Frequency Selection in Heaving Airfoil Wakes Using a High-Order Method

In this contribution, the unsteady, viscous and two dimensional flow over a plunging NACA0012 airfoil was simulated using a high-order numerical method associated with a moving frame of reference technique. The goal of using a high-order numerical method is to characterize heaving airfoil wakes with very fine temporal and spatial resolutions. This characterization is essential in understanding the transition process experienced by oscillating airfoils and which can enable more control on the transition. The response of motionless and periodically forced airfoils was considered separately. The flow was investigated at a mean incidence α = 0◦, Reynolds number Re = 104, and over a range of heaving frequencies and amplitudes. The resulting airfoil wakes were analyzed with respect to their frequency response and type. It is shown that for forced airfoils three regimes of frequency response exist: a natural regime, a lock-in regime, and a harmonic regime. The transition between these regimes was presented at constant frequency and constant amplitude of the forcing oscillations. The frequency regimes were then explored in detail and related to the wake types and to the wakes transition. The results obtained were in accordance with previously published experimental and computational investigations. Furthermore, a more detailed wake classification was presented, where two more wake configurations were captured. The role of the trailingand leading-edges in the creation of multiple-vortices-per-halfcycle shedding mode was investigated. Moreover, the interaction of the natural shedding frequency of the airfoil with the imposed forcing frequency and their contribution in the creation of multiple-vortices-per-half-cycle shedding mode was also investigated. These results showed that frequency interactions can be related to the appearance of the multiple-vortices-per-half-cycle modes.