Time varying flow structures are involved in a large percentage of fluid flows although there is still much unknown regarding their behavior. With the development of high spatiotemporal resolution measurement systems it is becoming more feasible to measure these complex flow structures, which in turn will lead to a better understanding of their impact. One method that has been developed for studying these flow structures is finite time Lyapunov exponents (FTLEs). These exponents can reveal regions in the fluid, referred to as Lagragnian coherent structures (LCSs), where fluid elements diverge or attract. Better knowledge of how these time varying structures behave can greatly impact a wide range of applications, from aircraft design and performance, to an improved understanding of mixing and transport in the human body. This work provides the development of new methodologies for measuring and studying three-dimensional time varying structures. Provided herein is a method to improve replacement of erroneous measurements in particle image velocimetry data, which leads to increased accuracy in the data. Also, a method for directly measuring the finite time Lyapunov exponents from particle images is developed, as well as an experimental demonstration in a three-dimensional flow field. This method takes advantage of the information inherently contained in these images to improve accuracy and reduce computational requirements. Lastly, this work provides an in depth look at the flow field for developing wall jets across a wide range of Reynolds numbers investigating the mechanisms that contribute to their development. / Ph. D.

<p dir="ltr">The Boeing-AFOSR Mach-6 Quiet Tunnel (BAM6QT) was used for a set of experiments aiming to characterize the stability regimes of stagnation point injection in noisy and quiet flow across an array of different injected gases. Four gases were used in this experiment: air, helium, carbon dioxide, and argon. These gases were injected at varying thrust coefficients, ranging from 0.0516 to 0.5666, using a 7 degree half-angle cone with a 19 mm radius spherical nose and a single 1.93 mm-radius sonic jet in the center of the model. The primary data collected consists of schlieren images gathered at a sample rate of 76 kHz. These data were then analyzed using a shock tracking software to measure the physical locations of flow features as well as through spectral proper orthogonal decomposition (SPOD) to analyze specific modes in the flow.</p><p dir="ltr">Through this analysis, it was observed that three principle modes exist in stagnation point injection regardless of the injecting gas: a high frequency vortex-coupled mode, a low frequency Mach-shock-rigid mode, and a hybrid mode residing between these two modes. The first two modes were observed in all stability regimes, whereas the hybrid mode was only observed in the bifurcated regime. Furthermore, the unsteady regime was observed to be mostly characterized by this first, vortex-coupled mode. Conversely, the steady regime was observed to be driven by the Mach-shock-rigid mode instead. This transition was measured to occur as the thrust coefficient was increased.</p><p dir="ltr">This research also found that freestream noise resulted in an amplified and widened frequency range within the Mach-shock-rigid mode. This same freestream noise did not appear to have an impact on the other two principle modes; however, in some cases the noise produced in the Mach-shock-rigid mode due to this freestream noise did in fact mask the other principle modes.</p><p dir="ltr">Lastly, it was observed that the thrust coefficient, in and of itself, is not the sole indicator of stability in stagnation point injection. Across the different injected gases in this research, transition between the stability regimes did not in fact occur at a constant thrust coefficient value. Additionally, even within the same injected gas, this transition did not occur at the same thrust coefficient value between noisy and quiet runs—indicating an effect of freestream noise on stability.</p>

With the maturity of conventional industrial robots, there has been increasing interest in designing robots that emulate realistic animal motions. This discipline requires careful and systematic investigation of a wide range of animal motions from biped, to quadruped, and even to serpentine motion of centipedes, millipedes, and snakes. Collecting optical motion capture data of such complex animal motions can be complicated for several reasons. Often there is the need to use many high-quality cameras for detailed subject tracking, and self-occlusion, loss of focus, and contrast variations challenge any imaging experiment. The problem of self-occlusion is especially pronounced for animals. In this thesis, we walk through the process of collecting motion capture data of a running lizard. In our collected raw video footage, it is difficult to make temporal correspondences using interpolation methods because of prolonged blurriness, occlusion, or the limited field of vision of our cameras. To work around this, we first make a model data set by making our best guess of the points' locations through these corruptions. Then, we randomly eclipse the data, use Gappy POD to repair the data and then see how closely it resembles the initial set, culminating in a test case where we simulate the actual corruptions we see in the raw video footage. / Master of Science

