Quantitative characteristics of back corona discharge intensity

Journal o[ Electrostatics, 23 (1989) 351-356 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands

QUANTITATIVE

CHARACTERISTICS

I.P. VERESHCHAGIN,

351

OF B A C K CORONA DISCHARGE

INTENSITY

V.A. ZHUKOV and A.V. KALININ

High Voltage Departament, Moscow (USSR)

Moscow Power Engineering

Institute,

SUMMARU It is shown that back corona intensity is a function of positive to negative ions current densities ratio, said current densities being measured in the area close up to the layer surface on which the back corona appears. Having analysed the back corona intensity data obtained it was found that density of direct corcns ions flow reaching the precipitated lauer surface didn't depends on the back corona intensity and could be determined with the help of voltage-current characteristics of unipolar corona discharge taking into account the layer voltage drop. The influence of powder layers physical properties and external electric field parameters to the back corona intensity has been studied. INTRODUCTION Recently technological an electric

found a wide application. with a high specific considerable discharge

processes

field on the particles

At the same time, using the materials

resistance

difficulties

(more than 5.10 8 Ohm-m)

gap and in decrease

It also causes the particle process

cessary to eliminate work out methods eliminating

The BC affects

it. The purpose

the efficiency

of

of all investigations

are complicated

into the operation

It seems a more reasonable

of electrical

field.

The drift velocity

apparatus.

approach not to fight BC but to make

of a technological

is the velocity

was to

and introduce

only in the case when BC essentially

meters

ne-

of BC onset moment and a way of

it. All these methods

some liminations

the de-

so greatly that it has been considered

for definition

serious liminations

of electric

of breakdown voltage.

charge reduction and, hence,

crease of their drift velocity. technological

encounter

as they give rise to the back corona

(BC), which results in the redistribution

field in the electrode

efficiency

based on a direct action of of dispersed material have

process.

of the particle reduction

impairs

One of the important

the

para-

drift in the electric

due to BC can be obtained

from the equation:

= wlw' = (~IE')2 (i -VJ+IJ_) 0304-3886/89/$03.50

I ( i+ ~J+IJ_ )

© 1989ElsevierSciencePublishersB.V.

(I)

352 I

where W, W

= the velocities of the particle drift in the field

with and without BC respectively;

E,E

= electric field strengths

with and without BC respectively;

J+,J_ = the current densities

of the positive and negative ions. As it follows from equation I, the BC intensity can be described by the ratio of positive to negative current densities

CBC =

J+/J_. Using this value, it is possible to estimate the efficiency decrease due to BC and expediency of the performance. EXPERIMENTS The experimental values of the BC intensity were obtained by means of probing as applied to the fields with a bipolar space charge. The so-called method of "a sectioned probe" was further developed (ref. I). Methods for processing the probing data were improved. These methods allowed to obtain the data on the total current density (J+, J_) and on the field potential in a point as well as strength values. A new improved design of a sectioned probe made it possible to obtain the mean field values with a back corona (BC) of a distinct descrete structure. The investigation of the characteristics of real field with BC showed that the field parameters and the ratios J+/J_ change qreatly along the field force lines.

That is why the data on the

BC intensity for the central part of the gap cannot be used for the area adjacent to the collection electrode. Probing in this area is also impossible owing to the "shadow" effect which is difficult to estimate. To overcome these obstacles a method for calculation was developed. It allows to determine the BC intensity values at the surface of the precipitated layer using the probing data from the central area of the gap. The above method is based on a system of differential equations which describes the processes in the external region of a stationary bypolar space charge (ref. 2):

iv

-

iv 5+ :div

(2) :

p,p

where $ = $+ + J_ = (p+k+ + p . k _ volume ion recombination.

)~;

E ~ = the coefficient of a

353

The solution of the system must satisfy the condition of the voltage balance: L fE

o

dl = U¢

eo where Uc

- ~U¢

(3)

- the corona voltage: a U e

powder layer;

~o , L

= the voltage drop on the

= the coordinates of the corona and the

collection electrodes. A simultaneous solution of the

system of differential equati-

ons (2) and of the integral equation

(3) together with the ana-

lysis of the field characteristics in the electrode gap, obtained by the probing method, yields the distribution of these characteristics over the whole gap. The required solution must satisfy the condition of the minimum of the objective function of the solution search in the from of a meansquare deviation of the experimental

and calculated characteristics of the field.

To simplity the identification of the electric field parameters distribution of BC the experiments were carried out in an electrode system "plate with needles - grid-collecting plate". Electric field in this electrode

system is undimensional.

The BC

fields of real powder layers and their models made as porous dielectric coatings were investigated.

