Numerical Study of an Oscillating Airfoil in Transonic Buffeting Flows

Numerical simulations are conducted to compute the aerodynamic flowfield response that is observed for a NACA0012 airfoil that undergoes prescribed harmonic oscillation at transonic Mach numbers. Large shock oscillations are observed for certain combinations of Mach number and steady mean angle of attack. These are termed as buffet in this paper. Prescribing an airfoil oscillation about the buffeting flowfield reveals a nonlinear interaction between the flowfields induced by the buffet and airfoil motion, respectively. At low airfoil-oscillation amplitudes, the time histories of the aerodynamic coefficients exhibit two frequencies, that of the buffet and that of the oscillating airfoil. As the airfoil amplitude increases, the flowfield response at the buffet frequency decreases. Beyond a certain level of airfoil amplitude, lock-in occurs: the flowfield response at the buffet frequency vanishes, and the flow system response predominantly assumes the frequency of the airfoil motion. The airfoil amplitude that will cause lock-in is dependent on the ratio between the frequency of the airfoil oscillation and the buffet frequency. The closer these frequencies are, the smaller the airfoil-oscillation amplitude that will cause lock-in. There is a broad analogy between this flow phenomenon and the flowfield of the von Karman vortex street found behind a cylinder with the cylinder undergoing a prescribed oscillation. This paper reviews that phenomenon, suggests an aerodynamic gain-phase model for the lock-in region, and suggests a possible relation between this flow mechanism and limit-cycle oscillation.