This thesis presents the implementation and validation of a new methodology developed by Glegg et al. (2004) for solving the trailing edge noise problem. This method is based on the premises that the noise produced by a surface can be computed by the integral of the cross product between the velocity and vorticity fields, of the boundary layer and shed vorticity (Howe (1978)). To extract the source terms, proper orthogonal decomposition is applied to the velocity cross spectrum to extract modes of the unsteady velocity and vorticity. The new formulation of the trailing edge noise problem by Glegg et al. (2004) is attractive because it applies to the high frequencies of interest but does not require an excessive computational effort. Also, the nature of the formulation permits the identification of the modes producing the noise and their associated velocity fluctuations as well as the regions of the boundary layer responsible for the noise production. The source terms were obtained using the direct numerical simulation of a turbulent channel flow by Moser et al. (1998). Two-point velocity and vorticity statistics of this data set were obtained by averaging 41 instantaneous fields. For comparisons purposes, experimental boundary layer data by Adrian et al. (2000) was chosen. Statistical reduction of 50 velocity fields obtained by particle image velocimetry was performed and analysis of the two-point correlation function showed features similar to the DNS data case. Also, proper orthogonal decomposition revealed identical dominant modes and eddy structures in the flow, therefore justifying considering the channel flow as an external boundary layer for noise calculations. Comparison of noise predictions with experimental data from Brooks et al. (1989) showed realistic results with the largest discrepancies, on the order of 5 dB, occurring at the lowest frequencies. The DNS results are least applicable at these frequencies, since these correspond to the longest streamwise lengthscales, which are the most affected by the periodicity conditions used in the DNS and also are the least representative of the turbulence in an external boundary layer flow. Most of the noise was shown to be produced by low-frequency streamwise velocity modes in the bottom 10% of the boundary layer and locations closest to the wall. Only 6 modes were required to obtain noise levels within 1 dB of the total noise. Finally, the method for predicting spatial velocity correlation from Reynolds stress data in wake flows, originally developed by Devenport et al. (1999, 2001) and Devenport and Glegg (2001), was adapted to boundary-layer type flows. This method, using Reynolds stresses and the prescription of a lengthscale to extrapolate the full two-point correlation, was shown to produce best results for a lengthscale prescribed as proportional to the turbulent macroscale. Noise predictions using modeled two-point statistics showed good agreement with the DNS inferred data in all but frequency magnitude, a probable consequence of the modeling of the correlation function in the streamwise direction. Other quantities associated to noise were seen to be similar to the ones obtained using the DNS. / Master of Science

The aim of this work was to understand the physical requirements as well as to develop methodology required to employ Time Resolved Digital Particle Image Velocimetry (TRDPIV) for measuring high speed, high magnification, near wall flow fields. Previous attempts to perform measurements such as this have been unsuccessful because of both limitations in equipment as well as proper methodology for processing of the data. This work addresses those issues and successfully demonstrates a test inside of a transonic turbine cascade as well as a high speed high magnification wall jet. From previous studies it was established that flow tracer delivery is not a trivial task in a high speed high back pressure environment. Any TRDPIV measurement requires uniform spatial seeding density, but time-resolved measurements require uniform temporal seeding density as well. To this end, a high pressure particle generator was developed. This advancement enhanced current capability beyond what was previously attainable. Unfortunately, this was not sufficient to resolve the issue of seeding all together, and an advanced data reconstruction methodology was developed to reconstruct areas of the flow field that where lost do to inhomogeneous seeding. This reconstruction methodology, based on Proper Orthogonal Decomposition (POD), has been shown to produce errors in corrected velocities below tradition spatial techniques alone. The combination of both particle generator and reconstruction methodology was instrumental for successfully acquiring TRDPIV measurements in a high speed high pressure environment such as a transonic wind tunnel facility. This work also investigates the development of a turbulent wall jet. This experiment helped in demonstrating the capability of taking high speed high magnification TRDPIV measurements. This experiment was very unique in that it is one of only a few experiments that studied the developing region of these jets. The Reynolds number ranged for this experiment from 150 – 10,000 which corresponded to velocities of 1 - 80 m/s. The results from this experiment showed good agreement with currently published time averaged data. Using scaling laws for fully developed jets a new scaling law was found for the developing region of the jet that could be applied to all Reynolds numbers in this study. A temporal investigation was also carried out using the temporal coefficients from POD. A vortex identification scheme was also applied to all of the Reynolds numbers showing clear trends as Reynolds number increased. / Master of Science

This thesis uses Proper Orthogonal Decomposition to model parametric and coupled systems. First, Proper Orthogonal Decomposition and its properties are introduced as well as how to numerically compute the decomposition. Next, a test case was used to show how well POD can be used to simulate and control a system. Finally, techniques for modeling a parametric system over a given range and a coupled system split into subdomains were explored, as well as numerical results. / Master of Science

