[ES] El interés en reducir el peso y resistencia aerodinámica de vehículos y en desarrollar fuentes de energía renovables se ha incrementado debido a la compleja situación ambiental y los requerimientos legales para reducir las emisiones de contaminantes y el consumo de combustibles. La industria aeronáutica ha propuesto nuevos diseños que integren conceptos como alas de alto alargamiento y materiales con elevada resistencia específica, como los materiales compuestos. Por su parte, conceptos similares se emplean en la generación de energía eólica. El radio de las palas de las turbinas eólicas se incrementa paulatinamente, siendo un ejemplo muy claro las grandes instalaciones off-shore. El uso de estructuras más alargadas y ligeras provoca mayor deformación debida a las cargas aerodinámicas. Este fenómeno se conoce como aeroelasticidad y combina los efectos de las cargas aerodinámicas, los efectos inerciales y las tensiones internas de la estructura. La combinación de las cargas anteriores provoca fenómenos de amortiguamiento de las vibraciones, o por el contrario, inestabilidades aeroelásticas. Diferentes metodologías pueden ser empleadas para simular los fenómenos aeroelásticos. La metodología más extendida para la simulación de las ecuaciones elásticas del sólido es la conocida como análisis de elementos finitos. Respecto a las ecuaciones de conservación del fluido, la mecánica de fluidos computacional es la herramienta de resolución para un problema arbitrario. La combinación de las metodologías anteriores puede ser empleada para el cálculo de fenómenos aeroelásticos. Sin embargo, el coste computacional de estas simulaciones es inasumible en la mayoría de casos de aplicación. Se requiere una metodología nueva capaz de reducir el coste de cálculo. Este trabajo se centra en el desarrollo de modelos de orden reducido que permitan resolver el problema acoplado sin pérdidas sustanciales de precisión. En primer lugar, la estructura tridimensional se reduce a una sección equivalente que reproduzca la física del sólido original. La sección equivalente se acopla con dos modelos aerodinámicos: simulaciones de mecánica de fluidos computacional y un modelo reducido basado en redes neuronales. Ambos modelos presentan elevada precisión respecto a las simulaciones tridimensionales. Sin embargo, algunos efectos como los efectos aerodinámicos tridimensionales, las distribuciones de carga aerodinámica, la presencia de materiales ortotrópicos y los acoplamientos estructurales no pueden ser simulados. Con el objetivo de resolver los limitantes del modelo anterior, se propone un segundo modelo de orden reducido. En este caso se trata de un algoritmo basado en elementos de viga. El algoritmo se diseña para ser capaz de incluir el cálculo de materiales ortotrópicos y diferentes tipos de problemas aeroelásticos. Inicialmente, se emplea el software para determinar su precisión en el cálculo de una viga de material compuesto y sección rectangular. Estos resultados se validan con las simulaciones tridimensionales. De este modo se demuestra la capacidad de la herramienta computacional para predecir las inestabilidades y los efectos de acoplamiento estructural provocados por la orientación de las fibras. Posteriormente, el algoritmo se emplea en la simulación de turbinas eólicas, mejorando los rangos de operación de las palas sin que ello suponga una penalización desde el punto de vista del peso de la misma. Finalmente, un ala basada en una estructura de membrana resistente es simulada. El cálculo obtiene una gran precisión en la predicción de la velocidad de flameo respecto a la simulación acoplada, siendo la única limitación del modelo la predicción de la distorsión de la membrana. El trabajo presente un conjunto de modelos de orden reducido que permiten disminuir el coste computacional de las simulaciones aeroelásticas en órdenes de magnitud. También, se proporcionan directrices para la selección del modelo reducido apropiado para los casos de interés. / [CA] L'interès a reduir el pes i la resistència aerodinàmica dels vehicles i a desenvolupar fonts d'energia renovables s'ha incrementat a causa de la complexa situació ambiental i els requeriments legals per a reduir les emissions de contaminants i el consum de combustibles. La indústria aeronàutica ha proposat nous dissenys que integren conceptes com ales d'alt allargament i materials amb elevada resistència específica, com ara els materials compostos. Per la seua banda, conceptes similars es fan servir en la generació d'energia eòlica. El radi de les pales de les turbines eòliques s'incrementa progresivament, sent un exemple molt clar les grans instal·lacions off-shore. L'ús d'estructures més allargades i lleugeres provoca més deformació deguda a les càrregues aerodinàmiques. Aquest fenomen es coneix com a aeroelasticitat i combina els efectes de les càrregues aerodinàmiques, els efectes inercials i les tensions internes de l'estructura. La combinació de les càrregues anteriors provoca fenòmens d'esmorteïment de les vibracions, o per contra, inestabilitats aeroelàstiques. Diferents metodologies poden ser emprades per simular els fenòmens aeroelàstics. La metodologia més estesa per a la simulació de les equacions elàstiques del sòlid és la coneguda com a anàlisi d'elements finits. Pel que fa a les equacions de conservació del fluid, la mecànica de