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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. Efficient aquatic locomotion using elastic propulsors with hybrid actuation

   https://doi.org/10.1017/jfm.2021.558  

   Demirer, Ersan ; Oshinowo, Oluwafikayo A. ; Alexeev, Alexander ( September 2021 , Journal of Fluid Mechanics)

   null (Ed.)

   Using computational modelling, we probe the hydrodynamics of a bio-inspired elastic propulsor with hybrid actuation that oscillates at resonance in a Newtonian fluid. The propulsor is actuated by a heaving motion at the base and by an internal bending moment distributed along the propulsor length. The simulations reveal that by tuning the phase difference between the external and internal actuation, the propulsor thrust and free-swimming velocity can be regulated in a wide range while maintaining high efficiency. Furthermore, the hybrid propulsor outperforms propulsors with either of the actuation methods. The enhanced performance is associated with the emerging bending pattern maintaining large tip displacement with reduced centre-of-mass displacement. The results are useful for developing highly efficient robotic swimmers utilizing smart materials as propulsors with simplified design and operation. 

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4. School cohesion, speed and efficiency are modulated by the swimmers flapping motion

   https://doi.org/10.1017/jfm.2021.551  

   Heydari, Sina ; Kanso, Eva ( September 2021 , Journal of Fluid Mechanics)

   Fish schools are ubiquitous in marine life. Although flow interactions are thought to be beneficial for schooling, their exact effects on the speed, energetics and stability of the group remain elusive. Recent numerical simulations and experimental models suggest that flow interactions stabilize in-tandem formations of flapping foils. Here, we employ a minimal vortex sheet model that captures salient features of the flow interactions among flapping swimmers, and we study the free swimming of a pair of in-line swimmers driven with identical heaving or pitching motions. We find that, independent of the flapping mode, heaving or pitching, the follower passively stabilizes at discrete locations in the wake of the leader, consistent with the heaving foil experiments, but pitching swimmers exhibit tighter and more cohesive formations. Further, in comparison to swimming alone, pitching motions increase the energetic efficiency of the group while heaving motions result in a slight increase in the swimming speed. A deeper analysis of the wake of a single swimmer sheds light on the hydrodynamic mechanisms underlying pairwise formations. These results recapitulate that flow interactions provide a passive mechanism that promotes school cohesion, and afford novel insights into the role of the flapping mode in controlling the emergent properties of the school. 

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5. 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)

   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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