Dynamical System Representation and Analysis of Unsteady Flow and Fluid-Structure Interactions
Hussein, Ahmed Abd Elmonem Ahmed
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A dynamical system approach is utilized to reduce the representation order of unsteady fluid flows and fluid-structure interaction systems. This approach allows for significant reduction in the computational cost of their numerical simulations, implementation of optimization and control methodologies and assessment of their dynamic stability. In the first chapter, I present a new Lagrangian function to derive the equations of motion of unsteady point vortices. This representation is a reconciliation between Newtonian and Lagrangian mechanics yielding a new approach to model the dynamics of these vortices. In the second chapter, I investigate the flutter of a helicopter rotor blade using finite-state time approximation of the unsteady aerodynamics. The analysis showed a new stability region that could not be determined under the assumption of a quasi-steady flow. In the third chapter, I implement the unsteady vortex lattice method to quantify the effects of tail flexibility on the propulsive efficiency of a fish. I determine that flexibility enhances the propulsion. In the fourth chapter, I consider the stability of a flapping micro air vehicle and use different approaches to design the transition from hovering to forward flight. I determine that first order averaging is not suitable and that time periodic dynamics are required for the controller to achieve this transition. In the fifth chapter, I derive a mathematical model for the free motion of a two-body planar system representing a fish under the action of coupled dynamics and hydrodynamics loads. I conclude that the psicform fish family are inherently stable under certain conditions that depend on the location of the center of mass.
General Audience Abstract
We present modeling approaches of the interaction between flying or swimming bodies and the surrounding fluids. We consider their stability as they perform special maneuvers. The approaches are applied to rotating blades of helicopters, fish-like robots, and micro-air vehicles. We develop and validate a new mathematical representation for the flow generated by moving or deforming elements. We also assess the effects of fast variations in the flow on the stability of a rotating helicopter blade. The results point to a new stable regime for their operation. In other words, the fast flow variations could stabilize the rotating blades. These results can also be applied to the analysis of stability of rotating blades of wind turbines. We consider the effects of flexing a tail on the propulsive force of fish-like robots. The results show that adding flexibility enhances the efficiency of the fish propulsion. Inspired by the ability of some birds and insects to transition from hovering to forward motion, we thoroughly investigate different approaches to model and realize this transition. We determine that no simplification should be applied to the rigorous model representing the flapping flight in order to model transition phenomena correctly. Finally, we model the forward-swim dynamics of psciform and determine the condition on the center of mass for which a robotic fish can maintain its stability. This condition could help in designing fish-like robots that perform stable underwater maneuvers.
- Doctoral Dissertations