fluids computacional és l'eina de resolució per a un problema arbitrari. La combinació de les metodologies anteriors pot ser emprada per al càlcul de fenòmens aeroelàstics. Tot i això, el cost computacional d'aquestes simulacions és inassumible en la majoria de casos d'aplicació. Cal una metodologia nova capaç de reduir el cost de càlcul. Aquest treball se centra en el desenvolupament de models d'ordre reduït que permeten resoldre el problema acoblat sense pèrdues substancials de precisió. En primer lloc, l'estructura tridimensional es reduix a una secció equivalent que reproduixca la física del sòlid original. La secció equivalent s'acobla amb dos models aerodinàmics. El primer empra les forces aerodinàmiques obtingudes mitjançant simulacions de mecànica de fluids computacional. Posteriorment es fa servir un model reduït basat en xarxes neuronals. Tots dos models presenten elevada precisió respecte a les simulacions tridimensionals. No obstant això, alguns efectes com ara els efectes aerodinàmics tridimensionals, les distribucions de càrrega aerodinàmica, la presència de materials ortotròpics i els acoblaments estructurals no poden ser simulats. Amb l'objectiu de resoldre els limitants del model anterior, es proposa un segon model dordre reduït. En aquest cas és un algorisme basat en elements de biga. L'algorisme es dissenya per ser capaç d'incloure el càlcul de materials ortotròpics i diferents tipus de problemes aeroelàstics. Inicialment, s'empra el programari per determinar-ne la precisió en el càlcul d'una biga de material compost i secció rectangular. Aquests resultats es validen amb les simulacions tridimensionals. D'aquesta manera, es demostra la capacitat de l'eina computacional per predir les inestabilitats i els efectes d'acoblament estructural provocats per l'orientació de les fibres. Posteriorment, l'algorisme s'empra en la simulació de turbines eòliques, millorant els rangs d'operació de les pales sense que això suposi una penalització des del punt de vista del pes. Finalment, una ala basada en una estructura de membrana resistent és simulada. El càlcul obté una gran precisió en la predicció de la velocitat de flameig respecte a la simulació acoblada, i l'única limitació del model és la predicció de la distorsió de la membrana. El treball presenta un conjunt de models reduïts que permeten disminuir el cost computacional de les simulacions aeroelàstiques en ordres de magnitud. També es proporcionen directrius per a la selecció del model reduït adequat per als casos d'interès. / [EN] The complex environmental situation and the legal requirements for decreasing pollutant emissions and fuel consumption have increased the interest in reducing the empty weight and drag of vehicles and developing renewable energy sources. Due to the former, the aviation industry has proposed new designs integrating high strength-to-weight ratios, such as composite materials and higher aspect ratio wings. These increases in aspect ratio have also been applied to wind energy generation. The rotors of wind turbines are increasing their diameters in recent years: a clear example is the massive off-shore facilities. Using larger and lightweight structures increases the effects of the aerodynamic loads on structural deformation. Structural dynamics are strongly connected to the air-structure interaction. This phenomenon, called aeroelasticity, combines the effect of the external aerodynamic loads, the inertial forces, and the internal elastic stress of the structure. The complex combination of all the previous effects may damp the vibrations of the structure, or on the contrary, they could increase their amplitude, resulting in an unstable phenomenon. The simulation of the aeroelastic phenomena can be performed using different approaches. The well-known finite element analysis is the most extended methodology for solving solid elastic equations. Regarding fluid conservation equations, computational fluid dynamics is the principal tool for resolving general aerodynamic problems. The aeroelastic simulations can be calculated by combining the previous algorithms. Nevertheless, the computational cost of these methodologies is excessive for a general engineering case. Therefore, new methodologies are required. This work focuses on developing aeroelastic reduced-order models that compute the coupled phenomena without substantial accuracy losses. Initially, the complete three-dimensional structure is reduced to an equivalent section that reproduces the structure. The equivalent structural section is coupled with two aerodynamic models. The first one uses the forces calculated with aeroelastic computational fluid dynamics. Then, a surrogate model based on artificial neural networks is combined with the equivalent section. Both models show accurate agreement compared to the complete three-dimensional simulations in predicting unstable velocity. However, the three-dimensional aerodynamic effects, load distribution, orthotropic materials, and structural couplings cannot be considered. In order to solve the previous limitations, a reduced-order model based on a beam element solver is proposed. The algorithm is designed to consider a general orthotropic material and different typologies of aeroelastic problems. Initially, the software is proven to simulate accurately a squared cross-section composite material