The initial slow viscous growth of the Tollmein-Schlichting wave in a canonical boundary layer transition is absent in bypass and wake-induced transitions. Although there have been a great deal of studies pertaining to bypass transition in boundary layers, the underlying breakdown mechanism is not clearly understood and it continues to be a subject of interest. Similarly, a wake-induced transition caused by Karman wake in the freestream remains poorly understood. The breakdown in this case is caused by anisotropic disturbances containing large scale unsteadiness in the freestream. Differing view points among workers on the transition process have also added to the complexities. In this thesis, bypass and wake-induced boundary layer transitions studied experimentally towards understanding various flow breakdown features are reported. The measurements were made on a flat plate boundary layer in a low-speed wind tunnel. The particle image velocimetry (PIV) technique was extensively used. Various grids were used to generate nearly isotropic freestream turbulence. A circular cylinder was placed at different heights from the plate leading edge to generate Karman wake in the freestream. Two cylinders of different diameters were used to vary the Reynolds number(based on the cylinder diameter). The PIV measurements being simultaneous over a large spatial domain enabled to assess various spatial transitional flow structures. In the case of bypass transition, the streamwise velocity fluctuation, u, is found to exhibit some organized negative and positive fluctuations that dominate the flow during transition, and confirm the simulation results reported in the literature. These positive and negative u fluctuations are found to be associated with the streak unsteadiness. By conditional sampling of these positive and negative u fluctuations, we find that urms (root-mean-squaredof u)can be expressed as a linear combination of urms,f and urms,b,i.e. urms = a(urms,f + urms,b); ais constant, and the subscripts fand bdenote the positive and nega-tive ufluctuations, respectively. Both urms,f and urms,b arefoundto follow the non-modal growth distribution. The wall-normal results clearly show that an inclined shear layer is often associated with an organized structure of negative ufluctuations and an inflectional in-stantaneous velocity profile. These inclined shear layers appear to be similar to those in ribbon-induced transition. The turbulent spot precursor appears to be the vortex shedding from an oscillating in-clined shear layer. Interestingly, the normalized vortex shedding fre-quency is found to be Reynolds number invariant, as in the case of ribbon-induced transition. The present study also confirms the sim-ulated turbulent spot features, including a thin log-law at the break-down stage. The spanwise plane PIV results reveal the signature of streak secondary instability in the flow in terms of symmetric and anti-symmetric streaks oscillations. The initial growth of streak amplitude is followed by a slow decay. The maximum streak amplitude is well above30% of the freestream velocity. These two aspects provide support to the streak instability analysis reported in the literature. While the present wake-induced transition study provides some sup-port to the available numerical simulation and experimental results, some new results have also emerged. The measured sharp rise in the disturbance energy during transition is found to be closer to the simulated result, compared to the difference reported in the literature. The spanwise vortices in the early stage, as also seen in other experimental studies, deform leading to the formation of lambda structures, the signature of which is found by the linear stochastic analysis. With increased Reynolds number and decreased cylinder height from the plate, the physical size of the lambda structure is found to decrease. These lambda structures are often found to appear in a staggered manner in the spanwise plane, as in the case of sub-harmonic boundary layer transition. Although a sub-harmonic peak in the frequency spectra is reported in the literature, as also in the present study, the clear staggered pattern went unnoticed. Streamwise streaks are subsequently generated due to the mean shear stretching of these lambda vortices. The spanwise spacing of these streamwise streaks is found to be comparable with the recent simulation results. Also, these streaks are found to undergo somewhat sinuous-like oscillations, compared to the only varicose type oscillations reported in the literature. The streak amplitude is found to saturate at about 35% of the freestream speed. Here again an inclined shear layer in the wall-normal plane is associated with organized negative u fluctuations and an inflectional instantaneous velocity profile. The movement of the peak urms towards the wall is found to be due to the positive u fluctuation, which follows a hairpin-like structure. The inclined shear layers herein are associated with the lambda or a hairpin-like structure. As in a by-pass transition, an inclined shear layer, vortex shedding from it, the imprint of which is also found in the linear stochastic analysis are present. The normalized high frequency shed vortices is found to be Reynolds number invariant in the present wake-induced transition, as in ribbon-induced and bypass transitions. Compared to the re-cent suggestion that the parent-offspring mechanism is the governing self-sustaining mechanism in the boundary layer, the present study suggests that streak-instability mechanism is also present. The proper orthogonal decomposition(POD) analysis of the experimental data was carried out with an emphasis on the bypass transition case studied. The first few energetic POD modes are found to capture the dominant flow structures, i.e. the organized positive and negative u fluctuations. In the case of bypass transition, the first two energetic POD modes are self-similar, i.e. independent of the freestream turbulent intensity and the Reynolds number. An attempt is also made to construct a low-dimensional model with the POD eigenfunction modes to predict the qualitative dynamics of bypass transition. This has revealed the existence of a traveling disturbance in the bypass transition. On the whole, the present study shows some similar breakdown features in bypass and wake-induced transitions, although more studies in this regard are essential.

Les méthodes de réduction de modèles offrent un cadre général permettant une réduction de coûts de calculs substantielle pour les simulations numériques. Dans cette thèse, nous proposons d’étendre le domaine d’application de ces méthodes. Le point commun des sujets discutés est la tentative de dépasser le cadre standard «bases réduites» linéaires, qui ne traite que les cas où les variétés solutions ont une petite épaisseur de Kolmogorov. Nous verrons comment tronquer, translater, tourner, étirer, comprimer etc. puis recombiner les solutions, peut parfois permettre de contourner le problème qui se pose lorsque cette épaisseur de Kolmogorov n’est pas petite. Nous évoquerons aussi le besoin de méthodes de stabilisation sur-mesure pour le cadre réduit. / Model reduction methods provide a general framework for substantially reducing computational costs of numerical simulations. In this thesis, we propose to extend the scope of these methods. The common point of the topics discussed here is the attempt to go beyond the standard linear "reduced basis" framework, which only deals with cases where the solution manifold have a small Kolmogorov width. We shall see how truncate, translate, rotate, stretch, compress etc. and then recombine the solutions, can sometimes help to overcome the problem when this Kolmogorov width is not small. We will also discuss the need for tailor-made stabilisation methods for the reduced frame.

