Abstract
We consider a flap gate farm, i.e. a series of P arrays, each made of Q neighbouring flap gates, in an open sea of constant depth, forced by monochromatic incident waves. The effect of the gate thickness on the dynamics of the system is taken into account. By means of Green's theorem a system of hypersingular integral equations for the velocity potential in the fluid domain is solved in terms of Legendre polynomials. We show that synchronous excitation of the natural frequencies of Sammarco et al. (2013) yields large amplitude response of gate motion. This aspect is fundamental for the optimisation of the gate farm for energy production.
Highlights
The flap gate systems, i.e. one or more floating bodies hinged at the bottom of the sea and rolling under incoming waves, have recently proved very effective to extract energy from the sea (Whittaker et al [1])
We consider a flap gate farm, i.e. a series of P arrays, each made of Q neighbouring flap gates, in an open sea of constant depth, forced by monochromatic incident waves
In order to evaluate the effects of the finite gate thickness 2b, the simplest case of P = Q = 1, i.e. the case of one gate in the open sea is considered
Summary
The flap gate systems, i.e. one or more floating bodies hinged at the bottom of the sea and rolling under incoming waves, have recently proved very effective to extract energy from the sea (Whittaker et al [1]). For one array of gates spanning the entire width of a channel, experiments showed that the gates can be excited to oscillate at half the incident wave frequency with a very large amplitude (Mei et al [2]). Li and Mei [5] found the (Q − 1) eigenfrequencies of one array made by Q identical gates spanning the full width of a channel. Large amplitude motions of the gates occur when the incident wave frequency approaches the eigenfrequencies. Monochromatic plane normal incidence waves of amplitude A, period T and angular frequency ω = 2 /T, coming from x =+ ∞, force the gates to oscillate back and forth. Note that the no flux condition (6) is given on the finite edges of each array facing the open sea, without channel walls.
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