Analysis of a Cylinder-Wire-Cylinder Electrode Configuration during Corona Discharge

Transcription

1 Analysis of a Cylinder-Wire-Cylinder Electrode Configuration during Corona Discharge K. KANTOUNA G.P. FOTIS K.N. KIOUSIS L. EKONOMOU G.E. CHATZARAKIS kkantouna@hotmail.com gfotis@gmail.com konstantinosq@gmail.com leekonom@gmail.com gea.xatz@aspete.gr ASPETE - School of Pedagogical and Technological Education, N. Heraklion, Athens, Greece Abstract: A cylinder-wire-cylinder electrode configuration was simulated by implementing open source Finite Element Method Magnetics (FEMM) software. The analysis consisted of two cylinders, one is charged with 1000V, while the other is grounded. Among the two cylinders there is a wire which is charged with 1000V. The maximum and the minimum electric field strength versus the distance between the three electrodes were determined. Field flow pattern has been visualized and the stored energy was measured with the FEMM software. Key-Words: Corona discharge, Electro-hydrodynamic (EHD) flow, Field flow pattern, Finite Element Method Magnetics (FEMM), High voltage, Stored energy 1. Introduction Kallio and Stock [1] made some experimental and simulation investigations with the finite element models finding that the electro-hydrodynamic (EHD) flow, which exists in electrostatic precipitators is a very complex flow phenomenon, strongly depended upon the corona discharge and precipitator inlet velocity. Dumitran et al. [2] investigated a cylinder-wire-plate electrode configuration under the corona discharge effect. Their results were that the non-uniformity of the electric field and the charge injection are depending on the geometry of the electrode system and affect the electric field and the space charge density distribution in the inter-electrode gap. Stishkov and Chirkov [3] used ANSYS to simulate a needle-plane electrode system. That was an effort to analyse the field s velocities and the electric characteristics of the EHD flow. They found that the EHD flow in the electrode system has a large volume charge density value and as a result a quite strong transverse electric field. Colas et al. [4] made an experimental setup of a wire-cylinder-plate electrode configuration and tried to maximize the power supplied to the flow so as to increase the acceleration. In relation to wire-wire electrode configuration they concluded that their setup increases the ionic wind velocity and the thrust. An electrostatic precipitator with a circular tube and a wire electrode mounted in the centre of the tube was modelled from Farnoosh et al. [5], so as to determine the collection efficiency for conductive diesel exhaust particulates. The wire was charged with negative high dc voltage and the tube was grounded. They found that by increasing the gas residence time, i.e. decreasing the inlet velocity, the particle charge-to-mass ratio increases and the particle removal efficiency increases too. In this work a cylinder-wire-cylinder electrode configuration has been simulated by implementing FEMM software. The maximum and the minimum electric field strength versus the distance between the three electrodes were determined, the field flow pattern has been visualized and the stored energy was measured with the FEMM software. 2. Wire-wire electrode configuration analysis A wire-wire model was used for the theoretical maximum electric field strength (E max ) approach with the use of Peek s formula [6]. (1) where: a is the radius of the electrodes and x, y are the coordinates of the first electrode, while the coordinates of the second are (x=0, y=0). The maximum electric field strength appears in the field for y=0. Hence: ISBN:

