京都大学 / 新制・課程博士 / 博士(情報学) / 甲第23544号 / 情博第774号 / 新制||情||132(附属図書館) / 京都大学大学院情報学研究科先端数理科学専攻 / (主査)准教授 藤原 宏志, 教授 磯 祐介, 教授 田口 智清 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

The digitalization of our community, robotization of our industry and electrification of our transports leads to an increasing demand of electric power, which relies on a strong and reliable grid. In order to continuously be able to deliver stable and qualitative electric power all over Sweden the grid needs to be expanded. To safely expand the grid, several laws, regulations and safety precautions needs to be followed and one of them applies to the magnetic field from high voltage power lines. This Master thesis aims to show two different ways of calculating the magnetic field from high voltage power lines. The first way is to take the transmission line catenary in account and the other is to approximate a straight line and show the magnetic field extension. It also aims to show how the field looks close to transmission poles, both straight and with angles, in order to find out if that changes the field outcome. Both ways of calculating the field shows the same magnetic field magnitude below the point where the catenary hangs down the most. With the catenary taken into account, the magnetic field strength is lower than with the approximation with straight line, and shows the real field extension from the powerline. Using the straight line approximation, the magnetic field is higher and constant below the whole power line. As both ways of calculating takes a high amount of time, the one that gives the real field extension is recommended to use for real life application.

[pt] Arnold no seu trabalho The asymptotic Hopf Invariant and its applications de 1986, considerou sobre um domínio (ômega maiúsculo) compacto de R3 com bordo suave e homología trivial campos X e Y de divergência nula e tangentes ao bordo de (ômega maiúsculo) e definiu o índice de enlaçamento assintótico lk(X; Y ) e o invariante de Hopf associados a X e Y pela integral I(X; Y ) igual a (integral em ômega maiúsculo de alfa produto d-beta), onde (d-alfa) igual a iX-vol e (d-beta) igual a iy-vol, e mostrou que I(X; Y ) igual a lk(X; Y ). Agora, no presente trabalho estenderemos estas definições de índices de enlaçamento assintótico lk(fi maiúsculo,xi maiúsculo) e de invariante de Hopf I(fi maiúsculo,xi maiúsculo), onde (fi maiúsculo) e (xi maiúsculo) são ações de Rk e de Rs, k mais s igual a n-1, respectivamente de difeomorfismos que preservam volume em (ômega maiúsculo n) a bola unitária fechada em Rn e mostraremos que lk (fi maiúsculo, xi maiúsculo) igual a I(fi maiúsculo,xi maiúsculo). / [en] V.I. Arnold, in his paper The algebraic Hopf invariant and its applications published in 1986, considered a compact domain (ômega maiúsculo) in R3 with a smooth boundary and trivial homology and two divergence free vector fields X and Y in (ômega maiúsculo) tangent to the boundary. He defined an asymptotic linking invariant lk(X; Y ) and a Hopf invariant associated to X and Y by the integral I(X; Y ) equal (integral em ômega maiúsculo de alfa produto d-beta) where (d-alfa) equal iX-vol e (d-beta) equal iy- vol. He showed that que I(X; Y ) equal lk(X; Y ). In the present work we extend these definitions of the asymptotic linking invariant lk(fi capital letter,xi capital letter) and the Hopf invariant I(fi maiúsculo,xi capital letter) where (fi capital letter) and (xi capital letter) are actions Rk and Rs, k plus s equal n-1 by volume preserving diffeomorphisms, on the closed unit ball (ômega capital letter n) in and we show lk (fi capital letter, xi capital lette r equal I(ficapital letter ,xi capital letter).

