A high resolution spectrally accurate three-dimensional flow solver is developed in order to simulate convection dominated fluid flows. The governing incompressible Navier Stokes equations along with the energy equation for temperature are discretized using a second-order accurate projection method which utilizes Adams Bashforth and Backward Differentiation formula for temporal discretization of the non-linear convective and linear viscous terms, respectively. Spatial discretization is performed using a Fourier/Chebyshev spectral method. Extensive tests on three-dimensional Taylor Couette flow are performed and it is shown that the method successfully captures the different states ranging from formation of Taylor vortices to wavy vortex regime. Next, the code is validated for convection dominated flows through a comprehensive comparison of the results for two dimensional Rayleigh Benard convection with the theoretical and experimental results from the literature. Finally, fully parallel simulations, with efficient utilization of computational resources and memory, are performed on a model three-dimensional axially homogeneous Rayleigh Benard convection problem in order to explore the high Rayleigh number flows and to test the scaling of global properties.

Several types of instability can affect the interface between two fluids. For instance, a Rayleigh-Taylor instability (or density fingering) is encountered when a heavier fluid is placed upon a lighter one in the gravity field and double diffusive instabilities can be triggered by differential diffusivity of the different species present in the fluid. <p>In this context our work aims to understand theoretically in which way a chemical reaction can induce and influence such instabilities in a fluid initially at rest.<p>To understand the dynamics resulting from the coupling between chemical reactions and hydrodynamical instabilities we use chemical fronts as model systems. These fronts result from the coupling between autocatalytical chemical reactions and diffusion and they allow to create a self-organized interface between the products and the reactants. As during a chemical reaction the density may vary due to solutal and thermal effects, the products and the reactants can have different densities which may trigger convection movements leading to the destabilization of the fronts.<p><p>We have in particular studied the influence of the exothermicity of the reaction on the fingering of chemical fronts, focusing first on the influence of heat losses through the walls of the set-up.<p>These leaks have a marked influence on the dynamics because they affect the temperature profiles and hence the density profiles too. We have also classified the various types of instabilities that may appear dues to solutal and thermal effects. We have found a new type of hydrodynamic instability of statically stable fronts induced by the chemical reaction. <p><p>We have furthermore analyzed an isothermal model with two chemical species. If they diffuse at different rates the front can be subject to diffusive instabilities as well. We have shown that the coupling between such a diffusive instability and fingering can trigger complex dynamics. We have eventually studied the influence of an external electric field on the diffusive instabilities and on fingering underlying the possibility to destabilize otherwise stable fronts./<p>Différents types d'instabilités hydrodynamiques peuvent affecter les interfaces entre deux fluides comme par exemple, une instabilité de Rayleigh-Taylor (ou digitation de densité) quand un fluide plus dense se trouve placé au-dessus d'un fluide moins dense dans le champ de gravité ou des instabilités de double diffusion induites par des différences entre les diffusivités d'un soluté et de la chaleur contenus dans les fluides. Dans ce contexte, notre thèse s'attache à comprendre de manière théorique comment une réaction chimique peut influencer ces instabilités voire les générer dans un fluide initialement au repos. Pour étudier les dynamiques résultant du couplage entre réactions chimiques et instabilités hydrodynamiques, nous utilisons des systèmes modèles: les fronts chimiques de conversion résultant de la compétition entre réactions chimiques autocatalytiques et diffusion créant une interface auto-organisée entre les réactifs et les produits. Comme au cours d'une réaction chimique la densité peut varier par des effets solutaux et thermiques, les produits et les réactifs de densités différentes peuvent générer des mouvements de convection qui conduisent à la déstabilisation des fronts. <p><p>Nous avons en particulier étudié l'influence de l'exothermicité de la réaction sur les instabilités de digitation de fronts chimiques, en nous focalisant dans un premier temps sur l'influence des pertes de chaleur par les parois du réacteur.