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There are numerous techniques for improving the mixing of fuel and oxidant species. However, many of these methods cannot be applied to combustion systems due to material limitations. A means of mixing the reacting species without physically invading the flow stream is therefore desired. In this work, induced electromagnetic forces known as Lorentz forces are considered as a means of enhancing the combustion of co-flowing reactant streams. To evaluate the effect of various parameters on the mixing process, a non-dimensional description is derived and used to develop a numerical model. Numerical experiments are performed based on a three level Box-Behnken design in which the dimensionless Lorentz force parameter, Reynolds number, and Euler number are varied. The Lorentz force parameter has a large effect on the mixing process. The Reynolds number has a minor effect on mixing, and the Euler number has a negligible effect. Confirmation of these results through experimental work is needed. Approaches that could be used to verify these results experimentally are outlined, and the construction and testing of a burner suitable for further experiments on Lorentz mixing is described. / Graduation date: 1997

Call number: LD2668 .T4 1978 T66 / Master of Science

The purpose of this research was to determine if it is feasible to apply Lorentz mixing to supersonic diffusion flames, such as those found in SCRAMjet engines. The combustion rate in supersonic diffusion flames is limited by the rate at which air and fuel mix. Lorentz mixing increases turbulence within a flow, which increases the rate at which species mix and thus increases the rate of combustion. In order to determine the feasibility of Lorentz mixing for this application, a two-dimensional model of supersonic reacting flow with the application of a Lorentz force has been examined numerically. The flow model includes the complete Navier-Stokes equations, the ideal gas law, and terms to account for diffusion of chemical species, heat release due to chemical reaction, change in species density due to chemical reaction, and the Lorentz forces applied during Lorentz mixing. In addition, the Baldwin-Lomax turbulence model is used to approximate turbulent transport properties. A FORTRAN program using the MacCormack method, a commonly used computational fluid dynamics algorithm, was used to solve the governing equations. The accuracy of the program was verified by using the program to model flows with known solutions. Results were obtained for flows with Lorentz forces applied over a series of power levels and frequencies. The results show significant increases in the rate of combustion when Lorentz mixing is applied. The amount of power required to drive Lorentz mixing is small relative to the rate at which energy is released in the chemical reaction. An optimum frequency at which to apply Lorentz mixing was also found for the flow being considered. The results of the current study show that Lorentz mixing looks promising for increasing combustion rates in supersonic reacting flows, and that future study is warranted. In particular, researchers attempting to improve combustion in SCRAMjet engines may want to consider Lorentz mixing as a way to improve combustion. / Graduation date: 1997

Using a two-dimensional nonlinear numerical simulation of a (viscous) stratified shear layer, strong instabilities resulted from the resonant interaction of a long linearly neutrally stable wave and the corresponding fastest growing wave. This linearly fastest growing wave, with optimal initial conditions, grows initially at a rate five times that predicted by linear theory. With other initial conditions, the linearly fastest growing wave may actually decay. The possibility of this type of interaction is suggested by the weakly nonlinear theory (cf. Maslowe, 1977). This coupled system of fourth order nonl inear partial differential equations was solved using a modified pseudospectral scheme for the spatial variables, incorporating the use of fast Fourier transforms to calculate spatial derivatives, and a second order Adams-Bashforth scheme for the temporal derivatives . / Dans cette etude, en utilisant une simulation numerique nonlineaire a deux dimensions d'une couche stratifiee, decollee et visqueuse, on obtint des resultats interessants a partir des cas correspondant a l'interaction resonnante d'une onde longue a stabilite neutre et d'une onde courte qui croit la plus rapidement selon la theorie lineaire. En utilisant certaines conditions initiales, l'onde courte croit initialement a un taux cinq fois superieur a celui predit par la theorie lineaire. Avec d'autres conditions initiales l'onde courte decroit. La possibilite de ce genre d'interaction est predite par la theorie faiblement nonlineaire (voir Maslowe, 1977). Ce systeme couple aux equations nonlineaires du quatrieme ordre aux derivees partielles, est resolu par une methode pseudo-spectrale modifiee, pour les variables spatiales, et une methode Adams-Bashforth du second ordre pour les derivees temporelles. fr

