Energy Harvesting Performance of Thick Oscillating Airfoils Using a Discrete Vortex Model

The energy harvesting performance of thick oscillating airfoils is predicted using an inviscid discrete vortex model (DVM). National Advisory Committee for Aeronautics (NACA) airfoils with different leading-edge geometries are modeled that undergo sinusoidal heaving and pitching with reduced frequencies, $k=fc/U∞$⁠, in the range $0.06−0.14$⁠, 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 midchord with heaving and pitching amplitudes of $h0=0.5c$ and $θ0=70 deg$⁠, respectively, known to be in the range of peak energy harvesting efficiencies. A vortex shedding initiation criteria is proposed based on the transient local wall stress distribution determined from computational fluid dynamics (CFD) simulations and incorporates both timing and location of leading-edge separation. The scaled shedding times are shown to be predicted over the range of reduced frequencies using a timescale based on the leading-edge shear velocity and radius of curvature. The convection velocity of the shed vortices is also modeled based on the reduced frequency to better capture the dynamics of the leading-edge vortex. An empirical trailing-edge separation correction is applied to the transient force results using the effective angle of attack modified to include the pitching component. Impulse theory is applied to the DVM to calculate the transient lift force and compares well with the CFD simulations. Results show that the power output increases with increasing airfoil thickness and is most notable at higher reduced frequencies where the power output efficiency is highest.