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1. Effect of Nonuniform Flexibility on Hydrodynamic Performance of Pitching Propulsors

   https://doi.org/10.1115/1.4041976  

   Zeyghami, Samane ; Moored, Keith W. ( April 2019 , Journal of Fluids Engineering)

   Many aquatic animals propel themselves efficiently through the water by oscillating flexible fins. These fins are, however, not homogeneously flexible, but instead their flexural stiffness varies along their chord and span. Here, we develop a simple model of these functionally graded materials where the chordwise flexibility of the foil is modeled by one or two torsional springs along the chord line. The torsional spring structural model is then strongly coupled to a boundary element fluid model to simulate the fluid–structure interactions. We show that the effective flexibility of the combined fluid–structure system scales with the ratio of the added mass forces acting on the passive portion of the foil and the elastic forces defined by the torsional spring hinge. Importantly, by considering this new scaling of the effective flexibility, the propulsive performance is then detailed for a foil with a flexible hinge that is actively pitching about its leading edge. The scaling allows for the resonance frequency of the fluid–structure system and the bending pattern of the propulsor to be independently varied by altering the effective flexibility and the location of a single torsional spring along the chord, respectively. It is shown that increasing the flexion ratio, by moving the spring away from the leading edge, leads to enhanced propulsive efficiency, but compromises the thrust production. Proper combination of two flexible hinges, however, can result in a gain in both the thrust production and propulsive efficiency. 

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2. 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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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. Geometric Characteristics of Flapping Foils for Enhanced Propulsive Efficiency

   https://doi.org/10.1115/1.4057018  

   Kelly, J. ; Khalid, M. S. ; Han, P. ; Dong, H. ( June 2023 , Journal of Fluids Engineering)

   The shape of a foil undergoing a combined pitching heaving motion is critical to its design in applications that demand high efficiency and thrust. This study focuses on understanding of how the shape of a foil affects its propulsive performance. We perform two-dimensional numerical simulations of fluid flows around a flapping foil for different governing parameters in the range of biological swimmers and bio-inspired underwater vehicles. By varying the foil shape using a class-shape transformation method, we investigate a broad range of foil-like shapes. In the study, we also show consistent results with previous studies that a thicker leading-edge and sharper trailing-edge makes for a more efficient foil shape undergoing a flapping motion. In addition, we explain that the performance of the foil is highly sensitive to its shape, specifically the thickness of the foil between the 18th and 50th percent along the chord of the foil. Moreover, we elucidate the flow mechanisms behind variations in performance metrics, particularly focused on constructive interference between the vortices generated at the leading-edge with the trailing-edge vortex, as well as the pressure field differences that lead to higher power consumption in less efficient foil shapes. 

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5. Experimental Investigation of the Unsteady Aerodynamics of Oscillating Airfoils in the Energy Harvesting Regime

   Siala, F.F ( July 2019 , Dissertation)

   The rising global trend to reduce dependence on fossil fuels has provided significant motivation toward the development of alternative energy conversion methods and new technologies to improve their efficiency. Recently, oscillating energy harvesters have shown promise as highly efficient and scalable turbines, which can be implemented in areas where traditional energy extraction and conversion are either unfeasible or cost prohibitive. Although such devices are quickly gaining popularity, there remain a number of hurdles in the understanding of their underlying fluid dynamics phenomena. The ability to achieve high efficiency power output from oscillating airfoil energy harvesters requires exploitation of the complexities of the event of dynamic stall. During dynamic stall, the oncoming flow separates at the leading edge of the airfoil to form leading ledge vortex (LEV) structures. While it is well known that LEVs play a significant role in aerodynamic force generation in unsteady animal flight (e.g. insects and birds), there is still a need to further understand their spatiotemporal evolution in order to design more effective energy harvesting enhancement mechanisms. In this work, we conduct extensive experimental investigations to shed-light on the flow physics of a heaving and pitching airfoil energy harvester operating at reduced frequencies of k = fc=U1 = 0.06-0.18, pitching amplitude of 0 = 75 and heaving amplitude of h0 = 0:6c. The experimental work involves the use of two-component particle image velocimetry (PIV) measurements conducted in a wind tunnel facility at Oregon State University. Velocity fields obtained from the PIV measurements are analyzed qualitatively and quantitatively to provide a description of the dynamics of LEVs and other flow structures that may be present during dynamic stall. Due to the difficulties of accurately measuring aerodynamic forces in highly unsteady flows in wind tunnels, a reduced-order model based on the vortex-impulse theory is proposed for estimating the aerodynamic loadings and power output using flow field data. The reduced-order model is shown to be dominated by two terms that have a clear physical interpretation: (i) the time rate of change of the impulse of vortical structures and (ii) the Kutta-Joukowski force which indirectly represents the history effect of vortex shedding in the far wake. Furthermore, the effects of a bio-inspired flow control mechanism based on deforming airfoil surfaces on the flow dynamics and energy harvesting performance are investigated. The results show that the aerodynamic loadings, and hence power output, are highly dependent on the formation, growth rate, trajectory and detachment of the LEV. It is shown that the energy harvesting efficiency increases with increasing reduced frequency, peaking at 25% when k = 0.14, agreeing very well with published numerical results. At this optimal reduced frequency, the time scales of the LEV evolution and airfoil kinematics are matched, resulting in highly correlated aerodynamic load generation and airfoil motion. When operating at k > 0:14, it is shown that the aerodynamic moment and airfoil pitching motion become negatively correlated and as a result, the energy harvesting performance is deteriorated. Furthermore, by using a deforming airfoil surface at the leading and trailing edges, the peak energy harvesting efficiency is shown to increase by approximately 17% and 25% relative to the rigid airfoil, respectively. The performance enhancement is associated with enhanced aerodynamic forces for both the deforming leading and trailing edges. In addition, The deforming trailing edge airfoil is shown to enhance the correlation between the aerodynamic moment and pitching motion at higher reduced frequencies, resulting in a peak efficiency at k = 0:18 as opposed to k = 0:14 for the rigid airfoil. 

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