Le principe du contrôle par flux de fuite magnétique (Magnetic Flux Leakage MFL) consiste à aimanter la pièce à contrôler par un champ magnétique et à détecter à l'aide d'un capteur magnétique les fuites des lignes du champ qui résultent de la présence d'un défaut dans la pièce. Dans le but d'améliorer les performances d'un dispositif de détection, le CEA et la société Vallourec collaborent pour développer un modèle numérique dédié au contrôle virtuel des défauts longitudinaux dans les tubes ferromagnétiques. Le dispositif expérimental comprend un circuit magnétique tournant à une vitesse constante autour du tube qui défile. Dans le cadre de cette thèse, on débute le problème de la modélisation sans tenir compte des effets de la vitesse de rotation, il s'agit donc de résoudre un problème d'électromagnétisme en régime magnétostatique.Pour résoudre ce problème, on propose de comparer une approche semi-analytique basée sur le formalisme des équations intégrales (EI) et une approche purement numérique utilisant les éléments finis (EF).Dans la première partie de cette thèse, après avoir établi le formalisme théorique par EI, un premier modèle considérant des matériaux ferromagnétiques à perméabilité magnétique constante (régime linéaire) a été mis en œuvre en 2D. Ce modèle a été appliqué pour un exemple de système extrait de la littérature et validé numériquement par une comparaison des résultats EI/EF. Pour une meilleure détection, il est opportun de saturer magnétiquement la pièce. Le matériau ferromagnétique est alors caractérisé par une courbe B(H) non-linéaire. Par conséquent, la deuxième partie de la thèse a été consacrée à la mise en œuvre du modèle en régime non linéaire qui tient compte de cette caractéristique.Différentes méthodes de discrétisation ont été étudiées afin de réduire le nombre d'inconnues et le temps de calcul. L'originalité de la thèse réside dans l'utilisation des fonctions d'interpolation d'ordre élevé (polynôme de Legendre) pour une discrétisation des équations intégrales par une approche de type Galerkin. Les premiers essais de validation numérique de ce modèle ont été effectués sur un système MFL simplifié. Des premiers essais de validation expérimentale pour des données obtenues par EF ont été effectués en deux phases : La première a consisté à vérifier le distribution du champ magnétique pour un tube sain et en régime magnétostatique. La deuxième phase a consisté à calculer la réponse d'un défaut dans le tube ferromagnétique en tenant en compte les effets éventuels de la rotation du circuit magnétique par rapport au tube. / The principle of the non destructive testing by magnetic flux leakage (MFL) is to magnetize the part to be inspected by a magnetic field and to detect a flaw thanks to magnetic leakage field lines due to the strong decreasing of the magnetic permeability in the flawed region. In order to improve the performance of detection, the CEA and the Vallourec society collaborate to develop a numerical model dedicated to the virtual NDT of longitudinal defects in ferromagnetic tubes. The experimental system includes a magnetic circuit rotating at a constant speed around the tube to be inspected. The modeling task is started without considering the effects of the rotational speed, so the magnetostatic regime is considered to solve the modeling problem. In the framework of this thesis, we propose to compare a semi-analytical approach based on the formalism of integral equations method (IEM) and a purely numerical approach using finite element method (FEM).In the first part of this thesis, the theoretical formalism was established. A first simple discretization scheme is been implemented in the linear regime considering a constant magnetic permeability. This first numerical model has been validated for a simplified MFL configuration extracted and modified from the literature.For better detection, it is wishable to magnetically saturate the piece under-test. The ferromagnetic material is then characterized by a B(H) curve. Therefore, the second part of the thesis was devoted to the implementation of the model in the non-linear regime that takes into account this non-linear characteristic. Different discretization schemes have been studied in order to reduce the number of unknowns and the computational time. The originality of the thesis lies in the use of basis function of high order (Legendre polynomials) associated to a Galerkin approach for the discretization of integral equations. The first numerical result has been validated on a simplified MFL system. The first results of the experimental validation based on simulated data obtain by FEM have been performed in two steps. The first one consists to verify the distribution of the magnetic field for a ferromagnetic tube without any defect and in the magnetostatic regime. The objective of the second one was to compute the response of the flaw and to evaluate the effects of the rotational speed of the magnetic circuit around the tube.

