Design of the Discharging Electrode of the Electrostatic Precipitator Depending on the Applied Voltage

. The article deals with the design of the diameter and the simulation of the distribution of the intensity of the electric field of the charging electrode of the electrostatic precipitator, given the supplied DC voltage. The purpose was to calculate the value of the critical intensity of the electric field, which must be exceeded when trying to achieve the state of corona discharge on the electrode, which is a condition for electrostatic separation. Subsequently, CFD simulations of two 3D models with electrode diameters of 1 and 4 mm were created, on which the distributions of the electric field intensity were observed a t a DC voltage of 20 kV. The simulations confirmed the results of the calculations that the corona discharge at a voltage of 20 kV will occur only on an electrode with a diameter of 1 mm.


Introduction
The article deals with the study of the influence of the diameter of charging electrodes on the operating parameters of a tubular electrostatic precipitator. An electrostatic precipitator is a device used for the secondary capture of solid particles (PM) using a corona discharge [1][2][3][4][5]. Such a device consists of a positive and a negative electrode, connected to a source of high DC voltage. The electrode connected to the positive pole of the voltage source is formed by a metal chimney pipe, and the electrode connected to the negative pole of the voltage source is formed by a conductive wire of circular diameter. PM flowing through the separator is charged by a negative electric charge, thanks to which they are attracted to the surface of the collecting (positive) electrode.
The function of electrostatic separation is conditioned by the formation of a coronary discharge on the charging electrode area. The formation of this type of discharge must be ensured by the supply of voltage with a value higher than the initial critical voltage. The size of this value affects the diameter of the charging electrode and the distance between the positive and the negative electrode. Likewise, the formation of a coronary discharge affects the shape of the charging electrode. Sharp edges on the surface of the electrode create favorable conditions for the formation of coronary discharge [6][7][8].
This paper investigates the influence of the diameter of the charging electrode on the operating parameters of a tubular electrostatic precipitator with a voltage of 20 kV. The essence was to calculate the value of the initial critical voltage using generally known relations and then to verify the occurrence of a corona discharge using numerical CFD simulation.
Numerical simulations using CFD software are commonly used tools in the design of various devices [9][10][11][12]. In the past, several works were devoted to numerical simulations of electrostatic precipitators, respectively charging electrodes, which were also the inspiration for this article.

Numerical calculations
Two 3D models are investigated in the work, Fig.1 consisting of an identical positive electrode with a diameter of 120 mm and a length of 500 mm, Fig. 2a.). The negative electrodes were different with a length of 300 mm and diameters of 1 mm and 4 mm, Fig.  2b.). The simulated voltage applied to the electrodes was set at 20 kV. All input parameters of the electrostatic precipitator are given in Tab. 1.  First, numerical calculations of basic electrical quantities determining the parameters of the precipitator were performed. An important parameter is the value of the critical initial voltage U0c, which is calculated from the value of the initial critical intensity of the electric field E0c. The initial critical voltage is the limit value of the applied voltage, which, if exceeded, corona discharge occurs at the charging electrode. This effect lasts until the value of the applied voltage does not exceed the value of the jump voltage Up. The course of voltage and current is displayed using V/A characteristics. The operating parameters were calculated based on generally available relationships, which were divided into 2 parts, a 1 mm diameter electrode and a 4 mm diameter electrode [13].
The critical initial field strength was calculated according to equation (1) where k1, k2 are quantities of the Whitehead-Brown equation, ϑ is the relative gas density, R is the radius of the collection electrode and r is the radius of the discharge electrode.
The critical initial voltage was calculated according to equation (2) The radius of the ionization region at pure gas was calculated according to equation (3) where U is the applied voltage.

