Theoretical Analysis of a Vertical Cylindrical Floater in Front of an Orthogonal Breakwater

Abstract

This study investigates the effect of an orthogonal-shaped reflecting breakwater on the hydrodynamic characteristics of a vertical cylindrical body. The reflecting walls are placed behind the body, which can be conceived as a floater for wave energy absorption. Linear potential theory is assumed, and the associated diffraction and motion radiation problems are solved in the frequency domain. Axisymmetric eigenfunction expansions of the velocity potential are introduced into properly defined ring-shaped fluid regions surrounding the floater. The hydrodynamic interaction phenomena between the body and the adjacent breakwaters are exactly taken into account by using the method of images. Results are presented and discussed concerning the exciting wave forces on the floater and its hydrodynamic coefficients, concluding that the hydrodynamics of a vertical cylindrical body in front of an orthogonally shaped breakwater differ from those in unbounded waters.

Hydrodynamic Efficiency of a Wave Energy Converter in Front of an Orthogonal Breakwater

“…For the heaving device: Applying the method of images, the investigated system (i.e., converter-orthogonal breakwater system) corresponds to an array of four similar WECs consisting of the initial converter and its three mirror virtual bodies with respect to the two vertical walls that are exposed to the action of four-directional surface waves (i.e., one propagating at angle β, a second at angle 180 − β, a third at angle 180 + β, and a fourth at angle 360 − β) without, however, the presence of the vertical walls [38]. Herein, four local cylindrical co-ordinate systems r q , θ q , z , q = 1, 2, 3, 4 are defined with origins at the intersection X q , Y q of the sea bottom with the vertical axis of symmetry of each converter (see Figure 2).…”

“…Applying the method of images on the WEC-breakwater system, the heave exciting forces on the converter when exposed to the action of a regular wave train propagating at an angle β, equal to the sum of the exciting forces acting on the WEC for wave angles β, 180 − β, 180 + β, 360 − β, assuming, however, the presence of three mirror bodies, placed with respect to the vertical walls, without the presence of the breakwater (see Figure 2). Concerning the motion dependent hydrodynamic coefficients of the converter, these equal the sum of the initial converter's coefficients in the j-th direction due to its own forced oscillation in heave direction supplemented by the corresponding hydrodynamic interaction coefficients on the initial converter, in the j-th direction, due to the forced oscillation of the image bodies (p = 2, 3, 4) in heave [38]. Similarly, after summing properly the pressure dependent coefficients of the initial OWC in the j-th direction due to its own unit inner air pressure head, with the corresponding coefficients of the initial OWC, in the same j-th direction, due to unit air pressure inside the image OWCs' chambers, the pressure hydrodynamic characteristics of the OWC-breakwater system were calculated.…”

“…Here, α j3 , b j3 terms stand for the added mass and damping coefficients in j-th direction, respectively, when the WEC is placed in front of the orthogonal breakwater due to body's own forced oscillation in heave direction. After applying the method of images, these terms equal to [38]:…”

“…Pioneering works on the wave effects on V-shaped breakwaters are [30][31][32][33]. Concerning the investigations on the behavior of WECs placed in front of V-shaped breakwaters, theoretical and experimental studies were developed in [34,35], whereas the effect of a sea-bottom fixed orthogonal breakwater on the hydrodynamics of bottom seated or floating cylindrical bodies has been studied in [36][37][38].…”

Effectiveness of Floating Breakwater in Special Configurations for Protecting Nearshore Infrastructures

“…The multiple lines of floating breakwaters were investigated in [17,18]. A similar but more theoretical problem was a cylinder in front of a vertical wall, such as in [19,20], where the wave diffractions from the cylinder were investigated, while a more complicated case where a truncated cylinder placed in front of an orthogonal breakwater was explored in [21]. These theoretical studies reveal the importance of the hydrodynamic interactions between breakwaters and floaters.…”