Augmentation of Inviscid Airfoil Theory to Predict and Model 2D Unsteady Vortex Dominated Flows

Abstract

A criterion for predicting flow separation and reattachment at the leading-edge using a Leading-Edge Suction Parameter (LESP) is presented. Stemming from inviscid theory, the LESP serves to predict the onset of separation or reattachment at the leading-edge for any unsteady motion using a critical value which is defined by the airfoil shape and Reynolds number of operation. This criterion is applied to a flat plate and an SD7003 airfoil undergoing various pitch and plunge motions and the critical LESP values for these airfoils are seen to predict the onset of separation or reattachment at the leading-edge, on both upper and lower surfaces. Separation at the leading-edge and subsequent formation of a leading-edge vortex (LEV) is accompanied by a loss in the leading-edge suction force resulting in increased drag. However, formation of LEV also serves to prevent separation at the trailing-edge and keeps the bound circulation intact, thus yielding high lift even at large angles of attack where the flow would have been fully separated otherwise. Using the criterion presented in this paper, it is possible to design kinematics which promote or suppress LEV formation by moving the LESP above or below its critical value.