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Fuel consumption and noise reduction trigger the evolution of aircraft engines towards Ultra High Bypass Ratio (UHBR) architectures. Their short air inlet design and the reduction of their interstage length lead to an increased circumferential inhomogeneity of the flow close to the fan. This inhomogeneity, called distortion, may have an impact on the tonal noise radiated from the fan module. Usually, such a noise source is supposed to be dominated by the interaction of fan-blade wakes with Outlet Guide Vanes (OGVs). At transonic tip speeds, the noise generated by the shocks and the steady loading on the blades also appears to be significant. The increased distortion may be responsible for new acoustic sources while interacting with the fan blades and the present work aims at evaluating their contribution. The effects of distortion on the other noise mechanisms are also investigated. The work is based on full-annulus simulations of the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations. A whole fan module including the inlet duct, the fan and the Inlet and Outlet Guide Vanes (IGVs/OGVs) is studied. The OGV row is typical of current engine architecture with an integrated pylon and two different air inlet ducts are compared in order to isolate the effects of inlet distortion. The first one is axisymmetric and does not produce any distortion while the other one is asymmetric and produces a level of distortion typical of the ones expected in UHBR engines. A description and a quantification of the distortion that is caused by both the potential effect of the OGVs and the inlet asymmetry are proposed. The effects of the distortion on aerodynamics are highlighted with significant modifications of the fanblade wakes, the shocks and the unsteady loading on the blades and on the vanes. Both direct and hybrid acoustic predictions are provided and highlight the contribution of the fan-blade sources to the upstream noise. The downstream noise is still dominated by the OGV sources but it is shown to be significantly impacted by the inlet distortion via the modification of the impinging wakes.

Et une quantification de la distorsion due à l’effet potentiel des OGVs et de celle due à l’asymétrie de l’entrée d’air sont proposées. Les effets de la distorsion sur l’aérodynamique sont mis en évidence avec notamment une modification importante des sillages des pales de la soufflante, des chocs et de la charge instationnaire exercée sur les différentes pales et aubes. Des prévisions Les objectifs en termes de réduction de la consommation et du bruit émis par les moteurs d’avions ont progressivement mené aux architectures à très grand taux de dilution (UHBR). Leur géométrie est caractérisée par une entrée d’air courte et par une réduction de l’espace entre la soufflante et les aubes du redresseur du flux secondaire (OGVs), entraînant alors une augmentation de l’inhomogénéité azimutale de l’écoulement au niveau de la soufflante. Cette inhomogénéité, appelée distorsion, pourrait impacter le bruit tonal généré par le module de la soufflante. Ce bruit est généralement supposé être dominé par le mécanisme d’interaction des sillages des pales de la soufflante avec les OGVs. En régime transsonique, le bruit de choc et le bruit de charge stationnaire deviennent également prépondérants. L’augmentation de la distorsion pourrait être à l’origine de nouvelles sources de bruit en interagissant avec les pales de la soufflante et l’objectif de cette thèse est d’évaluer leur contribution. Les effets de la distorsion sur les mécanismes de bruit déjà existants sont également analysés. Cette étude est réalisée à l’aide de simulations numériques des équations instationnaires de Navier-Stokes moyennées (URANS). Un module complet de fan est considéré sur 360 degrés et se compose d’un conduit d’entrée d’air, de la soufflante et des redresseurs des flux primaire et secondaire (IGVs/OGVs). Le redresseur du flux secondaire est typique des moteurs actuels avec un pylône intégré et deux entrées d’air différentes sont étudiées de manière à isoler les effets de la distorsion d’entrée d’air. La première est axisymétrique et ne produit donc pas de distorsion alors que la deuxième ne l’est pas et produit un niveau de distorsion typique de ceux attendus dans les moteurs UHBR. Une description acoustiques basées sur les approches directe et hybride sont réalisées et soulignent la contribution importante des sources localisées sur les pales de la soufflante sur le bruit amont. Le bruit aval reste dominé par les sources sur les OGVs mais est tout de même impacté par la distorsion d’entrée d’air via la modification des sillages. / Fuel consumption and noise reduction trigger the evolution of aircraft engines towards Ultra High Bypass Ratio (UHBR) architectures. Their short air inlet design and the reduction of their interstage length lead to an increased circumferential inhomogeneity of the flow close to the fan. This inhomogeneity, called distortion, may have an impact on the tonal noise radiated from the fan module. Usually, such a noise source is supposed to be dominated by the interaction of fan-blade wakes with Outlet Guide Vanes (OGVs). At transonic tip speeds, the noise generated by the shocks and the steady loading on the blades also appears to be significant. The increased distortion may be responsible for new acoustic sources while interacting with the fan blades and the present work aims at evaluating their contribution. The effects of distortion on the other noise mechanisms are also investigated. The work is based on full-annulus simulations of the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations. A whole fan module including the inlet duct, the fan and the Inlet and Outlet Guide Vanes (IGVs/OGVs) is studied. The OGV row is typical of current engine architecture with an integrated pylon and two different air inlet ducts are compared in order to isolate the effects of inlet distortion. The first one is axisymmetric and does not produce any distortion while the other one is asymmetric and produces a level of distortion typical of the ones expected in UHBR engines. A description and a quantification of the distortion that is caused by both the potential effect of the OGVs and the inlet asymmetry are proposed. The effects of the distortion on aerodynamics are highlighted with significant modifications of the fanblade wakes, the shocks and the unsteady loading on the blades and on the vanes. Both direct and hybrid acoustic predictions are provided and highlight the contribution of the fan-blade sources to the upstream noise. The downstream noise is still dominated by the OGV sources but it is shown to be significantly impacted by the inlet distortion via the modification of the impinging wakes.

Traditional active noise control (ANC) systems rely on a physical sensor to measure the error signal at the desired location of attenuation. The error signal is then used to update an adaptive controller, which ultimately attenuates the measured response. However, it is not always practical to use traditional ANC in real-world applications. For example, as small unmanned aerial systems (UAS) become more commonly used, community noise exposure also increases, along with the desire to reduce UAS noise. Traditional ANC systems that rely on physical sensors at observer locations are impractical, since a UAS does not typically have real-time access to the response at an observer's ears, which is realistically in the far-field. Virtual error sensing (VES) can augment an ANC system using near-field measurements to estimate the response at a desired far-field location. In this way, the VES technique effectively shifts the zone of quiet from the location of the physical sensor(s) to a different "virtual" location. This thesis begins by outlining past work that used traditional ANC methods and virtual error sensing techniques. Numerical modeling results showing the predicted spatial change in SPL achieved using a virtual sensor will be presented. Experimental tests used ANC to attenuate the noise from a single UAS rotor at far-field locations using a near-field microphone and the remote microphone technique (RMT) to develop the VES. The results of the VES alone and with an ANC approach at several far-field virtual locations will be presented and discussed. / Master of Science / Small unmanned aerial systems (sUAS) are becoming increasingly common for private, military, and commercial use, and as such, community noise exposure is increasing. Reducing the noise produced by UAS could help improve community acceptance. Active noise control (ANC) might be used to attenuate noise produced by sUAS, however, traditional ANC systems would require a physical sensor in the far-field, which is not feasible. A virtual error sensor (VES) could eliminate the need for a far-field sensor. This thesis describes the proposed VES strategy, and presents numerical simulations and experimental results that highlight both the benefits and limitations of the approach. Results of the VES system with and without an ANC approach are discussed. Experimental testing focused on attenuating the tonal noise produced by one 2-bladed rotor with a tip radius of 4.7 inches. Pressure variations caused by the blade rotation were measured in the near and far-field using electret microphones and externally polarized condenser microphones, respectively. The ANC system used the filtered-x least mean squares algorithm in conjunction with the VES system to estimate the far-field response. A 2-inch diameter speaker served as the secondary source to provide the appropriate control input to the system. Experimental results show reductions between 6-13 dB at varying far-field locations and rotation rates.

La conception des groupes moto-ventilateurs au sein de Valeo Systèmes Thermiques et la prédiction de leurs performances aérauliques reposent majoritairement sur les méthodes de développement virtuel, i.e. la conception assistée par ordinateur et la simulation numérique de la mécanique des fluides. Dans ce cadre, le présent travail propose une méthodologie de prédiction et de minimisation de la composante tonale du bruit d'un groupe moto-ventilateur. L'approche adoptée est hybride et dissocie la génération et la propagation du bruit. La propagation en champ libre est calculée avec une formulation intégrale de l'analogie de Ffowcs-Williams et Hawkings. Dans un premier temps, les termes-sources à la surface du rotor et du stator sont calculés par une simulation numérique instationnaire. La compacité de la pale ainsi que l'influence du maillage acoustique sur la prédiction sont ensuite investiguées. Finalement, les résultats sont comparés aux mesures expérimentales. Dans un deuxième temps, les sources acoustiques à la surface du stator sont calculées avec le modèle de Sears enrichi avec des données extraites d'une simulation stationnaire du rotor complet. Avant de procéder à la prédiction acoustique, l'influence du modèle de turbulence sur les résultats finaux est évaluée à travers une comparaison entre LES et RANS pour l'écoulement autour de profils extrudés. Enfin, la problématique de minimisation du bruit tonal est traitée en tant que problème d'optimisation où la géométrie d'une aube est paramétrée et où la recherche de l'optimum est conduite par un algorithme génétique. Cette optimisation a permis de concevoir un stator moins bruyant et adapté à l'écoulement en aval du rotor étudié. / The design of fan systems at Valeo Thermal Systems and the prediction of their aerodynamic performances rely mainly on virtual development methods, i.e. computer-aided-design and computational fluid dynamics. Within this context, this dissertation develops a methodology for predicting and minimizing the tonal noise of a fan system. The hybrid approach is used, thus separating noise generation and propagation. The free-field propagation is computed via an integral formulation of the Ffowcs-Williams and Hawkings analogy. In a first step, the source terms located at the surfaces of the rotor and the stator are extracted from an unsteady numerical simulation. The compactness of the blade and the influence of the acoustic mesh on the prediction are then investigated. Finally, the computational results are compared to the experimental ones. In a second step, the acoustic sources at the surface of the stator are computed with Sears' model. Its inputs are extracted from a steady simulation of the whole rotor. Before proceeding to the acoustic prediction, the influence of the turbulence model on the final results is assessed via a comparison between LES and RANS simulations of the flow around airfoils. Finally, minimizing tonal noise is formulated as an optimization problem. The shape of a stator-blade is parametrized and the optimization is conducted with a genetic algorithm. The resulting stator is less noisy and adapted to the flow downstream of the studied rotor.

Résumé : La réduction du bruit tonal des ventilateurs basse vitesse est un défi très important pour l’industrie. Lorsqu’il émerge du bruit large bande, ce rayonnement est la source de gênes auprès de la population, que ce soit pour de petits ventilateurs d’ordinateurs ou de gros ventilateur miniers. Afin de contrôler le bruit tonal, de nombreuses techniques ont été développées au fil de ces dernières décennies. Une méthode alliant simplicité et efficacité se démarque néanmoins : le contrôle par obstruction de l’écoulement. Malgré les études menées jusqu’alors, les mécanismes aéroacoustiques de réduction du bruit associés à cette méthode restent mal compris. Pour répondre à cette problématique, ce projet de Doctorat s’intéresse à l’étude de l’intéraction entre l’obstruction et le ventilateur au moyen de simulations aéro-acoustiques. De plus, une méthodologie numérique de design de l’obstruction est proposée afin de réduire les coûts associés aux multiples test expérimentaux. / Abstract : Tonal noise radiated by low-speed fans is a prime challenge for many industries. When this component emerges from the broadband noise, the acoustic radiation is particularly harsh for the human ear, whether it comes from a small computer cooling fan or from a large mine ventilation fan. Several methods have been developed over the last decades to control tonal noise. Nevertheless, one simple and efficient technique stands out: the adaptive passive control with flow obstruction. Despite all the research conducted on this method, the aeroacoustic mechanisms responsible for the noise reduction are not fully understood. Therefore, the present thesis aims at investing the obstruction-fan interaction using aeroacoustic simulations. Moreover, a numerical design methodology is proposed to reduce the cost induced by extensive experimental tests.

This work provides an experimental analysis of the acoustic footprint of a hexacopter in hover and low speed forward flight, comparison of aerodynamic performance and noise of eVTOL rotors operating in multiple facilities, and analysis of the noise associated with an outrunner brushless DC motor. Empirical and low-order models are used to predict aerodynamic performance, tonal noise, and broadband noise for isolated eVTOL rotors. In addition, a low noise, swept rotor design was evaluated. The acoustic footprint of a DJI Matrice 600 Pro hexacopter in hover and low speed forward flight was measured in the Virginia Tech Drone Park. The noise radiated by this vehicle was found to be dominated by tonal noise at low frequencies and dominated by broadband noise at high frequencies indicating that both are important when assessing the noise of these aircraft. Three distinct regions were observed in the frequency spectra of the noise. A-weighting measured acoustic spectra highlighted the importance of the mid-frequency broadband noise, in particular. The radiated noise in hover was also found to be similar to the noise of the vehicle during low-speed flyovers. Given this, significantly less complex measurements of an aircraft in hover or those associated with a rotor at static conditions may be used to assess the footprint of an eVTOL aircraft in low speed forward flight. The total vehicle noise was then decomposed by studying the performance and noise of isolated eVTOL rotors in multiple facilities and under different operating conditions. Facility effects on performance and noise were first assessed by experimentally studying two commercially available eVTOL rotors in an enclosed anechoic environment and an open environment. For experimental measurements that were conducted in the anechoic chamber, recirculation effects were shown to increase harmonic amplitudes more than 8 dB. Varying solidity screens were placed in the downstream wake of each rotor to delay the onset of recirculation. Placing the screens in the wake did not produce a noticeable effect on or delay recirculation within the confined testing environment. Measurements of the BPF and higher order harmonics of each rotor were found to be much more consistent in time when testing outdoors in an open-air environment. Amplitudes of these tones were also found to be like that of the spectral levels of the measurements conducted in the anechoic chamber once recirculation had been established. While the tonal levels were much more consistent throughout each measurement in the open-air environment, a significant amount of background noise was present and made characterizing the noise at low frequencies difficult. Environmental factors, mainly windspeed, were also found to impact the noise measurements which also added difficulty in characterizing the noise of the two tested rotors. In indoor facilities, the rotor inflow becomes contaminated due to recirculation shortly after the rotor reaches steady state and spectral levels of tones increased with increasing spectral averaging times. In outdoor environments, the inflow to the rotor disc becomes distorted due to changing wind conditions and turbulence in the atmosphere. Spectral levels of tones in the outdoor environment remained consistent in amplitude but exceeded those of the anechoic chamber significantly. Given this, environmental factors and recirculation were found to both increase the higher order harmonics. To mitigate these facility effects, measurements of force and noise were also conducted for the same two rotors in an anechoic open jet. Additionally, measurements were also conducted for a commercially available rotor along with a newly designed low noise swept rotor. Each of these rotors were tested in the anechoic open jet facility at static conditions and with the tunnel on. These measurements were accompanied with predictions of aerodynamic performance and tonal and broadband self-noise. BEMT was used to predict aerodynamic performance. Tonal noise associated with the rotor blade loading and thickness was predicted using F1A and rotor broadband self-noise was predicted using the model of BPM. The measured noise in this facility along with that from measurements in the anechoic chamber and outdoor environment were separated into tonal and broadband components by applying a phase averaging technique to the measured acoustic pressure time history. These results also show that in the indoor facility that the noise produced at the BPF is dominated by tonal sources, but the higher order harmonics can be attributed to broadband interactions particularly at static conditions. Broadband noise was drastically reduced by driving the tunnel at minimal inflow for the smallest rotor studied (R_tip= 120 mm). For the larger rotors (R_tip≥ 267 mm) broadband noise associated with BWI or TIN were not mitigated at low inflow speeds. Predictions of tonal noise at the BPF were within 3 dB for all observer locations when considering the smallest rotor studied. Predictions of the measured directivity at the BPF for the larger rotors were inaccurate although predictions of thrust agreed with the measured. The largest rotors tested were equal in diameter to that of the open jet inlet. Thus, the limits of the testing facility were exceeded and increased noise was produced as the rotor blades interacted with the shear layer of the open jet. Directivity patterns of each rotor were also found to vary with increasing rotational rate. Overall, these results show that for analyzing the noise at hover conditions, introducing a small amount of inflow may be a good option when trying to understand the tonal noise and allows one to characterize the tonal noise independent of the broadband. However, this was also shown to be heavily dependent on the rotor diameter with regards to the open jet inlet and experimentalist must take this into consideration. While these measurements provide an analysis of the noise in hover and low speed ascent, they do not assess the noise of the vehicle operating in forward flight. In forward flight the rotors are subjected to edgewise flows which have an effect on the radiated noise thus analyzing the noise of these rotors operating at an angle of attack to the incoming flow was assessed. These effects were investigated by experimentally measuring the performance and noise of the smallest rotor studied when operating at a yaw relative to the incoming flow. For increasing yaw at the examined wind tunnel velocities, the measured thrust was found to converge to the value for zero inflow. Contours of SPL as a function of yaw angle for no inflow and an inflow speed of 8 m/s showed spectral levels to be minimal for an in-plane observer from 5×BPF to 30×BPF. The broadband noise was found to increase significantly for increasing yaw angle and tunnel inflow speed. These results show once again that the broadband noise is especially important during forward flight and new methods that consider wake interaction are needed to predict the noise in this flight regime. The rotor geometric parameter of sweep was also assessed from measurements in the anechoic open jet by comparing the aerodynamic performance and noise of a commercially available 762 mm diameter CF30x10.5 T-motor eVTOL rotor to that of an in house designed low noise swept rotor. The addition of sweep was found to reduce noise associated with BWI or TIN as the separated broadband noise was found to be less than that of the commercially available rotor. Comparison of thrust at static conditions and with increasing advance ratios showed both rotors to have similar performance, thus the addition of sweep was effective at reducing noise without sacrificing performance. Lastly, the noise associated with the electric drive system of these aircraft which consists of an ESC and brushless DC motor was analyzed. Acoustic measurements were made with and without an acoustic enclosure installed on a brushless DC motor and was found to be effective at reducing noise associated with the electric motor. The effects of two ESC's as well as their switching rates were also studied. The noise was found to be similar for both ESCs at low frequencies. At high frequencies the measured noise spectrum was found to be different when controlling the motor with different ESC's and a higher switching rate was found to reduce the noise with increasing switching rate although not completely monotonically. / Doctor of Philosophy / A new class of multi-rotor VTOL electric aircraft is becoming a dominant advanced vehicle concept. Urban Air Mobility (UAM) vehicles are designed for short routes within urban environments carrying only a few passengers during each flight. Other smaller Unmanned Aerial Systems (UAS) are increasingly being used for delivery services or to perform tasks which are more easily accessed with this technology like inspection or photography. Thus, these vehicles are expected to operate in close proximity to the general populace exposing it to aircraft noise which is currently limited to communities surrounding airports. For successful integration into the airspace with minimal community annoyance, the mechanisms responsible for generation of the noise must be understood. Traditionally, for conventional rotorcraft (one main rotor), the tonal noise has been more of a concern than the broadband component. eVTOL vehicles are often equipped with multiple rotors that are lightly loaded and operate at lower tip speeds which can be time varying. Thus, there is an increased significance of broadband noise. Lastly, these aircraft are equipped with an electric drive system that gives rise to an additional noise source that is not present for conventional aircraft. Best practices for measuring eVTOL noise are not currently established. Measurement of eVTOL rotor noise is complicated by the increased significance of the broadband sources. These have been shown to be facility dependent. Given this, there is a need for high quality experimental data and an analysis of experimental data in multiple facilities for these rotors and drive systems. Capabilities of traditional models to predict conventional rotorcraft noise also need to be assessed for these rotors. These two issues have been assessed in this work by first assessing the character of an eVTOL aircraft in hover and low speed flyovers. Both tonal and broadband components of the radiated noise were found to be significant. A-weighting, which is a metric used to assess the response of the human ear to the radiated noise showed increased significance of the broadband noise. This was followed by a characterization of the noise of isolated eVTOL rotors in multiple environments. Facility effects were addressed, and a low order prediction model was developed using methods that are traditionally used to predict noise associated with conventional rotorcraft. Lastly, the noise associated with the electric drive system of these vehicles was assessed and recommendations on how to reduce this source of noise were made. These results can be used to guide experimentalists when performing measurements of eVTOL rotor noise at static conditions and provide an eVTOL rotor noise data set that can be used to validate existing and forthcoming aerodynamic and acoustic prediction methods.

Le bruit tonal d’interaction rotor-stator, généré par l’impact des sillages issus des pales d’un rotorsur la grille d’aubes d’un stator redresseur, contribue de manière déterminante au bruit d’origineaérodynamique des turbomachines axiales carénées, qui équipent une large part des systèmes de propulsionaéronautique et de conditionnement d’air. La prédiction du bruit par l’utilisation de simulationsnumériques demeure onéreuse, notamment dans les premières phases de conception lorsque de nombreusesconfigurations doivent être testées. Dans cette optique, l’approche analytique choisie dans cettethèse apporte une alternative tout à fait appropriée. Les modèles analytiques basés sur une fonctionde réponse aéroacoustique de profil isolé ne permettent pas de reproduire l’effet de grille engendrépar le nombre important d’aubes de stator. Inversement, de fortes approximations sont nécessairespour décliner les fonctions de réponse de grilles d’aubes existantes dans des configurations tridimensionnelles.Le formalisme proposé, basé sur la méthode de raccordement modal, permet d’introduiresimplement l’effet de grille dans une géométrie annulaire d’étage rotor-stator. Un modèle de réponse degrille rectilinéaire bidimensionnel est tout d’abord présenté pour la transmission d’ondes acoustiques àtravers le stator ainsi que pour la génération de bruit par l’impact de rafales hydrodynamiques. Dansce cadre, une analyse linéaire et non visqueuse est considérée, pour laquelle les modes acoustique ettourbillonnaire d’un gaz sont couplés par le biais des frontières rigides. Les perturbations de vitessesliées aux sillages sont modélisées comme des rafales convectées. Leur impact sur la grille de statorgénère des ondes acoustiques se propageant en amont, en aval ainsi que dans les espaces inter-aubesdu stator, vu comme un réseau périodique de guides d’ondes. Les sections de bords d’attaque et defuite des aubes sont considérées comme des interfaces sur lesquelles la continuité des fluctuations depression, de vitesse axiale et de vorticité est vérifiée. Un système d’équations est ainsi obtenu, puisrésolu par des projections sur les bases modales du conduit et des inversions matricielles. Le champacoustique rayonné est ainsi déterminé uniformément dans tout le domaine. Les résultats issus de cesmodélisations sont comparés à ceux des fonctions de réponse de grilles d’aubes rectilinéaires issues dela littérature, montrant un très bon accord avec les modèles basés sur la technique de Wiener-Hopf. Leformalisme est par la suite étendu aux grilles annulaires par l’ajout de fonctions de Bessel comme fonctionsde forme radiale exprimant les effets tridimensionnels. Finalement, une procédure est présentéepour rendre compte de l’hétérogénéité des aubes de stator, caractéristique des nouvelles architecturesde turbomachines. Cette méthodologie est basée sur l’emploi conjoint du principe du dipôle de bordd’attaque et de la fonction de réponse aéracoustique de la grille de stator à l’aide de la technique deraccordement modal. Le principe de dipôle de bord identifie le chargement instationnaire des aubesinduit par l’impact de rafales hydrodynamiques, calculé par le formalisme d’Amiet, avec la trace duchamp de pression acoustique produit par un dipôle placé au voisinage du bord de l’aube. Les prédictionsissues de ce modèle, appliqué dans un cadre bidimensionnel, sont ensuite comparées à des mesuresobtenues pendant la campagne d’essais du projet SEMAFOR. / The rotor-stator wake-interaction tonal noise, generated by the impingement of rotor wakes onoutlet guide vanes, plays a crucial role in the aerodynamic noise of axial-flow ducted fan stages. Thelatter are widely used in most aeronautic propulsion and air-conditioning systems. The noise predictionby means of numerical simulations remains expensive, especially at the preliminary design stage whennumerous configurations must be tested. In this respect, the analytical approach chosen in this thesisprovides a well suited alternative. The analytical modeling based on an isolated-airfoil response functioncan not reproduce the cascade effect introduced by the large number of stator vanes. Conversely, drasticapproximations are required to extend the current cascade response functions to three-dimensionalconfigurations. The proposed modeling based on the mode-matching technique simply introduces thecascade effect in an annular rotor-stator stage. A rectilinear cascade response function is firstly presentedto account for the acoustic transmission through the stator along with the wake-interaction noise.In this context, a linearized and non-viscous analysis is carried out, in which the acoustic and vorticalmodes of a gas are coupled at rigid physical boundaries. The velocity perturbations issued from thewakes are written as a sum of convected gusts. Their impingement on the cascade of vanes generatesacoustic waves propagating upstream, downstream of the cascade, as well as inside the inter-vane channelsof the stator, seen as a periodic array of bifurcated waveguides. The duct cross sections at theleading-edge and the trailing-edge of the vanes are seen as interfaces on which the continuity of thefluctuating pressure, axial velocity and vorticity is fulfilled. A system of linear equations is obtained,then solved by means of modal projections and matrix inversions. The acoustic field is then uniformlycalculated in the whole domain. Comparisons with rectilinear cascade response functions show a verygood agreement with predictions based on the Wiener-Hopf technique. The configuration of an annularcascade is addressed by introducing the Bessel functions as radial shape functions, expressing threedimensionaleffects. Finally, a procedure is presented to account for the heterogeneity of the statorvanes, typical of modern fan architectures. This approach is based on the combinaison of the leadingedgedipole principle and the cascade response function derived from the mode-matching technique.The edge-dipole principle identifies Amiet’s solution for the unsteady loading and the radiation of adipole approached very close to the edge of a half plane. The predictions provided by this modeling,applied in a two-dimensional configuration, are finaly compared to measurements performed in the testcampaign of the SEMAFOR project.

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.