Dissertations / Theses on the topic 'Tollmien-Schlichting wave'

This thesis is concerned with the effect that boundary layer instabilities have on laminar-turbulent transition over an aircraft wing. The receptivity analysis of the two-dimensional marginal separation flow with respect to suction/blowing is considered. The solution of the linearised perturbation equation is sought in the form of perturbations that are periodic in time. Numerical results are obtained and it is observed that for large enough frequencies Tollmien-Schlicting wave packets begin to form downstream of a source of perturbations. A receptivity analysis of an incompressible steady two-dimensional marginally separated laminar boundary layer with respect to three-dimensional unsteady perturbations is then considered. An asymptotic theory of this flow is constructed on the basis of an analysis of the Navier-Stokes equations at large Reynolds numbers by means of matched asymptotic expansions. Two particular cases are considered, one in which we assume that the solution is periodic in both time $T$ and the spanwise coordinate $Z$, and the second where the solution is periodic in time only. As a result an integro-differential equation is derived and studied numerically by means of a spectral method. The next mathematical formulation is the study of marginal separation theory for a swept wing. In this formulation, an additional equation for the spanwise velocity component $w$ is needed. Upon solving the triple-deck equations, an algebraic Fourier transform equation is obtained and solved numerically. Finally, the last chapter concerns itself with a numerical global stability of the two-dimensional unsteady marginal separation equation.

Als Teilprojekt des Themenkreises III "Transitionskontrolle" des Schwerpunkt-Forschungsprogramms "Transition" der Deutschen Forschungsgemeinschaft, konzentriert sich diese Arbeit auf experimentelle Grundlagenuntersuchungen zum laminar-turbulenten Grenzsichtumschlag. Die Experimente wurden in der Grenzschicht einer ebenen, parallel angeblasenen, hydraulisch glatten Platte durchgeführt. Einen besonderen Schwerpunkt bildet die Abhängigkeit der Entwicklung der Instabilitäten, der sogenannten Tollmien-Schlichting Wellen, von deren Schräglaufwinkel zur Plattenvorderkante. Weiterhin wird der Einfluss zahlreicher Parameter wie z.B. des Schalldruckpegels und der Anregungsfrequenz diskutiert. Die Anregung der Tollmien-Schlichting Wellen erfolgte über periodisches Ausblasen / Ansaugen von Luft durch oberflächenbündige Schlitze quer zur Strömungsrichtung. Mit einem zeitlich hochauflösenden, restlichverstärkendem Kamerasystem konnten Aufnahmen der Strömungsvisualisierung erzielt werden, die unter anderem die zeitliche Entwicklung von Wirbelstrukturen (Lambda- Wirbel) zeigen. Zur Analyse der experimentell gewonnen Daten werden vergleichend Berechnungen nach der "Linearen Stabilitätstheorie" diskutiert. Einen weiteren Schwerpunkt bilden Untersuchungen zur aktiven Transitionskontrolle. Dabei wird der künstlich angeregten Tollmien Schlichting Welle eine gegenphasige Störwelle stromab überlagert. Es konnte nachgewiesen werden, das mit diesem Verfahren entsprechend des Superpositionsprinzips, die anfängliche Störamplitude der Tollmien Schlichting Welle deutlich reduziert wird. Es kommt zu einer fast vollständigen Störauslöschung. Untersuchungen im Nahfeld der Störeinkopplung, sowohl im Bereich der Anregnung als auch der gegenphasigen Dämpfungseinkopplung, zeigen deren Auswirkung auf die Entwicklung der Grenzschicht
A sub-project of the working group III, "Transition Control" of the German Research Community's project "Transition", this paper is focused on experimental fundamental investigations in the field of laminar-turbulent transition. The experiments were carried out in the boundary layer of a flat plat with tangential blowing. The main topic is the development of instabilities, or so-called Tollmien-Schlichting Waves (TSWs), based on the oblique angle between the TSWs and the leading edge. In addition the influence of other parameters, including the sound-pressure level and the frequency of the TSWs are discussed. The instabilities are initialised by suction and blowing through flush, oblique slots in the surface of a flat plate. Pictures of the flow visualisation, recorded with a high-speed camera system, show the time-resolved development of structures (Lamda-Vortices) within the boundary layer. In order to analyse the experimental data, a comparison is made between it and numerical calculations corresponding to the Linear Instability Theory. Another main topic is the investigation of the active transition control. According to the Super Position Principle a second wave with opposite phase is superimposed on the TSW. It can be demonstrated that this technique works with oblique waves too. The initialised instabilities can almost completely be cancelled out. Investigations very close to the initialising slots of the TSW with a high special resolution show their influence on the development of the boundary layer

