Aerodynamic stiffness effect and sub-harmonic synchronization of aeroelastic system in the presence of dynamic stall

Abstract A computational study of forced aeroelastic system of an airfoil is performed under various free-stream velocities. The results show that, as the free-stream velocity increases, the natural frequency of the system is increasing due to the aerodynamic stiffness effect except for a certain velocity range where the sub-harmonic synchronization occurs. To explore the characteristics of aerodynamic stiffness alone, the free oscillation response under the same conditions are simulated. The simulation shows that the aerodynamic stiffness presents a non-monotonic characteristic with the increase of the free-stream velocity. Further investigation indicates that the trend of aerodynamic stiffness varying with free-stream velocity is closely related to different areas at which the minimum angle of attack is located, which are greater than zero, less than zero or less than the dynamic stall angle in opposite direction. Equivalent linearization analysis qualitatively explains the reasons for the different aerodynamic stiffness characteristics in the above three phases. Comparing the results of the forced and the free system, it is found that the natural frequency under the influence of aerodynamic stiffness in the second stage is close to the 1/2 sub-harmonic of forcing frequency, resulting in the sub-harmonic synchronization. Moreover, the occurrence of dynamic stall in the opposite direction is considered to be the mechanism of unlock from the 1/2 sub-harmonics of forcing frequency.