Doctoral Dissertations
Date of Award
8-2011
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Major
Aerospace Engineering
Major Professor
Joseph Majdalani
Committee Members
Trevor Moeller, Roy Schulz, Christian Parigger
Abstract
State of the art research in hydrodynamic stability analysis has moved from classic one-dimensional methods such as the local nonparallel approach and the parabolized stability equations to two-dimensional, biglobal, methods. The paradigm shift toward two dimensional techniques with the ability to accommodate fully three-dimensional base flows is a necessary step toward modeling complex, multidimensional flowfields in modern propulsive applications. Here, we employ a two-dimensional spatial waveform with sinusoidal temporal dependence to reduce the three-dimensional linearized Navier-Stokes equations to their biglobal form. Addressing hydrodynamic stability in this way circumvents the restrictive parallel-flow assumption and admits boundary conditions in the streamwise direction. Furthermore, the following work employs a full momentum formulation, rather than the reduced streamfunction form, accounting for a nonzero tangential mean flow velocity. This approach adds significant complexity in both formulation and implementation but renders a more general methodology applicable to a broader spectrum of mean flows. Specifically, we consider the stability of three models for bidirectional vortex flow. While a complete parametric study ensues, the stabilizing effect of the swirl velocity is evident as the injection parameter, kappa, is closely examined.
Recommended Citation
Batterson, Joshua Will, "The Biglobal Instability of the Bidirectional Vortex. " PhD diss., University of Tennessee, 2011.
https://trace.tennessee.edu/utk_graddiss/1056
Included in
Acoustics, Dynamics, and Controls Commons, Aerodynamics and Fluid Mechanics Commons, Heat Transfer, Combustion Commons, Propulsion and Power Commons