Als Teilprojekt des Themenkreises III "Transitionskontrolle" des Schwerpunkt-Forschungsprogramms "Transition" der Deutschen Forschungsgemeinschaft, konzentriert sich diese Arbeit auf experimentelle Grundlagenuntersuchungen zum laminar-turbulenten Grenzsichtumschlag. Die Experimente wurden in der Grenzschicht einer ebenen, parallel angeblasenen, hydraulisch glatten Platte durchgeführt. Einen besonderen Schwerpunkt bildet die Abhängigkeit der Entwicklung der Instabilitäten, der sogenannten Tollmien-Schlichting Wellen, von deren Schräglaufwinkel zur Plattenvorderkante. Weiterhin wird der Einfluss zahlreicher Parameter wie z.B. des Schalldruckpegels und der Anregungsfrequenz diskutiert. Die Anregung der Tollmien-Schlichting Wellen erfolgte über periodisches Ausblasen / Ansaugen von Luft durch oberflächenbündige Schlitze quer zur Strömungsrichtung. Mit einem zeitlich hochauflösenden, restlichverstärkendem Kamerasystem konnten Aufnahmen der Strömungsvisualisierung erzielt werden, die unter anderem die zeitliche Entwicklung von Wirbelstrukturen (Lambda- Wirbel) zeigen. Zur Analyse der experimentell gewonnen Daten werden vergleichend Berechnungen nach der "Linearen Stabilitätstheorie" diskutiert. Einen weiteren Schwerpunkt bilden Untersuchungen zur aktiven Transitionskontrolle. Dabei wird der künstlich angeregten Tollmien Schlichting Welle eine gegenphasige Störwelle stromab überlagert. Es konnte nachgewiesen werden, das mit diesem Verfahren entsprechend des Superpositionsprinzips, die anfängliche Störamplitude der Tollmien Schlichting Welle deutlich reduziert wird. Es kommt zu einer fast vollständigen Störauslöschung. Untersuchungen im Nahfeld der Störeinkopplung, sowohl im Bereich der Anregnung als auch der gegenphasigen Dämpfungseinkopplung, zeigen deren Auswirkung auf die Entwicklung der Grenzschicht.
A sub-project of the working group III, "Transition Control" of the German Research Community's project "Transition", this paper is focused on experimental fundamental investigations in the field of laminar-turbulent transition. The experiments were carried out in the boundary layer of a flat plat with tangential blowing. The main topic is the development of instabilities, or so-called Tollmien-Schlichting Waves (TSWs), based on the oblique angle between the TSWs and the leading edge. In addition the influence of other parameters, including the sound-pressure level and the frequency of the TSWs are discussed. The instabilities are initialised by suction and blowing through flush, oblique slots in the surface of a flat plate. Pictures of the flow visualisation, recorded with a high-speed camera system, show the time-resolved development of structures (Lamda-Vortices) within the boundary layer. In order to analyse the experimental data, a comparison is made between it and numerical calculations corresponding to the Linear Instability Theory. Another main topic is the investigation of the active transition control. According to the Super Position Principle a second wave with opposite phase is superimposed on the TSW. It can be demonstrated that this technique works with oblique waves too. The initialised instabilities can almost completely be cancelled out. Investigations very close to the initialising slots of the TSW with a high special resolution show their influence on the development of the boundary layer.

