DETERMINATION OF THE EFFECTIVE PERMITTIVITY OF A HETEROGENEOUS MATERIAL
Purpose. To develop a two-dimensional numerical-field model for determining the effective permittivity of a multicomponent material represented by a system of homogeneous volumes with known physical characteristics. Methodology. The model is based on the solution by the finite element method of an e...
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| Видавець: | National Technical University "Kharkiv Polytechnic Institute" and State Institution “Institute of Technical Problems of Magnetism of the National Academy of Sciences of Ukraine” |
|---|---|
| Дата: | 2020 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English Ukrainian |
| Опубліковано: |
National Technical University "Kharkiv Polytechnic Institute" and State Institution “Institute of Technical Problems of Magnetism of the National Academy of Sciences of Ukraine”
2020
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| Теми: | |
| Онлайн доступ: | http://eie.khpi.edu.ua/article/view/2074-272X.2020.2.09 |
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Electrical Engineering & Electromechanics| id |
eiekhpieduua-article-201172 |
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eiekhpieduua-article-2011722020-04-21T20:42:19Z DETERMINATION OF THE EFFECTIVE PERMITTIVITY OF A HETEROGENEOUS MATERIAL ОПРЕДЕЛЕНИЕ ЭФФЕКТИВНОЙ ДИЭЛЕКТРИЧЕСКОЙ ПРОНИЦАЕМОСТИ ГЕТЕРОГЕННОГО МАТЕРИАЛА Palchykov, O. O. эффективная диэлектрическая проницаемость электростатическое поле энергия метод конечных элементов цилиндрические объемы 621.3.011.5 effective permittivity electrostatic field energy finite element method cylindrical volumes 621.3.011.5 Purpose. To develop a two-dimensional numerical-field model for determining the effective permittivity of a multicomponent material represented by a system of homogeneous volumes with known physical characteristics. Methodology. The model is based on the solution by the finite element method of an electrostatic problem with the subsequent determination of the energy contained in the volume under consideration. Than we have compared this result with the energy of a flat capacitor with a rectangular cross-section of the plates and determined the effective permittivity of test material. We also have used Rayleigh, Odelevsky and Lichtenecker models and the model with a perpendicular arrangement of layers relative to the main electric flux. Results. Based on the developed field model, the effective permittivities for dry, wet and transformer oil-soaked insulating papers of various grades, including taking into account ash, are determined. We have proved that a macroscopically homogeneous multicomponent material is well approximated by uniformly spaced cylindrical volumes with a substance of different nature in a matrix of another substance. We have showed a significant error of the layer model and the Rayleigh model relative to the proposed model. We have showed the equivalence of models with the location of inclusions in the nodes of a rectangular and parallelogram mesh. Originality. For the first time we have proposed wet paper models with an asymmetric arrangement of a cylindrical volume of water with a circular and segment cross-section in a cylindrical pore. For the first time we have proposed models of insulating paper with evenly spaced cylindrical inclusions of different volumes. Practical value. The proposed model allows to calculate the effective permittivity of an inhomogeneous material with a given accuracy without restricting the shape of the components. Based on the proposed field model, it is possible to determine the Lichtenecker index, which allows to calculate the effective permittivity for any ratio of the volumes of the components of a heterogeneous material. Обосновано применение метода, основанного на численном расчете электростатического поля для определения эффективной диэлектрической проницаемости гетерогенного материала, который представляется системой однородных объемов с известными физическими характеристиками. Для сухой, влажной и пропитанной трансформаторным маслом изоляционных бумаг различных марок определены диэлектрические проницаемости. Результаты расчета по предложенным моделям сопоставлялись с результатами, полученными на основе слоистой модели, моделей Рэлея и Оделевского. Предложены аппроксимационные зависимости на основе обобщенного выражения Лихтенеккера для определения диэлектрической проницаемости изоляционных бумаг. National Technical University "Kharkiv Polytechnic Institute" and State Institution “Institute of Technical Problems of Magnetism of the National Academy of Sciences of Ukraine” 2020-04-21 Article Article application/pdf application/pdf http://eie.khpi.edu.ua/article/view/2074-272X.2020.2.09 10.20998/2074-272X.2020.2.09 Electrical Engineering & Electromechanics; No. 2 (2020); 59-63 Электротехника и Электромеханика; № 2 (2020); 59-63 Електротехніка і Електромеханіка; № 2 (2020); 59-63 2309-3404 2074-272X en uk http://eie.khpi.edu.ua/article/view/2074-272X.2020.2.09/201188 http://eie.khpi.edu.ua/article/view/2074-272X.2020.2.09/201189 Copyright (c) 2020 O. O. Palchykov https://creativecommons.org/licenses/by-nc/4.0 |
