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1. Effect of Actively-Controlled Trailing Edge Flap Upon Airfoil Energy Harvester

   https://doi.org/10.1115/FEDSM2022-87577  

   Strahl, Jordan; Liburdy, James (August 2022, Proceedings of the ASME 2022 Fluids Engineering Division Summer Meeting)

   Abstract An experimental study was undertaken to evaluate the power extraction of an airfoil undergoing large amplitude pitching and heaving using a trailing edge flapping motion for the application of energy harvesting for steady flow over the airfoil. The airfoil was a NACA0015 design, pitching at the 1/3 chord position, with an actively controlled trailing edge flap hinged at the 2/3 chord location (chord length of c = 150mm and aspect ratio AR = 2, however end plates were used to simulate a two-dimensional airfoil). Data were obtained over a range of wind speeds corresponding to Reynolds numbers in the 30,000–60,000 range in a low-speed wind tunnel with turbulence intensities below 2%. The results are characterized using the reduced frequency, k = fc/U∞ over the range of 0.04–0.08, where f is the oscillating frequency in Hz, and U∞ is the freestream velocity. The pitching and heaving amplitudes are θ0 = 70° and h0 = 0.6c respectively, with a phase delay of 90°. Two trailing edge motion profiles are presented, examining the relative phase of trailing edge flap to the pitching phase. For each motion, a positive and negative case are considered. This is a total of 4 trailing edge motion profiles. Trailing edge motion amplitudes of 20° and 40° are compared and results contrasted. Direct transient force measurements were used to obtain the cycle variation of induced aerodynamic loads (lift coefficient) as well as the power output and efficiency. Results are used to identify the influence of trailing edge flap oscillations on the overall performance for energy harvesting, with a maximum efficiency increase of 21.3% and corresponding cycle averaged heaving power coefficient increase of 29.9% observed as a result of trailing edge motion. 

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

   https://doi.org/10.1115/1.4056339  

   Kamrani Fard, Kiana; Ngo, Vickie; Pence, Deborah; Liburdy, Jim A. (November 2022, Journal of Fluids Engineering)

   Abstract 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. 

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3. Experimental Study of Inertia-based passive Deformation of a Heaving and Pitching Airfoil Operating in the Energy Harvesting Regime

   Siala, F.F.; Fard, K.; Liburdy, J.A. (October 2019, Physics of fluids)

   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. 

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4. On the noise generation and unsteady performance of combined heaving and pitching foils

   https://doi.org/10.1088/1748-3190/acd59d  

   Wagenhoffer, Nathan; Moored, Keith W.; Jaworski, Justin (May 2023, Bioinspiration & Biomimetics)

   Abstract A transient two-dimensional acoustic boundary element solver is coupled to a potential flow boundary element solver via Powell's acoustic analogy to determine the acoustic emission of isolated hydrofoils performing biologically-inspired motions. The flow-acoustic boundary element framework is validated against experimental and asymptotic solutions for the noise produced by canonical vortex-body interactions. The numerical framework then characterizes the noise production of an oscillating foil, which is a simple representation of a fish caudal fin. A rigid NACA 0012 hydrofoil is subjected to combined heaving and pitching motions for Strouhal numbers ($0.03 < St < 1$) based on peak-to-peak amplitudes and chord-based reduced frequencies ($0.125 < f^* < 1$) that span the parameter space of many swimming fish species. A dipolar acoustic directivity is found for all motions, frequencies, and amplitudes considered, and the peak noise level increases with both the reduced frequency and the Strouhal number. A combined heaving and pitching motion produces less noise than either a purely pitching or purely heaving foil at a fixed reduced frequency and amplitude of motion. Correlations of the lift and power coefficients with the peak root-mean-square acoustic pressure levels are determined, which could be utilized to develop long-range, quiet swimmers. 

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5. WAKE STRUCTURES AND EFFECT OF HYDROFOIL SHAPES IN EFFICIENT FLAPPING PROPULSION

   Kelly, J. (August 2021, ASME Fluids Engineering Division Summer Meeting)

   In this work, direct numerical simulation (DNS) is used to investigate how airfoil shape affects wake structure and performance during a pitching-heaving motion. First, a classshape transformation (CST) method is used to generate airfoil shapes. CST coefficients are then varied in a parametric study to create geometries that are simulated in a pitching and heaving motion via an immersed boundary method-based numerical solver. The results show that most coefficients have little effect on the propulsive efficiency, but the second coefficient does have a very large effect. Looking at the CST basis functions shows that the effect of this coefficient is concentrated near the 25% mark of the foils chord length. By observing the thrust force and hydrodynamic power through a period of motion it is shown that the effect of the foil shape change is realized near the middle of each flapping motion. Through further inspection of the wake structures, we conclude that this is due to the leading-edge vortex attaching better to the foil shapes with a larger thickness around 25% of the chord length. This is verified by the pressure contours, which show a lower pressure along the leading edge of the better performing foils. The more favorable pressure gradient generated allows for higher efficiency motion. 

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