Les écoulements instationnaires au-dessus de surfaces discontinues produisent d'important bruit aérodynamique. L'objectif de ce travail de thèse est l'étude aéroacoustique d'écoulement au-dessus de cavités bidimensionnelles rectangulaires, et de trouver des stratégies de réduction du bruit. Des simulations numériques directes des équations bidimensionnelles de Navier-Stokes compressibles ont été réalisées afin d'étudier l'influence des conditions initiales sur le mode d'oscillation de l'écoulement pour des cavités profonde et peu profonde. Les résultats montrent que dans le cas de cavités profondes, l'écoulement oscille selon un régime de couche de cisaillement suivant le second mode de Rossiter, et ce quelle que soit la condition initiale choisie. En revanche, dans le cas de cavités peu profondes, le régime d'oscillation observé peut être en couche de cisaillement ou bien en mode de sillage suivant la condition initiale choisie. Une analyse de sensibilité d'écoulement dans le cas de cavités profondes a été réalisé en utilisant une méthode adjointe. Les équations adjointes ont été forcées par une perturbation localisée sinusoïdale soit de la quantité de mouvement suivant x adjointe (au voisinage de la couche de cisaillement), soit de la densité adjointe (loin de la cavité). Les résultats désignent une région de l'écoulement très sensible à l'ajout de masse, et localisée au voisinage du coin supérieur amont de la cavité. Par conséquent, un actionneur de type soufflage/aspiration placé au bord d'attaque de la cavité agira sur les fluctuations de quantité de mouvement suivant x au voisinage de la couche de cisaillement et sur les fluctuations de pression au loin. / The unsteady flow over surface discontinuities produces high aerodynamic noise. The aim of this thesis is to study the aeroacoustics of two-dimensional rectangular cavities and to find strategies for noise reduction. Direct Numerical Simulation of the compressible Navier-Stokes equations is performed to investigate the influence of the initial condition on the oscillation modes in deep and shallow cavities. Results show that the deep cavity oscillates in shear layer regime at the second Rossiter mode regardless of the initial condition. On the other hand different initial conditions lead to a shear layer or wake mode in the shallow cavity case. A sensitivity analysis of the deep cavity is done by the use of adjoint methods. Local sinusoidal perturbations of x-momentum and density are applied to the adjoint equations. The results show a high sensitivity region to mass injection at the upstream corner. Therefore an actuator placed at the leading edge will modify the velocity fluctuations reaching the trailing edge and hence the pressure fluctuations in the far-field.

O método adjunto tem sido extensivamente utilizado como ferramenta de síntese no projeto de aeronaves por permitir que se obtenham sensibilidades de distintas medidas de mérito com relação a parâmetros que controlam a geometria de superfícies aerodinâmicas. O presente trabalho visa uma ampliação das aplicações da formulação contínua do método, ao utilizar propriedades físicas do escoamento nas fronteiras permeáveis do domínio computacional como parâmetros de controle de uma particular medida de mérito. Desse modo é possível, entre muitas possibilidades, determinar a sensibilidade de integrais como sustentação ou arrasto de uma aeronave com relação às condições de cruzeiro, por exemplo. Mais do que isso, essa informação pode ser obtida com a mesma solução adjunta computada para realizar otimização de forma. Vale destacar, ainda, que para que se consiga obter essa informação a partir das equações adjuntas, é necessário que se implemente condições de contorno baseadas em equações diferenciais características, resolvendo o problema de Riemann completo nas fronteiras do domínio. A implementação das usuais condições de contorno homogêneas, vastamente difundidas na literatura, resultaria em gradientes nulos. Esta nova abordagem do método é então aplicada a escoamentos modelados pelas equações de Euler 2-D compressíveis em estado estacionário. Ambos os problemas, físico e adjunto, são resolvidos numericamente com um código computacional que utiliza o método dos volumes finitos com segunda ordem de precisão no espaço e discretização centrada com dissipação artificial. As soluções estacionárias são obtidas ao se postular um termo tempo-dependente e integra-lo com um esquema Runge-Kutta de 5 passos e 2a ordem de precisão. As simulações são realizadas em malhas não-estruturadas formadas por elementos triangulares em 4 geometrias distintas: um bocal divergente, um perfil diamante, um aerofólio simétrico (NACA 0012) e o outro assimétrico (RAE 2822). Os gradientes adjuntos são então validados por meio da comparação com os obtidos pelo método de diferenças finitas nos regimes de escoamento subsônico, supersônico e transônico. / The adjoint method has been extensively used as an aircraft design tool, since it enables one to obtain sensitivities of many different mesures of merit with respect to parameters that control the aerodynamic surface geometry. This works aims to open up the possibilities of the method\'s applications by using flow physical properties at the permeable boundaries of the computational domain as control parameters of a particular measure of merit. This way it is possible, among many possibilities, to compute lift or drag sensitivities of an aircraft with respect to cruise conditions, for instance. Moreover, this information can be obtained with the same adjoint solution used to perform shape optimization. It is also worth noting that in order to obtain this information from the adjoint equations it is necessary to implement characteristics-based boundary conditions, resolving the complete Riemann problem at the boundaries of the computational domain. The use of the traditional homogeneous boundary conditions, widely spread in the literature, would lead the gradient to vanish. This new approach of the method is, then, applied to flows modeled by the 2-D steady state compressible Euler equations. Both, physical and adjoint problems are numerically solved with a computational code that makes use of a 2nd order finite volume method and central differences with artifficial dissipation. The steady solutions are obtained by postulating a time-dependent term and integrating it with a 5-stage 2nd order Runge-Kutta scheme. The simulations are performed on unstructured triangular meshes to 4 different geometries: a divergent nozzle, a diamond profile, a symmetric airfoil (NACA 0012) and a assymmetric airfoil (RAE 2822). The adjoint gradients are then validated by comparison with those obtained by finite differences method in subsonic, supersonic and transonic flow regimes.

