Harnessing Acoustic Black Hole Effect in Elastic Propulsors to Achieve Efficient Undulatory Locomotion*

Fish have evolved to various forms of swimming to better adapt to diverse environments and flow conditions. Anguilliform fish such as eel rely on travelling waves to achieve high efficiency in low to moderate Reynolds number flows. Tthunniform fish such as tuna almost exclusively use standing waves for fast locomotion at higher Reynolds numbers. Thus, traveling waves are of particular interest for developing efficient biomimetic robotic swimmers. However, generating traveling waves in finite-sized structures is far from being a trivial task. Here, we use the acoustic black hole (ABH) effect, a phenomenon arising in tapered structures that prevents wave reflection at the free end and therefore yields traveling flexural waves, to design biomimetic propulsors with a superior hydrodynamic efficiency. Using three-dimensional fully-coupled fluid structure interaction simulations, we demonstrate that ABH is an effective solution to generate travelling waves even in relatively short propulsors and can indeed drastically improve their hydrodynamic performance. We demonstrate this by modeling propulsors with different thickness profiles and characterizing their hydrodynamics as a function of their standing to traveling wave ratios.