The focus of the world is on the reduction of greenhouse gases, such as carbon dioxide, which contribute to the global warming currently experienced. Because most of the carbon dioxide emitted into the atmosphere is from fossil fuel combustion, alternative energy sources were developed and others are currently under study to see whether they will be good alternatives. One of these alternative sources of energy is the combustion of wood instead of coal. The advantages of wood are that it is a neutral carbon fuel source and that currently installed infrastructure used to combust coal can be retrofitted to combust wood or a mixture of wood and coal in an attempt to reduce the carbon dioxide emissions. Spent nuclear fuel has to be cooled so that the decay heat generated does not melt the containment system, which could lead to the unintentional release of radioactive material to the surroundings. The heat transfer mechanisms involved in the cooling have historically been analysed by assuming that the fluid and solid phases are at local thermal equilibrium (LTE) in order to simplify the analysis. The exergy destruction of the combustion of pine wood in an adiabatic combustor was investigated in this thesis using analytical and computational methods. The exergy destruction of the combustion process was analysed by means of the second law efficiency, which is the ratio of the maximum work that can be achieved by a Carnot engine extracting heat from the combustor, and the optimum work of the combustor. This was done for theoretical air combustion and various excess air combustions, with varied inlet temperatures of the incoming air. It was found that the second law efficiency reached an expected maximum for theoretical air combustion, and this held true for all varying air inlet temperatures. However, it was found that as the air inlet temperature was increased more and more, the maximum second law efficiency was the same for all excess air combustions, including the theoretical air combustion. It was also found that the results of the analytical and commercial computational fluid dynamics code compared well. Another analysis was conducted of irreversibilities generated due to combustion in an adiabatic combustor burning wood. This was done for a reactant mixture varying from a rich to a lean mixture. A non-adiabatic non-premixed combustion model of a numerical code was used to simulate the combustion process where the solid fuel was modelled by using the ultimate analysis data. The entropy generation rates due to the combustion and frictional pressure drop processes were computed to eventually arrive at the irreversibilities generated. It was found that the entropy generation rate due to frictional pressure drop was negligible when compared with that due to combustion. It was also found that a minimum in irreversibilities generated was achieved when the air-fuel mass ratio was 4.9, which corresponded to an equivalent ratio of 1.64, which was lower than the respective air-fuel mass ratio and equivalent ratio for complete combustion with theoretical amount of air of 8.02 and 1. Studieswere conducted to numerically analyse irreversibilities generated due to combustion in an adiabatic combustor burning wood. The first study analysed the effect of changing the incoming air temperature from 298 K to 400 K. The second study analysed the effect of changing the wall condition of the combustor from adiabatic to negative heat flux (that is heat leaving the system) for an incoming air temperature of 400 K. The irreversibilities generated in the combustor were calculated by computing the entropy generation rates due to the combustion, heat transfer and frictional pressure drop processes. For the first part of the study, it was found that for the minimum irreversibilities generated in the adiabatic combustor, the optimal air-fuel ratio (AF) corresponding to minimum irreversibilities slightly reduced from 4.9 to 4.8. In the second part of the study, it was found that by changing the wall condition from adiabatic to heat flux on the combustor, the AF corresponding to the minimum irreversibilities increased from 4.8 to 6. For the third part of the study, the combustor with a heat flux wall condition and a wall thickness simulated at an AF of 6, the sum of twice the wall thickness and the optimum diameter always added up to 0.32 m, resulting in the minimum irreversibilities. An analytical model was developed to minimise the thermal resistance of an air-cooled porous matrix