The Sun, by the virtue of its proximity to Earth, serves as an excellent astrophysical laboratory for testing our theoretical ideas. The Sun displays a plethora of visually awe-inspiring phenomena including flares, prominences, sunspots, corona, CMEs and uncountable others. It is now known that it is the magnetic field of the Sun which governs all these and also the geomagnetic storms at the Earth, which owes its presence to the interaction between the geomagnetic field and the all-pervading Solar magnetic field in the interplanetary medium. Since the solar magnetic field affects the interplanetary space around the Earth in a profound manner, it is absolutely essential that we develop a comprehensive understanding of the generation and manifestation of magnetic fields of the Sun. This thesis aims at developing a state-of-the-art dynamo code SURYA1taking into account important results from helioseismology and magnetohydrodynamics. This dynamo code is then used to study various phenomenon associated with solar activity including evolution of solar parity, response to stochastic fluctuations, helicity of active regions and prediction of future solar cycles. Within last few years dynamo theorists seem to have reached a consensus on the basic characteristics of a solar dynamo model. The solar dynamo is now believed to be comprised of three basic processes: (i)The toroidal field is produced by stretching of poloidal field lines primarily inside the tachocline – the region of strong radial shear at the bottom of the convection zone. (ii) The toroidal field so formed rises to the surface due to magnetic buoyancy to form active regions. (iii) Poloidal field is generated at the surface due to decay of tilted active regions – an idea attributed to Babcock (1961) & Leighton (1969). The meridional circulation then carries the poloidal field produced near the surface to the tachocline. The profile of the solar differential rotation has now been mapped by helioseismology and so has been the poleward branch of meridional circulation near the surface. The model I describe in this thesis is a two-dimensional kinematic solar dynamo model in a full sphere. Our dynamo model Surya was developed over the years in stages by Prof. Arnab Rai Choudhuri, Dr. Mausumi Dikpati, Dr. Dibyendu Nandy and myself. We provide all the technical details of our model in Chap. 2 of this thesis. In this model we assume the equatorward branch of the meridional circulation (which hasn’t been observed yet), to penetrate slightly below the tachocline (Nandy & Choudhuri 2002, Science, 296, 1671). Such a meridional circulation plays an important role in suppressing the magnetic flux eruptions at high latitudes. The only non-linearity included in the model is the prescription of magnetic buoyancy. Our model is shown to reproduce various aspects of observational data, including the phase relation between sunspots and the weak, efficient. An important characteristic of our code is that it displays solar-like dipolar parity (anti-symmetric toroidal fields across equator) when certain reasonable conditions are satisfied, the most important condition being the requirement that the poloidal field should diffuse efficiently to get coupled across the equator. When the magnetic coupling between the hemispheres is enhanced by either increasing the diffusion or introducing an α ff distributed throughout the convection zone, we find that the solutions in the two hemispheres evolve together with a single period even when we make the meridional circulation or the α effect different in the two hemispheres. The effect of diffusive coupling in our model is investigated in Chap. 3. After having explored the regular behaviour of the solar cycle using the dynamo code we proceed to study the irregularities of the Solar cycle.We introduce stochastic fluctuations in the poloidal source term at the solar surface keeping the meridional circulation steady for all the numerical experiments. The dynamo displays oscillatory behaviour with variable cycle amplitudes in presence of fluctuations with amplitudes as large as 200%. We also find a statistically significant correlation between the strength of polar fields at the endofone cycle and the sunspot number of the next cycle. In contrast to this there exist a very poor correlation between the sunspot number of a cycle and the polar field formed at its end. This suggests that during the declining phase of the sunspot cycle poloidal field generation from decaying spots takes place via the Babcock-Leighton