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This thesis explores a range of stability techniques applied to fluid structures that develop in various constant density flows. In particular, the stability of nonlinear structures which develop in rotating plane Couette flow is analyzed using Floquet theory, which allows the global stability of an important secondary nonlinear structure called a Taylor vortex to be determined. From this the distinct tertiary states which emerge as Taylor vortices break down are characterized and their bifurcation behaviour is studied. Also, non-modal stability analyses are conducted in rotating plane Couette flow and annular Poiseuille-Couette flow. In each case the growth mechanisms and the form of the perturbations responsible for the maximum linear energy amplification are discussed. Finally, the non-modal behaviour of the Papkovitch-Fadle operator is treated and its relevance to spatially developing disturbances in Stokes channel flow is examined. The mechanisms and the rates of convergence of the linear spatial energy amplification are investigated and contrasted with temporal energy amplification.

For over 100 years, researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized Navier-Stokes equations. However, for many simple flows, this approach has failed to match experimental results. Recently, new scenarios for transition have been proposed that are based on the non-normality of the linearized operator. These new "mostly linear" theories have increased our understanding of the transition process, but the role of nonlinearity has not been explored. The main goal of this work is to begin to study the role of nonlinearity in transition. We use model problems to illustrate that small unmodeled disturbances can cause transition through movement or bifurcation of equilibria. We also demonstrate that small wall roughness can lead to transition by causing the linearized system to become unstable. Sensitivity methods are used to obtain important information about the disturbed problem and to illustrate that it is possible to have a precursor to predict transition. Finally, we apply linear feedback control to the model problems to illustrate the power of feedback to delay transition and even relaminarize fully developed chaotic flows. / Ph. D.

La conception des nacelles doit répondre à des contraintes géométriques d’encombrement mais aussi à des spécifications motoristes qui précisent les niveaux de performance exigés. Au sol, l’une des principales contraintes imposées par le motoriste concerne le niveau de distorsion de pression totale dans le plan fan quand la nacelle est soumise à un vent de travers. Dans le cas le plus limitant, c’est-à-dire lorsque la direction du vent est perpendiculaire à l’axe de la nacelle, il se produit un décollement au niveau de l’entrée d’air côté vent. L’hétérogénéité de l’écoulement crée des efforts instationnaires sur les aubes du fan. Ces efforts peuvent amener à un régime de pompage endommageant ainsi le moteur. De plus, la tendance actuelle est de réaliser des nacelles courtes, réduisant la distance qu’à l’écoulement pour s’homogénéiser avant d’impacter le fan, conduisant à un couplage entre le décollement et le fan. Le but de cette étude est de simuler numériquement l’écoulement intervenant dans une nacelle courte soumise à un vent de travers et d’étudier l’impact de la présence du fan. Tout d’abord, la définition de la distorsion est basée sur les grandeurs totales. Ainsi, la compréhension du comportement des grandeurs totales au voisinage d’une paroi et l’influence des paramètres numériques sur leur évolution est nécessaire. Une approche analytique et numérique sur plaque plane a permis d’évaluer le comportement des grandeurs totales à la frontière externe de la couche limite et l’influence des paramètres numériques RANS sur leur évolution. Cette étude a permis de choisir les paramètres numériques utilisés pour la simulation de la nacelle. Pour faire ressortir l’influence du fan sur la distorsion, deux types de simulations ont été menés : une simulation de nacelle isolée et une simulation de l’ensemble complet nacelle/fan respectivement comparées à un essai en soufflerie sur une maquette de nacelle isolée et à un essai de moteur complet à échelle 1 :1 réalisé en « soufflerie » à veine ouverte. La description correcte de la distorsion nécessite de prendre en compte les phénomènes de transition. Une méthode innovante de prise en compte de la transition par équations de transport est utilisée. Comme le coût de calcul de l’ensemble complet est prohibitif, la question du découplage du calcul en injectant une distorsion, issue d’une simulation de nacelle isolée, dans un calcul de fan isolé est discutée. La distorsion par vent de travers intervient lorsque l’avion est au sol. Par conséquent, l’impact de la présence du sol est étudié dans le cas de la nacelle isolée. Enfin, le critère de distorsion utilisé présente plusieurs défauts importants et peut être remis en cause. Une nouvelle méthode de mesure et de calcul estétudiée. / Inlet design must fulfill geometrical constraints and engine requirements. One of these requirementsis the homogeneity of the flow impacting the fan which is quantified by the distortionlevels of stagnation pressure. When the airplane is on the ground and ready to take-off, crosswindconditions are critical for the distorsion level. The most critical case is when the wind directionis normal to the engine axis. Subsonic and supersonic separations occur near the inlet lip. Theso-created heterogeneity produces an unsteady stress on the fan blades which can lead to surge.Furthermore, short inlets are designed nowadays reducing the distance available for the flow tohomogenize before the fan leading to a coupling between the fan and the separated flow region.The aim of this study is to numerically predict the flow in a short inlet under crosswind conditionsand to investigate the fan influence on the distortion. First of all, the distortion definition isbased on stagnation quantities. Therefore, the stagnation quantities behavior and the numericalparameters influence must be investigated. The behavior of the stagnation quantities near theboundary layer edge is studied with analytical and numerical approaches. The numerical parameterschosen for the inlet simulation come from the so-obtained results obtained. In order tohighlight the fan influence on the distortion, two kinds of simulations were proceeded and comparedto experimental results : an isolated inlet simulation and a inlet/fan simulation. To correctlypredict the distortion, transition has to be be taken into account. Therefore an innovative solutionusing transport equations is used. As the computation cost for the inlet/fan computation isprohibitive, the decoupling which consists in injecting on a isolated fan the distortion obtainedduring a isolated inlet computation, is discussed. In fact, crosswind conditions occur when theairplane is on the ground, thus, the ground influence over the inlet distortion is studied for anisolated inlet. Finally, the distortion criterion used in this study has evidenced some strong defectsand can be questioned. Another approach of measurement with another criterion definitionis investigated.

