Electromagnetic Field Computation Research Articles

Effects of Multispectral Absorbing Coating on the Generated Voltage of Solar Radiation–Thermoelectric System

The effective utilization of solar energy is an important development direction to realize the exploration of clean energy. Herein, a model of solar radiation–thermoelectric generation (TEG) system is established, which is composed of solar absorbing coating and TEG component. Five different microscopic structures of coating are designed and the spectral absorption properties are numerically analyzed with the finite‐difference time‐domain method. Then, the absorbed solar energy and produced open‐circuit voltage with different coating structures are compared, with the coupling calculation of temperature field and electromagnetic field achieved. Additionally, the effects of structural size parameters on the output voltage performance are discussed. It can be observed that the absorbing coating can effectively improve the performance of TEG component, and the multilayer structure with appropriate gold particle diameter chosen is an optimization research direction for more efficient energy conversion.

Design and cooling of permanent magnet generator in MW-class space closed Brayton cycle system

The closed Brayton cycle (CBC) system is a prime energy conversion technology to convert heat from the reactor to electric power for space missions due to its light weight, compact and stable operation. The CBC system incorporates a permanent magnet generator (PMG) mounted on the CBC shaft with the turbine and compressor. To ensure safe operation of the CBC system, a small fraction of the working fluid is used to provide the required cooling. In this study, four different cooling schemes used in CBC system are concluded and the key dimensions of the PMG are obtained through mechanical design theory and electromagnetic theory. Comprehensive research on the electromagnetic field and loss calculation is then performed. Furthermore, the cooling paths of the PMG are designed and the resulting temperature profiles are calculated. Finally, different cooling schemes are compared and the appropriate cooling advice is proposed.

Comment on “Fast and accurate electromagnetic field calculation for substrate-supported metasurfaces using the discrete dipole approximation”

Abstract The article entitled “Fast and accurate electromagnetic field calculation for substrate-supported metasurfaces using the discrete dipole approximation (DDA)” written by W. Liu and E. McLeod presents a method for computing the Green function in presence of a substrate or multilayer in an efficient way. Unfortunately, the proposed method has been known for more than twenty years and significantly ameliorated. It can be found in its optimized version in some open-source DDA codes. In this comment, we recall the different approaches (and related papers) addressing the computation of the Green function of a multilayered system. We show that they address all the points raised by Liu and McLeod in their paper and provide more efficient solutions to their computational issues.

Electromagnetic Vibration and Noise Analysis of Linear Phase-Shifting Transformer

The advantages of adjustable angle phase-shifting and great expansibility make the linear phase-shifting transformer a novel type of power conversion device with a wide range of potential applications. However, during the procedure, there is a lot of noise. For the purposes of transformer design and vibration and noise reduction, it is crucial to investigate its electromagnetic vibration and noise. In this paper, the radial electromagnetic force wave considering the influence of the end effect as the source of the noise of the linear phase-shifting transformer was deduced and calculated. Based on this, the spectrum and space–time properties of the radial electromagnetic force waves were simulated and verified. Additionally, a finite element model was created using the Ansys Workbench 2022R1 platform to study the electromagnetic vibration and noise of the linear phase-shifting transformer. A joint simulation of the electromagnetic, structural, and sound fields was then performed. First, the transformer’s natural frequency was determined by modal analysis. After that, the transformer’s structure and the results of the transient electromagnetic field computation were combined and a harmonic response analysis was conducted to determine the vibration acceleration spectrum. Finally, in order to solve the sound pressure field, the transformer’s boundary vibration acceleration was coupled to the air domain. Furthermore, an analysis was conducted to determine the noise distribution surrounding the linear phase-shifting transformer. The joint simulation findings demonstrate that the linear phase-shifting transformer’s resonance, which produces larger electromagnetic vibration and noise, is indeed caused by the radial electromagnetic force. Simultaneously, the impact of the LPST core’s fixed components on the electromagnetic vibration and noise of the core was examined.

Influence of stator and rotor core material definition method on no‐load electromagnetic field calculation results for tubular hydrogenerator

AbstractIn this letter, the effects of various material definition approaches for stator and rotor cores on the no‐load electromagnetic field calculations of a 34 MW tubular hydrogenerator are investigated, utilizing the transient motion electromagnetic field time‐step finite element (FE) method. The findings indicate that employing a linear simplified definition for the stator core material maintains high accuracy and rationality in the calculation results of the no‐load electromagnetic field and voltage waveform while offering substantially greater computational efficiency than the non‐linear definition method. Conversely, using a linear simplified definition for the magnetic pole core material of the rotor significantly increases the error margin in the results, rendering them unacceptable.

Investigation of the influence mechanism of shield on the strong magnetic field during electromagnetic launch

The electromagnetic launch process generates low-frequency pulsed magnetic fields with peak values reaching Tesla-levels, imposing greater demands on the interference immunity of electronics within projectiles. However, during the propagation of low-frequency pulsed strong magnetic fields, their characteristics are affected by the shielding properties of the surrounding medium materials, resulting in modifications to the actual internal magnetic fields of the devices. This paper presents a theoretical analysis, numerical simulation, and experimental investigation based on the shielding mechanisms of conductive and magnetic materials to elucidate their impact on the pulsed magnetic fields. Additionally, leveraging previous work on electromagnetic railgun projectile magnetic field calculations, the shielding model is established to determine the shielding effects of different material combinations on the magnetic field during electromagnetic launch. The results reveal that both conductive and magnetic materials influence the amplitude, pulse width, and initiation time of the pulsed magnetic field, a finding validated through dynamic projectile-borne magnetic field testing.

Computer Simulation of Explosive Emission Processes in Strong Electromagnetic Fields

The paper discusses the problem of computer simulation of explosive emission processes in strong electromagnetic fields. In this work, a numerical method for calculating electron emission from the surface of a metal cathode for the axial symmetric geometry of a technical system is proposed. For modelling, the particle method and grid calculations of electromagnetic fields based on Maxwell’s equations are applied. The approach uses the representation of large smoothed Gaussian particles and implements calculations of the electromagnetic fields on Cartesian spatial grids. The software realization is directed towards on parallel computing. The calculation of the emission process in a coaxial cylindrical diode with magnetic self-insulation with the use of developed technique was carried out. The process is considered for two situations: with and without the longitudinal plasma layer. The calculations show that the presence of plasma leads to an increase in the emission current. This result is consistent with the results of experiments.

Optimal Control for a Superconducting Hybrid MagLev Transport System with Multirate Multisensors in a Smart Factory.

Recently, magnetic levitation systems have been applied and studied in various industrial fields. In particular, in-tracktype magnetic levitation conveyor systems are actively studied since they can effectively minimize electromagnetic effects in processes that require a highly clean environment. In this type of system, diverse and multiple sensors are structurally required so that the control performance of an integrated system is primarily governed by the slowest measuring sensor. This paper proposes a multisensor fusion compensator to integrate the outputs obtained from various sensors into one output with the single fastest time rate. Since the state of the system is estimated at a fast time rate, the optimal controller also guarantees fast performance and stability. The computation of electromagnetic fields and the control performance of the considered superconducting hybrid system were analyzed using a computer simulation based on finite element methods.

Analysis of leakage flux, losses, and temperature in large synchronous generator end zone under the multi‐layer screen thickness based on novel iterative method

AbstractThe multi‐layer screen is the key component in the large synchronous generator end zone. The leakage flux, losses, and temperature of end components are significantly affected by the thickness of multi‐layer screen in the synchronous generator. To investigate the influence of multi‐layer screen thickness on the end leakage flux, losses, and temperature in the synchronous generator end zone, 1407MVA nuclear power synchronous generator is studied. Three‐dimensional transient electromagnetic field model of synchronous generator end zone is established. Three‐dimensional transient electromagnetic field in the end zone of 1407MVA synchronous generator with the multi‐layer screen is calculated based on the novel iterative method. The flux density of end components is compared and studied in the end zone under the variation of multi‐layer screen thickness. Influence of the different thicknesses of multi‐layer screen on the losses of the shield plate, screen, finger plate, and stator end core is researched. The losses of end components obtained from 3D end electromagnetic field calculation are applied to the end zone as the heat source in the three‐dimensional fluid and thermal coupled field. The temperature distribution of the end components is determined. The accuracy of the calculated results is validated by the experimental values.

