The modern trend of gas turbines design is towards lighter, highly efficient,and more compact engines. Such situation imposes on engineers to continuouslysearch for improved and optimum designs. The thesis presented aims at researching possible performance improvements regarding axial gapdistance in transonic compressors. Decreasing the axial gap would result inlighter engines and achieve design goals. The influence of decreasing the axialgap on performance and structure integrity should be throughly analyzed. This thesis work includes numerical investigations on the axial gap distance effect on performance efficiency and related unsteady aerodynamics phenomena. The first one and a half compressor stages of a Siemens Gas Turbine are modeled in ANSYS CFX. Different axial gap models are simulated for differentconfigurations. The steady state solution is obtained to be initialized for transient time marching calculations. Furthermore, the computational cost of transient calculations is reduced through a geometry scaling technique. The unsteady behavior is further analyzed by a Harmonic Balance solver implemented in STAR-CCM+ software, and compared to a reference case transient calculations. The results obtained supports the presence of an optimalaxial gap distance for maximum efficiency in transonic compressors. Further, the harmonic balance method shows good possibilities for cost and time reductions in transonic compressors performance calculations.

Understanding distortion transfer and generation through fan and compressor blade rows is able to assist in blade design and performance prediction. Using full annulus unsteady RANS simulations, the effects of distortion as it passes through the rotor of a transonic fan at five radial locations (10%, 30%, 50%, 70%, and 90% span) are analyzed. The inlet distortion profile is a 90-degree sector with a 15% total pressure deficit. Fourier distortion descriptors are used in this study to quantitatively describe distortion transfer and generation. Results are presented and compared for three operating points (near-stall, design, and choke). These results are used to explain the relationship between inlet total pressure distortion, pressure-induced swirl, total pressure distortion transfer, total temperature distortion generation, and circumferential rotor work variation. It is shown that very large changes in pressure-induced swirl and distortion transfer and generation occur between near-stall and design, but only small changes are seen between design and choke. The greatest changes are shown to be near the tip. Local power variations are shown to correlate with total pressure distortion transfer and total temperature distortion generation.It can be difficult to predict the transfer of distortion through a fan or compressor because traditional experimental and computational methods are very expensive and time consuming. The Harmonic Balance approach is a promising alternative which uses Fourier techniques to represent fluid flow solutions and which can provide unsteady solutions much more quickly than traditional unsteady solvers. Relatively little work has been done to assess how much Fourier information is necessary to calculate a sufficiently accurate solution with the Harmonic Balance Solver. A study is performed to analyze the effects of varying the amount of modal content that is used in Harmonic Balance simulations. Inlet distortion profiles with varying magnitudes are used in order to analyze trends and provide insight into the distortion flow physics for various inlet conditions. The geometry is a single stage axial compressor that consists of an inlet guide vane followed by the NASA Stage 37 rotor. It is shown that simulations with greater magnitudes of distortion require more modal content in order to achieve sufficiently accurate results. Harmonic Balance simulations are shown to have significantly lower computational costs than simulations with a conventional unsteady solver.

No description available.

