Static Design of Cable Mooring Arrays for Offshore Guyed Towers

The key consideration in controlling the dynamic response of an offshore guyed tower subjected to environmental loading is the selection of the stiffness characteristics of the cable mooring array. In the present study, each cable in the array consists of three segments: a leading segment attached to the tower, a short heavy middle segment, and a seabed trailing segment attached at the extremity to an anchor pile. A nonlinear static model is presented in algorithmic form that defines the stiffness characteristics of the cable array. The model involves the inelastic static catenary equations coupled with conditions of geometric compatibility, formulated in terms of seven nondimensional system parameters. The effects of varying each of the system parameters on the stiffness characteristics of example cable arrays are presented and the implications for cable design are discussed.     

Dynamic motion and tension of marine cables being laid during velocity change of mother vessels

Flexible segment model （FSM） is adopted for the dynamics calculation of marine cable being laid. In FSM, the cable is divided into a number of flexible segments, and nonlinear governing equations are listed according to the moment equilibriums of the segments. Linearization iteration scheme is employed to obtain the numerical solution for the governing equations. For the cable being laid, the payout rate is calculated from the velocities of all segments. The numerical results are shown of the dynamic motion and tension of marine cables being laid during velocity change of the mother vessels.     

水下拖曳升沉补偿系统水动力数学模型研究

建立变缆长的水下拖曳升沉补偿系统水动力学偏微分方程组和边界条件.拖缆动力学模型基于Ablow and Schechter模型,拖体采用水下运载体六自由度方程模拟,运用有限差分法离散偏微分方程组和牛顿迭代法计算变缆长情况下拖体深度与拖缆各点张力的动态取值.数值计算结果表明采用收放拖缆的升沉补偿方法能够有效削弱母船升沉运动对拖体深度和拖缆张力的影响.     

Numerical simulation of towed cables

A numerical method for the dynamic simulation of towed cables is presented. The cable is loaded by fluid drag, tension, gravity and buoyancy, including the effects of weights and floats. The development of a cable can be simulated as well as the separation of a cable under excessive load and the subsequent behavior of the broken parts. The system is constructed from a set of generic elements representing such items as cable or rope strands, knots (reference points on rope sections), kinks (sliding reference points on cable sections that change length), cable ends and winches. A mathematical graph organizes these elements in a general and flexible fashion: it allows construction of complex systems and permits structural redefinition during the simulation. The nodes of the graph coincide with the various reference points of the problem, at which physical parameters are lumped and to which sets of ordinary differential equations are associated that define the motions of the points. The links of the graph describe the physical connections between the nodes. Application of new methods for solving stiff, sparse systems of coupled ordinary differential equations enables efficient simulation of snap-loads and other severe events. Results are presented that compare quantitatively with laboratory measurements. A further example shows the behavior of a breaking cable that is qualitatively reasonable.     

Steady-state analysis of undersea cables

A numerical solution and computer program developed to analyse undersea flexible cable problems is presented. The cable is subject to hydrodynamic loads from a surrounding fluid medium. The object is to determine the cable profile and tensile forces developed. The cable equations and boundary conditions result in a classical two-point boundary value problem. An iteration ‘shooting method’ is used for solution. The program has been written to analyse a class of towing and anchoring problems. However the analysis is general and applicable to most steady-state cable problems.     

波浪作用下缆船拖带系统非线性运动数值模拟

基于船舶操纵性运动方程和拖缆的三维动力学运动方程,提出了被拖点位置匹配的方法,建立了拖船—拖缆—被拖船系统整体非线性拖带动力学模型。为了考察被拖船航向稳定性与横向稳性的关系以及波浪载荷作用的影响,被拖船采用水平面四自由度运动方程,并引入了波浪的作用力和力矩。拖船采用PD控制方法较真实地模拟了拖船航向改变的运动过程。对一个拖船—拖缆—被拖船系统(5 000 t的拖船和3 000 t的被拖船)在时域内进行了规则波浪作用下拖带运动的模拟,计算结果表明被拖带船舶在波浪中运动呈现运动稳定、不稳定和临界状态3种可能的特性。根据模拟计算结果,认为波浪中拖带航向稳定是被拖带船舶保持稳性的必要条件。     

A finite element cable model and its applications based on the cubic spline curve

For accurate prediction of the deformation of cable in the towed system, a new finite element model is presented that provides a representation of both the bending and torsional effects. In this paper, the cubic spline interpolation function is applied as the trial solution. By using a weighted residual approach, the discretized motion equations for the new finite element model are developed. The model is calculated with the computation program complier by Matlab. Several numerical examples are presented to illustrate the numerical schemes. The results of numerical simulation are stable and valid, and consistent with the mechanical properties of the cable. The model can be applied to kinematics analysis and the design of ocean cable, such as mooring lines, towing, and ROV umbilical cables.     

Design of a prototype ocean current turbine—Part I: mathematical modeling and dynamics simulation

The “C-Plane” is a submerged variable depth ocean current turbine that is tethered to the sea floor and uses sustained ocean currents to produce electricity. As part of the development of a $\frac{1}{30}$th scale physical model of the C-Plane, a mathematical model and dynamics simulation of the prototype was developed and is presented in this paper. This three-dimensional mathematical model represents the C-Plane as a rigid body with moveable control surfaces that is moored with three linear elastic cable elements. Gravitational, buoyancy, hydrodynamic, cable, gyroscopic, and inertial forces are included and a PC-based dynamics simulation is created. The simulation demonstrates that the C-Plane is stable and capable of changing depth in all expected operating conditions. The C-Plane prototype can fly level from a height of 3 to 6 m using the configuration suggested in this paper. The maximum ascent rates of the C-Plane with a water speed of 0.3 m/s are 0.015 m/s when the pitch is fixed at 0° and 0.030 m/s when the pitch is fixed at 4°. The maximum descent rates of the C-Plane are 0.018 m/s when the pitch is held at 0° and 0.031 m/s if the pitch is held at −4°.     

Free vibrations of three-dimensional extensible marine cables with specified top tension via a variational method

This paper presents a model formulation that can be used for analyzing the three-dimensional vibration behaviours of an inclined extensible marine cable. The virtual work-energy functional, which involves strain energy due to axial stretching of the cable and virtual work done by external hydrostatic forces is formulated. The coupled equations of motion in the Cartesian coordinates of global systems are obtained by taking into account the difference between Euler’s equations and equilibrium equations. The method of Galerkin finite element is used to obtain the mass and stiffness matrices which are transformed into the local coordinate systems. Then the eigenvalue problem is solved to determine its natural frequencies and corresponding mode shapes. The model formulation developed herein is conveniently applied for the cases of specified top tension. The numerical investigations are carried out to demonstrate the validity of the model and to explore in details the influence of various parameters on the behaviours of marine cables. Results for the frequency avoidance phenomenon, maximum dynamic tension and coupled transverse mode shapes are presented and discussed.     

A reduced-dynamics variational approach for the assimilation of altimeter data into eddy-resolving ocean models

A new method of assimilating sea surface height (SSH) data into ocean models is introduced and tested. Many features observable by satellite altimetry are approximated by the first baroclinic mode over much of the ocean, especially in the lower (but non-equatorial) and mid latitude regions. Based on this dynamical trait, a reduced-dynamics adjoint technique is developed and implemented with a three-dimensional model using vertical normal mode decomposition. To reduce the complexity of the variational data assimilation problem, the adjoint equations are based on a one-active-layer reduced-gravity model, which approximates the first baroclinic mode, as opposed to the full three-dimensional model equations. The reduced dimensionality of the adjoint model leads to lower computational cost than a traditional variational data assimilation algorithm. The technique is applicable to regions of the ocean where the SSH variability is dominated by the first baroclinic mode. The adjustment of the first baroclinic mode model fields dynamically transfers the SSH information to the deep ocean layers. The technique is developed in a modular fashion that can be readily implemented with many three-dimensional ocean models. For this study, the method is tested with the Navy Coastal Ocean Model (NCOM) configured to simulate the Gulf of Mexico.     

Submarine cables: a challenge for ocean management

The international submarine cable industry is a major component of the global telecommunications system, providing important services and requiring increased levels of protection for the maintenance of global economic and maritime security, broadly defined. An overview is given of the submarine cable industry, including its technological developments, legal aspects, security considerations, and implications for integrated ocean planning and management. In the context of multiple ocean use, submarine cables can cause spatial conflicts with other ocean users, particularly the fishing industry. Issues to be examined include compensation for lost or damaged gear, legal liability for cable damage, and regulation and licensing of cables on the seabed of the continental shelf and the high seas. Recent industry-to-industry agreements and programs for compensation to fishers in the USA and Canada are significant advancements in the implementation of integrated approaches to ocean management and planning. The development of transparent and stable interdepartmental processes for the coordinated planning, management and regulation of submarine cables is required for national EEZs. The regulation of international cable industry practices must be harmonized with national management approaches.     

A floating tied system for an offshore airport

This paper presents a new system for a floating offshore airport. It consists of an assembly of precast boxes, each of them tied with a cable system. The (tension) cable system acts as a bracing against any lateral forces during airport operation. It also prevents the boxes from oscillating and moving during the airport construction and operation. The space inside each box can be utilized for other purposes. A top slab system consisting of precast and cast in situ concrete slabs will form the platform of the airport. Finally, a proposed method of construction is also presented. The new system offers an easier construction method and allows future airport extension and even relocation.     

Nonlinear dynamics of an elastic cable during laying operations in rough sea

A numerical approach for predicting motion and tension of extensible marine cables during laying operations in a rough sea is presented here. The solution methodology consists of dividing the cable into straight elements, which must satisfy an equilibrium equation and compatibility relations. The system of nonlinear differential equations is solved by the Runge–Kutta method, taking the effect of regular and/or irregular waves into account explicitly.

Illustrative applications of the method are given for a typical cable laying ship. The results are presented as rms values of the cable dynamic tension and corresponding dynamic factor for two different types of cable and several values of cable stiffness. The effect of axial deformation on the maximum tension at the shipboard pulley location is highlighted.     

深海平台系缆形状和张力分析

考虑海底地形的变化、系缆的拉伸形变及海流力等因素,研究了深海平台系缆形状和张力分析方法采用集中质量法,得到系缆方程组,采用牛顿法求解该非线性系缆方程组,建立系缆形状和张力的计算方法。计算了平坦海底和海底地形凹凸变化时水深1 018 m情况下的系缆形状、系泊张力和浮体平衡位置。计算结果表明,海底地形对于深海系泊系统张力影响较大,而计算系缆形状和张力、系泊浮体的运动时,需要考虑海底地形的影响。     

On the motions of the underwater remotely operated vehicle with the umbilical cable effect

In this paper, a hydrodynamic model is developed to simulate the six degrees of freedom motions of the underwater remotely operated vehicle (ROV) including the umbilical cable effect. The corresponding hydrodynamic forces on the underwater vehicle are obtained by the planar motion mechanism test technique. With the relevant hydrodynamic coefficients, the 4th-order Runge–Kutta numerical method is then adopted to solve the equations of motions of the ROV and the configuration of the umbilical cable. The multi-step shooting method is also suggested to solve the two-end boundary-value problem on the umbilical cable with respect to a set of first-order ordinary differential equation system. All operation simulations for the ROV including forward moving, ascending, descending, sideward moving and turning motions can be analyzed, either with or without umbilical cable effect. The current effect is also taken into consideration. The present results reveal that the umbilical cable indeed significantly affects the motion of the ROV and should not be neglected in the simulation.     

A tension measurement method of a towing cable or a buoy cable

An indirect tension measurement method of a towing cable in midwater or a buoy cable is proposed using underwater acoustic positioning systems, etc., to give the in-water cable tension. The most simple and traditional cable tension measurement method is to apply a mechanical tension meter at the one end of the cable, but the method has limits in the aspects of continuous monitoring and manual operation. However, the technique in this study is to apply the Pode's analysis of the equilibrium configuration and tension of a flexible twine, in which the cable tension is given as a function of the geometric positions of both ends of the cable. A set of nonlinear integral equations is formulated and solved numerically by the Newton-Raphson method. Then the inclination angles and the tensions at the lower and the upper ends of the cable could be obtained. The derived method enables us to track a towed object, to measure the tension of a towing cable or a buoy cable and is also applicable to the remotely operated vehicle (ROV) tethered to a mother ship.     

Investigation on a two-part underwater manoeuvrable towed system

A hydrodynamic model of a two-part underwater manoeuvrable towed system is proposed in which a depressor is equipped with active horizontal and vertical control surfaces, and a towed vehicle is attached to the lower end of a primary cable. In such a system the towed vehicle can be manoeuvred in both vertical and horizontal planes when it is towed at a certain velocity and the coupling effect of excitations at the upper end of the primary cable and disturbances of control manipulations to the towed vehicle can be reduced. In the model the hydrodynamic behavior of an underwater vehicle is described by the six-degrees-of-freedom equations of motion for submarine simulations. The added masses of an underwater vehicle are obtained from the three-dimensional potential theory. The control surface forces of the vehicle are determined by the wing theory. The results indicate that with relative simple control measures a two-part underwater manoeuvrable towed system enables the towed vehicle to travel in a wide range with a stable attitude. The method in this model gives an effective numerical approach for determining hydrodynamic characteristics of an underwater vehicle especially when little or no experimental data are available or when costs prohibit doing experiments for determining these data.     

应用于海洋站温盐传感器的缓冲止旋方法

为解决温盐传感器在海洋站应用中存在的电缆缠绕和壳体磨损等问题，保障传感器的长期业务化运行，文章提出改进温盐传感器安装方式的缓冲止旋方法。研究结果表明：在实验室环境下，通过以螺旋电缆代替直线电缆和设计缓冲浮子装置二者结合的温盐传感器安装方式，可有效减少电缆缠绕、避免传感器磕碰磨损和减小海流影响，同时安装简单、便于维护和具有广泛应用性。该方法仍须在海洋站实际应用中进一步验证和完善。     

An Integrated Hydrodynamics and Control Model of A Tethered Underwater Robot

An integrated hydrodynamics and control model to simulate tethered underwater robot system is proposed. The governing equation of the umbilical cable is based on a finite difference method, the hydrodynamic behaviors of the underwater robot are described by the six-degrees-of-freedom equations of motion for submarine simulations, and a controller based on the fuzzy sliding mode control (FSMC) algorithm is also incorporated. Fluid motion around the main body of moving robot with running control ducted propellers is governed by the Navier–Stokes equations and these nonlinear differential equations are solved numerically via computational fluid dynamics (CFD) technique. The hydrodynamics and control behaviors of the tethered underwater robot under certain designated trajectory and attitude control manipulation are then investigated based on the established hydrodynamics and control model. The results indicate that satisfactory control effect can be achieved and hydrodynamic behavior under the control operation can be observed with the model; much kinematic and dynamic information about tethered underwater robot system can be forecasted, including translational and angular motions of the robot, hydrodynamic loading on the robot, manipulation actions produced by the control propellers, the kinematic and dynamic behaviors of the umbilical cable. Since these hydrodynamic effects are fed into the proposed coupled model, the mutual hydrodynamic influences of different portions of the robot system as well as the hydrological factors of the undersea environment for the robot operation are incorporated in the model.     

Mooring forces and motion responses of pontoon-type floating breakwaters

The experimental and theoretical investigations on the behaviour of pontoon-type floating breakwaters are presented. A two-dimensional finite element model is adopted to study the behaviour of pontoon-type floating breakwaters in beam waves. The stiffness coefficients of the slack mooring lines are idealized as the linear stiffness coefficients, which can be derived from the basic catenary equations of the cable. The theoretical model is supported by an experimental programme conducted in a wave flume. The motion responses and mooring forces are measured for three different mooring configurations, and the results are reported and discussed in detail in this paper. The wave attenuation characteristics are presented for the configurations studied.