beam. The results are validated with the complete three-dimensional simulations, demonstrating the capabilities of the tool for predicting the instabilities and the effects of the fiber orientations. Then, the algorithm is used for simulating a wind turbine blade, and the algorithm results are used to improve the operation range of the blades without weight penalties. Finally, a resistant membrane wing is simulated, obtaining high accuracy in the prediction of the flutter velocity compared with the complete coupled simulation. In addition, the only limitation of the model is the prediction of the membrane distortion. The work presents a set of reduced-order models that allow for reducing the computational cost of the aeroelastic simulations by orders of magnitude. In addition, a decision pattern is provided for selecting the appropriate algorithm for the interest problem. / This thesis have been funded by Spanish Ministry of Science, Innovation and University through the University Faculty Training (FPU) program with reference FPU19/02201. / Cremades Botella, A. (2023). Fluid-structure interaction with the application to the non-linear aeroelastic phenomena [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/199249

<p>Positive displacement machines (PDMs) operate based on the principle of positive displacement, which necessitates a periodic alteration of volume. This volume variation is accomplished through relative motion between machine components. PDMs find extensive applications in diverse domains, encompassing fluid power systems, lubrication systems, fluid transport systems, fuel injection systems, and more. The primary distinction among PDMs lies in the geometric mechanisms employed for fluid displacement, as well as the flow distribution mechanisms they employ. PDMs can be broadly classified into piston machines, vane machines, screw machines, and gear machines. In fluid power systems, the most commonly used PDMs are the piston and gear machines. Piston machines can be further classified into radial piston machines, in-line piston machines, and axial piston machines. The most commonly used piston machines are the axial piston machine owing to their superior efficiency and compactness. Gear machines can be further classified into external gear machines, internal gear machines, and annular gear machines. The most commonly used gear machine is the external gear machine owing to its price.</p> <p><br></p> <p>PDMs typically involve multiple solid bodies in relative motion, with micron-level gaps between them. These gaps, known as lubricating interfaces, present a significant design challenge during the machine development process. They are a primary source of power losses and play a crucial role in determining the efficiency and durability of the machine. The lubricating interfaces must effectively balance loads and maintain a high-pressure fluid seal. Achieving this delicate balance necessitates a comprehensive understanding of the underlying physical phenomena. Lubricating interfaces generate substantial heat due to viscous dissipation, which directly impacts the operation of the entire machine. The viscosity of the working fluid rapidly decays with temperature, causing the warmer fluid within the lubricating interface to possess lower viscosity. Consequently, it can support lesser loads and is more prone to leakage. Moreover, as the solid bodies enclosing the warmer fluid heat up, they undergo thermal expansion, further changing the clearance and leading to a decline in performance. Additionally, the elevated temperature of the fluid within the lubricating interface affects the compressibility of the displacement chamber fluid, thereby influencing the pressurization characteristics of the entire unit. Thus, thermal effects play a critical role in the performance of PDMs.</p> <p><br></p> <p>  The ever-increasing market demand for more compact, efficient, and reliable designs requires a continuous process of design improvements over previous designs, and sometimes completely new designs. Sophisticated simulation tools are a necessity for such a design process. Additionally, these simulation tools also prove to be valuable in formulating design modifications in case of underperforming designs. Due to the complexity associated with the operation of such units, the simulation tools need to capture a wide variety of physical phenomena. Over the past few decades, owing to the increasing computing power of the desktop computer, several simulation tools have been proposed across the literature to aid the design process of such machines with each having limitations of their own.