Abstract
It is well known that swimming and flying near planar boundaries can lead to propulsive benefits. Steady ground effect reduces drag on fixed wing aircraft and lowers the cost of transport and increases range for animals, such as brown pelicans, herring gulls, black skimmers, etc. On the other hand, unsteady ground effect can cause near-boundary oscillating rigid and flexible hydrofoils to experience thrust benefits with little to no cost in efficiency. However, there has not been a systematic study on how different foil/fin kinematics and shapes take advantage or get penalized by the ground effect.
First, we explore the effect of asymmetric kinematics in the presence of ground effect. When swimming near a solid planar boundary, bio-inspired propulsors can naturally equilibrate to certain distances from that boundary. How these equilibria are affected by asymmetric swimming kinematics is unknown. We present here a study of near-boundary pitching hydrofoils based on water channel experiments and potential flow simulations. We found that asymmetric pitch kinematics do affect near-boundary equilibria, resulting in the equilibria shifting either closer to or away from the planar boundary. The magnitude of the shift depends on whether the pitch kinematics have spatial asymmetry (e.g. a bias angle, $\theta_0$) or temporal asymmetry (e.g. a stroke-speed ratio, $\tau$). Swimming at stable equilibrium requires less active control, while shifting the equilibrium closer to the boundary can result in higher thrust with no measurable change in propulsive efficiency.
Another set of different kinematics that we want to examine is the oscillation and undulation motions inspired by stingray locomotion. It is also found that this difference in swimming kinematics leads to many other distinctive differences among the batoid species, such as fin shapes (i.e. triangular, round, elliptical) and natural habitat (i.e. ground proximity). Near the ground, rays tend to be more undulatory (wave number $ > 1$) with round or elliptical pectoral fins; while far from the ground, rays tend to be more oscillatory (wave number $ < 1$) with pectoral fins shaped more like a triangle or birds' wings. We wonder how these differences in kinematics and morphology interact with each other, the surrounding fluid systems, and near-by solid boundaries to realize hydrodynamic benefits or penalties while swimming.
Even though many biologists and fluid dynamicists have proposed the correlation between batoid kinematics and morphology, it has not been systematically studied for decades due to complicated design requirements and challenges. This leads to the development of a first-of-kind stingray-inspired robotic propulsion platform, that overcomes many traditional design challenges to study batoid-inspired differences in fin kinetics and morphology. Through intricate components, such as the modular cam train system, Scotch-Yoke pitching mechanism, and swivel plate pivot system, this platform has the versatility to vary wave number, frequency ($St$), amplitude, and fin shape, allowing us to study a spectrum of fin motions running from oscillation to undulation while being able to alternate different fin shapes.
Furthermore, the stingray-inspired platform is integrated with force and torque sensors, an encoder, and a 3-axis traverse system to conduct direct force measurements at varying ground distances. In combination with multiple sets of Stereoscopic Particle Image Velocimetry (SPIV) experiments, potential flow simulations and force decomposition, and three-dimensional (3D) viscous simulations, we aim to study the force enhancement in the presence of ground effect, how wake structures differs across different swimming motions or fin shapes, and most importantly how do these parameters interact with each other.
This work reveals how different swimming kinematics or shapes could be used to alter the desired outcome with a nearby solid boundary, and it offers a starting point for understanding how stingray evolutionarily and hydro-dynamically use their environment to their advantage, whether it is to station-keep or swim at a high speed. This work can serve as a road-map on how one tested parameter may outperform another in a given situation and benefit not only the bio-inspired fluid mechanics community but also inspire the further study of stingray morphology and kinematics and biologically relevant robotic systems design.
