Este trabalho traz a aplicação da transformada wavelet (TW) para analisar os transitórios de alta freqüência em um sistema de transmissão causados por uma falta sustentada, com o objetivo de se determinar a precisa localização da mesma. A TW, ferramenta matemática empregada neste trabalho, é uma transformação linear muito parecida com a transformada de Fourier, com uma importante diferença: ela permite a localização no tempo de diferentes componentes de freqüência de um dado sinal. Esta localização permite a detecção no tempo da ocorrência de distúrbios abruptos, tais como os transitórios ocasionados por situações de faltas. Os sinais de ondas viajantes geradas pela ocorrência da falta aparecem como distúrbios superpostos aos sinais de freqüência fundamental que são registrados pelos relés. Processando-se estes sinais pelo emprego da TW, esta pode revelar o tempo de propagação dos sinais analisados entre o ponto de ocorrência do distúrbio e a localização física do relé. Conseqüentemente, dispondo-se do intervalo de tempo entre as ondas sobre uma dada linha de transmissão, a distância do ponto de falta pode então ser facilmente determinada, sendo esta a filosofia adotada neste trabalho. O problema delineado é abordado através da implementação prática de um algoritmo computacional. Nesta implementação, o usuário pode escolher a técnica de localização a ser empregada, utilizando-se de dados registrados em um ou em ambos os terminais da linha, conforme a sua necessidade e/ou disponibilidade dos recursos necessários. Com o objetivo de testar e validar a aplicabilidade do algoritmo de localização de faltas, utilizou-se de dados de sinais faltosos obtidos através de simulações do software ATP (Altenative Transients Program), levando-se em conta vários tipos de falta em diferentes localizações ao longo da linha, com diferentes ângulos de incidência, resistências de falta, freqüência de amostragem do sinal, etc. Também foi verificada a influência do acoplamento mútuo em caso de circuitos duplos de transmissão. Os resultados alcançados pelo algoritmo são promissores e demonstram uma ótima precisão e aplicabilidade do método proposto. / This work presents a wavelet transform (WT) application to analyze the high frequency transients in a transmission line caused by a fault, with the purpose of determining its accurate location. The WT is very similar to Fourier Transform (FT), with an important difference: it allows the time determination of different frequency components of a signal. This skill allows the detection of the time of the disturbance occurrence, such as fault transients. The traveling waves generated by the fault occurrence appear as superimposed disturbances on the power frequency signals recorded by the relay. By processing these signals using the WT, the propagation time between the fault point and the relay location can be determined. Consequently, the distance of the fault point can be easily calculated. The delineated problem is boarded through the practical implementation of a computational algorithm. In this implementation, the user can choose the location technique to be employee, using data registered in one or both the terminals of the line, according to the necessity and/or availability of the data. In order to evaluate the applicability of the proposed scheme, the simulation of the transmission line in a faulty condition was utilized. This work makes use of a digital simulator of a faulted EHV (Extra High Voltage) transmission lines known as Alternative Transients Program (ATP). A typical transmission line from CESP (Companhia Energética de São Paulo) were utilized. The simulated data obtained was very close to that found in practice. This study takes into account single phase to ground faults, phase-to-phase faults, phase-phase to ground and three phase faults. The data set was composed of various fault situations considering different fault locations, fault resistances and fault inception angles. The influence of the sampled rate used was also verified as well as the mutual coupling in case of double transmission circuits. The test results reached for the algorithm are promising and demonstrate a highly satisfactory degree of accuracy and applicability of the proposed method.

