[pt] Esta tese apresenta uma nova metodologia para a avaliação de índices de freqüência e duração (FeD) em estudos de confiabilidade composta geração e transmissão de sistemas de potência de grande porte. Os índices FeD são obtidos através do método de simulação Monte Carlo não seqüencial. São desenvolvidas duas técnicas de Lagrange associados à análise de desempenho de cada estado são utilizados para identificar a fronteira que separa os estados de falha e sucesso do sistema. A segunda usa os conceitos de probabilidade condicional e coerência do sistema para caracterizar a contribuição de cada componente nos índices de freqüência. A primeira técnica também é utilizada no cálculo de limites superiores destes índices. A aplicação da metodologia é ilustrada através de estudos de casos com três sistemas, de 24, 120 e 500 barras, derivados de sistemas reais. os estudos indicam que ambas as técnicas se constituem em alternativas bastante atraentes para a estimação dos índices FeD. a primeira técnica mostrou-se ser cerca de 30% mais eficiente que a segunda, em termos computacionais. Por outro lado, a segunda técnica é mais flexível e, também, de implementação mais fácil. Viabiliza-se portanto, a aplicação prática de índices de freqüência e duração no planejamento integrado de sistemas geração/transmissão / [en] This thesis presents a new methodology for frequency and duration (FeD) assessment in composite generation and transmission reliability evaluation of large scale power systems. The FeD indices are obtained from a nonsequential Monte Carlo simulation scheme. Two tecniques are developed to estimate the feD indices. In the first, the Lagrange multipliers associated to the adequacy assessment of each state are used to identify the boundary wall between failure and success states. The second approach uses the concept of conditional probability and system coherence to caracterize the contribuition of each component to the frequency indices. Also, the first technique is used to calculate upper bounds of these indices. The methodology is illustrated in case studies with three test systems, with 24, 120 and 500 buses, derived from real systems. The studies indicated that both tecniques are very attractive in estimating the FeD índices. The first approach was about 30% faster than the second one. On the other hand, the second approach is more flexible and easy to implement. The proposed approach allows the pratical utilization of frequency and duration indices in integrates generation/transmission planning studies.

L'objectif de cette thèse est de contribuer au développement et à la validation d'outils numériques permettant la Simulation aux Grandes Echelles (SGE) de l'allumage d'un écoulement turbulent diphasique dans une chambre de combustion. Pour ce faire, une méthode de dépôt d'énergie modélisant l'apport d'énergie lié au claquage de la bougie d'allumage a été implémentée dans la chaîne de calcul CEDRE. Cette méthode a été validée sur une simulation de l'allumage d'un écoulement laminaire purement gazeux d'air et de propane. Une SGE de l'écoulement d'air du MERCATO a été effectué à l'aide du solveur Navier-Stokes CHARME de CEDRE. Cette simulation reproduit fidèlement l'écoulement turbulent non-réactif dans la chambre de combustion. Une méthode d'injection simplifiée FIMUR a été ajoutée au solveur lagrangien SPARTE de CEDRE. Dans cette méthode, des gouttes sont injectées directement au nez de l'injecteur avec une distribution de vitesse et de taille imposée. Une SGE de l'écoulement turbulent diphasique dispersé non-réactif dans la chambre MERCATO a ensuite été réalisée avec cette méthode. La comparaison des champs particulaires moyens de vitesse et de taille obtenus par simulation numérique avec les données expérimentales est satisfaisante. Enfin, des SGE de l'allumage de la chambre MERCATO ont été effectuées à partir du champ diphasique non-réactif simulé et de la méthode de dépôt d'énergie développée. Selon l'instant du dépôt d'énergie, les simulations conduisent à des allumages réussis ou ratés. La propagation de la flamme dans la chambre pour un allumage réussi a fait l'objet d'une analyse détaillée pour tenter de déterminer les principaux facteurs l'influençant. / The goal of this thesis is to contribute to the development and validation of numerical tools for the Large Eddy Simulation (LES) of the ignition of a turbulent multiphase flow in a combustion chamber. An energy deposition method that models the energy supplied by the spark plug to the flow was implemented in the CEDRE code. This method was validated on a simulation of the ignition of a purely gaseous laminar propane-air flow. Then, a LES of the non-reacting gas flow in the monosector combustor MERCATO was performed with the Navier-Stokes solver CHARME of the CEDRE code. The comparison between simulations and experiments demonstrates that the main flow field features are well reproduced. In order to simulate the non-reacting dispersed two-phase flow of the same configuration, a simplified injection method called FIMUR was implemented in the Lagrangian solver SPARTE of the CEDRE code. In this method, droplets are injected directly at the tip of the injector with velocities deduced from experimental correlations while the size distribution is directly obtained from experimental data. The comparison of the mean droplet velocity and diameter fields in the vicinity of the injector between simulations and experiments appears satisfactory. Finally, LES's of the ignition of the MERCATO were performed using the non-reacting two-phase flow simulations and the aformentioned energy deposition method. Depending on the instant of energy deposition, the simulations lead to successful or failed ignitions. The flame propagation in a successful ignition was analysed in order to attempt to determine the physical phenomena at play and to better understand them.

