Yehia
82
Assessment of the Ionization Region in the Positive DC Coronas
Ashraf Yehia
Department of physics, Faculty of Science, Assiut University, Assiut 71516, Egypt
Abstract— The previous studies that already exposed to studying the ionization region of the positive dc corona discharges
in coaxial cylindrical electrodes at atmospheric conditions have been reviewed briefly in this paper. The review of these
studies has shown that there is a conflict in assessing the radius of the ionization region surrounding the axial discharge
electrodes stressed with a positive dc voltage in the atmospheric air. Therefore, the current–voltage characteristics of the
positive dc corona discharges generated in a coaxial wire-cylinder reactor has been measured at atmospheric pressure and
room temperature. A general method has been suggested for calculating the ionization radius by using the experimental
results of the corona current–voltage characteristics. The suggested method has been based on the theories of the positive
dc coronas, in addition to some physical parameters of the electrical discharge in the air reported in the literature. The
results calculated by the suggested method have been compared with the previous studies. Comparison of the results
demonstrates that the suggested method represents a suitable way for calculating the ionization radius of the positive dc
coronas generated in the investigated reactor under any discharge conditions.
Keywords— dc coronas, positive dc coronas, ionization region
I. INTRODUCTION
The main advantage of the corona discharges is that
they can be used easily in generating non-thermal
plasmas at atmospheric conditions with high rates for
gases flowing between two inhomogeneous electrodes
[1]. The disadvantage of the corona discharges, on the
other hand, is that the active volume of the ionization
region surrounding the high electric field electrode is
much smaller than the total discharge volume between
the two inhomogeneous electrodes. Therefore, the corona
discharges are not very well suitable for applications of
volume plasma chemistry, like the silent discharges.
However, the corona discharges are used in many
industrial applications, where only small concentrations
of excited or charged particles are needed. Typical
examples are electrostatic precipitators, spray coating
and electrophotography machines. The corona discharges
are also used in drying separation systems and in
radiation detectors. Other important applications of the
corona discharges include the surface treatment of
polymers and treatment of the flue gases [2].
Assessment of the ionization region of the positive
dc corona discharges in coaxial cylindrical electrodes at
atmospheric conditions has received the attention of
some investigators, maybe for three reasons. First, all the
physical processes that control the sequence of the
corona discharge modes, the power loss, audible noise, as
well as radio and TV interference, take place only inside
the ionization region. Secondly, all the gas phase plasma
chemical reactions are also created within this region.
Thirdly, the ozone concentration generated by positive dc
coronas is much smaller than that generated by negative
dc coronas under the same discharge conditions [3-5].
Corresponding author: Ashraf Yehia
e-mail address: yehia30161@hotmail.com
Received: May 22nd, 2008, Accepted: July 12th, 2008
Therefore, the positive dc corona discharges are
preferable for use with indoor air cleaning electrostatic
precipitators [6]. The great importance to control the
ozone generation in the design of any equipment utilizing
the corona discharges is well recognized [6, 7]. These, in
addition to the coaxial cylindrical electrodes are being
used over a wide range in various equipment [8]. From
another point of view, the investigators who studied the
ionization region did not agree on a definite criterion for
assessing its radius. Subsequently, there is some doubt in
assessing the ionization radius of the positive dc corona
discharges in the atmospheric air, where most equipment
works.
In this paper, the previous studies to assess the
ionization radius of the positive dc corona discharges in
coaxial cylindrical electrodes at the atmospheric pressure
and room temperature have been reviewed. A general
method has been suggested for calculating the ionization
radius of the positive dc coronas under any discharge
conditions by using the experimental results of the
current–voltage characteristics. The results calculated by
the suggested method have been compared with the
previous studies. All the physical quantities in the
equations reported in this paper are expressed in the
International System of units.
II. PREVIOUS STUDIES
A. Materials and reagents
The previous studies that exposed totally or
partially to assess the ionization radius (i. e., radius of the
corona sheath or radius of the glow region) of the
positive and negative dc corona discharges in coaxial
cylindrical electrodes at atmospheric conditions may be
summarized as follows:
(i) Some of the investigators [9-11] found
experimentally that the ionization radius ri of the positive
International Journal of Plasma Environmental Science and Technology Vol.2, No.2, SEPTEMBER 2008
83
dc coronas is determined only by the radius of the
discharge wire ro and is independent of the corona current
I. The ionization radius is usually represented by an
empirical equation of the general form:
(1)
ri = ro + C (ro ) n
where the constant C and the exponent n were
determined experimentally.
