Numerical simulation of the influences of sinker weight on the deformation and load of net of gravity sea cage in uniform flow

1IntroductionThe fish farming and aquaculture industry areexpanding and the demand for suitable locations forfish farms is increasing.In the future,more of thefish farms will be located offshore,as the number ofsuitable nearshore locations is limited.Futu…     

圆柱形沉浮式深海养殖网箱的受力分析

应用一系列力学关系，研究了深海圆柱形沉浮式养殖网箱所承受的波浪力情况。导出深海沉浮式养殖网箱的运动方程，并给出数值计算。在网箱波浪力的研究中采用绕射理论和Morison方程，讨论了在波高、波长及周期变化下水动力的变化趋势，得出网箱所受到的水平波浪力远大于竖直波浪力，波高的变化对波浪力的影响最大的结论，为深海网箱的设计校核提供1种参考方法。     

Numerical Analysis on the Effects of Submerged Depth of the Grid and Direction of Incident Wave on Gravity Cage

In this paper,the numerical model of the net cage with the grid mooring system in waves is set up by the lumped mass method and rigid kinematics theory,and then the motion equations of floating system,net system,mooring system,and floaters are solved by the Runge-Kutta fifth-order method.For the verification of the numerical model,a series of physical model tests have been carried out.According to the comparisons between the simulated and experimental results,it can be found that the simulated and experimental results agree well in each condition.Then,the effects of submerged depth of grid and direction of incident wave propagation on hydrodynamic behaviors of the net cage are analyzed.According to the simulated results,it can be found that with the increase of submerged depth of grid,the forces acting on mooring lines and bridle lines increase,while the forces on grid lines decrease;the horizontal motion amplitudes of floating collar decrease obviously,while the vertical motion amplitudes of floating collar change little.When the direction of incident wave propagation changes,forces on mooting lines and motion of net cage also change accordingly.When the propagation direction of incident wave changes from 0° to 45°,forces on the main ropes and bridle ropes increase,while the forces on the grid ropes decrease.With the increasing propagation direction of incident wave,the horizontal amplitude of the forces collar decreases,while the vertical amplitude of the floating collar has little variation.     

Numerical Study on the Hydrodynamic Characteristics of Biofouled Full-Scale Net Cage

The effect of biofouling on the hydrodynamic characteristics of the net cage is of particular interest as biofouled nettings can significantly reduce flow of well-oxygenated water reaching the stocked fish. For computational efficiency, the porous-media fluid model is proposed to simulate flow through the biofouled plane net and full-scale net cage. The porous coefficients of the porous-media fluid model can be determined from the quadratic-function relationship between the hydrodynamic forces on a plane net and the flow velocity using the least squares method. In this study, drag forces on and flow fields around five plane nets with different levels of biofouling are calculated by use of the proposed model. The numerical results are compared with the experimental data of Swift et al.(2006) and the effectiveness of the numerical model is presented. On that basis, flow through full-scale net cages with the same level of biofouling as the tested plane nets are modeled. The flow fields inside and around biofouled net cages are analyzed and the drag force acting on a net cage is estimated by a control volume analysis method. According to the numerical results, empirical formulas of reduction in flow velocity and load on a net cage are derived as function of drag coefficient of the corresponding biofouled netting.     

Analysis of hydrodynamic behavior of a submersible net cage and mooring system in waves and current

Failure of net cage and mooring system is of great concern to the marine aquaculture industry. To avoid the structure failure in storm waves and current during typhoon events, net cage can submerge below the water surface in practice. A submersible net cage and mooring system is analyzed by numerical simulation and physical model test. The numerical model is established based on the lumped mass method and principle of rigid body kinematics. A series of physical model tests are conducted to validate the numerical model of single net cage and grid mooring system in waves and current. Numerical results correspond well with data obtained from physical model test. The results indicate that when net cage is submerged below the water surface, the deformation of net cage in waves can be improved significantly, and the tension force on the anchor line, bridle line and grid line will decrease significantly. However, the tension force on the buoy line in the submergence condition is larger than that in the floating condition. Different relative submergence ratios are also considered in our numerical simulation, and a relative submergence ratio equal to 0.1 is suggested here. The tension reduction ratio (56%) for the four-cage system is larger than that for the single-cage (52%) and double-cage systems (44%).     

Numerical Study on the Hydrodynamic Characteristics of Biofouled Full-Scale Net Cage

The effect of biofouling on the hydrodynamic characteristics of the net cage is of particular interest as biofouled nettings can significantly reduce flow of well-oxygenated water reaching the stocked fish. For computational efficiency, the porous-media fluid model is proposed to simulate flow through the biofouled plane net and full-scale net cage. The porous coefficients of the porous-media fluid model can be determined from the quadratic-function relationship between the hydrodynamic forces on a plane net and the flow velocity using the least squares method. In this study, drag forces on and flow fields around five plane nets with different levels of biofouling are calculated by use of the proposed model. The numerical results are compared with the experimental data of Swift et al. (2006) and the effectiveness of the numerical model is presented. On that basis, flow through full-scale net cages with the same level of biofouling as the tested plane nets are modeled. The flow fields inside and around biofouled net cages are analyzed and the drag force acting on a net cage is estimated by a control volume analysis method. According to the numerical results, empirical formulas of reduction in flow velocity and load on a net cage are derived as function of drag coefficient of the corresponding biofouled netting.     

