This thesis examines the numerical solution to Burgers' equation on a finite spatial domain with various boundary conditions. We first conduct experiments to confirm the numerical solutions observed by other researchers for Neumann boundary conditions. Then we consider the case where the non-homogeneous Robin boundary conditions approach non-homogeneous Neumann conditions. Finally we numerically approximate the steady state solutions to Burgers' equation with both the homogeneous and non-homogeneous Robin boundary conditions. / Master of Science

The photoconductive properties of undoped hydrogenated amorphous silicon have been extensively studied. Measurements of optical absorption, dark d.c. conductivity, steady state photoconductivity, step response transient rise photoconductivity and impulse response flash decay photoconductivity have been made. In addition, computer simulation has been used to give an insight into the physical processes involved in the photoconductivity experiments.Two materials were used in the study, to provide a comparison. All the above measurements, except the transient measurements were made on sputtered material prepared by the author. a-Si:H prepared elsewhere by the glow discharge decomposition of silane was measured by all the above experiments, except optical absorption.The results obtained from the flow discharge material were interpreted as due to recombination in distributed states, which are restricted in energy, extending from the dark Fermi level upwards to 0.6eV below Ec. The capture cross section of these states was of a value expected for the neutral dangling bond, so they have been denoted as Do states. States outside this energy were seen to be ineffective as recombination centres. The model thus has features intermediate between a simple 2-trap system and a distributed density of states. Chapter 2 presents a detailed analysis of steady state photoconductivity for the case of a single correlated defect level, and demonstrates its near equivalence to a simple 2-defect one electron system. This partly justifies the subsequent use of one electron states in computer modelling. Computer simulation successfully predicts the form of the experimental step response. The flash decay required the existence of an extra discrete state at 0.4eV, but gave a better quantitative fit.The sputtered material appeared to have the recombination in the steady state controlled by discrete states 0.6eV below Ec, but inconsistencies remain between the interpretations of different measurements on this material.

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Steady and unsteady force and moment experiments were conducted in the Virginia Tech Stability wind tunnel using the Dynamic Plunge-Pitch-Roll (DyPPiR) model mount to perform rapid time-dependent,high-excursion maneuvers. The experiments were performed for a DARPA2 submarine model using three widely spaced 2-force-component loadcells and three tri-axial accelerometers to extract the aerodynamic loads. The DARPA2 model was tested with different body configurations in two different test sections. The body configurations for both the steady and unsteady experiments were the bare body hull, body with sail, body with stern appendages, and body with sail and stern appendages. Tests were done using trips on the bow and sail and with no trips. The bare hull configuration with no trips was the only body configuration tested in the six-foot-square test section with solid walls. All body configurations were tested in the six-foot-square test section with slotted walls that were used to reduce the blockage effects produced by the DyPPiR and model. The steady experiments were performed over a range of angles of attack and roll positions. Data were acquired through the series of angles the body encountered during the unsteady testing (-26° < ± <+26° ). The data for the tripped bare hull gave symmetric results while the data acquired for the bare hull with no trips did not. In the unsteady experiments the model was pitched in ramp maneuvers about the 1/4 chord location of the sail from 0° to -25° and from +25° to 0° in 0.3 seconds. Sine wave maneuvers at 3 Hz were also performed, plunging the model up and down with an amplitude of ±0.375 inches. The steady data agreed within uncertainties with previous data that were limited to the David Taylor Research Center (DTRC). There was a higher level of confidence in the steady data taken with trips due to the symmetry of the data. Effects of the sail and/or stern appendages were studied using the steady and unsteady data, but no quantitative value could be calculated due to the uncertainties. The unsteady data were modeled with a quasi-steady time-lag model, and all the unsteady data were found to lead the quasi-steady data. The unsteady data did have oscillations, but the overall aerodynamic trend was still present. The uncertainties were too large to discuss effects of any appendages, however. / Master of Science