The thesis deals with the flow in pipe bends and radial turbines geometries that are commonly found in an Internal Combustion Engine (ICE). The development phase of internal combustion engines relies more and more on simulations as an important complement to experiments. This is partly because of the reduction in development cost and the shortening of the development time. This is one of the reasons for the need of more accurate and predictive simulations. By using more complex computational methods the accuracy and predictive capabilities are increased. The disadvantage of using more sophisticated tools is that the computational time is increasing, making such tools less attractive for standard design purposes. Hence, one of the goals of the work has been to contribute to assess and improve the predictive capability of the simpler methods used by the industry. By comparing results from experiments, Reynolds Averaged Navier-Stokes (RANS) computations, and Large Eddy Simulations (LES) the accuracy of the different computational methods can be established. The advantages of using LES over RANS for the flows under consideration stems from the unsteadiness of the flow in the engine manifold. When such unsteadiness overlaps the natural turbulence the model lacks a rational foundation. The thesis considers the effect of the cyclic flow on the chosen numerical models. The LES calculations have proven to be able to predict the mean field and the fluctuations very well when compared to the experimental data. Also the effects of pulsatile exhaust flow on the performance of the turbine of a turbocharging system is assessed. Both steady and pulsating inlet conditions are considered for the turbine case, where the latter is a more realistic representation of the real flow situation inside the exhaust manifold and turbine. The results have been analysed using different methods: single point Fast Fourier Transforms (FFT), probe line means and statistics, area and volume based Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD). / Denna avhandling behandlar flödet i rörkrökar och radiella turbiner som vanligtvis återfinns i en förbränningsmotor. Utvecklingsfasen av förbränningsmotorer bygger mer och mer på att simuleringar är ett viktigt komplement till experiment. Detta beror delvis på minskade utvecklingskostnader men även på kortare utevklningstider. Detta är en av anledningarna till att man behöver mer exakta och prediktiva simuleringsmetoder. Genom att använda mer komplexa beräkningsmetoder så kan både nogrannheten och prediktiviteten öka. Nackdelen med att använda mer sofistikerade metoder är att beräkningstiden ökar, vilket medför att sådana verktyg är mindre attraktiva för standardiserade design ändamål. Härav, ett av målen med projektet har varit att bidra med att bedöma och förbättra de enklare metodernas prediktionsförmåga som används utav industrin. Genom att jämföra resultat från experiment, Reynolds Averaged Navier-Stokes (RANS) och Large Eddy Simulations (LES) så kan nogrannheten hos de olika simuleringsmetoderna fastställas. Fördelarna med att använda LES istället för RANS när det gäller de undersökta flödena kommer ifrån det instationära flödet i grenröret. När denna instationäritet överlappar den naturligt förekommande turbulensen så saknar modellen en rationell grund. Denna avhandling behandlar effekten av de cykliska flöderna på de valda numeriska modellerna. LES beräkningarna har bevisats kunna förutsäga medelfältet och fluktuationerna väldigt väl när man jämför med experimentell data. Effekterna som den pulserande avgasströmning har på turboladdarens turbin prestanda har också kunnat fastställas. Både konstant och pulserande inlopps randvillkor har används för turbinfallet, där det senare är ett mer realistiskt representation av den riktiga strömningsbilden innuti avgasgrenröret och turbinen. Resultaten har analyserats på flera olika sätt: snabba Fourier transformer (FFT) i enskilda punkter, medelvärden och statistik på problinjer, area och volumsbaserade metoder så som Proper Orthogonal Decomposition (POD) samt Dynamic Mode Decomposition (DMD). / <p>QC 20140919</p>

