Biomimetic propulsion under random heaving conditions, using active pitch control

Marine mammals travel long distances by utilizing and transforming wave energy to thrust through proper control of their caudal fin. On the other hand, manmade ships traveling in a wavy sea store large amounts of wave energy in the form of kinetic energy for heaving, pitching, rolling and other ship motions. A natural way to extract this energy and transform it to useful propulsive thrust is by using a biomimetic wing. The aim of this paper is to show how an actively pitched biomimetic wing could achieve this goal when it performs a random heaving motion. More specifically, we consider a biomimetic wing traveling with a given translational velocity in an infinitely extended fluid and performing a random heaving motion with a given energy spectrum which corresponds to a given sea state. A formula is invented by which the instantaneous pitch angle of the wing is determined using the heaving data of the current and past time steps. Simulations are then performed for a biomimetic wing at different heave energy spectra, using an indirect Source-Doublet 3-D–BEM, together with a time stepping algorithm capable to track the random motion of the wing. A nonlinear pressure type Kutta condition is applied at the trailing edge of the wing. With a mollifier-based filtering technique, the 3-D unsteady rollup pattern created by the random motion of the wing is calculated without any simplifying assumptions regarding its geometry. Calculated unsteady forces, moments and useful power, show that the proposed active pitch control always results in thrust producing motions, with significant propulsive power production and considerable beneficial stabilizing action to ship motions. Calculation of the power required to set the pitch angle prove it to be a very small percentage of the useful power and thus making the practical application of the device very tractable.