Non-linear stability boundaries of an elastically-mounted pitching wing

The aeroelastic stability boundaries of an elastically mounted pitching wing (NACA 0012) are experimentally studied in a circulating water flume. The structural properties of the wing are simulated and varied using a cyber-physical control system. At a small fixed damping, the torsional stiffness of the wing is systematically varied for different inertia values to test for the stability boundaries of the system. It is found that when the inertia value is large, the system dynamics bifurcates from stable fixed points to small-amplitude oscillations followed by large-amplitude limit cycle oscillations via a subcritical bifurcation. This bifurcation features a hysteretic bi-stable region and an abrupt jump of the pitching amplitude at the bifurcation point. Under this condition, the pitching frequency of the wing locks into its structural frequency, showing that the oscillations are dominated by the structural force. The presence of a secondary leading-edge vortex (LEV) is indicated by force and flow field measurements. As the inertia value decreases, the width of the bi-stable region shrinks. At a sufficiently low inertia, the system response changes gradually with the torsional stiffness without any hysteresis, revealing a supercritical bifurcation. Under this condition, no lock-in phenomenon is observed and the pitching frequency remains relatively constant at a value lower than the structural frequency, indicating dominating fluid force. The secondary LEV is absent. The Reynolds number is shown to have negligible effect on the present experimental results.