</p> <p><br></p> <p>  The objective of the present thesis is to propose a modeling approach that assists in the design process of positive displacement machines, addressing various limitations identified in the existing literature. The approach is intentionally designed to be generic, enabling its application across a diverse range of positive displacement machines. The modeling approach encompasses three distinct domains: the displacement chamber fluid domain, the lubricating interface fluid domain, and the solid domain. A novel thermal model that integrates all three domains is introduced. </p> <p><br></p> <p>  To validate the effectiveness of the proposed modeling approach, two separate validation studies are conducted. The first study focuses on a model for an isolated piston/cylinder interface of an axial piston machine, operating under the mixed lubrication regime. The model demonstrates a strong agreement with the measured data. The second study involves steady-state measurements of an entire axial piston machine. The model is validated by comparing the steady-state flow characteristics and temperature distribution on the valveplate, both of which are accurately captured by a single fully coupled model. The modeling approach developed in this study, specifically, the energy conservation in the lubricating interface, heat transfer in the solid bodies, and thermal deformation in the solid bodies are all generalized for applicability in different types of PDMs. However, the results presented in this thesis pertain to an axial piston machine.</p>

<p dir="ltr">New system-level codes are being developed for advanced reactors for safety analysis and licensing purposes. Thermal-hydraulics of advanced reactors is a challenging problem due to complex flow scenarios assisted by free jets and stratified flows that lead to turbulent mixing. For these reasons, the 0D or 1D models used for reactor plena in traditional safety analysis codes like RELAP cannot capture the physics accurately and introduce a large degree of modeling uncertainty. System-level calculation codes based on the advection-diffusion equation neglect turbulent fluctuations. These fluctuations are extremely important as they introduce higher-order moments, which are responsible for vortex stretching and the passage of energy to smaller scales. Alternatively, extremely detailed simulations with velocity coupling from the Navier-Stokes equations are able to capture turbulence effects accurately using DNS. These solutions are accurate because they resolve the flow into the smallest possible length and time scales (Kolmogorov scale) important to the flow, which makes DNS computationally expensive for simple geometries and impossible at the system level.</p><p dir="ltr">The flow field can be described through a reduced-order model using the principles of statistical mechanics. Statistical mechanics-based methods provide a method for extracting statistics from data and modeling that data using easily represented differential equations. The Kramers-Moyal (KM) expansion method can be used as a subgrid-scale (SGS) closure for solving the momentum equation. The stochastic Burgers equation is solved using DNS, and the DNS solutions are used to calculate the KM coefficients, which are then implemented as an SGS closure model. The KM method outperforms traditional methods in capturing the multi-scale behavior of Burgers turbulence. The functional dependencies of the KM coefficients are also uniform for several boundary conditions, meaning the closure model can be extended to multiple flow scenarios. </p><p dir="ltr">For the case of the Navier-Stokes equations, each particle trajectory tends to follow some scaling law. Kolmogorov hypothesized that the flow velocity field follows a -5/3 scaling in the inertial region where Markovian characteristics can be invoked to model the interaction between eddies of adjacent sizes. This law holds true in the inertial region where the flow is Markovian. For scalar turbulence, the scaling laws are affected by thermal diffusion. If a fluid has a Prandtl number close to one, the thermal behavior is dominated by momentum, so the spectra for velocity and temperature are similar. For small Prandtl number fluids, such as liquid metals, the thermal diffusion dominates the lower scales and the slope of the spectrum shifts from the -5/3 slope to a -3 slope, also called the Batchelor region. System-level thermal hydraulics codes need to be able to capture these behaviors for a range of Prandtl number fluids. The KM-based model can also be used as a surrogate for velocity or temperature fluctuations in scalar turbulence. Using DNS solutions for turbulent channel flow, the KM model is used to provide a surrogate for temperature and velocity signals at different wall locations in the channel for Pr = 0.004, Pr = 0.025, and Pr = 0.71. The KM surrogate matches well for all wall locations, but is not able to capture the viscous dissipation in the velocity signal, or the thermal dissipation in the low Prandtl number cases. The dissipation can be captured by implementing a Gaussian filter.</p><p dir="ltr">Statistical mechanics-based methods are not limited to modeling turbulence in a reactor. Renewable power generation, such as wind, can be modeled using the Ornstein-Uhlenbeck (OU) method, which allows the long-term trends and short-term fluctuations of wind power to be decoupled. This allows for large fluctuations in wind power to be scaled down to a level that a reactor can accommodate safely. </p><p dir="ltr">Since statistical mechanics methods are based in physics, the calculated coefficients provide some information about the inputted signal. In a high-temperature gas-cooled reactor, strong heating can cause flow that is expected to be turbulent to show laminar characteristics. This laminarization results in reduced heat removal. The KM coefficients can be used to classify the laminarization from probed velocity signals more effectively than traditional statistical analyses.</p>

No description available.

