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This study explores the feasibility of using the vortex impulse approach, based on experimen- tally generated velocity elds to estimate the energy harvesting performance of a sinusoidally apping foil. Phase-resolved, two-component particle image velocimetry measurements are conducted in a low-speed wind tunnel to capture the ow eld surrounding the apping foil at reduced frequencies of k = fc=U1 = 0.06 - 0.16, pitching amplitude of 0 = 70 and heaving amplitude of h0=c = 0:6. The model results show that for the conditions tested, a maximum energy harvesting eciency of 25% is attained near k = 0:14, agreeing very well with published numerical and experimental results in both accuracy and general trend. The vortex impulse method identies key contributions to the transient power production from both linear and angular momentum eects. The eciency reduction at larger values of reduced frequencies is shown to be a result of the reduced power output from the angular momentum. Further, the impulse formulation is decomposed into contributions from posi- tive and negative vorticity in the ow and is used to better understand the uid dynamic mechanisms responsible for producing a peak in energy harvesting performance at k = 0:14. At the larger k values, there is a reduction of the advective time scales of the leading edge vortex (LEV) formation. Consequently, the LEV that is shed during the previous half cycle interacts with the foil at the current half cycle resulting in a large negative pitching power due to the reversed direction of the kinematic motion. This vortex capture process signif- icantly decreases the total cycle averaged power output and energy harvesting eciency. These results show the link between the kinematic motion and LEV time scales that aect the overall power production. 

The vortex dynamics and lift force generated by a sinusoidally heaving and pitching airfoil during dynamic stall are experimentally investigated for reduced frequencies of k = fc=U1 = 0:06􀀀0:16, pitching amplitude of 0 = 75 and heaving amplitude of h0=c = 0:6. The lift force is calculated from the velocity fields using the nite-domain impulse theory. The concept of moment arm dilemma associated with the impulse equation is revisited to shed-light on its physical impact on the calculated forces. It is shown that by selecting an objectively dened origin of the moment-arm, the impulse force equation can be greatly simplied to two terms that have a clear physical meaning: (i) the time rate of change of impulse of vortical structures within the control volume and (ii) Lamb vector that indirectly captures the contribution of vortical structures outside of the control volume. The results show that the trend of the lift force is dependent on the formation of the leading edge vortex, as well as its time rate of change of circulation and chord-wise advection relative to the airfoil. Additionally, the trailing edge vortex, which is observed to only form for k  0:10, is shown to have lift-diminishing eects that intensies with increasing reduced frequency. Lastly, the concept of optimal vortex formation is investigated. The leading edge vortex is shown to attain the optimal formation number of approximately 4 for k  0:1, when the scaling is based on the leading edge shear velocity. For larger values of k the vortex growth is delayed to later in the cycle and doesn't reach its optimal value. The result is that the peak lift force occurs later in the cycle. This has consequences on power production which relies on correlation of the relative timing of lift force and heaving velocity. 

The effects of passive, inertia-induced surface deformation at the leading and trailing edges of an oscillating airfoil energy harvester are investigated experimentally at reduced frequencies of k = f c=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 deformation separately. It is shown that both forms of deformation may alter the leading edge vortex inception and detachment time scales, as well as the growth rate of the circulation. In addition, surface deformation 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 deforming leading and trailing edge segments are shown to increase the energy harvesting efficiency by approximately 17% and 25%, respectively. However, both the deforming 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 deforming 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 deforming trailing edge. 

Energy harvesting performance for a flapping foil device is evaluated to determine how activated leading edge motion affects the aerodynamic forces and the cycle power generated. Results are obtained for a thin flat foil that pitches about the midchord and operates in the reduced frequency range of k = f c/U of 0.06 - 0.10 and Reynolds numbers of 20,000 and 30,000 with a pitching amplitude of 70 and heaving amplitude of h0 = 0.5c. Time resolved data are presented based on direct force measurements and are used to determine overall cycle efficiency and coefficient of power. These results are compared against a panelbased discrete vortex model to predict power production. The model incorporates a leading edge suction parameter predictor for vortex shedding and empirical adjustments to circulatory forces. It is found that the leading edge motions that reduce the effective angle of attack early in a flapping stroke generate larger forces later in the stroke. Consequently, the energy harvesting efficiencies and power coefficients are increased since the generated aerodynamic loads are better synchronized with the foil motion. The efficiency gains are reduced with increasing reduced frequencies.