After nearly 50 years of development, Computational Fluid Dynamics (CFD) has become an indispensable component of research, forecasting, design, prototyping and testing for a very broad spectrum of fields including geophysics, and most engineering fields (mechanical, aerospace, biomedical, chemical and civil engineering). The fastest and most affordable CFD approach, called Reynolds-Average-Navier-Stokes (RANS) can predict the drag around a car in just a few minutes of simulation. This feat is possible thanks to simplifying assumptions, semi-empirical models and empirical models that render the flow governing equations solvable at low computational costs. The fidelity of RANS model is good to excellent for the prediction of flow rate in pipes or ducts, drag, and lift of solid objects in Newtonian flows (e.g. air, water). RANS solutions for the prediction of scalar (e.g. temperature, pollutants, combustable chemical species) transport do not generally achieve the same level of fidelity. The main culprit is an assumption, called Reynolds analogy, which assumes analogy between the transport of momentum and scalar. This assumption is found to be somewhat valid in simple flows but fails for flows in complex geometries and/or in complex fluids. This research explores optimization methods to improve upon existing RANS models for scalar transport. Using high fidelity direct numerical simulations (numerical solutions in time and space of the exact transport equations), the most common RANS model is a-priori tested and investigated for the transport of temperature (as a passive scalar) in a turbulent channel flow. This one constant model is then modified to improve the prediction of the temperature distribution profile and the wall heat flux. The resulting modifications provide insights in the model’s missing physics and opens new areas of investigation for the improvement of the modeling of turbulent scalar transport.

We study several unbounded operators with view to extending von Neumann's theory of deficiency indices for single Hermitian operators with dense domain in Hilbert space. If the operators are non-commuting, the problems are difficult, but special cases may be understood with the use representation theory. We will further study the partial derivative operators in the coordinate directions on the L2 space on various covering surfaces of the punctured plane. The operators are defined on the common dense domain of C∞ functions with compact support, and they separately are essentially selfadjoint, but the unique selfadjoint extensions will be non-commuting. This problem is of a geometric flavor, and we study an index formulation for its solution. The applications include the study of vector fields, the theory of Dirichlet problems for second order partial differential operators (PDOs), Sturm-Liouville problems, H.Weyl's limit-point/limit-circle theory, Schrödinger equations, and more.

No description available.

