This thesis investigates vortex dynamics of a plunging airfoil by studying the vorticity transport mechanisms of two-dimensional direct numerical simulations. The simulations were used to study a simplified flat airfoil in a freestream that was subject to pure plunging motion. Quantitative and qualitative analyses were used the validate the two-dimensional simulations and gain insight into the effects of eliminating three-dimensional physics in a nominally two-dimensional flow. Additionally, a parametric study was conducted to analyze the effects of Reynolds and Strouhal numbers on the transport of vorticity.

A novel numerical method solves the VIScous Vorticity Equation (VISVE) in 3D in order to model the Leading Edge Vortex (LEV) of propellers is proposed and implemented in this dissertation. The spatial concentration of the vorticity is exploited in the method, which is designed to be spatially compact and numerically efficient, in the meantime, capable of modeling complicated vorticity/solid boundary interaction in 2D and 3D. The numerical model can work as a viscous correction on top of the traditional Boundary Element Method (BEM) results. The proposed method is first applied in the case of a 2D hydrofoil at high angle of attack. The results are correlated with those from Navier-Stokes (N-S) simulation. The method is then used to model the LEV and tip vortex of a 3D swept wing. The results of the 3D simulation show great similarity to those from N-S. In the end, the method is applied in the case of propellers at low advance ratios. All the essential flow characteristics (LEV and tip vortex) are predicted. The objective of this dissertation is not developing a mathematically equivalent numerical method to the full-blown Reynolds-Averaged Navier-Stokes (RANS) solver, but inventing an accurate and computationally efficient tool to model the effects of the LEV on the propeller performance for engineering's purpose. / text

Man has always been fascinated by the flight of birds and insects. First attempts at flight involved flapping wings to mimic the birds and insects that had been observed in flight. Fixed wings proved to be a more practical approach and have been used for over 100 years for manned flight. Emphasis has been placed on flapping wing designs for micro air vehicles (MAVs) as research has shown that challenges arise in lift generation and stability in fixed wing flight as the scale decreases [1].This research explores the use of 3D, time-resolved, Synthetic Aperture PIV (SAPIV) in measuring flow velocities on the mechanical flapping wing of a MAV in tethered flight. The vortical structures on the MAV are measured using both SAPIV and 2DPIV to be able to analyze 2D and 3D velocity fields. The 3D vorticity plots and 2D slice vorticity plots show the three-dimensional nature of the Leading Edge Vortex (LEV) and Trailing Edge Vortex (TEV). 2DPIV plots and 2D slices from the 3D data show general agreement in the structure and behavior of the flow around the flapping wing. The lift and thrust generated by the MAV are measured using a force gauge. The wing tip is tracked in 2D and 3D for synchronization of the measured lift forces with the flow field measurements from the SAPIV. The positive and negative circulation are plotted against the measured lift and thrust forces. The measured lift and thrust forces from the force gauge are then compared to the calculated lift and thrust forces from the measured 3D circulation found through the SAPIV flow field measurements. A plane measured parallel to the LEV and TEV vortex cores allows the defining of a unit vector that is directed normal to the top of the wing and the LEV and TEV cores. The decomposition of the unit vector allows for the calculation of the lift and thrust generated by the circulation around the wing. The comparisons between the measured and calculated forces show good agreement in the case of the measured and calculated lift forces.

In summary the tilting mechanism helps to explain the overall flow structure and the stability of the leading edge vortex.; The leading edge vortex has been identified as the most critical flow structure for producing lift in flapping wing flight. Its stability depends on the transport of the entrained vorticity into the wake via spanwise flow. This study proposes a hypothesis for the generation and enhancement of spanwise flow based on the chordwise vorticity that results from the tilting of the leading edge vortex and trailing edge vortex. We investigate this phenomenon using dynamically scaled robotic model wings. Two different wing shapes, one rectangular and one based on Drosophila melanogaster (fruit fly), are submerged in a tank of mineral oil and driven in a flapping motion. Two separate kinematics, one of constant angular velocity and one of sinusoidal angular velocity are implemented. In order to visualize the flow structure, a novel three dimensional particle image velocimetry system is utilized. From the three dimensional information obtained the chordwise vorticity resulting from the vortex tilting is shown using isosurfaces and planar slices in the wake of the wing. It is observed that the largest spanwise flow is located in the area between the chordwise vorticity of the leading edge vortex and the chordwise vorticity of the trailing edge vortex, supporting the hypothesis that the vortex tilting enhances the spanwise flow. Additionally the LEV on the rectangular wing is found to detach at about 80% span as opposed to 60% span for the elliptical wing. Also, two distinct regions of spanwise flow, one at the base and one at the tip, are observed at the beginning of the sinusoidal kinematic, and as the velocity of the wing increases these two regions unionize into one. Lastly, the general distribution of vorticity around each wing is found to be nearly the same, indicating that different wing shapes do not greatly affect the distribution of vorticity nor stability mechanisms in flapping flight.

This thesis examines two important problems in fluid dynamics: that of a partially immersed sphere spinning in a bath of liquid and the measurement of flow velocities around a free flying butterfly. Although the actual problems are quite different, each problem incorporates many of the same principles and techniques. When a hard-boiled egg spins through a pool of milk on the kitchen counter, the milk rises up the sides of the egg and droplets are ejected. This phenomenon occurs when any partially submerged object whose radius increases upward from the fluid surface (e.g., spheres, inverted cones, rings, etc.), spins in a shallow bath of fluid. The fluid ejects from the surface at the maximum diameter in one of three ejection modes: jets, sheets, or sheet breakup. Additionally, a surprisingly large flow rate is induced by the spinning object. Spheres are used in this study to determine the effects of experimental parameters on the induced flow rate. High-speed imaging is used to experimentally characterize the modes of ejection and measure sheet breakup distance and velocities of liquid within liquid sheets. A theoretical model is derived using an integral momentum boundary layer analysis both beneath the free surface and in the thin film attached to the sphere. Experimental results are presented in comparison with predicted behavior with good agreement. The suitability of using a spinning sphere as a pump is also discussed. Second, the use of PIV to measure flow velocities around living species is becoming more widely adopted. Current efforts are starting to measure 3D, time-resolved velocities around insects in tethered flight. This work investigates the use of Synthetic Aperture PIV (SAPIV) in obtaining 3D, time-resolved volumetric velocity fields around a painted lady butterfly in free flight. Results are presented from several time steps during both the down stroke and upstroke of the butterfly showing the development of the leading edge vortex. The velocity field results have limited spatial resolution; however, the results show that SAPIV has potential in further investigating these flow structures. The reconstructed visual hull of the butterfly is also discussed.

Le développement de systèmes de propulsion alternatifs aux turboréacteurs actuels constitue un axe de recherche important dans le contexte aéronautique. L’open-rotor, moteur à hélices contrarotatives, constitue une piste sérieuse car il permet à la fois de réduire fortement la consommation de carburant et les émissions de gaz. Toutefois, les émissions sonores restent un défi pour ce type d’architecture, notamment du fait de l’absence de carénage. La compréhension des sources acoustiques et leur prévision est nécessaire afin de pouvoir, par la suite, réduire le bruit de ces moteurs. Les écoulements d’un doublet d’hélices contrarotatives sont complexes, en particulier pour l’hélice aval qui constitue l’axe d’étude de la thèse. Le travail présenté est dédié à une étude numérique, expérimentale et analytique et intervient dans le cadre de la chaire industrielle ADOPSYS entre Safran Aircraft Engines et l’Ecole Centrale de Lyon. L’objectif de ce travail est double. Il s’agit d’une part de réaliser une campagne expérimentale afin d’observer et de mieux comprendre le comportement de l’écoulement et de l’acoustique d’une pale en flèche, notamment en réponse à la présence d’un tourbillon de bord d’attaque. Un second objectif de la thèse était de constituer une base de données afin de comparer les prévisions obtenues avec un modèle analytique. Une méthode de calcul semi-analytique de la réponse aéroacoustique d’une pale aval en réponse à une excitation provenant de l’amont et prenant en compte les effets de charge et de géométrie a été développée. Une étude numérique d’un doublet d’hélices contrarotatives a servi de base à la définition de la géométrie de pale utilisée pendant l’étude. Celle-ci a été définie de façon à observer un tourbillon de bord d’attaque pour certains angles d’incidence. La maquette a ensuite été placée dans une soufflerie anéchoïque de l’Ecole Centrale de Lyon afin de réaliser une étude paramétrique. Des visualisations par enduit visqueux et des mesures de pression pariétale permettent de rendre compte de la présence du tourbillon de bord d’attaque à certains angles d’incidence. L’étude des spectres en champ lointain permet de distinguer un comportement en trois régimes, associés aux trois comportements du tourbillon de bord d’attaque. Des mesures de localisation de sources permettent de corroborer ces observations. Des prévisions analytiques du bruit émis par la pale et se basant sur le modèle d’Amiet ont également été réalisées. Dans un premier temps, les effets de la flèche sont pris en compte dans le modèle et celui-ci est alors appliqué à la pale de l’étude. Une meilleure adéquation des résultats est alors trouvée quand les effets de flèche sont pris en compte, en particulier dans les directions perpendiculaires à la pale. Le modèle est ensuite étendu afin de prendre en compte les effets de la jonction en pied de pale. Cette partie est exploratoire et le développement reste à approfondir. Un complément à l’expérience a consisté en l’étude de l’impact de sillages défilants sur la pale. Un système de barreaux rotatifs permet de générer des sillages périodiques représentatifs d’une interaction de sillages rotor-rotor. Les mesures réalisées montrent le comportement quasi-stationnaire du tourbillon. / The development of alternative propeller systems to turbojets is a main issue for research in the current context of aeronautical transport. Counter rotating open rotors are a candidate solution because they allow reduction of fuel consumption and gas emission. However, noise emissions are still a challenge for these types of configuration, in particular because they cannot benefit from the nacelle and the liners currently used in turbojet. The understanding of acoustic sources and their prediction is necessary in order to be able to reduce noise emission in the near future. Flows in an open-rotor are complex, in particular for the downstream propeller which is the subject of this approach.This work based on a numerical, experimental and analytical study and takes part in the ADOPSYS chair between Safran Aircraft Engines and l’Ecole Centrale de Lyon. This PhD has two main goals. The first one is to complete an experimental study in order to elucidate the behavior of the flow on a swept airfoil and the resulting acoustics, with a possibly developing leading-edge vortex. The measurements will be a data base for further comparison with analytical prediction. The second objective of the PhD consists in developing a semi-analytical modeling of the noise emitted by an airfoil in response to an incoming perturbation, taking into account the loading and geometry effects. A numerical study of a full counter-rotating system was used as a basis for designing the investigated airfoil. The latter was designed so that a leading-edge vortex could be formed on the surface for some angles of attack. The mock-up was then tested in an anechoic wind tunnel of Ecole Centrale de Lyon for various sets of parameters. Flow visualization and wall-pressure measurements indicated the presence of the leading-edge vortex for some angles of attack. The far-field measurements indicated three acoustic regimes, which can be associated with three behaviors of the leading-edge vortex. Source localization measurements corroborate these observations. Analytical predictions of the noise emitted by the airfoil and based on Amiet’s model were also performed. Firstly, the sweep angle is taken into account in the model. Secondly it is applied to the studied airfoil. A better match of the results is found when the sweep is considered, in particular in the perpendicular directions. The model in then extended in order to include the wall-junction. This part is exploratory and should be further developed. Finally, a complementary experimental investigation of the impingement of periodic wakes on the airfoil has been performed, using a system made of rotating bars, mimics true wake interactions. The measurements suggest that the leading-edge vortex has a quasi-steady behavior.

Oscillating-foil hydrokinetic turbines have gained interest over the years to extract energy from renewable sources. The influence of the sweep angle on the performance of a fully-passive oscillating-plate hydrokinetic turbine prototype was investigated experimentally in the present work. The sweep angle was introduced to promote spanwise flow along the plate in order to manipulate the leading edge vortex (LEV) and hydrodynamically optimize the performance of the turbine. In the present work, flat plates of two configurations were considered: a plate with a 6° sweep angle and an unswept plate (control), which were undergoing fully-passive pitch and heave motions in uniform inflow at the Reynolds numbers ranging from 15 000 to 30 000. The resulting kinematic parameters and the energy extraction performance were evaluated for both plates. Planar (2D) particle image velocimetry (PIV) was used to obtain patterns of the phase-averaged out-of-plane vorticity during the oscillation cycle. The circulation in the wake was then related to the induced-forces on the plate by calculating the moments of vorticity of the LEV with respect to the pitching axis of the plate. Tomographic (3D) PIV was implemented in evaluating the influence of the spanwise flow on the dynamics of the vortex structure in three-dimensional space. The rate of deformation of the vortex length was quantified by calculating the deformation terms embedded in the vorticity equations, then linked to the stability of the vortex. The results show evidence of delay of the shedding of LEV and increased vortex stability, in the case of the swept plate. The manipulation of the LEV by the spanwise flow was related to the induced kinematics exhibited by the prolonged heave forces experienced by the swept plate, which led to the higher power extraction performance at high inflow velocities. In the presence of spanwise flow, positive vortex stretching along the vortex line increased the stabilization of the vortex core and prevented the onset of helical vortex breakdown, observed in the case of the unswept plate. The use of the sweep profile on the plate has led to the improvement of energy extraction performance of the fully-passive hydrokinetic turbine. / Graduate

Cette thèse concerne l’aérodynamique de pales d'extrémité transsonique. Ces pales sont conçues pour maximiser le rendement en croisière, tout en générant la traction requise au décollage. Elles ont des profils fins et peu cambrés, travaillant à forte incidence au décollage, ce qui peut entraîner l’apparition d’un tourbillon de bord d’attaque (TBA). Or ce TBA présente des similitudes avec les tourbillons d’apex d’aile Delta, connus pour leur capacité à générer de la portance tourbillonnaire.Cette étude consiste à examiner l’intérêt du TBA pour les performances aérodynamiques.La démarche a consisté dans un premier temps à caractériser la topologie du TBA sur une maquette représentative d’une pale d’ Open Rotor, à l'aide d'essais PIV résolus en temps et de calculs RANS k-omega SST, et à évaluer la capacité de la simulation RANS à reproduire les caractéristiques d’intérêt pour cette étude. Un algorithme a été développé afin d'estimer la contribution de ce TBA à la portance à partir du champ de pression pariétal RANS.Afin d'expliciter l'influence des paramètres géométriques et de fonctionnement de la pale sur la portance tourbillonnaire, un modèle 1D de la portance tourbillonnaire a été développé puis couplé à la méthode de l'élément de pale.Les premières comparaison de géométries à iso-traction ont montré que la portance tourbillonnaire permet de générer la traction requise au décollage avec une surface alaire plus faible. Ces résultats ouvrent de nouvelles perspectives pour la conception de géométries avec un meilleur rendement en croisière. / This thesis deals with the aerodynamic properties of propeller blades. Those blades are designed to maximise cruise efficiency, while achieving the target thrust at take-off. Their thin, low-cambered profiles must work at high incidence at take-off, which may give rise to a leading-edge vortex (LEV).The topology of this LEV looks similar to Delta wing LEVs, which are known to generate vortex lift.the aim of this study is to explore the probable impact of the LEV on lift at take-off in order to reconsider propeller blade designs. The approach first consisted in caracterising the LEV topology on a model blade representative of an Open Rotor front blade, using both Time-Resolved PIV and RANS k-omega SST calculations. The comparison between both methods demonstrated the ability of RANS calculations to reproduce the LEV characteristics of interest to this study.Then, the LEV contribution to lift was evaluated thanks to an algorithm developed to estimate vortex lift contribution from RANS wall pressure fields.In order to explicit the influence of the blade's geometrical and functioning parameters on vortex lift, a 1D vortex lift model was developed and coupled to the Blade Element Momentum Theory.The first blade geometry comparative studies at iso-thrust showed that vortex lift enables to generate target thrust at take-off with a lower blade surface. This opens new perspectives for the design of blade geometries with enhanced cruise efficiency.

This thesis contributes to the state of the art in integrated design of insect-scale piezoelectric actuated flapping wing vehicles through the development of novel theoretical models for flapping wing aerodynamics and piezoelectric actuator dynamics, and integration of these models into a closed form design process. A comprehensive literature review of available engineered designs of miniature rotary and flapping wing vehicles is provided. A novel taxonomy based on wing and actuator kinematics is proposed as an effective means of classifying the large variation of vehicle configurations currently under development. The most successful insect-scale vehicles developed to date have used piezoelectric actuation, system resonance for motion amplification, and passive wing pitching. A novel analytical treatment is proposed to quantify induced power losses in normal hover that accounts for the effects of non uniform downwash, wake periodicity and effective flapping disc area. Two different quasi-steady aerodynamic modelling approaches are undertaken, one based on blade element analysis and one based on lifting line theory. Both approaches are explicitly linked to the underlying flow physics and, unlike a number of competing approaches, do not require empirical data. Models have been successfully validated against experimental and numerical data from the literature. These models have allowed improved insight into the role of the wing leading-edge vortex in lift augmentation and quantification of the comparative contributions of induced and profile drag for insect-like wings in hover. Theoretical aerodynamic analysis has been used to identify a theoretical solution for the optimum planform for a flapping wing in terms of chord and twist as a function of span. It is shown that an untwisted elliptical planform minimises profile power, whereas a more highly tapered design such as that found on a hummingbird minimises induced power. Aero-optimum wing kinematics for hovering are also assessed. It is shown that for efficient flight the flapping velocity should be constant whereas for maximum effectiveness the flapping velocity should be sinusoidal. For both cases, the wing pitching at stroke reversal should be as rapid as possible. A dynamic electromechanical model of piezoelectric bending actuators has been developed and validated against data obtained from experiments undertaken as part of this thesis. An expression for the electromechanical coupling factor (EMCF) is extracted from the analytical model and is used to understand the influence of actuator design variables on actuator performance. It is found that the variation in EMCF with design variables is similar for both static and dynamic operation, however for light damping the dynamic EMCF will typically be an order of magnitude greater than for static operation. Theoretical contributions to aerodynamic and electromechanical modelling are integrated into a low order design method for propulsion system sizing. The method is unique in that aside from mass fraction estimation, the underlying models are fully physics based. The transparency of the design method provides the designer with clear insight into effects of changing core design variables such as the maximum flapping amplitude, wing mass, transmission ratio, piezoelectric characteristics on the overall design solution. Whilst the wing mass is only around 10% of the actuator mass, the effective wing mass is 16 times the effective actuator mass for a typical transmission ratio of 10 and hence the wing mass dominates the inertial contribution to the system dynamics. For optimum aerodynamic effectiveness and efficiency it is important to achieve high flapping amplitudes, however this is typically limited by the maximum allowable field strength of the piezoelectric material used in the actuator.

The Counter-Rotating Open Rotors (CROR) are identified as a possible alternative to turbofan engines for middle-range aircrafts. Providing significant fuel savings and reducing the green-house gas emissions, they may lead however to an increased noise radiation due to the absence of nacelle shielding. To properly predict the acoustic radiation of such systems is then mandatory both to reduce the source mechanisms of the isolated engine and to offer an optimal noise installation solution. Such an objective is tackled in the present thesis in two steps. In a first part, the research aims at predicting the tonal noise radiated from the first propeller of CROR mounted on the rear fuselage by means of a pylon (pusher configuration), considering both the pylon-wake and the uniform ow effects. From the Ffowcs Williams & Hawkings' formalism, three noise sources are identified. First the unsteady loading is computed using a similar procedure to the one used for the rotor-rotor wake interaction noise prediction. The velocity deficit in the pylon wake is locally expanded in two-dimensional Fourier gusts in a reference frame attached to the front rotor. The unsteady lift induced by each gust on a blade segment is calculated using a linearized analytical response function that accounts for a realistic geometry. The steady loading is the second source contribution and is evaluated using both a software based on the lifting-line theory and some numerical simulations for different reference source surfaces. Finally the thickness noise due to the blade volume displacement is included in the analysis using Isom's formulation. From the linear acoustic assumptions, all these sources modelled as equivalent acoustic dipoles rotating in a uniformly moving atmosphere are then summed to calculate the far-field noise. The whole methodology is assessed against wind-tunnel test data and reference software predictions. A parametric study considering several pylon positionings and pylon-wake configurations with blowing is performed in order to emphasize the relative contribution of the three noise sources. Secondly, the rotor- rotor wake interaction noise being recognized as the most significant contribution in isolated configuration, its modelling is completed by introducing the dynamics of the vortex occurring near the rear-rotor leading edge. A semi-analytical methodology is developed to determine a vortex attached over a at plate embedded in a uniform ow with incidence. Applied to the case of a rear blade going through a front-rotor wake, it provides a first estimate of the noise contribution of the vortex. / Les hélices contrarotatives constituent une alternative possible aux turboréacteurs pour les avions moyens- courriers. Réduisant significativement la consommation de carburant et les émissions de gaz à effet de serre, ils peuvent néanmoins conduire à un rayonnement sonore accru de par l'absence de carénage. Prédire correctement le rayonnement sonore de telles motorisations est donc indispensable pour réduire les mécanismes sources propres au moteur isolé ou assurer une solution d'installation acoustique optimale. Un tel objectif est abordé dans cette thèse en deux temps. Dans un premier temps, l’étude vise à prédire le bruit tonal rayonné par la première hélice d'un moteur monté à l'arrière du fuselage (configuration dite en pousseur), en considérant les effets du sillage du pylône supportant le moteur et de l'écoulement moyen. Partant du formalisme de Ffowcs Williams & Hawkings, trois sources sonores sont identifiées à cet effet. La charge instationnaire, tout d'abord, est calculée en s'appuyant sur une méthodologie similaire à celle utilisée pour la prédiction du bruit d'interaction de sillages entre les deux rotors. Le déficit de vitesse dans le sillage du mât est décomposé localement en rafales bidimensionnelles dans un repère attaché au rotor amont. La portance instationnaire induite par chaque rafale sur un segment de pale est calculée en utilisant une fonction de réponse analytique linéarisée considérant une géométrie réaliste. Deuxième contribution, la charge stationnaire est évaluée au moyen d'un logiciel s'appuyant sur la théorie de la ligne portante mais également via des simulations numériques pour différentes surfaces sources de référence. Enfin, le bruit d'épaisseur associé au déplacement du volume de la pale est inclus dans l'analyse à partir de la formulation d'Isom. D'après les hypothèses de l'acoustique linéaire, toutes ces sources modélisées comme des dipôles acoustiques tournant dans une atmosphère uniforme en mouvement sont ensuite sommées pour calculer le bruit en champ lointain. L'ensemble de la méthodologie est comparé à des données d'essai et des prédictions d'un logiciel de référence. Une étude paramétrique considérant plusieurs positionnements du pylône et des configurations avec soufflage est effectuée afin de bien mettre en évidence les contributions relatives des trois sources sonores. Dans un deuxième temps, le bruit d'interaction de sillages étant reconnu comme la contribution majoritaire en configuration isolée, sa modélisation est complétée en introduisant la dynamique du tourbillon se développant au voisinage du bord d'attaque du rotor aval. Une méthodologie semi-analytique est développée pour déterminer un tourbillon attaché au-dessus d'une plaque plane plongée dans un écoulement uniforme avec incidence. Appliquée au cas d'une pale aval traversant le sillage du rotor amont, elle fournit une première estimation de la contribution sonore du tourbillon.