No presente trabalho foi implementado um modelo matemático para simular o sistema antigelo eletrotérmico de um aerofólio. Por meio do programa ONERA2D simulou-se o escoamento potencial completo com velocidade 44,7 m/s (100 mph) e 89,4 m/s (200 mph) em torno de um aerofólio perfil NACA0012 de corda 0,914 m (3 pés) com ângulo de ataque de 0°, e calculou-se a eficiência de coleta local de gotículas de água com diâmetro mediano volumétrico de 20 μm. Foram simuladas quatro condições de teste com diferentes distribuições de fluxo de calor nos aquecedores elétricos do sistema antigelo. O modelo previu a distribuição de temperaturas na superfície sólida do aerofólio e no filme de água líquida, e as distribuições de fluxo de água líquida sobre a superfície do aerofólio (\"runback water\") e de coeficiente de transferência de calor por convecção de calor entre a superfície do aerofólio e o escoamento gasoso. Os resultados da simulação obtidos com o modelo foram comparados com resultados experimentais da NASA e os resultados numéricos dos programas LEWICE/ANTICE (EUA) e CANICE (Canada). Para as regiões molhadas pelo filme de água líquida, obteve-se um desvio máximo de temperatura de 2,6°C entre os resultados do presente modelo e o resultados experimentais. Para as regiões secas, onde não existe o filme de água líquida sobre a superfície do aerofólio, obteve-se um desvio de máximo de temperatura de 8°C. As previsões para distribuição de vazão de \"runback\", posição do término do filme de água líquida foram comparadas com os resultados do programa LEWICE/ANTICE. O modelo desenvolvido simula com adequada aproximação os efeitos da transferência de calor e de massa por convecção entre a superfície não-isotérmica do aerofólio ou do filme de água líquida e o escoamento gasoso, bem como os efeitos da transição entre o escoamento laminar e o turbulento na camada limite dinâmica e térmica e ainda a influência do escoamento do filme de água líquida sobre o desempenho do sistema de antigelo do aerofólio. / An electro-thermal anti-ice system was simulated with a mathematical model developed in the present work. A 44.7 m/s (100 mph) and 89.4 m/s (200 mph) full potential flow around a 0.914 m (3 ft) chord NACA0012 airfoil with 0° angle of attack and the local water catch efficiency of 20 μm median volumetric diameter droplets impingement were calculated by the numerical code ONERA2D. Four test conditions were simulated with four different heat flux distributions of the anti-ice system according to the experimental work developed at NASA. The model predicted distributions of solid surface and liquid water film temperatures, runback water flow and convection heat transfer coefficient between airfoil or water surface and gaseous flow. The simulated results obtained by the mathematical model developed were compared to NASA experimental results and the ones predicted by the numerical codes LEWICE/ANTICE (US) and CANICE (Canada). For the regions wetted by the water film, the present model provided 2.6°C maximum temperature deviations between the predicted results and experimental data. For the dry regions, where there is no liquid water on the airfoil surface, an 8°C maximum temperature deviation was obtained. The runback flow and water film ending point position were compared to LEWICE/ANTICE numerical results. The developed model predicts adequately the convection heat and mass transfer effects between the non-isothermal airfoil or liquid water film surface and the gaseous flow, as well the effects of laminar to turbulent flow transition within dynamic and thermal boundary layer and the influence of the liquid water film flow on the anti-ice system performance.

Le travail de thèse présenté dans ce manuscrit propose une analyse expérimentale du dé-veloppement spatio-temporel d’une zone de mélange (air/hélium) initiée par instabilité deRichtmyer-Meshkov (IRM). Cette étude s’appuie sur la mise en oeuvre d’un tube à chocspositionné verticalement et sur le développement d’un nouveau protocole expérimental associéà un système innovant de génération de l’interface initiale entre les deux espèces gazeuses enprésence. Ce système est basé sur un dispositif d’obturation/ouverture composé d’un rideau rigiderétractable et d’une série volets mobiles. La caractérisation de l’interface initiale et de l’évolutionspatio-temporelle de la zone de mélange ainsi obtenue est effectuée en exploitant les résultats dedifférentes techniques de mesures telles que la visualisation strioscopique (Schlieren) résolue entemps, la tomoscopie plan laser (TPL) et la Vélocimétrie par Imagerie de Particules (PIV). Enpremier lieu, différentes campagnes de mesures visant à caractériser l’interface initiale ont permisde quantifier la répétabilité du système et de démontrer ses capacités à générer une interfacepériodique faiblement diffuse. Dans un second temps, une étude du mélange gazeux obtenu pourun jeu de paramètres expérimentaux donné, est proposée. L’analyse s’intéresse en particulieraux mécanismes d’initiation et de transition a la turbulence de la zone de mélange produite parl’IRM. L’interaction entre cette zone de mélange en cours de développement et le choc réfléchisur l’extrémité supérieure du tube (phénomène de rechoc) est également étudiée dans l’optique deconfirmer la transition turbulente de la zone de mélange. / This work proposes an experimental analysis of the spatio-temporal development of an air/heliummixing zone promoted by the Richtmyer-Meshkov instability (RMI). This study relies on the useof a vertical shock tube and on the development of a new experimental protocol associated with aninnovative device for the generation of an initial interface between two gazeous species. This deviceconsists a rigid retractable curtain and of a series of rotating shutters. The characterization ofthis initial interface and the spatio-temporal evolution of the RMI-induced mixing zone is carriedout by exploiting the results of various experimental methods such as time resolved Schlierenvisualizations, planar laser mie scattering and Particle Image Velocimetry (PIV). In a first step,various measurement campaigns have made it possible to quantify the repeatability of the newdevice and to demonstrate its ability to generate a periodic, weakly diffused interface. In a secondstep, a study of the gaseous mixing for a given set of experimental parameters is proposed. Theanalysis focuses on the understanding of the underlying mechanisms driving the gaseous interfaceformation and the transition to turbulence of the RMI-induced mixing. The interaction betweenthis mixing zone and the reflected shock from the upper end of the tube (re-shock phenomenon)is also studied in order to confirm the turbulent transition of the mixing zone.

