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1. 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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2. Effect of Actively-Controlled Trailing Edge Flap Upon Airfoil energy Harvesting

   Strahl, J. (April 2022, ASME Fluids Division Summer Meeting)

   The application of a flapping foil with prescribed trailing edge motion to energy harvesting in a low reduced frequency (k = fc/U∞) regime was experimentally studied. The effects of the phase and amplitude of the applied trailing edge motion upon time-variant power extraction capability have been measured and are interpreted. On these bases, an optimized motion profile is developed. The airfoil design used was NACA0015 in profile with a chord length of c = 150mm, the pitching axis located at the 1/3 chord position, and an actively-controlled trailing edge flap hinged at the 2/3 chord location. The pitching and heaving amplitudes are θ0 = 70◦ and h0 = 0.6c respectively, with a phase delay of 90◦. Although the aspect ratio was 2, end plates were used to minimize 3-dimensional effects and simulate a 2-dimensional airfoil. Data were collected in a low-speed wind tunnel with turbulence intensities below 2%. The Reynolds number (Rec = U∞c/ν) range was 27, 000 ≤ Rec ≤ 60, 000 with a corresponding reduced frequency range of 0.04 ≤ k ≤ 0.10. The proposed trailing edge motion profile offers a measured maximum increase of 25.6% in cycle-averaged heaving power coefficient over a rigid foil operating under the same conditions. Results indicate that smaller trailing edge amplitudes offer greater improvements, and demonstrate that the influence of trailing edge motion can be more pronounced at low reduced frequencies. 

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3. 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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4. Discrete Vortex Modeling of a Flapping Foil with Activated Leading Edge Motion

   Prier, M.W.; Liburdy, J.A. (July 2019, ASME-JSME-KSME 2019 Joint Fluids Conference)

   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. 

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5. Prediction of energy harvesting efficiency through a wake–foil interaction model for oscillating foil arrays

   https://doi.org/10.1017/jfm.2024.803  

   Ribeiro, Bernardo_Luiz R; Franck, Jennifer A (October 2024, Journal of Fluid Mechanics)

   This research investigates the wake–foil interactions between two oscillating foils in a tandem configuration undergoing energy harvesting kinematics. Oscillating foils have been shown to extract hydrokinetic energy from free-stream flows through a combination of periodic heave and pitch motions, at relatively higher amplitudes and lower reduced frequency than thrust generating foils. When placed in tandem, the wake–foil interactions can govern the energy harvesting efficiency of the system due to a reduced relative flow velocity in combination with a structured and coherent wake of vortices shed from the high amplitude flapping of upstream foils. This work utilizes simulations of two tandem foils to parameterize and model the energy harvesting performance as a function of array configuration and foil kinematics. Once the wake of the leading foil has been fully parameterized, the placement, phase angle and kinematic stroke of the second foil is utilized to estimate the time-dependent power curve. The algorithm predicts the power of the second foil through the mean and unsteady wake characteristics, including the direct impingement of a vortex with the trailing foil. 

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