Direct numerical simulations of the receptivity and instability of boundary layers on flat and curved surfaces are herein reported. Various flow models are considered with the aim to capture aspects of flows over straight and swept wings such as wall curvature, pressure variations, leading-edge effects, streamline curvature and crossflow. The first model problem presented, the flow over a swept flat plate, features a crossflow inside the boundary layer. The layer is unstable to steady and traveling crossflow vortices which are nearly aligned with the free stream. Wall roughness and free-stream vortical modes efficiently excite these crossflow modes, and the associated receptivity mechanisms are linear in an environment of low-amplitude perturbations. Receptivity coefficients for roughness elements with various length scales and for free-stream vortical modes with different wavenumbers and frequencies are reported. Key to the receptivity to free-stream vorticity is the upstream excitation of streamwise streaks evolving into crossflow modes. This mechanism is also active in the presence of free-stream turbulence. The second flow model is that of a Görtler boundary layer. This flow type forms on surfaces with concave curvature, e.g. the lower side of a turbine blade. The dominant instability, driven by a vertically varying centrifugal force, appears as pairs of steady, streamwise counter-rotating vortical rolls and streamwise streaks. The Görtler boundary layer is in particular receptive to free-stream vortical modes with zero and low frequencies. The associated mechanism builds on the excitation of upstream disturbance streaks from which the Görtler modes emerge, similar to the mechanism in swept-plate flows. The receptivity to free-stream vorticity can both be linear and nonlinear. In the presence of free-stream turbulence, nonlinear receptivity is more likely to trigger steady Görtler vortices than linear receptivity unless the frequencies of the free-stream fluctuations are very low. The third set of simulations considers the boundary layer on a flat plate with an elliptic leading edge. This study aims to identify the effect of the leading edge on the boundary-layer receptivity to impinging free-stream vortical modes. Three types of modes with streamwise, vertical and spanwise vorticity are considered. The two former types trigger streamwise disturbance streaks while the latter type excites Tollmien-Schlichting wave packets in the shear layer. Simulations with two leading edges of different bluntness demonstrate that the leading-edge shape hardly influences the receptivity to streamwise vortices, whereas it significantly enhances the receptivity to vertical and spanwise vortices. It is shown that the receptivity mechanism to vertical free-stream vorticity involves vortex stretching and tilting - physical processes which are clearly enhanced by blunt leading edges. The last flow configuration studied models an infinite wing at 45 degrees sweep. This model is the least idealized with respect to applications in aerospace engineering. The set-up mimics the wind-tunnel experiments carried out by Saric and coworkers at the Arizona State University in the 1990s. The numerical method is verified by simulating the excitation of steady crossflow vortices through micron-sized roughness as realized in the experiments. Moreover, the receptivity to free-stream vortical disturbances is investigated and it is shown that the boundary layer is most receptive, if the free-stream modes are closely aligned with the most unstable crossflow mode / QC 20101025

The laminar-turbulent transition in viscous fluid flows is one of the most intriguing problems in fluid dynamics today. In view of the enormous applications it has in a variety of fields such as aircraft design, turbomachinery, etc., scientists have now realized the importance of tackling this problem effectively. Three-dimensional flows are usually associated with pressure gradient, streamline curvature, streamline convergence / divergence etc., all acting simultaneously. Towards a better understanding of the transition process and modeling the transition zone, it is important to study the effect of each of these parameters on the transitional flow. The present work aims at studying experimentally the effect of lateral streamline convergence alone on the laminar-turbulent transition zone under constant stream-wise pressure. The experimental setup consists of a low turbulence wind tunnel with its test section modified to cause lateral streamline convergence under constant pressure. This is achieved by converging the side-walls and appropriately diverging the roof, thus maintaining a constant stream-wise pressure. The half angle of convergence is chosen as 100 , which is approximately the same as the half of the turbulent spot envelope in constant pressure two-dimensional flows. Experiments are carried out to analyze the development of the laminar and transitional boundary layers, intermittency distribution in the transition zone and the overall characteristics of an artificially induced turbulent spot. The laminar velocity profiles are found to be of the Blasius type for two-dimensional constant pressure flows. However, the converging streamlines are found to contribute to an increased thickness of the boundary layer as compared to the corresponding two-dimensional flow. The intermittency distribution in the transition zone is found to follow the universal intermittency distribution for two-dimensional constant pressure flow. A simple linear-combination model for two-dimensional flows is found to perform very well in predicting the measured velocity profiles in the transition zone. An artificially introduced turbulent spot is found to propagate along a conical envelope with an apex cone angle of 220 which is very nearly the value for a corresponding constant pressure two-dimensional flow. The spot shapes and celerities are also comparable to those in two-dimensional flow. In summary, the present study brings out many similarities between a constant pressure laterally converging flow and a constant pressure two-dimensional flow.