Submitted by Jaqueline Silva (jtas29@gmail.com) on 2016-09-08T17:05:05Z No. of bitstreams: 2 Dissertação - Brayan Maurício Rodrigues Garzon - 2016.pdf: 1077822 bytes, checksum: 22f0f3e54ede997e3bbec84f88406474 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Jaqueline Silva (jtas29@gmail.com) on 2016-09-08T17:05:21Z (GMT) No. of bitstreams: 2 Dissertação - Brayan Maurício Rodrigues Garzon - 2016.pdf: 1077822 bytes, checksum: 22f0f3e54ede997e3bbec84f88406474 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-09-08T17:05:21Z (GMT). No. of bitstreams: 2 Dissertação - Brayan Maurício Rodrigues Garzon - 2016.pdf: 1077822 bytes, checksum: 22f0f3e54ede997e3bbec84f88406474 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-03-04 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we study and show the existence of traveling waves solutions for a system of parabolic partial differential equations (PPDE’s) which model in-situ combustion process in porous medium. The in-situ combustion process is a thermal method to recovery oil from petrolific reservoirs. The system deduction is making considering two layers of porous rock and aplying the physical laws of balance energy, fuel mass, oxygen mass, total gas mass, and the Darcy’s law which link the pressure and volumetric flow rate. The traveling waves are obtained making an useful variavel change such that convert the PPDE’s system in an ordinary differential equations system (ODE’s) where the existence of heteroclinic orbits is equivalent to the existence of a traveling waves for the system of PPDE’s which connect the burned state to the unburned state. In the proof of the existence and uniquess of such orbits are used basic tools in Qualitative Ordinary Differential Equations Theory, Dynamical Systems, Perturbation Theory and TravelingWaves Theory with special mention to Singular Perturbation Theory and Melnikov Method inside of the perturbation theory. / Neste trabalho estudamos e mostramos a existência de soluções do tipo onda viajante para um sistema de equações diferenciais parciais parabólico (EDPP’s) que modela um processo de combustão in-situ através de um meio poroso. A combustão in-situ é um método térmico de recuperação de óleo de reservatórios petrolíferos. O sistema é deduzido considerando duas camadas de rocha porosa e aplicando as leis físicas de balanço de energia, de massa de combustível, oxigênio, gás total, e a lei de Darcy que relaciona a pressão e a vazão volumétrica dos fluidos considerados. As ondas viajantes são obtidas fazendo uma mudança de variáveis apropriada de modo que o sistema de EDPP’s se transforme num sistema de equações diferenciais ordinárias (EDO’s), onde a existência de uma orbita conectando dois equilíbrios corresponde-se com a existência de uma onda viajante do sistema de EDPP’s, conectando um estado totalmente queimado com um estado não queimado. Para a prova de existência e unicidade das referidas órbitas são utilizadas ferramentas básicas da Teoria qualitativa das Equações Diferenciais Ordinárias, Sistemas Dinâmicos, Teoria da Perturbação e Teoria de Ondas Viajantes, ressaltando dentro da teoria da perturbação a técnica da Perturbação Singular Geométrica e o Método de Melnikov.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-11-12T14:41:49Z No. of bitstreams: 1 rosmeryvioletaquispezavala.pdf: 2260352 bytes, checksum: 5065e53fcdfaaf4c24879ca0ea89cd54 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-11-23T11:06:29Z (GMT) No. of bitstreams: 1 rosmeryvioletaquispezavala.pdf: 2260352 bytes, checksum: 5065e53fcdfaaf4c24879ca0ea89cd54 (MD5) / Made available in DSpace on 2018-11-23T11:06:29Z (GMT). No. of bitstreams: 1 rosmeryvioletaquispezavala.pdf: 2260352 bytes, checksum: 5065e53fcdfaaf4c24879ca0ea89cd54 (MD5) Previous issue date: 2018-08-13 / Apresentamos um modelo para a injeção de ar em um meio poroso que contém combustível sólido levando em conta as perdas térmicas para rocha circundante. Em trabalhos anteriores, o modelo foi simplificado e todas as sequências de ondas para a solução de problemas de Riemann foram obtidas sem levar em conta as perdas térmicas. Nesse trabalho, é feito um primeiro passo para entender o efeito das perdas de calor, que são importantes especialmente em experimentos de laboratório. Para provar a existência e unicidade da solução de ondas viajantes, os efeitos de difusão e a dependência da densidade do gás na temperatura são desconsiderados. Também são apresentadas simulações numéricas que validam os resultados obtidos, bem como simulações numéricas para um sistema mais geral que considera termos difusivos. Por fim são comparadas as soluções numéricas para ambos sistemas e um exemplo numérico com valores típicos dos parâmetros para um modelo de combustão é apresentado. / We present a model for the injection of air into an underground porous medium that contains a solid fuel. In previous works the model was simplified and all wave sequences for the Riemann problem solution were obtained without taking into account thermal losses to the surrounding rock. In that work the first step was made to understand the effect of heat losses, which are important especially in laboratory experiments. In order to prove of the existence and uniqueness of the traveling wave solution, diffusion effects and the dependence of gas density on temperature were disregarded. We will also present numerical simulations that validate the results obtained, as well as numerical simulations for a more general system that considers diffusive terms. Furthermore, we will compare the numerical solutions for both systems and a numerical example with typical values of the parameters for a combustion model is presented.