Esta dissertação apresenta modelagem matemática e um método de solução numérica para problemas de conformação eletromagnética de chapas metálicas finas circulares utilizando uma bobina em espiral plana. O método foca especificamente o cálculo do campo eletromagnético gerado pela bobina e análise do circuito que modela o sistema de estampagem eletromagnética. A bobina plana é aproximada por círculos concêntricos carregando a corrente de descarga dos capacitores. Os cálculos das correntes induzidas e perfil da força eletromagnética na chapa e acoplamentos magnéticos entre a bobina e chapa metálica são realizados para o instante inicial, antes da deformação plástica da chapa. O método utiliza a lei de Biot-Savart, sendo que a solução das integrais obtidas para indução magnética é realizada através de métodos numéricos, considerando as simetrias do problema. Para verificação da modelagem matemática, da solução numérica e comprovação da viabilidade técnica deste processo, um dispositivo de estampagem eletromagnética foi desenvolvido e diversos experimentos foram realizados com chapas de alumínio. Os parâmetros investigados foram a espessura da chapa a ser deformada e a influência da presença de vácuo na cavidade da ferramenta. Os resultados experimentais demonstram concordância com os resultados da modelagem proposta. A presença de vácuo também demonstrou um incremento na deformação da chapa. A rotina desenvolvida no software Matlab fornece informações importantes para o processo e permite que se faça ajustes no dispositivo. / This dissertation presents a mathematical model and numerical method to solve the problems of electromagnetic forming of thin circular metal sheets by using a flat spiral coil. The method focuses specifically on the calculation of the electromagnetic field generated by the coil flat and circuit analysis modeling system electromagnetic forming. The flat coil is approximated by concentric circles carrying a discharge current of capacitors. The calculations of induced currents and profile of the electromagnetic force on the plate and magnetic coupling between the coil and sheet metal are made to the initial time, before the plastic deformation of the plate. The method uses the law of Biot-Savart, and the solution of the integral obtained for magnetic induction is performed by numerical methods, considering the symmetries of the problem. To verify the mathematical model, the numerical solution and proving the technical feasibility of this process, a electromagnetic forming device was developed and several experiments were made with aluminum plates. The parameters investigated were the thickness of the plate to be deformed and the influence of the vacuum in the cavity of the tool. The experimental results show agreement with the results of the proposed model. The presence of vacuum also showed an increase in the deformation of the plate. A routine developed in software Matlab provide important information for the process and allow to make adjustments on the device.

Les problèmes étudiés dans cette thèse ont trait à la dynamique des points vortex dans deux équations pour les fluides ou superfluides bidimensionnels. La première partie est dévolue à l'équation d'Euler incompressible. Nous y analysons le système mixte Euler-points vortex, introduit par Marchioro et Pulvirenti, qui décrit l'évolution d'un tourbillon obtenu par superposition de points vortex et d'une composante plus régulière. Nous examinons diverses problématiques telles que le lien entre les points de vue lagrangien et eulérien, l'unicité, l'existence et l'expansion du support du tourbillon. La seconde partie de la thèse est consacrée à une équation de Ginzburg-Landau complexe obtenue en ajoutant un terme de dissipation à l'équation de Gross-Pitaevskii. Après avoir examiné le problème de Cauchy dans l'espace d'énergie correspondant, nous étudions la dynamique des points vortex dans le cadre de données très bien préparées. Dans un dernier temps, nous considérons un autre régime asymptotique, sans vortex, dans lequel les solutions sont des perturbations de champs constants de module égal à un. Une dynamique de type ondes amorties pour la perturbation est mise en évidence.

Esta dissertação apresenta modelagem matemática e um método de solução numérica para problemas de conformação eletromagnética de chapas metálicas finas circulares utilizando uma bobina em espiral plana. O método foca especificamente o cálculo do campo eletromagnético gerado pela bobina e análise do circuito que modela o sistema de estampagem eletromagnética. A bobina plana é aproximada por círculos concêntricos carregando a corrente de descarga dos capacitores. Os cálculos das correntes induzidas e perfil da força eletromagnética na chapa e acoplamentos magnéticos entre a bobina e chapa metálica são realizados para o instante inicial, antes da deformação plástica da chapa. O método utiliza a lei de Biot-Savart, sendo que a solução das integrais obtidas para indução magnética é realizada através de métodos numéricos, considerando as simetrias do problema. Para verificação da modelagem matemática, da solução numérica e comprovação da viabilidade técnica deste processo, um dispositivo de estampagem eletromagnética foi desenvolvido e diversos experimentos foram realizados com chapas de alumínio. Os parâmetros investigados foram a espessura da chapa a ser deformada e a influência da presença de vácuo na cavidade da ferramenta. Os resultados experimentais demonstram concordância com os resultados da modelagem proposta. A presença de vácuo também demonstrou um incremento na deformação da chapa. A rotina desenvolvida no software Matlab fornece informações importantes para o processo e permite que se faça ajustes no dispositivo. / This dissertation presents a mathematical model and numerical method to solve the problems of electromagnetic forming of thin circular metal sheets by using a flat spiral coil. The method focuses specifically on the calculation of the electromagnetic field generated by the coil flat and circuit analysis modeling system electromagnetic forming. The flat coil is approximated by concentric circles carrying a discharge current of capacitors. The calculations of induced currents and profile of the electromagnetic force on the plate and magnetic coupling between the coil and sheet metal are made to the initial time, before the plastic deformation of the plate. The method uses the law of Biot-Savart, and the solution of the integral obtained for magnetic induction is performed by numerical methods, considering the symmetries of the problem. To verify the mathematical model, the numerical solution and proving the technical feasibility of this process, a electromagnetic forming device was developed and several experiments were made with aluminum plates. The parameters investigated were the thickness of the plate to be deformed and the influence of the vacuum in the cavity of the tool. The experimental results show agreement with the results of the proposed model. The presence of vacuum also showed an increase in the deformation of the plate. A routine developed in software Matlab provide important information for the process and allow to make adjustments on the device.