mechanism which involves randomness and destroys the correlation between sunspot number of a cycle and the polar at its end. In addition to this we also see that the time series of asymmetries in the sunspot activity follows the time series of asymmetries in the polar field strength with a lag of 5 years. We also compare our finding with available observational data. Although systematic measurements of the Sun’s polar magnetic field exist only from mid-1970s, other proxies can be used to infer the polar field at earlier times. The observational data indicate a strong correlation between the polar field at a sunspot minimum and the strength of the next cycle, although the strength of the cycle is not correlated well with the polar field produced at its end. We use these findings about the correlation of polar fields with sunspots to develop an elegant method for predicting future solar cycles. We feed observational data for polar fields during the minima of cycle n into our dynamo model and run the code till the next minima in order to simulate the sunspot number curve for cycle n+1. Our results fit the observed sunspot numbers of cycles 21-23 reasonably well and predict that cycle 24 will be about 30–35% weaker than cycle 23. We fit that the magnetic diffusivity in the model plays an important role in determining the magnetic memory of the Solar dynamo. For low diffusivity, the amplitude of a sunspot cycle appears to be a complex function of the history of the polar field of earlier cycles. Only if the magnetic diffusivity within the convection zone is assumed to be high (of order 1012cms−1), we are able to explain the correlation between the polar fiat a minimum and the next cycle. We give several independent arguments that the diffusivity must be of this order. In a dynamo model with diffusivity like this, the poloidal field generated at the mid-latitudes is advected toward the poles by the meridional circulation and simultaneously diffuses towards the tachocline, where the toroidal field for the next cycle is produced. The above ideas are put forward in Chap. 6. We next come to an important product of the dynamo process namely the magnetic helicity. It has been shown independently by many research groups that the mean value of the normalized current helicity αp= B (Δ×B)/B2in solar active regions is of the order of 10−8m−1, predominantly negative in the northern hemisphere, positive in the southern hemisphere. Choudhuri (2003, Sol. Phys., 215, 31)developed a model for production of the helicity of the required sign in a Babcock-Leighton Dynamo by wrapping of poloidal field lines around a fluxtube rising through the convection zone. In Chap. 7 we calculate helicities of solar active regions based on this idea. Rough estimates based on this idea compare favourably with the observed magnitude of helicity. We use our solar dynamo model to study how helicity varies with latitude and time. At the time of solar maximum, our theoretical model gives negative helicity in the northern hemisphere and positive helicity in the south, in accordance with observed hemispheric trends. However, we fit that during a short interval at the beginning of a cycle, helicities tend to be opposite of the preferred hemispheric trends. After calculating the sign and magnitude of helicity of the sunspots we worry about the distribution of helicity inside a sunspot. In Chap. 8 we model the penetration of a wrapped up background poloidal field into a toroidal magnetic flux tube rising through the solar convective zone. The rise of the straight, cylindrical flux tube is followed by numerically solving the induction equation in a comoving Lagrangian frame, while an external poloidal magnetic field is assumed to be radially advected onto the tube with a speed corresponding to the rise velocity. One prediction of our model is the existence of a ring of reverse current helicity on the periphery of active regions. On the other hand, the amplitude of the resulting twist depends sensitively on the assumed structure (ffvs. concentrated/intermittent) of the active region magnetic field right before its emergence, and on the assumed vertical profile of the poloidal field. Nevertheless, in the model with the most plausible choice of assumptions a mean twist comparable to the observational results. Our results indicate that the contribution of this mechanism to the twist can be quite find under favourable circumstances it can potentially account for most of the current helicity observed in active regions.

科学研究費補助金 研究種目:試験研究(B) 課題番号:06555177 研究代表者:佐々木 勝寛 研究期間:1994-1995年度

The continuously increasing demand for clean renewable energy has rekindled interest in multi-terminal high voltage direct current (HVDC) grids. Although such grids have several advantages and a great potential, their materialization has been thwarted due to the absence of HVDC breakers. In comparison with traditional alternating current (AC) breakers, they should operate and interrupt fault currents in a time frame of a few milliseconds. The aim of this thesis is focused on the design of ultra-fast electro-mechanical actuator systems suitable for such HVDC breakers.Initially, holistic multi-physics and hybrid models with different levels of complexity and computation time were developed to simulate the entire switch. These models were validated by laboratory experiments. Following a generalized analysis, in depth investigations involving simulations complemented with experiments were carried out on two of the sub-components of the switch: the ultra-fast actuator and the damper. The actuator efficiency, final speed, peak current, and maximum force were explored for different design data.The results show that models with different levels of complexity should be used to model the entire switch based on the magnitude of the impulsive forces. Deformations in the form of bending or elongation may deteriorate the efficiency of the actuator losing as much as 35%. If that cannot be avoided, then the developed first order hybrid model should be used since it can simulate the behavior of the mechanical switch with a very good accuracy. Otherwise, a model comprising of an electric circuit coupled to an electromagnetic FEM model with a simple mechanics model, is sufficient.It has been shown that using a housing made of magnetic material such as Permedyn, can boost the efficiency of an actuator by as much as 80%. In light of further optimizing the ultra-fast actuator, a robust optimization algorithm was developed and parallelized. In total, 20520 FEM models were computed successfully for a total simulation time of 7 weeks. One output from this optimization was that a capacitance of 2 mF, a charging voltage of 1100 V and 40 turns yields the highest efficiency (15%) if the desired velocity is between 10 m/s and 12 m/s.The performed studies on the passive magnetic damper showed that the Halbach arrangement gives a damping force that is two and a half times larger than oppositely oriented axially magnetized magnets. Furthermore, the 2D optimization model showed that a copper thickness of 1.5 mm and an iron tube that is 2 mm thick is the optimum damper configuration. / <p>QC 20150422</p>

Ces dernières années, la Méthode Intégrale de Volume (MIV) a reçu une attention particulière pour lamodélisation des problèmes électromagnétiques en basse fréquence. Son intérêt principal est l’absencedu maillage de la région air, ce qui rend la méthode légère et rapide. Associée aux méthodes decompression matricielle la MIV devient aujourd'hui une alternative compétitive à la méthode deséléments finis pour la modélisation de dispositifs électromagnétiques ayant un volume d'airprépondérant.Ce rapport porte sur le développement de deux formulations intégrales de volume pour la résolution deproblèmes magnétostatiques avec prise en compte des matériaux non linéaires, des aimants, desbobines, des circuits magnétiques avec ou sans entrefer et des régions minces magnétiques. Lapremière est une formulation en flux de mailles indépendantes basée sur l'interpolation par éléments defacette. La deuxième est une formulation en potentiel vecteur magnétique basée sur l'interpolation paréléments d'arête. L'application de ces formulations permet d’une part d'obtenir des résultats précismême en présence d’un faible maillage et d’autre part de résoudre aisément des problèmes nonlinéaires. Des méthodes de calcul de la force magnétique globale ainsi que du flux magnétique dansles bobines ont été également mises en oeuvre. Les développements informatiques ont été réalisés dansla plateforme MIPSE et ont été validés sur des problèmes académiques ainsi que sur quelquesdispositifs industriels. / In recent years, the Volume Integral Method (VIM) has been received particular attention formodeling of low frequency electromagnetic problems. The main advantage of this method is thatinactive regions do not to be discretized, which makes it light and rapid. Associated with matrixcompression methods, the VIM is a competitive alternative to the finite element method for modelingelectromagnetic devices containing a predominant air volume.This PhD thesis focuses on the development of two volume integral formulations for solvingmagnetostatic problems, in the presence of nonlinear materials, magnets, coils, multiply connectedmagnetic regions, and the presence of magnetic shielding. The first one is a mesh magnetic fluxformulation based on the interpolation of facet elements and the second one is a magnetic vectorpotential formulation based on the interpolation of edge elements. The application of theseformulations provides accurate results even with coarse meshes and allows solving straightforwardnonlinear magnetostatic problems. Methods for computing global magnetic force and magnetic fluxthrough a coil were also implemented as part of this work. Developments performed in the MIPSEplatform were validated on academic case-tests as well as some industrial devices.