<p dir="ltr">The dissolution profile is one of the most important critical quality attributes (CQAs) for pharmaceutical solid oral dosage forms, as failure to meet the dissolution specification can impact bioavailability. Dissolution tests are essential to assess lot-to-lot product quality and guide the development of new formulations. Therefore, predictive dissolution reduced-order models (ROM) are crucial for the successful implementation of any real-time release testing (RTRT) strategy. Mechanistic and semi-mechanistic ROMs of tablet dissolution for realizing quality by control (QbC) and RTRT frameworks in continuous manufacturing are still scarce or nonexistent. Moreover, realizing the underlying coupled mechanics of wetting, swelling, disintegration, and dissolution is still an open question. This dissertation contributes to developing a mechanistic ROM of pharmaceutical tablet dissolution for the design, optimization, and control of manufacturing processes. We follow several steps towards the progression of the mechanistic model development. First, we develop a semi-mechanistic ROM to capture the relationship between critical process parameters (CPPs), critical material attributes (CMAs), and dissolution profiles. We demonstrate the versatility and the capability of the semi-mechanistic ROM to estimate changes in dissolution due to process disturbances in tablet porosity, lubrication conditions, and moisture content in the powder blend. Next, to understand the underlying coupled mechanism of wetting, swelling, disintegration, and dissolution, we use dynamic micro-computed tomography (micro-CT) with a high temporal resolution to visualize water penetration through the porous network of immediate-release tablets. We couple liquid penetration due to capillary pressure described by the Lucas-Washburn theory with the first-order swelling kinetics of the excipients to provide a physical interpretation of the experimental observations. From the mechanistic understanding of the water penetration kinetics using the micro-CT tests, we propose a two-stage mechanistic ROM, which is comprised of (i) a mechanistic dissolution model of the active pharmaceutical ingredient (API) that solves a population balance model (PBM) for a given API crystal size distribution and dissolution rate coefficient, and (ii) a tablet wetting function that estimates the rate at which the API is exposed to the buffer solution. These two sub-models are coupled by means of convolution in time to capture the start time of the API dissolution process as water uptake, swelling, and disintegration take place. Finally, we demonstrate the versatility and the capability of the mechanistic API dissolution model and the two-stage tablet dissolution ROM to represent the dissolution profile of different pharmaceutical formulations and its connection with CMAs, CPPs, and other CQAs, namely initial API crystal size distribution, porosity, composition, and dimensions of the tablet. In all of the cases considered in this work, the estimations of the model are in good agreement with experimental data. </p>

<div>Adsorbent technology is widely used in many industrial applications including waste heat recovery, water purification, and atmospheric revitalization in confined habitations. Astronauts depend on adsorbent-based systems to remove metabolic carbon dioxide (CO₂) from the cabin atmosphere; as NASA prepares for the journey to Mars, engineers are redesigning the adsorbent-based system for reduced weight and optimal efficiency. These efforts hinge upon the development of accurate, predictive models, as simulations are increasingly relied upon to save cost and time over the traditional design-build-test approach. Engineers rely on simplified models to reduce computational cost and enable parametric optimizations. Amongst these simplified models is the axially dispersed plug-flow model for predicting the adsorbate concentration during flow through an adsorbent bed. This model is ubiquitously used in designing fixed-bed adsorption systems. The current work aims to improve the accuracy of the axially dispersed plug-flow model because of its wide-spread use. This dissertation identifies the critical model inputs that drive the overall uncertainty in important output quantities then systematically improves the measurement and prediction of these input parameters. Limitations of the axially dispersed plug-flow model are also discussed, and recommendations made for identifying failure of the plug-flow assumption.</div><div><br></div><div>An uncertainty and sensitivity analysis of an axially disperse plug-flow model is first presented. Upper and lower uncertainty bounds for each of the model inputs are found by comparing empirical correlations against experimental data from the literature. Model uncertainty is then investigated by independently varying each model input between its individual upper and lower uncertainty bounds then observing the relative change in predicted effluent concentration and temperature (<i>e.g.</i>, breakthrough time, bed capacity, and effluent temperature). This analysis showed that the LDF mass transfer coefficient is the largest source of uncertainty. Furthermore, the uncertainty analysis reveals that ignoring the effect of wall-channeling on apparent axial dispersion can cause significant error in the predicted breakthrough times of small-diameter beds.