La combustion d’hydrocarbures représente encore aujourd’hui une part très majoritaire de la production d’énergie mondiale, en particulier dans la propulsion aérospatiale. La plupart des brûleurs industriels sont alimentés par un carburant sous forme liquide, qui est injecté directement dans la chambre de combustion, ce qui génère une forte interaction entre le spray, l’écoulement turbulent et la zone de combustion. Cette interaction a déjà largement été étudiée, mais certaines questions restent ouvertes. En particulier, la prise en compte de la combustion de goutte isolée dans le cadre de la Simulation aux Grandes Echelles (‘Large Eddy Simulation’ LES) de géométries complexes reste un problème difficile. L’objectif de cette thèse est d’améliorer la modélisation de la combustion du spray dans le contexte de la LES de configurations complexes avec une approche Euler-Lagrange. Dans un premier temps, un modèle de combustion de gouttes incluant les différents régimes pour la LES, appelé MustARD pour « Multi-State Algorithm for Reacting Droplets », est proposé et validé dans plusieurs configurations académiques de complexité croissante. Dans un deuxième temps, MustARD est évalué sur une configuration de brûleur expérimental et comparé aux modèles classiques sans combustion de gouttes isolées. Cette étude montre que le régime de combustion de gouttes isolées n’est pas négligeable dans une telle configuration et qu’il modifie la structure de flamme. D’autre part, les comparaisons avec les résultats expérimentaux montrent que le modèle MustARD permet d’améliorer la précision des LES de sprays turbulents réactifs. / The combustion of hydrocarbons still represents the major part of the worldwide production of energy, especially for aerospace. Most industrials burners are fed with liquid fuel that is directly injected in the combustion chamber, generating a strong interaction between the spray, the turbulent flow and the combustion. This interaction has been widely studied, but is not yet fully understood. In particular, modeling individual droplet combustion, in the framework of Large Eddy Simulation (LES) of complex geometries, is a difficult issue. This work aims at improving models for spray combustion, in the context of two-phase reactive LES of complex configurations using an Euler-Lagrange approach. First, a droplet combustion model accounting for the various regimes and called MustARD for « Multi-State Algorithm for Reacting Droplets » is proposed and validated on several academic configurations of growing complexity. Second, MustARD is evaluated in the LES of a lab-scale burner and compared to classical models neglecting individual droplet combustion. Results show in particular the importance of the new model and its impact on the flame structure. Moreover, the comparison with experiments shows that MustARD contributes to improve the numerical prediction of LES of two-phase reacting flows.

In the present work, the objective is to present a study on the methods of optimization and to apply them in the solution of daily problems. In mathematics, optimization refers to the study of problems in which one wants to maximize or minimize a given function by systematically choosing the values of variables within a viable set. We can analyze optimization problems by di erentiability with and without constraints, introducing the Lagrange multiplier method. The resolutions presented, based on a small theoretical basis, are concerned to cover di erent approaches and provide the relationship of concepts. One of the methods to determine the maximum and minimum of functions is to use the calculation in several variables, which will be approached in this work. Possible situations related to everyday life are presented so that the optimization process can be approached by high school students. / No presente trabalho, o objetivo é apresentar um estudo sobre os métodos de otimização e aplicá-los na solucão de problemas cotidianos. Em matemática, otimização refere-se ao estudo de problemas em que se deseja maximizar ou minimizar uma determinada função através da escolha sistemática dos valores de variáveis dentro de um conjunto viável. Podemos analisar problemas de otimização por diferenciabilidade com e sem restrições, inroduzindo o método dos multiplicadores de Lagrange. As resoluções apresentadas, baseam-se numa pequena fundamentação teórica, têm a preocupação de abranger diferentes abordagens e proporcionar o relacionamento de conceitos. Um dos métodos de se determinar os máximos e mínimos de funções é utilizando-se o cálculo em várias variáveis, o qual será abordado nesse trabalho. Possíveis situações relacionadas ao cotidiano são apresentadas para que o processo de otimização possa ser abordado por alunos do Ensino Médio. / São Cristóvão, SE