(ii) Other investigators [12] found also by
experiment that the ionization radius ri of the positive and
negative dc coronas is dependent on the wire radius ro as
well as on the corona current I.
(iii) Others [13] explained that the ionization radius
ri of the positive and negative dc coronas is determined
by the following equation:
Vo
(2)
ri =
6
3 × 10 ln(R ro )
where Vo is the corona onset voltage and R is the
inner radius of the outer cylinder.
atmospheric conditions, the discharge space confined
between the two electrodes modifies to an ionization
region of radius ri surrounding the wire surface of radius
ro and a conduction region of length (R - ri), as illustrated
in figure (1). The boundary between the two regions is
defined as the position where the ionization coefficient α
is equal to the attachment coefficient η, i. e.,
(7)
α−η= 0
III. SOME PHYSICAL PARAMETERS OF THE ELECTRICAL
DISCHARGE IN THE AIR
The experimental results for the primary ionization
coefficient α and attachment coefficient η of the
electrical discharge in air reported in the literature [1416] have been modified in terms of the relative air
density δ to include the air pressure P, as well as its
temperature T, as follows:
⎛
⎞
⎡
⎜ δ ⎟⎤
(3)
α = δ ⎢363173.6001e − 16796000 ⎜⎜ E ⎟⎟ ⎥
⎝
⎠
⎣⎢
⎦⎥
2
⎡
⎛E⎞
⎛E⎞ ⎤
η = δ ⎢986.6511743 − 0.540831 × 10 −3 ⎜ ⎟ + 1.149183321 × 10 -10 ⎜ ⎟ ⎥
⎝δ⎠
⎝ δ ⎠ ⎥⎦
⎢⎣
(4)
in the range of ⎛⎜1.9 × 10 6 ≤ E ≤ 4.56 × 10 6 ⎞⎟ V
δ
⎝
⎠m
⎛
⎞
⎡
⎜ δ ⎟⎤
α = δ ⎢735832.0001e − 20079200 ⎜⎜ E ⎟⎟ ⎥
⎝
⎠
⎢⎣
⎥⎦
(5)
in the range of ⎛⎜ 4.56 × 10 6 ≤ E ≤ 18.24 × 10 6 ⎞⎟ V
δ
⎠m
⎝
where δ is given by
⎡ P
293 ⎤
δ=⎢
(K )⎥⎦
101325
T
⎣
(6)
IV. METHOD FOR CALCULATING THE IONIZATION RADIUS
IN THE GLOW DISCHARGE MODE OF POSITIVE DC CORONAS
When a positive dc corona starts at the onset
voltage Vo in a coaxial wire-cylinder reactor at
Fig. 1. Representation of the positive dc corona discharges in a coaxial
wire-cylinder reactor at atmospheric conditions.
The distance from the wire surface up to the inner
surface of the outer cylinder is called the radial
coordinate r (i. e., ro ≤ r ≤ R).
Within the ionization region, α is greater than η.
Therefore, the corona discharge plasma is generated only
within this region because of ionization by collisions
between the free electrons, which are sufficiently
accelerated in the electric field applied to the reactor, and
the air molecules. The ionization process produces a
series of successive generations of electron avalanche
progress toward the wire as the electrons are accelerated
toward its surface. The positive ions created in the wake
of electron avalanches drift out of the ionization region
and move along the conduction region to the outer
cylinder, while the electrons are neutralized in contact
with the positive surface of the wire [15]. In addition to
electrons and positive ions, various short-lived free atoms
and molecules in the ground and excited states, as well as
negative ions are also created as a result of the ionization
process. Some of the excited particles give up their
excess energy in the form of emitted radiation forming
the glow region that covers the wire surface and
distributes uniformly in space and time along it [7]. The
electrons necessary for maintenance of a self-sustained
discharge are produced by the photo-ionization process
of the air molecules [15].
