Mechanism of frequency lock-in in transonic buffeting flow

Frequency lock-in can occur on a spring suspended airfoil in transonic buffeting flow, in which the coupling frequency does not follow the buffet frequency but locks onto the natural frequency of the elastic airfoil. Most researchers have attributed this abnormal phenomenon to resonance. However, this interpretation failed to reveal the root cause. In this paper, the physical mechanism of frequency lock-in is studied by a linear dynamic model, combined with the coupled computational fluid dynamics/computational structural dynamics (CFD/CSD) simulation. We build a reduced-order model of the flow using the identification method and unsteady Reynolds-averaged Navier-Stokes computations in a post-buffet state. A linear aeroelastic model is then obtained by coupling this model with a degree-of-freedom equation for the pitching motion. Results from the complex eigenvalue analysis indicate that the coupling between the structural mode and the fluid mode leads to the instability of the structural mode. The instability range coincides with the lock-in region obtained by the coupled CFD/CSD simulation. Therefore, the physical mechanism underlying frequency lock-in is caused by the linear coupled-mode flutter - the coupling between one structural mode and one fluid mode. This is different from the classical single-degree-of-freedom flutter (e.g. transonic buzz), which occurs in stable flows; the present flutter is in the unstable buffet flow. The response of the airfoil system undergoes a conversion from forced vibration to self-sustained flutter. The coupling frequency certainly should lock onto the natural frequency of the elastic airfoil.