Fast and accurate electromagnetic field calculation for substrate-supported metasurfaces using the discrete dipole approximation

Abstract Metasurface design tends to be tedious and time-consuming based on sweeping geometric parameters. Common numerical simulation techniques are slow for large areas, ultra-fine grids, and/or three-dimensional simulations. Simulation time can be reduced by combining the principle of the discrete dipole approximation (DDA) with analytical solutions for light scattered by a dipole near a flat surface. The DDA has rarely been used in metasurface design, and comprehensive benchmarking comparisons are lacking. Here, we compare the accuracy and speed of three DDA methods—substrate discretization, two-dimensional Cartesian Green’s functions, and one-dimensional (1D) cylindrical Green’s functions—against the finite difference time domain (FDTD) method. We find that the 1D cylindrical approach performs best. For example, the s-polarized field scattered from a silica-substrate-supported 600 × 180 × 60 nm gold elliptic nanocylinder discretized into 642 dipoles is computed with 0.78 % pattern error and 6.54 % net power error within 294 s, which is 6 times faster than FDTD. Our 1D cylindrical approach takes advantage of parallel processing and also gives transmitted field solutions, which, to the best of our knowledge, is not found in existing tools. We also examine the differences among four polarizability models: Clausius–Mossotti, radiation reaction, lattice dispersion relation, and digitized Green’s function, finding that the radiation reaction dipole model performs best in terms of pattern error, while the digitized Green’s function has the lowest power error.

The Analysis of Permanent Magnet Vernier Synchronous Machine Vibration and Noise

The permanent magnet vernier synchronous machine (PMVSM) has the characteristics of high torque density and high power density and has advantages in the field of low-speed and high-torque applications. The PMVSM utilizes rich harmonics for torque enhancement, but it can also cause an increase in radial electromagnetic force and vibration noise. In this paper, we take a 12-slot 10-pole PMVSM as an example to analyze the source of radial electromagnetic force, vibration and noise. The electromagnetic finite-element model and structural finite-element model of the PMVSM are established for calculation. Through the analysis and calculation of two-dimensional electromagnetic fields, the radial electromagnetic force distribution of the PMVSM is obtained. We derive the radial electromagnetic force formula of the PMVSM and verify the correctness of the formula through harmonic analysis of the radial electromagnetic force. The sources of radial electromagnetic forces at various orders and frequencies within the PMVSM are analyzed and summarized by coupling the radial electromagnetic force obtained from the electromagnetic finite-element model to the structural finite-element model and conducting electromagnetic vibration harmonic response analysis on the PMVSM. The measured acceleration spectrum of the prototype is compared with the finite-element method (FEM) results, verifying the correctness of the finite-element simulation results for electromagnetic vibration.

High-accuracy calculation of singular electromagnetic fields in regions with re-entrant peripheries

Accurate analysis of the electromagnetic fields inside waveguides and cavities with re-entrant boundaries is crucial for many multi-scale device applications. In earlier approaches, the singularities that exist in electromagnetic field gradients inside such waveguides and cavities significantly reduce the accuracy of the calculations. In our scheme, these singular behaviors are treated using Hermite finite elements combined with analytical regularization of the action integral. We show that this approach provides considerably higher accuracy as compared with other methods employed in the literature. Specific calculations are presented for three typical regions: (a) an L-shaped waveguide, (b) an L-cavity, and (c) a cubic cavity with an octant removed to form a triple-junction corner. The method can be adapted to evaluate very high electromagnetic fields in any complex structures displaying “hot points.”

The Complex Impedance of the Hemispherical Ground Electrode: An Open Analytical Problem

The hemispherical ground electrode is a basic electrode whose analysis appears in many textbooks on electromagnetics in chapters dedicated to steady currents. Considering a soil with a given resistivity and an electrode with a given perimeter, the electrode DC resistance is simply calculated from the ratio resistivity/perimeter. Strangely, the generalization of this result to AC regimes is missing. The issue of the frequency-domain impedance of the hemispherical ground electrode has been avoided in the literature despite its trivial geometry. But the problem is indeed not easy; electromagnetic field calculation involves Legendre and Bessel functions; the application of boundary conditions involves an infinite set of points, and some integrals involved need to be calculated recursively. We analyzed the math and physics of the problem but failed to find a closed-form solution. This article with “negative results” can, however, be useful; on one hand it may prevent researchers from wasting their time following the same steps, and, on the other hand, it may attract the interest of new researchers to the subject, ultimately, accelerating its analytical solution (if the solution exists).