Cette thèse porte sur la modélisation des piles à combustible à membrane d'échange de protons (PEMFC), en vue de leur surveillance et de leur diagnostic par spectroscopie d'impédance. La première partie du document présente le principe de fonctionnement de ces piles, ainsi que l'état de l'art de la modélisation et des méthodes de surveillance et diagnostic. Le modèle physique multi échelle particulièrement détaillé publié en 2005 par A.A. Franco sert de point de départ. Il est simplifié de façon à aboutir à un système d'équations aux dérivées partielles en une unique dimension spatiale. L'objectif principal de la seconde partie est l'analyse harmonique du fonctionnement de la pile. En s'inspirant de travaux classiques sur l'analyse géométrique de réseaux de réactions électrochimiques, un modèle réduit compatible avec la thermodynamique est obtenu. Cette classe de systèmes dynamiques permet de déterminer, pour un tel réseau, une formule analytique de l'impédance de l'anode et de la cathode d'une pile PEMFC. Un modèle complet de la pile est obtenu en connectant ces éléments à des éléments représentant la membrane, les couches diffuses et les couches de diffusion des gaz. Les modèles précédents supposent la pile représentée par une cellule unique et homogène. Afin de permettre d'en décrire les hétérogénéités spatiales, nous proposons finalement un résultat de modélisation réduite d'un réseau de cellules représentées par leur impédance. Ce modèle approxime l'impédance globale du réseau par une "cellule moyenne", connectée à deux cellules "série" et "parallèle" représentatives d'écart par rapport à la moyenne. / This PhD thesis focuses on reduced modeling of PEM fuel cell for supervision and diagnosis by impedance spectroscopy. The first part of the document presents the principle of the PEM fuel cell, as well as the state of the art of modeling and of the methods for supervision and diagnosis. The multiscale dynamic model published in 2005 by A.A. Franco is particularly detailed and serves as a starting point. It is simplified, in order to obtain a system of partial differential equations in a single spatial dimension. The second part is devoted to harmonic analysis of the PEM Fuel cell. Inspired by classical work on the geometric analysis of electrochemical reactions networks, a model compatible with thermodynamics is obtained. This class of dynamic systems allows establishing, for such a network, an analytical formula of the impedance of the anode and the cathode of the PEM fuel cell. A complete model of the cell is obtained by connecting these elements to the membrane, diffuse layers and gas diffusion layer. The previous models assumed the PEM Fuel cell represented by a single, homogeneous, cell. In order to describe the possible spatial heterogeneities, we finally propose a result of reduced modeling for the impedance of a cell network. This model approximates the overall impedance of the network by a "mean cell", connected to two cells, put in "serial" and "parallel", and representative of the deviations from the average.

L'étude par continuation des solutions périodiques et quasi-périodiques est appliquée à plusieurs modèles issus du violon. La continuation pour un modèle à un degré de liberté avec friction régularisée permet de montrer la préservation, par rapport à la friction de Coulomb, des bifurcations de cycle limite (une vitesse maximale et une force minimale permettant le mouvement de Helmholtz) et de propriétés globales de la branche de solution (croissance de l'amplitude avec la vitesse, décroissance de la fréquence avec la force normale). L'équilibrage harmonique est évalué sur la friction régularisée et a des propriétés de convergence intéressantes (erreur faible, monotone, à décroissance rapide). La continuation sur un modèle à deux modes donne accès aux solutions de registres supérieurs, dont la stabilité coïncide avec l'expérience. La valeur retenue pour l'inharmonicité peut modifier fortement le diagramme de bifurcation. Une nouvelle méthode de continuation des solutions quasi-périodiques est proposée. Elle associe l'EH étendu à deux pulsations avec la Méthode Asymptotique Numérique. Une attention particulière est portée à la rapidité des calculs, face à la croissance rapide de la taille des systèmes à inverser. Un modèle de friction prenant en compte la température au point de contact est reformulé à l'aide d'une dérivée fractionnaire. Nous proposons une méthode de continuation de solutions périodiques de systèmes contenant des dérivées ou intégrales fractionnaires. Nous établissons une condition suffisante pour que les cycles asymptotiques du cadre causal (Caputo) soient solutions du cadre que nous avons choisi. / The continuation of periodic and quasi-periodic solutions is performed on several models derived from the violin. The continuation for a one degree-of-freedom model with a regularized friction shows, compared with Coulomb friction, the persistence of limit cycle bifurcations (a maximum bow speed and a minimum normal force allowing Helmholtz motion) and of global properties of the solution branch (increase of amplitude with respect to the bow speed, decrease of frequency with respect to the normal force). The Harmonic Balance Method is assessed on this regularized friction system and shows interesting convergence properties (the error is low, monotone and rapidly decreasing). For two modes the continuation shows higher register solutions with a plausible stability. A stronger inharmonicity can greatly modify the bifurcation diagram. A new method is proposed for the continuation of quasi-periodic solutions. It couples a two-pulsations HBM with the Asymptotic Numerical Method. We have taken great care to deal efficiently with large systems of unknowns. A model of friction that takes into account temperature of the contact zone is reformulated with a fractional derivative. We then propose a method of continuation of periodic solutions for differential systems that contain fractional operators. Their definition is usually restricted to causal solutions, which prevents the existence of periodic solutions. Having chosen a specific definition of fractional operators to avoid this issue we establish a sufficient condition on asymptotically attractive cycles in the causal framework to be solutions of our framework.

