Dissertations / Theses on the topic 'Biot-Savart'

Unsteady two-dimensional laminar flow of an incompressible viscous fluid over a periodically grooved wall is investigated by numerical simulation using two independent finite-difference methods. One is the vorticity-stream function method, and the other involves the vorticity-velocity induction law formulation. The fluid motion is initiated impulsively from rest and is assumed to be spatially periodic in the streamwise direction. The flow field, which includes the time development of the shear layer and the recirculating flow in the zone of separation, is examined in detail during the transient phase to the steady-state condition. The analytical and numerical formulations, which include the implementation of the boundary conditions, are derived in detail. The generation of vorticity at the solid surfaces is modelled differently in the two approaches. This vorticity production plays an important role in determining the surface-pressure distribution and the drag coefficient. Characteristics of the transient solution for a moderate Reynolds number in the laminar range are presented. Included with the graphical results are the temporal development of the constant stream function contours, including the dividing contour between the zone of separation and the main flow, and the constant vorticity contours. These latter contours show the interactions of separated vortices. The flow is found to approach a steady-state condition comprising an undisturbed uniform flow, a nonuniform irrotational flow, a shear layer adjacent to the grooved wall, and a recirculating vortex flow in the groove. Results also include the time development of the surface shear stress, surface pressure, drag coefficient and several typical velocity profiles, which characterize the flow in the recirculating region. Comparisons of the results obtained by the two numerical methods are made during the major development of the flow. The results showing the general features of the flow development including the time development of the shear layer, free shear layer and recirculating vortex flow are in good agreement. However, a significant deviation does exist at early times for the distribution of surface pressure, which accordingly has noticeable effect on the drag coefficient. Nevertheless, the gap between the distributions of surface pressure and drag coefficients dies out gradually as time progresses. The form of the stream function and vorticity contours at the steady state agrees well with those obtained from a recent numerical investigation of the steady flow in grooved channels.

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico. Programa de Pós-Graduação em Engenharia Elétrica.
Made available in DSpace on 2012-10-22T12:39:50Z (GMT). No. of bitstreams: 1 225375.pdf: 961702 bytes, checksum: 7a94a246bcce8f33f2f606eb793c643c (MD5)
Neste trabalho é proposto um sistema computacional para o cálculo de campos magnéticos em detectores de metais. Para analisar o campo magnético em um tipo específico de detector de metais, PDM (Portal Detector de Metais), foi necessário fazer um estudo bibliográfico deste equipamento e desenvolver uma ferramenta numérica para o cálculo tridimensional do campo que permitisse calcular o campo no interior da região de detecção de metais. Com a utilização da ferramenta numérica denominada BSmag (sistema computacional baseado na lei de Biot-Savart para cálculo de campos) foi possível calcular o vetor campo magnético nos pontos de interesse assim como mostrar a sua distribuição no interior do PDM. Na concepção do sistema utilizou-se à lei de Biot-Savart que pode ser considerada como uma discretização da lei de Ampère e que pode ser utilizada em uma grande quantidade de problemas práticos. Após medições realizadas em um equipamento PDM foi possível comparar estes resultados com os valores obtidos utilizando o BSmag. Através do desenvolvimento deste sistema pretendeu-se, além de verificar a eficácia do sistema computacional, conhecer as intensidades e distribuição dos campos magnéticos gerados por estes equipamentos o que pode contribuir para a melhoria destes dispositivos.

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.

Nel lavoro si dimostrano il Teorema della Divergenza e il Teorema di Stokes e le sue generalizzazioni a una curva chiusa di ordine k e a una varietà M, n-dimensionale, orientata con bordo. Successivamente si espongono due applicazioni alla fisica: l'elettromagnetismo e la formula del rotore. Nel primo caso si mostra come applicando il Teorema alle leggi di Biot-Savarat e di Faraday si ottengono le equazioni di Maxwell; nel secondo invece si osserva come il rotore rappresenti la densità superficiale di circuitazione.

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.

The doctoral thesis deals with the analysis of the flow in the circular and not circular cross-section pipes by methods using the distribution of the vorticity density. This analysis is particularly focused on the derivation of the new velocity profiles formulas using the above mentioned method. In this work is presented a historical overview of the derived velocity profiles. This overview of already derived velocity profiles will be a fundamental benchmark for newly derived velocity profiles. These new velocity profiles are derived for the circular and not circular cross-section pipes and the derivation is based on the analogy of electromagnetic induction by using Biot-Savart law. It is necessary to apply this analogy at first on solitary vortex filament. By taking this step is possible to get the value of the induced velocity from one solitary vortex filament. Subsequently it is possible to obtain the value of the induced velocity from the vorticity wall and afterwards from the vorticity density distribution over the cross section. This work contains also the results of the experimental measurements of the velocity profiles, and of the CFD simulations. Experimentally measured results are used besides other for the selecting of the most suitable CFD computational model. Selected CFD model will be subsequently declared as a reference model and the valid velocity profiles for this model will serve with the experimentally measured data as a benchmark for the newly derived velocity profiles.

