Abstract
Mathematical models are essential for the design and control of offshore systems, to simulate the fluid–structure interactions and predict the motions and the structural loads. In the development and derivation of the models, simplifying assumptions are normally required, usually implying linear kinematics and hydrodynamics. However, while the assumption of linear, small amplitude motion fits traditional offshore problems, in normal operational conditions (it is desirable to stabilize ships, boats, and offshore platforms), large motion and potential dynamic instability may arise (e.g., harsh sea conditions). Furthermore, such nonlinearities are particularly evident in wave energy converters, as large motions are expected (and desired) to enhance power extraction. The inadequacy of linear models has led to an increasing number of publications and codes implementing nonlinear hydrodynamics. However, nonlinear kinematics has received very little attention, as few models yet consider six degrees of freedom and large rotations. This paper implements a nonlinear hydrodynamic and kinematic model for an archetypal floating structure, commonplace in offshore applications: an axisymmetric spar-buoy. The influence of nonlinear dynamics and kinematics causing coupling between modes of motion are demonstrated. The nonlinear dynamics are shown to cause parametric resonance in the roll and pitch degrees of freedom, while the nonlinear kinematics are shown to potentially cause numerical instability in the yaw degree of freedom. A case study example is presented to highlight the nonlinear dynamic and kinematic effects, and the importance of including a nominal restoring term in the yaw DoF presented.
Highlights
The kinematics and dynamics of floating bodies is traditionally related to offshore engineering problems, such as naval applications and the design of large oil and gas platforms [1]
This paper presents a 6-DoF nonlinear model, relevant for conventional offshore applications as well as wave energy applications, including both nonlinear kinematics and nonlinear hydrodynamics
This paper proposes a model in six degrees of freedom for axisymmetric buoys, including nonlinear kinematics, Coriolis and centripetal forces, and nonlinear Froude–Krylov forces
Summary
The kinematics and dynamics of floating bodies is traditionally related to offshore engineering problems, such as naval applications and the design of large oil and gas platforms [1] For these applications, the main objective is usually to stabilize the motion of the floating objects, the resulting small amplitude motions are within the limits of where linear theory is sufficiently accurate for modeling the system. As the wave energy field grows in experience and maturity, the necessity of nonlinear models, for a comprehensive design of most WEC types, becomes increasingly apparent [10,11,12] For both traditional offshore engineering applications and novel WEC investigations, fully nonlinear hydodynamic models, such as the ones solving Navier–Stokes equations, can achieve a high level of accuracy in a broad range of operational and survival conditions.
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