Application of a modified variational formulation of the vector finite element method for modelling a harmonic electric field in areas with curved shields

2021 ◽  
pp. 26-41
Author(s):  
Дарья Владимировна Добролюбова ◽  
Элла Петровна Шурина
Keyword(s):  
Electric Field ◽  
Variational Formulation ◽  
Computational Cost ◽  
Surface Current ◽  
Local Source ◽  
Current Loop ◽  
Surface Current Density ◽  
Field Source ◽  
The Media ◽  
Cylindrical Shield

Рассматриваются особенности применения модифицированной вариационной постановки векторного метода конечных элементов (ВМКЭ), основанной на замене тонких сильнопроводящих объектов токонесущими поверхностями, для моделирования гармонического электрического поля в областях с криволинейными экранами при различном типе возбуждения поля. Исследуется применимость модифицированной вариационной постановки в широком диапазоне частот Purpose. The paper addresses applicability of the modified variational formulation of vector FEM for the harmonic electric field to the media with cylindrical shields. Thin highly conductive objects are treated as surfaces with the equivalent surface current density. We consider the excitation of the field by a local source (current loop) located either inside or outside the cylindrical shield. Methodology. The simulations are carried out on unstructured tetrahedral meshes. Since the modified variational formulation treats thin highly conductive objects as surfaces, only the surface of a cylinder is discretized. The results yielded by the modified variational formulation are compared with the results of the classic vector FEM. Findings. For the frequency range between 100 KHz and 100 MHz, the modified variational formulation provides correct results when the field source is located outside the cylindrical shield. The modified variational formulation reduces computational cost, since the volume of the thin shield is not discretized. When the field source is located inside the shield, the modified variational formulation gives valid results only in the proximity of the source. Originality/value. The limitations for the application of the reduced variational formulation for the modelling of harmonic electric field in the media with hollow cylindrical shields are investigated

A reduced formulation for modelling time-harmonic electromagnetic field in the media with thin highly conductive inclusions

2018 ◽  
Author(s):  
Э.П. Шурина ◽  
Д.В. Добролюбова ◽  
Е.И. Штанько
Keyword(s):  
Electric Field ◽  
Variational Formulation ◽  
Computational Cost ◽  
Surface Current ◽  
Wide Frequency Range ◽  
Geometrical Shape ◽  
Frequency Range ◽  
Surface Current Density ◽  
Time Harmonic ◽  
The Media

При решении задач электромагнетизма в широком частотном диапазоне в областях с тонкими пластинами, оболочками и экранами численными методами возникает проблема резкого роста сеточной дискретизации вблизи внутренних структур с разномасштабными габаритными размерами. В работе предложена модификация вариационной постановки векторного метода конечных элементов, основанная на снижении размерности модели в окрестности тонких включений, которая позволяет преодолеть эту проблему за счет специфического учета таких структур на уровне вариационной постановки. Так как редуцирование модели обычно приводит к появлению ограничений на область ее применимости, выполнено исследование диапазона допустимых частот, контрастности электрофизических характеристик матрицы и включений, геометрических особенностей внутренней структуры, для которых предложенная модель позволяет получить корректные с точки зрения физики результаты. Purpose. In this paper, we propose a reduced variational formulation for the Helmholtz equation for the electric field, in which thin highly conductive objects are approximated by surfaces with the equivalent surface current density. We conduct a study aimed at defining the range of application for the reduced variational formulation, focusing on highly contrasting thin objects of various geometrical shape and arrangement in a wide frequency range. Methodology. The modelling is performed on unstructured tetrahedral meshes. Since the reduced variational formulation treats thin highly conductive objects as surfaces, no volume mesh is constructed inside of them.We compare the results obtained by the vector FEM using the proposed variational formulation with the results obtained using standard formulation. Findings. Due to the fact that the proposed variational formulation does not require volume meshing of the thin objects, its computational cost is significantly lower. However, the reduced formulation yields correct results in a restricted frequency range. It also imposes some limitations on the minimal contrast and maximal thickness of the thin highly conductive objects. Originality/value. The proposed reduced variational formulation can be applied to simulate the time-harmonic electric field in the media with thin highly conductive inclusions of either regular or chaotic arrangement, as well as thin shielding plates or casings of various geometrical forms.

Study on the Influence of Electrode Collocation to Electric Field Characteristic of ESP

2014 ◽  
Vol 875-877 ◽  
pp. 1683-1686
Author(s):  
Cheng Liang Jia ◽  
You Shan Sun ◽  
Chao Huang ◽  
Wan Peng Zhang ◽  
Fang Chen
Keyword(s):  
Electric Field ◽  
Current Density ◽  
Surface Current ◽  
Electrode Configuration ◽  
Electrode Gap ◽  
Average Current Density ◽  
Surface Current Density ◽  
Discharge Electrode ◽  
Field Characteristic ◽  
Average Current

A laboratory-scale ESP with new electrode configuration was established to investigate the electric field characteristic. Eight teeth prick line and prick plate with the length of 20mm were employed as discharge electrodes, respectively. The effects of discharge electrode type and electrode gap on V-I characteristic and surface current density were studied. The results showed that the optimum electrode gaps were 350-400mm for eight teeth line and 300-350mm for prick plate, which could obtained higher average current density and lower variance.

scholarly journals Effect of Seawater and Fly Ash Contaminants on Insulator Surfaces Made of Polymer Based on Finite Element Method