<p>Ces fuites ont un effet marqué sur les instabilitités car elles affectent les profils de température et donc les profils de densité dans le système. Nous avons également classifié les différentes instabilités qui peuvent apparaître via des changements de densité dûs à des effets thermiques et solutaux et mis en évidence un nouveau type de déstabilisation hydrodynamique de fronts statiquement stables induit par une réaction chimique. <p>Nous avons ensuite analysé un modèle isotherme impliquant deux espèces chimiques. Si ces dernières diffusent a des vitesses différentes le front peut être sujet à une instabilité diffusive. Nous avons montré qu'un couplage entre une telle instabilité diffusive et de la digitation peut être à l'origine de dynamiques complexes. Nous avons ensuite considéré l'influence d'un champ électrique sur les instabilité diffusives et de digitation en soulignant la possibilié de déstabiliser via ce champ des fronts initialement stables. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Cette thèse est consacrée à la vérification de l'analogie entre l'instabilité viscoélastique (VEI) et l'instabilité magnéto-rotationnel (MRI) dans un écoulement képlérien, afin de mieux comprendre le transport du moment dans les disques d'accrétion. Le discriminant de Rayleigh élasto-rotationnel est établi pour clarifier le rôle de l'élasticité dans le VEI. L'analyse de stabilité linéaire (LSA) avec le modèle d’Oldroyd-B est effectuée pour prédire les paramètres critiques des modes viscoélastiques. Il fait apparaître également l'influence de l'élasticité, la viscosité polymérique et d'autres paramètres de contrôle pour le VEI. Des expériences bien contrôlées avec des solutions aqueuses de polyoxyéthylène (POE) et de polyéthylène glycol (PEG) sont effectuées. Nous avons observé le mode stationnaire axisymétrique supercritique avec des solutions de faible élasticité et modes désordonnés sous-critiques avec des solutions de grande élasticité. Les formes et les valeurs critiques de ces modes sont en bon accord avec les prédictions théoriques de LSA. Selon l'analogie, le mode axisymétrique stationnaire est probablement l'analogue de MRI standard, tandis que le mode désordonné est probable que l'analogue de MRI hélicoïdale. La thèse contient aussi des résultats théoriques expérimentaux sur quatre autres régimes de rotation et un cas de limite d'élasticité infinie. / This thesis is devoted to the verification of the analogy between the viscoelastic instability (VEI) and the magnetorotational instability (MRI) in a Keplerian flow, in order to get better understanding of the momentum transportation in accretion disks.The elasto-rotational Rayleigh discriminant is deduced to clarify the role of the elasticity in the VEI. The linear stability analysis (LSA) with Oldroyd-B model is performed to predict critical parameters of viscoelastic modes, and it reveals the influence of the elasticity, polymer viscosity on the VEI. Experiments with well controlled aqueous solutions of polyoxyethylene (POE) and polyethylene glycol (PEG) are conducted. We have observed supercritical stationary axisymmetric mode with solutions of small elasticity and subcritical disordered modes with solutions of large elasticity. Both the flow patterns and the critical values of these modes are in good agreement with the LSA predictions. According to the analogy, the stationary axisymmetric mode is likely the analog of the standard MRI while the disordered mode is likely the analog of the helical MRI. The thesis contains also theoretical and experimental results with four other rotation regimes and the limit case of infinite elasticity.

