Adaptive discretisation and dual-rate time-stepping of mooring cable dynamics (original) (raw)
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OMAE2003-37465 MODELLING OF SEABED INTERACTION IN FREQUENCY DOMAIN ANALYSIS OF MOORING CABLES
Mooring cables under wave loading interact dynamically with the seabed; this interaction is nonlinear and can be modelled in full only by performing lengthy time integration of the equations of motion. However, time domain integration is far too computationally expensive to be carried out for all load cases. A new method of modelling the interaction between a cable and the seabed in the frequency domain, but without considering fric-tional effects and impact, is therefore proposed. The section of cable interacting with the seabed is truncated and replaced with a system of coupled linear springs, with stiffnesses linearised from static catenary equations. These springs would model the behaviour of the truncated cable and hence the time-varying boundary condition at the touchdown. The entire cable-spring system is then analysed in the frequency domain with a centred finite difference scheme. The proposed method has shown to increase the accuracy of frequency domain analysis in certain cases with affordable computational overhead.
A Reduced Order Model for the Simulation of Mooring Cable Dynamics
DESCRIPTION In this paper the feasibility of a reduced order model (ROM) for the hydroelastic analysis of mooring lines is analysed. The local response of a piece of cable is studied through high fidelity fluid structure interaction (FSI) simulations. The high fidelity model is built by coupling a computational structural dynamics (CSD) solver with a computational fuid dynamics (CFD) solver using the approach of software components. The open-source finite volume method (FVM) solver OpenFOAM is used for the fluid computation, the open source finite element method (FEM) solver FEAP is used for the structural computation, and the component template library (CTL) is used as a common framework. The problem is solved using a block Gauss-Seidel algorithm with an Aitken's relaxation method. The local response of the cable is analysed and the feasibility of the ROM is discussed.
Simulation of Mooring Cable Dynamics Using a Discontinuous Galerkin Method
A new numerical model for simulating the dynamics of mooring cables is presented. The model uses the hp formulation of the discontinuous Galerkin method. Verification against analytical solutions for a static and a dynamic case is carried out and the model is shown to exhibit exponential convergence with increasing polynomial order of the expansion basis. A simulation of the cyclic movement of a cable endpoint is compared to experimental results, and there is a good agreement between the computed and measured tension force.
Mooring Dynamics: Computer Models and Experiments at a Sixty Foot Scale
Ihree cases from the experiment conducted in the hydroballistics tank of the Naval Surface Weapons Center in 1976 are compared to the SNAPLOAD and SEADYN computer models. Two of theruns simulate the anchor-last deployment of a mooring; the third shows the relaxation of a mooring displaced laterally, then released. The quality of the experimental data is evaluated by comparing each case to the static, elastic catenary equations at the start and finish of each run. The measured positions of points along the static catenaries are found typically to agree with the catenary calculations within 1 to 2 percent of the cable length. Tension measured at the fixed end typically agrees with the calculated value within about 12 percent. The SEADYN and SNAPLOAD computer models are found to reproduce all the significant motion and forces observed in the experiment. The "handbook" drag coefficients programmed in these models allow the cable motion sometimes to lead the data, sometimes to lag behind. More specific coefficients must be used when the rate of the dynamic motion is critical. Neither model included elastic hysteresis. The SEADYN program gave somewhat erratic tension values in the mooring line because tension waves were not damped by hysteresis. The SNAPLOAD model eliminated the tension variation through artificial damping. wie A lieC un.e Uq I. .°. .... . UNCLASSIFIED SgCURITY CLASSIPICATION OF 'MIS P446Mlhen Onto tntofed) 12
International Journal of Steel Structures, 2018
An effective numerical method is proposed for the three-dimensional nonlinear analysis of mooring cables using catenary theory. In this method, the mooring line is divided into finite number of catenary elements. In addition to self-weight, each catenary element is subjected to drag force due to steady ocean currents. The proposed procedure is validated by comparing the results with those of the shooting optimization and the finite element methods. Finally, a parametric study is conducted to study the effect of extensibility on the static response of mooring cables. The effects of fluid drag forces and cable extensibility on mooring cable tension, equilibrium configurations, and stressed lengths are illustrated for two-and three-dimensional mooring cable problems. From the numerical results, the method is found to be numerically stable, and it provides a more rational static response for mooring cables.
