No description available.

This dissertation introduces a general, predictive and cost-efficient reduced-order modeling (ROM) technique for characterization of flame response under acoustic modulation. The model is built upon the kinematic flame model–G-equation to describe the flame topology and dynamics, and the novelties of the ROM lie in i) a procedure to create the compatible base flow that can reproduce the correct flame geometry and ii) the use of a physically-consistent acoustic modulation field for the characterization of flame response. This ROM addresses the significant limitations of the classical kinematic model, which is only applicable to simple flame configurations and relies on ad-hoc models for the modulation field. The ROM is validated by considering the acoustically-excited premixed methane/air flames in conical and M-shape configurations. To test the model availability to practical burners, a confined flame configuration is also employed for model evaluation. Furthermore, to investigate the generality of the ROM to the burner flame, the performance of the ROM with respect to the V-shape and the swirled V-shape is investigated. The model accuracy is evaluated concerning flame geometrical features and flame describing function, and assessed by comparing the ROM results with both experimental measurements and direct- numerical-simulation results. It is found that the flame describing/transfer functions predicted by the ROM compare well with reference data, and are more accurate than those obtained from the conventional kinematic model built upon heuristically-presumed modulation fields.

The first objective of this Dissertation is to present a methodology to calculate analytically the mode shapes and corresponding natural frequencies and determine critical buckling loads of mechanically coupled microbeam resonators with a focus on micromechanical filters. The second objective is to adopt a nonlinear approach to build a reduced-order model and obtain closed-form expressions for the response of the filter to a primary resonance. The third objective is to investigate the feasibility of employing subharmonic excitation to build bandpass filters consisting of either two sets of two beams coupled mechanically or two sets of clamped-clamped beams. Throughout this Dissertation, we treat filters as distributed-parameter systems. In the first part of the Dissertation, we demonstrate the methodology by considering a mechanical filter composed of two beams coupled by a weak beam. We solve a boundary-value problem (BVP) composed of five equations and twenty boundary conditions for the natural frequencies and mode shapes. We reduce the problem to a set of three linear homogeneous algebraic equations for three constants and the frequencies in order to obtain a deeper insight into the relation between the design parameters and the performance metrics. In an approach similar to the vibration problem, we solve the buckling problem to study the effect of the residual stress on the static stability of the structure. To achieve the second objective, we develop a reduced-order model for the filter by writing the Lagrangian and applying the Galerkin procedure using its analytically calculated linear global mode shapes as basis functions. The resulting model accounts for the geometric and electric nonlinearities and the coupling between them. Using the method of multiple scales, we obtain closed-form expressions for the deflection and the electric current in the case of one-to-one internal and primary resonances. The closed-form solution shows that there are three possible operating ranges, depending on the DC voltage. For low DC voltages, the effective nonlinearity is positive and the filter behavior is hardening, whereas for large DC voltages, the effective nonlinearity is negative and the filter behavior is softening. We found that, when mismatched DC voltages are applied to the primary resonators, the first mode is localized in the softer resonator and the second mode is localized in the stiffer resonator. We note that the excitation amplitude can be increased without worrying about the appearance of multivaluedness when operating the filter in the near-linear range. The upper bound in this case is the occurrence of the dynamic pull-in instability. In the softening and hardening operating ranges, the adverse effects of the multi-valued response, such as hysteresis and jumps, limit the range of the input signal. To achieve the third objective, we propose a filtration technique based on subharmonic resonance excitation to attain bandpass filters with ideal stopband rejection and sharp rolloff. The filtration mechanism depends on tuning two oscillators such that one operates in the softening range and the other operates in the hardening range. Hardware and logic schemes are necessary to realize the proposed filter. We derive a reduced-order model using a methodology similar to that used in the primary excitation case, but with all necessary changes to account for the subharmonic resonance of order one-half. We observe that some manipulations are essential for a structure of two beams coupled by a weak spring to be suitable for filtration. To avoid these complications, we use a pair of single clamped-clamped beams to achieve our goal. Using a model derived by attacking directly the distributed-parameters problem, we suggest design guidelines to select beams that are potential candidates for building a bandpass filter. We demonstrate the proposed mechanism using an example. / Ph. D.

