This thesis describes the development, verification, and validation of a three dimensional time domain thermoacoustic solver. The purpose of the solver is to predict the frequencies, modeshapes, linear growth rates, and limit cycle amplitudes for combustion instability modes in gas turbine combustion chambers. The linearized Euler equations with nonlinear heat release source terms are solved using the finite volume method. The treatment of mean density gradients was found to be vital to the success of frequency and modeshape predictions due to the sharp density gradients that occur across deflagration waves. In order to treat mean density gradients with physical fidelity, a non-conservative finite volume method based on the wave propagation approach to the Riemann problem is applied. For modelling unsteady heat release, user input flexibility is maximized using a virtual class hierarchy within the OpenFOAM C++ library. Unsteady heat release based on time lag models are demonstrated. The solver gives accurate solutions compared with analytical methods for one-dimensional cases involving mean density gradients, cross-sectional area changes, uniform mean flow, arbitrary impedance boundary conditions, and unsteady heat release in a one-dimensional Rijke tube. The solver predicted resonant frequencies within 1% of the analytical solution for these verification cases, with the dominant component of the error coming from the finite time interval over which the simulation is performed. The linear iii growth rates predicted by the solver for the Rijke tube verification were within 5% of the theoretical values, provided that numerical dissipation effects were controlled. Finally, the solver is then used to predict the frequencies and limit cycle amplitudes for two lab scale experiments in which detailed acoustics data are available for comparison. For experiments at the University of Melbourne, an empirical flame describing function was provided. The present simulation code predicted a limit cycle of 0.21 times the mean pressure, which was in close agreement with the estimate of 0.25 from the experimental data. The experiments at Purdue University do not yet have an empirical flame model, so a general vortex-shedding model is proposed on physical grounds. It is shown that the coefficients of the model can be tuned to match the limit cycle amplitude of the 2L mode from the experiment with the same accuracy as the Melbourne case. The code did not predict the excitation of the 4L mode, therefore it is concluded that the vortex-shedding model is not sufficient and must be supplemented with additional heat release models to capture the entirety of the physics for this experiment.

One dimensional, linear, plane-wave modelling of silencer systems in the frequency domain provides an efficient means to analyse their acoustic performance. Software packages are available to analyse silencers within these modelling parameters; however, they are heavily restricted. The thesis develops an algorithm that increases the computational efficiency of the silencer analysis. The thesis concentrates on how data, within a software package, is stored, retrieved and analysed. The computational efficiency is increased as a result of the predictable patterns caused by the repetitive nature of exhaust system analysis. The work uses the knowledge gained from the construction of two previous algorithms of similar parameters; it isolates and maximises their advantages whilst minimising their associated disadvantages. The new algorithm is dependent on identifying consecutively sequenced exhaust components and sub-systems of such components within the whole exhaust system. The algorithm is further generalised to include multiple time-variant sources, multiple radiation points and exhaust systems that have a balance pipe. Another feature of the improved algorithm encompasses the option of modelling secondary noise sources such as might arise from flow generated noise or be included for active noise cancellation systems. The validation of these algorithmic techniques is demonstrated by comparison of the theoretical noise predictions with experimental or known results. These predictions are achieved by writing computational code using object orientated programming techniques in the language of c++ to implement the algorithms.