The aerodynamics of modern rotorcraft is highly complex and has proven to be an arduous challenge for computational fluid dynamics (CFD). Flow features such as massively separated boundary layers or transition to turbulence are common in engineering applications and need to be accurately captured in order to predict the vehicle performance. The recent advances in numerical methods and turbulence modeling have resolved each of these issues independent of the other. First, state-of-the-art hybrid RANS-LES turbulence closures have shown great promise in capturing the unsteady flow details and integrated performance quantities for stalled flows. Similarly, the correlation-based transition model of Langtry and Menter has been successfully applied to a wide range of applications involving attached or mildly separated flows. However, there still lacks a unified approach that can tackle massively separated flows in the transitional flow region. In this effort, the two approaches have been combined and expended to yield a methodology capable of accurately predicting the features in these highly complex unsteady turbulent flows at a reasonable computational cost. Comparisons are evaluated on several cases, including a transitional flat plate, circular cylinder in crossflow and NACA 63-415 wing. Cost and accuracy correlations with URANS and prior hybrid URANS-LES approaches with and without transition modeling indicate that this new method can capture both separation and transition more accurately and cost effectively. This new turbulence approach has been applied to the study of wings in the reverse flow regime. The flight envelope of modern helicopters has increased significantly over the last few decades, with design concepts now reaching advance ratios up to μ = 1. In these extreme conditions, the freestream velocity exceeds the rotational speed of the blades, and a large region of the retreating side of the rotor disk experiences reverse flow. For a conventional airfoil with a sharp trailing edge, the reverse flow regime is generally characterized by massive boundary layer separation and bluff body vortex shedding. This complex aerodynamic environment has been utilized to evaluate the new hybrid transitional approach. The assessment has proven the efficiency of the new hybrid model, and it has provided a transformative advancement to the modeling of dynamic stall.

The aerodynamic performance of lifting surfaces operating at low Reynolds number conditions is impaired by laminar separation. Understanding of the physical mechanisms and hydrodynamic instabilities that are associated with laminar separation and the formation of laminar separation bubbles (LSBs) is key for the design and development of effective and efficient active flow control (AFC) devices. For the present work, laminar separation and its control were investigated numerically by employing highly-accurate direct numerical simulations (DNS).For a LSB on a curved plate, the primary and secondary instability of the uncontrolled flow were investigated. An inviscid Kelvin-Helmholtz (KH) instability was found to be responsible for the shedding of predominantly two-dimensional (2D) vortices. The onset of transition was caused by temporally-growing three-dimensional (3D) disturbances inside the separated region, which were supported by elliptical and hyperbolic secondary instabilities. The hyperbolic instability was demonstrated to be of absolute/global nature. High-amplitude forcing using pulsed vortex generator jets and 2D time-periodic blowing was found to exploit the KH instability and lead to a significant reduction in bubble size. In addition, the 2D forcing was found to suppress the secondary instabilities such that transition to turbulence was delayed.The role of free-stream turbulence (FST) in the transition process was investigated for a LSB on a flat plate. FST was shown to cause the formation of streamwise-elongated streaks inside the boundary layer. For the uncontrolled LSB, increasing the FST levels led to accelerated transition and a reduction in bubble size. The stage of linear disturbance growth due to the inviscid KH instability was not ``bypassed''. Flow control by means of 2D periodic excitation was found to remain effective, since it could exploit the KH instability and suppress secondary absolute instabilities. Transition was initiated by an interaction of the 2D wave introduced by the forcing and the streamwise boundary-layer streaks. The interaction led to a spanwise modulation of the 2D wave, which was amplified due to a convective elliptical instability.

