Unsteady Aerodynamics of Airfoils and Characterization and Modeling of Axisymmetric Synthetic Jets

This thesis has two main parts. The aerodynamic part is motivated by the interest in unveiling the flying secrets of natural fliers, e.g. birds and insects. The understandings will provide insights in the design and control of micro air vehicles (MAVs) for improved aerodynamic performance. The second part of the thesis focuses on the study of synthetic jets for aerodynamic flow control over MAVs. This is motivated by the promising effects of synthetic jets in enhancing mixing and controlling flow separation.

The thesis starts with the unsteady aerodynamic modeling of a flat plate based on the Joukowski transformation and vortex method. The analytical solution includes both translational and rotational motions of the flat plate. The force calculation suggests that the lift generation caused by a stabilized leading edge vortex is a combined effect of the motions of both leading-edge and trailing-edge vortices. To extend this model to an arbitrarily-shaped airfoil, the wall boundary condition on the airfoil is enforced by introducing a bound vortex sheet at the location of the airfoil boundary. Furthermore, an analytical vortex-sheet formation condition is proposed to accurately evolve the wake vortices, and is based on the conservation laws of mass and momentum as well as Kelvin's circulation theorem. This condition resolves the paradox of the Giesing-Maskell model, which does not recover the steady-state Kutta condition.

The thesis continues with an investigation of synthetic jets in a quiescent environment. An effective-eddy-viscosity concept is adopted to provide a unified modeling approach for the entrainment and mixing of any round jet, continuous or synthetic. The experimental study is focused on characterizing the spreading and decay features in the transitional region and far field of synthetic jets. The far-field momentum flux of a synthetic jet is modeled by calculating the hydrodynamic impulse of the vortical structure formed in the near field. Synthetic jets issuing into a crossflow are also studied and a self-similar model is developed for the trajectory and velocity of the midplane flow field. It is found that the crossflow velocity is enhanced in the near field due to the induced effect of the tilted vortex rings. This finding provides an auxiliary explanation for the mechanism of a synthetic jet in flow-separation control.

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