made up of solid spheres with internal heat generation. This was done under the assumption of LTE. It was found that the predicted optimum sphere diameter and the minimum thermal resistance were both robust in that they were independent of the heat generation rate of the solid spheres. Results from the analytical model were compared with those from a commercial numerical porous model using liquid water and air for the fluid phase, and wood and silica for the solid phase. The magnitudes of the minima of both the temperature difference and the thermal resistance seemed to be due to equal contribution from the thermal conduction heat transfer inside the solid spheres and heat transfer in the porous medium. Because the commercial numerical porous model modelled only the heat transfer occurring in the porous medium, it expectedly predicted half of the magnitudes of the minima of the temperature difference and thermal resistance of those by the analytical model. / Thesis (PhD)--University of Pretoria, 2017. / Mechanical and Aeronautical Engineering / PhD / Unrestricted

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Wegen der zunehmenden Menge an LIBS-Daten von der Marsoberfläche sowie deren speziellen Herausforderungen bei der Analyse untersucht diese Arbeit, wie die Modellierung und Simulation von solchen LIBS-Spektren genutzt werden kann. Das Ziel ist es, Einblicke in die Eigenschaften von LIBS-Plasmen auf dem Mars zu erhalten und Modelle zu entwickeln, die bei der Analyse von realen Missionsdaten helfen können. Die Modellierung basiert sich auf einem stationären Plasma im lokalen thermischen Gleichgewicht (LTE). Das Plasma wird dabei in eine Reihe homogener Zonen unterteilt und Spektren werden mit dem Strahlungstransfer entlang einer eindimensionalen Sichtlinie durch diese Plasmazonen simuliert. Die Ergebnisse dieser Arbeit zeigen, dass auf LTE basierende Modelle gut auf LIBS-Spektren angewendet werden können, die unter Marsbedingungen gemessen wurden. Für zeitaufgelöste Daten kann die Anpassung eines Zwei-Zonen-Modells verwendet werden, um Einblicke in das Plasma zu erhalten und um die Elementkonzentrationen mit einer höheren Genauigkeit zu bestimmen, als es mit der Saha-Boltzmann-Methode möglich wäre. Allerdings sollten Nicht-Gleichgewichtseffekte in den frühesten und spätesten Phasen der Plasmalebensdauer berücksichtigt werden. Für zeitlich integrierte Spektren, wie sie bei aktuellen Marsmissionen gemessen werden, sind Anpassungen durch ein Zwei-Zonen-Modell aufgrund von zu langen Rechenzeiten nicht durchführbar. Stattdessen kann durch die Methode der spektralen Entmischung eine Überlagerung von Spektren unterschiedlicher Temperaturen und Dichten verwendet werden. Diese Methode ermöglicht keine direkten quantitativen Bestimmungen der Elementkonzentrationen, ist aber ein hervorragendes Werkzeug, um einen Überblick über die große Menge an Informationen zu erhalten, die in den Spektren enthalten sind. / Motivated by existing challenges in analysing LIBS spectra and the increasing quantity of Martian LIBS data, this thesis investigates the modelling and simulation of LIBS spectra for the application to LIBS data in Martian atmospheric conditions. This is done with the aim of providing insights into the characteristics of Martian LIBS plasmas as well as developing tools to assist the analysis of real mission data. The modelling of LIBS spectra is based on a stationary plasma in local thermal equilibrium (LTE). The plasma is then divided into a series of homogeneous zones and spectra are simulated using radiative transfer along a one-dimensional line-of-sight through the plasma zones. The results of this thesis show that spectral modelling based on LTE can be well applied to LIBS data in Martian atmospheric conditions. For time-resolved data, fits of a two-zone plasma model can be used to obtain insights into the plasma as well as improved concentration estimates compared to the Saha-Boltzmann plot method. However, attention to non-equilibrium effects should be given at the earliest and latest stages of the plasma lifetime. For time-integrated spectra, i.e. real mission data, fits of the two-zone model are not feasible due to too long computation times. Instead, a superposition of spectra of different temperatures and densities, i.e. the spectral unmixing method, can be used. Although not directly allowing for quantitative concentration estimates, the method is a great tool to overview the large amount of information contained in the spectra.

