Quasi-steady response of free-to-pivot flat plates in hover

Abstract

Using force measurements and flow visualization in a water tunnel, we consider motions of rigid flat plates with square edges free to pivot about the leading edge between incidence angles of ±45°. The plate's leading edge undergoes a prescribed periodic rectilinear translation. During most of the translation semi-stroke, the plate rests against its incidence limiter to produce a positive angle of attack; this reverses on the opposite semi-stroke, producing a motion akin to normal-hover with delayed rotation. Three aspect ratios are considered: a nominally 2D, or wall-to-wall plate spanning the tunnel test section, and plates of aspect ratios 3.4 and 5.5. Reynolds number effects in the range of 10000–31000 were not found to be significant. Aerodynamic force coefficient history was found to be aspect-ratio invariant, despite difference in flowfield evolution in the wake, and the force coefficients magnitude decreased for decreasing motion amplitudes. Flow visualization gives qualitative evidence for leading-edge and trailing-edge vortices, but no evidence was found of leading edge vortex stability or for contribution of vortices to aerodynamic loads, for sinusoidal or nonsinusoidal imposed motions of the plate. No evidence is found that the vortex system in the wake interacts with the plate during or after semi-stroke reversal. The main operative parameter governing aerodynamic force history is the ratio of semi-stroke amplitude to plate chord. Especially for the larger semi-stroke to chord ratios, aerodynamic response during the translational phase of motion is nearly quasi-steady, with decay in both thrust and force opposing the motion, in proceeding along each semi-stroke. The rotational phase of each semi-stroke is dominated by a loads spike as the plate approaches its incidence limiter. This spike largely disappears when the free-to-pivot plate is replaced with one with a prescribed rotational history. These findings offer favorable implications for analysis of flapping-wings using quasi-steady blade element models.