The effects of passive, inertia-induced surface flexibility at the leading and trailing edges of an oscillating airfoil energy harvester are investigated experimentally at reduced frequencies of k = fc/U∞ = 0.10, 0.14, and 0.18. Wind tunnel experiments are conducted using phase-resolved, two-component particle image velocimetry to understand the underlying flow physics, as well as to obtain force and pitching moment estimates using the vortex-impulse theory. Results are obtained for leading and trailing edge flexibility separately. It is shown that both forms of flexibility may alter the leading edge vortex inception and detachment time scales, as well as the growth rate of the circulation. In addition, surface flexibility may also trigger the generation of secondary vortical structures and suppress the formation of trailing edge vortices. The total energy harvesting efficiency is decomposed into contributions of heaving and pitching motions. Relative to the rigid airfoil, the flexible leading and trailing edge segments are shown to increase the energy harvesting efficiency by approximately 17% and 25%, respectively. However, both the flexible leading and trailing edge airfoils operate most efficiently at k = 0.18, whereas the peak efficiency of the rigid airfoil occurs at k = 0.14. It is shown that the flexible leading and trailing edge airfoils enhance the heaving contribution to the total efficiency at k = 0.18 and the negative contribution of the pitching motion at high reduced frequencies can be alleviated by using a flexible trailing edge.

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.

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The energy harvesting performance of thick oscillating airfoils is predicted using an inviscid discrete vortex model (DVM). NACA airfoils with different leading-edge geometries are modeled that undergo sinusoidal heaving and pitching with reduced frequencies, k = f c/U∞, in the range 0.06–0.14, where f is the heaving frequency of the foil, c the chord length, and U the freestream velocity. The airfoil pitches about the mid-chord with heaving and pitching amplitudes of h0 = 0.5c and θ0 = 70°, 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.

The energy harvesting performance of a flapping airfoil is studied through discrete vortex model. Results are obtained for a thin flat airfoil that undergoes a sinusoidal flapping motion for reduced frequencies of k = fC/U∞ = 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 h0 = 0.5C and θ0 = 70° respectively, as these numbers have been shown to give optimal energy harvesting results for a rigid airfoil. The study applies a panel-based discrete vortex model that incorporates a leading edge suction parameter criterion to understand the flow behavior around the airfoil. The leading edge suction parameter is found from 2D CFD simulations (Navier-Stokes equations solved in Fluent) for all K values. A correlation between the critical leading edge suction parameter and reduced frequency is found from the identified critical LESP values. An empirical trailing edge separation correction is also applied to the transient force results since flow separation at the trailing edge is anticipated. The parameters of interest from the model are transient distributions of force, power output, and overall efficiency. Model results are then validated against 2D CFD simulations. The effect of reduced frequency on power production and overall efficiency is finally studied to identify the optimal reduced frequency for energy harvesting applications.