The finite element methods (FEM) have been developed over decades, and together with the growth of computer engineering, they become more and more important in solving large-scale problems in science and industry. The objective of this thesis is to develop high-performance finite element methods (HP-FEM), with two main applications in mind: computational diffusion magnetic resonance imaging (MRI), and simulation of the turbulent flow past a vertical axis wind turbine (VAWT). In the first application, we develop an efficient high-performance finite element framework HP-PUFEM based on a partition of unity finite element method to solve the Bloch-Torrey equation in heterogeneous domains. The proposed framework overcomes the difficulties that the standard approaches have when imposing the microscopic heterogeneity of the biological tissues. We also propose artificial jump conditions at the external boundaries to approximate the pseudo-periodic boundary conditions which allows for the water exchange at the external boundaries for non-periodic meshes. The framework is of a high level simplicity and efficiency that well facilitates parallelization. It can be straightforwardly implemented in different FEM software packages and it is implemented in FEniCS for moderate-scale simulations and in FEniCS-HPC for the large-scale simulations. The framework is validated against reference solutions, and implementation shows a strong parallel scalability. Since such a high-performance simulation framework is still missing in the field, it can become a powerful tool to uncover diffusion in complex biological tissues. In the second application, we develop an ALE-DFS method which combines advanced techniques developed in recent years to simulate turbulence. We apply a General Galerkin (G2) method which is continuous piecewise linear in both time and space, to solve the Navier-Stokes equations for a rotating turbine in an Arbitrary Lagrangian-Eulerian (ALE) framework. This method is enhanced with dual-based a posterior error control and automated mesh adaptation. Turbulent boundary layers are modeled by a slip boundary condition to avoid a full resolution which is impossible even with the most powerful computers available today. The method is validated against experimental data of parked turbines with good agreements. The thesis presents contributions in the form of both numerical methods for high-performance computing frameworks and efficient, tested software, published open source as part of the FEniCS-HPC platform. / <p>QC 20180411</p>

<p>This thesis reports on a numerical and experimental investigation of the unsteady loading of high solidity vertical axis wind turbines (VAWTs). Two-dimensional, unsteady Reynolds averaged Navier-Stokes simulations of a small scale, high solidity, H-type Darrieus vertical axis wind turbine revealed the dominant effect of dynamic stall on the power production and vibration excitation of the turbine. Operation of the turbine at low blade speed ratios resulted in complex flow-blade interaction mechanisms. These include; dynamic stall resulting in large scale vortex production, vortex impingement on the source blade, and significant flow momentum extraction.</p> <p>To validate the numerical model, a series of full-scale experimental wind tunnel tests were performed to determine the aerodynamic loading on the turbine airfoils, vibration response behaviour, and wake velocity. In order to accomplish this, a complex force measurement and wireless telemetry system was developed. During the course of this investigation, high vibration response of the turbine was observed. This resulted in conditions that made it difficult or impossible to measure the underlying aerodynamic loading. A vibration mitigation methodology was developed to remove the effect of vibration from the measured aerodynamic forces. In doing so, an accurate and complete measurement of the aerodynamic loading on the turbine blades was obtained.</p> <p>Comparison of the two-dimensional numerical model results to the experimental measurements revealed a considerable over-prediction of the turbine aerodynamic force and power coefficients, and wake velocity. From this research, it was determined that the three-dimensional flow effects due to the finite aspect ratio of the turbine and blades, as well as parasitic losses, could be accounted for through the application of inlet velocity and turbine height correction factors. In doing so, the two-dimensional numerical model results could be properly scaled to represent the three-dimensional flow behaviour of the turbine prototype. Ultimately, a validated VAWT design tool was developed.</p> / Doctor of Philosophy (PhD)

