A Vortex Array Model of the Unsteady Wake of a Two-dimensional Pitching Airfoil

Motivated by recent interest in MAV aerodynamics, the present study is focused on obtaining a simplified, vortex-array model of the unsteady flow in the wake of an airfoil undergoing small-amplitude but high-reduced-frequency pitch oscillations. The model is used to predict the mean and unsteady velocity field in the wake of a NACA 0012 airfoil executing a sinusoidal as well as non-sinusoidal pitch oscillation. The model predictive accuracy is assessed by comparison to the LDV measurements of the streamwise velocity by Koochesfahani (\textit{AIAA J.} \textbf{37}, 1999) at a chord Reynolds number of 12,000 and a reduced frequency as high as 10. The results demonstrate the ability of the vortex-array model to successfully reproduce the experimentally measured mean and phase-averaged streamwise velocity profiles in the wake of the airfoil. Moreover, by using the model to reconstruct the complete velocity field in the wake, the mean streamwise force acting on the airfoil is computed for different frequencies, amplitudes and waveforms of the oscillation.