A General Empirical Formula of Current-Voltage Characteristics For Point-To-Plane Geometry Corona Discharges
A General Empirical Formula of Current-Voltage Characteristics For Point-To-Plane Geometry Corona Discharges
A General Empirical Formula of Current-Voltage Characteristics For Point-To-Plane Geometry Corona Discharges
corona discharges
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Abstract
With a point-to-plane geometry, the experimental investigation of the current–voltage
characteristics in corona discharges demonstrated that existing empirical formulae met with
some physical difficulties in explaining the results. By mathematically processing the
experimental data and applying the updated knowledge of corona inception, a new general
formula in characterizing the relationship of corona current–voltage was derived and expressed
as I = K(V − V0 )n . It was demonstrated that the exponent n falls into a limited scope of
1.5–2.0, and there always exists an optimal exponent n in the scope, which can be determined
by maximizing the R-square of regression. Of all the potentially influential factors, it was
disclosed that the point radius has the strongest influence on the optimal exponent n, and the
effects of ambient conditions and corona polarities are not noticeable. The optimal exponent n
holds a fixed value of 2.0 for microscopic points and of 1.5 for large points with a radius in
millimetres, but changes decreasingly with the radius for the points of microns. For given
experimental conditions, the optimal exponent n almost does not change with the
inter-electrode distance. Furthermore, it was demonstrated that the formula is applicable not
only for both negative and positive coronas in point-to-plane geometries but also for both
polarities in point-to-ring geometries. With the optimal exponent n, the formula can well
explain the inconsistencies met by other existing formulae and best represent the
characteristics of corona current–voltage with an accuracy of 1 µm.
(Some figures in this article are in colour only in the electronic version)
geometrical factors.
With a point-grid electrode geometry, recently Yamada [9]
modified the Townsend relation by considering the influence
of ambient temperature and of inter-electrode distance in his A2 A/D
P
empirical formula, which is expressed as PC
CP
I = C1 (T − 132)S −2.8 V (V − C2 T −1 S 0.39 ), (R-I1 ) A1
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J. Phys. D: Appl. Phys. 41 (2008) 065209 X Meng et al
(a)
Figure 3. Negative corona current–voltage characteristics.
3.1. The difficulties of existing formulae Figure 4. Testing of three empirical formulae with the experimental
data: (a) I /V as a function of the voltage V by applying (R-I) to the
The experimental data of this study are summarized in figure 3. experimental data; (b) I /((T − 132)S −2.8 V) as a function of the
Among the mentioned formulae, three ((R-I), (R-I1 ) and (R-II)) voltage V by applying (R-I1 ) to the experimental data; (c) I 1/2 as a
function of the voltage V by applying (R-II) to the experimental
are examined with the data and illustrated in figures 4(a)–(c), data. The solid lines are obtained by least squares fittings.
respectively. ((R-II1 ) is not tested particularly due to our
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J. Phys. D: Appl. Phys. 41 (2008) 065209 X Meng et al
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J. Phys. D: Appl. Phys. 41 (2008) 065209 X Meng et al
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J. Phys. D: Appl. Phys. 41 (2008) 065209 X Meng et al
(a)
Figure 10. The influence of preset corona inception currents (I0 :
µA) on the values of the exponent n with the inter-electrode
distance (S: mm).
(b)
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J. Phys. D: Appl. Phys. 41 (2008) 065209 X Meng et al
Figure 12. The change of the optimal exponent n along the Figure 14. The dependence of the corona inception voltage
inter-electrode distance (S: mm). The solid line is obtained by least (V0 : kV) on the inter-electrode distance (S: mm): V0 ∝ S 0.51 . The
squares fitting. solid line is obtained by least squares fitting.
4. Discussion
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J. Phys. D: Appl. Phys. 41 (2008) 065209 X Meng et al
(a)
Figure 16. The dependence of I 1/1.6 versus V with the experimental
data of this study. The solid lines are least squares fitting lines.
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J. Phys. D: Appl. Phys. 41 (2008) 065209 X Meng et al
Table 1. Effect of experimental conditions on the optimal exponent n of the proposed formula (F-I).
Figure 17. The effect of the exponent n of the formula (F-I) on the Figure 18. The effect of the exponent n of the formula (F-I) on the
COD value with the results in figure 2 (negative corona) and figure 5 COD value with the results in figure 1 (positive corona) of [23].
(positive corona) of [1]. The solid lines are obtained by least squares
fitting. inter-electrode distance on the optimal exponent n is negligible
and the formula (F-I) is applicable for the inter-electrode
distance ranging from 0 to 1 m. Furthermore, the effects of
of the formula (F-I) presents a descending tendency with the ambient conditions and corona polarity are not so noticeable.
point radius in the range of 1.5–2.0, and similar radii result
in similar exponents n (as shown in table 1). It is believed 5. Conclusions
that the effects of point radii on the optimal n result from the
strong dependence of the inception voltage V0 on point radii. With a point-to-plane geometry, experimental investigation
In addition, the diversities of the used tips in actual shapes seem of negative corona discharges demonstrates that all existing
no influence on the corona current–voltage characteristics, as empirical formulae met with some difficulties in describing the
referred by Henson [8]. From table 1, it is further confirmed current–voltage characteristics with the results of this study.