Un outil numérique destiné à la simulation instationnaire d'écoulements incompressibles visqueux partiellement confinés dans le cadre d'une approximation bi-dimensionnelle plane est présenté. Basé sur une méthode de Random Vortex hybride, il exploite l'équation de transport de la vorticité par une discrétisation adaptative sur des éléments lagrangiens à supports compacts. Des algorithmes destinés à améliorer la performance de calcul et la flexibilité sont également introduits. Une étude bibliographique raisonnée relative aux écoulements au travers d'expansions symétriques brusques est menée. Les paramètres déterminants sont dégagés. Différents régimes sont distingués : les transitions rencontrées à nombre de Reynolds croissant conduisent d'un écoulement recirculant symétrique stationnaire à des configurations asymétriques puis à l'apparition d'instabilités. Certaines justifications phénoménologiques sont proposées et les mécanismes mal cernés sont soulignés. La méthode numérique décrite est appliquée à la simulation de ces écoulements et les résultats obtenus comparés aux données expérimentales et numériques disponibles. Les prédictions effectuées sont en excellent accord dans le cas du régime symétrique stationnaire. A un nombre de Reynolds plus élevé, les calculs conduisent à des régimes asymétriques dont seule la nature est conforme aux résultats expérimentaux. Le déclenchement d'instabilités apparaît à une valeur de Reynolds plus faible qu'expérimentalement. Le rôle de la méthode numérique dans ces désaccords est suggéré, ainsi que d'éventuels palliatifs

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2017-11-16T09:48:38Z No. of bitstreams: 2 Dissertação - Arthur Melo Pereira - 2017.pdf: 8324435 bytes, checksum: a36f9e13810ace212ce9d44a66fc2fb4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)
Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-11-16T09:49:04Z (GMT) No. of bitstreams: 2 Dissertação - Arthur Melo Pereira - 2017.pdf: 8324435 bytes, checksum: a36f9e13810ace212ce9d44a66fc2fb4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)
Made available in DSpace on 2017-11-16T09:49:04Z (GMT). No. of bitstreams: 2 Dissertação - Arthur Melo Pereira - 2017.pdf: 8324435 bytes, checksum: a36f9e13810ace212ce9d44a66fc2fb4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-09-26
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In a society dependent on electric energy for the execution of various daily activities, it is normal that its use is increasingly increasing over time. In order to carry out the transportation of all electric energy, it is essential to use transmission lines, which with increasing energy demand inevitably have tended to multiply throughout the world, and especially in Brazil, given its continental dimensions. Considering the function of the transmission lines for the electrical system, its importance in the context of the electric power supply is remarkable. However, the lines constitute one of the great emitting sources of electric and magnetic fields of low frequency, which has caused concern and has been motivating fact of several studies, like the realized in this work. Therefore, in view of the scenario presented in the previous paragraph, it is necessary to establish ways of calculating the fields more and more precisely. For the calculation of the electric field is used the Image Method, the Maxwell Potential Coefficients Method and the Coulomb Law, and for the magnetic field the Biot-Savart's Law is used. The results obtained for the electric and magnetic fields were for infinite rectilinear geometries, finite rectilinear and for the conductors taking the form of a catenary, the latter geometry being the most real model for the arrangement of the conductors in a line. In all cases treated, an analytical and numerical approach was performed, in order to allow the calculation of the three geometries with accuracy. Taking advantage of the methodology of calculation of the fields, in addition this work proposes a method of support to the monitoring of transmission lines. The method consists of using the Genetic Algorithm associated to the values of the electric and magnetic fields measured to determine the parameters of the line, such as: phase spacing, cable-soil height, equivalent conductor diameter, current and operating voltage. Given the simplicity of implementation when compared to other methods, the achievement of satisfactory results and the need for a single measuring device to monitor the transmission line, the proposed method proves to be viable and promising to carry out the line monitoring process.
Em uma sociedade dependente da energia elétrica para a execução de diversas atividades do cotidiano, é normal que a sua utilização seja cada vez mais crescente no decorrer do tempo. Para realizar o transporte de toda energia elétrica é imprescindível o uso de linhas de transmissão, que com o aumento da demanda de energia inevitavelmente tenderam a se multiplicar pelo mundo e em especial pelo território brasileiro, dadas as suas dimensões continentais. Tendo em vista a função das linhas de transmissão para o sistema elétrico, é notável a sua importância no contexto do fornecimento de energia elétrica. No entanto, as linhas constituem uma das grandes fontes emissoras de campos elétricos e magnéticos de baixa frequência, o que tem causado preocupação e tem sido fato motivador de diversos estudos, como o realizado neste trabalho. Portanto, diante do cenário apresentado no parágrafo anterior, se faz necessário estabelecer formas de calcular os campos de maneira cada vez mais precisa. Para o cálculo do campo elétrico utiliza-se o Método das Imagens, o Método dos Coeficientes de Potencial de Maxwell e a Lei de Coulomb, já para o campo magnético a Lei de Biot-Savart é empregada. Os resultados obtidos para os campos elétricos e magnéticos foram para as geometrias retilíneas infinitas, retilíneas finitas e para os condutores assumindo a forma de uma catenária, sendo que essa última geometria constitui o modelo mais real quanto à disposição dos condutores em uma linha. Em todos os casos tratados foram realizadas uma abordagem analítica e numérica, de maneira a possibilitar o cálculo das três geometrias com exatidão. Aproveitando-se da metodologia de cálculo dos campos, adicionalmente este trabalho propõe um método de apoio ao monitoramento de linhas de transmissão. O método consiste em utilizar o Algoritmo Genético associado aos valores dos campos elétrico e magnético medidos para determinar os parâmetros da linha, como: espaçamento entre fases, altura cabo-solo, diâmetro equivalente dos condutores, corrente e tensão de operação. Dada a simplicidade de implementação quando comparado a outros métodos, a obtenção de resultados satisfatórios e a necessidade de um único aparelho de medição para monitorar a linha de transmissão, o método proposto mostra-se viável e promissor para realizar o processo de monitoramento de linhas.

