Stability analysis for laminar separation flutter of an airfoil in the transitional flow regime

Abstract

Laminar separation flutter (LSF) is a type of aeroelastic instability phenomenon characterized by small-amplitude low-frequency pitching oscillations of the airfoil. The present study aims to gain insight into the intrinsic dynamics of LSF via data-driven stability analysis. The proposed data-driven approach relies on the autoregressive with exogenous input (ARX) technique to design reduced-order models (ROMs) of unsteady aerodynamics in a state-space format. First, high-fidelity full-order numerical simulations of the LSF phenomenon are performed using the incompressible Unsteady Reynolds-Averaged Navier–Stokes equations and the Shear-Stress Transport k−ω turbulence model with Low-Reynolds-number correction. The calculated LSF responses show good agreement with previous experimental data in the literature. Then, linear stability analysis (LSA) of the aeroelastic system is carried out to reveal the underlying fluid-structure interaction mechanism. The LSA model is developed by coupling the ROM with the structure motion equation. LSA results indicate that the LSF phenomenon is primarily caused by the instability of the structure mode (SM), which is induced by the mutual repulsion effect between one static fluid mode (FM) and the SM. The presence of laminar separation near the trailing-edge of the airfoil can significantly reduce the stability of the static FM, which ultimately strengthens the fluid-structure coupling effect and leads to LSF. We would like to emphasize that LSF is essentially different from other flow-induced vibration phenomena, such as transonic buffeting of an airfoil and vortex-induced vibration of bluff bodies, for which the instabilities are triggered by the coupling between one dynamic FM and the SM. Finally, the effects of the mass ratio, structural damping ratio, and freestream turbulence intensity on the aeroelastic system are also investigated.