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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 expanding constant is a measure of graph connectivity that is important for certain applications. This paper discusses the mathematical foundations for the construction of Winnie Li's graphs and for the proof that Winnie Li's graphs are Ramanujan. The paper also establishes the implications of the Ramanujan property for the expanding constant. / Master of Science

SpinChem AB's rotating bed reactor (RBR) is a small cylindrical centrifuge that allowsfor eective convective reactions between chemical substances. The aim of my master'sdissertation was to develop a measurement system that could estimate the uid velocity insidethe RBR. This report covers a quick pre-study of dierent uid measurement methods,details how we designed and constructed the system using integrated circuits and other electroniccomponents, and illustrates calibration results and nal velocity measurements. Thesystem design was based on the architecture of hot-wire constant temperature anemometry(CTA), a technique that measures the uid velocity over a heated metal wire. The resultsof this project is the measurement system itself, and the calibration and velocity measurementsgathered from experimentation. Two issues we encountered was that the calibrationprocess resulted in an overestimation of the velocity in the order of 4000 cm/s, and thatthe response to changes in velocity rates was quite slow. However, a slight tuning of thetwo calibration constants A0 & B0 smoothed the velocity estimation out to 40 cm/s, whichis more what we would expect. This illustrated how sensitive the results were to errors inthe calibration. Further investigation of the slow response, and a more stringently executedcalibration setup, could make the CTA a potential candidate for estimating the uid velocityinside the RBR.

Desenvolveu-se um sistema para medir a constante dielétrica complexa de amostras dielétricas, de construção simples, versátil e de baixo custo. A medida é feita aplicando-se uma tensão senoidal e fazendo-se a aquisição do sinal aplicado e do sinal da resposta elétrica (carga elétrica). Emprega-se uma placa A/D para a aquisição de dados com taxa de amostragem de 100 Ksamples/seg e através da transformada de Fourier discreta destes sinais determina-se a impedância complexa da amostra, a partir da qual calcula-se a constante dielétrica complexa. A placa utilizada e o circuito de medida da carga elétrica introduzem defasagens indesejáveis nos sinais, cujas correções são feitas através de programa no computador usado para aquisição dos sinais. O sistema mostra um desempenho similar àqueles dos equipamentos comerciais para freqüências no intervalo de 0,1H.z a 1KHz, sendo testado com componentes resistivos e capacitivos e posteriormente em amostras de Teflon FEP, poli(fluoreto de vinilideno) e seus copolímeros com trifluoretileno. O sistema também foi utilizado para medir o deslocamento elétrico nos polímeros ferroelétricos sob a aplicação de campos elevados. Neste caso determinaram-se as curvas de histerese dielétrica e os deslocamentos de primeira, segunda e terceira ordem. / A low cost and a simple experimental system for measuring the complex dielectric constant of dielectric samples were developed. Measurements were performed measuring the electric charge response resulting from the application of a sinusoidal voltage. The system was based on an A/D acquisition board with sampling rate of 100 Ksamples/sec. The complex impedance was calculated using the discrete Fourier transform from which the complex dielectric constant was found. The phase differences introduced by the A/D board and the amplifiers circuits were connected by software. The setup showed that the results are comparable to that ones obtained with commercial impedance analyzers in the range of frequencies between 0.1 Hz and 1 KHz. Such measurements were obtained using resistors and/or capacitors and also using samples of Teflon FEP, PVDF and its copolymers with trifluorethylene. The setup was also capable to measure the electric displacement in ferroelectric polymers submitted to high fields. Hysteresis loops and the nonlinear electric displacement of first, second and third order were measured.

