Dynamics of a horizontal cylinder oscillating as a wave energy converter about an off-centred axis.
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Date
22/11/2011Author
Lucas, Jorge
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Abstract
The hydrodynamic properties of a horizontal cylinder which is free to pitch about an
off-centred axis are studied and used to derive the equations of motion of a wave energy
converter which extracts energy from incoming sea waves with a linear power-take-off
mechanism.
The present work follows from a recent study which compared the performance of an
off-centred cylinder with those of the Edinburgh Duck wave energy converter. The small
decrease in performance found is offset by a reduction in the likely costs associated with
the manufacturing of the cylindrical cam compared with those of the asymmetric profile.
As part of the survivability strategy in very energetic seas-states it had been planned
to completely submerge the device so as to reduce the mooring forces. However,
experiments with scale models show that a good absorption capacity is retained even
when fully-submerged. The hydrodynamic properties of a horizontal cylinder that
pierces the free-surface and of one that is fully submerged are therefore of central
concern in this study. These properties are well known for the case of very long cylinders
but they are now found for cylinders with different widths, drafts, submergence levels
and water-depths. The hydrodynamic forces and moments at the off-centred axis are,
furthermore, derived through the application of transformation formulae.
The equation of motion of the off-centred cylinder is derived for one degree of freedom and
its performance as a wave energy converter is analysed. A relationship which relates the
resonance of the device with the location of the off-centred axis and its mass distribution
is derived and used to optimize the design for average sea conditions attained at a real
location. Design cases associated with three diameters of the cylinder are looked into
detail for both a fully-submerged and free-surface piercing cylinder.
The one degree of freedom model is extended to include a multi-body which has three
degrees of freedom in order to describe the dynamics of a proposed wave powered
desalination system based on a cylindrical Duck device. This mathematical model is
derived through linearised Lagrangian equations of motion in which the hydrodynamic
forces are included as generalised external forces. The advantage of such approach is
to reduce the number of equations associated with multi-body systems by removing the
reaction forces of holomonic constraints from the system of equations to solve.
This model is validated through experiments with a scale model performed in the curved
tank of the University of Edinburgh with both regular waves and mixed seas.