Frequency lock-in phenomenon for oscillating airfoils in buffeting flows

Navier-Stokes based computer simulations are conducted to determine the aerodynamic flow field response that is observed for a NACA0012 airfoil that undergoes prescribed harmonic oscillation in transonic buffeting flows, and also in pre-buffet flow conditions. Shock buffet is the term for the self-sustained shock oscillations that are observed for certain combinations of Mach number and steady mean flow angle of attack even in the absence of structural motion. The shock buffet frequencies are typically on the order of the elastic structural frequencies, and therefore may be a contributor to transonic aeroelastic response phenomena, including limit-cycle oscillations. Numerical simulations indicate that the pre-shock-buffet flow natural frequency increases with mean angle of attack, while the flow damping decreases and approaches zero at the onset of buffet. Airfoil harmonic heave motions are prescribed to study the interaction between the flow fields induced by the shock buffet and airfoil motion, respectively. At pre-shock-buffet conditions the flow response is predominantly at the airfoil motion frequency, with some smaller response at multiplies of this frequency. At shock buffet conditions, a key effect of prescribed airfoil motions on the buffeting flow is to create the possibility of a lock-in phenomenon, in which the shock buffet frequency is synchronized to the prescribed airfoil motion frequency for certain combinations of airfoil motion frequencies and amplitudes. Aerodynamic gain-phase models for the lock-in region, as well as for the pre-shock-buffet conditions are suggested, and also a possible relationship between the lock-in mechanism and limit-cycle oscillation is discussed.