Frequency lock-in in pitch–heave stall flutter

Abstract

Coupled pitch–heave oscillations of a rigid but elastically mounted NACA0012 wing are experimentally investigated in a range of airspeeds corresponding to transitional Reynolds numbers (6.5 × 104–12.0 × 104). The elastic axis is set at 35% and the frequency ratio ω¯=ωh∕ωθ, is varied from 0.68 to 1.43. The system exhibits self-sustained large amplitude symmetric oscillations attributed to stall flutter in pitch. Pitch oscillation amplitudes are in the order of 40°, whereas the heave amplitude varies from 6% to 60% of chord length. For the most part the heave DOF plays a subordinate role as it is driven by the pitch dynamics; the system oscillates at a frequency determined by the pitch DOF. However, for a range of frequency ratios close to one, a strong coupling occurs from the heave to the pitch associated with a significant increase in heave amplitude and a lock-in of the LCO frequency onto the heave dictated frequency. This lock-in parallels classical observations of the elastically mounted cylinder in cross-flow interacting with its own wake in the form of von Kármán vortex street.