Volcanic eruption columns inject high concentrations of ash into the atmosphere. Some of this ash is carried downwind forming ash clouds in the atmosphere that are hazardous for private and commercial aviation. Current models rely on inputs such as plume height, duration, eruption rate, and meteorological wind fields. Eruption rate is estimated from plume height using relations that depend on the rate of air entrainment into the plume, which is not well quantified. A wind tunnel experiment has been designed to investigate these models by injecting a vertical air jet into a cross-flow. The ratio of the cross-flow and jet velocities is varied to simulate a weak plume, and flow response is measured using particle image velocimetry. The plumes are characterized and flow data relative to the centerline is examined to measure the growth of weak plumes and the entrainment velocity along its trajectory. It was found that cross-flow recirculates behind the jet and entrainment occurs both up and downstream of the jet. Analysis of the generation of turbulence enhanced results by identifying the transition point to bending plume and the growth of the shear layer in a bending plume. This provides information that can be used to improve models of volcanic ash concentration changes in the atmosphere.

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The analysis, finite element approximation, and numerical simulation of some control problems associated with fluid flows are considered. First, we consider a coupled solid/fluid temperature control problem. This optimization problem is motivated by the desire to remove temperature peaks, i.e., "hot spots", along the bounding surface of containers of fluid flows. The heat equation of the solid container is coupled to the energy equation for the fluid. Control is effected by adjustments to the temperature of the fluid at the inflow boundary. We give a precise statement of the mathematical model, prove the existence and uniqueness of optimal solutions, and derive an optimality system. We study a finite element approximation and provide rigorous error estimates for the error in the approximate solution of the optimality system. We then develop and implement an iterative algorithm to compute the approximate solution. Second, a computational study of the feedback control of the magnitude of the lift in flow around a cylinder is presented. The uncontrolled flow exhibits an unsymmetric Karman vortex street and a periodic lift coefficient. The size of the oscillations in the lift is reduced through an active feedback control system. The control used is the injection and suction of fluid through orifices on the cylinder; the amount of fluid injected or sucked is determined, through a simple feedback law, from pressure measurements at stations along the surface of the cylinder. The results of some computational experiments are given; these indicate that the simple feedback law used is effective in reducing the size of the oscillations in the lift. Finally, some boundary value problems which arise from a feedback control problem are considered. We give a precise statement of the mathematical problems and then prove the existence and uniqueness of solutions to the boundary value problems for the Laplace and Stokes equations by studying the boundary integral equation method. / Ph. D.

The increased use of infrared imaging as a flow visualization technique and as a validation technique for computational fluid dynamics (CFD) codes has led to an in-depth study of infrared band models. The ability to create fast and accurate images of airframe and plume infrared emissions often depends on the complexity of the band model. An infrared band model code has been created based largely on the band model published in NASA SP-3080, Handbook of Infrared Radiation from Combustion Gases. Improvements to the NASA SP-3080 model using the N I RA T AM data files have been made. The model and its theoretical basis are thoroughly described. Results are presented and are compared with results from the band models contained in SCORPIO and LOIR. / Master of Science

The k-epsilon turbulence model yields inconsistent and diffusive results for swirling and recirculating flows, which are characteristic of combustor geometries. Y. S. Chen and S. W. Kim propose a modification to the k-epsilon turbulence model which has shown improved predictions for several complex flows. This study evaluates the application of the Chen modification of the k-epsilon turbulence model to combustor geometries by applying the modification to two burner test cases which contain the elemental flow characteristics of an industrial gas turbine combustor. The modification is implemented into a commercial computational fluid dynamics (CFD) code. The results show an improved prediction of the location, shape and size of the primary centerline recirculation zone for both cases. The large swirl and axial velocity gradients, which are diffused by the standard k-epsilon model, are preserved by the Chen model. The overprediction of turbulent eddy viscosity in regions of high shear, which is characteristic of k-epsilon, is controlled by the Chen modification. In industrial combustor design, the prediction of the location, size and shape of primary flow features is of paramount importance. The Chen modification can, therefore, be considered a successful improvement to the k-epsilon model and can be considered applicable to combustor geometries. / Master of Science