that for certain experimental conditions the influence of the Based on the experimental data and the knowledge of corona
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J. Phys. D: Appl. Phys. 41 (2008) 065209 X Meng et al
inception, a new general formula was developed in this paper to of coating polymer powders on their minimum ignition
uncover the phenomena. This formula suggests that the corona energies J. Loss Prevention Process Indust. 17 59–63
[4] Goldman M, Goldman A and Sigmond R S 1985 The corona
current can be expressed as a function of the voltage-difference
discharge, its properties and specific uses Pure Appl. Chem.
between the applied voltage and the corona inception voltage 57 1353–62
with a power n. The scope of n is deduced in a range 1.5–2.0 [5] Dascalescu L, Sanuila A, Rafiroiu D, Iuga A and Morar R
and further confirmed with the results in earlier studies. The 1999 Multiple-needle corona electrodes for electrostatic
derivation and testing of the formula (F-I) suggest that there processes application IEEE Trans. Indust. Appl. 35 543–7
[6] Bhattacharyya S and Peterson A 2002 Corona
always exists an optimal exponent n in the range 1.5–2.0 for
wind-augmented natural convection: I. Single electrode
certain experimental conditions, which implies the best fittings studies J. Enhanced Heat Transfer 9 209–19
and can be determined by maximizing the value of R-square [7] Chang J-S, Lawless P A and Yamamoto T 1991 Corona
(COD) of the dependence of I 1/n versus V . It is disclosed that discharge processes IEEE Trans. Plasma Sci. 19 1152–66
the exponent n has a strong dependence on the point radius: [8] Henson B L 1981 A space-charge region model for
microscopic steady coronas from points J. Appl. Phys.
for microscopic points the exponent n is fixed as 2.0, for large
52 709–15
points with a radius of millimetres it holds as 1.5, and the [9] Yamada K 2004 An empirical formula for negative corona
exponent n decreases with the radius for points of micrometres. discharge current in point-grid electrode geometry J. Appl.
In addition, the effects of ambient conditions and corona Phys. 96 2472–5
polarities are not so noticeable. For this study, the optimal [10] Kip A F 1938 Positive-point-to-plane discharge in air at
atmospheric pressure Phys. Rev. 54 139–46
exponent n is determined around 1.6. As a result, the formula
[11] Giubbilini P 1988 The current-voltage characteristics of
(F-I) provides a very high accuracy on current prediction while point-ring corona J. Appl. Phys. 64 3730–2
the inter-electrode distance is within one metre, and the errors [12] Loeb L B, Kip A F, Hudson G G and Bennett W H 1941 Pulses
are less than 1 µA. Furthermore, in this paper this formula in negative point-to-plane corona Phys. Rev. 60 714–22
was demonstrated to be also applicable for both polarities [13] Bailey A G 1998 The science and technology of electrostatic
powder spraying transport and coating J. Electrost.
of coronas and point-to-ring geometries. In particular, this
45 85–120
new formula successfully explained the inconsistencies met [14] Trichel G W 1938 The mechanism of the negative point to
by other formulae, resulting from incorrectly weighing the plane corona near onset Phys. Rev. 54 1078–84
influence of voltage-difference on corona currents at given [15] Lama W L and Gallo C F 1974 Systematic study of the
experimental conditions. Consequently, its significance exists electrical characteristics of the ‘Trichel’ current pulses
from negative needle-to-plane coronas J. Appl. Phys.
not only in the practice but also in the scientific interest of
45 103–13
corona discharges. Potentially this formula may provide a [16] Parekh H, Salama M M A and Srivastava K D 1978
clue for more sophisticated studies of corona phenomena. Calculation of corona onset and breakdown voltage in short
point-to-plane air gaps J. Appl. Phys. 49 107–12
[17] English W N and Loeb L B 1949 Point-to-plane corona onsets
Acknowledgments J. Appl. Phys. 20 707–11
[18] Bandel H W 1951 Point-to-plane corona in dry air Phys. Rev.
The authors would like to thank Mr Xianzhong Zhu and 84 92–9
Mr Jianzhang Wen for their help and advice on the design [19] Weissler G L 1943 Positive and negative point-to-plane corona
of the experimental setup. in pure and impure hydrogen, nitrogen, and argon Phys.
Rev. 63 96–107
[20] English W N 1948 Positive and negative point-to-plane corona
References in air Phys. Rev. 74 170–8
[21] Akishev Yu, Grushin M, Kochetov I and Karal’nik V 2005
[1] Leal Ferreira G F, Oliveira O N and Giacometti J A 1986 Negative corona, glow and spark discharges in ambient air
Point-to-plane corona: corona–voltage characteristics for and transitions between them Plasma Sources Sci. Technol
positive and negative polarity with evidence of an electronic 14 S18–25
component J. Appl. Phys. 59 3045–9 [22] Cross J A 1987 Electrostatics: Principles, Problems and
[2] Cross J A 1985 An analysis of the current in a point-to-plane Applications (Bristol: Hilger)
corona discharge and the effect of a back-ionising layer on [23] Allibone T E, Jones J E, Saunderson J C, Taplamacioglu M C
the plane J. Phys. D: Appl. Phys. 18 2463–71 and Waters R T 1993 Spatial characteristics of electric
[3] Choi K S, Yamaguma M, Kodama T, Suzuki T, Joung J H, current and field in large direct-current coronas Proc. R.
Nifuku M and Takeuchi M 2004 Effect of corona charging Soc. Lond. A 441 125–46
10