Dynamic Response Analysis of Towed Cable During Deployment/Retrieval

A numerical approach was developed to analyze the transient behavior of towed cable during ac- tively controlled deployment/retrieval (DR).The cable motion is described by the lumped parameter method, its corresponding boundary conditions are presented.In view of its varying length during DR,two auxiliary arguments are introduced to describe its continuous varying length and discrete number of nodes(equations), the length is determined by the pay out(or reel-in) rate,which is then used to determine the node number by a logic relation.For the discrete mathematical model of towed cable,an algorithm was developed to deal with the discrete governing equations.The simulation results indicate that the cable experiences more com- plex motions due to its varying length,and tension fluctuates seriously in the startup and ending stage of deployment/retrieval.The effect of towing ship's motion in waves on cable during deployment/retrieval is also considered via numerical simulation.

Steady State Analysis of Towed Marine Cables

Efficient numerical schemes were presented for the steady state solutions of towed marine cables. For most of towed systems,the steady state problem can be resolved into two-point boundary-value problem,or initial value problem in some special cases where the initial values are available directly.A new technique was proposed and attempted to solve the two-point boundary-value problem rather than the conventional shooting method due to its algorithm complexity and low efficiency.First,the boundary conditions are transformed into a set of nonlinear governing equations about the initial values,then bisection method is employed to solve these nonlinear equations with the aid of 4th order Runge-Kutta method.In common sense,non-uniform (sheared) current is assumed,which varies in magnitude and direction with depth.The schemes are validated through the DE Zoysa's example,then several numerical examples are also presented to illustrate the numerical schemes.

Deghosting towed streamer data in τ/p domain based on rough sea surface reflectivity

Currently, the deghosting of towed streamer seismic data assumes a flat sea level and a sea-surface reflection coefficient of-1; this decreases the precision of deghosting. A new method that considers the rough sea surface is proposed to suppress ghost reflections. The proposed deghosting method obtains the rough sea surface reflection coefficient using Gaussian statistics, and calculates the optimized deghosting operator in the r/p domain. The proposed method is closer to the actual sea conditions, offers an improved deghosting operator, removes the ghost reflections from marine towed seismic data, widens the bandwidth and restores the low-frequency information, and finally improves the signal-to- noise ratio and resolution of the seismic data.

Steady-State Configuration and Tension Calculations of Marine Cables Under Complex Currents via Separated Particle Swarm Optimization?

Under complex currents, the motion governing equations of marine cables are complex and nonlinear, and the calculations of cable configuration and tension become difficult compared with those under the uniform or simple currents. To obtain the numerical results, the usual Newton-Raphson iteration is often adopted, but its stability depends on the initial guessed solution to the governing equations. To improve the stability of numerical calculation, this paper proposed separated the particle swarm optimization, in which the variables are separated into several groups, and the dimension of search space is reduced to facilitate the particle swarm optimization. Via the separated particle swarm optimization, these governing nonlinear equations can be solved successfully with any initial solution, and the process of numerical calculation is very stable. For the calculations of cable configuration and tension of marine cables under complex currents, the proposed separated swarm particle optimization is more effective than the other particle swarm optimizations.

Dynamic Effect Research of Cable-Lead-In Rod on Towed System

This paper aims to research the cable-lead-in rod effect on a towed system through mathematical modeling and numerical simulations.The rod dynamics,as a key part of this study,is modeled using the combination of cable node governing equations and kinematic constraint conditions.As the first attempt to analyze such a problem,the rod is simply treated as an elastic cable segment so as to be incorporated into the dynamics of the cable,and a set of algorithm is then proposed based on the kinematic constraint conditions to fully describe its motions.Meanwhile,the cable and the underwater vehicle are modeled by the traditional lumped mass method and the 6 degree-of-freedom maneuverability equations for submarines respectively;the coupling boundary conditions besides the rod dynamics are also given to form the whole system's model.Several numerical cases are performed to investigate the rod effect on the system in different maneuver situations.Some meaningful conclusions are drawn through comparative analysis.

Dynamic response of towed line array

Three-dimensional motion equations with consideration of the bending and torsional effects of a marine towed cable system under large elastic deformation conditions are formulated using the lumped parameter model. The lumped mass model is used to simulate a circular maneuver of a towed horizontal array that was first presented by Ablow. The results of this paper are in a good agreement with those obtained by finite difference schemes, and the minimum depth is closer to the experimental result. Although the calculations take more computation time, the lumped mass model is a good method, which can also be used to solve problems of towed line array, especially multi-branched towed line array, because of its flexibility.

Dynamic simulation of aerial towed decoy system based on tension recurrence algorithm

Dynamic model of aerial towed decoy system is established and simulations are performed to research the dynamic characteristics of the system. Firstly, Kinetic equations based on spinor are built, where the cable is discretized into a number of rigid segments while the decoy is modeled as a rigid body hinged on the cable. Then tension recurrence algorithm is developed to improve computational efficiency, which makes it possible to predict the dynamic response of aerial towed decoy system rapidly and accurately. Subsequently, the efficiency and validity of this algorithm are verified by comparison with Kane’s function and further validated by wind tunnel tests.Simulation results indicate that the distance between the towing point and the decoy’s center of gravity is suggested to be 5%–20% of the length of decoy body to ensure the stability of system.In up-risen maneuver process, the value of angular velocity is recommended to be less than0.10 rad/s to protect the cable from the aircraft exhaust jet. During the turning movement of aircraft, the cable’s extent of stretching outwards is proportional to the aircraft’s angular velocity.Meanwhile, the decoy, aircraft and missile form a triangle, which promotes the decoy’s performance.

A Study on Dynamic Response of Cable-Seabed Interaction

A numerical method is developed to investigate the dynamic response of cable-seabed interaction in this paper. The motion of cable is described by the Lumped Parameter Method, while the seabed, unlike the prevailing simplified model of elastic foundation, is modeled as an irregular continuous rigid surface with rebound and friction existing, and the forces exerted by the seabed consist of normal counterforce and isotropic tangential Coulomb friction resistance. To describe the detailed dynamic response, two coefficients are introduced by analogy with the theory of rigid body collision with friction. The cable-seabed kinematic and dynamic contact conditions are formulated subsequently, and are used to incorporate the seabed effect into the cable dynamics to produce a set of ordinary differential governing equations. In this paper, we employ 4th order Runge-Kutta method to solve these equations. Several simulation cases are presented to illustrate the seabed effect. The results show that friction and impact have a prominent influence on the statics and dynamics of the cable.

Dynamic Behavior of Two Part Towing Cable System During Turning

An improved numerical method is used to simulate the dynamic behavior of a two part towing cable systems during turnings. In U turns and full turns, periodical heave motions are found both for the towed vehicle and for the depressor. Periodic motions of the subsea units and of the cable surface tension are closely related to the turning parameters, such as turning velocity and turning radius. System parameters, such as length of the second cable and the vehicle bydrodynamics, also damp turning instability.