Vortex lock-in phenomenon in the wake of a plunging airfoil

The flow over a NACA0012 airfoil, oscillated sinusoidally in plunge, is simulated numerically using a two-dimensional Navier-Stokes solver at a Reynolds number of 20,000. The wake of the airfoil is visualized using a numerical particle tracing method for high reduced frequencies (1.0 < k < 10.0) and small nondimensional amplitudes (h < 0.1). Anomalous vortex shedding modes (involving multiple vortices shed per half-cycle of airfoil motion) observed experimentally in the literature are reproduced numerically and are shown to be the result of interaction between the plunging frequency and a natural bluff-body shedding frequency. This results in a vortex lock-in phenomenon analogous to that seen for oscillating cylinders. However, the lock-in boundary is not symmetric about the natural shedding frequency, due to the sharp trailing edge forcing the flow to separate at the trailing edge on the windward side of the airfoil for the majority of the plunge cycle at higher frequencies and amplitudes.