Inlet flow distortion is a non-uniform total pressure, total temperature, or swirl (flow angularity) condition at an aircraft engine inlet. Inlet distortion is a critical consideration in modern fan and compressor design. This is especially true as the industry continues to increase the efficiency and operating range of air breathing gas turbine engines. The focus of this paper is to evaluate the Computational Fluid Dynamics (CFD) Harmonic Balance (HB) solver in STAR-CCM+ as a reduced order method for capturing inlet distortion as well as the associated distortion transfer and generation. New methods for quantitatively describing and analyzing distortion transfer and generation are investigated. The geometry used is the rotor 4 fan geometry, consisting of one rotor and one stator. The inlet boundary condition is a 90-degree sector total pressure distortion profile with total pressure and swirl held constant. Multiple HB simulations with varying mode combinations and distortion intensities are analyzed and compared against full annulus Unsteady Reynolds Averaged Navier-Stokes (URANS) simulations. Best practices and recommendations for the implementation of the HB solver are given. The pre-existing Society of Automotive Engineers Aerospace Recommended Practice (SAE-ARP) 1420b descriptors are demonstrated to be inadequate for the purposes of analyzing distortion transfer and generation on a stage-to-stage basis. New implementations of Fourier methods are presented as an alternative to the SAE-ARP 1420b descriptors. These Fourier descriptors are shown to describe distortion transfer and generation to a higher degree of fidelity than the SAE-ARP 1420b descriptors. These new descriptors are demonstrated on the analysis of full annulus URANS and HB simulations. The HB solver is shown to be capable of capturing distortion transfer, generation and performance degradation. Recommendations for the optimal implementation of the HB method are given.

Dentro de los sistemas de comunicación han adquirido gran importancia las aplicaciones en alta frecuencia, lo que conlleva un gran desarrollo en este tipo de tecnologías; aplicaciones bajo ruido, potencia monolítico, etc. Este tipo de tecnologías precisan un conocimiento no lineal de los circuitos. Por ello el presente trabajo se ha orientado hacia la resolución de tres problemas no lineales fundamentales que son: modelización física, análisis no lineal de sistemas activos autónomos trabajando en microondas y el desarrollo de una formulación matemática compacta dirigida hacia la optimización gran señal de sistemas activos a transistor Mesfet. El trabajo se completa con una verificación experimental de los comportamientos simulados teóricamente lo que confiere a los métodos matemáticos un amplio rango de validez