Dans cette thèse nous étudions différents problèmes de graphes et multigraphes arêtes-coloriés tels que la connexité propre, la coloration forte d'arêtes et les chaînes et cycles hamiltoniens propres. Enfin, nous améliorons l'algorithme connu $O(n^4)$ pour décider du comportement d'un graphe sous opérateur biclique, en étudiant les bicliques dans les graphes sans faux jumeaux. Plus précisément, 1) Nous étudions d'abord le nombre $k$-connexité-propre des graphes, noté $pc_k(G)$, ç'est à dire le nombre minimum de couleurs nécessaires pour colorer les arêtes d'un graphe de façon à ce qu'entre chaque paire de sommets, ils existent $k$ chemins intérieurement sommet-disjoints. Nous prouvons plusieurs bornes supérieures pour $pc_k(G)$. Nous énonçons quelques conjectures pour les graphes généraux et bipartis et nous les prouvons dans le cas où $k = 1$. 2) Nous étudions l'existence de chaînes et de cycles hamiltoniens propres dans les multigraphes arêtes-coloriés. Nous établissons des conditions suffisantes, en fonction de plusieurs paramètres tels que le nombre d'arêtes, le degré arc-en-ciel, la connexité, etc. 3) Nous montrons que l'indice chromatique fort est linéaire au degré maximum pour tout graphe $k$-dégénéré où, $k$ est fixe. En corollaire, notre résultat conduit à une amélioration des constantes et donne également un algorithme plus simple et plus efficace pour cette famille de graphes. De plus, nous considérons les graphes planaires extérieurs. Nous donnons une formule pour trouver l'indice chromatique fort exact pour les graphes bipartis planaires extérieurs. Nous améliorons également la borne supérieure pour les graphes planaires extérieurs généraux. 4) Enfin, nous étudions les bicliques dans les graphes sans faux jumeaux et nous présentons ensuite un algorithme $O(n+m)$ pour reconnaître les graphes convergents et divergents en améliorant l'algorithme $O(n^4)$. / In this thesis, we study different problems in edge-colored graphs and edge-colored multigraphs, such as proper connection, strong edge colorings, and proper hamiltonian paths and cycles. Finally, we improve the known $O(n^4)$ algorithm to decide the behavior of a graph under the biclique operator, by studying bicliques in graphs withoutfalse-twin vertices. In particular: 1) We first study the $k$-proper-connection number of graphs, this is, the minimum number of colors needed to color the edges of a graph such that between any pair of vertices there exist $k$ internally vertex-disjoint paths. We denote this number $pc_k(G)$. We prove several upper bounds for $pc_k(G)$. We state some conjectures for general and bipartite graphs, and we prove all of them for the case $k=1$. 2) Then, we study the existence of proper hamiltonian paths and proper hamiltonian cycles in edge-colored multigraphs. We establish sufficient conditions, depending on several parameters such as the number of edges, the rainbow degree, the connectivity, etc. 3) Later, we showthat the strong chromatic index is linear in the maximum degree for any $k$-degenerate graph where $k$ is fixed. As a corollary, our result leads to considerable improvement of the constants and also gives an easier and more efficient algorithm for this familly of graphs. Next, we consider outerplanar graphs. We give a formula to find exact strong chromatic index for bipartite outerplanar graphs. We also improve the upper bound for general outerplanar graphs from the $3\Delta-3$ bound. 4) Finally, we study bicliques in graphs without false-twin vertices and then we present an $O(n+m)$ algorithm to recognize convergent and divergent graphs improving the $O(n^4)$ known algorithm.

La résolution des problèmes de contrôle optimal nécessite des temps de calcul et des capacités de stockage très élevés. Pour s’affranchir de ces contraintes, il est possible d’utiliser les méthodes de réduction de modèles comme la POD (Proper Orthogonal Decomposition). L’inconvénient de cette approche est que la base POD n’est valable que pour des paramètres situés dans un voisinage proche des paramètres pour lesquels elle a été construite. Par conséquent, en contrôle optimal, cette base peut ne pas être représentative de tous les paramètres qui seront proposés par l’algorithme de contrôle. Pour s’affranchir de cet handicap, une méthodologie de contrôle optimal utilisant des modèles réduits adaptatifs a été proposée dans ce manuscrit. Les bases réduites adaptées sont obtenues à l’aide de la méthode d’interpolation ITSGM (Interpolation on Tangent Subspace of Grassman Manifold) ou de la méthode d’enrichissement PGD (Proper Generalized Decomposition). La robustesse de cette approche en termes de précision et de temps de calcul a été démontrée pour le contrôle optimal (basé sur les équations adjointes) des équations 2D de réaction-diffusion et de Burgers. L’approche basée sur l’interpolation ITSGM a également été appliquée avec succès pour contrôler l’écoulement autour d’un cylindre 2D. Deux méthodes de réduction non intrusives, ne nécessitant pas la connaissance des équations du modèle étudié, ont également été proposées. Ces méthodes appelées NIMR (Non Intrusive Model Reduction) et HNIMR (Hyper Non Intrusive Model Reduction) ont été couplées à un algorithme génétique pour résoudre rapidement un problème de contrôle optimal. Le problème du contrôle optimal de l’écoulement autour d’un cylindre 2D a été étudié et les résultats ont montré l’efficacité de cette approche. En effet, l’algorithme génétique couplé avec la méthode HNIMR a permis d’obtenir les solutions avec une bonne précision en moins de 40 secondes. / The numerical resolution of adjoint based optimal control problems requires high computational time and storage capacities. In order to get over these high requirement, it is possible to use model reduction techniques such as POD (Proper Orthogonal Decomposition). The disadvantage of this approach is that the POD basis is valid only for parameters located in a small neighborhood to the parameters for which it was built. Therefore, this basis may not be representative for all parameters in the optimizer’s path eventually suggested by the optimal control loop. To overcome this issue, a reduced optimal control methodology using adaptive reduced order models obtained by the ITSGM (Interpolation on a Tangent Subspace of the Grassman Manifold) method or by the PGD (Proper Generalized Decomposition) method, has been proposed in this work. The robustness of this approach in terms of precision and computation time has been demonstrated for the optimal control (based on adjoint equations) of the 2D reaction-diffusion and Burgers equations. The interpolation method ITSGM has also been validated in the control of flow around a 2D cylinder. In the context of non intrusive model reduction, two non intrusive reduction methods, which do not require knowledge of the equations of the studied model, have also been proposed. These methods called NIMR (Non-Intrusive Model Reduction) and HNIMR (Hyper Non-Intrusive Model Reduction) were developed and then coupled to a genetic algorithm in order to solve an optimal control problem in quasi-real time. The problem of optimal control of the flow around a 2D cylinder has been studied and the results have shown the effectiveness of this approach. Indeed, the genetic algorithm coupled with the HNIMR method allowed to obtain the solutions with a good accuracy in less than 40 seconds.