In this thesis direct numerical simulations are used to investigate two phenomenain shear flows: laminar-turbulent transition over a flat plate and periodicvortex shedding induced by a jet in cross flow. The emphasis is on understanding and controlling the flow dynamics using tools from dynamical systems and control theory. In particular, the global behavior of complex flows is describedand low-dimensional models suitable for control design are developed; this isdone by decomposing the flow into global modes determined from spectral analysisof various linear operators associated with the Navier–Stokes equations.Two distinct self-sustained global oscillations, associated with the sheddingof vortices, are identified from direct numerical simulations of the jet incrossflow. The investigation is split into a linear stability analysis of the steadyflow and a nonlinear analysis of the unsteady flow. The eigenmodes of theNavier–Stokes equations, linearized about an unstable steady solution revealthe presence of elliptic, Kelvin-Helmholtz and von K´arm´an type instabilities.The unsteady nonlinear dynamics is decomposed into a sequence of Koopmanmodes, determined from the spectral analysis of the Koopman operator. Thesemodes represent spatial structures with periodic behavior in time. A shearlayermode and a wall mode are identified, corresponding to high-frequency andlow-frequency self-sustained oscillations in the jet in crossflow, respectively.The knowledge of global modes is also useful for transition control, wherethe objective is to reduce the growth of small-amplitude disturbances to delaythe transition to turbulence. Using a particular basis of global modes, knownas balanced modes, low-dimensional models that capture the behavior betweenactuator and sensor signals in a flat-plate boundary layer are constructed andused to design optimal feedback controllers. It is shown that by using controltheory in combination with sensing/actuation in small, localized, regionsnear the rigid wall, the energy of disturbances may be reduced by an order of magnitude.

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

Shear layer development over a NACA 0018 airfoil at a chord Reynolds number of 100,000 was investigated experimentally. The effects of experimental setup and analysis tools on the results were also examined. The sensitivity of linear stability predictions for measured separated shear layer velocity profiles to both the analysis approach and experimental data scatter was evaluated. Analysis approaches that are relatively insensitive to experimental data scatter were identified. Stability predictions were shown to be more sensitive to the analysis approach than to experimental data scatter, with differences in the predicted maximum disturbance growth rate and corresponding frequency of approximately 35% between approaches. A parametric study on the effects of experimental setup on low Reynolds number airfoil experiments was completed. It was found that measured lift forces and vortex shedding frequencies were affected by the end plate configuration. It was concluded that the ratio of end plate spacing to projected model height should be at least seven, consistent with the guideline for circular cylinders. Measurements before and after test section wall streamlining revealed errors in lift coefficients due to blockage as high as 9% and errors in the wake vortex shedding frequency of 3.5%. Shear layer development over the model was investigated in detail. Flow visualization images linked an observed asymmetry in wake velocity profiles to pronounced vortex roll-up below the wake centerline. Linear stability predictions based on the mean hot-wire profiles were found to agree with measured disturbance growth rates, wave numbers, and streamwise velocity fluctuation profiles. Embedded surface pressure sensors were shown to provide reasonable estimates of disturbance growth rate, wave number, and convection speed for conditions at which a separation bubble formed on the airfoil surface. Convection speeds of between 30 and 50% of the edge velocity were measured, consistent with phase speed estimates from linear stability theory.

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.

Shear layer development over a NACA 0018 airfoil at a chord Reynolds number of 100,000 was investigated experimentally. The effects of experimental setup and analysis tools on the results were also examined. The sensitivity of linear stability predictions for measured separated shear layer velocity profiles to both the analysis approach and experimental data scatter was evaluated. Analysis approaches that are relatively insensitive to experimental data scatter were identified. Stability predictions were shown to be more sensitive to the analysis approach than to experimental data scatter, with differences in the predicted maximum disturbance growth rate and corresponding frequency of approximately 35% between approaches. A parametric study on the effects of experimental setup on low Reynolds number airfoil experiments was completed. It was found that measured lift forces and vortex shedding frequencies were affected by the end plate configuration. It was concluded that the ratio of end plate spacing to projected model height should be at least seven, consistent with the guideline for circular cylinders. Measurements before and after test section wall streamlining revealed errors in lift coefficients due to blockage as high as 9% and errors in the wake vortex shedding frequency of 3.5%. Shear layer development over the model was investigated in detail. Flow visualization images linked an observed asymmetry in wake velocity profiles to pronounced vortex roll-up below the wake centerline. Linear stability predictions based on the mean hot-wire profiles were found to agree with measured disturbance growth rates, wave numbers, and streamwise velocity fluctuation profiles. Embedded surface pressure sensors were shown to provide reasonable estimates of disturbance growth rate, wave number, and convection speed for conditions at which a separation bubble formed on the airfoil surface. Convection speeds of between 30 and 50% of the edge velocity were measured, consistent with phase speed estimates from linear stability theory.