Finite-Core Vortex Array Model of the Wake of a Periodically Pitching Airfoil

Abstract

In this study, a simple vortex array model is employed to compute the unsteady velocity field in the wake of an airfoil undergoing harmonic as well as nonharmonic pitch oscillation. The parameters of the model are determined by minimizing the difference between the model predictions and existing single-component laser Doppler velocimetry measurements of the streamwise velocity in the near wake of an oscillating NACA 0012 airfoil, at a chord Reynolds number of 11,400. It is shown that the vortex array model is an effective tool for determination of the wake vortex parameters (circulation, core diameter, spacing, etc.) from pointwise measurements of only the streamwise component of the velocity. This is demonstrated through comparison of the vortex parameters estimated using the model with those obtained directly from whole-field measurements in a similar flow. In addition, the mean streamwise force acting on the airfoil is calculated using the model in conjunction with the integral momentum equation. Comparison of the model-predicted force coefficient and its dependence on the reduced frequency are found to be consistent with published experimental and computational data.