DOI: 10.25549/usctheses-c40-357049
title: Analyzing the aerodynamics and stability of Λ-flyers in oscillatory flows

description: Fluid-structure interactions are ubiquitous in natural and artificial environments. Examples range from biological locomotion—birds and insects flying—to engineering oriented systems such as micro-air vehicles. Understanding the wing-air interactions in biological systems is crucial to the design of bio-inspired engineering robots. Animal flight is the result of intertwined complex mechanisms, including sensory feedback, neural control, muscular actuation and aerodynamics, all combined to produce remarkable flight agility and robustness. Developing an understanding of flapping flight at each of these layers presents its unique challenges. At the flight mechanics level, passively flying bodies, that is to say, bodies moving solely under the influence of gravitational and aerodynamic forces with no internal actuation, have been proposed as surrogates to the flapping flight problem, given the vortical structures in the passive problem are similar to those shed in the active flapping problem. The substitution of the active flight problem by a passive analog can be particularly attractive because it simplifies the study of fluid-structure interactions and facilitates the analysis of passive stability. More specifically in this thesis, dynamics of rigid and elastic flyers in oscillatory flows are studied to unveil the flight behavior and its intrinsic or passive stability. The findings have profound implications on understanding the flight dynamics in live organisms as well as on the design of air-vehicles or other fluid devices. ❧ First, a two dimensional rigid Λ-flyer subject to gravity is considered in an oscillatory background flow of zero mean velocity. Recent experiments on inanimate pyramid-shaped objects in oscillating flows with zero mean component demonstrate that the resulting aerodynamic forces are sufficient to keep the object aloft. The mechanisms responsible for this lift production are fundamentally unsteady and depend on the shed vorticity. The unsteady, two-way coupling between the flyer and the surrounding fluid is computed in the context of an inviscid vortex sheet model. Hovering conditions are then examined in terms of four dimensionless parameters: mass, opening angle of the flyer, and oscillation amplitude, acceleration of the flow. The parameter values required for hovering indicate that at low oscillation frequencies, a flyer of fixed mass and shape requires a constant amount of flow acceleration to hover, irrespective of the frequency and speed of the oscillating flow. Meanwhile, at high oscillation frequencies, the flow speed required to hover is a constant. In either case, the aerodynamic hovering requirement—flow acceleration or flow speed—is an intrinsic property of the flyer itself. This physical insight could potentially imply that live organisms can manipulate their flapping motion to favor a larger oscillation amplitude or frequency. Next, the interplay between maneuverability and stability is explored in terms of two parameters: the flyer's shape and the aerodynamic effort, namely the flow acceleration. Optimal shapes are found to minimize the aerodynamic effort. A transition from unstable to stable hovering occurs post-optimal, that is to say, at increased aerodynamic effort. This result indicates that no extra effort, or even decreasing effort, is needed for a flyer to switch from stable to unstable, yet maneuverable state. ❧ Second, intrinsic flapping dynamics of a two dimensional elastic Λ-flyer—an insectile wing model—is investigated without aerodynamic effects. Insects use flight muscles attached at the base of the wings to produce impressive wing flapping frequencies. Inspired by this, an elastic torsional spring is added at the apex of the rigid flyer to construct the elastic wing system. The intrinsic self-oscillatory behavior of this insectile wing model is studied with the wing base fixed at a point and is examined as a function of the total energy and spring stiffness. Three types of behavior are identified: end-over-end rotation, chaotic motion, and periodic flapping. Interestingly, the Poincare section of periodic flapping decreases as energy increases but is favored as stiffness increases. These findings are consistent with the fact that insect wings and flight muscles are stiff. They further imply that, by adjusting their muscle stiffness to the desired energy level, insects can maintain periodic flapping mechanically for a range of operating conditions. ❧ Third, the dynamics of the elastic flyer placed in an oscillatory flow are studied under the effects of aerodynamics. In the context of the unsteady vortex sheet model, the flyer's flapping and rolling motions are explored according to five properties: mass, spring rest angle and spring stiffness of the flyer, and oscillation amplitude and acceleration of the background flow. With flapping amplitude and elastic energy storage as the two measurement metrics, flapping performance achieves an optimum at a finite spring stiffness, different from the value for resonance occurrence. Therefore, rather than resonance, the flyer relies on aerodynamic effects to improve flapping performance. Next, the flyer's rolling behavior falls into four categories: monostable, bistable, bistable oscillations and chaotic. Monostable flyers have the vertically-down position as its stable state; whereas, bistable flyers and bistable oscillations can also achieve the vertically-up stable position. These types of behavior are mapped onto spaces of flyer and flow parameters and the results show that the three stable types of behavior opt for lower oscillation amplitude of the background flow. These findings suggest one can indirectly tune the background flow oscillations to softly control flyers of specified properties for achieving the desired behavior.