Die vorliegende Arbeit befasst sich mit der Stabilitätsuntersuchung von offenen Naturumlaufsystemen als Grundlage zur Verwendung als passives Wärmeabfuhrsystem im Sicherheitsbehälter eines Siedewasserreaktors. Der Betrieb eines solchen Systems im Naturumlauf basiert einzig auf der Ausbildung eines Dichtegradienten, der infolge einer freien Konvektion zu einer Strömung innerhalb dieses Systems führt. Dieser Dichtegradient im Arbeitsfluid wird durch die Wärmezu- und -abfuhr hervorgerufen. Der sich ausbildende und kontinuierlich steigende Massenstrom geht bei Erreichen der Sättigungstemperatur in Massenstromoszillationen, den sogenannten Zweiphasenströmungsinstabilitäten, über. Mit steigender Temperatur des Arbeitsfluides kehrt der Massenstrom zu einer stabilen Strömung und kontinuierlichen Wärmeabfuhr zurück, jedoch als Zweiphasenströmung. Es wurde an der Technischen Universität Dresden eine Versuchsanlage errichtet, die den Gebäudekondensator des KERENA\textsuperscript{TM}(ehemals SWR1000)-Reaktorkonzepts nachstellt, um die Anlagen- und die Betriebscharakteristik hinsichtlich geometrischer Einflüsse zu bewerten. Mit Hilfe hochauflösender Temperatur und Volumendampfgehaltsmessung wurde festgestellt, dass bei parallel angeordneten Steigrohren die durch Kondensationsschläge hervorgerufenen Druckschläge stark reduziert oder sogar unterbunden werden konnten. So fungiert eines der Steigrohre als Puffer für rückströmendes unterkühltes Fluid aus der Wärmesenke in dem anderen. Zusammengefasst wurde zudem die Betriebscharakteristik in Stabilitätskarten, die die stabile Einphasenströmung, die instabile Zweiphasenströmung und die stabile Zweiphasenströmung eindeutig voneinander abgrenzt. Die Vorhersage der Stabilitätsgrenze zwischen instabiler und stabiler Zweiphasenströmung durch einen analytischen Ansatz ist gelungen. Das zugrundeliegende Modell für ein solches offenes Naturumlaufsystem wurde durch die Methode der gewichteten Residuen und die Finite-Volumen-Methode gelöst und mit Hilfe der Proper Orthogonal Decomposition auf ein Modell niedriger Ordnung reduziert (ROM). Vergleichsrechnungen mit einem entwickelten Abbild des Versuchsstandes GENEVA unter Verwendung des bereits validierten Systemcodes ATHLET der \textit{Gesellschaft für Anlagen- und Reaktorsicherheit (GRS) gGmbH} bestätigten die berechneten Betriebszustände und letztendlich die durch die lineare Stabilitätsuntersuchung ermittelte Stabilitätsgrenze. Eben dieses ROM bildet die Zweiphasenströmung mittels des \textit{Drift-flux mixture} Modells ab, welches die relativen Geschwindigkeiten jeder Phase berücksichtigt. Die nichtlineare Stabilitätsuntersuchung dieses ROMs ergab an ausgewählten Referenzbetriebspunkten superkritische Hopfbifurkationen, die nur durch die Detektion aufkommender stabiler Grenzzyklen während der numerischen Integration nachgewiesen werden konnten. Parameterstudien zur Stabilitätsanalyse können durch dieses ROMs unter erheblicher Reduktion von Rechenaufwand durchgeführt werden.

No description available.

This dissertation uses spatial filtering to develop a large eddy simulation reduced order model (LES-ROM) framework for fluid flows. Proper orthogonal decomposition is utilized to extract the dominant spatial structures of the system. Within the general LES-ROM framework, two approaches are proposed to address the celebrated ROM closure problem. No phenomenological arguments (e.g., of eddy viscosity type) are used to develop these new ROM closure models. The first novel model is the approximate deconvolution ROM (AD-ROM), which uses methods from image processing and inverse problems to solve the ROM closure problem. The AD-ROM is investigated in the numerical simulation of a 3D flow past a circular cylinder at a Reynolds number $Re=1000$. The AD-ROM generates accurate results without any numerical dissipation mechanism. It also decreases the CPU time of the standard ROM by orders of magnitude. The second new model is the calibrated-filtered ROM (CF-ROM), which is a data-driven ROM. The available full order model results are used offline in an optimization problem to calibrate the ROM subfilter-scale stress tensor. The resulting CF-ROM is tested numerically in the simulation of the 1D Burgers equation with a small diffusion parameter. The numerical results show that the CF-ROM is more efficient than and as accurate as state-of-the-art ROM closure models. / Ph. D.

