Bio-inspired propulsion: vortex ring formation from varied flexibility nozzles and modal dynamics of plunging tapered hydrofoils

Abstract

Many aquatic animals and flying insects rely on flexible bodies and appendages for efficient locomotion. The flexibility inherent in these organisms has been linked to increased thrust and efficiency across diverse operating conditions. In this work, two bio-inspired propulsion mechanisms are examined: the first investigates pulses of fluid ejected through nozzles of varying flexibility, and the second explores a tapered flexible foil subjected to varied heaving amplitudes. Jellyfish, squid, and siphonophores move by periodically contracting and expanding their bodies to expel and refill fluid from a flexible orifice, producing a series of vortex rings and stopping vortices. In this study, different volumes of fluid are ejected into a quiescent water tank through nozzles of varied stiffness to create vortex rings. Particle Image Velocimetry (PIV) is used to quantify thrust, and Finite-time Lyapunov Exponent (FTLE) fields are calculated to determine vortex ring pinch-off. It is found that the flexible nozzle stores and imparts elastic energy to the fluid, increasing the impulse of the ejected vortex ring. Impulse per unit volume is maximized at an optimal nozzle stiffness, wherein the damped natural frequency of the nozzle matches the fluid acceleration time. When the fluid decelerates, the more compliant nozzles collapse, suppressing unfavorable negative pressure regions from forming and instead eject additional fluid. Upon reopening, beneficial stopping vortices form within the nozzle, with circulation increasing with nozzle stiffness, indicating a second optimal stiffness criterion for a full expulsion-refill cycle analysis of this propulsion mechanism. The flexural rigidity observed in insect wings and fish fins is commonly nonuniform and typically decreases from leading to trailing edge. This variation in stiffness encourages the propagation of traveling waves along the structure, increasing propulsive performance over a wider frequency range. In this study, rectangular foils undergo a sinusoidal heaving motion with varied amplitude and frequency. 2D mode shapes and resonant frequencies are measured using a scanning laser vibrometer. PIV is used to quantify the thrust from the wake of the foil. The traveling wave behavior is quantified and correlated with the thrust measured in the foil wake.