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.     

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。     

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.     

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.     

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.     

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.     

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.     

Projectile motion in a resistant medium Part II: approximate solution and estimates

The motion of a particle which is projected into a resistant medium and subjected to a uniform gravitational field is considered. The drag force that acts upon the particle within the medium is proportional to the particle speed squared. The problem is formulated in terms of particle-speed and local-path-angle variables, and the equations of motion that result are non-linear and coupled. An exact solution to these equations can be obtained but involves quadratures which cannot be analytically evaluated in terms of standard functions. An approximate solution that is remarkably accurate is presented. This solution is based upon the so-called cubic law, which is motivated by certain properties of the exact solution. This solution is also utilized to obtain estimates for the maximum projectile range, optimal projection angle, and other quantities of interest related to the particle motion.     

Drag load modeling for multiple fractures in a borehole

Fracture mechanics modeling of multiple fractures generated by a tailored pressure pulse in a borehole is a complex, coupled gas dynamics/solid mechanics problem. The specific problem addressed in this paper is the determination of crack tip stress intensity factors for arbitrary drag loadings along the crack surfaces. Fracture networks containing an even number of equally spaced radial cracks of alternating lengths are used as models. Finite element calculations and integration schemes similar to those used for arbitrary normal loads along the crack surfaces are performed. Stress intensity factors arising from the drag loadings tend to increase with increasing crack length ratios. Thus, effects of drag loading may be significant in determining crack tip stress intensity factors for a multiple fracture network generated by a controlled gas pulse.     

Demonstration of a coupled floating offshore wind turbine analysis with high-fidelity methods

This paper presents results of numerical computations for floating off-shore wind turbines using, as an example, a machine of 10-MW rated power. The aerodynamic loads on the rotor are computed using the Helicopter Multi-Block flow solver developed at the University of Liverpool. The method solves the Navier–Stokes equations in integral form using the arbitrary Lagrangian–Eulerian formulation for time-dependent domains with moving boundaries. Hydrodynamic loads on the support platform are computed using the Smoothed Particle Hydrodynamics method, which is mesh-free and represents the water and floating structures by a set of discrete elements, referred to as particles. The motion of the floating offshore wind turbine is computed using a Multi-Body Dynamic Model of rigid bodies and frictionless joints. Mooring cables are modelled as a set of springs and dampers. All solvers were validated separately before coupling, and the results are presented in this paper. The importance of coupling is assessed and the loosely coupled algorithm used is described in detail alongside the obtained results.     

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.     

Numerical analysis on the propulsive performance and vortex shedding of fish‐like travelling wavy plate

Numerical analysis is carried out to investigate viscous flow over a travelling wavy plate undergoing lateral motion in the form of a streamwise travelling wave, which is similar to the backbone undulation of swimming fish. The two‐dimensional incompressible Navier–Stokes equations are solved using the finite element technique with the deforming‐spatial‐domain/stabilized space–time formulation. The objective of this study is to elucidate hydrodynamic features of flow structure and vortex shedding near the travelling wavy plate and to get into physical insights to the understanding of fish‐like swimming mechanisms in terms of drag reduction and optimal propulsive performance. The effects of some typical parameters, including the phase speed, amplitude, and relative wavelength of travelling wavy plate, on the flow structures, the forces, and the power consumption required for the propulsive motion of the plate are analysed. These results predicted by the present numerical analysis are well consistent with the available data obtained for the wave‐like swimming motion of live fish in nature. Copyright © 2005 John Wiley & Sons, Ltd.     

A general formula for the drag on a sphere placed in a creeping unsteady micropolar fluid flow

In the present work, we investigate the creeping unsteady motion of an infinite micropolar fluid flow past a fixed sphere. The technique of Laplace transform is used. The drag formula is obtained in the physical domain analytically by using the complex inversion formula of the Laplace transform. The well known formula of Basset for the drag on a sphere placed in an unsteady viscous fluid flow and that of Ramkissoon and Majumdar for steady motion in the case of micropolar fluids are recovered as special cases. The obtained formula is employed to calculate the drag force for some micropolar fluid flows. Numerical results are obtained and represented graphically.     

A drag coefficient model for Lagrangian particle dynamics relevant to high-speed flows

A blended drag coefficient model is constructed using a series of empirical relations based on Reynolds number, Mach number, and Knudsen number. When validated against experiments, the drag coefficient model produces matching values with a standard deviation error of 2.84% and a maximum error of 11.87%. The model is used in a Lagrangian code which is coupled to a hypersonic aerothermodynamic CFD code, and the particle velocity and trajectory are validated against experimental results. The comparative results agree well and show that the new blended drag coefficient model is capable of predicting the particle motion accurately over a range of Reynolds number, Mach number, and Knudsen number.     

控制棒驱动机构步跃提升碰撞的动力学建模

控制棒驱动机构(CRDM)在步跃提升时,钩爪部件会与承压壳体上的提升磁极发生面面碰撞。本文基于混合坐标法建立控制棒驱动机构有限元离散的刚-柔耦合动力学方程,用罚函数法计算了钩爪部件与承压壳体之间的碰撞力和应力分布情况。结果表明,刚柔耦合多体方法在仿真小变形碰撞时可以提高计算效率,同时又能达到与有限元方法同等的精度。进一步对碰撞模型不同区域的网格疏密和尺寸大小做了定量分析,得到了降低有限元网格数量的方法,可为工程中碰撞模型的网格划分提供参考。     

Hydrodynamics of a tandem fish school with asynchronous undulation of individuals

We perform numerical simulations using immersed boundary method for flow over a single and two fish in tandem performing traveling wave like motion for a range of Strouhal numbers. We investigate the hydrodynamic performance of single- and tandem-fish configurations using unsteady profiles of lateral side-force and drag coefficients, their time-averaged values, and wake behind these bodies. We present the spectra of hydrodynamic forces and find that the nature of these forces for a single fish resembles to those of stationary/oscillating bluff bodies and oscillating airfoils. For tandem cases, we vary the phase speed of undulatory motion of the rear fish while keeping the free-stream velocity constant. We show that hydrodynamic forces of the upstream and rear fish contain harmonics which are produced by nonlinear interaction of the oscillation frequencies of both fish. We find that the wake and time-averaged drag of the upstream fish remain almost independent of the undulating frequency of the rear fish at a certain Strouhal number. We also relate this observation with the absence of oscillation frequency of the rear fish in the Fourier spectra of hydrodynamic forces of the upstream fish. For the complete range of parameters, it is inferred that swimming in a tandem configuration seems more beneficial for the upstream fish. It happens due to wake-splitting effect of the rear fish that causes an enhancement of pressure in its wake. For the rear fish, it gains an advantage of drafting under certain conditions and its performance deteriorates at Strouhal numbers greater than 0.40.     

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.     

Numerical simulation of plate autorotation in a viscous fluid flow

A general formulation of the plane coupled dynamical and aerodynamical problem of the motion of a rigid body with a rotational degree of freedom in a viscous incompressible fluid flow is given. A computation technique for solving the Navier-Stokes equations based on the meshless viscous vortex domain method is used. The autorotation of a single plate and a pair of plates is investigated. The effect of the reduced moment of inertia and the Reynolds number on the angular rotation velocity is determined. The time dependences of the hydrodynamic loads are compared with the corresponding instantaneous flow patterns. The increased the autorotation velocity of two plates in tandem is detected.     

Motion of a slender body near the free surface of a compressible fluid

An analytic solution to the problem of motion of a slender rigid body in a semi-infinite domain of a compressible fluid is obtained for the case when the body moves in parallel to the free surface at a constant velocity. This problem is similar to the problem of motion of a hydrofoil ship whose wing-like device allows it to lift its hull above the water surface and to decrease the friction and drag forces limiting the speed of usual ships. During its motion in water, a hydrofoil produces a lift force. The obtained analytic solution allows one to derive explicit expressions for the drag force and for the lift force in the limiting cases of relatively small and large depths. When depth is small, the drag force is greater than that in an infinite medium, since the wave drag is additionally evolved. When the velocity increases and approaches the sound velocity, the forces exerted on the body increase without limit, which is typical for a linear formulation of the problem.