The scattering of waves by a finite thin plate in a two-dimensional wave guide and an array of finite thin plates, in the presence of subsonic mean flow, are formulated using a mode matching technique. The influence of mean flow on trapped modes in the vicinity of a finite thin plate in a two-dimensional wave guide is then investigated by putting the amplitude of the forcing term to zero in the scattering problem. The conditions for complex resonances are found, and numerical results are computed. The influence of mean flow on Rayleigh-Bloch modes is investigated by using a similar methodology. The condition for embedded trapped modes to exist is introduced next, and then numerical results for embedded trapped modes without mean flow are presented. Complex resonances without mean flow are then found by fixing the geometry of the waveguide. The influence of mean flow on complex resonances and embedded trapped modes is investigated subsequently. In addition, the investigation of scattering coefficients is discussed when the frequency of an incident wave is near the real part of the frequency of complex resonances or embedded trapped modes. Embedded trapped modes near an indentation in a strip wave guide, which may correspond to a two-dimensional acoustic wave guide or a channel of uniform water depth in water waves, are also found. Modes are sought which are either symmetric or anti-symmetric about the centreline of the guide and the centre of the indentation. In each case, a simple approximate solution is found numerically. Full solutions are then found by using a Galerkin approach in which the singularity near the indentation edge is modelled by choosing proper special functions. The final part of the thesis is devoted to spinning modes (Rayleigh-Bloch modes) in a cylindrical waveguide in the presence of radial fins. A mode matching technique is used to obtain the potential, and the coefficients in the expansion are found numerically by using an efficient Galerkin procedure. In addition, an existence proof for modes symmetric about the centre of the guide and the centre of the section with radial fins is given by applying a variational approach. The connection between Rayleigh-Bloch modes and trapped modes is discussed thereafter, and numerical results for a number of geometric configurations are presented.

The excitation mechanism of trapped diametral acoustic modes within a rectangular cavity-duct system is investigated both numerically and experimentally. The asymmetry inherent within the rectangular geometry introduces a preferred orientation, ensuring the excited diametral modes remain stationary. Three separate cavities are manufactured and tested. This included two asymmetric rectangular cross-sections and one symmetric square cavity. Experimental results indicate that the aeroacoustic responses of the three cavities are dominated by the strong excitation of trapped diametral modes. Numerical simulations indicate that the resolved radial acoustic particle velocity distributions are non-uniform at the upstream separation edge where the formation of vortical structures is initiated. As the cavity became smaller, and more asymmetric, the trapped nature of the acoustic modes decreased with an accompanied increase in the radiation losses and reduction in pulsation amplitude. Observations of the aeroacoustic measurements show evidence of three unique modal behaviours. The first case is the independent excitation of a single stationary mode where specific circumferential sections of the shear layer were excited and initiating the formation of vortical disturbances. These circumferential sections, and distribution of disturbances, were akin to the excited mode shape. The second case involved simultaneous excitation of two stationary modes. This suggested that the shear layer was exciting two modes simultaneously. Neighbouring circumferential sections, at the initial region of the shear layer, were being excited independently and at different resonant frequencies. Finally, a spinning trapped acoustic mode was observed in the symmetric square cavity. Due to the spinning nature, the excited circumferential portions and formation of vortices were non-uniform and rotated with the spinning acoustic mode. This resulted in the formation of a three-dimensional helical structure. / Thesis / Master of Applied Science (MASc)

La première partie concerne les interactions acoustique-vorticité dans les écoulements cisaillés linéaires incompressibles, qui peuvent être décomposés en la somme d’une partie hyperbolique et d’une partie rotation solide. L’écoulement de Couette en est un exemple. En utilisant la démarche non-modale , les équations d’évolution de perturbations compressibles se réduisent à une EDO de dimension trois en temps, qui dépend d’un paramètre adimensionné ε représentant le rapport entre le taux de cisaillement de l’écoulement et la fréquence des perturbations. Pour ε faible, la méthode WKB permet d’exhiber naturellement trois modes (deux modes acoustiques et un mode de vorticité) et permet de mettre en évidence des couplages entre ces modes. Ces couplages sont exponentiellement faible en 1/ε, et ne peuvent être pris en compte par une méthode asymptotique. Ils semblent être liés à la partie hyperbolique de l’écoulement. La seconde partie traite de la réflexion d'une onde par une surface de géométrie complexe. Une transformation conforme permet de transformer une frontière complexe en une frontière plane, mais fait apparaître des coefficients non constants dans les équations en volume. Celles-ci sont résolues au moyen de la méthode de la matrice d’impédance multimodale qui ramène le problème à une équation de Riccati pour la matrice d’impédance. Une méthode pour trouver des géométries admettant des modes piégés est proposée. Puis la méthode de résolution est appliquée à la modélisation de la couche limite visqueuse d’un fluide oscillant au contact d’une surface complexe périodique. Une solution perturbative est proposée. La présence de zones de recirculation est étudiée. / The first part is a study of the interactions between acoustic and vorticity perturbations in linear incompressible shear flows, which can decomposed as a sum of a hyperbolic part and of a rigid rotation part. The plane Couette flow is an example of such flows. By using the non-modal approach, the equations governing the evolution of compressible perturbations reduce to an ODE of dimension three in time, which depends on a dimensionless parameter ε representing the ratio between the shear rate of the flow and the frequency of the perturbations. For small ε values, the WKB method allows us to exhibit naturally three modes (two acoustic modes and one vorticity mode) and to highlight couplings between these modes. These couplings are exponentially small in 1/ε, and cannot be taken into account by an asymptotic method. They seem to be linked to the hyperbolic part of the flow.The second part deals with the reflection of a wave by a geometrically complex surface. A conformal mapping allows us to transform a complex boundary into a plane boundary, but makes appear varying coefficients in the bulk equations. These equations are then solved with the multimodal impedance matrix method, which reduce the problem to a Riccati equation for the impedance matrix. A method to find geometries allowing for the existence of trapped modes is proposed. Then the solving method is applied to the modeling of the viscous boundary layer of a fluid oscillating near a periodical rough surface. A perturbative solution is proposed. The presence of recirculation areas is studied.

<p>This thesis investigates the effect of different passive suppression techniques of different configurations on the flow-excited acoustic resonance of an internal axisymmetric cavity. This type of acoustic resonance is observed in many practical applications such as valves installed in steam pipe lines, and gas transport system. An experimental setup of a cavity-duct system has been altered to facilitate the study of the suppression and/or delay of resonance over the range of Mach number of 0.07-0.4. Three different cavity depths have been studied d=12.5 mm, 25 mm, and 50 mm deep. For each depth, the cavity length is changed from L=25 mm to 50 mm. The investigation matrix includes the study of two rounding radii, two chamfer geometries and three different types of spoilers, all located at the leading edge of the cavity. A reference case of no suppression seat installed for each of the examined cavity geometries is tested. Rounding off cavity edges for both radii has increased the acoustic pressure level, yet delayed the onset of resonance. Chamfering the upstream edge of the cavity delayed the onset of resonance as a result of increasing the cavity characteristic length which delays the coupling of the shear layer perturbations and the acoustic field. The delay and the suppression of resonance achieved by the chamfer depend on the size of the cavity. All spoiler configurations have proven effectiveness in delaying and suppressing resonance for all cavities. The choice of spoiler configuration would depend on cavity size and robustness/strength of acoustic resonance.</p> / Master of Science (MSc)

Sensitive nonlinear acoustic methods are suitable for material characterization. This thesis describes three nonlinear acoustic methods that are proven useful for detection of defects like cracks and delaminations in solids. They offer the possibility to use relatively low frequencies which is advantageous because attenuation and diffraction effects are smaller for low frequencies. Therefore large and multi-layered complete objects can be investigated in about one second. Sometimes the position of the damage is required. But it is in general difficult to limit the geometrical extent of low-frequency acoustic waves. A technique is presented that constrains the wave field to a localized trapped mode so that damage can be located.