# Mathematical modeling of the electric field in the planar and coaxial dielectric barrier discharge reactor in water treatment application

Mathematical modeling of the electric field in the planar and coaxial dielectric barrier... To design a pulse power water treatment system, it is necessary to design a reactor optimally. One of the most essential types of reactors used in water treatment is the dielectric barrier discharge (DBD) reactor. The purpose of this paper is to model the electric field in the two types of planar and coaxial reactors to have an accurate analytical formula for using in the optimal design according to the required electric field of the treatment.Design/methodology/approachThe method proposed in this paper focuses on the voltage of different areas in the reactor and different boundary conditions to obtain the surface charge density. In this regard, parameters of the dielectric and treated material, as well as the reactor dimension, have been affected in the equations. To confirm the analytical results, the finite element method simulation has been performed, and it shows the accuracy of this method.FindingsThe exact analytical equation of the electric field is found within the discharge zone of the planar and coaxial DBD reactors. These equations can predict the values of different parameters of the reactor required to purify the material before each design and it does not even require simulation.Originality/valueThe electric field formula presented in this paper can allow the manufacturers of pulse power water treatment systems to optimize their design easily, cost-effectively and in less time. Also, the formulas provided are completely general and remain effective for all materials. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Emerald Publishing

# Mathematical modeling of the electric field in the planar and coaxial dielectric barrier discharge reactor in water treatment application

, Volume 41 (5): 17 – Aug 26, 2022
17 pages

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# References (22)

Publisher
Emerald Publishing
ISSN
0332-1649
eISSN
0332-1649
DOI
10.1108/compel-08-2021-0309
Publisher site
See Article on Publisher Site

### Abstract

To design a pulse power water treatment system, it is necessary to design a reactor optimally. One of the most essential types of reactors used in water treatment is the dielectric barrier discharge (DBD) reactor. The purpose of this paper is to model the electric field in the two types of planar and coaxial reactors to have an accurate analytical formula for using in the optimal design according to the required electric field of the treatment.Design/methodology/approachThe method proposed in this paper focuses on the voltage of different areas in the reactor and different boundary conditions to obtain the surface charge density. In this regard, parameters of the dielectric and treated material, as well as the reactor dimension, have been affected in the equations. To confirm the analytical results, the finite element method simulation has been performed, and it shows the accuracy of this method.FindingsThe exact analytical equation of the electric field is found within the discharge zone of the planar and coaxial DBD reactors. These equations can predict the values of different parameters of the reactor required to purify the material before each design and it does not even require simulation.Originality/valueThe electric field formula presented in this paper can allow the manufacturers of pulse power water treatment systems to optimize their design easily, cost-effectively and in less time. Also, the formulas provided are completely general and remain effective for all materials.

### Journal

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic EngineeringEmerald Publishing

Published: Aug 26, 2022

Keywords: Electric field; Finite element method; DBD reactor; Pulse power; High voltage; Planar reactor; Coaxial reactor