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For nearly a decade, quasi-one-dimensional conductors have been the subject of intensive study. Theoretically, much attention has been devoted to the development of one-dimensional Fermi gas models, some which may be solved exactly, and to the calculation of their response functions. After a review of this theory, a different approach is adopted in the investigation of two models. The dielectric response theory of the three-dimensional Coulomb gas has been applied to an anisotropic system in which the particles interact with an effective one-dimensional long-range potential. Within the framework of the approximation of Singwi, Tosi, Land, and Sjolander, the dielectric properties of the model are examined in order to determine the conditions under which it is unstable with respect to formation of a charge density wave state. It is found that the positive neutralizing background must be polarizable in order for such an instability to occur. The same approximation method, when applied to a one-dimensional fermion gas with a ʃ-function interaction may be compared with the exact solution of Yang. This solution, which exists in the form of coupled integral equations, has been calculated numerically, and, as predicted by the Lieb-Mattis theorem, the ground state is found to be non-magnetic. The approximation of Singwi et al. proves to give better correlation energies than other inexact methods, particularly at higher densities. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The development of an appropriate solid-state kinetic model which represents the leaching process of phlogopite was investigated. Phlogopite samples were leached with nitric acid solutions of different concentrations, at different temperatures and for different reaction times. Leach liquors were analysed by ICP-OES for concentration, while the raw phlogopite and the acid-leached solid residues were analysed by XRF, XRD, ATR-FTIR, BET, TGA-DTG and SEM-EDS for characterisation to support the reaction rate model selection. It was found that the reaction was diffusion-controlled and the model which represents onedimensional diffusion through a flat plate (model D1) most accurately predicts the leaching behaviour. The observed activation energies and preexponential constants varied with initial acid concentration. The observed activation energies decreased from 98.8 – 88.9 kJ mol-1 as the initial acid concentration increased from 2 – 4 M, while the observed preexponential constants decreased from 3.30 x 10+12 – 2.30 x 10+11 min-1. Additional experiments were conducted at different temperatures, using different initial acid concentrations and over different reaction times to test the model. The experimental data points obtained (“testing data”) were in agreement with the predicted values. Analyses of the solid residues also revealed complementary results with respect to the leaching model selection. The raw phlogopite was found to be highly crystalline (XRD). Therefore, the absence of defects in the lattice means that the motion of H+ ions permeating into the lattice is restricted (Ropp, 2003; Schmalzried, 1995). This confirms that the leaching is internal diffusion-controlled since the mobility of constituents into the system is the controlling factor, and since the phlogopite particles are plate-like (SEM-EDS, BET) in shape, the use of the D1 model for one-dimensional diffusion through a flat plate is the recommended model to represent the leaching process. Furthermore, results obtained from the different analytical techniques were supportive of each other. It was also found that the amount of acid consumed is inequivalent to the amount theoretically required. Using the theoretically required acid concentration (2.45 M) results in incomplete conversion (< 80 % according to Kgokong (2017)). When initial acid concentrations between 2.4 – 2.6 M were used, only 88 – 91 % conversion was obtained after 6 hours of leaching at 65 °C, leaving behind excess H+ in solution. If fertiliser is the desired end product, it would be favourable to minimise the H+ concentration of the leach liquor. Therefore, the leaching process should be optimised so that the acidity of the leach liquor is minimised while obtaining complete leaching of all cations from the phlogopite particles into solution. Furthermore, since the SiO2 by-product is highly porous (surface area of 517 m2 g-1), its application in industrial adsorbents, catalysts, polymers, pigments, cement, etc. should be further explored. / Dissertation (MEng (Chemical Engineering))--University of Pretoria, 2020. / Chemical Engineering / MEng (Chemical Engineering) / Unrestricted

This document focuses on the procedure and results of creating a thermohydraulic model of the secondary cooling system of the SAFARI-1 research reactor at the Pelindaba facility of the South African Nuclear Energy Corporation (Necsa) to the west of Pretoria, South Africa. The secondary cooling system is an open recirculating cooling system that comprises an array of parallel-coupled heat exchangers between the primary systems and the main heat sink system, which consists of multiple counterflow-induced draught cooling towers. The original construction of the reactor was a turnkey installation, with no theoretical/technical support or verifiability. The design baseline is therefore not available and it is necessary to reverse-engineer a system that could be modelled and characterised. For the nuclear operator, it is essential to be able to make predictions and systematically implement modifications to improve system performance, such as to understand and modify the control system. Another objective is to identify the critical performance areas of the thermohydraulic system or to determine whether the cooling capacity of the secondary system meets the optimum original design characteristics. The approach was to perform a comprehensive one-dimensional modelling of all the available physical components, which was followed by using existing performance data to verify the accuracy and validity of the developed model. Where performance data is not available, separate analysis through computational fluid dynamics (CFD) modelling is performed to generate the required inputs. The results yielded a model that is accurate within 10%. This is acceptable when compared to the variation within the supplied data, generated and assumed alternatives, and when considering the compounding effect of the large amount of interdependent components, each with their own characteristics and associated performance uncertainties. The model pointed to potential problems within the current system, which comprised either an obstruction in a certain component or faulty measuring equipment. Furthermore, it was found that the current spray nozzles in the cooling towers are underutilised. It should be possible to use the current cooling tower arrangement to support a similar second reactor, although slight modifications would be required to ensure that the current system is not operated beyond its current limits. The interdependent nature of two parallel systems and the variability of the conditions that currently exist would require a similar analysis as the current model to determine the viability of using the existing cooling towers for an additional reactor. / Dissertation (MEng)--University of Pretoria, 2015. / Mechanical and Aeronautical Engineering / MEng / Unrestricted

