A leading-edge vortex initiation criteria for large amplitude foil oscillations using a discrete vortex model

Abstract

A leading-edge vortex initiation criterion of an oscillating airfoil is shown to provide a means to predict the onset of leading-edge separation. This result is found to collapse the occurrence of separation during the oscillation cycle when scaled using the leading-edge shear velocity determined from the foil oscillating kinematic motion. This is of importance in developing low order models for predicting energy harvesting performance, as is shown in this study using an inviscid discrete vortex model (DVM). Results are obtained for a thin flat airfoil undergoing sinusoidal heaving and pitching motions with reduced frequencies of k=fc/U∞ in the range of 0.06–0.16, where f is the heaving frequency of the foil, c is the chord length, and U∞ is the freestream velocity. The airfoil pitches about the mid-chord, and the heaving and pitching amplitudes of the airfoil are ho=0.5c and θ0=70°, respectively, illustrating results for conditions near peak efficiency for energy harvesting. The DVM uses a panel method, applicable to a wide range of foil geometries. An empirical trailing-edge separation correction is also applied to the transient force results. The vortex shedding criterion is based on the transient local wall stress distribution determined using a computational fluid dynamics (CFD) simulation, indicating the time and location of zero stress at the foil surface. In addition, the local pressure gradient minimum is also used as a local indicator. The effects of a wide range of Reynolds numbers on separation are shown for the given range of reduced frequencies. The use of the effective angle of attack, when modified to include the pitching component, is also shown to correlate the leading-edge vortex initiation time. The advantage of the proposed separation criteria is that it can be fully determined from the motion kinematics and then applied to a wide range of low order models. Model results are given for the transient lift force and compare well with the CFD simulations. It is noted that at higher reduced frequencies the DVM overpredicts portions of the transient loads possibly caused by the reversed viscous flow from the trailing edge.