Analysis of a Cylinder-Wire-Cylinder Electrode...

Analysis of a Cylinder-Wire-Cylinder Electrode Configuration during

Corona Discharge

K. KANTOUNA G.P. FOTIS K.N. KIOUSIS L. EKONOMOU G.E. CHATZARAKIS

[email protected] [email protected] [email protected] [email protected] [email protected]

ASPETE - School of Pedagogical and Technological Education, N. Heraklion, 141 21 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 (Emax) approach

with the use of Peek’s formula [6].

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:

(1)

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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

Emax for each configuration. For r = 25, 100 and

250µm, Εmax 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-wire-

cylinder 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

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 (Emax) 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 Emax 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 Emax 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.

(2)


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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.

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

d

(cm)

d'

(cm)

Emax

(·106

V/m)

Emin

(·104

V/m)

Eav

(·104

V/m)

Stored

Energy

(·1010

Joule)

R=R’= 10mm

d=2 d'=1 2.21 3.44 5.76 4.16

d'=2 2.83 3.12 5.98 3.80

d'=3 3.18 2.94 6.11 3.56

d=3 d'=1 1.76 2.31 3.74 3.80

d'=2 2.32 2.11 3.88 3.58

d'=3 2.65 2.00 3.96 3.42

d=4 d'=1 1.49 1.72 2.76 3.52

d'=2 2.01 1.59 2.85 3.38

d'=3 2.31 1.50 2.91 3.26

R=R’= 15mm d=2 d'=1 2.18 3.54 5.76 4.65

d'=2 2.86 3.18 5.99 4.19

d'=3 3.24 2.97 6.13 3.87

d=3 d'=1 1.71 2.40 3.73 4.30

d'=2 2.33 2.18 3.88 4.01

d'=3 2.68 2.05 3.96 3.78

d=4 d'=1 1.44 1.80 2.75 4.01

d'=2 1.99 1.66 2.85 3.80

d'=3 2.32 1.56 2.91 3.64

In figures 5 and 6 it can be seen the graphic

representation of Emax and Emin for the previous set

of calculations.

Fig. 5: Emax versus distance d΄, for R = 10 and 15mm

versus various distances d = 2, 3 and 4cm

Fig. 6: Emin 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.

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:


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∫=V

dVEDEnergy��

2

1

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. 8: Stored energy for radius of the cylinders R

equal to 10mm versus various distances d and d΄

Fig. 9: Stored energy for radius of the cylinders R

equal to 15mm versus various distances d and d΄

5. Flow field patterns in cylinder-

wire-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 500000V/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. 10: Electric field flow for R=10mm, r=25µm,

d=2cm and i) d΄=1cm, ii) d΄=2cm and iii) d΄=3cm







(3)

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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 wire-

cylinder arrangement.

References:

[1] G.A. Kallio, D.E. Stock, ‘Interaction of

electrostatic and fluid dynamic fields in wire-

plate electrostatic precipitators’, Journal of

Fluid Mechanic, vol.2401992, 2006, p. 133-166.

[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. 758-763.

[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. 1407-1413.

[4] D. F. Colas, A. Ferret, D. Z. Pai, D. A. Lacoste,

C. O. Laux, ‘Ionic wind generation by a wire-

cylinder-plate corona discharge in air

atmospheric pressure’, Journal of applied

physics, Vol. 108, Issue 10, 2010, pp. 103306.

[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. 1-5.

[6] F. W. Peek, ‘Dielectric phenomena in high

voltage engineering’, Mcgraw-hill Book

Company, 1st edition, 1915.

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