Innovative technologies for strengthening of internal surfaces of suspension parts of heavy-loaded machines by laser and high-frequency induction methods

In the article innovative methods of surface hardening of internal surfaces of machine parts by laser and highfrequency induction heating are presented. The relevance of applying the methods of laser and induction hardening for the internal surfaces of heavily loaded parts of quarry equipment is proved. The results of modeling and calculation of thermal and electromagnetic fields under the influence of an external electromagnetic field and laser radiation beams are presented. The original design of a complex of equipment for processing the internal surfaces of suspension parts by external electromagnetic field is described. The optimal designs of inductors with magnetic circuits made of various materials are shown. The study of the structure and properties obtained on the internal surfaces of heavily loaded suspension parts of cars, line of the BelAZ company, treated according to the optimal modes of surface induction exposure is given. The developed original technology and equipment of laser surface hardening, which makes it possible to increase the wear resistance of heavily loaded parts, is described. Data on the implementation of research results at JSC “BELAZ” – the Management Company of the Holding “BELAZ-HOLDING” for processing a wide range of heavily loaded suspension parts are given.

Analytical solution of the field integrals of a cylindrical grid element

Many axisymmetric physical problems related to the calculation of gravitational or electro-magnetic fields can be favorably described by a Poisson potential problem – or the associated field problem – on a cylindrical grid. Numerical integration of the field integrals on such a grid can become expensive in terms of computing time or requires to compromise the accuracy, respectively. Here the analytical solution of the field integrals over a cylindrical volume element are presented and a very efficient implementation is discussed. The results are useful, e.g., for modeling space-charge effects in beams in cylindrical coordinates or gravitational effects in galaxies. The numerical implementation is based on modified relations originally derived by Carlson. A new limiting value and a new transformation relation of the complex elliptic integral of third kind are presented.

Simulation of Emission Processes in Strong Electromagnetic Fields

The problem of calculating the processes of electron emission from metal surfaces in strong electromagnetic fields is considered with allowance for relativistic effects. One of the methods of simulation in these processes is the particle method combined with grid calculation of fields on the basis of Maxwell’s equations. Similar techniques have been developed since the 1960s to the present. However, existing approaches have certain limitations. In this work, for an axisymmetric geometry of the generating system, a new numerical technique simulating the processes of electron emission from metal cathode surfaces is presented. The technique uses the representation of large smoothed Gaussian particles and implements the calculation of electromagnetic fields on Cartesian spatial grids. The software implementation is oriented to parallel computing. The aim of numerical experiments was to determine the parameters of electron emission. Diode and triode cylindrical systems were chosen as test problems. In numerical calculations, the spatiotemporal characteristics of relativistic electron beams generated by emission processes are obtained, including the reproduction of the Child–Langmuir current. The numerical technique developed has confirmed its correctness and efficiency.

Разработка конструкции индуктора для закалки детали сложной формы

Due to active process of import substitution, domestic industry starts producing the parts previously purchased abroad. These parts are necessary for stable and reliable operation of various technical objects and systems. Thus, the development of a technological installation for hardening a metal profile is topical. The task is complicated by the fact that the profile has very thin irregularly shaped walls, which should be hardened only from the inside, while the outer wall of the profile should be heated minimally to maintain strength. The studies have been carried out on simulation models of electromagnetic and thermal fields, which make it possible to reproduce the process of induction heating of the research object. Since the part has the same shape along the entire length, the simulation of the process of its induction heating is performed in two-dimensional space. The authors have developed a simulation model of the process of induction heating of a part of a non-standard shape, which includes calculations of thermal and electromagnetic fields. The design of the inductor is proposed, supplemented with ferrite inserts, which makes it possible to achieve the temperature regime necessary for the hardening process. The developed simulation model makes it possible to evaluate the distribution of the thermal and electromagnetic fields of the part, thereby predicting getting the temperatures required for its hardening when using various designs of inductors. The results of numerical experiments are consistent with the physical concepts of induction heating and prove the possibility to use induction hardening for thin-walled parts of complex shape instead of laser hardening used for this type of parts. The proposed model can be used in engineering practice to design inductors of non-standard parts.

A hybrid enrichment strategy for the efficient construction of reduced order models by the proper generalized decomposition

PurposeThe calculation of electromagnetic fields can involve many degrees of freedom (DOFs) to achieve accurate results. The DOFs are directly related to the computational effort of the simulation. The effort is decreased by using the proper generalized decomposition (PGD) and proper orthogonalized decomposition (POD). The purpose of this study is to combine the advantages of both methods. Therefore, a hybrid enrichment strategy is proposed and applied to different electromagnetic formulations.Design/methodology/approachThe POD is an a-priori method, which exploits the solution space by decomposing reference solutions of the field problem. The disadvantage of this method is given by the unknown number of solutions necessary to reconstruct an accurate field representation. The PGD is an a-priori approach, which does not rely on reference solutions, but require much more computational effort than the POD. A hybrid enrichment strategy is proposed, based on building a small POD model and using it as a starting point of the PGD enrichment process.FindingsThe hybrid enrichment process is able to accurately approximate the reference system with a smaller computational effort compared to POD and PGD models. The hybrid enrichment process can be combined with the magneto-dynamic T-Ω formulation and the magnetic vector potential formulation to solve eddy current or non-linear problems.Originality/valueThe PGD enrichment process is improved by exploiting a POD. A linear eddy current problem and a non-linear electrical machine simulation are analyzed in terms of accuracy and computational effort. Further the PGD-AV formulation is derived and compared to the PGD-T-Ω reduced order model.

A novel representation of electromagnetic field interaction with vertically stratified structures

PurposeThe purpose of this study is to develop an efficient model to solve the electromagnetic forward problem using a novel semi-analytical approach to compute the electromagnetic fields because of the presence of a scatterer.Design/methodology/approachThe proposed model involves a novel formulation of a complete orthonormal set of radiating/nonradiating polarization currents. Furthermore, an integral equation-based representation is derived, and the appropriate boundary conditions are imposed to get the scattered electromagnetic field. An error term is introduced to evaluate the obtained results.FindingsThe proposed model was tested using several examples at different frequencies. The results of this study show that the novel representation exhibits fast convergence behavior and achieves highly accurate results, when compared to the results provided by the transmission line method.Originality/valueThe derived formulations presented in this study are significant in the electromagnetic forward modelling field because of the meaningful physical representation they provide. This is an important aspect that leads to precise calculation of electromagnetic fields for various applications.

Electromagnetic field calculation and analysis of short primary linear induction motor for electromagnetic launch

AbstractThe aim of this study is to determine the electromagnetic field spatial distribution and longitudinal end effect characteristics of short primary linear induction motor (SPLIM) in the field of electromagnetic launch. First, in accordance to the electromagnetic model assumption of SPLIM and one‐dimensional electromagnetic field theory, the analytical expression of the whole‐region magnetic flux density of air‐gap is derived using electromagnetic field boundary conditions in line with the actual physical meaning. Second, the finite element method used in comparing the analytical calculation values of key physical quantities, such as air‐gap flux density and secondary eddy current in a multidimensional manner under various static and dynamic working conditions and verifying the correctness of the analytical calculation of the electromagnetic field. On this basis, the air‐gap flux density of SPLIM is decomposed according to the different generation mechanisms, and the spatial distribution of each part of the flux density is studied. Spatial Fourier analysis of flux density is conducted, the end effect coefficient is defined, and the change rule of the end effect coefficient with the design parameters of the motor is studied. Finally, a megawatt‐class high thrust prototype test platform was built, and the measured electromagnetic force was compared with the electromagnetic force calculated by air gap magnetic field and secondary eddy current. The steady‐state error of the two was less than 2%, which verified the accuracy of the analysis and calculation.