</div><div><br></div><div>In addition to LDF mass transfer coefficient and axial-dispersion, equilibrium isotherms are known to be strong lever arms and a potentially dominant source of model error. As such, detailed analysis of the equilibrium adsorption isotherms for zeolite 13X was conducted to improve the fidelity of CO₂ and H₂O on equilibrium isotherms compared to extant data. These two adsorbent/adsorbate pairs are of great interest as NASA plans to use zeolite 13X in the next generation atmospheric revitalization system. Equilibrium isotherms describe a sorbent’s maximum capacity at a given temperature and adsorbate (<i>e.g.</i>, CO₂ or H₂O) partial pressure. New isotherm data from NASA Ames Research Center and NASA Marshall Space Flight Center for CO₂ and H₂O adsorption on zeolite 13X are presented. These measurements were carefully collected to eliminate sources of bias in previous data from the literature, where incomplete activation resulted in a reduced capacity. Several models are fit to the new equilibrium isotherm data and recommendations of the best model fit are made. The best-fit isotherm models from this analysis are used in all subsequent modeling efforts discussed in this dissertation.</div><div><br></div><div>The last two chapters examine the limitations of the axially disperse plug-flow model for predicting breakthrough in confined geometries. When a bed of pellets is confined in a rigid container, packing heterogeneities near the wall lead to faster flow around the periphery of the bed (<i>i.e.</i>, wall channeling). Wall-channeling effects have long been considered negligible for beds which hold more than 20 pellets across; however, the present work shows that neglecting wall-channeling effects on dispersion can yield significant errors in model predictions. There is a fundamental gap in understanding the mechanisms which control wall-channeling driven dispersion. Furthermore, there is currently no way to predict wall channeling effects a priori or even to identify what systems will be impacted by it. This dissertation aims to fill this gap using both experimental measurements and simulations to identify mechanisms which cause the plug-flow assumption to fail.</div><div><br></div><div>First, experimental evidence of wall-channeling in beds, even at large bed-to-pellet diameter ratios (<i>d</i>_bed/<i>d</i>_p=48) is presented. These experiments are then used to validate a method for accurately extracting mass transfer coefficients from data affected by significant wall channeling. The relative magnitudes of wall-channeling effects are shown to be a function of the adsorption/adsorbate pair and geometric confinement (<i>i.e.</i>, bed size). Ultimately, the axially disperse plug-flow model fails to capture the physics of breakthrough when nonplug-flow conditions prevail in the bed.</div><div><br></div><div>The final chapter of this dissertation develops a two-dimensional (2-D) adsorption model to examine the interplay of wall-channeling and adsorption kinetics and the adsorbent equilibrium capacity on breakthrough in confined geometries. The 2-D model incorporates the effect of radial variations in porosity on the velocity profile and is shown to accurately capture the effect of wall-channeling on adsorption behavior. The 2-D model is validated against experimental data, and then used to investigate whether capacity or adsorption kinetics cause certain adsorbates to exhibit more significant radial variations in concentration compared than others. This work explains channeling effects can vary for different adsorbate and/or adsorbent pairs—even under otherwise identical conditions—and highlights the importance of considering adsorption kinetics in addition to the traditional <i>d</i>_bed/<i>d</i>_p criteria.</div><div><br></div><div>This dissertation investigates key gaps in our understanding of fixed-bed adsorption. It will deliver insight into how these missing pieces impact the accuracy of predictive models and provide a means for reconciling these errors. The culmination of this work will be an accurate, predictive model that assists in the simulation-based design of the next-generation atmospheric revitalization system for humans’ journey to Mars.</div>

Cette thèse de doctorat porte sur le calcul par la méthode des éléments finis du comportement dynamique de réservoirs élastiques précontraints contenant un liquide interne à surface libre. Nous considérons que la pression hydrostatique exercée par le fluide interne incompressible sur les parois flexibles du réservoir est à l’origine de grands déplacements, conduisant ainsi à un état d’équilibre non-linéaire géométrique. Le changement de raideur lié à cet état précontraint induit un décalage des fréquences de résonances du problème de vibrations linéaires couplées.L’objectif principal du travail est donc d’estimer, par des approches numériques précises et efficaces, l’influence des non-linéarités géométriques sur le comportement hydroélastique du système réservoir/liquide interne autour de différentes configurations d’équilibre. La méthodologie développée s’effectue en deux étapes. La première consiste à calculer l’état statique non-linéaire par une approche éléments finis lagrangienne totale. L’action du fluide sur la structure est ici modélisée par des forces suiveuses hydrostatiques. La deuxième étape porte sur le calcul des vibrations couplées linéarisées. Un modèle d’ordre réduit original est notamment proposé pour limiter les coûts de calcul associés à l’estimation de l’effet de masse ajoutée. Enfin, divers exemples sont proposés et comparés à des résultats de la littérature (issus de simulations numériques ou d’essais