Flexible flapping airfoil propulsion at zero freestream velocity

Thrust generation for an airfoil plunging at zero freestream velocity, the case relevant to hovering birds and insects, has been studied. The objective was to investigate the effect of airfoil stiffness. Particle image velocimetry and force measurements were taken for three airfoils of relative bending stiffnesses 1:8:512 in a water tank. The deformation of the flexible airfoils produces an angle of attack that varies periodically with a phase angle with respect to the plunging motion. Amplitude and phase of this combined plunging/pitching motion play a major role in the flowfield and thrust generation. Vortex pairs or alternating vortex streets were observed depending on the amplitude and phase lag of the trailing edge. The strength of the vortices, their lateral spacing, and the time-averaged velocity of the induced jet were found to depend on the airfoil flexibility, plunge frequency, and amplitude. Direct force measurements confirmed that at high plunge frequencies the thrust coefficient of the airfoil with intermediate stiffness was greatest, although the least stiff airfoil can generate larger thrust at low frequencies. It is suggested that there is an optimum airfoil stiffness for a given plunge frequency and amplitude. The thrust/input-power ratio was found to be greater for the flexible airfoils than for the rigid airfoil.