Date of Award
Doctor of Philosophy (PhD)
Department of Aeronautics and Astronautics
Philip S. Beran, PhD
The three-dimensional, compressible Navier-Stokes equations are solved numerically to simulate vortex breakdown in tubes. Time integration is performed with an implicit Beam-Warming algorithm, which uses fourth-order compact operators to discretize spatial derivatives. Initial conditions are obtained by solving the steady, compressible, and axisymmetric form of the Navier-Stokes equations using Newton's method. Stability of the axisymmetric initial conditions is assessed through 3-D time integration. Unique axisymmetric solutions at a Reynolds number of 250 lose stability to 3-D disturbances at a critical value of vortex strength, resulting in 3-D and time-periodic flow. Axisymmetric solutions at a Reynolds number of 1000 contain regions of nonuniqueness. Within this region, 3-D time integration reveals only unique solutions, with nonunique, axisymmetric initial conditions converging to a unique solution that is steady and axisymmetric. Past the primary limit point, which approximately identifies critical flow, the solutions bifurcate into 3-D periodic flows.
DTIC Accession Number
Tromp, Jeffrey C., "The Dependence of the Time-Asymptotic Structure of 3-D Vortex Breakdown on Boundary and Initial Conditions" (1995). Theses and Dissertations. 6318.