Analysis of Oscillating Flow Over a 2D Airfoil with Flow Reversal

Previous researchers developed equations to model the induced flow on a 2D airfoil in the finite-state as opposed to the closed-form. Those models, however, were limited in that they could not handle an oscillating free stream that became negative. Recently, a new model was developed to include a single factor to carry the effects of the free stream changing signs. In developing this model, a Floquet instability was discovered at the instant when the flow changes direction. The effect of the instability grows with increasing number of oscillations of the sign of the free stream. The effects can be limited depending on the parameters of the flow. In this paper, the previous 2D model is amended to include a term that considers the effects of the induced flow from all previous vorticity segments that have been generated from each oscillation of the flow. This paper details the beginnings of the testing on the stability limits of the theory, based on changing the parameters of the free stream, airfoil, and timing. It is the intention of this research to further investigate the limits of this model in reversing flow in hopes of using the lessons learned to extend 3D finite-state models that are currently incapable of handling cases where the sign of the free-stream velocity changes as a result of the rotor reentering its own wake such as when a helicopter or quadcopter quickly descends after ascending to avoid an obstacle.