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No description available.

Diese numerische Arbeit untersucht, wie sich die laminar-turbulente Transition in der Grenzschicht einer ebenen Platte mit elektromagnetischen Kräften verzögern lässt. Erzeugt von einer Elektroden-Magnet-Anordnung in der Platte wirken jene Kräfte im wandnahen Bereich der Strömung. Sie sind wandparallel sowie stromab gerichtet und besitzen zwei Parameter, die Amplitude und die Eindringtiefe. Zwei- und dreidimensionale Direkte Numerische Simulationen, Grenzschichtgleichungslöser sowie lineare Stabilitätsanalyse werden eingesetzt, um zwei Ansätze der Transitionsverzögerung zu verfolgen: Zum einen die aktive Wellenauslöschung, bei der ankommende Grenzschichtinstabilitäten von gegenphasig angeregten Wellen bis zu 97% ausgelöscht werden. Zum anderen können elektromagnetische Kräfte die Grenzschicht beschleunigen und so zu deutlich stabilieren Grenzschichtprofilen führen. Über evolutionäre Optimierung wurde eine räumliche Verteilung von Eindringtiefe und Kraftamplitude gefunden, die den Energieeinsatz minimiert und gleichzeitig laminare Strömung sicherstellt; dennoch bliebt die energetische Effizienz der Beeinflussung unter Eins. / This numerical work investigates how electromagnetic forces may delay laminar-turbulent transition of a flat plate boundary layer. Generated by an array of electrodes and magnets flush mounted in the wall, those forces act within the wall-near flow. They are oriented in wall-parallel, downstream direction and are characterized by two parameters, namely amplitude and penetration depth. Two- and three-dimensional Direct Numerical Simulations, numerical solutions of boundary layer equations and linear stability analysis are applied to study two possible ways of transition delay: first, the so-called active wave cancellation, where an anti-wave cancels incoming boundary layer instabilities by up to 97%. A second option is have electromagnetic forces accelerate the boundary layer, thereby modifying its mean velocity profile for greatly enhanced stability. Using evolutionary optimization, a spatial distribution of force amplitude and penetration depth was obtained that maintains laminar flow while minimizing electrical power consumption of the actuator. However, the energetic efficiency of actuation remains less than unity.

The transition from a laminar to a turbulent flow strongly modifies the boundary layer properties.Understanding the mechanisms leading to transition is crucial to reliably predict aerodynamicperformances. For boundary layers subjected to high levels of external disturbances, the naturaltransition due to the amplification of the least stable mode is replaced by an early transition, calledBypass transition. This is the result of non-normal mode interactions that lead to a phenomenon oftransient growth of disturbances. These disturbances are known as Klebanoff modes and take theform of streamwise velocity streaks.This thesis aims at understanding this linear mechanism of transient growth and quantifying itsinfluence on the classical modal amplification of disturbances. This is done by computing theso-called optimal perturbations, i.e. the initial disturbances that undergo maximum amplificationin the boundary layer.These optimal perturbations are first determined for two-dimensional compressible boundary layersdeveloping over curved surfaces. In particular, we show that Klebanoff modes naturally evolvetowards Görtler vortices that occur over concave walls. Three-dimensional boundary layers arethen considered. In such configurations, transient growth provides an initial amplitude to crossflowvortices. Finally, applying the tools developed in this thesis to new flow cases such as swept wingsprovides further understanding of the phenomenon of transient growth for realistic geometries. / Le passage du régime laminaire au régime turbulent s’accompagne d’importantes modifications despropriétés physiques de la couche limite. La détermination précise de la transition est donc