Both experimental and theoretical studies have beenconsidered on flat plate boundary layers as well as on wakesbehind porous cylinders. The main thread in this work iscontrol, which is applied passively and actively on boundarylayers in order to inhibit or postpone transition toturbulence; and actively through the cylinder surface in orderto effect the wakecharacteristics. An experimental set-up for the generation of the asymptoticsuction boundary layer (ASBL) has been constructed. This studyis the first, ever, that report a boundary layer flow ofconstant boundary layer thickness over a distance of 2 metres.Experimental measurements in the evolution region, from theBlasius boundary layer (BBL) to the ASBL, as well as in theASBL are in excellent agreement with boundary layer analysis.The stability of the ASBL has experimentally been tested, bothto Tollmien-Schlichting waves as well as to free streamturbulence (FST), for relatively low Reynolds numbers (Re). For the former disturbances good agreement is foundfor the streamwise amplitude profiles and the phase velocitywhen compared with linear spatial stability theory. However,the energy decay factor predicted by theory is slightlyoverestimated compared to the experimental findings. The latterdisturbances are known to engender streamwise elongated regionsof high and low speeds of fluid, denoted streaks, in a BBL.This type of spanwise structures have been shown to appear inthe ASBL as well, with the same spanwise wavelength as in theBBL, despite the fact that the boundary layer thickness issubstantially reduced in the ASBL case. The spanwise wavenumberof the optimal perturbation in the ASBL has been calculated andis β = 0.53, when normalized with the displacementthickness. The spanwise scale of the streaks decreases withincreasing turbulence intensity (Tu) and approaches the scale given by optimalperturbation theory. This has been shown for the BBL case aswell. The initial energy growth of FST induced disturbances hasexperimentally been found to grow linearly as Tu2Rexin the BBL, the transitional Reynolds numberto vary as Tu-2, and the intermittency function to have a relativelywell-defined distribution, valid for all Tu. The wake behind a porous cylinder subject to continuoussuction or blowing has been studied, where amongst other thingsthe Strouhal number (St) has been shown to increase strongly with suction,namely, up to 50% for a suction rate of 2.5% of the free streamvelocity. In contrast, blowing shows a decrease ofStof around 25% for a blowing rate of 5% of the freestream velocity in the considered Reynolds number range. Keywords:Laminar-turbulent transition, asymptoticsuction boundary layer, free stream turbulence,Tollmien-Schlichting wave, stability, flow control, cylinderwake.
QC 20100607

The adaptation of Tollmien-Schlichting waves as they propagate over the leading and trailing edges of finite-length compliant panels is investigated by means of numerical simulation. The behaviour so determined is pertinent to the application of compliant walls for transition delay. We consider a model problem where the compliant panels form a section in the walls bounding a plane channel fluid flow. The results obtained are encouraging. They indicate that compliant panels with lengths comparable to the Tollmien-Schlichting wavelength can have a significant stabilising effect. In some instances, the passage of a Tollmien-Schlichting wave over the edges of a compliant panel leads to the excitation of stable flow-induced surface waves. The presence of such additional waves does not appear to be associated with any adverse effect upon the stability of the Tollmien-Schlichting wave. The numerical scheme used for the simulations derives from a mixed finite-difference/spectral discretisation of the linearised two-dimensional Navier-Stokes equations, which were taken in a vorticity-velocity formulation. Numerical stability problems were overcome by treating the inertia of the compliant wall and the fluid together when imposing the boundary conditions. This allowed the interactively coupled fluid and the wall motion to be computed without any prior restriction on the form taken by the disturbances. An investigation was also carried out into the linear stability of plane channel flow bounded by compliant walls throughout. In the case of the Tollmien-Schlichting mode this relied, for the most part, on the determination of numerical solutions to the Orr-Sommerfeld equation. Flow-induced surface waves could be studied more readily using an approximate analytic theory. Good agreement was achieved between the predictions of the analytic theory and numerical results obtained directly from the Orr-Sommerfeld equation, particularly for travelling wave flutter. The linear stability results for the wholly compliant-walled channel were used to analyse the behaviour displayed by Tollmien-Schlichting waves in the numerical simulations that were conducted with finite-length compliant panels.