| institution |
Electrical Engineering & Electromechanics |
| collection |
OJS |
| language |
English Ukrainian |
| topic |
эффективная диэлектрическая проницаемость электростатическое поле энергия метод конечных элементов цилиндрические объемы 621.3.011.5 effective permittivity electrostatic field energy finite element method cylindrical volumes 621.3.011.5 |
| spellingShingle |
эффективная диэлектрическая проницаемость электростатическое поле энергия метод конечных элементов цилиндрические объемы 621.3.011.5 effective permittivity electrostatic field energy finite element method cylindrical volumes 621.3.011.5 Palchykov, O. O. DETERMINATION OF THE EFFECTIVE PERMITTIVITY OF A HETEROGENEOUS MATERIAL |
| topic_facet |
эффективная диэлектрическая проницаемость электростатическое поле энергия метод конечных элементов цилиндрические объемы 621.3.011.5 effective permittivity electrostatic field energy finite element method cylindrical volumes 621.3.011.5 |
| format |
Article |
| author |
Palchykov, O. O. |
| author_facet |
Palchykov, O. O. |
| author_sort |
Palchykov, O. O. |
| title |
DETERMINATION OF THE EFFECTIVE PERMITTIVITY OF A HETEROGENEOUS MATERIAL |
| title_short |
DETERMINATION OF THE EFFECTIVE PERMITTIVITY OF A HETEROGENEOUS MATERIAL |
| title_full |
DETERMINATION OF THE EFFECTIVE PERMITTIVITY OF A HETEROGENEOUS MATERIAL |
| title_fullStr |
DETERMINATION OF THE EFFECTIVE PERMITTIVITY OF A HETEROGENEOUS MATERIAL |
| title_full_unstemmed |
DETERMINATION OF THE EFFECTIVE PERMITTIVITY OF A HETEROGENEOUS MATERIAL |
| title_sort |
determination of the effective permittivity of a heterogeneous material |
| title_alt |
ОПРЕДЕЛЕНИЕ ЭФФЕКТИВНОЙ ДИЭЛЕКТРИЧЕСКОЙ ПРОНИЦАЕМОСТИ ГЕТЕРОГЕННОГО МАТЕРИАЛА |
| description |
Purpose. To develop a two-dimensional numerical-field model for determining the effective permittivity of a multicomponent material represented by a system of homogeneous volumes with known physical characteristics. Methodology. The model is based on the solution by the finite element method of an electrostatic problem with the subsequent determination of the energy contained in the volume under consideration. Than we have compared this result with the energy of a flat capacitor with a rectangular cross-section of the plates and determined the effective permittivity of test material. We also have used Rayleigh, Odelevsky and Lichtenecker models and the model with a perpendicular arrangement of layers relative to the main electric flux. Results. Based on the developed field model, the effective permittivities for dry, wet and transformer oil-soaked insulating papers of various grades, including taking into account ash, are determined. We have proved that a macroscopically homogeneous multicomponent material is well approximated by uniformly spaced cylindrical volumes with a substance of different nature in a matrix of another substance. We have showed a significant error of the layer model and the Rayleigh model relative to the proposed model. We have showed the equivalence of models with the location of inclusions in the nodes of a rectangular and parallelogram mesh. Originality. For the first time we have proposed wet paper models with an asymmetric arrangement of a cylindrical volume of water with a circular and segment cross-section in a cylindrical pore. For the first time we have proposed models of insulating paper with evenly spaced cylindrical inclusions of different volumes. Practical value. The proposed model allows to calculate the effective permittivity of an inhomogeneous material with a given accuracy without restricting the shape of the components. Based on the proposed field model, it is possible to determine the Lichtenecker index, which allows to calculate the effective permittivity for any ratio of the volumes of the components of a heterogeneous material. |
| publisher |
National Technical University "Kharkiv Polytechnic Institute" and State Institution “Institute of Technical Problems of Magnetism of the National Academy of Sciences of Ukraine” |
| publishDate |
2020 |
| url |
http://eie.khpi.edu.ua/article/view/2074-272X.2020.2.09 |
| work_keys_str_mv |
AT palchykovoo determinationoftheeffectivepermittivityofaheterogeneousmaterial AT palchykovoo opredelenieéffektivnojdiélektričeskojpronicaemostigeterogennogomateriala |
| first_indexed |
2024-06-01T14:39:33Z |
| last_indexed |
2024-06-01T14:39:33Z |
| _version_ |
1800670043922497536 |