Lietuvių kalboje vartojama nemaža skolinių, vadinamųjų tarptautinių žodžių. Bendrinė tarptautinė leksika – tai viena svetimos leksikos dalis. Visgi egzistuoja ir dar viena, ne mažiau svarbi ir aktuali tarptautinės leksikos dalis – kitų šalių (tarptautiniai) tikriniai žodžiai. Šiai leksikos daliai tirti ir skirtas šis magistro darbas. Darbo tema – kitų šalių tikrinių žodžių kirčiavimas „Visuotinės lietuvių enciklopedijos“ I tome (VLE I). Šio leksikos klodo kirčiavimo tyrimai gana skurdūs, lyginant su savos kilmės tikrinių žodžių grupėmis, todėl taisyklingam kirčiavimui būtinų žinotinų bendrųjų dėsningumų išskyrimas pravartus ir tikslingas. Apskritai ši leksikos dalis Lietuvoje nedaug tirta, taigi darbo tema šiuo atveju pasirinkta neatsitiktinai, yra gana aktuali. Tirti „Visuotinės lietuvių enciklopedijos“ I tomo (VLE I) pavyzdžiai. Šio darbo tyrimo objektas – kitų šalių tikriniai žodžiai – tam tikri nelietuviškos kilmės asmenvardžiai ir vietovardžiai (asmenvardžių dalis gerokai – kone du kartus – didesnė). Žodžių „Kita“, į kurią įeitų kiti nelietuviški tikriniai žodžiai, atsisakyta, kadangi tokių pavadinimų dažniausiai pateikiamos tik originalo kalbos formos, o darbe, remiantis lietuvių kalbos kirčiavimo sistemos dėsningumais, nagrinėjamos tik adaptuotos formos. Pagrindinis magistro darbo tikslas – nustatyti kirčiavimo paradigmas, ištìrti ir pateikti kitų šalių tikrinių žodžių kirčiavimo dėsningumus „Visuotinės lietuvių enciklopedijos“ I tome. Siekiama ne tik akcentuoti... [toliau žr. visą tekstą] / Lithuanian language has many adopted words, they are called international words. Common international lexis – is one part of the foreign lexis. Also there is alike important part of international lexis – the proper words of foreign language. This paper of master degree is all about the proper words of foreign language. The goal of that essay is to research the proper words of foreign languages in the “Universal Lithuanian encyclopaedia” volume I (ULE I). That line of accentuation analysis is quit barren comparing to the groups of the native proper words. Therefore the exclusion of the consistency of the correct accentuation is useful and has its meaning and purpose. Mostly that part of lexis is very little researched in Lithuania. Accordingly to that fact has risen the purpose of writing the paper on such subject. Here were researched the examples of the “Universal Lithuanian encyclopaedia” volume I (ULE I). The subject of that research was the proper words of foreign language – some particular personal names and place-names (personal names were researched almost twice bigger part comparing to the place-names). Such words as „Other“, witch would include other foreign proper words were declined because the names of such words usually has the form of original language. In that work which is supported on the consistency of the accentuation in Lithuania language, was researched only adopted form of words. The main task of this paper of master degree is to set paradigms of the... [to full text]