一种基于有限元原理的养殖网箱耐流特性的数值计算方法

对养殖网箱在海流作用下变形而导致的网箱养殖空间减少的有效把握,是网箱设计计算的核心课题之一。本文提出1种基于有限元原理的用于预测养殖网箱耐流特性的数值模拟方法,以期依据计算机模拟结果,在一定程度上代替传统的模型试验和海上实际测试,寻找提高网箱耐流特性的技术措施和解决方案。     

Analysis of hydrodynamic behaviors of gravity net cage in irregular waves

Based on the lumped-mass method and rigid-body kinematics theory, a mathematical model of a gravity cage system attacked by irregular waves is developed to simulate the hydrodynamic response of cage system, including the maximum tension of mooring lines and the motion of float collar. The normalized response amplitudes (response amplitude operators) are calculated for the cage motion response in heave and surge, and the mooring line tension response, in regular waves. In addition, a statistical approach is taken to determine the motion and tension transfer functions in irregular waves. In order to validate the numerical model of a gravity cage attacked by irregular waves, numerical predictions have been compared with the experimental observations in the time and frequency domain. The effect of wave incident angle on the float collar motion, mooring line tension and net volume reduction of the gravity cage system in irregular waves is also investigated. The results show that at high frequencies, the cage system has no significant heave motion. It tends to contour itself to longer waves. The variation amplitude of mooring line forces decreases as the wave frequency increases. With the increasing of wave incident angle, the horizontal displacement of the float collar increases.     

Dynamic analysis of hydrodynamic behavior of a flatfish cage system under wave conditions

This paper presents a simulation model based on the finite element method. The method is used to analyze the motion response and mooring line tension of the flatfish cage system in waves. The cage system consists of top frames, netting, mooring lines, bottom frames, and floats. A series of scaled physical model tests in regular waves are conducted to verify the numerical model. The comparison results show that the simulated and the experimental results agree well under the wave conditions, and the maximum pitch of the bottom frame with two orientations is about 12o. The motion process of the whole cage system in the wave can be described with the computer visualized technology. Then, the mooring line tensions and the motion of the bottom frame with three kinds of weight are calculated under different wave conditions. According to the numerical results, the differences in mooring line tensions of flatfish cages with three weight modes are indistinct. The maximum pitch of the bottom frame decreases with the increase of the bottom weight.     

基于有限元方法对鲆鲽网箱耐流特性的数值模拟

鲆鲽网箱结构在海中受到水流的冲击作用会发生运动与变形,针对鲆鲽鱼特有的栖底习性,为确保网底结构的稳定有必要对其进行动力分析。为此利用有限元方法建立了流场中网箱受力和变形的数学计算模型,运用该数学模型对底框中加有支撑管结构并装配方形网目网衣的鲆鲽网箱整体位移进行了数值模拟。数值模拟结果表明,网箱的网衣部分在水流作用下形态变化比较大,网底的水平位移与垂直位移随流速的增加而增大,而网箱的底框架在不同流速条件下均能保持在水平位置,且未发生明显的倾斜。由此可见,此类鲆鲽网箱具有较好的耐流性能。     

Numerical Simulation of Dynamic Response of A Net Cage for Flatfish in Waves简

A numerical model of flatfish cage is built based on the lumped mass method and the principle of rigid body kinematics. To validate the numerical model, a series of physical model tests are conducted in the wave flume. The numerical results correspond well with the data sets from physical model test. The effect of weight of bottom frame, height of fish net and net shape on motion responses of fish cage and tension force on mooring lines is then analyzed. The results indicate that the vertical displacements of float collar and bottom frame decrease with the increase in the weight of bottom frame; the maximum tension force on mooring lines increases with the increasing weight of bottom frame. The inclination angles of float collar and bottom frame decrease with the increasing net height; the maximum tension force increases obviously with the increase of net height.     

Numerical simulation of the effects of fish behavior on flow dynamics around net cage

The computational fluid dynamics study is performed to analyze the impact of the cultured fish on the flow field through net cage and the deformation of net cage. The shear stress turbulent k-omega model is applied to simulate the flow field through the net cage, and the large deformation nonlinear structure model is adopted to conduct the structural analysis of the flexible net cage. To validate the net-fluid interaction model of the net cage in current, a series of physical model tests are conducted, which indicate that the numerical model can accurately simulate the flow field around the net cage and the deformation of the net cage. A fish model is used to simulate the effect of fish behavior on the flow pattern around the net cage and the deformation of the net cage. In addition, the flow fields around the net cage in current are investigated considering different fish group structures, fish swimming speeds, fish distributions and fish stocking densities. The results indicate that the circular movement of fish in the still water leads to a low pressure zone at the center of net cage, which causes a strong vertical flow along the center line of the net cage. The drag force on the net cage is significantly decreased with the increasing fish stocking density, but the most severe deformation of net cage occurred in the case of medium fish stocking density.     