crucialedans de nombreux cas pratiques. Lorsque la couche limite se développe dans un environnementextérieur faiblement perturbé, la transition est gouvernée par l’amplification du mode propre le moinsstable. Lorsque l’intensité des perturbations extérieures augmente, des interactions multimodalesentraînent une amplification transitoire des perturbations. Ce phénomène peut conduire à unetransition prématurée, appelée transition Bypass. Les perturbations prennent alors la forme destries longitudinales de vitesse appelées modes de Klebanoff.L’objectif de cette thèse est d’étudier ce mécanisme linéaire de croissance transitoire et soninfluence sur l’amplification modale classique des perturbations. Cela passe par la déterminationdes perturbations les plus amplifiées au sein de la couche limite, appelées perturbations optimales.Ces perturbations optimales sont d’abord calculées pour des couches limites bidimensionnelles etcompressibles se développant sur des surfaces courbes. En particulier, on montre que les modes deKlebanoff évoluent vers les tourbillons de Görtler qui se forment sur des parois concaves. Le cas plusgénéral de couches limites tridimensionnelles est ensuite envisagé. Pour de telles configurations, lacroissance transitoire fournit une amplitude initiale aux instabilités transversales. Enfin, l’applicationdes outils développés dans cette thèse fournit de nouveaux résultats pour des cas d’écoulementsautour de géométries réalistes comme une aile en flèche.

Em diversos escoamentos sobre superfícies há a presença de protuberâncias, como por exemplo rebites, parafusos e juntas. Estas protuberâncias podem influenciar a camada limite, acelerando a transição do escoamento do estado laminar para o estado turbulento. Em alguns casos isto pode ser indesejável, já que o escoamento turbulento implica necessariamente em uma força de atrito maior do que aquela referente ao escoamento laminar. Existem alguns aspectos neste tipo de escoamento que ainda não estão bem compreendidos. O objetivo deste trabalho é estudar a influência de uma rugosidade isolada no escoamento sobre uma superfície. Este estudo contribui para se entender o que ocorre em casos de maior complexidade. O estudo é de natureza computacional, em que se utiliza simulação numérica direta das equações de Navier-Stokes. A técnica de fronteiras imersas é utilizada para representar a rugosidade no escoamento sobre a superfície. O código numérico é verificado por meio do método de soluções manufaturadas. Comparações entre resultados experimentais, da teoria de estabilidade linear e numéricos também são utilizados para a validação do código. Resultados obtidos com diferentes alturas de rugosidade e variações no gradiente de pressão permitiram analisar a influência de elemento rugoso tridimensional em escoamentos de camada limite. / The presence of protuberances on surfaces, for example, rivets, screws and gaskets, can influence the boundary layer by accelerating the transition from laminar flow to turbulent flow. In some cases this may be undesirable, since the turbulent flow involves frictional forces greater than the ones at the laminar regime. There are some aspects of the flow in the boundary layer perturbed by a single roughness element that are not well understood. The aim of this work is to study the influence of an isolated roughness on the boundary layer. This study is a step towards to the understanding of what can happen in more complex cases. The nature of this study is computational, therefore a Direct Numerical Simulation code is used. The immersed boundary method is used to represent the roughness in the flow on the surface. The numerical code is verified via theMethod ofManufactured Solutions. Comparisons between experimental data, Linear Stability Theory and numerical results are also used for the validation of the code. Results obtained with different roughness heights and variations in the pressure gradient allowed the analysis of the influence of a three-dimensional roughness element in boundary layer flows.

Há a necessidade de prevenir formação de gelo nas asas e nos estabilizadores de aeronaves, pois as formas de gelo podem causar a degradação do desempenho aerodinâmico, o aumento de peso, bem como dificuldades de controle e manobra que, em casos críticos, leva a uma diminuição da margem de segurança operacional. Quando as aeronaves atravessam nuvens com gotículas de água sub-resfriadas, ou seja, em equilíbrio metaestável, o crescimento de gelo ocorre nas superfícies não protegidas. Usualmente, os sistemas antigelo térmicos de aerofólios são projetados, desenvolvidos e certificados com o auxílio de programas de simulação numérica. O presente trabalho visa desenvolver e implementar um modelo matemático para prever a transferência de calor e massa no escoamento bidimensional bifásico em torno de aerofólios de uso aeronáuticos, equipados com sistema de antigelo térmico operando em regime permanente. Em condições de formação de gelo, é necessário aquecer o bordo de ataque e controlar a temperatura da região protegida para que não ocorra formação de gelo. O sistema de aquecimento compensa os efeitos do resfriamento imposto principalmente pelos mecanismos acoplados de evaporação e transferência de calor por convecção, que são causados pelo escoamento do ar carregado de gotículas sub-resfriadas e pelo escoamento da água líquida residual. O modelo deverá estimar a distribuição de temperaturas de superfície e o coeficiente de transferência de calor com precisão ao uso em aplicações aeronáuticas. O presente trabalho implementou novos submodelos para: 1) estimar a molhabilidade da superfície do aerofólio por meio de um modelo matemático para caracterizar o escoamento da água líquida residual na padrão de filme e de filetes; 2) avaliar o comportamento dinâmico e térmico da camada-limite laminar e turbulenta por meio de análises integral e diferencial, que considera efeitos do gradiente de pressão, da transição laminar-turbulenta, da transpiração e da não uniformidade de temperatura da superfície e 3) estimar o início e o término da região de transição laminar-turbulenta. O presente trabalho seguiu um processo de desenvolvimento de código numérico que: verificou os resultados de cada submodelo separadamente para depois implementados no modelo do antigelo; validou os resultados da simulação de desempenho do sistema antigelo com os novos submodelos implementados. Os resultados obtidos foram considerados satisfatórios para o modelo do antigelo que utilizou os submodelos de ruptura de filme e formação de filetes pelo critério da Energia Mecânica Total Mínima, de camada-limite diferencial compressível e de previsão da transição laminar-turbulenta por correlações algébricas, que consideraram efeitos do gradiente de pressão e do nível de turbulência ao longe. / It is required to prevent ice accretion on wings and horizontal stabilizers because it may cause aerodynamic performance degradation, weight increase, flight control difficulties and, in critical cases, may lead to operational safety margins reduction. When aircraft flies through clouds containnig supercooled water droplets, which are in metastable equilibrium, ice will form in all non-protected surfaces. Usually, anti-ice protection systems are designed, developed and certified with a support from a numerical tool. The present describes the development and implementation of a mathematical model for prediction of heat and mass transfer in two-phase flow around airfoils, which are equipped with thermal anti-ice system and operating in steady state regime. Under icing conditions, it is necessary to heat and control the temperature of the airfoil surface at leading edge region to prevent ice formation. The heating system balances the evaporative cooling effects, which are caused by the coupled heat and mass convection transfer, imposed by the air flow loaded with supercooled water droplets and the runback water flow around the airfoil. The present work implemented submodels to: 1) estimate airfoil surface wetness factor by adopting a liquid water film flow model as well as a rivulet formation and flow model; 2) evaluate laminar and turbulent boundary layers with pressure gradient and laminar-turbulent transition over nonisothermal and permeable airfoil surface by implementing differential boundary layer analysis and 3) predict the onset position and length of laminar-turbulent transition region. The present paper followed a validation and verification process during the numerical code development. All sub-models results were verified separately against experimental data before their inclusion in anti-ice model.The results of anti-ice model with selected submodels were validated against reference cases. The results were considered suficiently accurate when solving the film breakdown and rivulets formation by total mechanical energy method, compressible boundary layer by differential analysis and laminar-turbulent transition prediction by algebraic correlations, which considered pressure gradient and freestream turbulence level.

