Propulsion through wake synchronization using a flapping foil

Abstract

The design issues associated with underwater vehicles operating in the surf zone or other high-energy environments are likely to have viable biomimetic solutions. The flapping fin is capable of producing high instantaneous forces, giving fish the ability to turn and accelerate rapidly, and fish are capable of sensing the flow characteristics in their environment using the lateral line, aiding obstacle entrainment, schooling, rheotaxis, and prey detection. A highly maneuverable vehicle that is capable of sensing the changing flows in its environment would have a considerably higher survival rate in dangerous currents. As an initial foray into the sensory and control methods that could be used by a biomimetic vehicle, we studied energy extraction through synchronization with an incoming Karman wake for both fish and mechanical flapping foils. Rainbow trout (Oncorhynchus mykiss) swimming within a flow channel voluntarily positioned themselves 4D downstream from a 2" D-section cylinder, and synchronized with the cylinder wake in both frequency and phase. The phase of the trout's lateral position relative to the wake, described through a Wake Function W(x, t) defined as the lateral-sum of vorticity at a point downstream from the cylinder, was 100Ê» for the head, 160Ê» for the center-of-mass, and 240Ê» for the tail, implying that the trout's mass was moving laterally with the flow in a low-power swimming mode, but that its head and tail had flow across them. A euthanized trout passively synchronized with the wake and accelerated forward towards the cylinder, through fluid-excited motion only, proving that trout benefit not only from drafting in the velocity deficit behind the cylinder, but also through interaction with the vortices in the wake.

(cont.) The thrust and efficiency of a heaving and pitching foil depends on how the foil interacts with the wake of an upstream cylinder. A systematic set of tests varying foil motion within the wake revealed that thrust was considerably more sensitive to wake interaction then efficiency, with the coefficient of thrust varying by 0.4, and the efficiency by 0.1, depending on the phase between foil and cylinder heave motions. Thrust and power input was always highest when the foil leading-edge motion opposed the lateral velocities in the wake, likely due to an increase in the angle-of-attack across the foil. When thrust production was high (CT 1), the foil was most efficient when it led the wake by 30Ê» for the leading-edge and 120Ê» for the trailing-edge, but when thrust was low (CT 0.3), efficiency was highest for interactions similar to that of the trout, leading the wake by 125Ê» for the leading-edge and 215Ê» for the trailing-edge. Since the trout's coefficient of thrust was also low, these results were in agreement despite the many differences between the fluid-mechanical systems. I designed and tested an algorithm that could synchronize the foil with an unknown wake using simple sensors and calculations. Additionally, I studied the foil moving passively in the wake using force-feedback to model the foil supports as a spring-mass-damper. The foil produced 0.27 N of thrust at a negative mean power input of 90 mW (energy extraction), a feat impossible for a passive device within a uniform stream.