Esta dissertação apresenta modelagem matemática e um método de solução numérica para problemas de conformação eletromagnética de chapas metálicas finas circulares utilizando uma bobina em espiral plana. O método foca especificamente o cálculo do campo eletromagnético gerado pela bobina e análise do circuito que modela o sistema de estampagem eletromagnética. A bobina plana é aproximada por círculos concêntricos carregando a corrente de descarga dos capacitores. Os cálculos das correntes induzidas e perfil da força eletromagnética na chapa e acoplamentos magnéticos entre a bobina e chapa metálica são realizados para o instante inicial, antes da deformação plástica da chapa. O método utiliza a lei de Biot-Savart, sendo que a solução das integrais obtidas para indução magnética é realizada através de métodos numéricos, considerando as simetrias do problema. Para verificação da modelagem matemática, da solução numérica e comprovação da viabilidade técnica deste processo, um dispositivo de estampagem eletromagnética foi desenvolvido e diversos experimentos foram realizados com chapas de alumínio. Os parâmetros investigados foram a espessura da chapa a ser deformada e a influência da presença de vácuo na cavidade da ferramenta. Os resultados experimentais demonstram concordância com os resultados da modelagem proposta. A presença de vácuo também demonstrou um incremento na deformação da chapa. A rotina desenvolvida no software Matlab fornece informações importantes para o processo e permite que se faça ajustes no dispositivo. / This dissertation presents a mathematical model and numerical method to solve the problems of electromagnetic forming of thin circular metal sheets by using a flat spiral coil. The method focuses specifically on the calculation of the electromagnetic field generated by the coil flat and circuit analysis modeling system electromagnetic forming. The flat coil is approximated by concentric circles carrying a discharge current of capacitors. The calculations of induced currents and profile of the electromagnetic force on the plate and magnetic coupling between the coil and sheet metal are made to the initial time, before the plastic deformation of the plate. The method uses the law of Biot-Savart, and the solution of the integral obtained for magnetic induction is performed by numerical methods, considering the symmetries of the problem. To verify the mathematical model, the numerical solution and proving the technical feasibility of this process, a electromagnetic forming device was developed and several experiments were made with aluminum plates. The parameters investigated were the thickness of the plate to be deformed and the influence of the vacuum in the cavity of the tool. The experimental results show agreement with the results of the proposed model. The presence of vacuum also showed an increase in the deformation of the plate. A routine developed in software Matlab provide important information for the process and allow to make adjustments on the device.

No description available.

A new vortex model for wind turbines was developed in order to evaluate the loads at the blades and other important characteristics of interest for the wind industry such as power and thrust coefficients. Nowadays, the calculation of these quantaties is done in a reliable and precise manner with LES simulation using actuator line or actuator disk models. However, LES simulations are computationally heavy and the model here developed aims at calculating the same quantities of interest in less time but still giving reliable and accurate results for any wind turbine model. The idea of a vortex model for wind turbines was developed by Segalini & Aöfredsson, J. Fluid Mech., vol. 725, pages 91-116, 2013, using vortex filaments to reproduce the vorticity on the blades and in the wake. Nevertheless, that model had some limitations, among which, the main one, was the impossibility to simluate wind turbines with varying circulation along the blade, something that is always present in reality. With this thesis it is proposed a model based on the one of Segalini & Alfredsson (2013) but with the introduction of a vortex sheet that allows to simulate a vorticity release from the wind turbine blades and hence wind turbines with varying circulation along the blades. The model was validated against a LES simulation of the Tjaereborg wind turbine by Sarmast, KTH Royal Institute of Technology, 2014, that utilized an actuator line model. The results confirmed the improvement of the vortex model compared to the previous one of Segalini & Alfredsson (2013) and gave consistent results regarding the flow field at the rotor plane and the loads on the blades.

No description available.