| dc.description.abstract | A hydrodynamic analysis of a free-floating bottom-less upright circular dock in waves conceived for the installation of spar-type floating offshore wind turbines (FOWT) is carried out in this work for incident wave frequencies near the first lateral sloshing resonance. The motions of the circular dock as well as the sloshing-induced motions of a FOWT’s spar floating inside the dock are studied through both semi-analytical and experimental methods in the frequency domain.
The diffraction and radiation problems in heave surge and pitch are tackled by a domain decomposition approach under linear potential flow assumptions. In addition, known theories used to describe sloshing waves in closed containers and based on a decomposition of the velocity potential into sloshing eigenmodes are here adapted for the open-bottom structure. This semi-analytical model is extended to include the effects of solid and perforated annular baffles installed on the internal wall of the dock. A reduced natural sloshing frequency as well as a damping ratio estimated from the energy dissipated by the flow separation at the sharp edge of the baffles are introduced in the free-surface boundary conditions to model the effects of the baffles on the sloshing eigenmodes. The equations of motions are solved, and both a sensitivity and eigenvalue analyses are carried out to assess the differences between the numerical and experimental models, emphasising in particular uncertainties related to the numerical modelling of the inertial matrix. Model tests were performed at the scale 1:100 on a 0.80m diameter model in regular waves with wave periods near the highest sloshing natural period. The internal free-surface elevation and model’s rigid body motions were measured, both for the case without and with a FOWT’s spar. Perforated and solid annular baffles of width-to-dock’s internal radius ratio 0.17 were installed inside the dock at various submergences. Few model tests included polystyrene foam balls of various sizes and quantities covering the entire internal water surface, which is shown to be a relatively inefficient way to damp sloshing waves unless an excessively large amount of them is placed in the dock. In addition, few tests in irregular waves were performed, generated from JONSWAP spectra with peak periods near sloshing resonance.
The amplitudes and phases of the bodies’ motions and of the free-surface elevation inside the dock are compared with those obtained with the semi-analytical model. The results present a good agreement for the highest ratio between the submergence of the baffle 𝑑𝐵 and the internal radius of the dock 𝑎 that was considered (i.e. 𝑑𝐵/𝑎 = 0.27), while numerical results tend to under-predict the damping ratio for lower baffle’s submergences, most likely due to free-surface interactions. The resonant peak amplitudes of the spar’s surge and pitch motions are reduced by almost half when a solid baffle is installed, with a strong dependency on the incident wave height due to viscous dissipation caused by the baffle. A significant reduction of the motions’ amplitudes is also observed for perforated baffles with resonant periods closer to the case without baffle. | en_US |