Au cours des dernières années, le transport aérien de passagers connaît un développement sans cesse croissant et continue ainsi d’accroire sa contribution aux émissions mondiale de CO2. Par conséquent, un effort commun entre les avionneurs est fait pour diminuer les émissions de CO2 et de polluants. Pour encourager cet effort, les réglementations deviennent de plus en plus drastiques en terme d'émissions et de polluants tels que le CO2, les NOx mais aussi le bruit. Ces nouvelles limitations sont à la fois définies à court et moyen-long termes pour inciter les motoristes à travailler sur les technologies de plus en plus efficientes.Pour concevoir des moteurs toujours plus performants tout en respectant ces réglementations à court terme, les motoristes travaillent sur l'optimisation de leurs technologies conventionnelles, en améliorant des leviers bien identifiés comme l'augmentation du taux de compression. Cependant, cette optimisation des turbomachines actuelles a déjà atteint un niveau de maturité très élevé. Il semble ainsi difficile de continuer indéfiniment leurs optimisations. Par conséquent, pour atteindre les objectifs à moyen-long terme, les motoristes sont dès aujourd'hui en train d'étudier des nouveaux systèmes propulsifs avancés comme les chambres de Combustion à Volume Constant (CVC) qui peuvent accroître le rendement thermique. Contrairement aux chambres de combustion traditionnelles, qui fonctionnent à flux continu, les chambres CVC opèrent de façon cyclique afin de créer un volume constant pendant la phase de combustion et libérer les gaz chauds dans les étages de turbines.Pendant cette thèse, une approche numérique permettant d'évaluer ce type de chambres est développée. Tout l'enjeu est de pouvoir étudier des chambre de combustion intégrant des parties mobiles, qui permettent de créer le volume constant dédié à la combustion tout en évitant les fuites à travers ces systèmes mobiles lors de l'élévation de la pression dans la chambre. Cette modélisation doit aussi prédire correctement les phases transitoires comme l'admission des gaz frais, qui pilote la phase de combustion. Cette étude utilise des objets immergés pour modéliser les parties mobiles. Les objectifs de cette thèse sont de rendre ces objets immergés imperméables et adapter la méthode aux différents modèles utilisés pour étudier les milieux réactifs tels que le modèle de combustion ECFM-LES ou encore l'injection liquide Lagrangienne utilisée pour résoudre l'injection du fuel.Dans cette étude, une nouvelle formulation est développée puis testée sur différents cas tests de plus en plus représentatifs des chambres CVC. Cette approche numérique est ensuite évaluée sur une chambre réel étudiée expérimentalement au laboratoire PPRIRME de Poitiers. Dans cette dernière étude, deux cas non réactifs permettent de comparer les évolutions de pression à deux endroits dans la dispositif expérimental, ainsi que les champs de vitesse au sein de la chambre de combustion, aux simulations réalisées. Pour ces cas complexes, l'utilisation des objets immergés permet de prédire les résultats expérimentaux à un coût attractif.Un des cas non réactif est ensuite carburé et allumé pour confronter l'évolution pression et les champs de vitesse dans la chambre de combustion des résultats numériques obtenus aux mesures expérimentales. L'approche numérique développée a permis d’enrichir les données expérimentales, d'analyser les variabilités cycle-à-cycle rencontrées au banc et d'identifier les leviers qui permettraient d'optimiser ce type d’architecture. / Over the past few years, aircrafts have become a common means of transport, thus continuously increasing their contribution to global CO2 emissions. Consequently, there is a common effort between aircraft manufacturers to reduce CO2 and pollutant emissions. To encourage this effort, regulations are becoming more and more stringent on the emissions and pollutants like CO2, NOx and noise. These regulations are both defined in the short and medium-long terms to urge aircraft manufacturers to work on more and more efficient technologies.In order to design more efficient engines while respecting the short term objectives, engine manufacturers are working on the improvement of conventional architectures by using well-known levers like the increase of the Overall Pressure Ratio (OPR). However, the optimization of the present turbomachinery has already reached a high level of maturity and it seems difficult to continuously enhance their performances. Consequently, to reach the medium-long term objectives, engine manufacturers are working on new advanced propulsion systems such as the Constant Volume Combustion (CVC) chambers, which can increase the thermal efficiency of the system. Contrary to present turbomachinery which are burning fresh gases continuously, CVC chambers operate cyclically so as to create the constant vessel dedicated to the combustion phase and to expand the burnt gases into turbine stages.In this PhD thesis, a numerical approach is developed to allow the evaluation of these kind of combustors. The challenge is to be able to evaluate CVC chambers by taking into account the moving parts which create the constant volume and avoid mass leakages through these moving parts during the increase of the combustion chamber pressure when the combustion occurs. This approach also has to correctly predict unsteady phases like the intake, which directly controls the combustion process.These moving parts are modeled with a Lagrangian Immersed Boundary (LIB) method .The main goals of this thesis is to make the LIB as airtight as possible and to render this approach compatible with the different models which are adapted to analyse reactive flows such as the ECFM-LES combustion model or Lagrangian liquid injection, used for fuel sprays. In this study, a new formulation is developed and tested on several test cases from very simple ones to cases more representative of CVC chambers.Then, this approach is evaluated on a real chamber experimentally analysed in PPRIME laboratory in Poitiers. Two non-reactive operating points are used to compare the experimental pressure at two positions in the apparatus and the experimental velocity fields in the combustion chamber with the numerical results. In this complex configuration, the LIB method allows the prediction of the experimental results with a low CPU cost. As in the experiment, one non-reactive case is carburized and ignited to compare the measured pressure and the velocity fields in the combustion chamber with the simulations. The proposed numerical approach allows the data enhancement of the experiment and then the analysis of the cycle-to-cycle variability encountered during the experimental measurements. Last but not least, this method enables the identification of the different levers that could decrease the variability and then could improve operability of this type of combustors.

A presente dissertação aborda o pensamento arquitetônico europeu dos anos sessenta. Foca, particularmente, sobre a produção \"visionária\" do holandês Victor Nieuwenhuys (cujo pseudônimo era \"Constant\"), do grupo de arquitetos ingleses Archigram e dos grupos de arquitetos e designers italianos Archizoom e Superstudio. Analisa em que medida o avanço tecnológico e as novas teorias de informação/comunicação influem sobre tal arquitetura, produzindo uma hibridização entre conceitos advindos de diferentes esferas disciplinares. Avalia, como estudos de caso, alguns exemplos destas projeções: o projeto para a New Babylon, de Constant; a Plug-in City, de Archigram; o Monumento Continuo, de Superstudio; e a No-Stop City, de Archizoom; e como estas articulam a busca por emancipação social e/ou coletiva e as implicações do projeto arquitetônico com a crescente afirmação de uma sociedade de massas orientada para o consumo. Indaga, finalmente, sobre como estas propostas de cidades - ou não-cidades - ficcionais relacionam-se com as transformações sociais, políticas e econômicas em curso, quais as suas implicações em relação ao panorama histórico no qual se situam e que tipo de contribuição trazem para o debate acerca dos problemas das cidades reais. / The following thesis approaches European sixties\' architectural thinking. It focuses particularly on the \"visionary\" production of Dutch Victor Nieuwenhuys (whose pseudonym was \"Constant\"), English group of architects Archigram and Italian groups of architects and designers Archizoom and Superstudio. It analyses in which point technological advance and new information/communication theories act on such architecture, producing a hybridization among concepts coming from different disciplinary fields. It evaluates, as case studies, some examples of those projections: Constant\'s project for New Babylon; Archigram\'s Plug-in City; Superstudio\'s Continuous Monument; and Archizoom\'s No-Stop City; and how they articulate the search for social and/or individual emancipation and architectural project\'s implications with the increasing affirmation of a consumption-oriented mass society. Finally, it inquiries how these proposals of fictional cities - or non-cities - relate themselves to the ongoing social, political and economic transformations, what are their implications in relation to the historic moment where they are situated and what kind of contribution they bring to the debate over real cities.

Face à l’explosion du trafic aérien attendue ces prochaines années, l’impact de l’aviation civile sur l’environnement est un enjeu majeur. Les instances environnementales internationales comme l’ACARE (Conseil Consultatif pour la Recherche Aéronautique en Europe), en partenariat avec les grands groupes aéronautiques internationaux, ont fixé des objectifs drastiques pour préserver l’environnement : une réduction des émissions de CO2de 75 %et une réduction de 90 % des rejets d’oxydes d’azote dans l’atmosphère sont attendues d’ici 2050 par rapport aux avions fabriqués au début du 21èmesiècle. Les turbomachines actuelles possédant un degré de maturité très élevé ne permettront pas d’atteindre ces objectifs. Les motoristes cherchent donc à étudier de nouveaux concepts en rupture technologique pour les horizons 2050, comme les moteurs à détonation, ou encore les moteurs de type combustion à volume constant. Actuellement, les phénomènes physiques associés à la combustion du kérosène dans ce type de moteur sont encore mal documentés. L’objectif de cette thèse est donc de contribuer à l’amélioration de la connaissance et de la compréhension de ces phénomènes physiques.Au cours de cette étude, les flammes de pré-mélanges de kérosène et d’air sont étudiées expérimentalement grâce à des diagnostics optiques (strioscopie,PIV) et métrologiques. Le processus de combustion est notamment étudié dans des conditions thermodynamiques semblables à celles rencontrées dans un moteur aéronautique. La phase de propagation est dans un premier temps analysée dans des conditions laminaires et adiabatiques à travers la détermination de la vitesse fondamentale de flamme non-étirée, grandeur qui pilote le processus de combustion. Puis la sensibilité du front de flamme à l’étirement et la formation des instabilités de combustion sont dans un second temps examinées. Enfin, la phase d’allumage des pré-mélanges de kérosène et d’air dans des conditions aérodynamiques critiques est elle aussi traitée.Un second point abordé au cours de cette étude concerne la reproduction d’un kérosène réel par un substitut constitué d’un nombre d’espèces limité pour simplifier les problématiques industrielles et les études amont. En effet, la composition d’un kérosène commercial est complexe et variée et l’utilisation d’un représentant permet de modéliser numériquement le phénomène de combustion plus facilement. La pertinence de quelques surrogates plus ou moins représentatifs, formulés dans la littérature et élaborés au cours de différents travaux est notamment traitée dans cette étude en comparant les résultats obtenus avec ceux d’un kérosène commercial. De plus, la modélisation de ces kérosènes de substitution par un schéma cinétique valide estégalement analysée.Ce travail prend place dans le cadre de la chaire industrielle CAPA sur la combustion alternative pour la propulsion aérobie financée par SAFRANTech, MBDA et l’ANR. / With air traffic expected to soar in the next few years, the impact of civil aviation on the environment is a major issue. International environmental organizations such as ACARE (the Advisory Council for Aeronautical Research and Innovation in Europe), in partnership with the main international aeronautical groups, have set drastic objectives to preserve the environment: a reduction of 75 % of CO2emissions and a reduction of 90 % of nitrogen oxide emissions into the atmosphere are sought by 2050, with reference to aircraft produced at the beginning of the 21st century. Current turboshaft engines have a very high degree of maturity and may not achieve these objectives. Engineers are therefore aiming to study new concepts that will become technological breakthroughs at the 2050 horizon, such as detonation engines or constant volume combustion engines. Currently, the physical phenomena associated with the combustion of kerosene in those kinds of engines are still poorly documented. The objective of this PhD thesis is to contribute to the improvement of the knowledge and understanding of these physical phenomena. In this work, premixed flames of kerosene and air are experimentally studied with optical diagnostics (Schlieren, PIV) and metrology techniques. The combustion process is here studied in thermodynamic conditions similar to those encountered in an aeronautical engine. First, the propagation phaseis analyzed in laminar and adiabatic conditions through the determination of the unstretched laminar burning velocity, which drives the combustion process. Then, in a second stage, the sensitivity of the flame front to stretch and the formation of combustion instabilities are examined. Finally, the ignition phase of premixed flames of kerosene and air under critical aerodynamic conditions is also investigated. A second issue tackled in this work is the reproduction of a real kerosene by a surrogate made up of a limited number of species, to simplify industrial problems and initial studies. Indeed, the composition of a commercial kerosene is complex and can vary, and the use of a surrogate allows an easier numerical simulation of the combustion process. The relevance of some more or less representative surrogates, formulated in the literature and elaborated all through different studies, is also studied in this thesis, by comparing the results obtained with those of a commercial kerosene. In addition, the modelling of those surrogates by a valid chemical kinetic mechanism is also analyzed. This research was conducted within the CAPA industrial Chair project dedicated to innovative combustion modes for air-breathing propulsion, financially supported by SAFRAN Tech, MBDA and France’s ANR national research agency.

Scientists and engineers measure dielectric constant because it gives them better understanding of materials and helps them to know how to integrate these materials into their design processes;it also helps them to shorten design life cycle,and aside these two functions,it has numerous uses all of which cannot be enumerated in this section.Owing to its usefulness,various measurement methods of dielectric constant of materials have been developed over the years.Each method has its limitations which affect the accuracy of the measurement;these limitations range from frequency,temperature,and  mearsurement environment to material under test.   In this thesis,four most common methods of measuring dielectric constant were discussed and the most accurate one,the resonant method,was chosen and worked on .The project was executed by making a mathematical analysis of the ring resonator which was later simulated in HFSS to get results which would be comparable to ones obtained in  laboratory measurements.   The ring was fabricated and taken to the laboratory for measurement.Two monopole antennas were connected to the two ports of a VNA with one antenna serving as the transmitter and the other serving as the receiver.   The resonant frequencies obtained were combined with the geometric parameters of the ring resonator and that of the MUT in equations written into MATLAB scripts;this equations were used to extract the dielectric constant of the MUT.

By using the finite element method to solve the appropriate momentum and energy equations the friction factors and Nusselt numbers for fully developed laminar flow were determined for one- and two-dimensional flow systems. The Nusselt numbers were determined for domain boundaries subjected to a constant heat flux (H1) or a constant surface temperature (T) around the computational boundaries and in the axial directions. C++ programs, that were rewritten and extended from previous programs, were used to solve the laminar flow and to determine the values. The required wall shear stresses and heat fluxes were directly obtained for a duct as part of the primary finite-element solution; these values were then used to determine the Nusselt number and friction factor for the specific duct. The computations were performed for circular-, annular-, trapezoidal-, rectangular- and triangular ducts. Special emphasis was placed on trapezoidal ducts since only a limited number of studies have been performed on trapezoidal duct shapes and none of these studies employed the finite element method. Excellent agreement was found when the determined values were compared with the values reported in the literature. In general, the agreement of the values improved as the number of elements was increased. It was, therefore, concluded that the methods used in this study yielded friction factors and Nusselt numbers that are very accurate and usable. / Thesis (M.Ing. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2009.