Orientador: Jose Mario Martinez Perez / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-13T22:53:44Z (GMT). No. of bitstreams: 1 Castelani_EmersonVitor_D.pdf: 695936 bytes, checksum: 9434e07a75cde154320a5156daf73684 (MD5) Previous issue date: 2009 / Resumo: Ao resolver problemas de programação não linear usando métodos do tipo Lagrangiano Aumentado, um fenômeno chamado voracidade pode ocorrer. Quando este fenômeno ocorre, o método busca pontos muito infactíveis com valor de função objetivo muito pequeno. Tais fatos ocorrem, em geral, na primeiras iterações e então, o parâmetro de penalidade precisa crescer excessivamente, tornado os subproblemas mal condicionados, prejudicando assim a convergência. Desta forma, o propósito deste trabalho é adicionar restrições de caixas adaptativas (região de confiança) a cada subproblema em cada iteração externa, de modo que, a distância entre dois iterando consecutivos das iterações externas é controlada. O novo método inibe a possibilidade do fenômeno de voracidade. Resultados de convergência, limitação de parâmetro de penalidade e exemplos numéricos são apresentados / Abstract: When we solve nonlinear programming problems by means of algorithms of kind of Augmented Lagrangian, a phenomenon called greediness may occur. Unconstrained minimizers attract the iterates at early stages of the calculations and, so, the penalty parameter needs to grow excessively, in such a way that ill-conditioning harms the overall convergence. In this sense, the proposal of this work is to add an adaptive artificial box constraint (trust-region) to the subproblem at every outer iteration, in such a way that the distance between consecutive outer iterates is controlled. The new method inhibits the possibility of greediness phenomenon. Convergence proofs and numerical examples are given / Doutorado / Otimização / Doutor em Matemática Aplicada

Apresentaremos uma classe de energias potenciais $\\Pi \\in C^{\\infty}(\\Omega,R)$ que são s-decidíveis e que admitem funções auxiliares de Cetaev da forma $\\langle abla j^s\\Pi(q),q angle$, $q\\in \\Omega \\subset R^n$ que são s-resistentes. / We will present a class of potential energies $\\Pi \\in C^{\\infty}(\\Omega,R)$ that are s-decidable and that admit auxiliary functions of Cetaev of the form $\\langle abla j^s\\Pi(q),q angle$, $q \\in \\Omega \\subset R^n$ which are s-resistant.

Orientador: Vera Lucia da Rocha Lopes / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-12T04:23:12Z (GMT). No. of bitstreams: 1 JimenezUrrea_Liliana_M.pdf: 3576733 bytes, checksum: 0e211564f3f081c060195cfa21aa4135 (MD5) Previous issue date: 2008 / Resumo: Neste trabalho apresentamos métodos de minimização irrestrita, de uma função objetivo F de várias variáveis, que não fazem uso nem do gradiente da função objetivo - métodos derivative-free, nem de aproximações do mesmo. Nosso objetivo básico foi estudar e comparar o desempenho de métodos desse tipo propostos por M. J. D. Powell, que consistem em aproximar a função F por funções quadráticas - modelos quadráticos - e minimizar tal aproximação em regiões de confiança. Além do algoritmo de Powell de 2002 - UOBYQA - são testados: uma variante dele, na qual utilizamos a escolha de alguns parâmetros, por nós estabelecida, e também a nova versão de NEWUOA, proposta por Powell em 2006. Todos os testes foram realizados com problemas da coleção de Hock-Schittkowski. São comparados os resultados numéricos obtidos pelos métodos de Powell: entre eles mesmos e também entre eles e um método de busca padrão de autoria de Virginia Torczon, o qual define, em cada iteração, um conjunto padrão de direções de busca a partir do ponto atual, procurando melhores valores para F. / Abstract: In this work we study numerical methods to solve problems of nonlinear programming without constraints, which do not make use, neither of the gradient of the objective function, nor of approaches to it. A method that consists on the approximation of the function F by a quadractic model, due to Powell (2002), UOBYQA, and a variant of this method were implemented. A new version of the NEWUOA, introduced by Powell in 2006, was also implemented. Besides the Powell algorithm, commentaries of the implementations are done. Numerical tests of such implementations with problems of the Hock-Schittkowski collection, are made at the end of the work. There are also comparisons of the Powell methods among themselves, and also a comparison among the Powell methods with a pattern search method, which looks for the improvement of the value of the objective function throughout a set of directions, depending on the current point. Such a method is due to Virginia Torczon. / Mestrado / Otimização / Mestre em Matemática Aplicada

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-07-12T11:34:57Z No. of bitstreams: 1 henriqueluismoreiramonteiro.pdf: 6497394 bytes, checksum: e4ba6289e2d5a09f203b42d5461ff1b1 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-07-17T11:53:38Z (GMT) No. of bitstreams: 1 henriqueluismoreiramonteiro.pdf: 6497394 bytes, checksum: e4ba6289e2d5a09f203b42d5461ff1b1 (MD5) / Made available in DSpace on 2018-07-17T11:53:38Z (GMT). No. of bitstreams: 1 henriqueluismoreiramonteiro.pdf: 6497394 bytes, checksum: e4ba6289e2d5a09f203b42d5461ff1b1 (MD5) Previous issue date: 2018-04-04 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho é proposto um método para estimar a impedância de maneira invasiva, utilizando uma estrutura com controle de distúrbio, filtro para eliminar os componentes harmônicos contidos na rede e um interpolador em caso de variação de frequência. A impedância é um parâmetro importante para a análise da estabilidade de uma rede elétrica, pois através de sua estimação pode-se verificar, por exemplo, se há a presença de ressonância. Para provocar os distúrbios nos sinais de tensão e corrente utiliza-se o Sinal da Gaussiana Modulada (SGM), que pode ter seu decaimento controlado pelos parâmetros da função. Em relação à presença dos componentes harmônicos de fundo, que influenciam na estimação da impedância, é proposta uma versão do filtro Sliding Window Recursive Discrete Fourier Transform (SWRDFT), para estimar e eli-minar esses componentes, com o objetivo de permanecer somente o sinal de distúrbio. Sobre o desvio de frequência, outra questão que compromete a estimação da impedância, é proposta uma estrutura de interpolação, utilizando o método de Lagrange. A função da interpolação é estabelecer a sincronização dos sinais de corrente e tensão antes de serem processados para determinar o valor da impedância. Para validar os resultados, são realizados testes em redes no Simulink, RTDS, dSPACE e utilizando em um circuito experimental. Para os resultados são considerados Sistemas Elétricos com ressonância, com presença de componentes harmônicos de fundo e com variação de frequência. Para todos os casos a estimação obteve resultados satisfatórios. / This work proposes a method to estimate the power grid impedance in an invasive form, using a disturbance control structure, a filter to eliminate the harmonic components contained in the power grid and an interpolator in case of frequency variation. The impedance is an important parameter for the power grid stability analysis because through its estimation it can be verified, for example, if there is the presence of resonance. To insert the disturbances in the voltage and current signals, the Gaussian Modulated Signal (GMS) is used, which may have its decay controlled by the function parameters. Regarding the presence of the harmonic components, which influence the estimation of impedance, a version of the Sliding Window Recursive Discrete Fourier Transform (SWRDFT) is proposed to estimate and eliminate these components in order to remain only the disturbance signal. Regarding the frequency deviation, another issue that affects the impedance estimation, an interpolation structure is proposed, using the Lagrange method. The function of the interpolation is to establish the synchronization of the current and voltage signals before being processed to determine the impedance value. To validate the results, tests with grids on Simulink, RTDS, dSpace and using an experimental circuit are performed. Results consider Electrical Systems with resonance, with the presence of background harmonic components and frequency variation. For all cases, the estimation results were satisfactory.

