Doctoral Dissertations
Date of Award
5-2010
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Major
Mechanical Engineering
Major Professor
Joseph Majdalani
Committee Members
Basil N. Antar, Bruce W. Bomar, Boris A. Kupershmidt, Roy J. Schulz
Abstract
This dissertation is concerned with the mathematical modeling of the flow in a porous cylinder with a focus on applications to solid rocket motors. After discussing the historical development and major contributions to the understanding of wall injected flows, we present an inviscid rotational model for solid and hybrid rockets with arbitrary headwall injection. Then, we address the problem of pressure integration and find that for a given divergence free velocity field, unless the vorticity transport equation is identically satisfied, one cannot find an analytic expression for the pressure by direct integration of the Navier-Stokes equations. This is followed by the application of a variational procedure to seek novel solutions with varying levels of kinetic energies. These are found to cover a wide spectrum of admissible motions ranging from purely irrotational to highly rotational fields. Subsequently, a second law analysis as well as an extension of Kelvin's energy theorem to open boundaries are presented to verify and corroborate the variational model. Finally, the focus is shifted to address the problem of laminar viscous flow in a porous cylinder with regressing walls. This is tackled using two different analytical techniques, namely, perturbation and decomposition. Comparisons with numerical Runge--Kutta solutions are also provided for a variety of wall Reynolds numbers and wall regression speeds.
Recommended Citation
Saad, Tony, "Theoretical Models for Wall Injected Duct Flows. " PhD diss., University of Tennessee, 2010.
https://trace.tennessee.edu/utk_graddiss/748
Included in
Aerodynamics and Fluid Mechanics Commons, Fluid Dynamics Commons, Partial Differential Equations Commons, Propulsion and Power Commons