Accretion disks are ubiquitous in astrophysics. They are found in active galactic nuclei, around newly formed stars, around compact stellar objects, like black holes, neutron stars etc. When the ambient matter with sufficient initial angular momentum falls towards a central massive object, forming a disk shaped astrophysical structure, it is called an accretion disk. There are both ionized and neutral disks depending on their temperatures. Generally, in accretion disks, Gravitational force is balanced by the centrifugal force (due to the presence of angular momentum of the matter) and the forces due to gas pressure, radiation pressure and advection. Now, the matter to be accreted needs to lose angular momentum. For most of the accretion disks, the mass of the central object is much higher than the mass of the disk, giving rise to a dynamics governed by a central force. Therefore we can neglect the effect of self-gravity of the disk. Balancing the Newtonian gravitational force and centrifugal force leads to a Keplerian rotation profile of the accreting matter with the angular velocity ∼ r−3/2, where r is the distance from the central object. The Keplerian disk model is extremely useful to explain several flow classes (e.g. emission of soft X-ray in disks around stellar mass black holes). Due to the presence of differential rotation and hence shear viscosity, the matter can slowly lose its angular momentum and falls towards the central object. In this way, the accreting matter in the disk releases its gravitational potential energy and gives rise to luminosity that we observe. However, the molecular viscosity originated from the microscopic physics (due to the collisions between molecules) of the disk matter is not sufficient to explain the observed luminosity or accretion rate. For example, it can be shown that the temperature arisen from the dissipation of energy due to molecular viscosity (which is around 50000K for optical depth τ = 100) is much less than the temperature observed in these systems (around 107K). In my thesis, I have addressed the famous problem of infall of matter in astrophysical accretion disks. In general, the emphasis is given on the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows, which are extensively seen in astrophysics, are Rayleigh-stable, but must be turbulent in order to explain observed data (observed temperature, as described above). Since the molecular viscosity is negligible in these systems, for a very large astrophysical length scale, Shakura and Sunyaev argued for turbulent viscosity for energy dissipation and hence to explain the infall of matter towards the central object. This idea is particularly attractive because of its high Reynolds number (Re ∼ 1014). However, the Keplerian disks, which are relevant to many astrophysical applications, are remarkably Rayleigh stable. Therefore, linear perturbation apparently cannot induce the onset of turbulence, and consequently cannot provide enough viscosity to transport matter inwards. The primary theme of my thesis is, how these accretion disks can be made turbulent in the first place to give rise to turbulent viscosity. With the application of Magnetorotational Instability (MRI) to Keplerian disks, Balbus and Hawley showed that initial seed, weak magnetic fields can lead to the velocity and magnetic field perturbations growing exponentially. Within a few rotation times, such exponential growth could reveal the onset of turbulence. Since then, MRI has been a widely accepted mechanism to explain origin of instability and hence transport of matter in accretion disks. Note that for flows having strong magnetic fields, where the magnetic field is tightly coupled with the flow, MRI is not expected to work. Hence, it is very clear that the MRI is bounded in a small regime of parameter values when the field is also weak. It has been well established by several works that transient growth (TG) can reveal nonlinearity and transition to turbulence at a sub-critical Re. Such a sub-critical transition to turbulence was invoked to explain colder, purely hydrodynamic accretion flows, e.g. quiescent cataclysmic variables, proto-planetary and star-forming disks, the outer region of the disks in active galactic nuclei etc. Baroclinic instability is another plausible source for vigorous turbulence in colder accretion disks. Note that while hotter flows are expected to be ionized enough to produce weak magnetic fields therein and subsequent MRI, colder flows may remain to be practically neutral in charge and hence any instability and turbulence therein must be hydrodynamic. However, in the absence of magnetic effects, the Coriolis force does not allow any significant TG in accretion disks in three dimensions, independent of Re, while in pure two dimensions, TG could be large at large Re. However, a pure two-dimensional flow is a very idealistic case. Nevertheless, in the presence of magnetic field, even in three dimensions, TG could be very large (Coriolis effects could not suppress the growth). Hence, in a real three-dimensional flow, it is very important to explore magnetic TG. However, as mentioned above, the charge neutral Rayleigh-stable astrophysical flows have hardly any magnetic field (e.g. protoplanetary disks, quiescent cataclysmic variables etc.). Also, the hydrodynamic Rayleigh-stable Taylor-Couette flows and plane Couette flows in the laboratory experiments are seen to be turbulent without the presence of any magnetic field, while they are shown to be stable in linear stability analysis. It is a century old unsolved problem to explain hydrodynamically, the linear instability of Couette flows and other Rayleigh-stable Flows, which are observed to be turbulent, starting from laboratory experiments to astrophysical observations. Therefore, as in one hand, the hydrodynamic instability of the astrophysical accretion flows and laboratory shear flows (e.g. Rayleighstable Taylor-Couette flow, plane Couette flow etc.) has to be understood, on the other hand, the magnetohydrodynamic (MHD) instability of the hotter flows has also to be investigated to understand the nature of MHD instability clearly, whether it arises due to MRI or TG. I have investigated the effect of stochastic noise (which is generated by the shearing motion of the disk layers) on the hydrodynamics and magnetohydrodynamics of accretion disks and explain how stochastic noise can make accretion Disks turbulent. It is found that such stochastically driven flows exhibit large temporal and spatial correlations of perturbations, and hence large energy dissipations of perturbation with time, which presumably generates instability and turbulence. I have also given in my thesis, a plausible resolution of the hydrodynamic turbulence problem of the accretion flows and laboratory shear flows (as discussed above) from pure hydrodynamics, invoking the idea of Brownian motion of particles. I have shown that in any shear flow, very likely, the stochastic noise is generated due to thermal fluctuations. Therefore, the shear flows must be studied including the effect of stochastically driving force and hence the governing equations should not be deterministic. Incorporating the effects of noise in the study of the above mentioned shear flows, I have shown in my thesis that hydrodynamic Rayleigh-stable flows and plane Couette flows can be linearly unstable. I have also investigated the importance of transient growth over magnetorotational instability (MRI) to produce turbulence in accretion disks. Balbus and Hawley asserted that the MRI is the fastest weak field instability in accretion disks. However, they used only the plane wave perturbations to study the instability problem. I have shown that for the flows with high Reynolds number, which are indeed the case for astrophysical accretion disks, transient growth can make the system nonlinear much faster than MRI and can be a plausible primary source of turbulence, using the shearing mode perturbations. Therefore, this thesis provides a plausible resolution of hydrodynamic turbulence observed in astrophysical accretion disks and some laboratory shear flows, such as, Rayleigh-stable Taylor-Couette flows and plane Couette flows. Moreover, this thesis also provides a clear understanding of MHD turbulence for astrophysical accretion disks.

The Master's thesis deals with the mechanical design of electric machine rotor. Within the first two chapters of the practical part of the thesis two simplified computational models of the rotor (level 1 models) are compiled. Specifically, the model of flexible rotor mounted on rigid supports and model of rigid rotor mounted on flexible supports. The essence of these computational models lies in solvability using simple equations. Using these models can save time when constructing a pre-design of the rotor geometry. The following chapter is devoted to comparing different approaches to computational modeling of rotor using FEM. A predetermined preliminary design of a high-speed massive rotor is investigated. Computational models of different levels at stress-strain analysis and modal analysis are presented. It also includes a suggestion on how to proceed effectively in a given analysis.

This thesis describes and models wirelesss transmission intereferences in real communication channels. A signal received on a fading channel is subjected to a multiplicative distortion and to the usual additive noise. Real channel adds to the signal noise and fadings. Gaussian noise is a result of channel awgn. Fadings is implicated by multipath propagation of signal in Rayleigh and Rician channels. Main goal of this project is to program BERsolve, which is created in tool GUIDE in Matlab. User program BERsolve makes it possible to analyse bit error rate and symbol error rate for some types of channel models, which are defined by standard COST207. BERsolve offers some other functions i.e. display time behaviour, constellation diagram and spectrum. This program provides us with an overview representation of problem by multipath interferences in communication channels.

The subject of this work deals with the problem of channel estimation for CDMA systems. This method of multiple access when individual users share the same full bandwidth simultaneously and are differentiated with any of pseudorandom sequences, is now the most perspective method. That is proved by its wide implementation in mobile networks of the third generation and higher systems. This work describes basic theory principles of spread spectrum, above all DS-CDMA (Direct Sequence-CDMA) and furthermore some phenomena of radio wireless channel that affect changes in transmitted signal in its way from transmitter to receiver. Terms of fading, multipath propagation, loss, refraction, scattering of the wave and Rice and Rayleigh probability density functions are mentioned. The third chapter deals with yet known and used capabilities of channel estimation. Differences, advantages and disadvantages of so-called blind estimation or training-based estimation are discussed. Two algorithms: LS method and sliding correlator are analyzed in more detail. There is also description of their simulations in Matlab and some results of these simulations are discussed. The last chapter deals with comparison of main characteristics and achievable accuracy of wireless channel impulse response estimation by both methods, and their possible utilization in real live.