The results obtained allow

to determine a dependence of the voltage drop on the layer

~U e

on the current density from the ions of the direct corona J_ e~ This dependence has similar character for all the cases. 0 < J-t~

< Jcr

When

the voltage drop value was increased monotonously

up to the breakdown voltage value Uar

= Ear ° H ~

. V~nen J e~>jc~

(with BC) the voltage drop was practically unchanged and kept at the level of Usr

. The stability of this parameter made it possib-

le to neglect changes in

m Ue

in BC field calculations.

DISCUSSION Subsequent probing and the calculation of the electrical charac teriristics distribution for powder layers as well as for various models allowed to obtain the basic relationships for the ratio J+/J_ at the layer surface as a function of the electric field characteristics. It was found that the BC intensity is not practically affected by the field strength. Experiments were carried out with the same values of ionic current densities and different average values of field strength. It was possible to create the above mentioned conditions due to independent power supply to the

354

plate with needies and to the metallic grid. The experiments showed that the effect of the field strength appears only in pulling the BC ions out from the layer surface into the gap and does not change the value Cs¢ near the layer surface. Owing to this circumstance

the dependence of the ratio J+/J_ on J_ ~

may

be considered valid for any electrode system and should be called a generalized dependence of the BC intensity for a given powder layer. The analisys of generalized dependences allowed to find out that the current density of direct corona ions has the same value at the layer surface as before outset of BC. In other words, the appearance of the BC ions in the gap and

connected with it redis-

tribution of all the field characteristics does not result in a change in the ion flow reaching the surface of the dielectric layer in the steady-state regime. The phenomena was fully confirmed by a number of experiments, directly and indirectly. An analisys of the physical nature of this phenomena showed that it is connected with processes

occu-

ring in the electrode gap, particularly, with the regulating effect of the volume ion recombination which plays the role of feedback when J-ew deviates from Ju.~p The stability of J-ew allowed to develop simple methods for determining the ratio J+/J_ at the surface of the precipitated layer using the current-voltage relationships of the corona gap in the presence and in the absence of the powder layer on the col lection electrode. For this purpose it is necessary to determine the total current density Jo

with BC for the working voltage U

(fig. I). Using the current-voltage curves of the gap for unipolar corona Ju.[p is found for U¢ - aU~ ( a U e is determined from the maximum difference in the current density curves before the BC outset for the same current densities), The BC intensity is calculated from:

c,c

= J+/J_ = (Jo

- J~p

)/J~p

= Jo/Ju~p

- I

(4)

Numerous comparisons of the experimental values of C~¢ obtained by the probing method and the current-voltage relationships for various models of powder layers and epoxy powder layers showed a good agreement for various performances. A device for predicting the BC intensity was developed based

355

J @J

0

.M

J- ~

0

Jc~

f

Uma x

U c- Uma x

Uc

Voltage, U (KV) Fig. I. Current-voltage characteristics and their treatment with the purpose to determine the BC intensity. I - clean collection electrode 2 - porous dielectric coating on the collection electrode. on the aboye methods. This device was used to determine experimentally the generalized dependences of the BC intensity for a large number

of powder materials, which emBrase practically all fields

of industrial electrostatics where back corona occurs. The The electrophysical

characteristics of the powder layers chan-

ged in the following range: the particle size 2a = I + 90 j~ the specific electrical resistance p v = 8"109 + 2"1015 ohm.m;

;

the layer thickness h = O,1 $ 6 mm; the layer packing density factor Kpa = 0,3 • 0,6. CO NCTJUSIO NS The experiment

showed that the dependence of J+/J_

always approximately of the same character

from

J-e~

(fig. 2).

In the first region there is no BC observed and J + / J

is

zero. In the second region when J - g ~ > Jc~ the intensity of BC rises linearly due to the formation of stable ionization processes in single discharge channels. In the third region

(when

356

1,0 h=280+380#w I

0,8 +

4~ .r4

0,6 h=160-200 24

.r4

0,4 O

o o ~4 o ~q

0,2

0

2

4

Current

~8 10 density,

12 14 J_ e~ ( 10-4 A/m2)

~ig. 2. The dependence of the BC intensity on the current density of the direct corona at the collection electrode. X = calculated data based on the current-voltage relationships; 0 = data obtained by probing. C8c

is constant)

occurs a grov~h of the nember of breakdo~m

channels and of the pulse frequency; tion processes remaining the s ~ e .

the character of the ionisa-

A number of relationships for the BC dependences on the physical characteristics of the powder layers was established: - with the grov~h of the powder layer thickness its structure chnnges resulting in the increase of the BC intensity; - the increased amount and size of air inclusions also results in the rise in the BC intensity; - an increase of the specific electric conductivity causes a reduction in the critical current density, the maximum value of the ratio J + / J remaining practiCally the same. REFERENCES I 2

S. Masuda, A. ~izuno, Initiation condition and mode of back discharde, J. Electrost., 7(4), (1977/1978), 35-52. V.I. Popkov~ Izvestiya AN SSSR, 0TN, 1948, No 1 pp.12-28 (in Russian).