Hydrodynamic performance of flapping wings for augmenting ship propulsion in waves

Experiments with actively pitch-controlled and spring-loaded oscillating foils

“…As in Politis and Politis [15] and Belibassakis and Politis [4], the pitch-controlled angle of attack is taken as a constant times . We denote this constant the pitch-control parameter, w pc .…”

Ship propulsion in waves by actively controlled flapping foils

“…In the present approach we use the equations of motion derived in the body-fixed frame of reference linearised by assuming small oscillatory amplitudes. Seakeeping analysis in the frequency domain is used to obtain the motions and responses of the examined system (ship and flapping wing) in the vertical plane; see also Belibassakis and Politis [11]. The coupled equation of heave and pitch motion of the ship (with corresponding complex amplitudes 30 and 50 ) is as follows (taking the origin at the centre of gravity): a jk and b jk , j, k = 3, 5, are added mass and damping coefficients, m is the total mass of the ship and wing and p = − iω en Um is a Coriolis term.…”

“…In general, due to the oscillatory thrust developed by the foil, ship responses are also coupled with surge motion. However, considering the large mass of ship, in conjunction with installation of energy storage and power feed smoothing systems, at first level of approximation that effect is neglected, as proposed by Belibassakis and Politis [11].…”

“…useful propulsive thrust, with simultaneous reduction of unwanted responses; see, for example, Rozhdestvensky and Ryzhov [7] for an extensive review, Naito and Isshiki [8] for a review in flapping-bow wings on ship propulsion, and Bøckmann and Steen [9] and Terao and Sakagami [10] for recent experimental research and full-scale applications, respectively. Working in the above direction Belibassakis and Politis [11] proceed by substituting the passive pitching setup by an active pitching control, using a proper control mechanism and a pitch setup algorithm, on the basis of the (known) random motion history of the wing. As illustrated in Fig.…”

“…More specifically, we consider operation of the foil in head waves characterised by a given frequency spectrum, corresponding to specific sea states. The heaving motion of the foil is calculated using the energy spectrum of the incident wave field and the Response Amplitude Operator (RAO) of the ship at the location of the foil, taking into account the coupled dynamics, as described in Belibassakis and Politis [11]. The performance of active pitch control of the flapping hydrofoil is investigated in the case of random motion, as well as the effects of foil submergence and its horizontal location along the (forward part of the) ship.…”