Two-dimensional (2D) roughnesses induce premature transition to turbulence in laminar boundary layers by amplifying the disturbances in the flow and promoting the development of non-linearities. The present thesis aims at furthering our understanding of this phenomenon's underlying mechanisms and elucidating the effects of the different geometrical parameters of the roughness' cross section. Semi-circular and semi-elliptical 2D roughnesses were placed in turns on a flat plate in a low-subsonic, low-disturbance laminar flow and transition was detected by means of cumputing the hot-wire velocity signal's intermittency. It is shown that increasing the roughness element's aspect ratio delays the onset of transition. On the other hand, enlargning the roughness' size does not necessarily result in the promotion of transition: the data suggests that the most destabilizing size depends on the free-steam velocity and the disturbance environment. Single-frequency Tollmien-Schilchting (TS) waves were then forced into the boundary layer by means of the periodic suction and blowing produced by a loudspeaker's membrane. The critical amplitude of the TS waves impining of the roughness at sub-critical free-steam velocities was determined and a series of velocity profiles were measured and then phase-averaged. Different growth rates are observed for different roughtnesses and the amplitude at which TS wave breakdown occurs increases with increasing aspect ratio and diminishes with growing roughness height.
Tvådimensionella (2D) ytråheter i gränsskikt ger i regel ett tidigare omslag från laminär till turbulent strömning genom att de förstärker tillväxten av hastighetsstörningar och främjar utvecklingen av icke-linjäriteter. Denna uppsats syftar till att öka vår förståelse av detta fenomens underliggande mekanismer och belysa effekterna av de olika geometriska parametrarna som beskriver ytråhetens tvärsnitt. Halvcirkulära och semi-elliptiska 2D-ytråheter placerades i tur och ordning på en plan platta i ett lågsubsoniskt laminärt flöde med mycket små bakgrundsstörningar. Omslaget bestämdes genom att beräkna intermittensen av tidssignalen från en varmtrådssensor. En slutsats är att omslaged fördröjs vid ökat tvärsnittsförhållande under konstant höjd. Samtidigt resulterar en ökad höjd av ytråheten inte alltid en tidigareanläggning av omslaget, mätresultaten tyder även på att de mest destabiliserande parametrarna är friströmshastigheten och dess bakgrundsstörning. Linjära periodiska störningar, så kallade Tollmien-Schlichting (TS) vågor, genererades sedes mera för specifika frekvenser i gränsskiktet genom att alternativt applicera sugning och blåsning genom ett tvärsnitsspår i plattan med hjälp av ett högtalarmembran. Den kritiska amplituden av TS vågor som anströmmar ytråheten vid en subkritisk friströmshastighet bestämdes och en serie av tidsupplösta hastighetsprofiler mättes tätt i strömmningsriktningen som sedan kunde fasmedelvärdesbildas. Olika tillväxthastigheter av TS vågorna observerades för olika ytråheter och amplituden vid vilken TS vågen bryts ner och skapar turbulens ökar vid ett ökat tvärsnittsförhållande (för konstant höjd) och minskar vid en ökad ytråhetshöjd.

Pour depasser le cadre de la theorie locale de la triple deck de stewartson et williams, on etablit une formulation en triple couche et en double echelle longitudinale jusqu'au second ordre des developpements asymptotiques. Celle-ci exige une utilisation precise de la regle du raccord asymptotique dont on donne l'expression appropriee. L'utilisation de developpements non reguliers, tenant compte de l'epaississement de la couche limite, s'avere particulierement bien adaptee aux ecoulements sur une plaque presentant une serie d'indentations. En effet, cette nouvelle approche montre que l'on peut traiter simultanement les problemes du premier et second ordre, dans chaque couche, par la resolution d'un probleme unique. Elle met egalement en evidence l'existence d'une nouvelle longueur caracteristique des indentations qui contribue a une meilleure interpretation du phenomene de deplacement de la couche limite. Dans une premiere partie, on etudie la reduction de la trainee laminaire en fonction des parametres geometriques des indentations ainsi que des variations locales du nombre de reynolds. Dans la seconde, on examine la stabilite lineaire et faiblement non lineaire des ecoulements generes par les perturbateurs. Dans le cadre de la theorie de la stabilite lineaire parallele, conduisant a l'equation d'orr - sommerfeld, on caracterise analytiquement et numeriquement l'apparition d'ondes de tollmien - schlichting ainsi que l'influence de la geometrie des indentations sur l'amplification de ces ondes. Des lors, une configuration geometrique optimisee des perturbateurs est construite pour simultanement reduire la trainee laminaire et reculer l'abscisse du debut de la transition. Enfin, a l'aide d'un code pse (parabolized stability equations) de l'onera-cert, on exprime les variations qualitatives des resultats de la stabilite lineaire lorsque l'on tient compte des effets faiblement non lineaires.

