On the mechanism of frequency lock-in vibration of airfoils during pre-stall conditions

Potential frequency lock-in vibration can frequently occur in aircraft flying at separated flow conditions during take-off and landing stages, severely threatening the safety of the aircraft. A deeper understanding of the lock-in phenomenon in pre-stall (steady separated flow) conditions is necessary to improve aircraft reliability and safety. In this paper, a reduced-order model (ROM) for the pitching NACA0012 airfoil in steady separated flow is established. A linear aeroelastic model is then obtained by coupling the ROM with the structural dynamical equation with the pitching degree of freedom, and it is verified by the computational fluid dynamics/computational structural dynamics (CFD/CSD) simulation. Next, the mechanism of frequency lock-in vibration is revealed by the ROM-based aeroelastic model of different structural natural frequencies. Results from the complex eigenvalue analysis indicate that the instability can be divided into two patterns. At high frequencies, the flutter frequency locked onto the natural frequency of the structure, and it is dominated by the instability of structural mode. At low frequencies, the flutter frequency follows the fluid characteristic frequency, which is dominated by the instability of the fluid mode. Finally, the effects of the angle of attack and mass ratio are investigated. The damping of dominant fluid mode decreases with the increase of angle of attack, which affects the structural mode through coupling effects. Therefore, the angle of attack influences the upper boundary of the coupling system's instability (high frequency boundary). On the contrary, the mass ratio mainly influences the lower boundary of instability (low frequency boundary), because fluid mode becomes unstable at low frequencies merely when the mass ratio is relatively low.