Beating phenomenon in frequency lock-in 2DOF stall flutter

Abstract

A particular behaviour is observed in the pitch-heave stall flutter of a NACA0012 airfoil at transitional chord-based Reynolds numbers during lock-in. When the air speeds is such that the airfoil oscillates at the pitch structural natural frequency, and the structural natural frequencies of the two motions are close and their ratio ω̄ (= fh∕fθ) is smaller than 1, the system exhibits a beating phenomenon in both pitching and heaving motions. The modulated amplitude of the two motions presents a phase shift allowing a feedback energy transfer alternatively from pitch to heave and from heave to pitch. Through this energy exchange, the limit cycle oscillation (LCO) is maintained with two frequencies. This phenomenon fades when the ratio ω̄ become greater than one.