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The onset of summer stratification in temperate lakes and reservoirs forces a decoupling of the hypolimnion from the epilimnion that is sustained by strong density gradients in the metalimnion. These strong gradients act as a barrier to the vertical transport of mass and scalars leading to bottom anoxia and subsequent nutrient release from the sediments. The stratification is intermittently overcome by turbulent mixing events that redistribute mass, heat, dissolved parameters and particulates in the vertical. The redistribution of ecological parameters then exerts some control over the ecological response of the lake. This dissertation is focused on the physics of deep vertical mixing that occurs beneath the well-mixed surface layer in stratified lakes and reservoirs. The overall aim is to improve the ability of numerical models to reproduce deep vertical mixing, thus providing better tools for water quality prediction and management. In the first part of this research the framework of a one-dimensional mixed-layer hydrodynamic model was used to construct a pseudo two-dimensional model that computes vertical fluxes generated by deep mixing processes. The parameterisations developed for the model were based on the relationship found between lake-wide vertical buoyancy flux and the first-order internal wave response of the lake to surface wind forcing. The ability of the model to reproduce the observed thermal structure in a range of lakes and reservoirs was greatly improved by incorporating an explicit turbulent benthic boundary layer routine. Although laterally-integrated models reproduce the net effect of turbulent mixing in a vertical sense, they fail to resolve the transient distribution of turbulent mixing events triggered by local flow properties defined at far smaller scales. Importantly, the distribution of events may promote tertiary motions and ecological niches. In the second part of the study a large body of microstructure data collected in Lake Kinneret, Israel, was used to show that the nature of turbulent mixing events varied considerably between the epilimnion, metalimnion, hypolimnion and benthic boundary layer, yet the turbulent scales of the events and the buoyancy flux they produced collapsed into functions of the local gradient Richardson number. It was found that the most intense events in the metalimnion were triggered by high-frequency waves generated near the surface that grew and imparted a strain on the metalimnion density field, which led to secondary instabilities with low gradient Richardson numbers. The microstructure observations suggest that the local gradient Richardson number could be used to parameterise vertical mixing in coarse-grid numerical models of lakes and reservoirs. However, any effort to incorporate such parameterisations becomes meaningless without measures to reduce numerical diffusion, which often dominates over parameterised physical mixing. As a third part of the research, an explicit filtering tool was developed to negate numerical diffusion in a threedimensional hydrodynamic model. The adaptive filter ensured that temperature gradients in the metalimnion remained within bounds of the measured values and so the computation preserved the spectrum of internal wave motions that trigger diapycnal mixing events in the deeper reaches of a lake. The results showed that the ratio of physical to numerical diffusion is dictated by the character of the dominant internal wave motions.

This thesis examines the mixing times for one-dimensional interacting particle systems. We use the coupling method to study the mixing rates for particle systems on the circle which move according to specific permutations e.g., transpositions and 3-cycles. / Graduation date: 2008

[Truncated abstract] Mine lakes are a water body created after an open-cut mine ceases operating. The lakes develop in the former mine-pit due to the combination of groundwater inflow, surface run-off and, in some cases, due to rapid filling from river diversion. While potentially valuable water resources, these lakes often have poor water quality and managing the water body is an important part of the overall process of mine site rehabilitation. As mine lakes form in man-made pits, they have a bathymetry that is typically quite distinct from natural lakes and this can, in turn, strongly influence the hydrodynamics and hence the water quality of the water body. Despite the potential importance of these water bodies, there have been very few studies on the hydrodynamics of mine lakes. This study describes a field investigation of the hydrodynamics of a former coal mine lake, Lake Kepwari, in south-western Western Australia. In particular, this study examines the hydrodynamic processes in both the surface mixing layers and the internal mixing in the density stratified lake. Wind sheltering in the surface mixing layer occurs due to the presence of the steep walls and lake embankments. A week long field experiment was conducted in December 2003 using a combination of moored thermistor chains with meteorological stations and the deployment of rapid vertical profiling turbulent microstructure instruments and CTD drops from two boats operating on the lake. ... Simulations indicated that inclusion of a site specific sheltering effect, based on the results of the field campaign, significantly improved the models‘ performance in capturing the surface mixed layer deepening associated with episodic strong wind events that occur on the lake. Considerable internal mixing was indicated by the high dissipation rates observed, particularly near the boundaries. Large basin-wide diffusivities were also calculated from the heat budget method over long periods, showed a consistency with time, and were slightly higher in summer than during the Autumn Winter period. Although light, there are persistent winds over the lake and yet little basin-scale internal wave activity or seiching. It is hypothesized that any seiching motion was rapidly damped by strong mixing over the hydraulically rough bathymetry bathymetry created by the remnant benches from the open cut mining operation itself. This boundary mixing, in turn, drives secondary relaxation currents that transport mixed fluid from the boundaries to the interior, resulting in high effective basin-wide diffusivities. A simple boundary mixing model is proposed to describe this process.