Pour les compresseurs axiaux et centrifuges, la minimisation du jeu, entre l’extrémité des aubes et le carter qui les entoure, augmente l’efficacité aérodynamique des turbomachines mais favorise également l’apparition de contacts structuraux. En présence du contact, les deux structures échangent de l’énergie et le système peut devenir instable lorsque ses fréquences propres, exprimées dans le même repère, sont égales. Nous verrons qu’il existe également la possibilité de créer des réponses forcées lorsque les harmoniques de la vitesse de rotation coïncident avec les fréquences propres de la structure fixe ou tournante. Dans les deux cas, les structures peuvent subir des endommagements assez importants. La maitrise de l’interaction aube-carter est donc logiquement un phénomène que les constructeurs de turbomachines doivent intégrer lors de la définition d’un moteur. Ainsi, dans l’étape de conception des compresseurs, il faut prévoir le comportement vibratoire du système en prenant en compte les phénomènes physiques les plus influents. Dans ce contexte, ce travail de recherche est focalise sur l’étude du comportement mécanique et thermomécanique résultant de l’interaction aube-carter entre un compresseur centrifuge (ou rouet) expérimental du premier étage de compression d’un moteur d’hélicoptère et son couvercle qui est recouvert d’un matériau abradable afin de réduire la sévérité du contact. L’objectif majeur des travaux présentes dans ce manuscrit est d’établir un scénario plausible pour expliquer les divers phénomènes présents lors du contact et de créer une base de données expérimentales, dans un environnement de laboratoire au travers d’un essai réaliste et maitrisé. Puis, il s’agit de confronter et valider les interprétations expérimentales sur un modèle numérique. Pour atteindre nos objectifs, nous avons utilisé un dispositif d’essai adapté afin de fournir des données fiables sur le comportement dynamique et thermomécanique en situation de contact aube-carter. L’analyse des résultats expérimentaux et numériques montre des évènements transitoires concomitants entre la structure fixe et tournante. Le contenu spectral des réponses est caractérise par la présence d’harmoniques de la vitesse de rotation et de sidebands, qui influencent le comportement dynamique du système lorsqu’ils coïncident avec les fréquences propres des structures. / In axial and centrifugal compressors, minimizing the clearance between the blade tips of the impeller and its surrounding casing increases the aerodynamic efficiency, but also the probability of contacts. An energy exchange is then produced between the two structures, leading to forced excitation of the natural modes and potentially to dynamical instabilities, such as interaction phenomena. In both cases, the structures suffer subsequent structural damages. Mastering blade-to-casing interactions is thus a phenomenon that turbomachinery manufacturers must incorporate into the design process of an engine. Compressor designers must predict the vibration behavior of the system, taking into account the predominant physical phenomena. In this context, this work focuses on the study of the dynamic and thermomecanichal behavior resulting from blade-to-casing interactions between a low-pressure centrifugal compressor (or impeller) and a casing lined with abradable coating. The main purpose of this work is to build a likely scenario to explain the various phenomena present when contact occurs, and the creation of a database for subsequent comparisons with numerical simulations. To achieve this, a test rig heavily instrumented has been used in order to better understand the influence of various physical phenomena (dynamic, wearing, heating). Analysis of experimental and numerical results shows transient events, characterized by a simultaneous increase in amplitude on both the rotating and stationary structures. The spectral content of the response highlights the presence of harmonics of the rotating speed and some sidebands aside from the main excited frequencies, which may cause the system to become unstable when they coincide with the natural frequencies of structures.

