The dynamics of geometrically compliant mooring systems

Abstract

Geometrically compliant mooring systems that change their shape to accommodate deformations are common in oceanographic and offshore energy production applications. Because of the inherent geometric nonlinearities, analyses of such systems typically require the use of a sophisticated numerical model. This thesis describes one such model and uses that model along with experimental results to develop simpler forms for understanding the dynamic response of geometrically compliant moorings.The numerical program combines the box method spatial discretization with the generalized-α method for temporal integration. Compared to other schemes commonly employed for the temporal integration of the cable dynamics equations, including box method, trapezoidal rule, backward differences, and Newmark's method, the generalized-α algorithm has the advantages of second-order accuracy, controllable numerical dissipation, and improved stability when applied to the nonlinear problem. The numerical program is validated using results from laboratory and field experiments.Field experiment and numerical results are used to develop a simple model for dynamic tension response to vertical motion in geometrically compliant moorings. As part of that development, the role of inertia, drag, and stiffness in the tension response are explored. For most moorings, the response is dominated by inertial and drag effects. The simple model uses just two terms to accurately capture these effects, including the coupling between inertia and drag. The separability of the responses to vertical and horizontal motions is demonstrated and a preliminary model for the response to horizontal motions is presented.The interaction of the mooring line with the sea floor in catenary moorings is considered. Using video and tension data from laboratory experiments, the tension shock condition at the touchdown point and its implications are observed for the first time. The lateral motion of line along the bottom associated with a shock during unloading may be a significant cause of chain wear in the touchdown region. Results from the laboratory experiments are also used to demonstrate the suitability of the elastic foundation approach to modeling sea floor interaction in numerical programs.

Forward and inverse problems in towed cable hydrodynamics

“…Similar numerical schemes like the box method obtain similar performance in terms of the accuracy of the approximation but are reportedly more prone to numerical instabilities. The generalized alpha method suggested in (Gobat 2000) and (Gobat et al 2001) rectifies the instability by enforcing additional temporal averaging on the conventional box method scheme of (, Ablow et al 1983). In applying the derivative discretization rule (10) the forward problem in consideration is cast in a matrix form as (Milinazzo et al 1987),…”

“…Apart from Newton's method, alternative schemes for the forward problem include the Runge-Kutta integration which is implemented on the space dependent differential equations after the time derivatives are eliminated by FD discretization (Ablow et al 1983). The method is fairly robust to numerical instabilities although special suppression routines like those implemented in (Gatti 2002) and (Gobat 2000) are necessary to ensure that the solution remains a bounded norm in the presence of Crank-Nicholson noise.…”

Mathematical Modelling of Mooring Systems for Wave Energy Converters—A Review

“…As the frequency increases, nonlinear drag (which increases with the square of frequency) provides very large lateral resistance, causing the mooring line to 'freeze' in place and the WEC motion to be then accommodated elastically by the mooring line [64]. The thesis by Gobat [65] focuses on the dynamics of geometrically compliant moorings.…”

“…Polachek et al [45] later added cable extensibility, thereby offering a thorough method for treating the nonlinear mooring line dynamics. Their discretisation method would nowadays be categorized as a lumped mass method, whereby the mass and externally applied forces are lumped at a discrete number of points/nodes, which are connected by massless springs [65]. The lumped mass method and other spatial discretisation approaches, such as finite differences and finite element methods (FEMs), are outlined in this subsection.…”

“…The history, development and usage of the different numerical schemes used for the temporal discretisation and integration of mooring line dynamics is outlined in Gobat [65] and the references therein. Thomas [13] performs an investigation of time integration schemes for mooring line dynamics and gives a thorough review of the different available schemes and their derivations.…”