Cette thèse s’inscrit dans le cadre des études des phénomènes électromagnétiques dansles régions frontales des grands turbo-générateurs. L’objectif de la thèse est d’estimer apriori le champ magnétique axial en fonction du point de fonctionnement afin d’éviterles possibles dégradations du circuit magnétique (dus aux points chauds et tensions entretôles, qui sont liés à la composante axiale du champ).Une maquette à échelle réelle a été spécialement conçue et réalisée dans le but d’améliorerla compréhension physique des phénomènes : les pertes, la pénétration du champ magnétiqueet les tensions entre tôles sont analysés.Les simulations par éléments finis sont ensuite utilisées : les avantages et inconvénientsseront discutés, ainsi qu’une comparaison critique des résultats par rapport aux mesuresexpérimentales sur la maquette. La région frontale d’un turbo-alternateur est aussi entièrementmodélisée.Enfin, un modèle simple du flux axial est développé. Ses coefficients sont déterminés àl’aide de simulations par éléments finis, mais il peut ensuite être utilisé en temps réel afind’estimer le flux axial correspondant à un point de fonctionnement quelconque. / This work aims to improve the knowledge of electromagnetic phenomena that occurin the end region of large turbo-generators. The goal of this work is to evaluate theaxial magnetic flux density with regard to the operating conditions (such as active orreactive power) in order to prevent potential deterioration of the stator. Indeed, the axialmagnetic field is known to induce hot points or voltages between laminations that maycause insulation breakdown and thus stator faults.An experimental apparatus in real scale has been designed and built. Its purpose is tostudy precisely the following phenomena: losses, axial magnetic flux density penetration,voltage across adjacent voltages.Finite element simulations (FEM) are also used: their advantages and drawbacks arediscussed, and the results are compared with the experimental measures. The wholeend-region of a turbo-generator is also simulated.Finally, a simple model of the axial magnetic flux is proposed. Its parameters are basedon the results of the FEM model, but it may be used in real time to evaluate the axialmagnetic flux density of any operating point.

The aim of this thesis is to design a drive for seal-less centrifugal pump. Designed motor with axial magnetic flux is a double-sided structure with an internal coreless stator. The construction of the seal-less pump is based on a patent no. 17818, which was created at the Victor Kaplan Department of Fluid Engineering BUT. Potential use of this assembly is mainly in the food industry, possibly in the field of chemically aggressive liquids. The whole design is based on coordination between analytical equations and finite element method of the software ANSYS Maxwell. The temperature ratios inside the motor were investigated when cooling with air by the iterative solution of thermal circuit. The work includes research on the topic of constructing the axial machines and their applications in pumps. A comprehensive specification of the entire seal-less centrifugal pump is given in Chapter 4.

Táto práca pojednáva o problematike vytvárania a simulácie reluktančnej sieti synchrónneho stroja s V tvarovanými permanentnými magnetmi v programe PSpice. Na začiatku sa oboznámime s konštrukciou a parametrami stroja a potom vyvodíme základné rovnice na výpočet každého prvku siete. Vypočítame každý prvok tohto stroja a potom vytvoríme túto sieť v PSpice. Na začiatku je simulovaná sieť statická a všetky magnetické odpory sú lineárne. Neskôr nahradíme lineárne odpory reprezentujúce plechy nelineárnymi a počítame s precovnou teplotou permanentných magnetov. Potom porovnáme naše výsledky s FEM metódou počítanými hodnotami a vypočítame indukované napätie v jednej cievke stroja. Na záver vypočítame výkonovú a momentovú charakteristiku stroja.

This thesis deals with distribution of magnetic fields in the DC machine. Part of this thesis is the introduction of DC machines, principles of operation and distribution of DC machines. There is also discussed electrically commutated motors. The thesis demonstrates the types of permanent magnets and their properties. Then there is an analysis of the magnetic field electrically commutated motor Atas Nachod in the Ansoft Maxwell. Using Ansoft Simplorer, switching is carried out of the engine. Another part of this work is the analysisthe magnetic field electrically commutated motor Atas Nachod for three types of slot of the stator of the engine. Here it is seen what impact the change has slot on the distribution of magnetic field in the EC motor. Finally, training is carried out measurements of electrically commutated motor BOYANG BY92BL48-4000-2200.

This master´s thesis is focused on obtaining electrical energy from vibration control car using electromagnetic dampers. The primary use of the electromagnetic damper is the production of electrical energy, which can then be used to power electrical appliances in your car or battery charging. The thesis is divided into six main parts: a literature review of possible ways of getting electricity from the car damping, theoretical and mathematical analysis of problems, the choice of design with computational analysis of dampers and power calculation.