适用于沙坝上Bragg反射的二阶Boussinesq方程数学模型及其数值验证

在二阶 Boussinesq 方程基础上,通过引入含水深导数项对该方程进行了理论上的改进,使得该方程在应用于无限沙坝 Bragg反射问题时与理论解析解在更大范围内符合.基于该改进的高阶 Boussinesq 方程,在非交错网格下建立了混合 4 阶的Adams-Bashforth- Moulton 格式的数学模型.将数值模型应用到有限个连续沙坝上波浪传播变形问题的数值模拟中,通过两点法给出数值波浪反射系数,将这些反射系数与已有的实验数据进行对比,对比表明改进后的模型计算出的反射系数与实验结果吻合更好,这验证了本文理论改进的有效性.     

系泊船非线性波浪力时域计算:二维模型

为找到具有工程实用价值的港口系泊船波浪力的时域计算方法,建立了在港口中存在系泊船时非线性波浪力时域计算的垂直二维耦合模型:用Boussinesq方程计算船的两侧的外域,用欧拉方程计算船底面下的内域,两域在交界面处的连接条件是流量连续和压力相等.将复平面内的边界元方法应用于所研究问题,对耦合模型进行了验证.进行了相关模型实验,实验结果与数值计算结果比较表明这两种数值计算模型都具有满意的精度,但耦合模型的计算效率要远远高于边界元方法的计算效率.本耦合模型的数学处理简单,可适用于工程计算.     

Computation of Viscous Uniform and Shear Flow over A Circular Cylinder by A Finite Element Method

The incompressible viscous uniform and shear flow past a circular cylinder is studied. The two-dimensional Navier-Stokes equations are solved by a finite element method. The governing equations are discretized by a weighted residual method in space. The stable three-step scheme is applied to the momentum equations in the time integration. The numerical model is firstly applied to the computation of the lid-driven cavity flow for its validation. The computed results agree well with the measured data and other numerical results. Then, it is used to simulate the viscous uniform and shear flow over a circular cylinder for Reynolds numbers from lO0 to lO00. The transient time interval before the vortex shedding occurs is shortened considerably by introduction of artificial perturbation. The computed Strouhal number, drag and lift coefficients agree well with the experimental data. The computation shows that the finite element model can be successfully applied to the viscous flow problem.     

具有精确色散性的非线性波浪水平二维数学模型

建立具有色散性的水平二维非线性波浪方程,方程的非线性近似到了三阶。方程以波面升高和自由表面速度势表达的微分-积分型数学方程,给出方程的数值求解方法和算例,对方程积分项的处理给出了计算方法。计算结果与Boussinesq方程模型和缓坡方程模型的对应计算结果进行了对比。     

The applicability of the shallow water equations for modelling violent wave overtopping

The shallow water equations (SWE) have been used to model a series of experiments examining violent wave overtopping of a near-vertical sloping structure with impacting wave conditions. A finite volume scheme was used to solve the shallow water equations. A monotonic reconstruction method was applied to eliminate spurious oscillations and ensure proper treatment of bed slope terms. Both the numerical results and physical observations of the water surface closely followed the relevant Rayleigh probability distributions. However, the numerical model overestimated the wave heights and suffered from the lack of dispersion within the shallow water equations. Comparisons made on dimensionless parameters for the overtopping discharge and percentage of waves overtopping between the numerical model and the experimental observations indicated that for the lesser impacting waves, the shallow water equations perform satisfactorily and provide a good alternative to computationally more expensive methods.     

Numerical analysis of hydrodynamic behaviors of two net cages with grid mooring system under wave action

Based on rigid kinematics theory and lumped mass method,a mathematical model of the two net cages of grid mooring system under waves is developed.In order to verify the numerical model,a series of physical model tests have been carried out.According to the comparisons between the simulated and the experimental results,it can be found that the simulated and the experimental results agree well in each wave condition.Then,the forces on the mooring lines and the floating collar movement are calculated under different wave conditions.Numerical results show that under the same condition,the forces on the bridle ropes are the largest,followed by forces on the main ropes and the grid ropes.The horizontal and the vertical float collar motion amplitudes increase with the increase of wave height,while the relationship of the horizontal motion amplitude and the wave period is indistinct.The vertical motion amplitude of the two cages is almost the same,while on the respect of horizontal motion amplitude,cage B(behind cage A,as shown in Fig.4) moves much farther than cage A under the same wave condition.The inclination angle of the floating system both in clockwise along y axis and the counter one enlarges a little with the increase of wave height.     

Hydrodynamic behavior of a straight floating pipe under wave conditions

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

Numerical simulation of the hydrodynamic behaviour of submerged plane nets in current

The aim of this paper is to investigate the shape and tension distribution of fishing nets in current. A numerical model is developed, based on lumped mass method to simplify the net. The motion equation is set up for each lumped mass. The Runge–Kutta–Verner fifth-order and sixth-order method is used to solve these simultaneous equations, and then the displacement and tension of each lumped mass are obtained. In order to verify the validity of the numerical method, model tests have been carried out. The results by the numerical simulation agree well with the experimental data.