Yehia
84
The electric field strength E at any point along
the radial coordinate r in the coaxial cylindrical corona
space is given by [17]:
E=
⎡ ⎛ ro ⎞2 ⎤ ⎡ Vo
⎤
⎢1 − ⎜ ⎟ ⎥ + ⎢
⎥
(
)
r
r
ln
R
r
μ
2 π ε o i ⎣⎢ ⎝ ⎠ ⎦⎥ ⎣
o ⎦
I
2
(8)
where I is the corona current per unit length of the
discharge wire, єo is the permittivity of the free space
( ε o = 8.854 × 10 -12 F/m ) and µi is the mobility of the
positive ions ( μ = 1.8 × 10 -4 m 2 /V.S ) [10]. In equation (8),
i
the first term is ascribed to the space charge while the
second term results from the Laplacian field (i. e., free
space field) at the onset of the corona discharge [18].
The operating parameters of the coaxial wirecylinder reactor (ro and R) and the corona current–
voltage characteristics (Vo and I) have been used to
calculate the ionization radius ri as follows:
(i) The electric field strength E is determined as a
function of the radial coordinate r stating from the wire
surface in the range of ro ≤ r ≤ R by using equation (8),
but in steps with a small increment of Δ r = 10-6 m.
(ii) The ionization coefficient α and the attachment
coefficient η, as well as the difference between them (α η), are determined corresponding to each value of E by
using equations (3) - (6).
(iii) When the electric field strength E attains a
critical value that makes α − η = 0 (equation 7), this
critical value becomes equating to the field strength at
the outer boundary of the ionization region Ei and the
radial coordinate r becomes also equating to the
ionization radius ri itself, i. e., when α − η = 0 ,
(9)
r = ri and E = Ei
V. EXPERIMENTAL SETUP AND MEASURING TECHNIQUE
A. Experimental setup
Figure (2) shows a schematic diagram of the
experimental setup used in this study. The setup was
composed of the following:
High-voltage dc power supply. The power supply
consisted of a step-up transformer (220/50 × 103 Vrms, 50
Hz), two rectifying diodes connected in series (100 × 103
V, 20 × 10-3 A), a charging capacitor (20 × 10-9 F, 40 ×
103 V), and a load resistor (106 Ω, 150 × 103 V).
Coaxial wire-cylinder reactor. The dimensions of
the outer cylinder were 0.025 m an inner radius R and 0.2
m length. The radius of the axial discharge wire was
variable in the range of 2.5 × 10-5 ≤ ro ≤ 1.75 × 10-3 m.
The wires were made from stainless steel, nickel and
copper. The two ends of the outer cylinder were provided
with insulators to adjust the discharge wire along its axis
and to flow the air through it.
B. Measuring technique
Fig. 2. Schematic diagram of the experimental setup used in this study.
The coaxial wire-cylinder reactor was connected to
the high-voltage dc power supply and fed by normal air
flowing with a slow constant rate of Q = 1.666 × 10-5
m3/s at atmospheric pressure and room temperature from
an air compressor to sweep the generated ozone outside
the reactor, as shown in figure (2). The electric power
input to the setup was controlled with a regulating
transformer (2200 W) fed from an ac power source (220
Vrms, 50 Hz). The net output positive dc voltage was
applied to the discharge wire and measured by using a
1000: 1 high-voltage divider connected to a digital
multimeter (Sanwa-CD721, auto voltage range from
0.001 to 1000 V). The outer cylinder was grounded
through another digital multimeter (Goldtool-UT60A,
auto current range from 0.01 × 10-6 to 10 A) for
measuring the corona current. The corona current I was
measured as a function of the voltage applied to the
reactor V. The average temperature during the
experimental measurements was about 294 K.
VI. COMPARISON OF THE PRESENT RESULTS WITH THE
PREVIOUS STUDIES
In order to compare the present results with the
previous studies, the results of the ionization radius ri as a
function of the radius of the discharge wire ro in figure
(7) were plotted as follows:
The dotted and the solid curves in figure (7)
indicate the results of the present study. The dotted curve
represents the minimum values of ri at the corona onset
voltage Vo while the solid curve represents the maximum
values of ri at the corona current of I = 0.01 A/m (just
before the spark over voltage) as a function of the wire
radius ro.
85
International Journal of Plasma Environmental Science and Technology Vol.2, No.2, SEPTEMBER 2008
The different symbols, only in figure (7), represent
results for ri as a function of ro calculated by using
Cobine‫ۥ‬s equation [9]:
(10)
ri = ro + 0.03 (ro ) 0.5
Waters and Stark equation [10]:
(11)
ri = ro + 0.106188 (ro ) 0.6
and Takahashi et at equation [11]:
(12)
ri = ro + 0.139035 (ro ) 0.65
as well as Awad and Caslte equation [13] (i. e.,
equation 2 in the text).
VII. RESULTS AND DISCUSSION
The experimental and calculated results in figures
(3) - (6) show the following:
The onset voltage Vo necessary for generating a
self-sustained corona discharge in the air molecules
inside the reactor decreases as the radius of the wire ro
decreases as shown in figure (3). This is explained by the
increase of the corona onset field Eo at the wire surface
with the decreasing of its radius ro as confirmed by
Whitehead‫ۥ‬s empirical equations [15] for dc coronas, and
depicted in figure (3). The result is that the corona
current I (per unit length of the discharge wire) increases
with the decreasing of the wire radius ro for the same
voltage applied to the reactor V, as shown in figure (4).
Therefore, thin discharge wires are preferable in the
design of the electrostatic precipitators to achieve high
efficiency in the charging process [6].
The ionization radius ri increases linearly with
increasing the corona current I as shown in figure (5),
whatever radius of the discharge wire ro. Moreover, the
rate of increasing the ionization radius with the corona
current (i. e., dri / dI) increases slowly as the radius of the
discharge wire ro increases. When the voltage applied to
the reactor is increased from the corona onset voltage Vo
up to near the spark over voltage, the maximum
percentage for the increase in the ionization radius ri with
the smallest wire radius of ro = 2.5 × 10-5 m is about
9.5 % while with the largest wire radius of ro = 1.75 × 103
m is about 7.9 %. This trend is in agreement with the
experimental results of Evans and Inculet [12] for
positive dc coronas. On the other hand, Takahashi et al
[11] measured the ionization radius ri of the positive dc
coronas generated in coaxial cylindrical electrodes at
atmospheric conditions by using photoelectric and
photographic systems. They found experimentally (in
figure 8 of their study) that the ionization radius ri
increases with increasing the applied voltage V for the
same radius of the discharge wire ro. However, they
ignored the variations in the ionization radius ri with
increasing the voltage without justification, and
considered its average value over range of the applied
voltage as a constant radius for the ionization region.
Probably, Takahashi et al [11] built their concept, for
ignoring the increase in the ionization radius with the
voltage, on assumption that the space charge within the
ionization region is to some degree bipolar, and
Fig. 3. The corona onset voltage Vo and the corresponding corona onset
field Eo at the wire surface as a function of radius of the discharge wire
ro.
Fig. 4. Current–voltage characteristics of the positive dc coronas
generated in the reactor for different radii ro of the discharge wire.
subsequently the electric field distribution along its
thickness (ri – ro) remains constant at the Laplacian field
Eo. Accordingly, the ionization radius ri should remain
also constant whatever the applied voltage or the corona
current (i. e., Eo ro = Ei ri = constant), as supposed before
[10]. There is no experimental evidence to support this
assumption and the results of Takahashi et al [11]
themselves disallow it. Another probability may be that
Yehia
Fig. 5. The ionization radius ri of the positive dc coronas as a function
of the corona current I for different radii ro of the discharge wire.
Fig. 6. The electric field strength E as a function of the ionization
radius ri for a discharge wire of radius ro = 5 × 10-4 m at the corona onset
voltage Vo and different corona currents I.
the maximum increase in the ionization radius with the
applied voltage is small comparatively from their opinion
and is in range of the acceptable errors for this type of
experiment; especially the glow emitted from the
86
ionization region just outside it makes its outer boundary
not sharp enough. Figure (6) demonstrates that the radius
of the ionization region ri expands outward with
increasing the corona current I as a result of enhancement
in the field strength due to the positive ions of low
mobility created in the wake of electron avalanches near
the outer boundary of the region, as expressed by the first
term in equation (8). On the contrary, the corona onset
field Eo at the wire surface remains constant at the
Laplacian field whatever the corona current I as
confirmed by the experiment [10]. Thus, the bipolar
assumption that implies to (Eo ro = Ei ri = constant) does
not hold approximately when any corona current I flows
through the reactor, as shown by a previous study [15].
Comparison of the present results with the previous
studies for the ionization radius ri as a function of radius
of the discharge wire ro in figure (7) is summarized as
follows:
Waters and Stark equation [10] agrees well with the
present results in the intense range of the corona current
where ri is maximum, whatever the radius of the
discharge wire ro. This is explained by the fact that
Waters and Stark [10] derived equation (11) from a wide
range of the experimental results. Moreover, they
established a stable glow discharge in the air surrounding
to the axial discharge electrodes during their
measurements by using a radioactive β source in the form
of a flat foil placed on the inner surface of the outer
cylinder.
