In this dissertation the influence of vane sweep on rotor-stator interaction noise is investigated. In an analytical approach, the interaction of a convected gust, representing the rotor viscous wake, with a cascade of finite span swept airfoils, representing the stator, is analyzed. The analysis is based on the solution of the exact linearized equations of motion. High-frequency convected gusts for which noise generation is concentrated near the leading edge of the airfoils are considered. In a preliminary study, the problem of an isolated finite span swept airfoil interacting with a convected gust is analyzed. Using Fourier transform methods and the Wiener-Hopf technique, an approximate solution for this problem is developed. Closed form expressions for the acoustic farfield are obtained and used in a parametric study to assess the effect of airfoil sweep on noise generation. Results indicate that sweep can substantially reduce the farfield noise levels for a single airfoil. Utilizing the single airfoil model, an approximate solution to the problem of noise radiation from a cascade of finite span swept airfoils interacting with a convected gust is derived. Only upstream radiated noise is considered. Neglecting the weak coupling between the adjacent leading edges at high frequencies, the cascade solution is constructed as a superposition of acoustic farfields emanating from an infinite number of isolated airfoils. A parametric study of noise generated by gust-cascade interaction is then carried out to assess the effectiveness of vane sweep in reducing rotor-stator interaction noise. The results of the parametric study show that, over a fairly wide range of conditions, sweep is beneficial in reducing noise levels. One conclusion of particular importance is that rotor wake twist or circumferential lean substantially influences the effectiveness of vane sweep. The orientation of the vane sweep must be chosen to enhance the natural phase lag caused by wake lean, in which case rather small sweep angles substantially reduce the noise levels.

An array of small, lightweight acoustic sources was investigated to determine how such an arrangement of sources would acoustically interact with a duct similar to that of a turbofan engine inlet. The sources were cylindrically curved aluminum panels excited in vibration by the application of a sinusoidally varying voltage to a piezoceramic actuator bonded to them. The finite element method was used as a design tool to size the panel based on desired vibration characteristics. A boundary element acoustic analysis was used to predict the acoustic output from various arrangements of sources. The central portion of the research was a series of experiments using an array of twelve sources arranged circumferentially in a duct. Measurements of the performance of each source revealed that the performance of the acoustic sources varied from source to source. This variation was assumed to have been caused by differences in the quality of the bond of each of the piezoceramic actuators to the panels. Directivity measurements were made in the far field. Measurements were also taken of the pressure field established in the duct cross-section. Modal decomposition was applied to the data. It was found that the dominant acoustic modes in the duct are those whose cut-on frequencies were near the frequency of excitation. / Master of Science

Résumé:<p><p>Cette dissertation s’intéresse aux méthodes numériques dans le domaine de l’acoustique. Les propriétés acoustiques d’un produit sont devenues une part intégrante de la conception. En effet, de nos jours le bruit est perçu comme une nuisance par le consommateur et constitue un critère de vente. Il y a de plus des normes à respecter. Les méthodes numériques permettent de prédire la propagation sonore et constitue dès lors un outil de conception incontournable pour réduire le temps et les coûts de développement d’un produit.<p><p>Cette dissertation considère la propagation d’ondes acoustiques dans le domaine fréquentiel en tenant compte de la présence d’un écoulement. Nous pouvons citer comme application industrielle, le rayonnement d’une nacelle de réacteur d’avion. Le but de la thèse est de proposer une nouvelle méthode et démontrer ses performances par rapport aux méthodes actuellement utilisées (i.e. la méthode des éléments finis).<p><p>L’originalité du travail consiste à étendre la méthode de partition de l’unité polynomiale dans le cadre de la propagation acoustique convectée, pour des domaines extérieurs. La simulation acoustique dans des domaines de dimensions infinies est réalisée dans ce travail à l’aide d’un couplage entre éléments finis et éléments infinis.<p><p>La dissertation présente la formulation de la méthode pour des applications axisymétriques et tridimensionnelles et vérifie la méthode en comparant les résultats numériques obtenus avec des solutions analytiques pour des applications académiques (i.e. propagation dans un conduit, rayonnement d’un multipole, bruit émis par la vibration d’un piston rigide, etc.). Les performances de la méthode sont ensuite analysées. Des courbes de convergences illustrent à une fréquence donnée, la précision de la méthode en fonction du nombre d’inconnues. Tandis que des courbes de performances présentent le temps de calcul nécessaire pour obtenir une solution d’une précision donnée en fonction de la fréquence d’excitation. Ces études de performances montrent l’intérêt de la méthode présentée.<p><p>Le rayonnement d’un réacteur d’avion a été abordé dans le but de vérifier la méthode sur une application de type industriel. Les résultats illustrent la propagation pour une nacelle axisymétrique en tenant compte de l’écoulement et la présence de matériau absorbant dans la nacelle et compare les résultats obtenus avec la méthode proposée et ceux obtenus avec la méthode des éléments finis.<p><p>Les performances de la méthode de la partition de l’unité dans le cadre de la propagation convectée en domaines infinis sont présentées pour des applications académiques et de type industriel. Le travail effectué illustre l’intérêt d’utiliser des fonctions polynomiales d’ordre élevé ainsi que les avantages à enrichir l’approximation localement afin d’améliorer la solution sans devoir créer un maillage plus fin.<p><p><p>Summary:<p><p>Environmental considerations are important in the design of many engineering systems and components. In particular, the environmental impact of noise is important over a very broad range of engineering applications and is increasingly perceived and regulated as an issue of occupational safety or health, or more simply as a public nuisance. The acoustic quality is then considered as a criterion in the product design process. Numerical prediction techniques allow to simulate vibro-acoustic responses. The use of such techniques reduces the development time and cost.<p><p>This dissertation focuses on acoustic convected radiation in outer domains such as it is the case for turbofan radiation. In the current thesis the mapped infinite partition of unity method is implemented within a coupled finite and infinite element model. This method allows to enrich the approximation with polynomial functions. <p><p>We present axisymmetric and three-dimensional formulations, verify and analyse the performance of the method. The verification compares computed results with the proposed method and analytical solutions for academic applications (i.e. duct propagation, multipole radiation, noise radiated by a vibrating rigid piston, etc.) .Performance analyses are performed with convergence curves plotting, for a given frequency, the accuracy of the computed solution with respect to the number of degrees of freedom or with performance curves, plotting the CPU time required to solve the application within a given accuracy, with respect to the excitation frequency. These performance analyses illustrate the interest of the mapped infinite partition of unity method.<p><p>We compute the radiation of an axisymmetric turbofan (convected radiation and acoustic treatments). The aim is to verify the method on an industrial application. We illustrate the radiation and compare the mapped infinite partition of unity results with finite element computations.<p><p>The dissertation presents the mapped partition of unity method as a computationally efficient method and illustrates its performances for academic as well as industrial applications. We suggest to use the method with high order polynomials and take the advantage of the method which allows to locally enrich the approximation. This last point improves the accuracy of the solution and prevent from creating a finer mesh.<p> / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished