785 research outputs found

    A Structural Analysis of Field/Circuit Coupled Problems Based on a Generalised Circuit Element

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    In some applications there arises the need of a spatially distributed description of a physical quantity inside a device coupled to a circuit. Then, the in-space discretised system of partial differential equations is coupled to the system of equations describing the circuit (Modified Nodal Analysis) which yields a system of Differential Algebraic Equations (DAEs). This paper deals with the differential index analysis of such coupled systems. For that, a new generalised inductance-like element is defined. The index of the DAEs obtained from a circuit containing such an element is then related to the topological characteristics of the circuit's underlying graph. Field/circuit coupling is performed when circuits are simulated containing elements described by Maxwell's equations. The index of such systems with two different types of magnetoquasistatic formulations (A* and T-Ω\Omega) is then deduced by showing that the spatial discretisations in both cases lead to an inductance-like element

    3D direct and inverse solvers for eddy current testing of deposits in steam generator

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    We consider the inverse problem of estimating the shape profile of an unknown deposit from a set of eddy current impedance measurements. The measurements are acquired with an axial probe, which is modeled by a set of coils that generate a magnetic field inside the tube. For the direct problem, we validate the method that takes into account the tube support plates, highly conductive part, by a surface impedance condition. For the inverse problem, finite element and shape sensitivity analysis related to the eddy current problem are provided in order to determine the explicit formula of the gradient of a least square misfit functional. A geometrical-parametric shape inversion algorithm based on cylindrical coordinates is designed to improve the robustness and the quality of the reconstruction. Several numerical results are given in the experimental part. Numerical experiments on synthetic deposits, nearby or far away from the tube, with different shapes are considered in the axisymmetric configuration.Comment: 3

    Arbitrary order spline representation of cohomology generators for isogeometric analysis of eddy current problems

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    The eddy current problem has many relevant practical applications in science, ranging from non-destructive testing to magnetic confinement of plasma in fusion reactors. It arises when electrical conductors are immersed in an external time-varying magnetic field operating at frequencies for which electromagnetic wave propagation effects can be neglected. Popular formulations of the eddy current problem either use the magnetic vector potential or the magnetic scalar potential. They have individual advantages and disadvantages. One challenge is related to differential geometry: Scalar potential based formulations run into trouble when conductors are present in non-trivial topology, as approximation spaces must be then augmented with generators of the first cohomology group of the non-conducting domain. For all existing algorithms based on lowest order methods it is assumed that the extension of the graph-based algorithms to high-order approximations requires hierarchical bases for the curl-conforming discrete spaces. However, building on insight on de Rham complexes approximation with splines, we will show in the present submission that the hierarchical basis condition is not necessary. Algorithms based on spanning tree techniques can instead be adapted to work on an underlying hexahedral mesh arising from isomorphisms between spline spaces of differential forms and de Rham complexes on an auxiliary control mesh

    Systems of Differential Algebraic Equations in Computational Electromagnetics

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    Starting from space-discretisation of Maxwell's equations, various classical formulations are proposed for the simulation of electromagnetic fields. They differ in the phenomena considered as well as in the variables chosen for discretisation. This contribution presents a literature survey of the most common approximations and formulations with a focus on their structural properties. The differential-algebraic character is discussed and quantified by the differential index concept

    THREE-DIMENSIONAL STEADY STATE AND TRANSIENT EDDY CURRENT MODELING

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    Maglev transportation using electrodynamic wheels is a promising new technology aimed at providing a low cost, high-speed and environmental friendly mode of transportation. In this technology, Halbach permanent magnet rotors, termed electrodynamic wheels, are simultaneously rotated and translationally moved above a conductive non-magnetic guideway. The time-changing magnetic field created in the airgap between the rotors and guideway induces eddy currents in the guideway which in turn interact with the magnetic rotor field to produce suspension and propulsion or braking forces which are required for maglev transportation. This technology offers an integrated suspension and propulsion system. In this dissertation the eddy current distribution in the conductive guideway has been modeled in three-dimension. An approach for the computation of the static magnetic fields due to the Halbach rotor has been presented using novel magnetic charge sheet concept. Finite element models have been developed to study the steady state and transient eddy current field distribution. Three analytic models have been developed to compute the electromagnetic forces and torque acting on the rotor as well as joule loss in the guideway. The models include the heave, translational and rotational motion of the magnetic rotor for dynamic simulation. The developed analytic and finite element models are highly generic and thus can be applied to any magnetic source. The developed finite element models have been validated by comparing it with commercial finite element software and previously developed boundary coupled steady state finite element model. Commercial finite element software and two experimental setups have been used to verify the developed analytic models. Computational efficiency of the presented models has been compared with the previously developed finite element model and commercial software. Good performance of the developed models has been achieved

    An Overview of Methods and a New Three-Dimensional FEA and Analytical Hybrid Technique for Calculating AC Winding Losses in PM Machines

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    This article proposes a new hybrid analytical and numerical finite element (FE) based method for calculating ac eddy current losses in wire windings and demonstrates its applicability for axial flux permanent magnet electric machines. The method takes into account three-dimensional (3-D) field effects in order to achieve accurate results and yet greatly reduce computational efforts. The new 3-D FE-based method is advantageous as it employs minimum simplifications and considers the end turns in the eddy current path, the magnetic flux density variation along the effective length of coils, and the field fringing and leakage, which ultimately increases the accuracy of simulations. This study is one of the first ones to compare meticulous 3-D finite element analysis (FEA) models with more approximate, but faster solution methods, which can be employed in the optimization process. The accuracy of the 3-D FEA calculations has been confirmed through tests on a prototype axial flux permanent magnet machine. The proposed method is applicable for cases with majority of ac copper losses induced due to external magnetic flux sources, such as permanent magnets. Examples of such machines designs are coreless or open slot PM machines with conductors sizes smaller than skin depth

    Simulation of Transient Effects in High-Temperature Superconducting Magnets

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    Particle colliders for high-energy physics are important tools for investigating the fundamental structure of matter. In circular accelerators, the collision energy of particles is proportional to the bending magnetic field and the radius of the machine. As a consequence, circular accelerators such as the Large Hadron Collider at CERN have traditionally relied on high-field magnets made of low-temperature superconductors, confining the particle beams within a complex of acceptable dimensions. This class of superconductors shows a practical limit in the achievable magnetic field in the magnet aperture of about 8 T for a Nb-Ti alloy, and 16 T for a Nb3Sn compound. Overcoming these limits requires the use of high-temperature superconductors (HTS) in accelerator magnets, in particular rare-earth barium copper oxide (ReBCO) tapes. With respect to the low-temperature counterpart, accelerator magnets based on ReBCO tapes are known to behave differently in terms of magnetic field quality and protection from quench events. The tapes are equivalent to wide and anisotropic mono-filaments, resulting in screening currents detrimentally affecting the magnetic field quality, in particular at low currents. At the same time, quenches are less likely to occur due to the enhanced thermal stability of the tapes, but are more difficult to detect and mitigate. Moreover, the dynamic behavior of accelerator magnets is also affected by the surrounding circuitry which must be taken into account, leading to multiphysics, multirate and multiscale problems. Numerical methods play a crucial role for overcoming the challenges related to magnetic field quality and quench protection. In this work, the magnetothermal dynamics in high-temperature superconducting magnets is modeled by means of an eddy-current problem in the time domain. A mixed field formulation is developed to cope with the nonlinear resistivity law of superconducting materials. The formulation is complemented with distribution functions for the coupling of external voltage and/or current source quantities. Further simplifications are discussed in case of tapes with high aspect ratio, and multifilamentary conductors. Moreover, a field-circuit coupling interface is derived as an optimized Schwarz transmission condition, such that the formulation can be used in field-circuit coupled problems by means of co-simulation methods. The implementation of the formulation in the finite element method is verified against analytical and reference solutions available in literature, and validated against measurements on the HTS-based dipole magnet Feather-M2. As a case-study, the formulation is applied to proof-of-concept ReBCO screens for the passive field-error cancellation in accelerator magnets. The proposed design is called HALO (harmonics-absorbing layered object) as it is made of stacks of tapes arranged in layers which are fully scalable and expandable. The screens are positioned such that their persistent magnetization shapes the magnetic field in the magnet aperture, canceling the undesired field imperfections. Experimental measurements at 77 K in liquid nitrogen show a significant reduction of the field error, up to a factor of four. Moreover, numerical extrapolation for accelerator-like conditions shows that a careful design of the superconducting screens allows matching the typical field quality requirements for accelerator magnets

    3D Capacitance Extraction With the Method of Moments

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    In this thesis, the Method of Moments has been applied to calculate capacitance between two arbitrary 3D metal conductors or a capacitance matrix for a 3D multi-conductor system. Capacitance extraction has found extensive use for systems involving sets of long par- allel transmission lines in multi-dielectric environment as well as integrated circuit package including three-dimensional conductors located on parallel planes. This paper starts by reviewing fundamental aspects of transient electro-magnetics followed by the governing dif- ferential and integral equations to motivate the application of numerical methods as Method of Moments(MoM), Finite Element Method(FEM), etc. Among these numerical tools, the surface-based integral-equation methodology - MoM is ideally suited to address the prob- lem. It leads to a well-conditioned system with reduced size, as compared to volumetric methods. In this dissertation, the MoM Surface Integral Equation (SIE)-based modeling approach is developed to realize electrostatic capacitance extraction for 3D geometry. MAT- LAB is employed to validate its e?ciency and e?ectiveness along with design of a friendly GUI. As a base example, a parallel-plate capacitor is considered. We evaluate the accu- racy of the method by comparison with FEM simulations as well as the corresponding quasi-analytical solution. We apply this method to the parallel-plate square capacitor and demonstrate how far could the undergraduate result 0C = A ? =d\u27 be from reality. For the completion of the solver, the same method is applied to the calculation of line capacitance for two- and multi-conductor 2D transmission lines
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