Simulation of Marine Towing Cable Dynamics Using a Finite Elements Method
Journal of Marine Science and Engineering
A numerical model to study the towing maneuver for floating and submerged bodies has been developed. The proposed model is based on the dynamic study of a catenary line moving between two bodies, one body with imposed motion, and the other free to move. The model improves previous models used to study the behavior of mooring systems based on a finite element method by reducing the noise of the numerical results considering the Rayleigh springs model for the tension of the line. The code was successfully validated using experimental results for experimental data from different authors and experiments found in the literature. Sensitivity analysis on the internal damping coefficient and the number of elements has been included in the present work, showing the importance of the internal damping coefficient. As an example of the application of the developed tool, simulations of towing systems on a real scale were analyzed for different setups. The variation of the loads at the towed body...
Dynamic Model for Catenary Mooring: Experimental Validation of the Wave Induced Load
This note presents a model for the dynamic simulation of a catenary mooring line (or a submarine power cable). In general, mooring lines are subject to a direct wave load (e.g. drag, inertia) in addition to the induced load due to movement of the vessel to which they are linked. Specific aim of this note is to present, calibrate and validate the numerical response to direct wave action, by comparisons with physical model tests. Tests were carried out at the wave flume of the Maritime Laboratory of IMAGE Department, Padova University, within the framework of a Master thesis. Wave induced loads were measured at the fairlead of a compliant chain, with the peculiarity that the fairlead was hinged to a fixed point, the chain being simply subject to the load induced by regular (slightly non-linear) waves. The equations describing the dynamic movements of the chain in Comsol Multiphysics are written in weak form. It is concluded that the model well represents the tests when the drag coefficient is equal to 1.2-1.4 and applied to an area equal to the maximum apparent width.
Mooring Line Damping Estimation by a Simplified Dynamic Model
Volume 1: Offshore Technology; Special Symposium on Ocean Measurements and Their Influence on Design, 2007
When predicting slowly varying resonant vessel motions, a realistic estimate of the motion damping is crucial. Mooring line damping, which is mainly induced by the drag force on line, can dominate the total damping of catenary moored systems and methods for predicting mooring line damping are therefore required. Based on a simplified dynamic model of mooring line tension, an approach to estimate the corresponding damping is presented in this paper. Short-term time domain simulations of dynamic line tension are carried out to verify the accuracy of the simplified frequency domain approach. Compared with the simulation results, the practical simplified method proposed herein gives a maximum 30% lower prediction of the damping coefficient of each mooring line and an about 20% smaller estimate of the total line damping and therefore yields conservative estimates of the low frequency vessel motions.
Nonlinear Dynamic Analysis of Multi-component Mooring Lines Incorporating Line-seabed Interaction
Research Journal of Applied Sciences, Engineering and Technology, 2013
In this study, a deterministic approach for the dynamic analysis of a multi-component mooring line was formulated. The floater motion responses were considered as the mooring line upper boundary conditions while the anchored point was considered as pinned. Lumped parameter approach was adopted for the mooring line modelling. The forces considered were the submerged weights of mooring/attachment, physical/added inertia, line tension, fluid/line relative drag forces and line/seabed reactive forces. The latter interactions were modelled assuming that the mooring line rested on an elastic dissipative foundation. An iterative procedure for the dynamic analysis was developed and results for various mooring lines partially lying on different soils were obtained and validated by conducting a comparative study against published results. Good agreement between numerical and published experimental results was achieved. The contribution of the soil characteristics of the seabed to the dynamic behaviour of mooring line was investigated for different types of soil and reported.