The design of power amplifiers within a circuit simulator requires a good non-linear model that accurately predicts the electormagnetic behaviour of the power transistor. In recent years, a certain class of large signal frequency-dependent black-box behavioural modeling techniques known as Poly-Harmonic Distortion (PHD) models has been devised to mimic the non-linear unmatched RF transistor. These models promise a good prediction of the device behaviour under multi-harmonic periodic continuous wave inputs. This thesis describes the capabilities of the PHD modeling framework and the theoretical type of behaviour that it is capable of predicting. Specifically, the PHD framework cannot necessarily predict the response of a broadband aperiodic signal. This analysis will be performed by deriving the PHD modeling framework as a simplification of the Volterra series kernel functions under the assumption that the power transistor is operating under continuous periodic multi-harmonic voltage and current signals in a stable circuit. A PHD model will be seen as a set of describing functions that predict the response of the Device Under Test (DUT) for any given non-linear periodic continuous-wave inputs that have a specific fundamental frequency. Two popular implementations of PHD models that can be found in the literature are the X-parameter and Cardiff models. Each model formulates the describing functions of the general PHD model differently. The mathematical formulation of the X-parameter and Cardiff models will be discussed in order to provide a theoretical ground for comparing their robustness. The X-parameter model will be seen as the first-order Taylor series approximation of the PHD model describing functions around a Large Signal Operating Point (LSOP) of the device under test. The Cardiff large-signal model uses Fourier series coefficient functions that vary with the magnitude of the large signal(s) as the PHD model describing functions. This thesis will provide a breakdown of the measurement procedure required for the extraction of these models, the challenges involved in the measurement, as well as the mathematical extraction of the model coe cients from measurement data. As each of these models contain have extended versions that enhance the predictive capability of the model under stronger nonlinear modes of operation, a comparison is used to represent the cost of increasing model accuracy as a function of the increasing model complexity for each model. The order of complexity of each model can manifest itself in terms of the mathematical formulation, the number of parameters required and the measurement time that is required to extract each model for a given DUT. This comparison will fairly assess the relative strengths and weaknesses of each model.

The design of power amplifiers within a circuit simulator requires a good non-linear model that accurately predicts the electormagnetic behaviour of the power transistor. In recent years, a certain class of large signal frequency-dependent black-box behavioural modeling techniques known as Poly-Harmonic Distortion (PHD) models has been devised to mimic the non-linear unmatched RF transistor. These models promise a good prediction of the device behaviour under multi-harmonic periodic continuous wave inputs. This thesis describes the capabilities of the PHD modeling framework and the theoretical type of behaviour that it is capable of predicting. Specifically, the PHD framework cannot necessarily predict the response of a broadband aperiodic signal. This analysis will be performed by deriving the PHD modeling framework as a simplification of the Volterra series kernel functions under the assumption that the power transistor is operating under continuous periodic multi-harmonic voltage and current signals in a stable circuit. A PHD model will be seen as a set of describing functions that predict the response of the Device Under Test (DUT) for any given non-linear periodic continuous-wave inputs that have a specific fundamental frequency. Two popular implementations of PHD models that can be found in the literature are the X-parameter and Cardiff models. Each model formulates the describing functions of the general PHD model differently. The mathematical formulation of the X-parameter and Cardiff models will be discussed in order to provide a theoretical ground for comparing their robustness. The X-parameter model will be seen as the first-order Taylor series approximation of the PHD model describing functions around a Large Signal Operating Point (LSOP) of the device under test. The Cardiff large-signal model uses Fourier series coefficient functions that vary with the magnitude of the large signal(s) as the PHD model describing functions. This thesis will provide a breakdown of the measurement procedure required for the extraction of these models, the challenges involved in the measurement, as well as the mathematical extraction of the model coe cients from measurement data. As each of these models contain have extended versions that enhance the predictive capability of the model under stronger nonlinear modes of operation, a comparison is used to represent the cost of increasing model accuracy as a function of the increasing model complexity for each model. The order of complexity of each model can manifest itself in terms of the mathematical formulation, the number of parameters required and the measurement time that is required to extract each model for a given DUT. This comparison will fairly assess the relative strengths and weaknesses of each model.

Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-10-10T18:52:25Z No. of bitstreams: 1 DESIANE MAIARA GOMES DOS SANTOS – DISSERTAÇÃO (PPGFísica) 2015.pdf: 6011160 bytes, checksum: a5021549766593cfe2eb8fe5314ea39b (MD5) / Made available in DSpace on 2018-10-10T18:52:25Z (GMT). No. of bitstreams: 1 DESIANE MAIARA GOMES DOS SANTOS – DISSERTAÇÃO (PPGFísica) 2015.pdf: 6011160 bytes, checksum: a5021549766593cfe2eb8fe5314ea39b (MD5) Previous issue date: 2015-04-10 / Capes / Nesta dissertação, analisamos a dinâmica de osciladores parametricamente forçados, com enfoque na amplificação de pequenos sinais. Iniciamos por uma revisão da ressonância paramétrica e da amplificação paramétrica em um oscilador linear parametricamente excitado. Em seguida, estudamos dois tipos de osciladores não-lineares parametricamente forçados e concluímos a dissertação com a análise de um dímero parametricamente excitado. Basicamente, analisamos os fenômenos de ressonância paramétrica e de amplificação paramétrica, comparando os resultados obtidos analiticamente (via métodos da média ou do balanço harmônico) com os obtidos via integração numérica das equações do movimento. Em todos os casos, obtivemos a linha de transição para a instabilidade paramétrica do oscilador paramétrico. Nós excitamos os amplificador paramétrico com e sem dessintonia entre entre o bombeamento e o sinal externo ac. Verificamos que o ganho da amplificação paramétrica depende da sensitivamente na fase do sinal externo ac e na amplitude do bombeamento. Mostramos que tais sistemas podem ser facilmente utilizados para recepção e decodificação de sinais com modulação de fase. Além disso, obtivemos séries temporais, envelopes e transformadas de Fourier para a resposta da amplificação paramétrica de pequenos sinais ac. Especificamente nos casos dos osciladores de Duffing parametricamente forçados, obtivemos e analisamos linhas de bifurcação e a amplitude dos ciclos limites como função da frequência e da amplitude de bombeamento. Adicionalmente, conseguimos obter uma relação analítica para os ganhos do sinal e do idler dos osciladores não-lineares parametricamente forçados pelo método do balanço harmônico. Os resultados obtidos implicam que os amplificadores paramétricos não-lineares podem ser excelentes detectores, especialmente em pontos próximos a bifurcações para instabilidade, em que apresentam altos ganhos e largura de banda bem estreitas. Por último, investigamos também o comportamento de dois osciladores lineares acoplados e parametricamente estimulados, com e sem força externa ac. Tais sistemas são muito sensíveis à fase do sinal a ser amplificado e podem ser utilizados para criar amplificadores sintonizáveis em função do parâmetro de acoplamento. / In this dissertation, we studied the dynamics of parametrically-driven oscillators, with a focus on the amplification of small signals. We begin with a revision of parametric resonance and parametric amplification in a linear oscillator parametrically excited. Next, we studied two types of nonlinear parametrically-driven oscillators and finished the dissertation with an analysis of a parametric dimer. Basically, we analyzed the phenomena of parametric resonance and parametric amplification by comparing the results obtained analytically (via the averaging or harmonic balance methods) with those of numerical integration of the equations of motion. In all cases, we obtained the transition line to parametric instability of the parametric oscillator. We excited the parametric amplifier with and without detuning between the pump and the external signal. We found that the parametric amplification depends sensitively on the phase of the external ac signal and on the internal pump amplitude. We showed that such amplifiers can be easily used for the reception and decoding of signals with phase modulation. Furthermore, we obtained time series, envelopes, and Fourier transforms of the response of the parametric amplifier to small external ac signals. Specifically in the cases of the parametrically-driven Duffing oscillators, we obtained and analysed the bifurcation lines and the amplitude of limit cycles as function of the pump amplitude and frequency. In addition, we derived an expression for the signal and idler gains of the nonlinear parametrically-driven oscillators with the harmonic balance method. The results imply that the nonlinear parametric amplifiers can be excellent detectors, specially near bifurcations to instability, due to their high gains and narrow bandwidths. Finally, we studied the dynamics of two linear oscillators coupled and parametrically excited, with and without external ac driving. We found that such systems have a wealth of dynamical responses. They present parametric amplification that is dependent on the coupling parameter and on the phases of the external ac signals. Such systems may be used as tunable amplifiers.