Over the past century, great strides have been made in the advancement of mine fire knowledge since the 1909 Cherry Mine Fire Disaster, one of the worst in U.S. history. However, fire hazards remain omnipresent in underground coal mines in the U.S. and around the world. A precise fire numerical analysis (simulation) before any fire events can give a broad view of the emergency scenarios, leading to improved emergency response, and better health and safety outcomes. However, the simulation cost of precise large complex dynamical systems such as fire in underground mines makes practical and even theoretical application challenging. This work details a novel methodology to reduce fire and airflow simulation costs in order to make simulation of complex systems around fire and mine ventilation systems viable. This study will examine the development of a Reduced Order Model (ROM) to predict the flow field of an underground mine geometry using proper orthogonal decomposition (POD) to reduce the airflow simulation cost in a nonlinear model. ROM proves to be an effective tool for approximating several possible solutions near a known solution, resulting in significant time savings over calculating full solutions and suitable for ensemble calculations. In addition, a novel iterative methodology was developed based on the physics of the fluid structure, turbulent kinetic energy (TKE) of the dynamical system, and the vortex dynamics to determine the interface boundary in multiscale (3D-1D) fire simulations of underground space environments. The proposed methodology was demonstrated to be a useful technique for the determination of near and far fire fields, and could be applied across a broad range of flow simulations and mine geometries. Moreover, this research develops a methodology to analyze the tenable limits in a methane fire event in an underground coal mine for bare-faced miners, mine rescue teams, and fire brigade teams in order to improve safety and training of personnel trained to fight fires. The outcomes of this research are specific to mining although the methods outlined might have broader impacts on the other fields such as tunneling and underground spaces technology, HVAC, and fire protection engineering industries. / Ph. D.

Dans le domaine automobile, les modules électroniques de puissance des produits mécatroniques voient leur puissance sans cesse s'accroître, tout en étant confinés dans des volumes de plus en plus réduits. Au cours de leur fonctionnement, les composants semi-conducteurs et leur assemblage subissent ainsi des contraintes électro-thermo-mécaniques sévères, susceptibles d'entraîner leur destruction et de provoquer la défaillance du produit. L'étude de la fiabilité et le calcul de la durée de vie de tels produits dépendent des températures de jonction calculées au niveau des puces des composants de puissances. De surcroît, le contexte d'applications embarquées requiert de maîtriser, outre les paramètres électriques et mécaniques, les paramètres thermiques tels que les températures de jonctions et les puissances dissipées au niveau des composants, qu'il est nécessaire de réguler et contrôler en temps réel afin d'assurer le bon fonctionnement du produit. L'objectif de cette thèse est ainsi de proposer une méthode d'identification de modèles réduits dans le but d'estimer le comportement thermique des modules électroniques de puissance, en se fondant uniquement sur les données d'entrées et les résultats issus d'une simulation numérique d'un modèle détaillé du système étudié. Dans cette thèse, une nouvelle méthode d'identification, nommée « Kernel Identification Method », est développée. Cette méthode a été validée sur une application industrielle traitant d'un problème thermique couplé solide/fluide dont le comportement est essentiellement régi par de la convection forcée. Une étude exploratoire portant sur l'identification de problèmes non linéaires où la convection naturelle joue le rôle dominant est ensuite proposée. A cet effet, deux méthodes d’identification non-paramétrique sont proposées : (i) une première méthode basée sur l’extension de la méthode Kernel Identification Method ; et (ii) une deuxième méthode basée sur la variante dite « Unscented » du filtre de Kalman. / In automotive applications, the thermal dissipation of power electronics modules in mechatronic products is constantly increasing, whereas these products are confined in increasingly reduced volumes. During their operation, the semiconductor components and their environment are then submitted to severe electro-thermo-mechanical stresses that could cause their damage and lead to the product failure. The reliability and lifetime prevision of such products depend on the temperature junction located at the chip of power components. Furthermore, in order to ensure the safe operation of embedded applications, it is essential to perform a real-time control of thermal parameters such as the junction temperatures and power dissipated on the power components, in addition to the electrical and mechanical parameters. The objective of this thesis is to develop an identification method aimed at producing reduced thermal models to estimate the thermal behaviour of power electronic modules. Designed in a non-intrusive framework, this method post-processes the input data and the results produced by the numerical simulation of a detailed of the system under study. In this thesis, a new identification method, called "Kernel Identification Method" is developed. It has been validated on an industrial application dealing with a thermally coupled solid / fluid problem mainly governed by forced convection. An exploratory study of nonlinear problems identification where the natural convection plays the dominant role is then proposed. To this end, two identification methods of nonparametric nature are proposed: (i) a method based on the extension of the Kernel Identification Method; and (ii) a second method based on the "unscented" variant of the Kalman filter.

[pt] Este trabalho apresenta um método para calcular a resistência à fadiga de uma torre de perfuração considerando a elevação da superfície do mar, a dinâmica da plataforma na qual a torre está instalada e a dinâmica da própria torre. Modelos de ordem reduzida são utilizados para obter a elevação da superfície do mar e a dinâmica torre, e as incertezas nos parâmetros dos componentes do sistema podem ser incluídas na análise também. As análises podem ser feitas para vários estados de mar, conforme sua distribuição de probabilidade, e nenhuma hipótese sobre a distribuição de probabilidade precisa ser feita inicialmente. O histograma de distribuição de ciclos de tensão para toda vida útil do equipamento é obtido usando um procedimento de contagem de ciclos Rainflow. Os resultados e as incertezas nos mesmos são discutidos. / [en] This work presents a method for evaluation of the fatigue resistance of a drilling tower considering the sea surface elevation, the dynamics of the platform on which the tower is installed and the dynamics of the tower itself. Reduced order models are used for obtaining the sea surface elevation and the dynamics of the tower, and the uncertainties on the parameters of the components of the system can be included in the analysis as well. The analysis can be done for several sea states, according its probability distribution, and no assumption about the probability distribution of the stress ranges has to be made previously. The histogram for the distribution of stress ranges for the entire working life of the equipment is obtained using a Rainflow technique. The results and the uncertainties on them are discussed.

Les réseaux de distribution d’eau consistent en de grandes infrastructures réparties dans l’espace qui assurent la distribution d’eau potable en quantité et en qualité suffisantes. Les modèles mathématiques de ces systèmes sont caractérisés par un grand nombre de variables d’état et de paramètres dont la plupart sont incertains. Les temps de calcul peuvent s’avérer conséquents pour les réseaux de taille importante et la propagation d’incertitude par des méthodes de Monte Carlo. Par conséquent, les deux principaux objectifs de cette thèse sont l’étude des techniques de modélisation à ordre réduit par projection ainsi que la propagation spectrale des incertitudes des paramètres. La thèse donne tout d’abord un aperçu des méthodes mathématiques utilisées. Ensuite, les équations permanentes des réseaux hydrauliques sont présentées et une nouvelle méthode de calcul des sensibilités est dérivée sur la base de la méthode adjointe. Les objectifs spécifiques du développement de modèles d’ordre réduit sont l’application de méthodes basées sur la projection, le développement de stratégies d’échantillonnage adaptatives plus efficaces et l’utilisation de méthodes d’hyper-réduction pour l’évaluation rapide des termes résiduels non linéaires. Pour la propagation des incertitudes, des méthodes spectrales sont introduites dans le modèle hydraulique et un modèle hydraulique intrusif est formulé. Dans le but d’une analyse plus efficace des incertitudes des paramètres, la propagation spectrale est ensuite évaluée sur la base du modèle réduit. Les résultats montrent que les modèles d’ordre réduit basés sur des projections offrent un avantage considérable par rapport à l’effort de calcul. Bien que l’utilisation de l’échantillonnage adaptatif permette une utilisation plus efficace des états système pré-calculés, l’utilisation de méthodes d’hyper-réduction n’a pas permis d’améliorer la charge de calcul. La propagation des incertitudes des paramètres sur la base des méthodes spectrales est comparable aux simulations de Monte Carlo en termes de précision, tout en réduisant considérablement l’effort de calcul. / Water distribution systems are large, spatially distributed infrastructures that ensure the distribution of potable water of sufficient quantity and quality. Mathematical models of these systems are characterized by a large number of state variables and parameter. Two major challenges are given by the time constraints for the solution and the uncertain character of the model parameters. The main objectives of this thesis are thus the investigation of projection based reduced order modelling techniques for the time efficient solution of the hydraulic system as well as the spectral propagation of parameter uncertainties for the improved quantification of uncertainties. The thesis gives an overview of the mathematical methods that are being used. This is followed by the definition and discussion of the hydraulic network model, for which a new method for the derivation of the sensitivities is presented based on the adjoint method. The specific objectives for the development of reduced order models are the application of projection based methods, the development of more efficient adaptive sampling strategies and the use of hyper-reduction methods for the fast evaluation of non-linear residual terms. For the propagation of uncertainties spectral methods are introduced to the hydraulic model and an intrusive hydraulic model is formulated. With the objective of a more efficient analysis of the parameter uncertainties, the spectral propagation is then evaluated on the basis of the reduced model. The results show that projection based reduced order models give a considerable benefit with respect to the computational effort. While the use of adaptive sampling resulted in a more efficient use of pre-calculated system states, the use of hyper-reduction methods could not improve the computational burden and has to be explored further. The propagation of the parameter uncertainties on the basis of the spectral methods is shown to be comparable to Monte Carlo simulations in accuracy, while significantly reducing the computational effort.