The thesis essentially consists of two parts. In the first part we consider the evolution of weakly non-linear, modulated disturbances in marginally unstable systems, and address the question of when the Ginzburg-Landau equation is relevant in describing such systems. In the second, we consider secondary instabilities of Tollmien-Schlichting waves in High Reynolds-Number boundary layer and channel flows. In §1.1 we give a brief background and review previous work in the study of modulated disturbances in marginally unstable parallel flows. In §1.2 we briefly outline the approach of Stewartson and Stewart in proposing that the Ginzburg-Landau equation describes the evolution of line disturbances and of Davey et al in proposing that the Davey-Stewartson equations describe the evolution of point disturbances, and propose that a small logarithmic change to the scaling is needed to account for the first effects of weak non-linearity. In §1.3 we give the modifications necessary for a line disturbance and find the resulting amplitude equations for Plane Poiseuille Flow. We show that in the subcritical case the solution terminates in a finite time singularity. In §1.4 and §1.5 we extend the analysis to point disturbances, and again show that a finite-time singularity is encountered for a subcritical system. In §1.6 we extend this analysis to obtain amplitude equations for three dimensional Poiseuille Couette flow, which we rescale to reduce to (essentially) the equations for two dimensional PPF. The implications of this revised analysis are described in §1.7. In §2.1, we give a brief summary and review previous work studying secondary instability of Tollmien-Schlichting waves in high Reynolds Number boundary layer and channel flows, particularly in order to attempt to explain the formation of subharmonic TS modes observed in many experiments. §2.2 summarises the well-known theory of the High Reynolds-Number lower branch of the neutral curve regime for a boundary layer, and describes the evolution of linear TS modes in the high frequency lower branch regime. §2.3 considers weakly non-linear phase-locked resonant triad interactions and demonstrates that a central mode can interact with two oblique subharmonics to cause superexponential growth of the subharmonics.

La transition laminaire-turbulent au sein de la couche limite qui se développesur les parois des aéronefs augmente fortement la traînée de frottement. Ainsi, afin derépondre à une problématique à la fois environnementale et économique, une piste envisagéepour réduire la consommation en carburant des aéronefs du futur est de diminuerla trainée en reculant cette transition le plus en aval possible. Dans ce cadre, l’objectifde cette thèse est de caractériser expérimentalement et numériquement l’effet d’actionneursà plasma de type Décharge à Barrière Diélectrique sur la transition. Alimentés parune haute tension alternative, ces actionneurs actifs produisent une force volumique pulséequi permet, sous certaines conditions, de modifier les profils de vitesse moyenne dansla couche limite et de reculer la transition. Sous d’autres conditions, le caractère instationnairede cette force volumique peut entrainer une amplification des instabilités modalesnaturellement présentes dans la couche limite (ondes de Tollmien-Schlichting) et ainsiconduire à une transition prématurée. Une première expérience a permis de mettre enévidence cette compétition entre l’effet moyen stabilisant et l’effet instationnaire déstabilisanten mesurant respectivement un recul et une avancée de la transition. Parallèlementà ces activités expérimentales, une étude numérique, basée sur des analyses destabilité linéaire, a montré que l’effet moyen de la force volumique permettait d’atténuerune large gamme de fréquences d’ondes TS dans la couche limite et d’expliquer le reculde transition observé expérimentalement. En se concentrant sur l’effet moyen, une secondeexpérience a permis d’étudier l’influence de la position de l’actionneur ainsi quel’effet cumulatif de plusieurs actionneurs sur le recul de transition
The boundary layer transition from a laminar to a turbulent state increases thewall friction drag. Particularly on future aircrafts, one way of reducing fuel consumption,and answering both an environmental and economic issue, consists in delaying the transitionfarther downstream. In this context, the aim of this work is to characterize the impactof Dielectric Barrier discharge (DBD) plasma actuators on the boundary layer transition.When powered with an alternative high voltage, these active actuators produce apulsed body force which is tangential to the wall and, under some conditions, enablesto modify the boundary layer mean velocity profiles to delay the transition. Under otherconditions, the unsteady body force amplifies modal instabilities (Tollmien-Schlichtingwaves) may destabilize the boundary layers, leading to a promoted transition. A first experimentenabled to highlight this competition between the stabilizing mean effect andthe destabilizing unsteady effect by measuring respectively a transition delay and a transitionpromotion. A numerical study based on local stability analyses wass conducted inparallel and showed that a wide frequency range of TS waves is damped by the mean bodyforce, which explains the transition delay. A second experiment, focusing on the mean effect,enabled to show the influence of the actuator position and the cumulative effect ofseveral actuators on the transition delay