The diploma thesis Simulation of Multipath Propagation of Multistate Modulations is focused on the development of an appropriate algorithm in MATLAB environment, which is capable to simulate the impact of the multipath propagation on received signal (error rate) on the basis of given parameters of the transmission channels. Mechanisms and characteristics of the wave propagation in communication environment, types of digital modulations and their most important parameters are described in the first part of this thesis. The second part is focused on the simulation itself. Created GUI (Graphical User Interface) is able to display constellation diagrams of transmitted and received signals, as well as their bit error rate. It is also possible to compare these data with the data of signal, which is passed by a non-fading channel.

The objective of this diploma thesis is a dynamic analysis of a cable-stayed walkway. The RFEM structural analysis software is used for the calculation. Design principles of the structure are explained and analysis of the construction phases is then performed. The eigenmodes of the structure are calculated for various material combinations. The thesis examines the effects of moving loads and earthquake effects using several different methods. A comparison of the various loading effects on the structure and also the calculation methods is presented at the conclusion.

In verfahrenstechnischen Anlagen der Flüssig-Flüssig-Stoffübertragung kommt es an der Phasengrenze zwischen den nicht mischbaren Flüssigphasen häufig zur Ausbildung hydrodynamischer Instabilitäten. Sie sind mit komplexen Geschwindigkeitsfeldern in den Flüssigphasen, insbesondere in den grenzschichtnahen Regionen verbunden und führen zu einem starken Anstieg der pro Zeiteinheit übertragenen Stoffmenge. Die Lösung der Diffusionsgleichung reicht in diesem Fall zur Vorausberechnung des für Auslegungszwecke bedeutsamen Stoffdurchgangskoeffizienten nicht mehr aus. Chemische Reaktionen stellen Quellen oder Senken von Wärme und Stoff dar, die das Auftreten von Instabilitäten begünstigen und die mathematische Beschreibung zusätzlich erschweren. Im Rahmen der vorliegenden Arbeit wurden experimentelle und numerische Untersuchungen zum Flüssig-Flüssig-Stoffübergang in einem vertikalen Kapillarspalt durchgeführt. Reaktionsfreie Stoffübergänge und solche mit einer exothermen chemischen Reaktion an der Phasengrenze zeigten eine große Vielfalt von Konvektionsstrukturen, wie Rollzellen, Thermiken und das doppeldiffusive Fingerregime. Die Visualisierung der Transportvorgänge erfolgte durch das Schattenschlierenverfahren. Die Beobachtungen wurden hinsichtlich geometrischer Eigenschaften von Konvektionsstrukturen sowie deren zeitlicher Änderung ausgewertet. Dazu zählten insbesondere das Längenwachstum von Thermiken und horizontale Wellenlängen von Fingerstrukturen. Zur mathematischen Beschreibung der Phänomene im Kapillarspalt wurde ein Modell entwickelt, welches auf den gekoppelten, zweidimensionalen Transportgleichungen von Impuls, Wärme und Stoff beruht. Es berücksichtigt dichte- und grenzflächenspannungsgetriebene Instabilitätsmechanismen sowie die besonderen Durchströmungseigenschaften des Kapillarspalts. Die Phasengrenze wurde als eben angenommen. Die Lösung der Modellgleichungen erfolgt auf numerischem Wege durch ein Computerprogramm. Das Modell ist in der Lage, die beobachteten Instabilitätsphänomene qualitativ richtig wiederzugeben. Mit Hilfe von Simulationsrechnungen konnte der Mechanismus aufgeklärt werden, der zum schnelleren Rückgang des Stoffdurchgangskoeffizienten im Rollzellenregime der rein grenzflächenspannungsgetrieben Instabilität im Vergleich zum Vorgang mit überlagerter Dichtekonvektion führt. Des Weiteren gelang der Nachweis des doppeldiffusiven Fingerregimes beim Stoffübergang mit exothermer Grenzflächenreaktion. Die berechnete Erhöhung des Stoffdurchgangskoeffizienten stimmt mit Angaben in experimentellen Arbeiten anderer Autoren überein.