Les simulations numériques RANS, utilisées en aérodynamique pour évaluer la performance d'une forme, sont coûteuses en temps de calcul. Comme une optimisation nécessite l'étude de plusieurs dizaines de formes différentes, ce coût limite le champ des problèmes envisageables. <br />Un nouvel optimiseur basé sur des surfaces de réponse construites par une méthode de Krigeage est proposé. A un surcout modéré, la solution obtenue est meilleure. De plus, cet optimiseur semble aussi capable de traiter des problèmes de grande dimension en interpolant le vecteur gradient aux points de construction du Krigeage. <br />En optimisation multidisciplinaire, les surfaces de réponse sont largement employées pour échanger facilement des données entre différentes disciplines. Ainsi, une approche d'optimisation bi-niveau avec couplage fluide/structure par surface de réponse est étudiée. L'application considérée traite de l'intégration d'une installation motrice (positionnement) sur un avion de transport civil.

This thesis deals with receptivity mechanisms of three-dimensional, crossflow-dominated boundary layers. The receptivity of two model problems, a swept-flat-plate and a swept-wing boundary layer, is investigated by solving the parabolised stability equations (PSE) as well as by performing direct numerical simulations (DNS).Both flow cases are known to exhibit strong inflectional instabilities, the crossflow disturbances, whose excitation by external disturbances such as surface roughness or free-stream vorticity is studied. One focus is on worst-case scenarios. This involves the determination of optimal conditions, i.e. those disturbance environments yielding the largest possible response inside the boundary layer. A new method on the basis of the PSE is presented which allows to study optimal disturbances of swept-flat-plate boundary layers. These take the form of tilted streamwise vortices. While convected downstream they develop into streamwise streaks experiencing strong non-modal growth. Eventually, they turn into crossflow disturbances and undergo exponential growth. Non-modal growth is thus found to optimally excite crossflow disturbances and can be related to a receptivity mechanism of three-dimensional boundary layers. Evaluating effects of compressibility reveals that the potential for both non-modal and modal growth increases for higher Mach numbers. It is shown that wall cooling has diverse effects on disturbances of non-modal and modal nature. While destabilising the former it attenuates the growth of modal disturbances. Concave curvature on the other hand is found to be equally destabilising for both types of disturbances. The adjoint of the linearised Navier-Stokes equations is solved for a swept-wing boundary layer by means of DNS. The adjoint solution of a steady crossflow disturbance is computed in the boundary layer as well as in the free-stream upstream of the leading edge. This allows to determine receptivity to incoming free-stream disturbances and surface roughness as well as the corresponding worst-case scenarios. Upstream of a swept wing the optimal initial free-stream disturbance is found to be of streak-type which convects downstream towards the leading edge. It entrains the boundary layer a short distance downstream of the stagnation line. While minor streamwise vorticity is present the streak component is dominant all the way into the boundary layer where the optimal disturbance turns into a crossflow mode. Futher, the worst-case surface roughness is determined. It takes a wavy shape and is distributed in the chordwise direction. It is shown that, under such optimal conditions, the swept-wing boundary layer is more receptive to surface roughness than to free-stream disturbances. Another focus of this work has been the development and evaluation of tools for receptivity prediction. Both DNS and direct and adjoint solutions of the PSE are used to predict the receptivity of a swept-wing boundary layer to localised surface roughness. The configuration conforms to wind tunnel experiments performed by Saric and coworkers at the Arizona State University. Both the DNS and the PSE are found to predict receptivity amplitudes which are in excellent agreement with each other. Though the predicted disturbance amplitudes are slightly lower than experimental measurements the overall agreement with experimental results is very satisfactory. Finally, a DNS of the stabilisation of a transitional swept-wing boundary layer by means of discrete roughness elements is presented. This control approach is found to completely suppress transition to turbulence within the domain studied and confirms experimental results by Saric &amp; coworkers. / QC 20111124