expérimentaux) pour montrer l’efficacité et la validité des différentes approches numériques développées dans ce travail. / This doctoral thesis focuses on the calculation by the finite element method of the dynamic behavior of prestressed elastic tanks containing an internal liquid with a free surface. We consider that the hydrostatic pressure exerted by the incompressible internal fluid on the flexible walls of the tank causes large displacements, thus leading to a geometric non-linear equilibrium state. The change of stiffness related to this prestressed state induces a shift in the resonance frequencies of the coupled linear vibration problem. The main objective of the work is therefore to estimate, through precise and efficient numerical approaches, the influence of geometric nonlinearities on the hydroelastic behavior of the reservoir/internal liquid system around different equilibrium configurations. The methodology developed is carried out in two stages. The first one consists in calculating the non-linear static state by a total Lagrangian finite element approach.The action of the fluid on the structure is modelled here by hydrostatic following forces. The second step is the calculation of linearized coupled vibrations. In particular, an original reduced order model is proposed to limit the calculation costs associated with the estimation of the added mass effect. Finally, various examples are proposed and compared with results from the literature (from numerical simulations or experimental tests) to show the effectiveness and validity of the different numerical approaches developed in this work.

Sound criteria for partial order reduction for probabilistic concurrent systems have been presented in the literature. Their realization relies on a depth-first search-based approach for generating the reduced model. The drawback of this dynamic approach is that it can hardly be combined with other techniques to tackle the state explosion problem, e.g., symbolic probabilistic model checking with multi-terminal variants of binary decision diagrams. Following the approach presented by Kurshan et al. for non-probabilistic systems, we study partial order reduction techniques for probabilistic concurrent systems that can be realized by a static analysis. The idea is to inject the reduction criteria into the control flow graphs of the processes of the system to be analyzed. We provide the theoretical foundations of static partial order reduction for probabilistic concurrent systems and present algorithms to realize them. Finally, we report on some experimental results.

In der vorliegenden Arbeit wird die Entwicklung eines effizienten Verfahrens zur parametrischen Finite Elemente Simulation von Mikrosystemen und zum Export dieser Modelle in Elektronik- und Systemsimulationswerkzeuge vorgestellt. Parametrische FE-Modelle beschreiben den Einfluss von geometrischen Abmessungen, Schwankungen von Materialeigenschaften und veränderten Umgebungsbedingungen auf das Funktionsverhalten von Sensoren und Aktuatoren. Parametrische FE-Modelle werden für die Auswahl geeigneter Formelemente und deren Dimensionierung während des Entwurfsprozesses in der Mikrosystemtechnik benötigt. Weiterhin ermöglichen parametrische Modelle Sensitivitätsanalysen zur Bewertung des Einflusses von Toleranzen und Prozessschwankungen auf die Qualität von Fertigungsprozessen. In Gegensatz zu üblichen Sample- und Fitverfahren wird in dieser Arbeit eine Methode entwickelt, welche die Taylorkoeffizienten höherer Ordnung zur Beschreibung des Einflusses von Designparametern direkt aus der Finite-Elemente- Formulierung, durch Ableitungen der Systemmatrizen, ermittelt. Durch Ordnungsreduktionsverfahren werden die parametrischen FE-Modelle in verschiedene Beschreibungssprachen für einen nachfolgenden Elektronik- und Schaltungsentwurf überführt. Dadurch wird es möglich, neben dem Sensor- und Aktuatorentwurf auch das Zusammenwirken von Mikrosystemen mit elektronischen Schaltungen in einer einheitlichen Simulationsumgebung zu analysieren und zu optimieren. / The thesis deals with advanced parametric modeling technologies based on differentiation of the finite element equations which account for parameter variations in a single FE run. The key idea of the new approach is to compute not only the governing system matrices of the FE problem but also high order partial derivatives with regard to design parameters by means of automatic differentiation. As result, Taylor vectors of the system’s response can be expanded in the vicinity of the initial position capturing dimensions and physical parameter. A novel approaches for the parametric MEMS simulation have been investigated for mechanical, electrostatic and fluidic domains in order to improve the computational efficiency. Objective of reduced order modeling is to construct a simplified model which approximates the original system with reasonable accuracy for system level design of MEMS. The modal superposition technique is most suitable for system with flexible mechanical components because the deformation state of any flexible system can be accurately described by a linear combination of its lowest eigenvectors. The developed simulation approach using parametric FE analyses to extract basis functions have been applied for parametric reduced order modeling. The successful implementation of a derivatives based technique for parameterization of macromodel by the example of microbeam and for exporting this macromodel into MATLAB/Similink to simulate dynamical behavior has been reported.