Ce travail de thèse a pour objectif de simuler numériquement des écoulements de gaz dans des matrices poreuses dont les pores sont de taille micrométrique. On étudie l'influence des phénomènes de glissement hydrodynamique qui apparaissent lorsque la dimension caractéristique de micro- conduites est caractérisée par des nombres de Knudsen compris entre Kn = 0,01 et Kn = 0,1.Le mémoire de thèse est composé de cinq chapitres suivis d'une conclusion dans laquelle nous présentons quelques perspectives pour une suite de ce travail. Le chapitre I constitue le travail préliminaire de thèse qui s'est ensuite orienté vers des approches complémentaires. Le principe des méthodes d'homogénéisation périodique est d'abord exposé. Suit une présentation de deux méthodes de résolution dans l'espace de Fourier : l'approche en déformation et l'approche en contrainte. L'extension de ces méthodes à la résolution d'écoulements régis par l'équation de Stokes est ensuite décrite. Des applications aux cas d'écoulements à travers des réseaux de cylindres, avec condition d'adhérence ou avec condition de glissement, sont ensuite discutées. Deux techniques de modélisation des phénomènes de transport dans des milieux poreux saturés par un fluide monoconstituant sont présentées dans le second chapitre. La première est basée sur la méthode des développements asymptotiques, appelée aussi méthode d'homogénéisation. On explique que le processus consiste en trois étapes : description locale, localisation et description macroscopique. La seconde technique s'appuie sur la méthode de calcul de moyennes à l'échelle d'un VER. Le point de départ de cette méthode est basé sur des théorèmes donnant les expressions des moyennes de tous les opérateurs intervenant dans une équation de transport. Après une brève présentation du logiciel commercialisé que nous avons utilisé, nous exposons les études de convergence spatiale que nous avons effectuées et nous comparons nos solutions avec des résultats de la littérature dans le chapitre III. Diverses géométries sont considérées (allant de géométries planes à des empilements 3D de cubes ou de sphères).L'effet du glissement sur la perméabilité de milieux microporeux est abordé dans le chapitre IV. Le formalisme résultant de l'homogénéisation de structures périodiques est utilisé pour simuler numériquement des écoulements isothermes de gaz dans divers empilements de complexités croissantes. Les perméabilités sont déterminées en calculant les moyennes spatiales des champs de vitesses, solutions des équations de Stokes. Les valeurs obtenues en imposant des conditions d'adhérence sont comparées à celles obtenues avec des conditions de glissement du premier ordre. Dans le chapitre V, nous présentons des solutions pour des écoulements anisothermes et étudions l'effet du glissement sur la conductivité effective de milieux microporeux 2D et 3D. Dans ce chapitre, nous résolvons les équations de Navier-Stokes et de l'énergie en imposant des conditions de symétries dans une ou deux directions. A partir des solutions locales, sont calculées les moyennes intrinsèques des champs de vitesse et de température. Nous considérons des cas pour lesquels la condition d'équilibre thermique local peut être considérée comme satisfaite et d'autres correspondant à un non-équilibre thermique (NTLE). On détermine les conductivités de dispersion en fonction du nombre du Péclet et on montre l'influence du glissement sur les composantes longitudinales et transverses pour différentes porosités et longueur de glissement. Dans les cas NLTE, le coefficient macroscopique de transfert fluide-solide est aussi calculé / This thesis aims at numerically simulating gas flows in porous matrices with micro-sized pores. We study the influence of hydrodynamic slip phenomena that appear when the characteristic dimension of micro pores is characterized by Knudsen numbers between Kn = 0.01 and Kn = 0.1.The thesis consists of five chapters followed by a conclusion in which we present some perspectives for further studies. Chapter I is the preliminary work of thesis that turned into complementary approaches. The principle of periodic homogenization methods is first exposed. We present then two methods in the Fourier space: the stress approach and the strain approach. The extension of these methods for solving flows governed by the Stokes equation is described in what follows. Applications to flows through networks of cylinders, subjected to no slip or slip condition, are then discussed. Two techniques for modeling transport phenomena in porous media saturated by a mono-component fluid are presented in the second chapter. The first is based on the method of asymptotic expansions, also known as homogenization method, based on the concept of separation of scales. It is explained that the process consists of three steps: local description, localization and macroscopic description. The second technique is based on the method of averaging at the level of a representative elementary volume (REV). The starting point of this method is based on the equations of Continuum Mechanics and theorems giving the averaged expressions of all operators involved in a transport equation. We show that it extends easily to gas flows in micro porous media. After a short presentation of the commercial software used, we present the spatial convergence studies carried out and we compare our solutions with the results of the literature in Chapter III. Various geometries are considered (plane to 3D geometries made of cubes or spheres), but these comparisons are limited to isothermal flows. The effect of slip on the permeability in micro porous media is discussed in Chapter IV. The resulting formalism of the periodic homogenization structures is used for numerical simulation of isothermal gas in various geometries of increasing complexity. The permeabilities are determined by calculating the spatial averages of velocity fields, solutions of the Stokes equations. The values obtained by imposing no slip conditions are compared with first order slip conditions. We discuss the relative increase in permeability due to slip according to the geometry of the pores. In Chapter V, we present the solutions for anisothermal flows and we study the effect of slip on the effective conductivity in 2D and 3D microporous media. In this chapter, we solve the Navier-Stokes and energy equations by imposing symmetry conditions in one or two directions. The intrinsic mean velocity and temperature fields are calculated from these local solutions. We consider cases where the local thermal equilibrium condition can be considered as satisfied and other corresponding to a non-local thermal equilibrium (NLTE). We determine the dispersion conductivity based on the Péclet number and show the influence of velocity slip on longitudinal and transverse components for various porosities and slip lengths. In NLTE cases, the macroscopic fluid-to-solid heat transfer coefficient is also calculated