Hydrodynamics of a Free Floating Vertical Axisymmetric Oscillating Water Column Device

Abstract

This paper aims at presenting a general formulation of the hydrodynamic problem of a floating or restrained oscillating water column device. Three types of first-order boundary value problems are investigated in order to calculate the velocity potential of the flow field around the device. The horizontal and vertical exciting wave forces, the rolling moment, the hydrodynamic parameters, the volume flows, and the drift forces are obtained in order to find the loads on the structure. The efficiency rate of the device is calculated in connection with the absorbed power and the capture length of energy absorption. Finally, the resulting wave motion inside and outside the device and the inner air pressure are examined. Journal of Applied MathematicsA nearshore or onshore OWC device was analysed among others by McCormick 3,4 , Evans 5 , Sarmento et al. 6 , Evans and Porter 7 , and Kokkinowrachos et al. 8 , for 2D and 3D geometries of OWC devices with infinitesimal wall thickness. Hydrodynamic analysis on a freely floating oscillating water column device could benefit from previous worldwide studies on the dynamics of ships in wavy seas. The first theoretical analysis of a floating oscillating water column device has been presented by Masuda 9 . He developed a navigation buoy powered by wave energy, and equipped with an air turbine, while later promoted the construction of a floating barge 80 m × 12 m , named Kaimei, which housed several OWCs equipped with different types of air turbines 10 . Recently, Martins-Rivas and Mei 11 presented an analysis on an OWC device mounded at the tip of a breakwater with infinitesimal wall thickness and Falcão et al. 12 studied the dynamics of an OWC spar buoy.In the present contribution, a vertical axisymmetric oscillating water column device with finite wall thickness is examined that is free to move in finite depth waters. Numerical results are given from the solution of three boundary value problems, namely, the diffraction problem body fixed in waves, atmospheric pressure on the OWC , the radiation problem resulting from the forced oscillations of the body in otherwise still water, also under atmospheric conditions above the OWC, and the radiation problem resulting from an oscillating pressure head acting on the inner free surface of the OWC. Particularly, numerically evaluated linear exciting wave forces in the horizontal and vertical directions along with the volume flow, the added mass and wave damping coefficients are calculated for the freely floating device. In view of evaluating the rigid body motions of the device, the motion equations are solved in the frequency domain, for various values of turbine parameters related to the pressure drop inside the oscillating chamber. The developed method is based on matched axisymmetric eigenfunction expansions of the velocity potential in properly defined ring-shaped fluid regions around the device and could be considered as an extension of the methods employed by Miles and Gilbert 13 , Garrett 14 , and Yeung 15 as far as a circular...

Wave power extraction from a bottom-mounted oscillating water column converter with a V-shaped channel

“…Note here that I m is unbounded as r → ∞, while K m is unbounded as r → 0 [22]. Hence, in view of the range of radial direction r in the sub-domain (2), both I m and K m should be included in the expression for the complex amplitude ψ 2 (see also [23]). The above expression also satisfies the boundary conditions at the two vertical plates (i.e.…”

Oscillating-water-column wave energy converters and air turbines: A review

“…This is the case of a two-dimensional OWC with vertical thin walls [132], a vertical thin-walled circular cylindrical OWC [133] and a circular cylindrical OWC at the tip of a breakwater [134] or the tip of a coastal corner [135]. More complex geometries include a floating vertical axisymmetric OWC [136] and a twodimensional dual-chamber OWC on stepped bottom [137]. For non-diffracting OWC structures, analytical solutions can be derived from the expressions for the wave field induced by time-harmonic surface pressure distributions [124].…”

Theoretical modelling of oscillating water column wave energy converters

“…Compared with the previous two OWC devices, another radiated wave field is generated by the heaving motion of the system. The correction of the optimization of turbine characteristics presented by Mavrakos & Konispoliatis (2012) has been given. It is found that the maximum extraction efficiency, under the corrected optimization of turbine characteristics, can be the same as that where a circular OWC device with thin walls is fixed in waves.…”

“…For harnessing wave energy in deeper water, a floating OWC device with a circular pontoon, which is connected to sea bed by a mooring system attached by a linear power takeoff (PTO) system, is proposed as well. Compared to the free floating OWC device by Mavrakos & Konispoliatis (2012), the integrated mooring system is beneficial to control the phase difference between the wave motion inside the air chamber and the motion of the pontoon and improve the efficiency of the floating OWC system.…”

“…In literature, the hydrodynamics of a free floating vertical axisymmetric oscillating water column wave energy converter in three modes (i.e., surge, heave and pitch) has been studied by Mavrakos & Konispoliatis (2012). However, in their paper, the optimization of the turbine parameter g T opt (g T = χ) (the same notation in Mavrakos & Konispolistis' paper) should be corrected.…”