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A Numerical Determination Of Bifurcation Points For Low Reynolds Number Conical Flows, Larry K. Waters
A Numerical Determination Of Bifurcation Points For Low Reynolds Number Conical Flows, Larry K. Waters
Theses and Dissertations
It has long been established that supersonic flow over axisymmetric conical bodies at high angles of attack tend to develop a side force due to vortical asymmetry. One of the proposed reasons for the asymmetry is a bifurcation point in the solution of the Navier-Stokes equations. This study investigated the possible existence of a bifurcation point in the Navier-Stokes equations for subsonic flow. Newton's method, with gauss elimination, was used- to solve the steady-state, viscous, compressible Navier-Stokes equations in spherical coordinates assuming conical similarity.
Hoph Bifurcation In Viscous, Low Speed Flows About An Airfoil With Structural Coupling, Mark J. Lutton
Hoph Bifurcation In Viscous, Low Speed Flows About An Airfoil With Structural Coupling, Mark J. Lutton
Theses and Dissertations
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.