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 and micro-air vehicles, 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 within three distinct experimental cases--2D plunging airfoil, 3D plunging airfoil and 2D plunging airfoil with suction applied at the leading edge--were analyzed in order to characterize the formation and evolution of the leading-edge vortex (LEV).
Three-dimensional representations of the velocity and vorticity fields were obtained via multi-plane particle image velocimetry (PIV) measurements and used to perform a vorticity flux analysis that served 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, and a method for correcting dynamic pressure data was developed and validated for the application within the current study.
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 terms demonstrated vorticity generation and transport characteristics that were consistent among all three cases that were investigated. Three-dimensional vorticity fluxes were found to be an almost negligible contributor to the overall circulation budget, mostly due to the individual terms canceling each other out. In all cases, the diffusive flux of vorticity from the surface of the airfoil was shown to act primarily as a sink of LEV vorticity, with a magnitude roughly half that of the flux of vorticity emanating from the leading-edge shear layer.
Inspection of the chordwise distribution of the diffusive flux within the 2D case showed it to correlate very well with the evolution of the flow field. Specifically, the diffusive flux experienced a major increase during the phase interval in which the LEV remained attached to the downstream boundary layer. It was also noted that the accumulation of secondary vorticity near the leading edge prevented the diffusive flux from continuing to increase after the roll-up of the LEV. This result was validated within the 3D case, which demonstrated that maintaining an LEV that stays attached to the downstream boundary layer produces a larger diffusive flux of vorticity--presumably enhancing both lift and thrust.
Through the use of a spanwise array of suction ports, the suction case was able to successfully alter the total circulation of the flow by removing positive vorticity from the opposite-signed vortex (OSV) that formed beneath the LEV. This removal of positive vorticity produced a measured increase in the total lift, and it was noted that weakening this region of secondary vorticity allowed the LEV to impose more suction on the surface of the airfoil. However, it was also noted that weakening the OSV resulted in a loss of thrust, which was attributed to the loss of suction that occurred near the leading edge when the removal of secondary vorticity caused the energetic OSV to be reverted into a low energy region of separated flow.
The physical insights provided by this work can form the basis of novel flow control strategies for enhancing the aerodynamic loads produced in unsteady, separated flows.