Flexibility induces ‘unsteady actuator disk’ type of action for a foil flapping in the absence of free stream

Birds, insects, fish use wing, fin flexibility to their advantage, but knowing ‘how?’ is non-trivial due to the intricately coupled fluid-flexible-surface interactions. The surface selected to understand such interactions is a two-dimensional rigid foil, to which is attached at the trailing edge a thin chordwise flexible flap, pitching in quiescent water - a case relevant to hovering. Flapping flexible foil produces a reverse Benard-Karman vortex jet. Interestingly, time mean shows an accelerating flow in the downstream, similar to an ‘idealized actuator disk’, but, with some differences. We show (being reported for the first time) that the flapping flexible foil can be thought of as an ‘unsteady actuator disk’. Ellington (1984) modeled unsteady force generation for a hovering insect with ‘pulsed actuator disk’ that applies pressure impulses to the air passing through. Using PIV data, we present mechanism of how flexibility induces the unsteady actuator disk type action: deformations of flexible flap during ‘active period’ orient the generated pressure gradients in the jet direction, thus causing the flow acceleration. In stark contrast, if rigid, the same flap would orient the pressure gradients in transverse direction, which is not useful for propulsion as well as hovering.