In any research program we begin with a hypothesis and when our expected results do not concur with the observed results we must try and understand the dynamics behind the changed process. In this study we were trying to understand the flux between regional groundwater systems, surface waters and sedimentation processes in order to predict the fate of contaminants entering one of the larger bodies of water in the world- Lake Ontario. This lake has increased levels of tritium due to anthropogenic inputs. Our first approach to the problem was to look at tritium fluxes within the system . Hydrological balances were constructed and a series of sediment cores were taken longitudinally and laterally across the lake. The second approach was to quantify the sediment accumulation rate (SAR) within the depositional basins and zones of erosion in order to improve the linkage between erosion control (sedimentation) and the water quality program. In the last chapter the movement of tritium, by molecular diffusion, through the clayey-silts of Lake Ontario is quantified in terms of an effective diffusion coefficient. In these sediments effective diffusion equals molecular diffusion. In a laboratory experiment four cores of lake sediment were spiked with tritium . The resulting concentration gradient changes in the sediment porewaters after six weeks could be modeled by an analytical one- dimensional diffusive transport equation. Results calculated the average lab diffusion coefficient to be 2. 7 x 10 - 5cm 2. sec -1 which is twice that determined by Wang et al, 1952 but still reasonable. Short cores (50 cm) from lake Ontario had observed tritium concentrations with depth that reflected a variable diffusive profile. The increases and decreases in tritium with depth could be correlated between cores. Monthly tritium emission data was obtained and correlations between peaks in the tritium profile and emissions were observed. Monthly variations in release emissions corresponded to approximately a one centimeter slice of core. An average calculated diffusion coefficient of theses cores was 1. 0 x 10 -5 cm 2. sec -1 which compares to Wang's coefficient of 1. 39 x 10 -5 cm 2. sec -1. This implies that tritium is moving through the sediment column at a rate equal to diffusion. The results were obtained for smoothed values. It was not possible to model the perturbations of the data with a one dimensional model. The dynamics of the system imply that tritium could be used as a biomonitor for reactor emissions, mixing time and current direction scenarios and that a better understanding of this process could be gained by future coring studies and a new hypothesis.

This thesis makes contributions to the solution of Hadamard's problem through an examination of the question of the validity of Huygens'principle for the non-self-adjoint scalar wave equation on a Petrov type D spacetime. The problem is split into five further sub-cases based on the alignment of the Maxwell and Weyl principal spinors of the underlying spacetime. Two of these sub-cases are considered, one of which is proved to be incompatible with Huygens' principle, while for the other, it is shown that Huygens' principle implies that the two principal null congruences of the Weyl tensor are geodesic and shear-free. Furthermore, an unpublished result of McLenaghan regarding symmetric spacetimes of Petrov type D is independently verified. This result suggests the possible existence of counter-examples of the Carminati-McLenaghan conjecture.

In any research program we begin with a hypothesis and when our expected results do not concur with the observed results we must try and understand the dynamics behind the changed process. In this study we were trying to understand the flux between regional groundwater systems, surface waters and sedimentation processes in order to predict the fate of contaminants entering one of the larger bodies of water in the world- Lake Ontario. This lake has increased levels of tritium due to anthropogenic inputs. Our first approach to the problem was to look at tritium fluxes within the system . Hydrological balances were constructed and a series of sediment cores were taken longitudinally and laterally across the lake. The second approach was to quantify the sediment accumulation rate (SAR) within the depositional basins and zones of erosion in order to improve the linkage between erosion control (sedimentation) and the water quality program. In the last chapter the movement of tritium, by molecular diffusion, through the clayey-silts of Lake Ontario is quantified in terms of an effective diffusion coefficient. In these sediments effective diffusion equals molecular diffusion. In a laboratory experiment four cores of lake sediment were spiked with tritium . The resulting concentration gradient changes in the sediment porewaters after six weeks could be modeled by an analytical one- dimensional diffusive transport equation. Results calculated the average lab diffusion coefficient to be 2. 7 x 10 - 5cm 2. sec -1 which is twice that determined by Wang et al, 1952 but still reasonable. Short cores (50 cm) from lake Ontario had observed tritium concentrations with depth that reflected a variable diffusive profile. The increases and decreases in tritium with depth could be correlated between cores. Monthly tritium emission data was obtained and correlations between peaks in the tritium profile and emissions were observed. Monthly variations in release emissions corresponded to approximately a one centimeter slice of core. An average calculated diffusion coefficient of theses cores was 1. 0 x 10 -5 cm 2. sec -1 which compares to Wang's coefficient of 1. 39 x 10 -5 cm 2. sec -1. This implies that tritium is moving through the sediment column at a rate equal to diffusion. The results were obtained for smoothed values. It was not possible to model the perturbations of the data with a one dimensional model. The dynamics of the system imply that tritium could be used as a biomonitor for reactor emissions, mixing time and current direction scenarios and that a better understanding of this process could be gained by future coring studies and a new hypothesis.