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
Fig. 11: Electric field flow for R=10mm, r=25µm,
d=3cm and i) d΄=1cm, ii) d΄=2cm and iii) d΄=3cm
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
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Fig. 14: Electric field flow for R=15mm, r=25µm,
d=3cm and i) d΄=1cm, ii) d΄=2cm and iii) d΄=3cm
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 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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