Unified Scaling for Flapping Fins

Abstract

Conventional scaling for steady-fin or flapping-fin forces in a uniform flow is by definition incompatible with the scaling that has been developed for hovering flapping fins. Most flapping-fin-based vehicles will need to operate in all three operating regimes: fixed fin in cruise, flapping in cruise, and flapping in hover. A unified normalization scheme is proposed to enable smooth and optimal transition of the scaling rules between these regimes. A rigid flapping foil was experimentally tested in a towing tank. The generated side force was found to be a function only of the fin bias angle and the vector magnitude of the inflow and flapping speeds. The thrust was found to be a function of the ratio of fin flapping speed to total speed magnitude in addition to bias and speed magnitude. As an application of this scaling, an algorithm to synthesize the foil motion parameters for a desired thrust and side force regardless of vehicle speed was tested experimentally on a single foil in real time.

Rolling and pitching oscillating foil propulsion in ground effect

“…From figure 15 it is evident that every nominal 2D section along the span of the foil will produce a suction force, yet the foil as a whole produces a repulsion force! For self-propelled underwater vehicles using variations on median paired pectoral fin propulsors (Licht 2008, Beal et al 2013, Siegenthaler et al 2013, both the foil motion and the fluid flow are necessarily threedimensional. For underwater vehicles propelled using variations on the caudal fin Chhabra 2002, Rufo andSmithers 2011), the foil motion more closely approximates heaving and pitching with spanwise flow allowed around both tips, as in the 2D+ case.…”

Feedback-Induced Flutter Instability of a Flexible Beam in Fluid Flow

“…There are a number of ways to predict the kinematic conditions under which efficient force production occurs. The Strouhal number [8] and quasi-steady relationships [9] have been used for rolling and pitching fins, and slender-body theory [10,11] is a simple way to predict positive thrust for continuous bodies. Continuous flexible elements require dynamic modeling at the outset of the design, and a significant amount of work has been performed to understand the production and control of traveling waveforms produced by fluid-loaded flexible beams.…”