Ce travail se concentre sur l'étude de la dynamique des dislocations dans le réseau cristallin et il est découpé en deux parties : la première partie porte sur les mouvements horizontaux d'une chaîne d'atomes en interaction contenant une dislocation. Bien que, la deuxième partie traite de l'accumulation de dislocations formant ce qu'on appelle des murs de dislocations. Dans la première partie, nous considérons une généralisation complètement nonlinéaire des équations de diffusion de réaction discrète également appelée “modèles de Frenkel-Kontorova complètement amortis” qui décrivent la dynamique des défauts cristallins (dislocations) dans un réseau. Nous étudions à la fois : les non-linéarités bistable et monostable. Dans des conditions suffisantes, nous montrons l'existence et l'unicité des ondes progressives pour le cas de non-linéarité bistable. Pour le cas monostable, nous étudions l'existence de la branche des solutions d'ondes progressives pour une non-linéarité Lipschitz général. Nous montrons également que la vitesse minimale est positive et délimitée ci-dessous. Dans cette partie, nous étudions aussi la généralisation du modèle de Frenkel-Kontorova pour laquelle nous pouvons ajouter un paramètre de force motrice. Nous illustrons également, dans ce cas, la variation de la vitesse de propagation des ondes progressives en fonction du paramètre de force. Dans la deuxième partie, nous étudions l'accumulation des dislocations dans les murs de dislocations. Nous montrons en fait la convergence de plusieurs dislocations qui interagissent sur les murs de dislocations. Nous présentons aussi les résultats de quelques expériences numériques qui confirment les résultats théoriques que nous obtenons / This work focuses on the study of the dislocation dynamics in the crystal lattice and it is splitted into two parts : the first part is concerned with the horizontal motion of a chain of interacting atoms containing a dislocation. While, the second part deals with the accumulation of dislocations forming what is known as walls of dislocations. In the first part, we consider a fully nonlinear generalization of the discrete reaction diffusion equations “fully overdamped Frenkel-Kontorova models” that describe the dynamics of crystal defects (dislocations) in a lattice. We study both : the bistable and the monostable non-linearities. Under sufficient conditions, we show the existence and uniqueness of traveling wave solution for the bistable non-linearity case. For the monostable case, we study the existence of branch of traveling waves solutions for general Lipschitz non-linearity. We also prove that the minimal velocity is non-negative and bounded below. In this part, we as well study the generalization of Frenkel-Kontorova model for which we can add a driving force parameter. We also illustrate, in this case, the variation of the velocity of propagation of traveling waves in terms of the parameter force. In the second part, we study the accumulation of dislocations in walls of dislocations. We prove actually the convergence of several interacting dislocations to walls of dislocations. We also present results of some numerical experiments that confirm the theoretical results that we obtain

No description available.

L'étude théorique de la transition vers la turbulence d'écoulements en tuyau de fluides non newtoniens rhéofluidifiants (fluides de Carreau) est menée, avec l'approche consistant à calculer des «~structures très cohérentes~» sous la forme d'«~ondes non linéaires~». Pour cela un code pseudo-spectral de type Petrov-Galerkin, permettant de suivre des solutions ondes non linéaires tridimensionnelles dans l'espace des paramètres par continuation, est développé. Ce code est validé par comparaison à des résultats existants en fluide newtonien, et grâce à un test de consistance en fluide non newtonien. Une convergence spectrale exponentielle est obtenue dans tous les cas. Ce code est utilisé pour chercher (guidé par des résultats expérimentaux récents) de nouvelles solutions de nombre d'onde azimutal fondamental égal à 1, sans succès pour l'instant. Par contre des solutions de nombre d'onde azimutal fondamental égal à 2 ou 3 sont obtenues par continuation à partir du cas newtonien. La rhéofluidification induit, en termes