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Turbulence is ubiquitous in naturally-occurring and man-made flows. Despite its importance in scientific and engineering applications, the transition from smooth laminar flow to disorganized turbulent flow is poorly understood. In some cases, the transition can be understood in the context of linear stability theory, which predicts when the underlying laminar solution will become unstable as a parameter is varied. For a large class of flows, however, this approach fails spectacularly, with theory predicting that the laminar flow is stable but experiments and simulations showing the emergence of spatiotemporal complexity. In this dissertation, the direct or subcritical transition to turbulence in Taylor-Couette flow (i.e., the flow between independently rotating co-axial cylinders) is studied experimentally. Chapter 1 discusses different scenarios for the transition to turbulence and recent advances in understanding the subcritical transition within the framework of dynamical systems theory. Chapter 2 presents a comprehensive review of earlier investigations of linearly stable Taylor-Couette flow. Chapter 3 presents the first systematic study of long-lived super-transients in Taylor-Couette flow with the aim of determining the correct dynamical model for turbulent dynamics in the transitional regime. Chapter 4 presents the results of experiments regarding the stability of Taylor-Couette flow to finite-amplitude perturbations in the form of injection/suction of fluid from the test section. Chapter 5 presents numerical investigations of axisymmetric laminar states with realistic boundary conditions. Chapter 6 discusses in detail the implementation of time-resolved tomographic particle image velocimetry (PIV) in the Taylor-Couette geometry and presents preliminary tomographic PIV measurements of the growth of turbulent spots from finite-amplitude perturbations. The main results are summarized in Chapter 7.

Karhunen-Lo`{e}ve decomposition is a well established tool, in areas such as signal processing, data compression and low-dimensional modeling. In computational fluid mechanics (CFD) too, KL decomposition can be used to achieve reduced storage requirements, or construction of relatively low-dimensional models. These relatively low-dimensional models, can be used to investigate the dynamics of the flow field in a qualitative manner. Employment of these reduced models is beneficial, as the they can be studied with even stringent computing resources. In addition, these models enable the identification and investigation of interactions between flowlets of different nature (the flow field is decomposed into these flowlets). However, one should not forget that, the reduced models do not necessarily capture the entire dynamics of the original flow, especially in the case of turbulent flows. In the presented study, a KL basis is used to construct reduced models of Navier-Stokes equations in the case of wall-bounded turbulent flow, using Galerkin projection. The resulting nonlinear dynamical systems are then used to investigate the dynamics of transition to turbulence in plane Poiseuille flow in a qualitative fashion. The KL basis used, is extracted from a flow filed obtained from a direct numerical simulation of plane Poiseuille flow.

The majority of this work is concerned with the local-linear convective instability analysis of the incompressible boundary-layer flows over prolate spheroids and oblate spheroids rotating in otherwise still fluid. The laminar boundary layer and the perturbation equations have been formulated by introducing two distinct orthogonal coordinate systems. A cross-sectional eccentricity parameter e is introduced to identify each spheroid within its family. Both systems of equations reduce exactly to those already established for the rotating sphere boundary layer. The effects of viscosity and streamline-curvature are included in each analysis. We predict that for prolate spheroids at low to moderate latitudes, increasing eccentricity has a strong stabilizing effect. However, at high latitudes of ϴ ≥ 60, increasing eccentricity is seen to have a destabilizing effect. For oblate spheroids, increasing eccentricity has a stabilizing effect at all latitudes. Near the pole of both types of spheroids, the critical Reynolds numbers approach that for the rotating disk boundary layer. However, in prolate spheroid case near the pole for very large values of e, the critical Reynolds numbers exceed that for the rotating disk. We show that high curvature near the pole of prolate spheroids is responsible for the increase in critical Reynolds number with increasing eccentricity. For both types of spheroids at moderate eccentricity, we predict that the most amplified modes travel at approximately 76% of the surface speed at all latitudes. This is consistent with the existing studies of boundary-layer flows over the related rotating-disk, -sphere and -cone geometries. However, for large values of eccentricity, the traveling speed of the most amplified modes increases up to approximately 90% of the surface speed of oblate spheroids and up to 100% in the prolate spheroid case.