In this work we study vertical, acoustic propagation in a non-homogeneous media for a spatially-compact, time-harmonic source. An analytical, 2-layer model is developed representing the acoustic pressure disturbance propagating in the atmosphere. The validity of the model spans the distance from the Earth's surface to 30,000 meters. This includes the troposphere (adiabatic), ozone layer (isothermal), and part of the stratosphere (isothermal). The results of the model derivation in the adiabatic region yield pressure solutions as Bessel functions of the First (J) and Second (Y) Kind of order $-\frac{7}{2}$ with an argument of $2 \Omega \tau$ (where $\Omega$ represents a dimensionless frequency and $\tau$ is a dimensionless vertical height in z (vertical coordinate)). For an added second layer (isothermal region), the pressure solution is a decaying sinusoidal, exponential function above the first layer. In particular, the vertical, acoustic propagation is examined for various configurations. These are divided into 2 basic classes. The first class consists of examining the pressure response function when the source is located on boundary interfaces, while the second class consists of situations where the source is arbitrarily located within a finite layer. In all instances, a time-harmonic, compact source is implicitly understood. However, each class requires a different method of solution. The first class conforms to a general boundary value problem, while the second requires the use of Green's functions method. In investigating problems of the first class, 3 different scenarios are examined. In the first case, we apply our model to a semi-infinite medium with a time-harmonic source ($e^{-i \omega t}$) located on the ground. In the next 2 cases, a semi-infinite medium is overlain on the previous medium at a height of z=13,000 meters. Thus, there exist two boundaries: the ground and the layer interface between the 2 media. Sources placed at these interfaces represent the 2nd and 3rd scenarios, respectively. The solutions to all 3 cases are of the form $A \frac{J_{-\frac{7}{2}}(2 \Omega \tau)}{{\tau}^{-\frac{7}{2}}} + B \frac{Y_{-\frac{7}{2}}(2 \Omega \tau)}{{\tau}^{-\frac{7}{2}}}$, where \textit{A} and \textit{B} are constants determined by the boundary conditions. For the 2nd class, we examine the application to a time-harmonic, compact source placed arbitrarily within the 1st layer. The method of Green's functions is used to obtain a particular solution for the model equations. This result is compared with a Fast Field Program (FFP) which was developed to test these solutions. The results show that the response given by the Green's function compares favorably with that of the FFP. Keywords: Linear Acoustics, Inhomogeneous Medium, Layered Atmosphere, Boundary Value Problem, Green's Function Method

La cristallisation assistée par ultrasons permet de diminuer le temps d'induction et la largeur de la zone métastable, de modifier la distribution de tailles, de modifier le faciès des cristaux et d'augmenter le nombre des cristaux formés. L'origine microscopique de cet effet reste à ce jour non élucidée. Les ultrasons de puissance engendrent dans un liquide la naissance et l'oscillation très violente de milliards de petites bulles de gaz, phénomène appelé cavitation. Le cycle d'une de ces bulles sur une période acoustique consiste en une phase explosive suivie d'une implosion violente. A la fin de l'implosion, la pression peut atteindre 1 GPa. Plusieurs hypothèses sur les mécanismes mis en jeu sont proposées dans la littérature : refroidissement de la solution et augmentation de la pression au voisinage de l'interface, évaporation du solvant dans la bulle, et ségrégation des molécules ou des ions du soluté au voisinage de la bulle lors de la phase implosive. Afin d'examiner l'influence de la pression, des expériences de cristallisation du sulfate de zinc heptahydraté ont été menées (mesure de temps d'induction). Ce sel présente une solubilité indépendante de la pression entre 0 et 10 000 bars. Nos expériences ont montré que le temps d'induction est fortement diminué en présence d'ultrasons. Ce résultat nous permet d'affirmer que la pression au voisinage de la bulle n'entre pas en jeu dans le mécanisme de la nucléation primaire du ZnSO4,7H2O en présence d'ultrasons. Après l'étude de l'effet de la sursaturation, nous avons essayé d'exploré l'effet de la puissance ultrasonore, du gaz dissous et de la hauteur du liquide dans la cuve sur le temps d'induction. Il a été constaté que les ultrasons permettent de diminuer le temps d'induction. Il a été observé que la courbe du temps d'induction en fonction de la hauteur de la solution présente un minimum. Un autre volet de cette thèse réservé à la modélisation et la simulation. Dans un premier temps, la concentration en clusters ou agrégats moléculaires au voisinage de la bulle été calculée dans le cas du ZnSO4,7H2O grâce à la théorie de la ségrégation en fonction de la pression acoustique. La simulation montre qu'il y a une sur-concentration des clusters (jusqu'à 25 fois supérieure à la concentration stationnaire) augmentant ainsi la probabilité de contact des clusters, durant un temps très court, pouvant ainsi modifier le processus global de nucléation. Dans un deuxième temps, la modélisation/simulation de l'acoustique par COMSOL est réalisée en vue de déterminer les résonances de notre système (liquide + parois de la cuve). Les résonances observées sont cohérentes avec les mesures de temps d'induction. / Power ultrasound is known to enhance crystals nucleation, and nucleation times can be reduced by oneup to three orders of magnitude for several organic or inorganic crystals. The precise physics involved in this phenomenon still remains unclear, and various mechanisms involving the action of inertial cavitation bubbles have been proposed. In this paper, two of these mechanisms, pressure and ségrégation effects, are examined. The first one concerns the variations of supersaturation induced by the high pressures appearing in the neighbourhood of a collapsing bubble, and the second one results from the modification of clusters distribution in the vicinity of bubble. Crystallisation experiments were performed on zinc sulphate heptahydrate ZnSO4. 