de nombres de Reynolds critiques, un retard à l'apparition de ces ondes par rapport au cas newtonien. Ce retard est caractérisé, et le parallèle est fait avec divers résultats expérimentaux qui montrent un retard à l'apparition de bouffées turbulentes en fluides non newtoniens / The transition to turbulence in pipe flows of shear-thinning fluids is studied theoretically. The method used is the computation of `exact coherent structures' that are tridimensional nonlinear waves. For this purpose a pseudo-spectral Petrov-Galerkin code is developped, which also allows to follow solution branches in the parameter space with continuation methods. This code is validated by recovering already published results in the Newtonian case, and by a consistency test in the non-Newtonian case. A spectral exponential convergence is obtained in all cases. This code is used to seek (guided by recent experimental results) new solutions of fundamental azimuthal wavenumber equal to 1,without success at the time being. On the contrary solutions with a fundamental azimuthal wavenumber equal to 2 and 3 are obtained by continuation from the Newtonian case. The shear-thinning effects induce, in terms of critical Reynolds numbers, a delay for the onset of these waves, as compared with the Newtonian case. This delay is characterized. An analogy is made with various experimental results that show a delay in the transition to turbulence, more precisely, in the onset of `puffs', in non-Newtonian fluids

Cette thèse porte sur l'analyse mathématique de modèles de réaction-dispersion de la forme [delta]tu=D(u) +f(x,u). L'objectif est de comprendre l'influence du terme de réaction f, de l'opérateur de dispersion D, et de la donnée initiale u0 sur la propagation des solutions de ces équations. Nous nous sommes intéressés principalement à deux types d'équations de réaction-dispersion : les équations de réaction-diffusion où l'opérateur de dispersion différentielle est D=[delta]2z et les équations intégro-différentielles pour lesquelles D est un opérateur de convolution, D(u)=J* u-u. Dans le cadre des équations de réaction-diffusion en milieu homogène, nous proposons une nouvelle approche plus intuitive concernant les notions de fronts progressifs tirés et poussés. Cette nouvelle caractérisation nous a permis de mieux comprendre d'une part les mécanismes de propagation des fronts et d'autre part l'influence de l'effet Allee, correspondant à une diminution de la fertilité à faible densité, lors d'une colonisation. Ces résultats ont des conséquences importantes en génétique des populations. Dans le cadre des équations de réaction-diffusion en milieu hétérogène, nous avons montré sur un exemple précis comment la fragmentation du milieu modifie la vitesse de propagation des solutions. Enfin, dans le cadre des équations intégro-différentielles, nous avons montré que la nature sur- ou sous-exponentielle du noyau de dispersion J modifie totalement la vitesse de propagation. / This thesis deals with the mathematical analysis of reaction-dispersion models of the form [delta]tu=D(u) +f(x,u). We investigate the influence of the reaction term f, the dispersal operator D and the initial datum u0 on the propagation of the solutions of these reaction-dispersion equations. We mainly focus on two types of equations: reaction-diffusion equations (D=[delta]2z and integro-differential equations (D is a convolution operator, D(u)=J* u-u). We first investigate the homogeneous reaction-diffusion equations. We provide a new and intuitive explanation of the notions of pushed and pulled traveling waves. This approach allows us to understand the inside dynamics the traveling fronts and the impact of the Allee effect, that is a low fertility at low density, during a colonisation. Our results also have important consequences in population genetics. In the more general and realistic framework of heterogeneous reaction-diffusion equations, we exhibit examples where the fragmentation of the media modifies the spreading speed of the solution. Finally, we investigate integro-differential equations and prove that emph{fat-tailed} dispersal kernels J, that is kernels which decay slower than any exponentially decaying function at infinity, lead to acceleration of the level sets of the solution u.