Im Bereich der industriellen Metallurgie und Kristallzüchtung treten bei zahlreichen Anwendungen, wo magnetische Wechselfelder zur induktiven Beeinflussung von leitfähigen Werkstoffen eingesetzt werden, auch Strömungen mit freier Oberfläche auf. Das Anwendungsspektrum reicht dabei vom einfachen Aufschmelzen eines Metalls in einem offenen Tiegel bis hin zur vollständigen Levitation. Auch der sogenannte RGS-Prozess, ein substratbasiertes Kristallisationsverfahren zur Herstellung siliziumbasierter Dünnschichtmaterialien, ist dafür ein Beispiel. Um bei solchen Prozessen die Interaktion von Magnetfeld und Strömung zu untersuchen, ist die numerische Simulationen ein wertvolles Hilfsmittel. Für beliebige dreidimensionale Probleme werden entsprechende Berechnungen bisher durch eine externe Kopplung kommerzieller Programme realisiert, die für Magnetfeld und Strömung jeweils unterschiedliche numerische Techniken nutzen. Diese Vorgehensweise ist jedoch im Allgemeinen mit unnötigem Rechenaufwand verbunden. In dieser Arbeit wird ein neu entwickelter Methodenapparat auf Basis der FVM vorgestellt, mit welchem sich diese Art von Berechnungen effizient durchführen lassen. Mit der Implementierung dieser Methoden in foam-extend, einer erweiterten Version der quelloffenen Software OpenFOAM, ist daraus ein leistungsfähiges Werkzeug in Form einer freien Simulationsplattform entstanden, welches sich durch einen modularen Aufbau leicht erweitern lässt. Mit dieser Plattform wurden in foam-extend auch erstmalig dreidimensionale Induktionsprozesse im Frequenzraum gelöst.

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.

碩士
國立臺灣大學
土木工程學研究所
88
In this study, velocity-vorticity formulation and Biot-Savart law are used to solve the two-dimensional steady incompressible stokes flow. The boundary element method is chosen to discrete the governing equations. The geometric shapes of the flow field include both the circular and square cavity flows which all exist exact or series solutions. The boundary conditions of vorticity for the vorticity transport equation are determined by the principle of the relationship between circulation and vorticity, namely, the Stokes theorems. To demonstrate the model feasibility, the results of two-dimensional steady incompressible Stokes flows of the square cavity flows are compared with the Fourier series solutions of [Burggraf , 1966] ；and results of the circular cavity flows are also used to compared with exact solution of [Hwu et al. , 1997]。 The present study show that good results are obtained for all the cases simulated except at the singular points of the boundary.

Dissertação de Mestrado Integrado em Engenharia Electrotécnica e de Computadores apresentada à Faculdade de Ciências e Tecnologia
A evolução tecnológica e o elevado desenvolvimento industrial que caracteriza a civilização contemporânea, torna a sociedade fortemente dependente de energia. Devido a esta evolução, houve um aumento do uso de aparelhos elétricos e consequentemente um aumento das redes elétricas, surgindo assim um aumento na intensidade de campos magnéticos originados pela corrente elétrica que percorre as redes e os aparelhos. Este aumento intensidade de campos magnéticos originou uma preocupação na sociedade sobre os efeitos do campo magnético na saúde dos seres humanos. Foi esta a motivação para este trabalho: desenvolver o software ‘EASYMAG’ para calcular a densidade do fluxo magnético originado por correntes elétricas em condutores, utilizando a lei de Biot-Savart.O software desenvolvido tem incorporadas as seguintes funcionalidades: verificação da introdução correta dos dados, alertando o utilizador se um circuito constituído por várias linhas estiver aberto; visualização gráfica do circuito elétrico definido pelo utilizador com cores diferentes consoante o circuito seja unifilar ou bifilar; cálculo da densidade do fluxo magnético nos pontos indicados pelo utilizador, mostrando a localização onde esse valor é máximo e mínimo; visualização gráfica da densidade do fluxo magnético nos pontos definidos pelo utilizador; guardar simulação feita pelo utilizador.O software ‘EASYMAG’ é inovador comparado com os outros softwares existentes, porque utiliza o Excel como método de introdução de dados, conseguindo assim representar o circuito elétrico pretendido pelo utilizador, sem que este tenha que programar em Matlab o circuito, tornando ainda o software ‘EASYMAG’ acessível para todas as pessoas com conhecimento básico de Matlab.Para validar o software foram usados três exemplos teóricos. O software, nestes três exemplos, obteve resultados com um erro muito pequeno, dependendo do número de pontos usados para a representação dos elementos circuitais, curva e solenoide. O software desenvolvido é assim uma ferramenta fiável para o cálculo de casos teóricos e práticos da densidade do fluxo magnético originado por correntes elétricas em condutores, sendo o erro associado próximo de zero.
The technological evolution and the high industrial development that characterizes the contemporary civilization, makes the society strongly dependent on energy. Due to this evolution, there has been an increase of the electrical devices usage and consequently an increase of the electrical networks, arising an increase in the intensity of magnetic fields originated by the electric current that runs through the networks and electrical devices. This increased intensity of magnetic fields has given rise to the concern in the society about the effects of magnetic fields on human health. This was the motivation for this work: to develop the software 'EASYMAG' to calculate the magnetic flux density originated by electric currents in conductors, using the Biot-Savart law. The developed software incorporates the following functionalities: verification of the correct data entry, alerting the user if a circuit consisting of several lines is open; graphical visualization of the electrical circuit defined by the user with different colors depending on whether the circuit is unifilar or bifilar; calculation of the magnetic flux density at the points indicated by the user, showing the location where this value is maximum and minimum; graphical display of magnetic flux density at user-defined points; save simulation done by the user. The software 'EASYMAG' is innovative compared to other existing software, because it uses Excel as a data entry method, representing the desired electrical circuit without having to program the circuit in Matlab, making the software 'EASYMAG' accessible to all people with basic knowledge of Matlab. Three theoretical examples are presented to validate the software. The software, in these three examples, obtained results with a very small error, depending on the number of points used for the representation of the circuit elements, curve and solenoid. The developed software is a reliable tool for the calculation of theoretical and practical cases of the magnetic flux density originated by electric currents in conductors, the associated error being close to zero.

Im Bereich der industriellen Metallurgie und Kristallzüchtung treten bei zahlreichen Anwendungen, wo magnetische Wechselfelder zur induktiven Beeinflussung von leitfähigen Werkstoffen eingesetzt werden, auch Strömungen mit freier Oberfläche auf. Das Anwendungsspektrum reicht dabei vom einfachen Aufschmelzen eines Metalls in einem offenen Tiegel bis hin zur vollständigen Levitation. Auch der sogenannte RGS-Prozess, ein substratbasiertes Kristallisationsverfahren zur Herstellung siliziumbasierter Dünnschichtmaterialien, ist dafür ein Beispiel. Um bei solchen Prozessen die Interaktion von Magnetfeld und Strömung zu untersuchen, ist die numerische Simulationen ein wertvolles Hilfsmittel. Für beliebige dreidimensionale Probleme werden entsprechende Berechnungen bisher durch eine externe Kopplung kommerzieller Programme realisiert, die für Magnetfeld und Strömung jeweils unterschiedliche numerische Techniken nutzen. Diese Vorgehensweise ist jedoch im Allgemeinen mit unnötigem Rechenaufwand verbunden. In dieser Arbeit wird ein neu entwickelter Methodenapparat auf Basis der FVM vorgestellt, mit welchem sich diese Art von Berechnungen effizient durchführen lassen. Mit der Implementierung dieser Methoden in foam-extend, einer erweiterten Version der quelloffenen Software OpenFOAM, ist daraus ein leistungsfähiges Werkzeug in Form einer freien Simulationsplattform entstanden, welches sich durch einen modularen Aufbau leicht erweitern lässt. Mit dieser Plattform wurden in foam-extend auch erstmalig dreidimensionale Induktionsprozesse im Frequenzraum gelöst.