Cette thèse concerne le développement, l'extension et l'application d'une formulation stochastique des équations de la mécanique des fluides introduite par Mémin (2014). La vitesse petite échelle, non-résolue, est modélisée au moyen d'un champ aléatoire décorrélé en temps. Cela modifie l'expression de la dérivée particulaire et donc les équations de la mécanique des fluides. Les modèles qui en découlent sont dénommés modèles sous incertitude de position. La thèse s'articulent autour de l'étude successive de modèles réduits, de versions stochastiques du transport et de l'advection à temps long d'un champ de traceur par une vitesse mal résolue. La POD est une méthode de réduction de dimension, pour EDP, rendue possible par l'utilisation d'observations. L'EDP régissant l'évolution de la vitesse du fluide est remplacée par un nombre fini d'EDOs couplées. Grâce à la modélisation sous incertitude de position et à de nouveaux estimateurs statistiques, nous avons dérivé et simulé des versions réduites, déterministe et aléatoire, de l'équation de Navier-Stokes. Après avoir obtenu des versions aléatoires de plusieurs modèles océaniques, nous avons montré numériquement que ces modèles permettaient de mieux prendre en compte les petites échelles des écoulements, tout en donnant accès à des estimés de bonne qualité des erreurs du modèle. Ils permettent par ailleurs de mieux rendre compte des évènements extrêmes, des bifurcations ainsi que des phénomènes physiques réalistes absents de certains modèles déterministes équivalents. Nous avons expliqué, démontré et quantifié mathématiquement l'apparition de petites échelles de traceur, lors de l'advection par une vitesse mal résolu. Cette quantification permet de fixer proprement des paramètres de la méthode d'advection Lagrangienne, de mieux le comprendre le phénomène de mélange et d'aider au paramétrage des simulations grande échelle en mécanique des fluides. / This thesis develops, analyzes and demonstrates several valuable applications of randomized fluid dynamics models referred to as under location uncertainty. The velocity is decomposed between large-scale components and random time-uncorrelated small-scale components. This assumption leads to a modification of the material derivative and hence of every fluid dynamics models. Through the thesis, the mixing induced by deterministic low-resolution flows is also investigated. We first applied that decomposition to reduced order models (ROM). The fluid velocity is expressed on a finite-dimensional basis and its evolution law is projected onto each of these modes. We derive two types of ROMs of Navier-Stokes equations. A deterministic LES-like model is able to stabilize ROMs and to better analyze the influence of the residual velocity on the resolved component. The random one additionally maintains the variability of stable modes and quantifies the model errors. We derive random versions of several geophysical models. We numerically study the transport under location uncertainty through a simplified one. A single realization of our model better retrieves the small-scale tracer structures than a deterministic simulation. Furthermore, a small ensemble of simulations accurately predicts and describes the extreme events, the bifurcations as well as the amplitude and the position of the ensemble errors. Another of our derived simplified model quantifies the frontolysis and the frontogenesis in the upper ocean. This thesis also studied the mixing of tracers generated by smooth fluid flows, after a finite time. We propose a simple model to describe the stretching as well as the spatial and spectral structures of advected tracers. With a toy flow but also with satellite images, we apply our model to locally and globally describe the mixing, specify the advection time and the filter width of the Lagrangian advection method, as well as the turbulent diffusivity in numerical simulations.