Este trabalho apresenta o estudo e o desenvolvimento de um algoritmo híbrido para detecção, classificação e localização de faltas em sistemas com três terminais utilizando como principal ferramenta a transformada wavelet (TW) em suas versões discreta (TWD) e estacionária (TWE). O algoritmo é dito híbrido, pois alia duas metodologias para localizar a falta. A primeira baseada na análise de componentes de alta freqüência (ondas viajantes) e a segunda, baseada na extração dos componentes fundamentais para o cálculo da impedância aparente. A metodologia proposta foi concebida de maneira a trabalhar com dados sincronizados dos três terminais ou apenas dados locais para estimar a localização da falta. O localizador híbrido escolhe automaticamente qual a melhor técnica de localização ser utilizada para alcançar uma localização confiável e precisa. Deste modo, um método pode suprir as dificuldades do outro, ou, no mínimo, fornecer mais informações para que, junto ao conhecimento do operador, uma localização próxima da ótima possa ser alcançada. Com o objetivo de testar e validar a aplicabilidade do algoritmo de localização de faltas híbrido para linhas com três terminais, utilizou-se de dados de sinais faltosos obtidos através de simulações do software ATP (Altenative Transients Program), levando-se em conta a variação de diversos parâmetros que poderiam influenciar o desempenho do algoritmo proposto. Os resultados alcançados pelo algoritmo frente às situações avaliadas são bastante animadores, apontando a uma promissora aplicabilidade do mesmo. / This work presents a study and development of a hybrid algorithm for fault detection, classification and location in tree terminal lines based on wavelet transform (WT). It will be presented in two versions: discrete wavelet transform (DWT) and stationary wavelet transform (SWT). The algorithm is called hybrid because it uses two fault location methodologies: one based on fundamental components and other based on traveling waves. The proposed methodology works either with synchronized tree terminal data or only local data. The hybrid fault locator chooses automatically which location technique to be used in order to reach a reliable and accurate fault location. In this manner, this technique can avoid some difficulties present in other techniques, aiming to reach an optimized fault location. The proposed hybrid fault location was evaluated by simulated fault signals obtained by alternative transient program (ATP). In the tests, several parameters, which would influence the performance of the hybrid algorithm, were varied, such as: fault inception angle, fault resistance, fault type, etc. The results obtained by the proposed methodology are very encouraging and it points out to a very promising application.

Este trabalho apresenta o estudo e o desenvolvimento de um algoritmo híbrido para detecção, classificação e localização de faltas em sistemas com três terminais utilizando como principal ferramenta a transformada wavelet (TW) em suas versões discreta (TWD) e estacionária (TWE). O algoritmo é dito híbrido, pois alia duas metodologias para localizar a falta. A primeira baseada na análise de componentes de alta freqüência (ondas viajantes) e a segunda, baseada na extração dos componentes fundamentais para o cálculo da impedância aparente. A metodologia proposta foi concebida de maneira a trabalhar com dados sincronizados dos três terminais ou apenas dados locais para estimar a localização da falta. O localizador híbrido escolhe automaticamente qual a melhor técnica de localização ser utilizada para alcançar uma localização confiável e precisa. Deste modo, um método pode suprir as dificuldades do outro, ou, no mínimo, fornecer mais informações para que, junto ao conhecimento do operador, uma localização próxima da ótima possa ser alcançada. Com o objetivo de testar e validar a aplicabilidade do algoritmo de localização de faltas híbrido para linhas com três terminais, utilizou-se de dados de sinais faltosos obtidos através de simulações do software ATP (Altenative Transients Program), levando-se em conta a variação de diversos parâmetros que poderiam influenciar o desempenho do algoritmo proposto. Os resultados alcançados pelo algoritmo frente às situações avaliadas são bastante animadores, apontando a uma promissora aplicabilidade do mesmo. / This work presents a study and development of a hybrid algorithm for fault detection, classification and location in tree terminal lines based on wavelet transform (WT). It will be presented in two versions: discrete wavelet transform (DWT) and stationary wavelet transform (SWT). The algorithm is called hybrid because it uses two fault location methodologies: one based on fundamental components and other based on traveling waves. The proposed methodology works either with synchronized tree terminal data or only local data. The hybrid fault locator chooses automatically which location technique to be used in order to reach a reliable and accurate fault location. In this manner, this technique can avoid some difficulties present in other techniques, aiming to reach an optimized fault location. The proposed hybrid fault location was evaluated by simulated fault signals obtained by alternative transient program (ATP). In the tests, several parameters, which would influence the performance of the hybrid algorithm, were varied, such as: fault inception angle, fault resistance, fault type, etc. The results obtained by the proposed methodology are very encouraging and it points out to a very promising application.