Student Number : 9803192Y - MSc(Eng) Dissertation - School of Mechanical, Industrial and Aeronautical Engineering - Faculty of Engineering and the Built Environment / A computational °uid dynamics (CFD) study was carried out to improve the aero- dynamic performance of an agile high angle of attack missile. The normal force generated by the missile strakes had to be increased at the low angles of attack and the large side forces, experienced at high angles of attack due to the formation of steady asymmetric vortices had to be eliminated using strakelets on the missile nose. The ¯rst objective was achieved by increasing the missile strake span from 0:06D to 0:13D. The larger strake span increased the e®ective diameter of the missile body and prevented °ow reattachment to the body, a problem that was experienced when the strake span was 0:06D. Due to °ow separating further away from the body, strong vortices formed on the missile strakes, resulting in an increase in the normal force generated by the missile strakes at low angles of attack. The second objective was two-fold. Prior to analysing the e®ect of the strakelets on a steady asymmetric °ow¯eld, the steady asymmetric °ow¯eld had to ¯rst be created. This was achieved by placing a permanent, geometric perturbation on the missile nose. The size of the perturbation used in the study, which was determined by an iterative process, did not force °ow separation at low angles of attack and resulted in a steady asym- metric °ow¯eld that was representative of that on a blunt-ogive body. The e®ect of changing the span of the strakelets and the axial position of the strakelets were then investigated. It was found that the strakelets with a span of 0:09D, placed 1D from the nose tip eliminated the side forces by forcing vortex symmetry. Increasing or decreasing the span of the strakelet, positioned 1D from the nose tip or placing the strakelets with a span of 0:09D closer or further away from the nose tip did not eliminate the steady vortex asymmetry.

The exponential advancements in the field of electronics and power generation have resulted in increased pressure on the thermal management of these systems where the desire for enhanced heat transfer is prevalent. A technique for enhancing heat transfer that has gained sufficient attention over the past two decades is to suspend nano-sized metallic particles in a base fluid in order to enhance its thermophysical properties. Fluids produced in such a manner are commonly termed nanofluids. Due to the promising heat transfer capabilities of nanofluids, many industrial applications are beginning to implement these fluids in their thermal practices. One of the potential applications where nanofluids may be used which has received a great deal of research attention is jet-impingement heat transfer. Concerning the existing publications on nanofluid jet impingement, most works within the steady state regime are limited to the cooling of Al2O3-water nanofluids, while transient studies do not account for cooling without the effects of boiling phenomena and for surfaces other than steel. In this study, six particle volume fractions of TiO2-water ranging between 0.025 and 1% were prepared and characterised for appropriate cooling tests. The study was conducted within both the steady and transient state with the main objective of evaluating the thermal performance of the selected nanofluid and to determine the optimum particle concentration for jet-impingement cooling applications. Therefore, an experimental rig was designed and manufactured where a copper target surface of 42 mm was impinged upon by a 1.65 mm orifice nozzle at a non-dimensional nozzle-to-target height of 4. The results indicated that the use of nanofluids in impingement applications produced adverse effects, depending on the particle fraction considered. With respect to the steady-state cooling tests, the copper surface was subjected to a constant heat flux of 145 watt and cooled by the different fluids at Reynolds numbers ranging between approximately 10 000 and 30 000. A maximum enhancement of 14.75% was observed in the measured Nusselt numbers, which occurred at a particle volume concentration of 0.05%. When increasing the volume fraction above 0.1%, unfavourable effects were observed for the heat transfer of the system in comparison with the base case tests of DI-water. Such trends were characterised by the trade-off between the enhancement in thermal conductivity and viscosity, both of which were increased with an increase in particle concentration. As for the effect of Reynolds number on the resulting thermal performance, a directly proportional relation was shown and could be described by the forced convection effect. The transient impingement tests showed that particle concentrations less than 0.1% produced an enhancement in cooling efficiency, while those of higher volume fractions showed negative effects. According to these tests the maximum enhancement was also obtained at a volume fraction of 0.05% and produced an average cooling efficiency enhancement of 16%. The results of the investigation clearly showed that the use of TiO2-water nanofluids in jet-impingement cooling applications produced thermal enhancement depending on the selected particle concentration. / Dissertation (MEng)--University of Pretoria, 2019. / NRF / Mechanical and Aeronautical Engineering / MEng / Unrestricted

Analytical three-dimensional temperature field in the liquid and heat-affected zones and prediction of the three-dimensional fusion zone shape around the keyhole produced by a moving high-intensity beam are provided. Determination of the fusion zone shapes is of fundamental and practical importance to understand properties and microstructures of joints. In this work, the keyhole is idealized by a paraboloid of revolution in a finite workpiece subject to an incident flux of a Gaussian distribution.Introducing analytical solutions of three-dimensional analytical temperature field, the dimensionless width, leading and rear edges, and depth of the fusion zone are analytically found to be a function of the dimensionless parameters governing beam power per unit penetration, location of the workpiece surface and shape of the keyhole. The dimensionless parameters governing the keyhole shape can be evaluated from a force balance at the keyhole base. The results show the effects of welding parameters, such as the dimensionless beam power, Peclet number, cavity opening radius, Biot number, thickness of workpiece, and the parameter approximating convection, on the shape of the fusion zone and the temperature of keyhole surface. A significant difference in the fusion zone shapes predicted between the line-source solution and this work indicates the strong effects of three-dimensional heat transfer. Agreement between the prediction from this work and available experimental data is achieved.

Three testing procedures were developed in this research to allow expeditious characterization of soil unsaturated flow properties using steady state centrifuge methods. The first testing procedure, referred to as the “instrumented” procedure, focuses on using in-flight measurement of the suction and volumetric water content of soil samples under centrifugation. The measurements are used to calculate the soil water retention curve and hydraulic conductivity function (K-function) of soil samples. A good agreement was found between results determined using the “instrumented” procedure and standard testing methods. Several possible sources of inaccuracy were determined with the “instrumented” procedure. The void ratio, the changes of which were not measured, was found to decrease during centrifugation and the lower boundary condition, which was not accounted for in the evaluation, was found to affect a large portion of the sample. In order to improve the accuracy of results, two additional testing procedures were developed that accounted for these issues and incorporated the void ratio of the soil as an additional variable. The first additional procedure was used to measure the soil water retention surface (SWRS) of soil samples while the second was used to measure the unsaturated hydraulic conductivity surface (K-surface) of soil samples. Both new procedures, referred to as the “hydrostatic” and “imposed flow” procedures, were used to characterize the unsaturated flow properties of a low plasticity clay (“RMA” soil). The unsaturated flow characteristics of the RMA soil were evaluated for a wide range of void ratio and three compaction moisture conditions. As a result, the effects of void ratio and compaction moisture content on the unsaturated flow characteristics could be determined for the RMA soil. The compaction water content was shown to have significant effects on both the retention behavior and the unsaturated hydraulic conductivity of the RMA soil. In general, increases in compaction water content resulted in a decrease of large pore sizes in the soil, resulting in higher water retention and lower unsaturated hydraulic conductivity. The void ratio was found to have comparatively lesser, but still significant, effects on both retention and conductivity characteristics. Specifically, decreases in void ratio were shown to reduce the unsaturated hydraulic conductivity. In addition, decreases in void ratio were shown to result in either increases or decreases on the soil water retention, depending on the level of suction in the soil. A good agreement was found between results obtained using standard methods and those from the hydrostatic and imposed flow procedures. Accordingly, steady state centrifuge methods were ultimately found to provide a both expeditious and accurate method for characterizing the unsaturated flow properties of soil. / text

In this thesis, we address the problem of steady propagation of a gaseous detonation weakly confined by an inert gas. The effect of the lateral divergence is modelled using Watt’s Straight Streamline Approximation and a newly derived simpler nozzle model in a hydrodynamic average description. The prediction of the models was compared against the detonation velocity data obtained numerically by Mi et al and Reynaud et al. Very good agreement is found for weakly stable detonations at low activation energy with all models. These models, however, fail to capture the dynamics of unstable gaseous detonations characterized by delayed energy release, long induction lengths and higher activation energies. This inconsistency is treated by different models for the macroscopic kinetics: the underlying chemical kinetics model applicable for a laminar formulation, an effective kinetic rate adjustment to account for the detonation thickening owing to the cellular instability and a new ignition delay distribution model conditioned on the distribution of shock temperatures at the shock. The study illustrates that the reaction zone thickening of detonation waves and the delayed energy release are responsible for its limits. Future work should be extended to incorporate more accurate sub-cellular models to capture other effects, such as the ignition of gases via turbulent mixing in very irregular detonations.