A Numerical Study of an Oscillating Airfoil in Transonic Flows With Large Shock Wave Oscillations

Numerical simulations are conducted to compute the aerodynamic flow field 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 "buffet" in this paper. Prescribing an airfoil oscillation about the buffeting flow field reveals a nonlinear interaction between the flow fields 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 flow field response at the buffet frequency decreases. Beyond a certain level of airfoil amplitude lock-in occurs - the flow field 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 flow field of the Von Karman vortex street found behind a cylinder with the cylinder undergoing a prescribed oscillation. The paper reviews this phenomenon, suggests an aerodynamic gain-phase model for the lock-in region, and also suggests a possible relation between this flow mechanism and limit-cycle oscillation.