Because Takahashi et al [11] derived their equation
(12) from limited experimental results using only four
discharge wires having radii in the range of 2.5 × 10-4 ≤
ro ≤ 1.5 × 10-3 m, their equation agree only with the
present results in the same range of ro, but in the weak
range of the corona current where ri is minimum. With
the small discharge wires of ro < 2.5 × 10-4 m, Takahashi
et al equation [11] predicts radii for the ionization region
relatively smaller than that predicted by either the present
study or Waters and Stark equation [10]. However, most
of the discharge wires that are being used in real
applications have radii of ro < 2.5 × 10-4 m [6].
Waters and Stark [10] proved that the electric field
strength at the outer boundary of the ionization region is
constant at Ei = 2.38 × 106 V/m whatever the radius of
the discharge electrode ro. With the present study, it was
found that the value of this field is also constant but at Ei
= 2.419 × 106 V/m as shown in figure (6), whatever the
discharge conditions (ro and I). On the other hand, Awad
and Castle [13], as well as Cobine [9] derived equations
(2) and (10) respectively, proceed on the assumption that
the field strength at the outer edge of the ionization
region Ei is constant at the critical breakdown voltage of
the air (i. e., Ei = 3 × 106 V/m), as expressed in equation
(2). It is well known that this critical value of the
breakdown voltage is valid only in the case of electrical
discharges in air confined inside a uniform electric field
(free space charge field) between two parallel plate
electrodes at atmospheric conditions. With the positive
dc corona discharges in a non-uniform electric field
inside the reactor, the physical mechanism is somewhat
International Journal of Plasma Environmental Science and Technology Vol.2, No.2, SEPTEMBER 2008
87
3- The surface conditions of the discharge electrodes
such as the roughness or the contamination that
modify the corona discharge characteristics.
Moreover, the value of the secondary ionization
coefficient γ that fits the experimental results is a subject
of intense debate between the different investigators [20].
This explains clearly why the method suggested in this
paper represents an accurate way for calculating the
ionization radius ri of the positive dc coronas generated
in coaxial cylindrical electrodes under any discharges
conditions.
VIII. CONCLUSION
Fig. 7. Comparison between the present study and the previous studies
for the ionization radius ri of the positive dc coronas as a function of
radius of the discharge wire ro.
different because of the positive ions flowing in the
conduction region toward the outer cylinder. The positive
ions create an opposing space charge field at the outer
boundary of the ionization region during their transient in
the conduction region. Therefore, the field strength at the
outer boundary of the ionization region Ei should be less
than the critical value of 3 × 106 V/m, as confirmed in the
present study. This clearly explains why Cobine‫ۥ‬s
equation [9], as well as Awad and Castle equation [13],
predict so much small radii for the ionization region in
figure (7) compared with the present study over the
whole range of ro.
It is known that the corona onset voltage Vo and the
critical avalanche length (i. e., the outer boundary of the
ionization region ri) in the non-uniform electric fields
between coaxial wire-cylinder electrodes can be
determine by using Townsend breakdown criterion for
the self-sustaining electrical discharge of the form
[10,19]:
⎡ r
⎤
(13)
γ ∫ o (α − η)dr − 1 = 1
⎢e ri
⎣
⎥
⎦
where γ is the secondary ionization coefficient.
However, this criterion does not account for the
following:
1- The difference between the onset voltage of
positive and negative coronas for the same
discharge conditions.
2- The radius of the ionization region ri under any
discharge conditions unlike the corona onset
voltage Vo.
According to analysis of the results presented in this
paper, one may conclude the following:
1- The radius of the ionization region of the
positive dc coronas generated in coaxial
cylindrical electrodes at atmospheric conditions
depends not only on the wire radius but also on
the corona current (or the applied voltage).
2- The previous studies do not account for the
radius of the ionization region of the positive dc
coronas generated in coaxial cylindrical
electrodes at atmospheric conditions under
voltage stress.
3- The method suggested in this paper is valid for
calculating the radius of the ionization region of
the positive dc coronas generated in coaxial
cylindrical electrodes under any discharge
conditions.
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