2 where: a and x in (1) are represented as r, and d in (2), respectively. A set of theoretical calculations was carried out for d and V equal to 2cm and 1000V respectively and various values for the radius r, in order to define E max for each configuration. For r = 25, 100 and 250µm, Ε max was found to be 2.99, 9.47 and 4.60 MV/m respectively. 3. Setting FEMM s parameters A number of parameters, that affects the mesh of the model, must be set in the finite element method magnetic simulation software, in order to have as accurate results as possible in the cylinder-wirecylinder simulation, which follows. In order the parameters to be set, a wire - wire model was simulated in FEMM and its results were compared with the theoretical results. Figure 1 depicts a schematic view of a wire-wire model with distance d between the electrodes, length L and radius r of each one electrode. Fig. 1: Wire wire model Figure 2 depicts the wire-wire electrode model as it was simulated in FEMM software. Fig. 2: wire-wire simulation model (2) Where r the radius of both electrodes, d the distance between them, and A equal to B, which are the values that define the distance between the electrodes and the air bounding box area. For speed reasons in the simulation procedure, the model setup has been middle cut simulated. This technique does not affect the results. The left wire (emitter) was charged with 1000V and the right wire (collector) is electrically grounded (0V). The values of the radius r of the wires and the distance d between them have been set as in the theoretical procedure, so as to compare the theoretical maximum electric field strength (E max ) values with the simulation values. The parameters that affect the mesh of the models and that must be regulated are the air bounding box size, the local element size along line, the minimum angle influence, the maximum arc segment and the mesh. For the air bounding box size, different values of A and B dimensions as multiples of distance d have been analyzed. After a number of comparisons between the theoretical and the simulation results, and for A and B values equal to d/4, d/2, d, 2 d, 3 d and 4 d it was revealed that from the values of 2 d and over, the results were equal to the theoretical ones. Hence one of these values can be used as representative. The parameter local element size along line is depicted in figure 3, and determines the mesh density between the two electrodes. Fig. 3: Schematic view of wire wire electrode configuration with distance d between the electrodes The area between the electrodes must be dense. For different values of element size along line equal to 2000, 1000, 500, 250, 100, 50 and 10µm it was observed that as the local element size along line decreases, the dense in the area between the electrodes increases and the values of E max are getting closer to the theoretical investigation values. The parameter minimum angle influence defines how much the minimum angle will be constrained in the triangle meshing program. For minimum angle values equal to 20, 25, 28, 29, 30, 31, 32, 33 and 33.2 degrees was observed that as the minimum angle values was increasing, the area between the whole box was increasing too. The parameter maximum arc segment determines how dense will be the area around the electrodes. For the values 5, 2, 1, 0.5, 0.1 and 0.01 degrees the simulation values of the maximum electric strength were compared with the theoretical values. From this comparison, it was observed that as the local element size along line decreases, the dense in the area around the electrodes increases and the values of E max are getting closer to the theoretical values. Another parameter that was examined was the mesh size. The mesh affects the whole area inside the air bounding box. Analysing the previous parameters, it is concluded that the mesh size does not play important role, hence an auto mesh size was appropriate for the simulations. ISBN:

3 4. Computational procedure of a cylinder-wire-cylinder electrode configuration A cylinder-wire-cylinder model was simulated in finite element method magnetics software as shown in figure 4, where r is the radius of the wire, R is the radius of the cylinder, d is the distance between the wire and the right cylinder and d is the distance between the wire and the left cylinder. In figures 5 and 6 it can be seen the graphic representation of E max and E min for the previous set of calculations. Fig. 5: E max versus distance d, for R = 10 and 15mm versus various distances d = 2, 3 and 4cm Fig. 4: Cylinder-wire-cylinder configuration The parameters were set with the values, minimum angle size 32 degrees, local element size along line 10µm, maximum arc segment size 0.1 degrees, auto mesh size and box size expressed by the formula B=A=3 d. The left cylinder and the cylindrical wire were the emitters (1000V) and the right cylinder was the grounded collector (0V). It was considered air as insulating material inside the area, with relative permittivity 1. Some set of calculations were carried out with radius of the cylinders R = 10 and 15mm, constant radius of the wire r = 25µm, distances d = 2, 3 and 4cm and distances d = 1, 2 and 3cm. Table 1 shows the results of the calculations. Table 1:Cylinder-wire-cylinder configuration results Fig. 6: E min versus distance d, for radius R = 10 and 15mm versus various distances d = 2, 3 and 4cm The representation of an indicative electric field distribution in a cylinder-wire-cylinder electrode configuration is shown in figure 7. R=R = 10mm R=R = 15mm Emax ( 10 6 Emin ( 10 4 Eav ( 10 4 Stored Energy ( Joule) d (cm) d' (cm) d=2 d'= d'= d'= d=3 d'= d'= d'= d=4 d'= d'= d'= d=2 d'= d'= d'= d=3 d'= d'= d'= d=4 d'= d'= d'= Fig. 7: Electric field strength fluctuation of a cylinder - wire cylinder configuration for R = 10mm, r -=25µm, d = 1cm and d = 2cm The stored energy that is contained inside the bounding box was calculated in FEMM software with the equation: ISBN:

4 Energy= 1 2 V D E dv (3) where: V is the voltage, D is the electric flux density and E is the electric field intensity. In figures 8 and 9 it can be seen the graphic representation of the field Stored Energy. Fig. 10: Electric field flow for R=10mm, r=25µm, d=2cm and i) d =1cm, ii) d =2cm and iii) d =3cm Fig. 8: Stored energy for radius of the cylinders R equal to 10mm versus various distances d and d Fig. 11: Electric field flow for R=10mm, r=25µm, d=3cm and i) d =1cm, ii) d =2cm and iii) d =3cm Fig. 9: Stored energy for radius of the cylinders R equal to 15mm versus various distances d and d 5. Flow field patterns in cylinderwire-cylinder electrode configuration In this phase an analysis of the air flow field has been made. For better visualization of the differentiations in the flow field pattern, the colours of the boundaries were set with the following values, lower bound equal to 0V/m, upper bound equal to 50000V/m, grid size 6000µm and scaling factor 150 (figures 10-12). For the next simulations with R=15mm, the boundaries were set with the values of lower bound equal to 0V/m, upper bound equal to V/m, grid size 6000µm and scaling factor 150. The change in the boundaries has been made for better visualisation of the differentiations in the flow field pattern (figures 13-15). Fig. 12: Electric field flow for R=10mm, r=25µm, d=4cm and i) d =1cm, ii) d =2cm and iii) d =3cm Fig. 13: Electric field flow for R=15mm, r=25µm, d=2cm and i) d =1cm, ii) d =2cm and iii) d =3cm ISBN:

5 Fig. 14: Electric field flow for R=15mm, r=25µm, d=3cm and i) d =1cm, ii) d =2cm and iii) d =3cm [3] Yu. K. Stishkov, V. A. Chirkov, Computer simulation of EHD flows in a needle-plane electrode system, Technical physics, Vol. 53, No. 11, 2008, pp [4] D. F. Colas, A. Ferret, D. Z. Pai, D. A. Lacoste, C. O. Laux, Ionic wind generation by a wirecylinder-plate corona discharge in air atmospheric pressure, Journal of applied physics, Vol. 108, Issue 10, 2010, pp [5] N. Farnoosh, K. Adamiak, G. S. P. Castla, 3D numerical study of wire-cylinder precipitator for collecting ultrafine particles from diesel exhaust, IEEE, 2011, pp [6] F. W. Peek, Dielectric phenomena in high voltage engineering, Mcgraw-hill Book Company, 1st edition, Fig. 15: Electric field flow for R=15mm, r=25µm, d=4cm and i) d =1cm, ii) d =2cm and iii) d =3cm 6. Conclusions In this paper the structure of the EHD flow in a cylinder-wire-cylinder electrode configuration on the basis of the of FEMM s simulation results was studied. It was observed that increasing the distance d, the maximum electric strength and stored energy are decreased. Furthermore, the distance d is proportional to the maximum electric field strength and to the stored energy. Finally it is concluded that a cylinder-wire-cylinder electrode configuration with the right cylinder closer to the wire produces efficiency relatively higher than a typical wirecylinder arrangement. References: [1] G.A. Kallio, D.E. Stock, Interaction of electrostatic and fluid dynamic fields in wireplate electrostatic precipitators, Journal of Fluid Mechanic, vol , 2006, p [2] L. M. Dumitran, L. Dascalescu, P. V. Notingher, P. Atten, Modelling of corona discharge in a cylinder wire plate electrode configuration, Journal of electrostatics, Vol. 65, Issue 12, 2007, pp ISBN: