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.     

Nonlinear Finite Element Analysis of Ocean Cables

This study has focused on developing numerical procedures for the dynamic nonlinear analysis of cable structures subjected to wave forces and ground motions in the ocean. A geometrically nonlinear finite element procedure using the isoparamnetrie curved cable element based on the Lagrangian folmulation is briefly summarized. A simple and accurate method to determine the initial equilibrium state of cable systems associated with self-weights, buoyancy and the motion of end points is presented using the load incremental method combined with penalty method. Also the Newmark method is used for dynamic nonlinear analysis of ocean cables. Numerical examples are presented to validate the present numerical method.     

A flexible-segment-model-based dynamics calculation method for free hanging marine risers in re-entry

In re-entry,the drilling riser hanging to the holding vessel takes on a free hanging state,waiting to be moved from the initial random position to the wellhead.For the re-entry,dynamics calculation is often done to predict the riser motion or evaluate the structural safety.A dynamics calculation method based on Flexible Segment Model(FSM) is proposed for free hanging marine risers.In FSM,a riser is discretized into a series of flexible segments.For each flexible segment,its deflection feature and external forces are analyzed independently.For the whole riser,the nonlinear governing equations are listed according to the moment equilibrium at nodes.For the solution of the nonlinear equations,a linearization iteration scheme is provided in the paper.Owing to its flexibility,each segment can match a long part of the riser body,which enables that good results can be obtained even with a small number of segments.Moreover,the linearization iteration scheme can avoid widely used Newton-Rapson iteration scheme in which the calculation stability is influenced by the initial points.The FSM-based dynamics calculation is timesaving and stable,so suitable for the shape prediction or real-time control of free hanging marine risers.     

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.     

A finite difference approximation for dynamic calculation of vertical free hanging slender risers in re-entry application

The dynamic calculations of slender marine risers, such as Finite Element Method (FEM) or Modal Expansion Solution Method (MESM), are mainly for the slender structures with their both ends hinged to the surface and bottom. However, for the re-entry operation, risers held by vessels are in vertical free hanging state, so the displacement and velocity of lower joint would not be zero. For the model of free hanging flexible marine risers, the paper proposed a Finite Difference Approximation (FDA) method for its dynamic calculation. The riser is divided into a reasonable number of rigid discrete segments. And the dynamic model is established based on simple Euler-Bernoulli Beam Theory concerning tension, shear forces and bending moments at each node along the cylindrical structures, which is extendible for different boundary conditions. The governing equations with specific boundary conditions for riser’s free hanging state are simplified by Keller-box method and solved with Newton iteration algorithm for a stable dynamic solution. The calculation starts when the riser is vertical and still in calm water, and its behavior is obtained along time responding to the lateral forward motion at the top. The dynamic behavior in response to the lateral parametric excitation at the top is also proposed and discussed in this paper.     

An improved particle swarm optimization algorithm with harmony strategy for the location of critical slip surface of slopes

The determination of optimal values for three parameters required in the original particle swarm optimization algorithm is very difficult.It is proposed that two new parameters simulating the harmony search strategy can be adopted instead of the three parameters which are required in the original particle swarm optimization algorithm to update the positions of all the particles.The improved particle swarm optimization is used in the location of the critical slip surface of soil slope,and it is found that the improved particle swarm optimization algorithm is insensitive to the two parameters while the original particle swarm optimization algorithm can be sensitive to its three parameters.     

THEORETICAL CALCULATION AND EXPERIMENT RESEARCH ON THE HYDRODYNAMIC PERFORMANCE OF UNDERWATER CABLES

In this paper, the resistance, character and calculation of underwater cables are explored, and the formulae of the resistance, resistance coefficient and the tension as well as the cable behavior of circlesection cables in a uniform stream are obtained. Moreover, a wind-tunnel test of circle-section cables with different streams and angles is carried out. It shows that the calculated results are in good agreement with the test data.     

A Geometrically Exact Formulation for Three-Dimensional Numerical Simulation of the Umbilical Cable in A Deep-Sea ROV System

This paper proposes a geometrically exact formulation for three-dimensional static and dynamic analyses of the umbilical cable in a deep-sea remotely operated vehicle(ROV) system. The presented formulation takes account of the geometric nonlinearities of large displacement, effects of axial load and bending stiffness for modeling of slack cables. The resulting nonlinear second-order governing equations are discretized spatially by the finite element method and solved temporally by the generalized-a implicit time integration algorithm, which is adapted to the case of varying coefficient matrices. The ability to consider three-dimensional union action of ocean current and ship heave motion upon the umbilical cable is the key feature of this analysis. The presented formulation is firstly validated, and then three numerical examples for the umbilical cable in a deep-sea ROV system are demonstrated and discussed, including the steady configurations only under the action of depth-dependent ocean current, the dynamic responses in the case of the only ship heave motion, and in the case of the combined action of the ship heave motion and ocean current.     

Nonlinear waves in a fluid-filled thin viscoelastic tube

In the present paper the propagation property of nonlinear waves in a thin viscoelastic tube filled with incompressible inviscid fluid is studied. The tube is considered to be made of an incompressible isotropic viscoelastic material described by Kelvin--Voigt model. Using the mass conservation and the momentum theorem of the fluid and radial dynamic equilibrium of an element of the tube wall, a set of nonlinear partial differential equations governing the propagation of nonlinear pressure wave in the solid--liquid coupled system is obtained. In the long-wave approximation the nonlinear far-field equations can be derived employing the reductive perturbation technique (RPT). Selecting the exponent α of the perturbation parameter in Gardner--Morikawa transformation according to the order of viscous coefficient η, three kinds of evolution equations with soliton solution, i.e. Korteweg--de Vries (KdV)--Burgers, KdV and Burgers equations are deduced. By means of the method of traveling-wave solution and numerical calculation, the propagation properties of solitary waves corresponding with these evolution equations are analysed in detail. Finally, as a example of practical application, the propagation of pressure pulses in large blood vessels is discussed.     

Numerical Simulation of the Three-Dimensional Wave-Induced Currents on Unstructured Grid

By coupling the three-dimensional hydrodynamic model with the wave model, numerical simulations of the three-dimensional wave-induced current are carried out in this study. The wave model is based on the numerical solution of the modified wave action equation and eikonal equation, which can describe the wave refraction and diffraction. The hydrodynamic model is driven by the wave-induced radiation stresses and affected by the wave turbulence. The numerical implementation of the module has used the finite-volume schemes on unstructured grid, which provides great flexibility for modeling the waves and currents in the complex actual nearshore, and ensures the conservation of energy propagation. The applicability of the proposed model is evaluated in calculating the cases of wave set-up, longshore currents, undertow on a sloping beach, rip currents and meandering longshore currents on a tri-cuspate beach. The results indicate that it is necessary to introduce the depth-dependent radiation stresses into the numerical simulation of wave-induced currents, and comparisons show that the present model makes better prediction on the wave procedure as well as both horizontal and vertical structures in the wave-induced current field.     

A coastal ocean model of semi-implicit finite volume unstructured grid

A two-dimensional coastal ocean model based on unstructured C-grid is built, in which the momentum equation is discretized on the faces of each cell, and the continuity equation is discretized on the cell. The model is discretized by semi-implicit finite volume method, in that the free surface is semi-implicit and the bottom friction is implicit, thereby removing stability limitations associated with the surface gravity wave and friction. The remaining terms in the momentum equations are discretized explicitly by integral finite volume method and second-order Adams-Bashforth method. Tidal flow in the polar quadrant with known analytic solution is employed to test the proposed model. Finally, the performance of the present model to simulate tidal flow in a geometrically complex domain is examined by simulation of tidal currents in the Pearl River Estuary.     

Dynamic Analysis of Towed and Variable Length Cable Systems

Towed cable systems are frequently used in marine measurements where the length of the towed cable varies during launch and recovery. In this paper a novel method for modeling variable length cable systems is introduced based on the finite segment formulation. The variable length of the towed cable is described by changing the length of the segment near the towing point and by increasing or decreasing the number of the discrete segments of the cable. In this way, the elastic effects of the cable can be easily handled since geometry and material properties of each segment are kept constant. Experimental results show that the dynamic behavior of the towed cable is consistent between the model and the physical cable. Results show that the model provides numerical efficiency and simulation accuracy for the variable length towed system.     

Configuration analysis of deepwater S-lay pipeline

The safety of offshore pipeline has drawn a great deal of attention during deepwater installation due to the combined actions of high external pressure, axial tension, and bending moment. Meanwhile, the pipeline configuration has a remarkable effect on the structural behaviour of the tube. The special studies focus on the deepwater S-lay technique in the present paper. The stiffened catenary theory is applied to establish the static equilibrium governing differential equation of a pipe element, and the solution equations of the total pipeline configuration from a lay-barge over a stinger to the seabed are derived. The numerical iteration method for solving pipeline configuration is described in detail, and the corresponding program is developed to conduct the analysis of effects of various parameters such as laying water depth, pipe diameter, thickness of concrete weighted coating layer, stinger length, control strain, and axial tension on pipeline configuration. The results show that the laying water depth, the submerged weight of the pipe, and the axial tension are the critical factors influencing pipeline configuration. In addition, geometrical parameters of the stinger such as length, radius, and shape have an important effect on the pipe-laying capacity of the vessel. The validity of the program is further verified by means of a comparison with results obtained from the commercial finite element software OFFPIPE.     

A baroclinic typhoon model with a moving multi-nested grid and variational adjustment initialisation Ⅰ. Numerical method

A baroclinic typhoon model with a moving multi-nested grid is applied in marine environmental forecasts.This paper describes the numerical methods of the model including governing equations, finite differencing, split scheme and time integration.     

Three Dimensional Baroclinic Numerical Model for Simulating Fresh and Salt Water Mixing in the Yangtze Estuary

For simulating fresh and salt water mixing in estuaries, a three dimensional nonlinear baroclinic numerical model is developed, in which the gradients of horizontal pressure contain the gradient of barotropic pressure arising from the gradi-ent of tidal level and the gradient of baroclinic pressure due to the gradient of salinity. The Eulerian-Lagrangian method is employed to descretize both the momentum equations of tidal motion and the equation of salt water diffusion so as to im-prove the computational stability and accuracy. The methods to provide the boundary conditions and the initial conditions are proposed, and the criterion for computational stability of the salinity fields is presented. The present model is used for modeling fresh and salt water mixing in the Yangtze Estuary. Computations show that the salinity distribution has the characteristics of partial mixing pattern, and that the present model is suitable for simulalion of fresh and salt waler mixing in ihe Yanglze Esluary.     

Study on Flow Field Around Vertical Breakwater Under Different Overtopping Conditions Based on Numerical Simulation

A numerical wave flume is constructed based on the Reynolds Averaged Navier-Stokes (RANS) equations with turbulence closure by a modified k-ε model to study the viscous interactions of waves with vertical breakwaters for different overtopping cases. The governing equations,the turbulence model,boundary conditions,and solution method for the numerical wave flume are introduced briefly. The reliability of the numerical wave flume is examined by comparing the numerical results with the experimental measurement...     

Modeling of Motion of Particle Clouds Formed by Dumping Dredged Material

The motion of particle clouds formed by dumping dredged material into quiescent waters is experimentally and numerically studied. In the numerical model, the particle phase is modeled by the dispersion model, and turbulence is calculated by the large eddy simulation. The governing equations, including the filtered Navier-Stokes equations and mass transport equation, are solved based on the operator-splitting algorithm and an implicit cubic spline interpolation scheme. The eddy viscosity is evaluated by the modified Smagorinsky model including the buoyancy term. Comparisons of main flow characteristics, including shape, size, average density excess, moving speed and the amount of particles deposited on the bed, between experimental and computational results show that the numerical model well predicts the motion of the cloud from the falling to spreading stage. The effects of silt-fence on the motion of the particle cloud are also investigated.     

A Numerical Model for Nonlinear Wave Propagation on Non-uniform Current

On the basis of the new type Boussinesq equations (Madsen et al.,2002),a set of equations explicitly including the effects of currents on waves are derived.A numerical implementation of the present equations in one dimension is described.The numerical model is tested for wave propagation in a wave flume of uniform depth with current present.The present numerical results are compared with those of other researchers.It is validated that the present numerical model can reasonably reflect the nonlinear influences of currents on waves.Moreover,the effects of inputting different incident boundary conditions on the calculated results are studied.     

Numerical Calculation for Nonlinear Waves in Water of Arbitrarily Varying Depth with Boussinesq Equations

Based on the high order nonlinear and dispersive wave equation with a dissipalive term, a numerical model for nonlinear waves is developed. It is suitable to calculate wave propagation in water areas with an arbitrarily varying bottom slope and a relative depth h/ L0≤ 1. By the application of the completely implicit slagger grid and central difference algorithm, discrete governing equations are obtained. Although the central difference algorithm of second-order accuracy both in time and space domains is used to yield the difference equations, the order of truncation error in the difference equation is the same as that of the third-order derivatives of the Boussinesq equation. In this paper, the correction to the first-order derivative is made, and the accuracy of the difference equation is improved. The verifications of accuracy show that the results of the numerical model are in good agreement with those of analytical solutions and physical models.