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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Autor principal:	O. O. Palchykov
Formato:	article
Lenguaje:	EN RU UK
Publicado:	National Technical University "Kharkiv Polytechnic Institute" 2020
Materias:	effective permittivity electrostatic field energy finite element method cylindrical volumes Electrical engineering. Electronics. Nuclear engineering TK1-9971
Acceso en línea:	https://doaj.org/article/10a157e10ddc4923a659188f099f8565
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spelling	oai:doaj.org-article:10a157e10ddc4923a659188f099f85652021-12-02T17:53:58ZDETERMINATION OF THE EFFECTIVE PERMITTIVITY OF A HETEROGENEOUS MATERIAL10.20998/2074-272X.2020.2.092074-272X2309-3404https://doaj.org/article/10a157e10ddc4923a659188f099f85652020-04-01T00:00:00Zhttp://eie.khpi.edu.ua/article/view/2074-272X.2020.2.09/201188https://doaj.org/toc/2074-272Xhttps://doaj.org/toc/2309-3404Purpose. 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.O. O. PalchykovNational Technical University "Kharkiv Polytechnic Institute"articleeffective permittivityelectrostatic fieldenergyfinite element methodcylindrical volumesElectrical engineering. Electronics. Nuclear engineeringTK1-9971ENRUUKElectrical engineering & Electromechanics, Iss 2, Pp 59-63 (2020)
institution	DOAJ
collection	DOAJ
language	EN RU UK
topic	effective permittivity electrostatic field energy finite element method cylindrical volumes Electrical engineering. Electronics. Nuclear engineering TK1-9971
spellingShingle	effective permittivity electrostatic field energy finite element method cylindrical volumes Electrical engineering. Electronics. Nuclear engineering TK1-9971 O. O. Palchykov DETERMINATION OF THE EFFECTIVE PERMITTIVITY OF A HETEROGENEOUS MATERIAL
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.
format	article
author	O. O. Palchykov
author_facet	O. O. Palchykov
author_sort	O. O. Palchykov
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
publisher	National Technical University "Kharkiv Polytechnic Institute"
publishDate	2020
url	https://doaj.org/article/10a157e10ddc4923a659188f099f8565
work_keys_str_mv	AT oopalchykov determinationoftheeffectivepermittivityofaheterogeneousmaterial
_version_	1718379152743071744

DETERMINATION OF THE EFFECTIVE PERMITTIVITY OF A HETEROGENEOUS MATERIAL

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