Numerical simulations
In this part, attention is paid to the verification of the value of the electric field intensity on the proposed electrodes using CFD simulations in the ANSYS Fluent software. Using simulations, it is possible to verify whether a given electrode will be suitable for the occurrence of a corona discharge at a given applied DC voltage.
The mesh of the model with a 1 mm electrode consisted of 1 802 684 elements, with tetrahedrons cells on the collecting electrode and the multizone method on the discharging electrode. The quality of the mesh was considered adequate based on an average value of the orthogonal quality at 0.78 and the skewness at 0.22. The simulation was based on the komega SST turbulence model. In terms of boundary conditions, the inlet velocity of 0.5 m/s was applied at the inlet as air. The outlet was defined as a pressure outlet with a gauge pressure of 0 Pa. Turbulence was defined as 5% for turbulent backflow intensity and 10 for turbulent backflow turbulent viscosity ratio for both inlet and outlet. The boundaries of precipitators were defined as stationary walls with no-slip shear conditions.
The mesh of the model with a 4 mm electrode consisted of 1 431 263 elements, with tetrahedrons cells on the collecting electrode and the multizone method on the discharging electrode. The quality of the mesh was considered adequate based on an average value of the orthogonal quality at 0.78 and the skewness at 0.22. The simulation was based on the komega SST turbulence model. In terms of boundary conditions, the inlet velocity of 0.5 m/s was applied at the inlet as air. The outlet was defined as a pressure outlet with a gauge pressure of 0 Pa. Turbulence was defined as 5 % for turbulent backflow intensity and 10 for turbulent backflow turbulent viscosity ratio for both inlet and outlet. The boundaries of precipitators were defined as stationary walls with no-slip shear conditions.
The electric potential was applied by MHD module as conducting walls for collecting and discharging electrodes. 20 kV was considered applied voltage on the discharging electrode.

Results
The electric field intensity values of both solved electrodes were calculated and verified according to the mentioned procedure. The results of numerical calculations are recorded in Tab. 2. U0c 17.65 · 10 3 V 35.63 · 10 3 V z 6 · 10 -4 m 9.5 · 10 -4 m CFD simulations confirmed that at the considered supply DC voltage, the corona effect will occur only on an electrode with a diameter of 1 mm. In Fig. 3. the 2D plane on which the field intensity was monitored is shown.   Fig. 5 show the distribution of the intensity of the electric field of individual electrodes. As expected, the distribution of the electric field strength is located close to the electrode and exceeds the required initial critical value of the electric field strength near the electrode surface, in the ionization region z. The intensity of the electric field in the case of an electrode with a diameter of 1 mm reached a maximum of 9.47·10 6 V·m -1 , which exceeds the value of the initial critical intensity, and a corona discharge will occur on the electrode at the given voltage. On the contrary, with an electrode with a diameter of 4 mm, there will be no corona discharge, because the value of the field intensity reached a maximum of 3.09·10 6 V·m -1 . To achieve the desired condition, a voltage higher than the calculated value of the initial critical voltage would have to be applied.

Conclusion
The work was focused on determining the diameter of the charging electrode of the electrostatic precipitator using numerical calculation and numerical simulation. Two 3D models with electrode diameters of 1 and 4 mm were designed. In both cases, the supplied voltage of 20 kV was simulated, based on which the value of the critical intensity of the electric field was calculated. With the help of CFD simulations, it was verified whether in the given cases corona discharge will occur on the surfaces of the electrodes. The simulations confirmed the results of the calculations that the corona discharge will occur at a voltage of 20 kV only on an electrode with a diameter of 1 mm. The value of the critical intensity of the electric field was calculated at 7.37·10 6 V.m -1 . The calculated value of the electric field intensity using CFD simulation was 9.47·106 V·m-1. With a 4 mm diameter electrode, the applied voltage would have to exceed approximately 36 kV for a corona discharge to occur. Such numerical verification is an effective tool that can be used in the design of electrostatic precipitator electrodes for capturing solid pollutants in the stack. In this way, it is also possible to optimize the electrodes into different shapes, in which basic numerical calculations would be difficult to implement.