7H2O, which has been chosen for its pressure-independent solubility, so that pressure variations have no effect on supersaturation. As observed in past studies on other species, induction times were found lower under insonification than under silent conditions at low supersaturations, which casts some doubts on a pure pressure effect. The interfacial energy between the solid and the solution was estimated from induction times obtained in silent conditions, and, using classical nucléation theory, the steady-state distribution of the clusters was calculated. Segregation theory was then applied to calculate the over-concentrations of n-sized clusters at the end of the collapse of a 4 lmbubble driven at 20 kHz by different acoustic pressures. The over-concentration of clusters close to the critical size near a collapsing bubble was found to reach more than one order of magnitude, which may favour the direct attachment process between such clusters, and enhance the global nucleation kinetics. The effects of acoustic cavitation on crystallization of ZnSO4. 7H2O was observed in a sono-reactor build-up from a large emitting area transducer located at the bottom of the vessel. The experimental results have shown that the dissipated acoustic power passes through a maximum at about 15±1 cm, and that the induction-time passes through a minimum for the same liquid-level. The dissipated-power and the induction-time are found to be well correlated as the liquid height was varied. The acoustics of the sono-reactor was studied with linear acoustics, accounting for the wall vibrations by using the COMSOL software. Theoretical dissipated acoustic powers were compared to the experimental ones.

La thèse porte sur la simulation, en régime fréquentiel, du rayonnement acoustique en écoulement subsonique quelconque et dans un domaine infini. L'approche choisie s'appuie sur la résolution d'un système équivalent aux équations d'Euler linéarisées : le modèle de Galbrun. Ce modèle repose sur une représentation mixte Lagrange-Euler et aboutit à une équation dont l'unique inconnue est la perturbation du déplacement Lagrangien. Une des difficultés de l'approche de Galbrun est qu'une discrétisation directe de cette équation par une méthode d'éléments finis standard n'est pas stable. Un moyen de contourner cet obstacle est d'écrire une équation augmentée en ajoutant une nouvelle inconnue, le rotationnel du déplacement, appelée par abus vorticité. Cette approche conduit à un système qui couple une équation de type équation des ondes avec une équation de transport en régime fréquentiel. Et elle permet l'utilisation de couches parfaitement adaptées (PML) pour borner le domaine de calcul. La première partie du manuscrit est dédiée à l’étude de l’équation de transport harmonique et de sa résolution numérique, en particulier par un schéma de type Galerkin discontinu. Un des points délicats est lié au caractère oscillant des solutions de l'équation. Une fois cette étape franchie, la résolution du problème de propagation acoustique a été abordée. Une approximation basée sur l'utilisation d'éléments finis mixtes continus-discontinus avec couches parfaitement adaptées (PML) a été étudiée. En particulier, les caractères bien posés des problèmes continu et discret ainsi que la convergence du schéma numérique ont été démontrés sous certaines conditions sur l'écoulement porteur. Enfin, une mise en œuvre a été effectuée. Les résultats montrent la validité de cette approche mais aussi sa pertinence dans le cas d'écoulements complexes, voire d'écoulements dits instables / This thesis deals with the numerical simulation of time harmonic acoustic propagation in an arbitrary mean flow in an unbounded domain. Our approach is based on an equation equivalent to the linearized Euler equations called the Galbrun equation. It is derived from a mixed Eulerian-Lagrangian formulation and results in a single equation whose only unknown is the perturbation of the Lagrangian displacement. A direct solution using finite elements is unstable but this difficulty can be overcome by using an augmented equation which is constructed by adding a new unknown, the vorticity, defined as the curl of the displacement. This leads to a set of equations coupling a wave like equation with a time harmonic transport equation which allows the use of perfectly matched layers (PML) at artificial boundaries to bound the computational domain. The first part of the thesis is a study of the time harmonic transport equation and its approximation by means of a discontinuous Galerkin scheme, the difficulties coming from the oscillating behaviour of its solutions. Once these difficulties have been overcome, it is possible to deal with the resolution of the acoustic propagation problem. The approximation method is based on a mixed continuous-Galerkin and discontinuous-Galerkin finite element scheme. The well-posedness of both the continuous and discrete problems is established and the convergence of the approximation under some mean flow conditions is proved. Finally a numerical implementation is achieved and numerical results are given which confirm the validity of the method and also show that it is relevant in complex cases, even for unstable flows