In this thesis it has been investigated if LQG control could be used to mitigate torsional oscillations in a variable speed, fixed pitch wind turbine. The wind turbine is a vertical axis wind turbine with a 40 m tall axis that is connected to a generator. The power extracted by the turbine is delivered to the grid via a passive rectifier and an inverter. By controlling the grid side inverter the current is controlled and hence the rotational speed can be controlled. A state space model was developed for the LQG controller. The model includes both the dynamics of the electrical system as swell as the two mass system, consisting of the turbine and the generator connected with a flexible shaft. The controller was designed to minimize a quadratic criterion that punishes both torsional oscillations, command following and input signal magnitude. Integral action was added to the controller to handle the nonlinear aerodynamic torque. The controller was compared to the existing control system that uses a PI controller to control the speed, and tested usingMATLAB Simulink. Simulations show that the LQG controller is just as good as the PI controller in controlling the speed of the turbine, and has the advantage that it can be tuned such that the occurrence of torsional oscillations is mitigated. The study also concluded that some external method of dampening torsional oscillations should be implemented to mitigate torsional oscillations in case of a grid fault or loss of PWM signal.

Rotating convection in the Earth's core produces columnar vortices of radius ~10 km or less near the inner core boundary. Small-scale motions in the core can travel as Alfvén waves in the face of Ohmic diffusion, provided the ratio of the magnetic diffusion time th to the Alfvén wave travel time tA (measured by the Lundquist number S0) is much greater than unity. These motions transfer angular momentum from the core to the mantle, a process that can help explain variations in length of day. Vortices subject to the combined influence of a magnetic field and background rotation give rise to fast and slow Magneto-Coriolis (MC) waves whose damping is not well understood. This thesis investigates the long-time evolution of magneto hydrodynamic (MHD) waves generated by an isolated, small-scale motion in an otherwise quiescent, electrically conducting fluid. The first part of the study focuses on the damping of small-scale Alfvén waves, which is independent of rotation. For a plausible magnetic field strength in the Earth's core, it is shown that flows of lengthscale ~ 5 km or larger can propagate across the core as damped Alfvén waves on sub-decadal timescales. The second part of the study looks at MC waves generated from an isolated blob under rotation and a uniform axial magnetic field. The decay laws for these waves are obtained by considering the decay of fast and slow waves individually. While the fast waves are subject to strongly anisotropic magnetic diffusion, the slow waves diffuse isotopically. New timescales are derived for the onset of damping and the transition from the wave-dominated to the diffusion-dominated (quasi-static) phase of decay. This study shows for the first time that MC waves originating from small-scale vortices of magnetic Reynolds number Rm ~ 1 can be long-lived. The results of this study are extendible to small-scale MHD turbulence under rotation, whose damped wave phase has not been adequately addressed in the literature. Furthermore, it is thought that this study would help place a lower bound on the poloidal magnetic field strength in the Earth’s core.

The first part of this thesis deals with the examination of the eccentricity of the crank mechanism for individual variables kinematics and dynamics of crank mechanism, analyticaly computed in Matlab. Then it compares the different possibilities of balancing moments of inertia forces and propose a specific design chosen for the value of eccentricity. In the second part is designed a model of crankshaft mechanism based on the investigated parameters. These parameters were carried out by structural analysis in Ansys.

This Thesis is devoted to the investigation of superfluid helium flows due to torsional oscillators. In its first part, flow due to a torsionally oscillating disc suspended on a tungsten filament is studied (building upon the work of A. C. Hollis Hallett from 1952). Measurements of the motion of the torsionally oscillating disc were performed in superfluid helium at temperatures between 1.265 K and 2.157 K at saturated vapour pressure. Time traces of the disc angular deflection were obtained, and critical parameters related to the turbulent flow stability were determined. In laminar flow, scaling of drag forces with the dimensionless Donnelly number was verified. Based on these results, and comparison with the original work, a scenario of the decay of turbulent flow was suggested. The second part of this work is focused on the development and construction of a similar experiment for mK temperatures. A new type of oscillator was designed, a so-called "pillbox", and a series of testing measurements was performed both at room and mK temperatures.

