Session A08: Biofluids: General Locomotion I

Analysis of Shrimp Appendage Cupping on Swimming Performance through a Bio-inspired Model

Shrimp can adapt to their environment through dynamic morphology, contributing to their remarkable maneuverability and efficiency during swimming. Integral to this morphological adaptability of shrimp is the cupping of leg appendages (pleopods) during their power and recovery stroke. Cupping occurs through the change in the cupping angle between each endopodite and exopodite pair that make up a pleopod. This cupping angle contributes to the actuation of the exopodite to spread outward (abduction) during the power stroke and to move inward (adduction) during the recovery stroke. Previous studies have given insight into these pleopod kinematics. However, the optimal angle of pleopod cupping for different swimming modes and hydrodynamic conditions still needs to be explored. Here, we use biological studies of shrimp to guide the design of a robotic pleopod, which we leveraged to investigate the hydrodynamics of pleopod cupping. Through Particle Image Velocimetry (PIV) experiments and force measurements, we examine the thrust, lift, and vortex generation across a range of cupping angle configurations. We compare the cupping angle of optimal efficiency to the cupping angle found in shrimp (approximately 35°) to understand the trade-off between lift and thrust generation. Implementing the optimal cupping angle will ensure the maneuverability of future underwater metachronal robots under different environmental conditions.   

Integrated efficiency: a performance metric for oscillating appendages.

Current widely-used propulsion efficiency metrics depend on a moving body’s overall dynamics. For example, the Froude efficiency uses the body speed, thrust force, and input power. However, in many cases one must evaluate the performance of a globally fixed propulsor, which these efficiency metrics do not address. For example, behavioral experiments often use tethered animals, where swimming speed is not defined. Numerical simulations frequently target fixed appendages to lower computational costs. Robotic platforms usually begin their development at the propulsor scale when studying potential locomotion strategies. Here we present a new efficiency metric (the integrated efficiency) which considers the force and velocity distributions along an appendage. The integrated efficiency can be computed for propulsors independently from the full-body swimming dynamics, yielding additional useful performance data. We perform experiments on bio-inspired flexible robotic paddles, showing (via the integrated efficiency) how the propulsor’s deformed shape during the beat cycle impacts performance in producing thrust and lift. The integrated efficiency can be used to improve animal propulsion studies and as a design parameter for future bio-inspired robots and devices.   

Effects of varying number of paddles in a metachronal paddling system

Many aquatic invertebrates use a locomotion strategy known as "metachronal paddling" in which a series of appendages ("paddles") are stroked in a coordinated – but not synchronized – fashion. A number of previous studies have examined how the metachronal coordination of a fixed number of paddles can increase the propulsive forces relative to synchronous paddling. However, another interesting aspect of this strategy as observed in nature is that the number of paddles varies both across species and across stages of development – many crustaceans that employ metachronal locomotion undergo larval and juvenile development stages during which they grow additional swimming legs. In this study, we examine how changing the number of paddles affects the swimming speed, tip vortex dynamics and pressure in the wake of the metachronal paddling system. We found that increasing the number of paddles results in a decrease in circulation in the paddle-tip vortex generated during the paddle's thrust-generating power stroke, likely due to destructive interactions between high- and low-pressure zones on opposite sides of adjacent paddles. Additionally, we found that increasing the number of paddles resulted in linearly increased swimming speed, but a nonlinear decrease in swimming speed per paddle.   

Going around the bend to evaluate the role of coalescence in metachronal swimming

Metachronal swimming is achieved by sequentially beating closely spaced flexible appendages. The distinct differential stiffness of the appendages keeps them rigid during the power stroke to maximize thrust but enables significant bending during the recovery stroke. The effect bending has on the near flow and forces during the recovery stroke has received little attention despite being crucially important in reducing drag. We combine μ-CT measurements with in vivo velocimetry experiments on shrimp (Palaemonetes vulgaris) and their robotic analog to explore the underlying mechanisms enabling differential stiffness and drag reduction during metachrony. We find that the concave geometry of the legs (pleopods) makes them twice as flexible during the recovery versus the power stroke. Simultaneous kinematics and particle image velocimetry data show that bending enables inter-pleopod interactions causing three legs to coalesce at any time during the recovery stroke. Contrary to the power stroke, these complementary mechanisms shed no observable wake. We used these results to design a scaled robot with five morphologically accurate pleopod analogs mounted in series that integrate differential stiffness. We compare the thrust and drag forces against rigid pleopods to test the hypothesis that bending and coalescence effectively reduce the drag of three legs to that of only one. Considering appendage stiffness leverages our understanding of metachronal propulsion for designing novel underwater robots.   