Determining the homotopy type of one-dimensional Peano continua has been an open question of some interest. We give a complete invariant of the homotopy type of such continua, which consists of a pair of subspaces together with a relative homology group. Along the way, we describe reduced forms for one-dimensional Peano continua.

An unsteady, finite-rate, one-dimensional model has been developed for the analysis for gas-turbine combustors. The basis of the model is the one-dimensional, integral form of the conservation equations for multi-species, non-equilibrium, reacting mixtures. Special procedures were devised for the flow-division of the inlet flow into primary- and annular-flows, for both straight- and reverse-flow combustors. This allows the model to handle complete combustor configurations, which at present are beyond the reach of more sophisticated CFD tools. The model was validated with a steady-state analytical solution for a basic problem, and with steady-state results from a production code applied to a production combustor. Additional calculations show the ability of the code to predict blow-out due to rich and lean mixtures, and to predict the response of a combustor to perturbations in operating and boundary conditions. / Ph. D.

In this thesis, a one-dimensional, two-fluid model is developed in MATLAB-Simulink. The model features a mass, momentum, and energy balance for each fluid--an ideal gas and an incompressible liquid. The simulation may model a straight pipe section, or a pipe section that involves a cross-sectional area change. Rough models of interphase heat transfer and interphase friction are included. Currently, phase change is not modeled in the simulation Also, a single-fluid model was developed before the two-fluid model, as an intermediate step in developing the two-fluid model. The single-phase simulation applies a mass, momentum, and energy balance for the single fluid, and ideal gas. The single-fluid model was validated by incompressible flow, Fanno flow, and isentropic flow models. The incompressible model demonstrated the simulations ability to properly balance pressure and frictional forces. The Fanno flow model showed that the simulation could capture compressibility effects. The isentropic flow model validation verified that the simulation could model area change properly. The two-fluid model was validated using the Homogeneous Equilibrium Model (HEM). An analytical model of HEM flow with frictional pressure drop was developed to compare against the simulation results. To achieve the HEM, interphase effects were tuned so that the liquid and gas phases had similar temperatures and velocities. Under these conditions, the simulation matched the analytical model. The thesis goal is to create a solid foundation for an open-source, one-dimensional, two-fluid model that is easier to use and modify than current nuclear system analysis software. / Master of Science

One-Dimensional modeling of dual mode scramjet and ramjet flowpaths is a useful tool for scramjet conceptual design and wind tunnel testing. In this thesis, modeling tools that enable detailed analysis of the flow physics within the combustor are developed as part of a new one-dimensional MATLAB-based model named VTMODEL. VTMODEL divides a ramjet or scramjet flow path into four major components: inlet, isolator, combustor, and nozzle. The inlet module provides two options for supersonic inlet one-dimensional calculations; a correlation from MIL Spec 5007D, and a kinetic energy efficiency correlation. The kinetic energy efficiency correlation also enables the user to account for inlet heat transfer using a total temperature term in the equation for pressure recovery. The isolator model also provides two options for calculating the pressure rise and the isolator shock train. The first model is a combined Fanno flow and oblique shock system. The second model is a rectangular shock train correlation. The combustor module has two options for the user in regards to combustion calculations. The first option is an equilibrium calculation with a "growing combustion sphere" combustion efficiency model, which can be used with any fuel. The second option is a non-equilibrium reduced-order hydrogen calculation which involves a mixing correlation based on Mach number and distance from the fuel injectors. This model is only usable for analysis of combustion with hydrogen fuel. Using the combustion reaction models, the combustor flow model calculates changes in Mach number and flow properties due to the combustion process and area change, using an influence coefficient method. This method also can take into account heat transfer, change in specific heat ratio, change in enthalpy, and other thermodynamic properties. The thesis provides a description of the flow models that were assembled to create VTMODEL. In calculated examples, flow predictions from VTMODEL were compared with experimental data obtained in the University of Virginia supersonic combustion wind tunnel, and with reported results from the scramjet models SSCREAM and RJPA. Results compared well with the experiment and models, and showed the capabilities provided by VTMODEL. / Master of Science

<p> Weirs of the conventional shape are amenable to analysis based on an assumption of one-dimensional flow and a number of computational routines have been developed for this type of transition problem. When critical flow occurs in a highly non-uniform section, a more sophisticated approach is necessary. </p> <p> In conjunction with laboratory tests on a typical compound control, a mathematical mode was formulated for the development of the stage-discharge relation. It is felt that this model will allow an accurate prediction for water quantity from fluctuating sources. </p> / Thesis / Master of Engineering (MEngr)

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