[pt] Nesta tese, a teoria das hastes de Cosserat é revisitada e aplicada à dinâmica de coluna de perfuração. O objetivo é estudar o comportamento dessas estruturas dentro de poços de petróleo curvos. Para atingir este objetivo, um modelo estrutural determinístico é construído onde as tubos de perfuração (drill-pipes) e o conjunto de fundo (bottom hole assembly) são considerados como uma estrutura unidimensional de Cosserat. Em seguida, é desenvolvida uma estratégia para tratar o contato lateral em poços com configuração curvilínea. Depois disso, o problema de contorno livre é tratado mediante uma estratégia que considera como a condição de borda evolui à medida que a estrutura de perfuração avança. Isto é feito mediante uma formulação de interação broca-rocha que deve considerar a dinâmica de corte. Para isso, uma equação extra, de advecção, é resolvida junto com as equações de movimento de Cosserat. Em seguida, alguns casos de aplicação são apresentados. Numa primeira instancia, alguns elementos do problema são avaliados separadamente. Seguidamente, eles são integrados e analisados de forma conjunta. Por exemplo, primeiramente uma coluna de perfuração sem contato de fundo (off-bottom) é simulada, ou seja, sem contato broca-rocha, para estudar o comportamento e a implementação da estratégia para o contato lateral. Aqui também são calibrados alguns dos parâmetros do modelo de atrito. Em seguida, a estratégia para contabilizar o corte na rocha é implementada em um modelo 2-DOF de baixa dimensão e em um semi-discreto onde a dinâmica de torção é modelada como uma equação de onda. Os resultados mostram que o uso de abordagens contínuas resulta mais apropriade que aquelas onde se utilizam modelos de baixa dimensãom, particularmente quando são consideradas colunas longas, e quando há interesse em analisar não apenas o comportamento da broca, mas também o comportamento do sistema mecânico ao longo dos tubos de perfuração. Isso é reforçado por outro exemplo onde a dinâmica de corte é combinada com a formulação de Cosserat. Observações semelhantes do ponto de vista qualitativo são encontradas. Resumindo os resultados obtidos, as diferenças nas previsões dadas pelos modelos de baixa dimensão e o de unidimensional de Cosserat justificam o desenvolvimento e aplicação da abordagem com esta formulação em estruturas de perfuração. Finalmente, a modo de introduzir outro aspecto importante em colunas de perfuração e que pode ser uma linha de pesquisa para continuar o trabalho, a variabilidades presente em elementos como rocha, inclui-se um caso de aplicação considerando um poço horizontal e um campo estocástico de atrito. / [en] In this thesis, the theory of Cosserat rods is applied to the dynamics of drill-strings. The main objective is to evaluate the behaviour of these strings when they move within curved wells. To achieve this goal, a deterministic structural model is constructed, where the drill-pipes and the bottom hole assembly are taken as a Cosserat rod. Next, a strategy to deal with the lateral contact in curved well configurations is developed. After that, the free boundary problem is assessed: while drilling, the boundary changes due to cutting, modifying the position of the soil and, consequently, changing the bit-rock interaction forces. For this reason, a bit-rock model that can account for the cutting dynamics is adopted, in which an extra advection equation is solved together with the equations of motion of the Cosserat rod. Next, application cases are provided. First, some effects included in the model are tested in isolation, such as the lateral friction, the lateral contact, and the cutting. After that, they are all combined. In the first analysis, an off-bottom string is simulated, i.e. without contact at the bit. This allows testing the formulation associated with the lateral contact. Also, the calibration of the lateral friction parameters is made. Following that, the strategy to account for the cutting at the bit is implemented in a low-dimensional 2-DOF model, and in a semi-discrete model with a continuous wave equation for the torsional dynamics. The results show that the use of continuous approaches is more appropriate than low-dimensional models. Especially when long columns are considered, and when there is interest in understanding not only the behaviour at the bit but also along drill-pipes. This finding is reinforced by another application where the cutting dynamics are combined with the Cosserat rod formulation. Again, similar observations from a qualitative point of view are found. Overall, the differences in the results between the lumped low-dimensional models and the continuous Cosserat rod justify the development and application of the Cosserat approach to drilling structures. Finally, an introductory stochastic analysis concerning the variability of the rock is presented as an introduction to a future line of research, where stochasticity is included. / [es] En esta tesis, la teoria de Cosserat para elementos unidimensionales es revisitada y aplicada a la simulación de columnas de perforación. El objetivo es estudiar el comportamiento de estas estructuras en pozos de geometría curva. Para alcanzar este objetivo se construye un modelo determinístico. En este modelo, los caños de perforación (drill-pipes) y el conjunto de fondo (bottom hole assembly) son modelados como una estructura unidimensional de Cosserat. Seguidamente, una estrategia para tratar con el contacto lateral en pozos curvos es desarrollada. Luego, el problema de frontera libre es estudiado: durante la perforación, la condición de borde cambia debido al cambio del perfil altimétrico del terreno, alterando su posición y consecuentemente las fuerzas asociadas a la interacción broca-roca. Por esta razón, se decide utilizar un modelo de interacción broca-roca que tiene en cuenta la dinámica del corte. En este abordaje una ecuación extra, la ecuación de advección, es resuelta en forma acoplada con las ecuaciones del movimiento de la estructura de Cosserat. Algunos ejemplos de aplicación son presentados. En una primera instancia, algunos de los elementos del problema son estudiados en forma aislada. Luego combinados en un modelo completo. Por ejemplo, el caso de una columna sin contacto de fondo (off-bottom) es tratado para evaluar el comportamiento y la implementación de la estrategia mencionada para detectar el contacto lateral. Además, se efectúa la calibración de alguno de los parámetros relacionados con la fricción lateral. Luego, la estrategia para considerar el corte en la punta es implementada en un modelo de 2-DOF, y en otro semi-discreto donde se considera un modelo de ecuación de onda para la dinámica torsional. Los resultados muestran que el uso de formulaciones continuas es más apropiado que aquellas formulaciones donde se utilizan modelos de dimensiones reducidas, particularmente cuando se estudia columnas largas donde el interés se centra en entender no solo el comportamiento de la broca sino también a lo largo de la tubería. Este resultado es reforzado por otro caso de aplicación en donde se combina la dinámica de corte con un modelo de Cosserat. Observaciones similares son vistas en el comportamiento cualitativo de la solución. En resumen, las diferencias observadas en los diferentes ejemplos de aplicación entre los modelos de dimensiones reducidas y el modelo continuo de Cosserat justifican el desarrollo y la aplicación de la teoría de Cosserat a estructuras de perforación. Finalmente, dado que uno de los objetivos planteados también es considerar la variabilidad en algunos elementos como ser las propiedades de la roca, un caso de aplicación considerando un pozo horizontal es mostrado.