Ce travail s’inscrit dans le cadre de la prévision des oscillations de pression interne des moteurs à propergol solide. Il consiste à étudier la transition laminaire-turbulent de l’écoulement interne,modélisé par celui dans un conduit cylindrique à paroi débitante, et son lien avec l’instabilité naturelle de cet écoulement, le Vortex Shedding Pariétal (VSP). La démarche s’est organisée en trois temps. Des mesures antérieures sur un montage gaz froid, reproduisant l’écoulement modèle,sont analysées afin de mettre en évidence la transition laminaire-turbulent. Cette transition est ensuite imposée dans des simulations URANS afin de permettre l’étude de son influence sur les modes VSP. Enfin, une approche LES est mise en place pour simuler le développement de la transition dans les conditions de l’expérience ; dans ce but, une stratégie de perturbation spatiale de l’écoulement est utilisée. Cette étude met en avant quatre résultats principaux. La transition laminaire-turbulent découle de l’amplification spatiale des modes VSP. La simulation de ce processus met en évidence une forte influence de la perturbation numérique ajoutée à l’écoulement. D’autre part, les simulations URANS montrent que la transition réduit l’amplification des modes VSP et les oscillations de pression interne résultantes. Le rôle de la transition dans l’absence d’oscillations de pression lorsque le domaine a un grand rapport d’aspect, jusqu’alors supposé dans la littérature,est ainsi confirmé. Une particularité importante de cette transition est qu’elle dépend de la position radiale, l’écoulement étant turbulent près de la paroi débitante et laminaire au cœur. / The present work is related to the prediction of oscillations in solid rocket motors inner flow. It consists in a study of the laminar-turbulent transition of the motor’s inner flow, which is represented by a cylindrical injection-driven flow, and the relation between this phenomenon and the natural instability named Parietal Vortex Shedding (PVS). Three aspects have been analyzed.First of all, previous cold-gas experiments – reproducing the injection driven flow – are analyzed in order to highlight the transition laminar-turbulent transition. This transition is then imposedin URANS simulations to enable a study of its influence on the PVS modes. Finally, Large Eddy Simulations are performed to simulate the laminar-turbulent process. A strategy based on spatial steady disturbances is used to ease this process. The mains conclusions of this work are the following ones. The laminar-turbulent transition is a consequence of the spatial amplification of PVS modes. Simulations of this process highlight a strong influence of the injected numerical disturbances. The URANS simulations show that this transition reduces the amplification of PVSmodes, and the resulting pressure oscillations levels. These results confirm the role of the transitionin the absence of pressure oscillations when the motor cavity is long. A distinctive feature ofthis transition is its dependence on the radial position, which leads to the coexistence of a laminar region in the channel core and a turbulent region near the injecting wall at a given axial position.

Diese numerische Arbeit untersucht, wie sich die laminar-turbulente Transition in der Grenzschicht einer ebenen Platte mit elektromagnetischen Kräften verzögern lässt. Erzeugt von einer Elektroden-Magnet-Anordnung in der Platte wirken jene Kräfte im wandnahen Bereich der Strömung. Sie sind wandparallel sowie stromab gerichtet und besitzen zwei Parameter, die Amplitude und die Eindringtiefe. Zwei- und dreidimensionale Direkte Numerische Simulationen, Grenzschichtgleichungslöser sowie lineare Stabilitätsanalyse werden eingesetzt, um zwei Ansätze der Transitionsverzögerung zu verfolgen: Zum einen die aktive Wellenauslöschung, bei der ankommende Grenzschichtinstabilitäten von gegenphasig angeregten Wellen bis zu 97% ausgelöscht werden. Zum anderen können elektromagnetische Kräfte die Grenzschicht beschleunigen und so zu deutlich stabilieren Grenzschichtprofilen führen. Über evolutionäre Optimierung wurde eine räumliche Verteilung von Eindringtiefe und Kraftamplitude gefunden, die den Energieeinsatz minimiert und gleichzeitig laminare Strömung sicherstellt; dennoch bliebt die energetische Effizienz der Beeinflussung unter Eins. / This numerical work investigates how electromagnetic forces may delay laminar-turbulent transition of a flat plate boundary layer. Generated by an array of electrodes and magnets flush mounted in the wall, those forces act within the wall-near flow. They are oriented in wall-parallel, downstream direction and are characterized by two parameters, namely amplitude and penetration depth. Two- and three-dimensional Direct Numerical Simulations, numerical solutions of boundary layer equations and linear stability analysis are applied to study two possible ways of transition delay: first, the so-called active wave cancellation, where an anti-wave cancels incoming boundary layer instabilities by up to 97%. A second option is have electromagnetic forces accelerate the boundary layer, thereby modifying its mean velocity profile for greatly enhanced stability. Using evolutionary optimization, a spatial distribution of force amplitude and penetration depth was obtained that maintains laminar flow while minimizing electrical power consumption of the actuator. However, the energetic efficiency of actuation remains less than unity.