Train transportation is a vital part of the transportation system of today anddue to its safe and environmental friendly concept it will be even more impor-tant in the future. The speeds of trains have increased continuously and withhigher speeds the aerodynamic effects become even more important. One aero-dynamic effect that is of vital importance for passengers’ and track workers’safety is slipstream, i.e. the flow that is dragged by the train. Earlier ex-perimental studies have found that for high-speed passenger trains the largestslipstream velocities occur in the wake. Therefore the work in this thesis isdevoted to wake flows. First a test case, a surface-mounted cube, is simulatedto test the analysis methodology that is later applied to a train geometry, theAerodynamic Train Model (ATM). Results on both geometries are comparedwith other studies, which are either numerical or experimental. The comparisonfor the cube between simulated results and other studies is satisfactory, whiledue to a trip wire in the experiment the results for the ATM do not match.The computed flow fields are used to compute the POD and Koopman modes.For the cube this is done in two regions of the flow, one to compare with a priorpublished study Manhart & Wengle (1993) and another covering more of theflow and especially the wake of the cube. For the ATM, a region containing theimportant flow structures is identified in the wake, by looking at instantaneousand fluctuating velocities. To ensure converged POD modes two methods toinvestigate the convergence are proposed, tested and applied. Analysis of themodes enables the identification of the important flow structures. The flowtopologies of the two geometries are very different and the flow structures arealso different, but the same methodology can be applied in both cases. For thesurface-mounted cube, three groups of flow structures are found. First groupis the mean flow and then two kinds of perturbations around the mean flow.The first perturbation is at the edge of the wake, relating to the shear layerbetween the free stream and the disturbed flow. The second perturbation isinside the wake and is the convection of vortices. These groups would then betypical of the separation bubble that exists in the wake of the cube. For theATM the main flow topology consists of two counter rotating vortices. Thiscan be seen in the decomposed modes, which, except for the mean flow, almostonly contain flow structures relating to these vortices. / QC 20100518 / Gröna Tåget

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.

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Reduced-order models are frequently used in the simulation of complex flows to overcome the high computational cost of direct numerical simulations, especially for three-dimensional nonlinear problems. Proper orthogonal decomposition, as one of the most commonly used tools to generate reduced-order models, has been utilized in many engineering and scientific applications. Its original promise of computationally efficient, yet accurate approximation of coherent structures in high Reynolds number turbulent flows, however, still remains to be fulfilled. To balance the low computational cost required by reduced-order modeling and the complexity of the targeted flows, appropriate closure modeling strategies need to be employed. In this dissertation, we put forth two new closure models for the proper orthogonal decomposition reduced-order modeling of structurally dominated turbulent flows: the dynamic subgrid-scale model and the variational multiscale model. These models, which are considered state-of-the-art in large eddy simulation, are carefully derived and numerically investigated. Since modern closure models for turbulent flows generally have non-polynomial nonlinearities, their efficient numerical discretization within a proper orthogonal decomposition framework is challenging. This dissertation proposes a two-level method for an efficient and accurate numerical discretization of general nonlinear proper orthogonal decomposition closure models. This method computes the nonlinear terms of the reduced-order model on a coarse mesh. Compared with a brute force computational approach in which the nonlinear terms are evaluated on the fine mesh at each time step, the two-level method attains the same level of accuracy while dramatically reducing the computational cost. We numerically illustrate these improvements in the two-level method by using it in three settings: the one-dimensional Burgers equation with a small diffusion parameter, a two-dimensional flow past a cylinder at Reynolds number Re = 200, and a three-dimensional flow past a cylinder at Reynolds number Re = 1000. With the help of the two-level algorithm, the new nonlinear proper orthogonal decomposition closure models (i.e., the dynamic subgrid-scale model and the variational multiscale model), together with the mixing length and the Smagorinsky closure models, are tested in the numerical simulation of a three-dimensional turbulent flow past a cylinder at Re = 1000. Five criteria are used to judge the performance of the proper orthogonal decomposition reduced-order models: the kinetic energy spectrum, the mean velocity, the Reynolds stresses, the root mean square values of the velocity fluctuations, and the time evolution of the proper orthogonal decomposition basis coefficients. All the numerical results are benchmarked against a direct numerical simulation. Based on these numerical results, we conclude that the dynamic subgrid-scale and the variational multiscale models are the most accurate. We present a rigorous numerical analysis for the discretization of the new models. As a first step, we derive an error estimate for the time discretization of the Smagorinsky proper orthogonal decomposition reduced-order model for the Burgers equation with a small diffusion parameter. The theoretical analysis is numerically verified by two tests on problems displaying shock-like phenomena. We then present a thorough numerical analysis for the finite element discretization of the variational multiscale proper orthogonal decomposition reduced-order model for convection-dominated convection-diffusion-reaction equations. Numerical tests show the increased numerical accuracy over the standard reduced-order model and illustrate the theoretical convergence rates. We also discuss the use of the new reduced-order models in realistic applications such as airflow simulation in energy efficient building design and control problems as well as numerical simulation of large-scale ocean motions in climate modeling. Several research directions that we plan to pursue in the future are outlined. / Ph. D.