Le bruit tonal rayonné au bord de fuite des profils à faible nombre de Reynolds est un phénomène observé sur les ailes de drones ou micro-drones qui sont utilisés partout dans la vie quotidienne. La diminution de ce bruit va augmenter la survivabilité et l'efficacité des appareils dans le domaine militaire. De plus, cela va augmenter le champ des applications civiles et minimiser la pollution par le bruit. La réduction efficace du bruit est indispensable et, par conséquent, une compréhension complète du processus de rayonnement du bruit tonal du profil est nécessaire. Malgré le fait que des essais dédiés aient été réalisés depuis les années 70, il reste beaucoup de détails à expliquer. Le travail présenté est dédié à une étude expérimentale et analytique du bruit tonal. C'est une partie de collaboration entre l'Ecole Centrale de Lyon et Embry- Riddle Aeronautical University. Le but est de réaliser une caractérisation exhaustive des paramètres acoustiques et aérodynamiques du bruit tonal de bord de fuite d'un profil et de produire une base de données qui pourra être utilisée pour valider les simulations numériques réalisées dans le futur. Le profil symétrique NACA-0012 ainsi que le profil asymétrique SD7003 ont été testés pour une série d'angles d'incidence (de -10° à 10°) dans la soufflerie anéchoïque à jet ouvert de l'Ecole Centrale de Lyon pour des nombres de Reynolds modérés (0.6x105 < Rec < 2.6x105). Les mesures de pression aux parois et de pression acoustique en champ lointain pour différentes configurations ont permis d'observer une structure en escalier de la signature du bruit, de déterminer quelle face du profil a produit le bruit et de distinguer le rôle de la boucle de rétroaction. Des techniques supplémentaires de post-traitement comme l'analyse temps-fréquence ont montré l'existence de plusieurs régimes (un régime de commutation entre deux états, un régime d'une seul fréquence et un régime à plusieurs fréquences) de l'émission de bruit. L'analyse de bi-cohérence a montré qu'il y a des couplages nonlinéaires entre les fréquences. Une étude par l'anémométrie à fil chaud et par des techniques de visualisation de l'écoulement a montré que la formation d'une bulle de décollement est une condition nécessaire mais pas suffisante pour la génération du bruit. De plus, la localisation de la bulle est aussi importante et elle doit être suffisamment proche du bord de fuite. En outre, l'analyse de stabilité linéaire des résultats de simulations numériques a montré que des ondes de Tollmien-Schlichting sont transformées en ondes de Kelvin-Helmholtz dans la zone du décollement. Une prédiction analytique de l'amplitude des fréquences pures émises dans le champ lointain a été effectuée sur la base du modèle d'Amiet en supposant que le champ de pression pariétal est bidimensionnel. Les mesures de pression proches du bord de fuite du profil ont été prises comme données d'entrée. Les amplitudes prédites sont globalement en accord avec les mesures acoustiques. Après l'analyse de tous les résultats la description suivante du processus de rayonnement de sons purs peut être proposée. Les ondes de Tollmien-Schlichting qui se développent initialement dans la couche limite se transforment en ondes de Kelvin-Helmholtz le long de la couche de cisaillement de la bulle de décollement. Au bord de fuite du profil elles sont converties en ondes acoustiques qui forment un couplage fort avec les instabilités de couche limite plus en amont de l'écoulement, pilotant elles-mêmes le déclenchement de ces instabilités
The tonal trailing-edge noise generated by transitional airfoils is a topic of interest because of its wide area of applications. One of them is the Unmanned Air Vehicles operated at low Reynolds numbers which are widely used in our everyday life and have a lot of perspectives in future. The tonal noise reduction will increase the survivability and effectiveness of the devices in military field. Moreover it will enlarge the range of civil use and minimize noise pollution. The effective noise reduction is needed and therefore the complete understanding of the tonal noise generation process is necessary. Despite the fact that investigation of the trailing-edge noise was started since the seventies there are still a lot of details which should be explained. The present work is dedicated to the experimental and analytical investigation of the tonal noise and is a part of the collaboration project between Ecole Centrale de Lyon and Embry-Riddle Aerospace University. The aim is to conduct an exhaustive experimental characterization of the acoustic and aerodynamic parameters of the trailing-edge noise and to produce a data base which can be used for further numerical simulations conducted at Embry-Riddle Aerospace University. A symmetric NACA-0012 airfoil and a slightly cambered SD7003 airfoil at moderate angles of attack (varied from -10° à 10°) were tested in an open-jet anechoic wind tunnel of Ecole Centrale de Lyon at moderate Reynolds numbers (0.6x105 < Rec < 2.6x105). Measurements of the wall pressure and far-field acoustic pressure in different configurations allowed to observe the ladder-type structure of the noise signature, to determine which side produced tones and to distinguish the role of the acoustic feedback loop. Additional post-processing techniques such as time-frequency analysis showed the existence of several regimes (switching regime between two tones, one-tone regime and multiple-tones regime) of noise emission. The bicoherence analysis showed that there are non-linear relationships between tones. The investigation of the role of the separation area by hot-wire anemometry and flow visualization techniques showed that the separation bubble is a necessary but not a suficient condition for the noise generation. Moreover the location of the bubble is also important and should be close enough to the trailing edge. Furthermore the linear stability analysis of accompanying numerical simulation results showed that the Tollmien-Schlichting waves transform to the Kelvin-Helmholtz waves at the separation area. An analytical prediction of the tone levels in the far-field was done using Amiet's model based on the assumption of perfectly correlated sources along the span. The wall-pressure measurements close to the trailing edge were used as an input data. The comparisons of the predicted levels and measured ones showed a good agreement. After analysis of all results the following description of the tonal noise mechanism is proposed. At some initial point of the airfoil the Tollmien-Schlichting instabilities start. They are traveling downstream and continued to Kelvin-Helmholtz waves along the shear-layer of the separation bubble. These waves reach the trailing edge, scatter from it as acoustic waves, which move upstream. The acoustic waves amplify the boundary layer instabilities at some frequencies for which the phases of both motions match and creates the feedback loop needed to sustain the process

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

A novel laminar flow control based on generation of spanwise mean velocity gradients (SVG) in a flat plate boundary layer is investigated where disturbances of different types are introduced in the wall-bounded shear layer. The experimental investigations are aimed at; (i) generating stable and steady streamwise streaks in the boundary layer which set up spanwise gradients in the mean flow, and (ii) attenuating disturbance energy growth in the streaky boundary layers and hence delaying the onset of turbulence transition. The streamwise streaks generated by four different methods are investigated, which are spanwise arrays of triangular/rectangular miniature vortex generators (MVGs) and roughness elements, non-linear pair of oblique waves, and spanwise-periodic finite discrete suction. For all the investigated methods the boundary layer is modulated into regions of high- and low speed streaks through formation of pairs of counter-rotating streamwise vortices. For the streaky boundary layers generated by the MVGs a parameter study on a wide range of MVG configurations is performed in order to investigate the transient growth of the streaks. A general scaling of the streak amplitudes is found based on empiricism where an integral amplitude definition is proposed for the streaks. The disturbances are introduced as single- and broad band frequency twodimensional Tollmien–Schlichting (TS) waves, and three-dimensional single and a pair of oblique waves. In an attempt to obtain a more realistic configuration compared to previous investigations the disturbances are introduced upstream of the location were streaks are generated. It is shown that the SVG method is efficient in attenuating the growth of disturbance amplitudes in the linear regime for a wide range of frequencies although the disturbances have an initial amplitude response to the generation of the streaks. The attenuation rate of the disturbance amplitude is found to be optimized for an integral streak amplitude of 30% of the free-stream velocity which takes into account the periodic wavelength of the streaky base flow. The stabilizing effect of the streamwise streaks can be extended to the nonlinear regime of disturbances which in turn results in transition to turbulence delay. This results in significant drag reduction when comparing the skin friction coefficient of a laminar- to a turbulent boundary layer. It is also shown that consecutive turbulence transition delay can be obtained by reinforcing the streaky boundary layer in the streamwise direction. For the streaky boundary layer generated by pair of oblique waves their forcing frequency sets the upper limit for the frequency of disturbances beyond which the control fails.

QC 20160208

The main aim of this thesis was to understand the mechanism behind the classical transition scenario inside the boundary layer over an airfoil and eventually attempting to control this transition utilizing passive devices for transition delay. The initial objective of analyzing the transition phenomenon based on TS wave disturbance growth was conducted at 90 Hz using LDV and CTA measurement techniques at two different angles of attack. This was combined with the studies performed on two other frequencies of 100 and 110 Hz, in order to witness its impact on the neutral stability curve behavior. The challenges faced in the next phase of the thesis while trying to control the transition location, was to understand and encompass the effect of adverse pressure gradient before setting up the passive control devices, which in this case was miniature vortex generators. Consequently, several attempts were made to optimize the parameters of the miniature vortex generators depending upon the streak strength and stability. Finally, for 90 Hz a configuration of miniature vortex generators have been found to successfully stabilize the TS wave disturbances below a certain forcing amplitude, which also led to transition delay.

Disturbances introduced in wall-bounded .ows can grow andlead to transition from laminar to turbulent .ow. In order toreduce losses or enhance mixing in energy systems, afundamental understanding of the .ow stability is important. Inlow disturbance environments, the typical path to transition isan exponential growth of modal waves. On the other hand, inlarge disturbance environments, such as in the presence of highlevels of free-stream turbulence or surface roughness,algebraic growth of non-modal streaks can lead to transition.In the present work, the stability of wall-bounded .ows isinvestigated by means of linear stability equations valid bothfor the exponential and algebraic growth scenario. Anadjoint-based optimization technique is used to optimize thealgebraic growth of streaks. The exponential growth of waves ismaximized in the sense that the envelope of the most ampli.edeigenmode is calculated. Two wall-bounded .ows areinvestigated, the Falkner–Skan boundary layer subject tofavorable, adverse and zero pressure gradients and the Blasiuswall jet. For the Falkner–Skan boundary layer, theoptimization is carried out over the initial streamwiselocation as well as the spanwise wave number and the angularfrequency. Furthermore, a uni.ed transition-prediction methodbased on available experimental data is suggested. The Blasiuswall jet is matched to the measured .ow in an experimentalwall-jet facility. Linear stability analysis with respect tothe growth of two-dimensional waves and streamwise streaks areperformed and compared to the experiments. The nonlinearinteraction of introduced waves and streaks and the .owstructures preceding the .ow breakdown are investigated bymeans of direct numerical simulations.

Descriptors: Boundary layer, wall jet, algebraic growth,exponential growth, lift-up e.ect, streamwise streaks,Tollmien-Schlichting waves, free-stream turbulence, roughnesselement, transition prediction, Parabolized StabilityEquations, Direct Numerical Simulation.

Active flow control in laminar boundary layers can reduce wall friction on a wing, if laminar-turbulent transition is delayed. In this thesis, (re-)active flow control for active cancellation of Tollmien-Schlichting (TS) waves in a two-dimensional laminar boundary layer is investigated. The TS-waves that initiate the transition to turbulence are attenuated with a DBD plasma actuator by superposition. Active wave cancelation requires the use of control algorithms and their stability is influenced by variable inflow conditions. Model-based (Linear-Quadratic-Gaussian) and adaptive control algorithms (filtered-x-LMS) are investigated under realistic (varying) inflow conditions in wind-tunnel and in-flight experiments. The further developed delayed-x-LMS algorithm allows a stable and robust controller operation for active wave cancelation in flight. All experimental results are validated by direct numerical simulations and linear stability theory. Furthermore, the challenges for the application of DBD plasma actuator arrays to delay natural transition are pointed out. The simplification of transfer paths for reducing the required computational power is discussed.

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.