A nonlinear model for the dynamics of moored floating platforms

Abstract

Among the renewable energies, the exploitation of offshore wind energy in deep waters is becoming more and more important, and it is expected to increase even more because of the intrinsic potential and the large availability of this resource. Deep-water wind turbines are usually installed over moored floating supports. Their dynamics depends on the complex interaction between the system and the environment making the use of numerical models almost inevitable for the design and optimization of such structures. In this context, a nonlinear model for the dynamics of moored floating platforms is developed. The dynamic problem of the platform is formulated in the framework of the dynamics of rigid bodies, referring to the mixed representation of the motion, which consists in the simultaneous use of two different bases. The formulation is developed for a wide range of loads (forces and torques) with particular attention to the transformations of the state variables. Both follower and non-follower loads are considered. The differential problem is solved with a recently developed time integration algorithm that considers the Lie group structure of the configuration space overcoming some critical aspects associated with the typical use of nautical angles and their time derivatives. The resulting formulation is very general and in principle can be exploited for the study of every system modelled as a rigid body, such as ships and hulls. The developed dynamic solver can be coupled with other models to study specific problems. In this work the assessment of the loads related to both the mooring system and the hydrodynamic action is addressed. In particular, mooring lines are modelled by means of a quasi-static formulation, whereas wave loads are evaluated with the linear hydrodynamic theory. In general, both the formulations guarantee a satisfying level of accuracy, even though in some specific cases the inertia and damping of the mooring lines as well as higher-order hydrodynamic terms should be included to improve the reliability of the model. The numerical model is tested against a number of dynamic problems for which the exact analytic solution is known, allowing a detailed assessment of the capabilities of the method. The dynamics of moored floating platforms is then investigated discussing the effect of different strategies of simulation on the system response and the role of the main parameters affecting the motion.