Interaction of Boundary Layer and Blade Vibration at Ultra-Low Advance Ratios and Low Reynolds Numbers in a Novel Flapping and Spinning Propulsor

Abstract

The nonlinear thrust properties of a small, near-hovering, conventional-looking propulsor are examined. When the propulsive power versus displacement of large and small manmade underwater vehicles is compared against that of large and small fish (distinguishing their red and white muscle distributions), universal trends are observed for cruising and maneuvering irrespective of size. While there is an overlap in the low displacement range of 0.1 to 1 m3, manmade propulsors have rotating blades that are fixed, but animals use flapping pectoral fins. With this cue, a small and novel propulsor has been built where the fins/blades can both flap and spin. The blade pitch can also be varied, allowing the production of reverse thrust. The nondimensional parameter range of thrust production in both the flapping and spinning modes is determined. When the advance ratio (J) and Reynolds number (Rec) are ultra-low in the spinning mode, the blade boundary layer couples with small pitch oscillations, and a bimodal behavior ensues. Boundary layer fence and rough blade surfaces shift the behavior to higher effective pitch angles, but the bi-modal behavior persists. A quasi-steady thrust modeling is carried out of the spin mode when the boundary layer couples with the inadvertent small pitch oscillation and when it does not. Temporal modeling indicates that, at ultra-low values of J and Rec, the boundary layer and blade vibration interaction can be described as a Lienard (nonlinear) oscillator. The potential mechanism of interaction between blade vibration and rotation, and of their modeling, is discussed.