposed as a new concept in marine aquaculture, replacing the conventional net cages in order to meet ecological challenges related to fish lice and escapes. A closed fish cage can be compared to a floating tank structure with an internal free surface. Several types of closed cages have been suggested, and they are categorised according to structural properties as flexible membrane structures (fabric), semi-flexible structures (glass fibre) and rigid structures (steel or concrete). To be able to develop safe and reliable structures, more knowledge is required on the seakeeping behaviour of closed cages in waves and the structural response to the wave loads. This paper builds on a theory presented in Strand and Faltinsen (2019) on the linear wave loads on a 2D closed flexible fish cage. A modelling error has been found in Strand and Faltinsen (2019), however, all the main conclusions are in hold. The error has been corrected in the model in the present paper. The present paper extends the model to include bending in the structural model to be able to handle semi-flexible structures where bending stiffness is significant. In this paper, the linear theory of a 2D semi-flexible closed fish cage in waves is developed and analysed to investigate the structural response of the semi-flexible closed cage in waves. We have compared a quasi-static analysis with a fully coupled hydroelastic analysis to investigate if it is a valid and conservative assumption to assume that the stresses in the structure can be assumed quasi-static. If a hydroelastic analysis is necessary or not, is dependent on the stiffness of the structure. We have investigated what happens with the stress in the curved beam part of the closed fish cage for increasing and decreasing stiffness relative to a reference composite structure. One stiffer and two softer cases have been analysed. One major concern for the structural stresses in a closed cage is the effect of sloshing. Sloshing is internal wave motion inside the cage and have multiple resonance periods. The results indicate that to use the quasi-static assumption in structural stress calculation is conservative within the given frequency range for all examined stiffnesses and frequencies, except the frequencies very close to the second sloshing frequency. Close to the second sloshing frequency for all the examined stiffnesses, a localised peak can be observed in the coupled hydroelastic results. The second sloshing frequency is a frequency connected to a symmetric sloshing mode. Rigid body motion is not affected at the symmetric sloshing frequency for an assumed rigid structure, and are therefore also not visible in the stress results from the quasi-static analysis. The structural stress in irregular sea was calculated. These results show no indication of increased stress close to the second sloshing frequency. However, this is not a surprising result since the stress peak is very localised in frequency, and the accumulated effect on the stress standard deviation is therefore small.     

Experimental and numerical investigation on the damping effect of net cages in waves

A series of laboratory experiments were conducted to investigate the damping effect of net cages in waves. The wave transmission coefficient of the net cage was investigated with different wave periods, wave heights, numbers of net cages, net solidities, measurement positions, geometrical shapes of the net cage and Reynolds numbers. The experimental results show that the net cage has noticeable influence on wave propagation and the damping effect of net cages has a close relationship with many parameters. For multiple net cages, the transmission coefficient tends to increase as the wave period increases. The transmission coefficient of net cages decreases with increasing wave height. As the number of net cages increases, the wave transmission coefficient will decrease gradually. The damping effect of net cages on wave propagation tends to increase with increasing net solidity. The measurement position has an effect on the value of wave transmission coefficient. For net cages with different geometrical shapes, the circular net cage has more noticeable damping effect than the square net cage. A numerical model is introduced to simulate the interaction between waves and net cages with the fishing net treated as the porous media fluid model. The wave transmission coefficient downstream from net cages shows good agreement between experimental and numerical results. The study will contribute to understanding of the damping effect of a large fish farm on wave propagation.     

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。     

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.     

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.     

Numerical study of a well boat operating at a fish farm in current

Dynamic response of a well boat operating at a fish farm in current is investigated numerically. An objective is to determine the operational conditions of the well boat. In terms of the fish farm, a realistic set-up (with single cage) is considered, including a floating collar, an elastic sinker tube, a flexible-closed net cage and a complex mooring system. A time-domain solution is used to find the steady configuration and response. Transverse viscous current loads are estimated using the cross-flow principle. The drag coefficients are obtained empirically by considering cross-sectional details, free surface and three-dimensional (3D) flow effects. The drag force is experimentally validated. The effect of the ship wake on the net loading is also assessed.The most critical scenario with the well boat placed at the weather side of the fish farm is analyzed in detail. Critical response variables for operational limits are the maximum anchor-line tensions and floater stresses. Numerical results show that the anchor loads will increase more than 40% in small current velocities and up to 90% in high current velocities due to the viscous current loads on the boat. There is also a strong increase of the floating collar deformations and stresses when the well boat is in contact with the floating collar.A sensitivity analysis has been carried out to identify the physical parameters affecting the anchor loads and the maximum stress in the floating collar. From our studies, the anchor loads are more sensitive to current direction, bottom weight system, sinker tube depth and mooring line properties (pretension load, anchor chain weight, etc.) and less sensitive to other parameters such as floating collar stiffness and cross-sectional drag coefficients of the well boat. The shading effect of the well boat on the fish-farm inflow has been examined and appeared not negligible with 4% to 10% reduction of the anchor loads for the studied current conditions. The maximum stress in the floating collar is sensitive to well-boat loads related parameters (current direction, cross-sectional drag coefficient) and pretension load in the anchor line; not so sensitive to net loading related parameters such as sinker tube depth and sinker tube weight.Lastly, the operational conditions of the well boat at the fish farm were discussed. Numerical results show that the maximum stresses in the floating collar should be of major concern. The loads in the mooring lines are moderate compared with the corresponding breaking limits.     

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.     

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.     

Investigations on the porous resistance coefficients for fishing net structures

The porous media model has been successfully applied to numerical simulation of current and wave interaction with traditional permeable coastal structures such as breakwaters. Recently this model was employed to simulate flow through and around fishing net structures, where the unknown porous resistance coefficients were adjusted by fitting the available experimental data. In the present paper, a new approach was proposed to calculate the porous resistance coefficients based on the transformation of Morison type load model. The transformation follows the principle that the total forces acting on a net panel from Morison type load model should be equal to the forces obtained from the porous media model. In order to account for the interaction effects in-between the twines, two coefficients were introduced, and they were calibrated by minimizing the least square error function. Extensive validation cases were carried out to examine the performance of the numerical model. This includes steady current flow through plane net panels and circular fish cages, and wave interaction with plane net panels. A variety of fishing nets with different solidity ratios were used in the validation cases, from which it was seen that the overall agreement between the numerical and experimental results is fair.     

Numerical modeling of current loads on a net cage considering fluid–structure interaction

In this paper we propose and discuss a numerical method to model the current loads on a net cage. In our numerical model, the fluid–structure interaction is taken into consideration. The net cage is modeled on the mass-spring model; the flow field is modeled by the finite volume method (FVM). A novel hybrid volume approach is used to add the resistance force of the net cage into the flow field for coupling the fluid and net. The net resistance to the flow is calculated directly by the net’s current load using Newton’s Third Law. The resistance force is discretized in the hybrid volume and represented in the source term of the Navier–Stokes equation. By using the hybrid volume method, the mesh grid is separated from the net shape, and sparse grid (0.1 m) can be used to calculate the flow field for computational efficiency. Based on the detailed flow field, we can predict the net’s current load more accurately. The final results are derived by the segregated iterative calculation of net shape and flow field. Current forces acting on both rigid and flexible net cages are simulated at water velocity from 0 to 1 m/s; the simulation results of proposed numerical method are compared with the existing experiments, good agreements are shown in both flow field and current force, the mean normalized absolute error of the current force between simulations and measurements is about 5%.     

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.     

Hydroelastic analysis of surface wave interaction with concentric porous and flexible cylinder systems

The present study deals with the hydroelastic analysis of gravity wave interaction with concentric porous and flexible cylinder systems, in which the inner cylinder is rigid and the outer cylinder is porous and flexible. The problems are analyzed in finite water depth under the assumption of small amplitude water wave theory and structural response. The cylinder configurations in the present study are namely (a) surface-piercing truncated cylinders, (b) bottom-touching truncated cylinders and (c) complete submerged cylinders extended from free surface to bottom. As special cases of the concentric cylinder system, wave diffraction by (i) porous flexible cylinder and (ii) flexible floating cage with rigid bottom are analyzed. The scattering potentials are evaluated using Fourier–Bessel series expansion method and the least square approximation method. The convergence of the double series is tested numerically to determine the number of terms in the Fourier–Bessel series expansion. The effects of porosity and flexibility of the outer cylinder, in attenuating the hydrodynamic forces and dynamic overturning moments, are analyzed for various cylinder configurations and wave characteristics. A parametric study with respect to wave frequency, ratios of inner-to-outer cylinder radii, annular spacing between the two cylinders and porosities is done. In order to understand the flow distribution around the cylinders, contour plots are provided. The findings of the present study are likely to be of immense help in the design of various types of marine structures which can withstand the wave loads of varied nature in the marine environment. The theory can be easily extended to deal with a large class of problems associated with acoustic wave interaction with flexible porous structures.     

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.     

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.     

螺旋侧板和水深对浮式风机动态响应的影响

为研究漂浮式风力机平台动态响应的优化措施,提出平台附加螺旋侧板的方式。建立基于Spar平台的5MW风力机整机模型,利用有限元软件进行水动力计算,得到不同水深条件下,风力机平台在风、浪、流载荷联合作用下的频域特性,通过与不附加螺旋侧板情况下的动态特性参数对比,探讨螺旋侧板是否对结构的频响特性起到提升作用。结果表明,附加螺旋侧板后,结构的垂荡和纵摇的运动幅值和所受波浪力均得到了显著抑制;与纵荡和纵摇相比,垂荡运动的幅值和所受波浪力所受影响更显著;水深变化对结构响应的幅值有着显著影响。     

Growth and structure of nematic spherulites under shallow thermal quenches

The growth kinetics, shape, interfacial and internal orientation texture of a submicron nematic spherulite arising during the isotropic-to-nematic liquid crystal phase transformation under shallow thermal quenches is analyzed using theory, scaling, and numerical simulations based on the Landau – de Gennes model (The Physics of Liquid Crystals, 2nd edn. Clarendon, Oxford). The numerical computations from this model yield interfacial cusp formation that relaxes through the nucleation of two disclination lines of topological charge +1/2 and subsequently leads to intra-droplet texturing and a net topological charge within the spherulite of +1. The timing of these events suggests that cusp formation at the interface is intimately associated with the interfacial defect shedding mechanism (J. Chem. Phys. 124:244902, 2006) for shallow quenches. These results are different than predictions for deep quenches (J. Chem. Phys. 124:244902, 2006) where interfacial defect shedding leads to four defects and a net topological charge of +2. A liquid crystal dynamic shape equation is derived from the Landau – de Gennes model to account for the interface shape changes in terms of surface viscosity, the driving forces due to the uniaxial nematic-isotropic free energy difference, capillary forces, and friction forces, and used to semi-quantitatively show that during cusp formation and defect shedding, gradient elasticity, capillary forces and friction play significant roles in decelerating and accelerating the surface. An interfacial eigenvalue analysis shows that during the shallow quench, disclination lines nucleate within the interface itself and then texturize the nematic droplet as they migrate from within the interface to the bulk of the growing nematic droplet. After defect shedding, the spherulite is nearly circular and grows with constant velocity, in agreement with experiments. The results shed new light on intra-spherulite texturing mechanisms in phase ordering under weak driving forces.