On Compressible Gaseous Motions in Swirl Dominated Combustors

In this dissertation, a number of models are derived to describe swirling flows. Both generalized compressible Bragg-Hawthorne and vorticity-stream function frameworks are determined and left in a generic form suitable for describing a number of different scenarios. These systems are solved for the bidirectional vortex flowfield by means of a Rayleigh-Janzen perturbation, which expands the governing equations in terms of the Mach number squared. The resulting equations are solved to provide a semi-analytical solution after the evaluation of a handful of numerical integrals. These solutions further the understanding of compressible flow in swirl-combustors, as previous compressible studies are primarily experimental or numerical in nature. Additionally, an alternative swirl velocity model is discussed which uses the balancing of pressure and shear forces to arrive at a piecewise velocity model. The model is compared to experimental data using a method that enables the adjustment of laminar models to account for the effects of turbulence. A modified least-squares approach is developed to handle the movable boundary in the piecewise velocity formulation.