Characteristics of flow field induced by a swimming calanoid copepod

Calanoid copepods are capable of switching swimming modes between feeding, cruising and intermittent jumping for different purposes in different environments. In this work, we report an experimental study of the flow fields induced by individual copepod (Pseudodiaptomus annandalei) swimming in a water layer without background flow, with the aid of a high-speed camera and particle image velocimetry technology. It is found that the characteristic length scales of the vortices induced by the cruising and jumping processes are 2.0±0.6 mm and 2.7±0.6 mm, respectively. However, the typical time scales for the vortex production (∼0.015s) and dissipation (∼0.15s) do not depend on the swimming behavior. The energy dissipation rate for these copepod-induced vortices is on the order of 10^-5 m²/s³. Interestingly, the flow fields induced by the feeding and jumping behaviors exhibit a -5/3 like scaling in their energy spectra, which is often reported in the inertial subrange of turbulent flows. The implications of the present results (based on individual level) for the movement pattern of population-level and in a turbulent environment will be discussed.   

Hydrodynamics of water entry for a bio-inspired array of horizontal cylinders at intermediate Reynolds numbers

Many organisms use arrays of long semi-parallel bristles to capture food and facilitate locomotion. The function of these bristled appendages depends on how fluid flows between adjacent bristles: they may be hydrodynamically solid “paddles” or porous “rakes”, depending on Reynolds number and bristle spacing. Some flying insects use such appendages to facilitate takeoff from the water surface; however, our understanding of bristled appendages at an air-water interface is limited, as previous work has been confined to fully submerged arrays. Inspired by the hairy legs of aerial-aquatic insects, we experimentally investigate the surface tension-dominated interaction of a parallel array of horizontally oriented cylinders with the air-water interface. We use high speed videography and Particle Image Velocimetry (PIV) to measure the deformation of the interface and the flow under the array across a range of intermediate Reynolds numbers, and explore the effects of cylinder spacing and impact velocity. We find that lower Re corresponds to more flow through the array, in contrast to previous work on submerged arrays. Our results provide insight into the biomechanics of aerial-aquatic locomotion as well as a new avenue for bio-inspired design in semi-aquatic environments.    

Propulsion through asymmetry: Examining flow-structure interactions of Ctenophore appendages with asymmetric stiffness

Ctenophores (or comb jellies) utilize multiple rows of flexible appendages known as ctenes for propulsion. Their unique propulsion mechanism relies on the metachronal beating of these ctenes. Unlike a rigid oar that moves back and forth in water, these ctenes exhibit an asymmetrical beating pattern that allows ctenophores to move effectively through their aquatic environments. The ctenes display a difference in flexibility during the power stroke and the recovery stroke. The ctenes are stiffer during the power stroke, enabling them to generate a stronger propulsive force. During the recovery stroke, the ctenes become more flexible, which reduces drag, allowing the ctenophore to maintain its forward momentum. This study delves into the intriguing mechanics of ctenophore propulsion, focusing on the role of asymmetric stiffness in effective propulsion. For this, we combined an existing in-house immersed-boundary-method-based flow solver with a nonlinear finite-element solid-mechanics solver for three-dimensional fluid-structure interaction (FSI) simulations. The FSI is achieved through a two-way coupling method. This study aims to provide valuable insights for bio-inspired engineering, particularly for designing underwater robots, indicating the potential to enhance propulsion efficiency through flexible and asymmetrical structures.   

Lift-based propulsion for fastest-swimming whirligig beetles (Gyrinidae)

Whirligig beetles, Gyrinidae, are the fastest swimmers among insects. This one-centimeter-long aquatic beetle can achieve a peak acceleration of 100 ms^-2 and a top velocity of 1 ms^-1. The swimming mechanisms of the whirligig have been previously studied in a tethered state, which suggested that their oar-like rudder legs create drag for propulsion. In our study, we present leg and body kinematics of Dineutus discolor to show that the thrust generation in high-speed free swimming relies on lift. We found that the rudder legs had nearly no motion relative to the surrounding fluid along the axis of swimming. Instead, the legs were subjected to drastic transverse motions, in which large lift force was generated. Our force estimation suggests that the lift associated with the transverse leg motions is comparable to the thrust required for overcoming hydrodynamic drag and generating large acceleration.