Effects of Non-Uniform Stiffness on Propulsive Performance of Canonical and Bio-inspired Foils

Traditional underwater vehicle design is usually composed of a rigid hull and rotating propeller. The vehicle is driven by steady thrust produced from the rotation of the propeller. In the last 20 years, researchers have been inspired by biology to develop vehicle test platforms that use unsteady lift-based propulsion mechanisms for swimming. One common type of lift-based propulsion is body-caudal-fin (BCF) propulsion, where the fish contracts its body muscle to produce a side-way motion of its peduncle and caudal fin. To design a high-performance bio-inspired propulsor, fluid-structure interaction behind BCF swimming needs to be better understood before exploring the design space of a propulsor with high performance. The body and fins of fish are structures with non-uniform flexibility that undergo complex motion underwater. However, most previous studies have used simplified models regarding flexibility distribution or shape to study bio-inspired propulsion. The purpose of this dissertation is to study and develop new mechanical models with additional complexity compared to those, such as non-uniform flexibility distribution inspired by tuna peduncle and caudal fin rays.
In this dissertation, a combination of experimental and computational methods was employed to study the role of non-uniform stiffness in underwater propulsion, and its effects on propulsive performance and wake structure. Mechanical testing was employed to quantify the range of stiffness observed in biology, serving as guidance for design of experiments and simulation. A variety of propulsors with canonical and bio-inspired shapes were designed and tested under pure heave or pitch motion inside a water tunnel setup with uniform incoming flow. Propulsive performance including thrust, power, and efficiency were measured for each trial, and Particle Image Velocimetry (PIV) was used to visualize 2D/3D flow structure for certain cases of outlying performance. The data collected from water tunnel experiments were both used for validating the Computational Fluid Dynamics (CFD) solver and serving as baseline cases for the larger design space. Then CFD was employed to simulate additional kinematics and material design to help exploring propulsor design beyond biology or rapid prototyping capability.
With a simplified tuna tail model, the effects of phase offset and peduncle joint stiffness are studied. The results of computational study of phase offset show that a passively flexing foil is as efficient or more efficient than any foil model where the caudal peduncle is actively controlled. The experimental results show that although there is no one optimal peduncle stiffness across all parameter spaces, there are clear differences in performance due to peduncle stiffness. Design should be focused on the ability to actively modulate stiffness such that we can achieve optimal performance at any set of swimming parameters.
With simplified square and rectangular foil models, the effects of anisotropic stiffness and shape are studied. Results show that the square foils with pure chordwise stiffness distribution have overall higher thrust and efficiency than foils with pure spanwise stiffness distribution. When comparing all the square foils, the trend of efficiency versus frequency always has a local maximum within the range of frequencies tested. A highly flexible square foil (with similar properties as most flexible fish propulsor) has the highest efficiency at lower frequency. However additional stiffness is needed to maintain efficiency when frequency increases.