Vortices interacting with the solid surface of aerodynamic bodies are prevalent across a broad range of geometries and applications, such as dynamic stall on wind turbine and helicopter rotors, the separated flows over flapping wings of insects, birds, formation of the vortex wakes of bluff bodies, and the lift-producing vortices formed by aircraft leading-edge extensions and delta wings. This study provides fundamental insights into the formation and evolution of such vortices by considering the leading-edge vortices formed in variations of a canonical flapping wing problem.
Specifically, the vorticity transport for three distinct maneuvers are examined, a purely rolling wing, a purely pitching wing and a rolling and pitching wing, of aspect-ratio two. Once the maneuvers are characterized, a passive bleed hole will be introduced to a purely rolling wing, to alter flow topology and vorticity transport governing the circulation on the wing.
Three-dimensional representations of the velocity and vorticity fields were obtained via plenoptic particle image velocimetry (PPIV) measurements are used to perform a vorticity flux analysis that serves to identify the sources and sinks of vorticity within the flow. Time-resolved pressure measurements were obtained from the surface of the airfoil, and used to characterize the flux of vorticity diffusing from the solid surface.
Upon characterizing all of the sources and sinks of vorticity, the circulation budget was found to be fully accounted for. Interpretation of the individual vorticity balance contributions demonstrated the Coriolis acceleration did not contribute to vorticity generation and was a correction term for the apparent vorticity. The transport characteristics varied among the three cases that were investigated. The spanwise convective contribution was signification over various spanwise locations for the pure roll case. For the pure pitch the shear layer contribution and the diffusive contribution. The circulation was dependent the pitch rate, which was evident only at the beginning of the motion, and circulation growth at later times depended only on the pitch angle.The combined pitch roll cases, the transport behavior strongly resembled that of pitch, with little evidence of roll influence, despite that the flow structure and circulation distribution on the inboard part of the wing exhibited roll-like behaviors. In the final case where the wing is pitching and rolling , the shear layer contribution was balanced by the diffusive contribution, similar to that of the pure pitch case. By adding a passive bleed hole to the purely rolling cases, it was found to alter the both the flow topology and vorticity transport.