Cette thèse est une entreprise commune de VINCI Technologies et du laboratoire CNRS CORIA. De nombreux injecteurs comportent une zone de mélange interne dans laquelle les phases liquides et gazeuses sont toutes deux présentes dans une proportion significative. Par conséquent, cette zone appartient à la catégorie des écoulements diphasiques denses. Pour simuler la dispersion du liquide et caractériser le spray de ces injecteurs, des modèles appropriés sont nécessaires. Les points clés de cette approche sont la dispersion du liquide qui peut être associé au flux liquide turbulent et la quantité de surface liquide-gaz. En particulier, ce manuscrit rapporte, d’une part le développement théorique des modèles de la famille ELSA et, d’autre part, les approximations industrielles correspondantes. Le solveur proposé bascule dynamiquement du spray ICM au spray de sous- maille, à travers le concept ELSA et grâce à l’indicateur basé sur la résolution (IRQ). D’autre part, une fois la zone diluée se forme, l’approche ELSA est couplée à la méthode d’écoulement multiphase, qui vise à déterminer la distribution du spray à l’aide de l’équation WBE. Cette dernière équation est résolue avec une méthode hybride Euler-Lagrange. Le but est de résoudre l’équation WBE avec une approche stochastique Lagrangienne, tout en préservant la compatibilité avec la description Eulerienne de l’écoulement diphasique, basée sur ELSA, pour tirer parti des deux approches. Finalement, ces approches développées ont été utilisées pour des applications industrielles montrant leur robustesse et leur capacité à aider dans le processus de développement de nouveaux injecteurs. / This PhD is a joint venture between VINCI Technologies and the CNRS Laboratory CORIA. For its application, VINCI Technologies, developed mainly oil-related equipments and in particular injection/atomization systems. Some of these injectors are characterized by a very big geometrical dimensions (several meters long), that leads to very high Reynolds and Weber number. In addition, many injectors incorporate an internal mixing zone, in which liquid and gas phases are both present in a significant proportion. Consequently, this zone belongs to the dense two-phase flow category. To simulate the liquid dispersion and to characterize the spray formation special from these injectors, appropriate models are required. On its side, the CORIA team, has developed a suitable approach, so-called ELSA, based on the pioneering work of Borghi and Vallet [1, 2]. Key points of this approach are the liquid dispersion that can be associated to the turbulent liquid flux and the amount of liquid-gas surface that can be used to determine eventually the Sauter mean diameter (SMD) of the spray. During this PhD, the applications proposed by V INCI Technologies, have promoted a review of a large part of the multiphase flow approaches to find the more appropriate for each case. This has been the opportunity to clarify the range of application of each approach, and therefore stress the necessity to develop coupled approaches, in order to cover the proposed application in the most suitable way. In particular, this manuscript reports, in one hand, the theoretical development of the ELSA family models, and on the other hand, the corresponding industrial approximations. Since ELSA approaches are originally developed for RANS simulation of the dense zone, it has been extended to LES description. The link of this approach to the DNS¡ ICM approach, has been studied with a special care. The resulting proposed solver, switches dynamically from ICM to subgrid spray, through the ELSA concept, and thanks to resolution based indicator (IRQ). On the opposite side, once the dispersed spray is formed, the ELSA approach is coupled to multiphase flow method, that aims to determine the spray distribution through the WBE equation. This later equation, is solved with an original hybrid Euler-Lagrange method. The purpose is to solve the WBE equation with a Lagrange stochastic approach, and at the same time, preserving the compatibility to the Euler description of two-phase flow, based on ELSA, to benefit from both approaches. This coupled approach has been tested against academic experimental data coming from ECN research initiative, a combined DNS and experimental measurement of dispersed spray on a Diesel jet, and under an air-blast atomizer numerical test case, for which the mean liquid volume fraction has been measured. Eventually, these developed approaches have been applied to industrial application showing there robustness and their capacity to help in the process of design development of new injectors.

This report analyzes and compares Barycentric Lagrange interpolation to Cardinal Trigonometric interpolation, with regards to computational cost and accuracy. It also covers some edge case scenarios which may interfere with the accuracy and stability. Later on, these two interpolation methods are applied on parameterized curves and surfaces, to compare and contrast differences with the standard one dimensional scenarios. The report also contains analysis of and comparison with regular Lagrange interpolation. The report concludes that Barycentric Lagrange interpolation is generally speaking more computationally efficient, and that the inherent need for periodicity makes Cardinal Trigonometric interpolation less reliable in comparison. On the other hand, Barycentric Lagrange interpolation is difficult to implement for higher dimensional problems, and also relies heavily on Chebyshev spaced nodes, something which can cause issues in a practical application of interpolation. Given ideal scenarios, Cardinal Trigonometric interpolation is more accurate, and for periodic functions generally speaking better than Barycentric Lagrange interpolation. Regular Lagrange interpolation is found to be unviable due to the comparatively big computational cost.