On étudie des phénomènes de séparation d'écoulement avec deux approches différentes. Dans la première partie, on considère des écoulements 2D, instationnaires, incompressibles et non visqueux. Un modèle analytique-numérique, basé sur la jonction d'une transformation conforme et d'une méthode aux tourbillons ponctuels, est construit pour définir l'écoulement potentiel dans un domaine doublement connecté où les corps sont caractérisés par une variation temporelle de leur circulation. En particulier, on s'intéresse à l'étude de l'écoulement autour d'un VAWT avec deux pales. Dans la seconde partie on considère des écoulements visqueux et compressibles. On construit un solveur qui résoud les équations de Navier-Stokes en y introduisant une technique de pénalisation: les corps sont modélisés comme des milieux poreux ayant une porosité très petite par rapport à la porosité du fluide extérieur. Cette technique permet d'utiliser des maillages cartésiens pour des géométries très complexes. / In the present work flow separation phenomena are investigated by means of two different approaches. In the first part, 2D unsteady incompressible inviscid flows are studied. An analytical-numerical model, based on the conjunction of a conformal mapping and a point vortex method, is built to define the potential flow field in a doubly connected domain where bodies are characterized by a variation in time of their circulation. In particular, the study of the unsteady flow past a 2-blade Darrieus VAWT is addressed. Until now the study of vortex motions has only been described in doubly-connected flow fields where the circulations have a constant null value. The flow field here analysed has a deep unsteadiness, which determines the circulations varying in time: so a technique is developed to uniquely define the circulations around the bodies. Three conditions result necessary to be imposed: in addition to the two Kutta conditions at the trailing edges, another one has to be imposed in order to respect the Kelvin theorem. With a classical configuration, this machine, experiencing angles of attack of opposite values, gives rise to complex vortex shedding phenomena that reduce its performances and stress its structure. In order to control the flow separation from the blades, an innovative solution is qualitatively investigated which consists of taking blade profiles provided with vortex trapping cavities. Interesting results are obtained, even if in the limit of inviscid flow. In the second part compressible viscous flows are taken into account. A fully Navier-Stokes equations solver is implemented introducing the penalization technique. The idea is to replace the bodies by the fluid, in a way that also into the bodies the penalized Navier-Stokes equations remain valid, respecting the boundary conditions on their contours. Starting from this purpose, the bodies are considered as porous media with a little porosity with respect to that of the external flow, which tends to infinity. This technique allows simple Cartesian meshes to be used, also for very complex geometries like those of industrial interest. The resulting code is tested on different flow fields, both steady and unsteady, both subsonic and supersonic, obtaining always a good agreement with other theoretical and numerical results described in literature.

La technique d'intégration des systèmes éoliens verticaux (VAWT) au service des logements individuels, collectifs et tertiaires est une approche intéressante pour les acteurs de la maitrise d'énergie pour promouvoir une utilisation rationnelle de l'énergie. Le choix de l'implantation d'une éolienne en milieu urbain est déterminé par la hauteur des bâtiments, la vitesse du vent et l'intensité de turbulence du site. Les conditions de vents sévères à faible altitude sont favorables à une implantation de VAWT. Dans certaines villes, la hauteur moyenne des bâtiments est relativement faible et ceci fait qu'en ces lieux, les VAWTs sont appréciables par rapport aux HAWTs. La mécanique des fluides numériques (CFD) est mise en œuvre pour modéliser les écoulements d'air au travers d'éoliennes et des bâtiments. Un problème CFD modélisé avec un modèle de turbulence approprié donneront des résultats de simulations qui s'approcheront des réalités physiques et des résultats de l'expérimentation. Dans cette étude, les modèles standard k-" et SST k-! ont été utilisés. Après analyse des possibilités d'intégration d'une VAWT, la toiture reste la zone d'intégration la plus intéressante. En plus de l'étude aérodynamique, nous avons entamé une modélisation électrique de la chaîne de conversion de l'éolienne en utilisant le logiciel Matlab/Simulink. Le travail a été effectué dans le but de déterminer la puissance électrique susceptible d'être produite par l'éolienne. Pour finaliser cette étude, un modèle de couplage électrique de VAWTs avec un bâtiment considéré comme un modèle de charge est présenté. / The building integration of the vertical axis wind turbine (VAWT) to supply the individual, collective and tertiary residences consumption is an interesting approach that can help architects and the actors of the energy control to promote a rational use of renewable energy in the in homes. The choice of the location of the urban wind turbine type is determined by building height, wind speed and turbulence intensity of the site. The severe conditions of wind at low altitude are favorable for a VAWT installation. In some cities, the average buildings height is low, in these places, the VAWTs must be appreciable compared to the HAWTs. The modelling of the air flow through the wind turbine and the couple building-wind turbine involves the computation fluid dynamics (CFD). A problem modeled with a suitable turbulence model will give results that approach the physical reality and the experiment results. In this study, the standard k-" and SST k-! models were used. After analyzing the possibilities of VAWT integration, the roof is the most interesting integration area. In addition to CFD method, we have started to study the electrical model of the VAWT. The work was conducted to determine the electrical power generated by the wind turbine using Matlab/Simulink software. To complete the study, a VAWT model coupled with a building where the building is considered as a consumption model is presented.