Energies ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 8581
Author(s):  
I Made Yulistya Negara ◽  
I. G. N. Satriyadi Hernanda ◽  
Dimas Anton Asfani ◽  
Mira Kusuma Wardani ◽  
Bonifacius Kevin Yegar ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fly Ash ◽  
Electric Field ◽  
Leakage Current ◽  
Current Density ◽  
Surface Current ◽  
Surface Current Density ◽  
Current Leakage ◽  
Element Method

Polymer is an insulating substance that has become increasingly popular in recent years due to its benefits. Light density, superior dielectric and thermal properties, and water-resistant or hydrophobic properties are only a few of the benefits. The presence of impurities or pollutants on the insulator’s surface lowers its dielectric capacity, which can lead to current leakage. The influence of seawater and fly ash pollutants on the distribution of the electric field and the current density of the insulator was simulated in this study. The finite element method was used to execute the simulation (FEM). Polymer insulators are subjected to testing in order to gather current leakage statistics. The tested insulator is exposed to seawater pollution, which varies depending on the equivalent salt density deposit value (ESDD). The pollutant insulator for fly ash varies depending on the value of non-soluble deposit density (NSDD). The existence of a layer of pollutants increased the value of the electric field and the value of the surface current density, according to the findings. Both in simulation and testing, the ESDD value of seawater pollutants and the NSDD value of fly ash contaminants influenced the value of the leakage current that flowed. The greater the ESDD and NSDD values are, the bigger the leakage current will be.

Single-peak-regulation and wide-angle dual-band metamaterial absorber based on hollow-cross and solid-cross resonators

2020 ◽  
Vol 91 (3) ◽  
pp. 30901
Author(s):  
Yibo Tang ◽  
Longhui He ◽  
Jianming Xu ◽  
Hailang He ◽  
Yuhan Li ◽  
...  
Keyword(s):  
Transverse Electric ◽  
Surface Current ◽  
Dielectric Substrate ◽  
Transverse Magnetic ◽  
Metamaterial Absorber ◽  
Absorption Peak ◽  
Dual Band ◽  
Single Peak ◽  
Wide Angle ◽  
Surface Current Density

A dual-band microwave metamaterial absorber with single-peak regulation and wide-angle absorption has been proposed and illustrated. The designed metamaterial absorber is consisted of hollow-cross resonators, solid-cross resonators, dielectric substrate and metallic background plane. Strong absorption peak coefficients of 99.92% and 99.55% are achieved at 8.42 and 11.31 GHz, respectively, which is basically consistent with the experimental results. Surface current density and changing material properties are employed to illustrate the absorptive mechanism. More importantly, the proposed dual-band metamaterial absorber has the adjustable property of single absorption peak and could operate well at wide incidence angles for both transverse electric (TE) and transverse magnetic (TM) waves. Research results could provide and enrich instructive guidances for realizing a single-peak-regulation and wide-angle dual-band metamaterial absorber.

Variational formulation for the equilibrium condition of a conducting fluid in an electric field

1983 ◽  
Vol 32 (2) ◽  
pp. 55-61 ◽  
Author(s):  
N. Sujatha ◽  
P. H. Cutler ◽  
E. Kazes ◽  
J. P. Rogers ◽  
N. M. Miskovsky
Keyword(s):  
Electric Field ◽  
Equilibrium Condition ◽  
Variational Formulation ◽  
Conducting Fluid

scholarly journals Radar Cross-Section Formulation of a Shell-Shaped Projectile Using Modified PO Analysis

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Mohammad Asif Zaman ◽  
Md. Abdul Matin
Keyword(s):  
Differential Geometry ◽  
Cross Section ◽  
Current Density ◽  
Surface Current ◽  
Radar Cross Section ◽  
Analysis Procedure ◽  
Physical Optics ◽  
Surface Current Density ◽  
Filtering Method ◽  
Good Agreement

A physical optics based method is presented for calculation of monostatic Radar Cross-Section (RCS) of a shell-shaped projectile. The projectile is modeled using differential geometry. The paper presents a detailed analysis procedure for RCS formulation using physical optics (PO) method. The shortcomings of the PO method in predicting accurate surface current density near the shadow boundaries are highlighted. A Fourier transform-based filtering method is proposed to remove the discontinuities in the approximated surface current density. The modified current density is used to formulate the scattered field and RCS. Numerical results are presented comparing the proposed method with conventional PO method. The results are also compared with published results of similar objects and found to be in good agreement.

scholarly journals Electrohydrodynamics of stationary cone-jet streaming

2015 ◽  
Vol 471 (2182) ◽  
pp. 20150290 ◽  
Author(s):  
Andrey V. Subbotin ◽  
Alexander N. Semenov
Keyword(s):  
Velocity Field ◽  
Electric Field ◽  
Flow Velocity ◽  
Entropy Production ◽  
Cone Angle ◽  
Surface Current ◽  
Conductive Liquid ◽  
Flow Velocity Field ◽  
Principle Of Maximum Entropy ◽  
Principle Of Maximum

We discover novel types of stationary cone-jet steams emitting from a nozzle of a syringe loaded with a conductive liquid. The predicted cone-jet-flow geometries are based on the analysis of the electrohydrodynamic equations including the surface current. The electric field and the flow velocity field inside the cone are calculated. It is shown that the electric current along the conical stream depends on the cone angle. The stable values of this angle are obtained based on the Onsager’s principle of maximum entropy production. The characteristics of the jet that emits from the conical tip are also studied. The obtained results are relevant both for the electrospraying and electrospinning processes.

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