Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Aeronautics and Astronautics

First Advisor

Philip S. Beran, PhD


The locations of Hopf bifurcation points associated with the viscous, incompressible flow about a NACA 0012 airfoil with structural coupling are computed for very low Reynolds numbers (<2000). A semi-implicit, first-order-accurate time integration algorithm is employed to solve the stream function-vorticity form of the Navier-Stokes equations. The formulation models the inclusion of simple structural elements affixed to the airfoil and captures the resulting airfoil motion. The equations describing the airfoil motion are integrated in time using a fourth-order Runge-Kutta algorithm. The dissertation is divided into two parts. In part one, numerical experiments are performed in the laminar regime to determine if the structural model of the airfoil has an effect upon the location of the Hopf bifurcation point when compared with the fixed airfoil. Results are reported for a variety of structural characteristics, including variations of torsional and linear spring constants, inertial properties, structural coupling, and structural damping. The structure of the solution space is explored by means of phase plots. In part two, the Baldwin-Lomax turbulence model is implemented to model turbulent flow. A numerical effort is made to predict the onset of unsteady flow.

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The author's Vita page is omitted.